Advances on hot extrusion and simulation of light alloys : selected, peer reviewed papers from the International Conference on Extrusion and Benchmark (ICEB), Dortmund 2009, Germany,

Advances on Hot Extrusion

and Simulation of Light Alloys

Advances on Hot Extrusion and

Simulation of Light Alloys

Selected, peer reviewed papers from the International Conference

on Extrusion and Benchmark (ICEB),

Dortmund 2009, Germany, September 16. -17. 2009

Edited by

A. Erman Tekkaya and Nooman Ben Khalifa

TRANS TECH PUBLICATIONS LTD Switzerland • UK • USA

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Volume 424 of Key Engineering Materials ISSN 1013-9826 Full text available online at http://www.scientific.net

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Preface

This special issue of the journal “Key Engineering Materials” contains peer reviewed papers presented at the International Conference on Extrusion and Benchmark (ICEB). They give an insight into the latest advances in extrusion technology and its simulation. The papers cover a wide range of topics and are grouped into the categories of: benchmark, microstructure, seam welds & composite extrusion, material flow & constitutive equations, dies & tools, and process control & optimization. However, many more topics such as new materials (magnesium and composites) and new profiles (composite profiles), have been covered.

In particular the benchmark part at the conference aimed at exploiting FEM code capabilities and users´ knowledge in the simulation of an industrial extrusion process as it was experimentally realized by the conference organizers. In the 2009 edition of the benchmark, a two-hole die has been used for producing two U-shape profiles with different supporting legs. The experiments have been strictly monitored. The influence of die deformation on the extrusion speed, temperature distribution and distortion of the two profiles is reported and analyzed. Due to the complexity of this matter, the benchmark should not be considered as a contest: Instead, it should be recognized as an opportunity to detect, explore and discuss various issues about common simulation practice, with each participant having his/her own particular interest. We hope that these results will serve for the improvement of the existing simulation skills and also help to develop the future benchmark experiments.

Finally, we would like to express our gratitude to the reviewers of the submitted papers, principally to our co-organizers Professor Luca Tomesani and Dr. Lorenzo Donati of University of Bologna, for their hard work and critical but constructive remarks, which helped the conference to maintain a high scientific level. We hope that the proceedings will become a source of valuable information useful in scientific work for researchers, engineers and students and we were pleased to welcome everyone to Dortmund to the international Extrusion Conference and Benchmark.

Prof. Dr. -Ing. A. Erman Tekkaya Nooman Ben Khalifa Conference chairman Conference organizer

Committees

Conference Chair

Prof. A. Erman Tekkaya, IUL Dortmund University of Technology, DE

Scientific Committee

Dr. C. Bruni, DIPMEC, Marche Polytechnic University, IT Prof. S. Bruschi, DIMS, University of Trento, IT Dr. L. Donati, DIEM, University of Bologna, IT

Prof. I. Duplancic, University of Split, HR Dr. M. El Mehtedi, DIPMEC, Marche Polytechnic University, IT

Prof. J. Hirsch, Hydro, DE Prof. P. Hora, IVP, ETH Zurich, CH

Prof. J. Hueting, DET, University of Twente, NL Dr. A.J. Koopman, DET, University of Twente, NL

Prof. H. J. McQueen, Concordia University, CA Prof. F. Micari, DTMPIG, University of Palermo, IT

Prof. W. Misiolek, Lehigh University, US Dr. S. Müller, ERC, TU Berlin, DE

Prof. Neitzert, School of Engineering, Auckland University of Technology, NZ Dr. M. Schaper, IW, University Hannover, DE

Prof. T. Sheppard, University Bournemouth, GB Prof. C. Sommitsch, TUG, Graz University of Technology, AT

Prof. G. Tani, DIEM University of Bologna, IT Prof. A. E. Tekkaya, IUL, Dortmund University of Technology, DE

Prof. L.Tomesani, DIEM, University of Bologna, IT Prof. H. Valberg, NTNU, Norwegian University, NO

Dr. X. Velay, University Bournemouth, GB Dr. J. Zhou, LMP, Delft University, NL

Industrial Committee

W. Dalla Barba, Italtecno/Interall, IT A. Den Bakker, Nedal Aluminium B.V., NL

H. Gers, Honsel AG, DE V. Giacomelli, Compes S.p.A., IT

Dr. A. Klaus, LeanSigma, DE J. Maier, WEFA Inotec GmbH, DE G. Olcelli, Olex Technologies, CA

G. T. Rajsky, Extrusion Technology for Aluminum Profiles Foundation, USA M. Rompato, Pandolfo Alluminio, IT

R. Rusticelli, Phoenix International, IT Dr. A.Bacha, Alcan Extruded Products, Sierre, CH

Table of Contents

Preface

Committees

I. KeynotesCombined Numerical Simulation and Microstructure Characterization for Prediction ofPhysical Properties in Extruded Aluminum AlloysW.Z. Misiolek and W.R. Van Geertruyden 1

Towards Predictive Control of Extrusion Weld Seams: An Integrated ApproachA.J. den Bakker, R.J. Werkhoven, W.H. Sillekens and L. Katgerman 9

II. Extrusion BenchmarkExtrusion Benchmark 2009 Experimental Analysis of Deflection in Extrusion DiesD. Pietzka, N. Ben Khalifa, L. Donati, L. Tomesani and A.E. Tekkaya 19

III. Microstructure and Heat TreatmentPhysically Based Microstructure Modelling of AA6082 during Hot ExtrusionF. Krumphals, P. Sherstnev, S. Mitsche, S. Randjelovic and C. Sommitsch 27

An Assessment of the Grain Structure Evolution during Hot Forward Extrusion ofAluminum Alloy 7020A. Foydl, N. Ben Khalifa, A. Brosius and A.E. Tekkaya 35

Modeling and Simulation of Microstructure Evolution in Extruded Aluminum ProfilesF. Parvizian, T. Kayser and B. Svendsen 43

Simulation of the Quench Sensitivity of the Aluminum Alloy 6082A. Güzel, A. Jäger, N. Ben Khalifa and A.E. Tekkaya 51

Simulation of Gas and Spray Quenching during Extrusion of Aluminium AlloysM. Reich, S. Schöne, O. Kessler, M. Nowak, O. Grydin, F. Nürnberger and M. Schaper 57

An Approach to Simulate Shape Distortion due to Cooling in Aluminum ExtrusionS. Bikass, B. Andersson and X. Ma 65

Analysis of Polypropylene Deformation in a 135° ECAE Die: Experiments and Three-Dimensional Finite Element SimulationsB. Aour, F. Zaïri, M. Naït-Abdelaziz, J.M. Gloaguen and J.M. Lefebvre 71

IV. Seam Welds and Composite ExtrusionAnalysis of Joint Quality along Welding PlaneE. Ceretti, L. Filice, L. Fratini, F. Gagliardi, C. Giardini and D. La Spisa 79

Accurate Welding Line Prediction in Extrusion ProcessesT. Kloppenborg, N. Ben Khalifa and A.E. Tekkaya 87

Simulation of Porthole Die Extrusion Process Comparing NEM and FEM ModellingI. Alfaro, F. Gagliardi, E. Cueto, L. Filice and F. Chinesta 97

Numerical Analysis of Aluminum Alloys Extrusion through Porthole DiesJ. Zasadziński, A. Rękas, W. Libura, J. Richert and D. Leśniak 105

Simulation of the Co-Extrusion of Hybrid Mg/Al ProfilesJ. Muehlhause, S. Gall and S. Mueller 113

Effect of Tube Wall Thickness in Joining of Aluminum Tube and Holed Rib by ExtrusionT. Moroi, T. Kuboki and M. Murata 121

Numerical and Experimental Investigations of the Production Processes of CoextrudedAl/Mg-Compounds and the Strength of the InterfaceK. Kittner and B. Awiszus 129

The Use of Extruded Profiles as Filling Material in Friction Stir Welding (FSW)L. Donati and L. Tomesani 137

b Advances on Hot Extrusion and Simulation of Light Alloys

V. Material Flow and Constitutive EquationsAnalysis of Metal Flow of Aluminum through Long Choked Die ChannelsH.S. Valberg 145

Friction in Double Action ExtrusionL.L. Wang, J. Zhou and J. Duczczyk 153

A New Cone-Friction Test for Evaluating Friction Phenomena in Extrusion ProcessesC. Karadogan, R. Grueebler and P. Hora 161

Modelling of Thermo-Mechanical Behaviour of Magnesium Alloys during IndirectExtrusionS. Ertürk, D. Steglich, J. Bohlen, D. Letzig and W. Brocks 167

Numerical Analysis of Four-Hole Extrusion of Aluminum AlloysW. Libura, A. Rękas and D. Leśniak 173

Computer-Aided Simulation of Metal Flow through Curved Die for Extrusion of SquareSection from Square BilletK.P. Maity, A.K. Rout and K. Majhi 181

Three Dimensional Upper Bound Modelling for Extrusion of Round-to-Octagon SectionUsing Linearly Converging DieK.P. Maity and A.K. Rout 189

VI. Dies and ToolsMeasuring the Deformation of a Flat Die by Applying a Laser Beam on a Reflecting SurfaceW. Assaad, H.J.M. Geijselaers and K.E. Nilsen 197

Creep-Fatigue Interaction in the AISI H11 Tool SteelB. Reggiani, M. D’Ascenzo, L. Donati, J. Zhou and L. Tomesani 205

FEM-Assisted Design of a Multi-Hole Pocket Die to Extrude U-Shaped Aluminum Profileswith Different Wall ThicknessesG. Fang, J. Zhou and J. Duczczyk 213

Localization of the Shear Zone in Extrusion Processes by Means of Finite Element AnalysisM. Kammler 221

A Case Study to Solve the Problem of Wall Thickness Attenuation during Extrusion toProduce a Complex Hollow Magnesium ProfileL.X. Li, J. Zhou, X. He, J. Zhou and J. Duczczyk 227

Manufacturing of Carbon/Resin Separator by Die Sliding ExtrusionM. Hoshino and K. Suzuki 235

VII. Process Control and OptimizationPrediction of the Extrusion Load and Exit Temperature Using Artificial Neural NetworksBased on FEM SimulationJ. Zhou, L.X. Li, J. Mo, J. Zhou and J. Duczczyk 241

Contrasting Models to Determine the Approximate Extrusion Process Conditions for theFirst BilletM. Sabater and M.L. García-Romeu 249

Study of Flow Balance and Temperature Evolution over Multiple Aluminum ExtrusionPress Cycles with HyperXtrude 9.0A. Farjad Bastani, T. Aukrust and I. Skauvik 257

Numerical Design of Extrusion Process Using Finite Thermo-Elastoviscoplasticity withDamage. Prediction of Chevron Shaped CracksC. Labergère, K. Saanouni and P. Lestriez 265

Integrated Extruder Plant Automation with Learning ControlM. Pandit 273

Combined numerical simulation and microstructure characterization for prediction of physical properties in extruded aluminum alloys

W. Z. Misiolek1, a, W. R. Van Geertruyden2,b 1Institute for Metal Forming, Lehigh University, Bethlehem, PA, USA

2EMV Technologies LLC., Bethlehem, PA, USA [email protected], [email protected]

Keywords: Aluminum Alloys, Extrusion, PCG, Torsion, GDRX, CDRX, Recrystallization Abstract. The extrusion process provides conditions for non-uniform metal flow depending on strain, strain rate and temperature of deformation as well as deformation zone geometry. As a result of these conditions significant microstructure gradients are present within the extrudate. The extreme case of the microstructure gradient is a formation of the peripheral coarse grain structure (PCG). This phenomenon is present in many structural aluminum alloys extrudates and its presence should be eliminated or at least significantly reduced because of the mechanical properties and aesthetic points of view. A number of experiments, including physical and numerical simulations, were performed in order to understand and model the origin of the PCG in indirect extrusion of 6xxx alloys. These experiments included different alloy chemistry, various temperatures, extrusion ratios and extrusion speeds allowing analysis of their influence. Parallel to the experimental results the numerical simulation of the metal flow showing the origin of the metal in different extrudate location was performed using software package DEFORM TM. A review of performed research will be followed by the analysis of the results and discussion of future needs.

Introduction

The understanding of a material’s response to deformation conditions is vital in order to predict the microstructural development during industrial forming process such as extrusion. During hot deformation of aluminum alloys, the material frequently is subjected to high values of strain and strain rates, yet most information and data on hot deformation of metals in literature is limited to relatively low strain and strain rate conditions. Previous investigations by the authors using Finite Element Modeling (FEM) have found that the strain and strain rate at the surface of an extrusion can reach levels exceeding 6 and 40s-1 respectively.[1] The study of microstructural development of a 6061 aluminum alloy during torsion test was performed due to its industrial significance. It has been found that the microstructural development in most aluminum alloys consists of a complex combination of dynamic restoration and hardening mechanisms. These mechanisms manifest themselves in several types of dynamic recrystallization types: Discontinuous Dynamic Recrystallization (DDRX), Continuous Dynamic Recrystallization (CDRX), and Geometric Dynamic Recrystallization (GDRX) [2]. DDRX, which involves the nucleation and growth of new grains during deformation, has been found to be unlikely to occur in Al-Mg-Si alloys[3]. Other forms of dynamic recrystallization that have been observed in Al alloys include geometric dynamic recrystallization (GDRX) as proposed by McQueen and Humphreys[4-6]. GDRX grains form as a grain is heavily deformed to the point where its grain boundaries begin to “pinch off” and form new, equiaxed grains with high misorientation (>15). Additionally, continuous dynamic recrystallization (CDRX) occurs whereby new, highly misoriented grains form as the subgrains that form during deformation gradually increase in misorientation [7,8]. A satisfactory understanding of microstructure development during deformation is also critical as an input data for the numerical modeling of metal forming processes. In order to provide useful microstructure information for modeling purposes it is necessary to obtain microstructure response information to a wide range of strain, strain rate and temperature deformation parameters and therefore the torsion test can be a very valuable experiment and source of microstructure data.

Combined numerical simulation and microstructure characterization for prediction of physical properties in extruded aluminum alloys

W. Z. Misiolek1, a, W. R. Van Geertruyden2,b 1Institute for Metal Forming, Lehigh University, Bethlehem, PA, USA

2EMV Technologies LLC., Bethlehem, PA, USA [email protected], [email protected]

Keywords: Aluminum Alloys, Extrusion, PCG, Torsion, GDRX, CDRX, Recrystallization Abstract. The extrusion process provides conditions for non-uniform metal flow depending on strain, strain rate and temperature of deformation as well as deformation zone geometry. As a result of these conditions significant microstructure gradients are present within the extrudate. The extreme case of the microstructure gradient is a formation of the peripheral coarse grain structure (PCG). This phenomenon is present in many structural aluminum alloys extrudates and its presence should be eliminated or at least significantly reduced because of the mechanical properties and aesthetic points of view. A number of experiments, including physical and numerical simulations, were performed in order to understand and model the origin of the PCG in indirect extrusion of 6xxx alloys. These experiments included different alloy chemistry, various temperatures, extrusion ratios and extrusion speeds allowing analysis of their influence. Parallel to the experimental results the numerical simulation of the metal flow showing the origin of the metal in different extrudate location was performed using software package DEFORM TM. A review of performed research will be followed by the analysis of the results and discussion of future needs.

Introduction

The understanding of a material’s response to deformation conditions is vital in order to predict the microstructural development during industrial forming process such as extrusion. During hot deformation of aluminum alloys, the material frequently is subjected to high values of strain and strain rates, yet most information and data on hot deformation of metals in literature is limited to relatively low strain and strain rate conditions. Previous investigations by the authors using Finite Element Modeling (FEM) have found that the strain and strain rate at the surface of an extrusion can reach levels exceeding 6 and 40s-1 respectively.[1] The study of microstructural development of a 6061 aluminum alloy during torsion test was performed due to its industrial significance. It has been found that the microstructural development in most aluminum alloys consists of a complex combination of dynamic restoration and hardening mechanisms. These mechanisms manifest themselves in several types of dynamic recrystallization types: Discontinuous Dynamic Recrystallization (DDRX), Continuous Dynamic Recrystallization (CDRX), and Geometric Dynamic Recrystallization (GDRX) [2]. DDRX, which involves the nucleation and growth of new grains during deformation, has been found to be unlikely to occur in Al-Mg-Si alloys[3]. Other forms of dynamic recrystallization that have been observed in Al alloys include geometric dynamic recrystallization (GDRX) as proposed by McQueen and Humphreys[4-6]. GDRX grains form as a grain is heavily deformed to the point where its grain boundaries begin to “pinch off” and form new, equiaxed grains with high misorientation (>15). Additionally, continuous dynamic recrystallization (CDRX) occurs whereby new, highly misoriented grains form as the subgrains that form during deformation gradually increase in misorientation [7,8]. A satisfactory understanding of microstructure development during deformation is also critical as an input data for the numerical modeling of metal forming processes. In order to provide useful microstructure information for modeling purposes it is necessary to obtain microstructure response information to a wide range of strain, strain rate and temperature deformation parameters and therefore the torsion test can be a very valuable experiment and source of microstructure data.

Key Engineering Materials Vol. 424 (2010) pp 1-8© (2010) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/KEM.424.1

In order to isolate friction and its influence on heat transfer conditions and temperature distribution within the extruded material the indirect extrusion process was selected. The material used was 6061 aluminum alloy with a chemistry within the Aluminum Association’s standards for this alloy. In order to understand the effect of chemistry on recrystallization response, two alloys representing Cr:Mn ratios of 1:1 (Low Cr) and 2:1 (High Cr) were used. Total Cr + Mn levels in wt. % were as follows: 0.17 (Low Cr), and 0.35 (High Cr). The samples used for both the small-scale extrusion and torsion experiments were sectioned from the mid-radius of the homogenized industrial billets. More detailed information about sample preparation is available in literature. [9, 10]

The Peripheral Coarse Grain Extrusion Laboratory Experiments

The peripheral coarse grain (PCG) structure is among surface imperfections formed during extrusion that results in an undesirable product that must be scrapped. In the presented investigation, documented in details in [9] the phenomenon of PCG is analyzed. Both mechanical properties and surface quality of an extrudate can be affected by PCG formation. The focus of this research is to understand the origin and mechanism of PCG formation as well as the effect of extrusion conditions on its development. In general, the PCG structure can be controlled by several factors: monitoring the exit temperature and extrusion speed, increasing or decreasing recrystallization inhibiting elements, and maximizing the extrusion ratio to obtain a critical strain.[11] Previous investigations have attempted to understand and predict PCG formation.[12-18] Many times, PCG formation is attributed to the strain gradient inherent in the extrusion process. A higher strain has been found to exist at the surface of an extrudate, and therefore, conditions of a coarse grain recrystallized region are favored. Despite previous work on the development of the PCG structure in extrusion, there still does not exist a clear understanding on the origin of this surface recrystallization phenomenon. During indirect extrusion, the billet remains stationary within the container eliminating friction at the billet/container interface. As the die progresses during indirect extrusion, the peripheral billet material is continuously “scraped” off the container wall and flows into the shear zone of the billet continuing to the subsurface layers of the extrudates [19]. Due to this scraping, a true Dead Metal Zone (DMZ) never forms. Instead, the material at the die face undergoes heavy deformation, unlike that seen in direct extrusion, and can “leak” to the surface layers of the final product. A DMZ is typically characterized as a region of stagnant material due to the container and tooling configuration in extrusion. Valberg does state that some billet material can remain at the die face but will become heavily deformed as extrusion progresses [19]. Despite the claim by Valberg that a dead metal zone never forms during indirect hot extrusion of aluminum, there is still confusion whether dead metal zone formation does actually occur. Thus, it must be mentioned that for the purpose of the present work, the term “Dead Metal Zone” will be used to describe the area of metal at the die face regardless of the strain it may or may not experience. Despite previous attempts to predict recrystallized depth in the extrudate, knowledge on the precise threshold depth has not yet been achieved, especially for 6xxx alloys. Small-scale indirect extrusions were performed on a 40 ton servo – hydraulic press. The material

for small – scale extrusion was machined to cylindrical billets with dimensions of 3.81 cm in height and 3.05 cm in diameter. Two billet temperatures, extrusion ratios, ram speeds, and alloy chemistries were utilized to investigate the effect of process parameters on PCG depth. All extrusions were performed to 75% completion and quenched with a forced air quench. Billet discard material remaining in the chamber after extrusion ceases was subsequently removed from the chamber and water quenched after approximately 60 seconds. Interrupted extrusions were performed in order to understand the billet microstructure evolution at 25, 50, and 75% completion. Electron Backscatter Diffraction (EBSD) analysis was also performed. The samples used for

analysis were taken from the half – length of the extrudate as well as the extrusion discard. In order to quantify the grain and subgrain boundary misorientation and size, maps were taken from the center to the surface of the extrudates used in the analysis.

In order to isolate friction and its influence on heat transfer conditions and temperature distribution within the extruded material the indirect extrusion process was selected. The material used was 6061 aluminum alloy with a chemistry within the Aluminum Association’s standards for this alloy. In order to understand the effect of chemistry on recrystallization response, two alloys representing Cr:Mn ratios of 1:1 (Low Cr) and 2:1 (High Cr) were used. Total Cr + Mn levels in wt. % were as follows: 0.17 (Low Cr), and 0.35 (High Cr). The samples used for both the small-scale extrusion and torsion experiments were sectioned from the mid-radius of the homogenized industrial billets. More detailed information about sample preparation is available in literature. [9, 10]

The Peripheral Coarse Grain Extrusion Laboratory Experiments

The peripheral coarse grain (PCG) structure is among surface imperfections formed during extrusion that results in an undesirable product that must be scrapped. In the presented investigation, documented in details in [9] the phenomenon of PCG is analyzed. Both mechanical properties and surface quality of an extrudate can be affected by PCG formation. The focus of this research is to understand the origin and mechanism of PCG formation as well as the effect of extrusion conditions on its development. In general, the PCG structure can be controlled by several factors: monitoring the exit temperature and extrusion speed, increasing or decreasing recrystallization inhibiting elements, and maximizing the extrusion ratio to obtain a critical strain.[11] Previous investigations have attempted to understand and predict PCG formation.[12-18] Many times, PCG formation is attributed to the strain gradient inherent in the extrusion process. A higher strain has been found to exist at the surface of an extrudate, and therefore, conditions of a coarse grain recrystallized region are favored. Despite previous work on the development of the PCG structure in extrusion, there still does not exist a clear understanding on the origin of this surface recrystallization phenomenon. During indirect extrusion, the billet remains stationary within the container eliminating friction at the billet/container interface. As the die progresses during indirect extrusion, the peripheral billet material is continuously “scraped” off the container wall and flows into the shear zone of the billet continuing to the subsurface layers of the extrudates [19]. Due to this scraping, a true Dead Metal Zone (DMZ) never forms. Instead, the material at the die face undergoes heavy deformation, unlike that seen in direct extrusion, and can “leak” to the surface layers of the final product. A DMZ is typically characterized as a region of stagnant material due to the container and tooling configuration in extrusion. Valberg does state that some billet material can remain at the die face but will become heavily deformed as extrusion progresses [19]. Despite the claim by Valberg that a dead metal zone never forms during indirect hot extrusion of aluminum, there is still confusion whether dead metal zone formation does actually occur. Thus, it must be mentioned that for the purpose of the present work, the term “Dead Metal Zone” will be used to describe the area of metal at the die face regardless of the strain it may or may not experience. Despite previous attempts to predict recrystallized depth in the extrudate, knowledge on the precise threshold depth has not yet been achieved, especially for 6xxx alloys. Small-scale indirect extrusions were performed on a 40 ton servo – hydraulic press. The material

for small – scale extrusion was machined to cylindrical billets with dimensions of 3.81 cm in height and 3.05 cm in diameter. Two billet temperatures, extrusion ratios, ram speeds, and alloy chemistries were utilized to investigate the effect of process parameters on PCG depth. All extrusions were performed to 75% completion and quenched with a forced air quench. Billet discard material remaining in the chamber after extrusion ceases was subsequently removed from the chamber and water quenched after approximately 60 seconds. Interrupted extrusions were performed in order to understand the billet microstructure evolution at 25, 50, and 75% completion. Electron Backscatter Diffraction (EBSD) analysis was also performed. The samples used for

analysis were taken from the half – length of the extrudate as well as the extrusion discard. In order to quantify the grain and subgrain boundary misorientation and size, maps were taken from the center to the surface of the extrudates used in the analysis.

2 Advances on Hot Extrusion and Simulation of Light Alloys

Fig. 1: Microstructure of the AA6061 extrudate showing GDRX and PCG grains, extrusion ratio-20, temperatue-400 oC, ram speed-1.3mm/s.

Based on results from small – scale indirect extrusion experiments, it was found that the depth of the PCG structure is related to the energy supplied to the deformed material. It has been determined that the mechanism of coarse grain formation is a static process, due to the presence of coarse, recrystallized grains in the extrudate and absence in the partially extruded billet. It was determined that the PCG structure forms rapidly, on the order of seconds after the material exits the die. The so-called “Dead Metal Zone” in indirect extrusion is comprised of a fine, equiaxed grain structure in a hemispherical shape after the billet has been extruded to 75% completion. The microstructure in the DMZ region after extrusion suggests that deformation conditions in the DMZ of an indirectly extruded billet are much more severe than have been assumed in the literature. The structure of the extrudate surface likely originates from grain fragmentation at the DMZ / shear zone interface. This grain fragmentation closely resembles the CDRX or GDRX mechanisms already established in the literature.

Hot Torsion Experiments

The results and conclusions of the torsion testing has been described and discussed in detail in literature [B]. The torsion conditions used are shown in Table I. The value of the Zener Hollomon was obtained using equation 1 and a calculated Q value of 155,880 J/mol-K using equation 2. The maximum Z value is calculated for the surface of the torsion sample, where the strain rate is the highest.

−=

•

RTQ

Z expε (1)

where: R = Gas Constant, = strain rate, Z = Zener Hollomon parameter, Q = Activation Energy, and T = Absolute Temperature

( )

ε=

•

Td

dQ

1ln

(2)

In order to test samples and characterize the deformed structure, a very high quenching rate was needed and was accomplished using a water quench spray. After initial trials, it was found that the quenching system allowed for the sample to be quenched to below 100C within less than 1 second of the end of twisting. Therefore, the cooling rate after deformation was at least 380C/s.

Fig. 1: Microstructure of the AA6061 extrudate showing GDRX and PCG grains, extrusion ratio-20, temperatue-400 oC, ram speed-1.3mm/s.

Based on results from small – scale indirect extrusion experiments, it was found that the depth of the PCG structure is related to the energy supplied to the deformed material. It has been determined that the mechanism of coarse grain formation is a static process, due to the presence of coarse, recrystallized grains in the extrudate and absence in the partially extruded billet. It was determined that the PCG structure forms rapidly, on the order of seconds after the material exits the die. The so-called “Dead Metal Zone” in indirect extrusion is comprised of a fine, equiaxed grain structure in a hemispherical shape after the billet has been extruded to 75% completion. The microstructure in the DMZ region after extrusion suggests that deformation conditions in the DMZ of an indirectly extruded billet are much more severe than have been assumed in the literature. The structure of the extrudate surface likely originates from grain fragmentation at the DMZ / shear zone interface. This grain fragmentation closely resembles the CDRX or GDRX mechanisms already established in the literature.

Hot Torsion Experiments

The results and conclusions of the torsion testing has been described and discussed in detail in literature [B]. The torsion conditions used are shown in Table I. The value of the Zener Hollomon was obtained using equation 1 and a calculated Q value of 155,880 J/mol-K using equation 2. The maximum Z value is calculated for the surface of the torsion sample, where the strain rate is the highest.

−=

•

RTQ

Z expε (1)

where: R = Gas Constant, = strain rate, Z = Zener Hollomon parameter, Q = Activation Energy, and T = Absolute Temperature

( )

ε=

•

Td

dQ

1ln

(2)

In order to test samples and characterize the deformed structure, a very high quenching rate was needed and was accomplished using a water quench spray. After initial trials, it was found that the quenching system allowed for the sample to be quenched to below 100C within less than 1 second of the end of twisting. Therefore, the cooling rate after deformation was at least 380C/s.

Key Engineering Materials Vol. 424 3

Table 1: Sample conditions used in hot torsion testing.

Alloy Defrmation Temperature [C ]

Effective Strain Strain rate [s-1]

Maximum Zener Hollomon Parameter, Zmax [s-1]

6061 Low Cr 400 1, 2.5, and 3.5 15 2.0 x 1013

6061 Low Cr 400 1, 2.5, and 3.5 30 4.0 x 1013

6061 Low Cr 482 1, 2.5, and 3.5 15 9.7 x 1011

6061 Low Cr 482 1, 2.5, and 3.5 30 1.9x1012

6061 High Cr 400 1 and 2.5 15 2.0 x 1013

6061 High Cr 400 1 and 2.5 30 4.0 x 1013

6061 High Cr 482 1 and 2.5 15 9.7 x 1011

6061 High Cr 482 1 and 2.5 30 1.9x1012

The ductility of the two alloys was also markedly different where the maximum effective strain achieved before fracture was 2.75 for the high Cr 6061 alloy and 3.85 for the low Cr 6061 aluminum alloy. The values of maximum effective strain for each alloy were surprisingly low, and it was thought this might be due to poor homogenization. After torsion testing of the same material after further homogenization, similar values for maximum strain were achieved. It is possible that the low strain values are due to the selected geometry of the torsion sample and different state of stress than present in extrusion. The lower fracture strain of the high Cr 6061 alloy also suggests that its ductility is lower than the low Cr 6061 alloy.

Fig. 2: EBSD Orientation map at the mid radius and mid – length of the hot torsion sample. The testing parameters were: εeff. = 3.5, Zmax = 2.01x1013. Notice the fragmentation of the grains,

especially in regions marked by arrows.

The results of hot torsion experiments revealed that the microstructure corresponding to the highest effective strain at the torsion sample surface consists of a fine, equiaxed grain structure. These grains are likely produced by a dynamic recrystallization process such as geometric dynamic recrystallization or continuous dynamic recrystallization. It can be reasonably concluded that the equiaxed grain microstructure is not a result of a static process due to the very high quenching rate after hot torsion testing. The critical effective strain for fine, equiaxed grain development in torsion was greater than 2.5 in torsion. At a strain of 3.5, it was determined that the as – deformed grain size decreased with higher values of Zener Hollomon parameter. The dominant mechanism of the break

Table 1: Sample conditions used in hot torsion testing.

Alloy Defrmation Temperature [C ]

Effective Strain Strain rate [s-1]

Maximum Zener Hollomon Parameter, Zmax [s-1]

6061 Low Cr 400 1, 2.5, and 3.5 15 2.0 x 1013

6061 Low Cr 400 1, 2.5, and 3.5 30 4.0 x 1013

6061 Low Cr 482 1, 2.5, and 3.5 15 9.7 x 1011

6061 Low Cr 482 1, 2.5, and 3.5 30 1.9x1012

6061 High Cr 400 1 and 2.5 15 2.0 x 1013

6061 High Cr 400 1 and 2.5 30 4.0 x 1013

6061 High Cr 482 1 and 2.5 15 9.7 x 1011

6061 High Cr 482 1 and 2.5 30 1.9x1012

The ductility of the two alloys was also markedly different where the maximum effective strain achieved before fracture was 2.75 for the high Cr 6061 alloy and 3.85 for the low Cr 6061 aluminum alloy. The values of maximum effective strain for each alloy were surprisingly low, and it was thought this might be due to poor homogenization. After torsion testing of the same material after further homogenization, similar values for maximum strain were achieved. It is possible that the low strain values are due to the selected geometry of the torsion sample and different state of stress than present in extrusion. The lower fracture strain of the high Cr 6061 alloy also suggests that its ductility is lower than the low Cr 6061 alloy.

Fig. 2: EBSD Orientation map at the mid radius and mid – length of the hot torsion sample. The testing parameters were: εeff. = 3.5, Zmax = 2.01x1013. Notice the fragmentation of the grains,

especially in regions marked by arrows.

The results of hot torsion experiments revealed that the microstructure corresponding to the highest effective strain at the torsion sample surface consists of a fine, equiaxed grain structure. These grains are likely produced by a dynamic recrystallization process such as geometric dynamic recrystallization or continuous dynamic recrystallization. It can be reasonably concluded that the equiaxed grain microstructure is not a result of a static process due to the very high quenching rate after hot torsion testing. The critical effective strain for fine, equiaxed grain development in torsion was greater than 2.5 in torsion. At a strain of 3.5, it was determined that the as – deformed grain size decreased with higher values of Zener Hollomon parameter. The dominant mechanism of the break


up of grains at this strain appears to be CDRX at low values of Z and GDRX at high values Z. Fig.s 2 shows an EBSD orientation map as well as the grain size distribution from the mid – radius of the sample deformed at Zmax = 2.01x1013. It can be seen that there is an intensive fragmentation of the grain, both at the grain boundaries and within the grains themselves. Here, grains are loosely defined as regions of similar texture, due to the disappearance of a well – defined grain regions. Fig.s from 3 to 6 show the EBSD results, which are confirming small grain formation as a result of high deformation and recovery mechanisms.

Fig. 3: EBSD Orientation map at the surface of the mid – length of the hot torsion sample. The testing parameters were: ε = 3.5, Z = 9.72x10.

Fig. 4: EBSD Boundary map of the same region as Fig. 3. The dark lines represent misorientations above 15deg.


up of grains at this strain appears to be CDRX at low values of Z and GDRX at high values Z. Fig.s 2 shows an EBSD orientation map as well as the grain size distribution from the mid – radius of the sample deformed at Zmax = 2.01x1013. It can be seen that there is an intensive fragmentation of the grain, both at the grain boundaries and within the grains themselves. Here, grains are loosely defined as regions of similar texture, due to the disappearance of a well – defined grain regions. Fig.s from 3 to 6 show the EBSD results, which are confirming small grain formation as a result of high deformation and recovery mechanisms.


Fig. 4: EBSD Boundary map of the same region as Fig. 3. The dark lines represent misorientations above 15deg.



Fig. 6: EBSD Boundary map of the same region as Fig. 5. The dark lines represent misorientations above 15 deg.

.umerical Modeling Simulation

Numerical modeling packages are very helpful in predicting state variables of hot deformation processes. The indirect extrusion process of aluminum alloy 6061 has been analyzed using DEFORM TM software [20]. The software accuracy was evaluated first by comparing its metal flow predictions to the results published in literature by Valberg [19]. Then the software was used to show a location of the material within the billet to form so called “Dead Metal Zone” as a result of extrusion. Additionally, it was possible to present the material from DMZ leaking into surface of the extrudade supporting a hypothesis presented in this paper. Metal Flow analysis also allowed conclusion that the material within the DMZ is not a material, which was there from the beginning of the deformation. In other words it is material, which flowed there and therefore is deformed. This statement further supports a theory that DMZ in the indirect extrusion process is highly deformed and should not be referred to as dead metal zone.

Fig. 7: Numerical simulation prediction of metal flow and corresponding microstructure of the DMZ in indirect extrusion process showing source of material within the DMZ as a function of time.

Bandar proposed a model combining contributions from CDRX and GDRX able to predict formation of coarse grain structure as a function of state variables.[20, 21]. Based on the numerical modeling predictions for hot extrusion of 6061 aluminum alloy verified by experiments listed in literature [19] the state variables: temperature, strain, strain rate, and stress were established. This was achieved with the finite element modeling package DEFORM 2-D. These state variables were then used in a dynamic recrystallization (DRX) model that incorporates both continuous dynamic recrystallization (CDRX) and geometric dynamic recrystallization (GDRX) to predict grain structure evolution. The performed simulation was verified by experimental torsion tests from literature [10].

Fig. 6: EBSD Boundary map of the same region as Fig. 5. The dark lines represent misorientations above 15 deg.

.umerical Modeling Simulation

Numerical modeling packages are very helpful in predicting state variables of hot deformation processes. The indirect extrusion process of aluminum alloy 6061 has been analyzed using DEFORM TM software [20]. The software accuracy was evaluated first by comparing its metal flow predictions to the results published in literature by Valberg [19]. Then the software was used to show a location of the material within the billet to form so called “Dead Metal Zone” as a result of extrusion. Additionally, it was possible to present the material from DMZ leaking into surface of the extrudade supporting a hypothesis presented in this paper. Metal Flow analysis also allowed conclusion that the material within the DMZ is not a material, which was there from the beginning of the deformation. In other words it is material, which flowed there and therefore is deformed. This statement further supports a theory that DMZ in the indirect extrusion process is highly deformed and should not be referred to as dead metal zone.

Fig. 7: Numerical simulation prediction of metal flow and corresponding microstructure of the DMZ in indirect extrusion process showing source of material within the DMZ as a function of time.

Bandar proposed a model combining contributions from CDRX and GDRX able to predict formation of coarse grain structure as a function of state variables.[20, 21]. Based on the numerical modeling predictions for hot extrusion of 6061 aluminum alloy verified by experiments listed in literature [19] the state variables: temperature, strain, strain rate, and stress were established. This was achieved with the finite element modeling package DEFORM 2-D. These state variables were then used in a dynamic recrystallization (DRX) model that incorporates both continuous dynamic recrystallization (CDRX) and geometric dynamic recrystallization (GDRX) to predict grain structure evolution. The performed simulation was verified by experimental torsion tests from literature [10].


The objective of linking the state parameters with the predicted grain structure response in the material was achieved [21]. This approach has been further refined and applied to surface grain structure formation in hot rolling of aluminum alloy 6061. [22]

Summary

In the analysis of aluminum alloy hot deformation, there is a need for a combined approach including use of physical modeling, material characterization and numerical modeling. These techniques are complimentary to each other and their combination provides comprehensive understanding of grain structure development. This methodology encompassing the variety of techniques should be applied for prediction of surface defects in deformation processing in order to obtain accurate and reliable data.

Acknowledgments

The authors would like to thank the U.S. Department of Energy Office of Industrial Technologies (contract DE – FC07 – O1ID14191) and Alcoa, Inc. for their support of this research. Partial support of Wojciech Z. Misiolek is provided by the Loewy Family Foundation through the Loewy Professorship at Lehigh University. . Additionally, the authors are grateful to Dr. Paul Wang, Ms. Heather Browne, Dr. Alexander Bandar and Mr. Luigi DePari Jr. for their research contribution and discussions on the subject.

References

[1] W. Van Geertruyden, W. Misiolek, P. Wang, in ASM Conference, Pittsburgh, PA, October, 2003.

[2] T. Pettersen, B. Holmedal, and E. Nes, Metallurgical and Materials Transactions A, vol. 34A, 2003, p. 2737.

[3] R.D. Doherty, D.A.H., F.J. Humphreys, J.J. Jonas, D.J. Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Materials Science and Engineering A, vol. A238, 1997, p. 219.

[4] H. J. McQueen, W. Blum, Materials Science and Engineering A. Vol. 290, (2000) No. 1-2, p. 95.

[5] H.J. McQueen O. Knustad, N. Ryum, and J.K. Solberg, Scripta Materialia, vol. 19, 1985, p. 73.

[6] F.J Humphreys, Proc. 6th International conference of Strength of Metals and Alloys, ed. Gifkins, Melbourne, Australia, vol. 1, 1982, p.625.

[7] S. Gourdet, F. Montheillet, Acta Materialia, vol. 53, 2003, p. 2685.

[8] C. Chovet, S. Gourdet, and F. Montheillet, Materials Science Forum, vol. 331 – 337, 2000, p. 733.

[9] W. Van Geertruyden, H. M. Browne, W. Z. Misiolek, P. Wang, Metallurgical and Materials Transactions A, vol. 36A, No.4, April 2005, p. 1049.

[10] W. Van Geertruyden, W. Z. Misiolek, P. Wang, Materials Science & Engineering A, 419 (2006),p. 105

[11] P. Saha, Aluminum Extrusion Technology, ASM International, Metals Park, OH, 2000, p.26

[12] X. Duan and T. Sheppard, TMS Annual Meeting: Hot Deformation of Aluminum Alloys, May 2003, p. 99.

[13] T. Furu, H.E. Vatne, Materials Science Forum, vol. 331 – 337, 2000, p. 843.

The objective of linking the state parameters with the predicted grain structure response in the material was achieved [21]. This approach has been further refined and applied to surface grain structure formation in hot rolling of aluminum alloy 6061. [22]

Summary

In the analysis of aluminum alloy hot deformation, there is a need for a combined approach including use of physical modeling, material characterization and numerical modeling. These techniques are complimentary to each other and their combination provides comprehensive understanding of grain structure development. This methodology encompassing the variety of techniques should be applied for prediction of surface defects in deformation processing in order to obtain accurate and reliable data.

Acknowledgments

The authors would like to thank the U.S. Department of Energy Office of Industrial Technologies (contract DE – FC07 – O1ID14191) and Alcoa, Inc. for their support of this research. Partial support of Wojciech Z. Misiolek is provided by the Loewy Family Foundation through the Loewy Professorship at Lehigh University. . Additionally, the authors are grateful to Dr. Paul Wang, Ms. Heather Browne, Dr. Alexander Bandar and Mr. Luigi DePari Jr. for their research contribution and discussions on the subject.

References

[1] W. Van Geertruyden, W. Misiolek, P. Wang, in ASM Conference, Pittsburgh, PA, October, 2003.

[2] T. Pettersen, B. Holmedal, and E. Nes, Metallurgical and Materials Transactions A, vol. 34A, 2003, p. 2737.

[3] R.D. Doherty, D.A.H., F.J. Humphreys, J.J. Jonas, D.J. Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Materials Science and Engineering A, vol. A238, 1997, p. 219.

[4] H. J. McQueen, W. Blum, Materials Science and Engineering A. Vol. 290, (2000) No. 1-2, p. 95.

[5] H.J. McQueen O. Knustad, N. Ryum, and J.K. Solberg, Scripta Materialia, vol. 19, 1985, p. 73.

[6] F.J Humphreys, Proc. 6th International conference of Strength of Metals and Alloys, ed. Gifkins, Melbourne, Australia, vol. 1, 1982, p.625.

[7] S. Gourdet, F. Montheillet, Acta Materialia, vol. 53, 2003, p. 2685.

[8] C. Chovet, S. Gourdet, and F. Montheillet, Materials Science Forum, vol. 331 – 337, 2000, p. 733.

[9] W. Van Geertruyden, H. M. Browne, W. Z. Misiolek, P. Wang, Metallurgical and Materials Transactions A, vol. 36A, No.4, April 2005, p. 1049.

[10] W. Van Geertruyden, W. Z. Misiolek, P. Wang, Materials Science & Engineering A, 419 (2006),p. 105

[11] P. Saha, Aluminum Extrusion Technology, ASM International, Metals Park, OH, 2000, p.26

[12] X. Duan and T. Sheppard, TMS Annual Meeting: Hot Deformation of Aluminum Alloys, May 2003, p. 99.

[13] T. Furu, H.E. Vatne, Materials Science Forum, vol. 331 – 337, 2000, p. 843.


[14] W. Libura, J. Zasadzinski, Proceedings of the 5th Aluminum Extrusion Technology Seminar ET ‘92, Chicago, IL, AA & AEC, vol. II, 1992, p. 485.

[15] H. Yang, Proceedings of the 7th Aluminum Extrusion Technology Seminar ET ‘00, Chicago, IL, AA & AEC, vol. I, 2000, p. 371.

[16] N. Parson, S. Barker, A. Shalanski, C. Jowett, Proceedings of the 8th Aluminum Extrusion Technology Seminar ET ‘04, Orlando, FL, AA & AEC, vol. I, 2004, p. 11.

[17] Z. Peng, T. Sheppard, Proceedings of the 8th Aluminum Extrusion Technology Seminar ET ‘04, Orlando, FL, AA & AEC, vol. I, 2004, p. 79.

[18] E. Sweet, S. Caraher, N. Danilova, X. Zhang, Proceedings of the 8th Aluminum Extrusion Technology Seminar ET ‘04, Orlando, FL, AA & AEC, vol. I, 2004, p. 115.

[19] H. Valberg, Proceedings of 5th International Aluminum Extrusion Technology Seminar, 1996, Vol. I, p. 95.

[20] A. R. Bandar, PhD Dissertation, Lehigh University, Bethlehem, PA, USA, 2005

[21] L. DePari Jr., W. Z. Misiolek, A. R. Bandar, W. H. Van Geertruyden, Computer Methods in Materials Science, vol. 7 (2007) No. 1, p. 5

[22] L. DePari Jr., W. Z. Misiolek, Acta Materialia, vol. 56 (2008), p. 6174

[14] W. Libura, J. Zasadzinski, Proceedings of the 5th Aluminum Extrusion Technology Seminar ET ‘92, Chicago, IL, AA & AEC, vol. II, 1992, p. 485.

[15] H. Yang, Proceedings of the 7th Aluminum Extrusion Technology Seminar ET ‘00, Chicago, IL, AA & AEC, vol. I, 2000, p. 371.

[16] N. Parson, S. Barker, A. Shalanski, C. Jowett, Proceedings of the 8th Aluminum Extrusion Technology Seminar ET ‘04, Orlando, FL, AA & AEC, vol. I, 2004, p. 11.

[17] Z. Peng, T. Sheppard, Proceedings of the 8th Aluminum Extrusion Technology Seminar ET ‘04, Orlando, FL, AA & AEC, vol. I, 2004, p. 79.

[18] E. Sweet, S. Caraher, N. Danilova, X. Zhang, Proceedings of the 8th Aluminum Extrusion Technology Seminar ET ‘04, Orlando, FL, AA & AEC, vol. I, 2004, p. 115.

[19] H. Valberg, Proceedings of 5th International Aluminum Extrusion Technology Seminar, 1996, Vol. I, p. 95.

[20] A. R. Bandar, PhD Dissertation, Lehigh University, Bethlehem, PA, USA, 2005

[21] L. DePari Jr., W. Z. Misiolek, A. R. Bandar, W. H. Van Geertruyden, Computer Methods in Materials Science, vol. 7 (2007) No. 1, p. 5

[22] L. DePari Jr., W. Z. Misiolek, Acta Materialia, vol. 56 (2008), p. 6174


Towards predictive control of extrusion weld seams: an integrated approach

A.J. den Bakker1,a, R.J. Werkhoven2,b , W.H. Sillekens2,c and L. Katgerman3,d 1 Nedal Aluminium, PO Box 2020, 3500 GA Utrecht, Netherlands

2 TNO Science & Industry, PO Box 6235, 5600 HE Eindhoven, Netherlands 3 Delft University of Technology, Mekelweg 2, 2628 CD Delft, Netherlands

a [email protected], b [email protected], c [email protected], d [email protected]

Keywords: aluminium alloys, weld seams, metal flow, structure evolution, modelling Abstract. Longitudinal weld seams are an intrinsic feature in hollow extrusions produced with porthole dies. The formation of longitudinal weld seams is a solid bonding process, controlled by the local conditions in the extrusion die. Being the weakest areas within the extrusion cross section, it is desirable to achieve adequate properties of these weld seams. In our research, the concept of a weld seam integrity indicator as a means of quantifying bonding efficiency is introduced. The value of this indicator depends on a number of factors: the material flow within the die weld chambers, an adequate pressure level acting on the weld planes and finally the evolution of the metal microstructure. Optimisation of the welding conditions leads to a higher value of the weld seam integrity indicator and thus to improved weld seam properties. The objective of the research presented in this paper is to assess the feasibility of this concept.

In lab-scale experiments, AA6060 and AA6082 aluminium alloy billets were formed into strips by means of the direct hot extrusion process. By utilising porthole dies a central longitudinal weld seam is formed. The effect of different geometries of the weld chamber and the processing conditions on the quality of the weld seam are investigated. Characterisation of these weld seams through mechanical testing, focusing on the ability of the weld seam area to accommodate plastic deformation following the onset of plastic instability, and microstructural analysis provides insight into bonding performance. The outcome of this characterisation provides a basis for an estimation of the weld seam indicator. Through computer modelling, the particular process conditions related to weld seam formation are calculated and correlated with the experimental results. The experimental results clearly demonstrate that weld seam formation is controlled by a combination of factors as described above. Inadequate fulfilment of these conditions, verified by the FE-simulations, is the cause of inferior weld seams, associated with low values of the weld seam integrity indicator.

Through further elaboration of the concepts presented in this work, the weld seam integrity indicator is to be developed, with the future aim of predicting the weld seam performance through finite element simulations.

Introduction

Extruded shapes can be divided into two main categories: solid sections and hollow sections. For the latter, the cross-sectional area is bordered by a single continuous curve defining the outer perimeter and an internal curve for each enclosed void. Hollow sections are generally produced with tools in which a core, or mandrel, is internally suspended in the die by means of legs or bridges. In multi-hollow sections, the number of cores equals the number of voids. Given the geometrical flexibility and the efficiency of use, porthole dies are the most common tooling configuration for the production of (multi-)hollow sections. In extrusion through porthole dies, the pre-heated aluminium billet is split into separate metal streams flowing around the legs, to be re-joined in the welding chambers, thus forming longitudinal weld seams. The joining of the metals streams occurs under conditions of pressure, strain/shear and temperature, but without the

Towards predictive control of extrusion weld seams: an integrated approach

A.J. den Bakker1,a, R.J. Werkhoven2,b , W.H. Sillekens2,c and L. Katgerman3,d 1 Nedal Aluminium, PO Box 2020, 3500 GA Utrecht, Netherlands

2 TNO Science & Industry, PO Box 6235, 5600 HE Eindhoven, Netherlands 3 Delft University of Technology, Mekelweg 2, 2628 CD Delft, Netherlands

a [email protected], b [email protected], c [email protected], d [email protected]

Keywords: aluminium alloys, weld seams, metal flow, structure evolution, modelling Abstract. Longitudinal weld seams are an intrinsic feature in hollow extrusions produced with porthole dies. The formation of longitudinal weld seams is a solid bonding process, controlled by the local conditions in the extrusion die. Being the weakest areas within the extrusion cross section, it is desirable to achieve adequate properties of these weld seams. In our research, the concept of a weld seam integrity indicator as a means of quantifying bonding efficiency is introduced. The value of this indicator depends on a number of factors: the material flow within the die weld chambers, an adequate pressure level acting on the weld planes and finally the evolution of the metal microstructure. Optimisation of the welding conditions leads to a higher value of the weld seam integrity indicator and thus to improved weld seam properties. The objective of the research presented in this paper is to assess the feasibility of this concept.

In lab-scale experiments, AA6060 and AA6082 aluminium alloy billets were formed into strips by means of the direct hot extrusion process. By utilising porthole dies a central longitudinal weld seam is formed. The effect of different geometries of the weld chamber and the processing conditions on the quality of the weld seam are investigated. Characterisation of these weld seams through mechanical testing, focusing on the ability of the weld seam area to accommodate plastic deformation following the onset of plastic instability, and microstructural analysis provides insight into bonding performance. The outcome of this characterisation provides a basis for an estimation of the weld seam indicator. Through computer modelling, the particular process conditions related to weld seam formation are calculated and correlated with the experimental results. The experimental results clearly demonstrate that weld seam formation is controlled by a combination of factors as described above. Inadequate fulfilment of these conditions, verified by the FE-simulations, is the cause of inferior weld seams, associated with low values of the weld seam integrity indicator.

Through further elaboration of the concepts presented in this work, the weld seam integrity indicator is to be developed, with the future aim of predicting the weld seam performance through finite element simulations.

Introduction

Extruded shapes can be divided into two main categories: solid sections and hollow sections. For the latter, the cross-sectional area is bordered by a single continuous curve defining the outer perimeter and an internal curve for each enclosed void. Hollow sections are generally produced with tools in which a core, or mandrel, is internally suspended in the die by means of legs or bridges. In multi-hollow sections, the number of cores equals the number of voids. Given the geometrical flexibility and the efficiency of use, porthole dies are the most common tooling configuration for the production of (multi-)hollow sections. In extrusion through porthole dies, the pre-heated aluminium billet is split into separate metal streams flowing around the legs, to be re-joined in the welding chambers, thus forming longitudinal weld seams. The joining of the metals streams occurs under conditions of pressure, strain/shear and temperature, but without the


occurrence of liquid phases, i.e. a solid-state bonding process. Influenced by the particular local process conditions, micro-structural reorganisation processes such as recovery, re-crystallisation and grain growth occur, having an obvious bearing on weld-seam formation. Issues concerning extrusion weld seams. As indicated above, the formation of longitudinal weld seams is influenced by the particular local conditions ruling the solid-state bonding process including the micro-structural evolution. If the combination of parameters is unfavourable, weld-seam defects can occur, leading to sub-standard properties of the hollow section. Porosity can occur on weld seams when air or gas is entrapped. This can occur when voids are formed in the aluminium bulk just prior to extrusion of the billet; e.g., in shearing of the discard, poorly matching billet faces or a significant mismatch between the billet surface contour and the container. Although this will predominantly influence the transverse weld seams, effects can continue into the formation zone of the longitudinal weld seam. In other instances, porosity can develop due to the formation of gas pockets in the die as described by Akeret [1] and Valberg et al. [2]. In this case the defect is uniquely related to the flow pattern in a particular die.

Similar to porosity, foreign matter can become entrapped in the aluminium and subsequently manifest itself in the weld seam. Such occurrences can be related to grease or oil from the extrusion equipment, excess of lubricants or oxides, either originating from the casting process or formed during the pre-heating of the billet. These are typically external factors and not directly related to the solid-state bonding process as such.

A third category consists of cases where the formation of sound weld seams is hampered by unfavourable operating conditions, including the flow in the die, the mechanics of bonding and the micro-structural evolution. Although bonds with inferior (mechanical) properties are formed, the particular underlying defect may not be obvious from visual observation, as is particularly the case for so-called ‘kissing bonds’ described by Oosterkamp et al. [3]. Furthermore it should be noted that the actual properties of weld seams may differ from those of the parent material. Not necessarily does this infer that an inferior bond is formed, as the discussion arises when weld-seam properties may be deemed inadequate. Nevertheless, in general the goal is to produce weld seams with properties similar to those of the other parts of the section.

Weld-seam property prediction. The work outlined in this paper is part of a project designed to develop a method to predict weld seam quality, taking into account the effects of different alloys as well as of process conditions and tooling geometry.

The formation of weld seams has been addressed by several others, often utilising numerical techniques to calculate the local conditions in the welding chamber, resulting in a conclusion concerning the weld-seam quality. Under the presumption of suitable flow conditions, several methods have been proposed to relate the particular operating conditions and tooling geometry to the resulting weld-seam integrity. Many of these methods centre on a mechanical interpretation of the solid-state bonding process; that is, for achieving an adequate level of pressure on the welding plane, as described in e.g. [4, 5, 6] and in a comprehensive review by Donati et al. in [7]. For specific well-defined conditions, the outcome of these models – expressed by a value for the weld-seam criterion – can be correlated with experimental results.

Thus, trends between tooling effects and weld-seam properties are revealed. However, these models are not generally applicable and the criterion needs to be ‘calibrated’ for a particular alloy, process conditions and die configuration. Moreover, these criteria merely give a global indication of weld-seam quality, thereby disregarding particular cases where only partial bond formation occurs on the weld plane. Consequently, a truly comprehensive treatment of the weld-seam formation process must take into account all prerequisites for bonding, notably: 1) converging metal flow in the die to ensure sustained contact between the rejoining streams along the entire bonding plane, 2) a pressure on the bonding plane that exceeds a particular threshold value, and 3) micro-structural reorganisation to ensure atomic registry of the bonding plane. These factors are to be incorporated in a weld-seam integrity function Iws as described below.

occurrence of liquid phases, i.e. a solid-state bonding process. Influenced by the particular local process conditions, micro-structural reorganisation processes such as recovery, re-crystallisation and grain growth occur, having an obvious bearing on weld-seam formation. Issues concerning extrusion weld seams. As indicated above, the formation of longitudinal weld seams is influenced by the particular local conditions ruling the solid-state bonding process including the micro-structural evolution. If the combination of parameters is unfavourable, weld-seam defects can occur, leading to sub-standard properties of the hollow section. Porosity can occur on weld seams when air or gas is entrapped. This can occur when voids are formed in the aluminium bulk just prior to extrusion of the billet; e.g., in shearing of the discard, poorly matching billet faces or a significant mismatch between the billet surface contour and the container. Although this will predominantly influence the transverse weld seams, effects can continue into the formation zone of the longitudinal weld seam. In other instances, porosity can develop due to the formation of gas pockets in the die as described by Akeret [1] and Valberg et al. [2]. In this case the defect is uniquely related to the flow pattern in a particular die.

Similar to porosity, foreign matter can become entrapped in the aluminium and subsequently manifest itself in the weld seam. Such occurrences can be related to grease or oil from the extrusion equipment, excess of lubricants or oxides, either originating from the casting process or formed during the pre-heating of the billet. These are typically external factors and not directly related to the solid-state bonding process as such.

A third category consists of cases where the formation of sound weld seams is hampered by unfavourable operating conditions, including the flow in the die, the mechanics of bonding and the micro-structural evolution. Although bonds with inferior (mechanical) properties are formed, the particular underlying defect may not be obvious from visual observation, as is particularly the case for so-called ‘kissing bonds’ described by Oosterkamp et al. [3]. Furthermore it should be noted that the actual properties of weld seams may differ from those of the parent material. Not necessarily does this infer that an inferior bond is formed, as the discussion arises when weld-seam properties may be deemed inadequate. Nevertheless, in general the goal is to produce weld seams with properties similar to those of the other parts of the section.

Weld-seam property prediction. The work outlined in this paper is part of a project designed to develop a method to predict weld seam quality, taking into account the effects of different alloys as well as of process conditions and tooling geometry.

The formation of weld seams has been addressed by several others, often utilising numerical techniques to calculate the local conditions in the welding chamber, resulting in a conclusion concerning the weld-seam quality. Under the presumption of suitable flow conditions, several methods have been proposed to relate the particular operating conditions and tooling geometry to the resulting weld-seam integrity. Many of these methods centre on a mechanical interpretation of the solid-state bonding process; that is, for achieving an adequate level of pressure on the welding plane, as described in e.g. [4, 5, 6] and in a comprehensive review by Donati et al. in [7]. For specific well-defined conditions, the outcome of these models – expressed by a value for the weld-seam criterion – can be correlated with experimental results.

Thus, trends between tooling effects and weld-seam properties are revealed. However, these models are not generally applicable and the criterion needs to be ‘calibrated’ for a particular alloy, process conditions and die configuration. Moreover, these criteria merely give a global indication of weld-seam quality, thereby disregarding particular cases where only partial bond formation occurs on the weld plane. Consequently, a truly comprehensive treatment of the weld-seam formation process must take into account all prerequisites for bonding, notably: 1) converging metal flow in the die to ensure sustained contact between the rejoining streams along the entire bonding plane, 2) a pressure on the bonding plane that exceeds a particular threshold value, and 3) micro-structural reorganisation to ensure atomic registry of the bonding plane. These factors are to be incorporated in a weld-seam integrity function Iws as described below.


In this work, we consider the bonding plane (i.e., the evolving contact surface between the rejoining metal streams) as a distribution of N elements, with a discrete “snap” function Wi. Depending on the local conditions, the processing history and micro-structural evolution, each element is assigned a discrete value, designating a non-bonding (Wi=0) or bonding (Wi=1) status. The weighted summation of these values over the bonding plane is then an indication of the weld-seam integrity Iws:

∑=

=

=i

iiws W

I

0

1

. (1)

The weld-seam property Pws is related to the bond property Pb of the bulk material:

bwsws PIP α= (2)

Thus, for a fully bonded structure Iws = 1. For Iws = 0, and hence Pws = 0, no bond is formed. For other values of Iws the weld seam will possess intermediate property values. These are not necessarily proportional to Iws, as indicated by α, a factor related to the damage mechanism causing the weld seam to fail. The objective of this research is to correlate a selected set of process parameters with Wi.

Experimental

In the laboratory-scale extrusion experiments described below, attention is focussed on the flow characteristics. Additionally the effect of process conditions combined with the alloy characteristics on the resulting grain structure of the weld seam is assessed through micro-structural analysis of the samples. Further evaluation of the bond structure is performed through studies of the fracture surfaces of samples derived from destructive testing.

The extrusion tests were performed on a 50 ton laboratory-scale press as described elsewhere [8]. In the trials a flat strip with dimensions 15 x 3 mm was extruded, with an extrusion ratio of 11. A porthole die was used in which a weld seam was formed in the centre of the strip, resulting from a die part containing a single leg perpendicular to the strip orientation fixed in front of the die plate as shown in Fig 1. The dies employed in these initial experiments featured varying welding chamber depths, t. Keeping the welding chamber height constant, a deep chamber of t = 10 mm in die B1.10 facilitates a converging metal flow and thus is expected to ease weld-seam formation, while a shallow chamber of t = 2 mm in die B1.2 impedes converging metal flow and hence increases the risk of poorly bonded weld seams.

Fig. 1: Die set-up in experiments; the weld chamber depth is denoted by the value t.

AA6060 and AA6082 billets with a diameter of 25 mm, prepared from industrial DC cast and homogenised feedstock, were extruded under tightly controlled conditions. Tests were performed at pre-set billet temperatures and extrusion speeds. Directly following extrusion, the product was air

In this work, we consider the bonding plane (i.e., the evolving contact surface between the rejoining metal streams) as a distribution of N elements, with a discrete “snap” function Wi. Depending on the local conditions, the processing history and micro-structural evolution, each element is assigned a discrete value, designating a non-bonding (Wi=0) or bonding (Wi=1) status. The weighted summation of these values over the bonding plane is then an indication of the weld-seam integrity Iws:

∑=

=

=i

iiws W

I

0

1

. (1)

The weld-seam property Pws is related to the bond property Pb of the bulk material:

bwsws PIP α= (2)

Thus, for a fully bonded structure Iws = 1. For Iws = 0, and hence Pws = 0, no bond is formed. For other values of Iws the weld seam will possess intermediate property values. These are not necessarily proportional to Iws, as indicated by α, a factor related to the damage mechanism causing the weld seam to fail. The objective of this research is to correlate a selected set of process parameters with Wi.

Experimental

In the laboratory-scale extrusion experiments described below, attention is focussed on the flow characteristics. Additionally the effect of process conditions combined with the alloy characteristics on the resulting grain structure of the weld seam is assessed through micro-structural analysis of the samples. Further evaluation of the bond structure is performed through studies of the fracture surfaces of samples derived from destructive testing.

The extrusion tests were performed on a 50 ton laboratory-scale press as described elsewhere [8]. In the trials a flat strip with dimensions 15 x 3 mm was extruded, with an extrusion ratio of 11. A porthole die was used in which a weld seam was formed in the centre of the strip, resulting from a die part containing a single leg perpendicular to the strip orientation fixed in front of the die plate as shown in Fig 1. The dies employed in these initial experiments featured varying welding chamber depths, t. Keeping the welding chamber height constant, a deep chamber of t = 10 mm in die B1.10 facilitates a converging metal flow and thus is expected to ease weld-seam formation, while a shallow chamber of t = 2 mm in die B1.2 impedes converging metal flow and hence increases the risk of poorly bonded weld seams.

Fig. 1: Die set-up in experiments; the weld chamber depth is denoted by the value t.

AA6060 and AA6082 billets with a diameter of 25 mm, prepared from industrial DC cast and homogenised feedstock, were extruded under tightly controlled conditions. Tests were performed at pre-set billet temperatures and extrusion speeds. Directly following extrusion, the product was air


quenched and subsequently artificially aged to the peak strength condition. Extrusion was performed in ‘billet-to-billet’ mode, where each consecutive billet was extruded directly onto the previous billet, without removal of any discard. Care was taken in sampling to avoid the incorporation of material originating from any transition areas resulting from this extrusion mode. Cross-sectional samples from the extruded lengths were polished and etched for inspection by means of light optical microscopy. Further samples were characterised by means of mechanical testing, focusing on the ductility characteristics. For this purpose transverse tensile samples were prepared with the weld seam located at the midpoint of the test piece. Tensile tests were performed at room temperature at a fixed crosshead speed. The fracture surfaces of the samples were studied by scanning electron microscopy (SEM) in order to relate the morphology of the fracture surface to relevant features of the weld seams.

Modelling

The metal flow was modelled using Virtual Extrusion Laboratory (VEL) a commercial finite-element (FE) code from Compuplast for plastic extrusion, utilising a module specifically adapted to simulate the aluminium extrusion process. Constitutive material behaviour for the alloys investigated in this project was determined through hot compression tests, with testing conditions within the range encountered in extrusion. The simulation model considers a steady-state condition, assuming a billet of infinite length flowing through the container and die. In the actual extrusion process, the billet is pushed by the ram through the container and die and its volume is continuously reducing. Full 3D model of the dies were constructed, specifically taking into account the design of the leg and the welding chamber geometry. Fig. 2 shows the 3D geometry with billet, container, die and rectangular (15 x 3 mm) outflow profile. In this first set-up of the simulation model only the aluminium in the tool is considered.

Fig. 2: Exploded view of the full 3D geometry (left) and the aluminium domain (right)

Thermal boundary conditions were applied utilising experimentally determined temperatures at various location in the container and the die. At the inlet the ram moves with a constant velocity. This is applied as a constant inlet velocity. At the outlet, a normal velocity condition is applied forcing the outflow in extrusion direction. Finally, a sticking friction condition on the outside boundary of the aluminium is applied.

Results

Images depicting characteristic microstructures are presented in Fig. 3. These micrographs clearly exhibit the different microstructural behaviour of the alloys utilised in these experiments: AA6060 shows a fully recrystallised grain structure, whilst alloy AA6082 has a fibrous microstructure related to the high strains cause by the severe deformation conditions operating inside the die. Around the edges of the extrusions, local conditions have caused recrystallisation commonly identified as the peripheral coarse grain zone (PCG). In certain instances an equivalent phenomenon can also be observed as an envelope of coarse grains surrounding the weld seam.

quenched and subsequently artificially aged to the peak strength condition. Extrusion was performed in ‘billet-to-billet’ mode, where each consecutive billet was extruded directly onto the previous billet, without removal of any discard. Care was taken in sampling to avoid the incorporation of material originating from any transition areas resulting from this extrusion mode. Cross-sectional samples from the extruded lengths were polished and etched for inspection by means of light optical microscopy. Further samples were characterised by means of mechanical testing, focusing on the ductility characteristics. For this purpose transverse tensile samples were prepared with the weld seam located at the midpoint of the test piece. Tensile tests were performed at room temperature at a fixed crosshead speed. The fracture surfaces of the samples were studied by scanning electron microscopy (SEM) in order to relate the morphology of the fracture surface to relevant features of the weld seams.

Modelling

The metal flow was modelled using Virtual Extrusion Laboratory (VEL) a commercial finite-element (FE) code from Compuplast for plastic extrusion, utilising a module specifically adapted to simulate the aluminium extrusion process. Constitutive material behaviour for the alloys investigated in this project was determined through hot compression tests, with testing conditions within the range encountered in extrusion. The simulation model considers a steady-state condition, assuming a billet of infinite length flowing through the container and die. In the actual extrusion process, the billet is pushed by the ram through the container and die and its volume is continuously reducing. Full 3D model of the dies were constructed, specifically taking into account the design of the leg and the welding chamber geometry. Fig. 2 shows the 3D geometry with billet, container, die and rectangular (15 x 3 mm) outflow profile. In this first set-up of the simulation model only the aluminium in the tool is considered.

Fig. 2: Exploded view of the full 3D geometry (left) and the aluminium domain (right)

Thermal boundary conditions were applied utilising experimentally determined temperatures at various location in the container and the die. At the inlet the ram moves with a constant velocity. This is applied as a constant inlet velocity. At the outlet, a normal velocity condition is applied forcing the outflow in extrusion direction. Finally, a sticking friction condition on the outside boundary of the aluminium is applied.

Results

Images depicting characteristic microstructures are presented in Fig. 3. These micrographs clearly exhibit the different microstructural behaviour of the alloys utilised in these experiments: AA6060 shows a fully recrystallised grain structure, whilst alloy AA6082 has a fibrous microstructure related to the high strains cause by the severe deformation conditions operating inside the die. Around the edges of the extrusions, local conditions have caused recrystallisation commonly identified as the peripheral coarse grain zone (PCG). In certain instances an equivalent phenomenon can also be observed as an envelope of coarse grains surrounding the weld seam.


Fig. 3: Optical micrographs of cross-sections of extrusions with the weld seam oriented vertically, at the midpoint in each micrograph. From left to right: AA6060/die B1-2; AA6060/die B1-10; AA6082/die B1-2 and AA6082/die B1-10.

Another feature which is clearly visible, is the presence of a void around the mid-thickness location in samples from die B1-2. This void was consistently observed in all inspected samples produced with this die, regardless of the alloy or other processing conditions. Although no void is present in samples originating from die B2-10, a delineation of the weld seam can be traced. This is most evident in the AA6082 samples, where a delineation can be observed over approximately the entire thickness of the strip, however also in the case of the AA6060 samples an indication of the weld seam can be observed, in particular at the mid-thickness area of the sample.

The mechanical performance of the weld seams was characterised by the value Gdf, calculated as the difference between the ultimate tensile strength (UTS) and tensile strength at fracture (FS) for each combination of alloy, billet temperature and die type. Gdf is thus an indication of the capacity of the material to accommodate additional deformation, following the onset of necking. Under the assumption that plastic instability will initiate in the weld seam, the value for Gdf is an appropriate measure for the weld seam performance. From the results in Fig. 4 it can be observed that die B1.10 with a deep welding chamber results in higher values for Gdf for alloy AA6060.

Fig. 4: mechanical performance of weld seam samples for alloy AA6060 (left) and AA6082 (right). Each column denotes a combination of die type and billet temperature.

In the case of alloy AA6060 the results show a consistent pattern, with die B1-10 leading to higher values for Gdf than die B1-2. Therefore the quality of the weld seams produced by die B1-10 is better than those produced by die B1-2. Additionally, an elevated billet temperature leads to higher values for Gdf in the case of die B1-10, whilst no significant effect can be observed for die B1-2.In the case of alloy AA6082, the results are less evident: low results for Gdf are obtained for die B1-2 as is the case for alloy AA6060, however also for die B1-10 low results are obtained at a billet temperature of 450ºC. For both alloys a comparison with the properties in longitudinal direction is included, signifying the inferior properties of the material containing a weld seam.

To gain insight into the mechanical response of the materials, the fracture surfaces of several samples were characterised by means of scanning electron microscopy (SEM), Fig. 5.

Fig. 3: Optical micrographs of cross-sections of extrusions with the weld seam oriented vertically, at the midpoint in each micrograph. From left to right: AA6060/die B1-2; AA6060/die B1-10; AA6082/die B1-2 and AA6082/die B1-10.

Another feature which is clearly visible, is the presence of a void around the mid-thickness location in samples from die B1-2. This void was consistently observed in all inspected samples produced with this die, regardless of the alloy or other processing conditions. Although no void is present in samples originating from die B2-10, a delineation of the weld seam can be traced. This is most evident in the AA6082 samples, where a delineation can be observed over approximately the entire thickness of the strip, however also in the case of the AA6060 samples an indication of the weld seam can be observed, in particular at the mid-thickness area of the sample.

The mechanical performance of the weld seams was characterised by the value Gdf, calculated as the difference between the ultimate tensile strength (UTS) and tensile strength at fracture (FS) for each combination of alloy, billet temperature and die type. Gdf is thus an indication of the capacity of the material to accommodate additional deformation, following the onset of necking. Under the assumption that plastic instability will initiate in the weld seam, the value for Gdf is an appropriate measure for the weld seam performance. From the results in Fig. 4 it can be observed that die B1.10 with a deep welding chamber results in higher values for Gdf for alloy AA6060.

Fig. 4: mechanical performance of weld seam samples for alloy AA6060 (left) and AA6082 (right). Each column denotes a combination of die type and billet temperature.

In the case of alloy AA6060 the results show a consistent pattern, with die B1-10 leading to higher values for Gdf than die B1-2. Therefore the quality of the weld seams produced by die B1-10 is better than those produced by die B1-2. Additionally, an elevated billet temperature leads to higher values for Gdf in the case of die B1-10, whilst no significant effect can be observed for die B1-2.In the case of alloy AA6082, the results are less evident: low results for Gdf are obtained for die B1-2 as is the case for alloy AA6060, however also for die B1-10 low results are obtained at a billet temperature of 450ºC. For both alloys a comparison with the properties in longitudinal direction is included, signifying the inferior properties of the material containing a weld seam.

To gain insight into the mechanical response of the materials, the fracture surfaces of several samples were characterised by means of scanning electron microscopy (SEM), Fig. 5.


Fig. 5: SEM images of the fracture surfaces of transverse tensile samples. Top left: AA6060/die B1-2; top right: AA6060/die B1-10; bottom left: AA6082/die B1-2 and bottom right: AA6082/die B1-10.

Fig. 6: SEM-images from the central area of the fracture surface; left: AA6082/die B1-10, right: AA6082/die B1-2

Like the images obtained by light optical microscopy as shown in Fig. 3., the remnants of a void can be observed in the samples originating from die B1-2. In these samples the remnants of the void are visible as a single central longitudinal depression. Surrounding this area the surface is densely populated with dimples, a morphology which suggests a relatively ductile fracture behaviour. As the depression is present along the entire length of the sample surface it can be concluded that the extrusions contains a central hollow channel, where flow conditions in the die prohibit complete filling of the die weld chamber. The fracture surfaces of samples from die B1.10 also exhibit

Fig. 5: SEM images of the fracture surfaces of transverse tensile samples. Top left: AA6060/die B1-2; top right: AA6060/die B1-10; bottom left: AA6082/die B1-2 and bottom right: AA6082/die B1-10.

Fig. 6: SEM-images from the central area of the fracture surface; left: AA6082/die B1-10, right: AA6082/die B1-2

Like the images obtained by light optical microscopy as shown in Fig. 3., the remnants of a void can be observed in the samples originating from die B1-2. In these samples the remnants of the void are visible as a single central longitudinal depression. Surrounding this area the surface is densely populated with dimples, a morphology which suggests a relatively ductile fracture behaviour. As the depression is present along the entire length of the sample surface it can be concluded that the extrusions contains a central hollow channel, where flow conditions in the die prohibit complete filling of the die weld chamber. The fracture surfaces of samples from die B1.10 also exhibit


longitudinal patterns (striations), despite the fact that no voids were observed in the light optical micrographs. It may be argued that, although no voids were observed, local areas are present were bond formation between the surfaces is minor, i.e. similar to kissing bonds as described previously. This perception is augmented by the enlargements presented in Fig. 6. The morphology of the central area of material from die B1-10 consists of small dimples, resulting from fracture, whilst the surface structure of the central area of the sample originating from die B2-10 exhibits no fracture-related features. FE Modelling results. The effect of the tooling geometry on the pressure distribution is presented in Fig. 7. Only the results for alloy AA6060 are shown, as the contours for AA6082 are similar. The deep weld chamber of die B1-10 results in a gradual decline of the pressure from the mandrel support to the die exit. Conversely, the weld chamber geometry of die B1-2 results in very low pressure levels on the weld plane. For this die, a detailed study of the pressure distribution shows that a localised ‘pocket’ of low pressure is present at the central part of the weld seam, coinciding with the location of the void occurring in the extrusions produced with this die.

Fig. 7: pressure distribution from FE-simulations. A cross-section through the mid-thickness of the billet and the extruded strip is shown (top), together with the relative pressure distribution on the weld plane (bottom).

Discussion

As described in the introduction, weld-seam formation is considered to be controlled by the combination of three features: 1) a suitable flow geometry in the die, enabling renewed contact between the formerly separated metal streams, 2) an adequate level of interfacial pressure on the bond plane to avoid separation of the contact surfaces and 3) atomic registry of lattice planes through evolution of the microstructure. Complete fulfilment of these condition results in weld seams with properties similar to those obtained in the bulk transverse orientation. The effect of controlling factors is expressed by the value of the weld seam integrity indicator, Iws, which is controlled by the distribution of the local bonding state, Wi, for each discretised element on the bond plane.

longitudinal patterns (striations), despite the fact that no voids were observed in the light optical micrographs. It may be argued that, although no voids were observed, local areas are present were bond formation between the surfaces is minor, i.e. similar to kissing bonds as described previously. This perception is augmented by the enlargements presented in Fig. 6. The morphology of the central area of material from die B1-10 consists of small dimples, resulting from fracture, whilst the surface structure of the central area of the sample originating from die B2-10 exhibits no fracture-related features. FE Modelling results. The effect of the tooling geometry on the pressure distribution is presented in Fig. 7. Only the results for alloy AA6060 are shown, as the contours for AA6082 are similar. The deep weld chamber of die B1-10 results in a gradual decline of the pressure from the mandrel support to the die exit. Conversely, the weld chamber geometry of die B1-2 results in very low pressure levels on the weld plane. For this die, a detailed study of the pressure distribution shows that a localised ‘pocket’ of low pressure is present at the central part of the weld seam, coinciding with the location of the void occurring in the extrusions produced with this die.

Fig. 7: pressure distribution from FE-simulations. A cross-section through the mid-thickness of the billet and the extruded strip is shown (top), together with the relative pressure distribution on the weld plane (bottom).

Discussion

As described in the introduction, weld-seam formation is considered to be controlled by the combination of three features: 1) a suitable flow geometry in the die, enabling renewed contact between the formerly separated metal streams, 2) an adequate level of interfacial pressure on the bond plane to avoid separation of the contact surfaces and 3) atomic registry of lattice planes through evolution of the microstructure. Complete fulfilment of these condition results in weld seams with properties similar to those obtained in the bulk transverse orientation. The effect of controlling factors is expressed by the value of the weld seam integrity indicator, Iws, which is controlled by the distribution of the local bonding state, Wi, for each discretised element on the bond plane.


The results of the extrusion trials demonstrate that the required conditions for sound weld seams are not met. Although the results in the tensile test results are already an indication, the metallographic analysis results provide a justification for the proposed framework for weld seam formation, specifically including the effects of microstructural evolution. When considering the effects of metal flow patterns, it is obvious that the metal flow in die B1-2 does not result in joined metal streams over the entire weld plane, and a void is created throughout the length of the extrusion. The occurrence of the void is also inferred by the FE-simulations, as a localised pocket with a very low value for the interfacial pressure, coinciding with the void location, is predicted. In this case it is obvious that the weld seam properties cannot achieve the maximum value, as the cross sectional area is reduced in comparison with fully bonded weld seam. In terms of the weld seam indicator, Wi = 0 for all elements lying on the void surface and thus Iws will be less than unity.

In conformity with the FE-results, the extrusions from die B1-10 do not contain any apparent voids, indicating that contact between the bond planes was established. From the SEM-analysis of the fracture surfaces it is however observed that a only a minor degree of bonding occurs in the central area of the cross-section, and at other locations on the fracture surface where bond formation also appears to be less well-developed. The lesser bonded areas cannot be related to any geometrical features in the tooling set-up. It is therefore assumed that the combination of local conditions (notably strain, strain rate and temperature) in combination with the stochastically occurring microstructural variations determine the microstructural evolution and thus the local bond state, i.e. the value of Wi. The foregoing may also contribute to a clarification for the very low properties of alloy AA6082 extruded at 450°C with die B1-10: the low temperature hampers the microstructural evolution of the alloy and thereby prevents any recombining of lattice orientations to produce a favourable grain morphology over the bond plane. It is clear that these inferior bond structures call for more a detailed analysis, to be performed in future studies.

Conclusions

Laboratory scale extrusion trials were executed to assess the effects of die geometry, process conditions and alloy composition on the weld seam properties of an extruded strip. The weld seams were characterised through mechanical testing and the analysis of the microstructure. A concept for the weld seam quality was proposed, based on material flow, pressure distribution and microstructural evolution of the bond plane. Through computer simulations the operating conditions in the die were assessed and related to the experimental results. This work has led to the following outcome:

Results were obtained for die geometries with a different weld chamber depths: a shallow weld chamber leads to an un-bonded area within the weld plane, causing low values in mechanical testing. Increasing the weld chamber depth leads to consistently improved properties for alloy AA6060, in contrast to the results for alloy AA6082 where improved results are only obtained at a high billet temperature. For the investigated cases, the occurrence of a void could be inferred from FE modelling, thus providing scope for predictive assessment of flow conditions, as input for the weld seam indicator. From the SEM-inspection of the fracture surfaces of the tensile samples it was observed that in the weld seams obtained with a deep weld chamber exhibit areas where bond formation is still inferior, despite the absence of voids. Therefore it is concluded that, although favourable flow conditions are achieved (being a primary condition for bond formation), the supplementary conditions for bond formation, controlling the microstructural rearrangement on the bond plane, is only satisfied at selective locations in the die, thus demonstrating the need for the incorporation of a microstructure based predictive factor in the weld seam integrity indicator.

Acknowledgements

This research was partially carried out under the project number MA.08089 in the framework of the Research Program of the Materials innovation institute M2i.

The results of the extrusion trials demonstrate that the required conditions for sound weld seams are not met. Although the results in the tensile test results are already an indication, the metallographic analysis results provide a justification for the proposed framework for weld seam formation, specifically including the effects of microstructural evolution. When considering the effects of metal flow patterns, it is obvious that the metal flow in die B1-2 does not result in joined metal streams over the entire weld plane, and a void is created throughout the length of the extrusion. The occurrence of the void is also inferred by the FE-simulations, as a localised pocket with a very low value for the interfacial pressure, coinciding with the void location, is predicted. In this case it is obvious that the weld seam properties cannot achieve the maximum value, as the cross sectional area is reduced in comparison with fully bonded weld seam. In terms of the weld seam indicator, Wi = 0 for all elements lying on the void surface and thus Iws will be less than unity.

In conformity with the FE-results, the extrusions from die B1-10 do not contain any apparent voids, indicating that contact between the bond planes was established. From the SEM-analysis of the fracture surfaces it is however observed that a only a minor degree of bonding occurs in the central area of the cross-section, and at other locations on the fracture surface where bond formation also appears to be less well-developed. The lesser bonded areas cannot be related to any geometrical features in the tooling set-up. It is therefore assumed that the combination of local conditions (notably strain, strain rate and temperature) in combination with the stochastically occurring microstructural variations determine the microstructural evolution and thus the local bond state, i.e. the value of Wi. The foregoing may also contribute to a clarification for the very low properties of alloy AA6082 extruded at 450°C with die B1-10: the low temperature hampers the microstructural evolution of the alloy and thereby prevents any recombining of lattice orientations to produce a favourable grain morphology over the bond plane. It is clear that these inferior bond structures call for more a detailed analysis, to be performed in future studies.

Conclusions

Laboratory scale extrusion trials were executed to assess the effects of die geometry, process conditions and alloy composition on the weld seam properties of an extruded strip. The weld seams were characterised through mechanical testing and the analysis of the microstructure. A concept for the weld seam quality was proposed, based on material flow, pressure distribution and microstructural evolution of the bond plane. Through computer simulations the operating conditions in the die were assessed and related to the experimental results. This work has led to the following outcome:

Results were obtained for die geometries with a different weld chamber depths: a shallow weld chamber leads to an un-bonded area within the weld plane, causing low values in mechanical testing. Increasing the weld chamber depth leads to consistently improved properties for alloy AA6060, in contrast to the results for alloy AA6082 where improved results are only obtained at a high billet temperature. For the investigated cases, the occurrence of a void could be inferred from FE modelling, thus providing scope for predictive assessment of flow conditions, as input for the weld seam indicator. From the SEM-inspection of the fracture surfaces of the tensile samples it was observed that in the weld seams obtained with a deep weld chamber exhibit areas where bond formation is still inferior, despite the absence of voids. Therefore it is concluded that, although favourable flow conditions are achieved (being a primary condition for bond formation), the supplementary conditions for bond formation, controlling the microstructural rearrangement on the bond plane, is only satisfied at selective locations in the die, thus demonstrating the need for the incorporation of a microstructure based predictive factor in the weld seam integrity indicator.

Acknowledgements

This research was partially carried out under the project number MA.08089 in the framework of the Research Program of the Materials innovation institute M2i.


Gert ten Brink is gratefully acknowledged for his assistance in the SEM-analysis.

References

[1] R. Akeret: Journal of the Institute of Metals, Vol. 100 (1972) pp. 202–207. [2] H. Valberg, T. Loeken, M. Hval, B. Nyhus, C. Thaulow: International Journal of Materials and

Product Technology, Vol. 10, no. 5-6 (1995) p. 222–267. [3] A. Oosterkamp, L.D. Oosterkamp, A. Nordeide: Welding Journal, (2004) p. 225S–231S. [4] J. Gasiorczyk, J. Richert: Seventh International Aluminum Extrusion Technology Seminar,

Vol. 2, (2000), pp. 195-202. [5] B. Bourqui, A. Huber, C. Moulin, A. Brunetti, Y. Krähenbühl: The first International Congress

of the Extruders' Division of the European Aluminium Association, (2002). [6] Y.A. Khan, H. Valberg, I. Irgens: 12th International ESAFORM Conference on Material

Forming (2009). [7] L. Donati, L. Tomesani: Mater. Sci. Forum Vol. 604-605 (2009), p. 121-131 [8] A.J. den Bakker , W.H. Sillekens and E. Meijers: Aluminium 2000 – 6th World Congress and

Exhibition (2007).

Gert ten Brink is gratefully acknowledged for his assistance in the SEM-analysis.

References

[1] R. Akeret: Journal of the Institute of Metals, Vol. 100 (1972) pp. 202–207. [2] H. Valberg, T. Loeken, M. Hval, B. Nyhus, C. Thaulow: International Journal of Materials and

Product Technology, Vol. 10, no. 5-6 (1995) p. 222–267. [3] A. Oosterkamp, L.D. Oosterkamp, A. Nordeide: Welding Journal, (2004) p. 225S–231S. [4] J. Gasiorczyk, J. Richert: Seventh International Aluminum Extrusion Technology Seminar,

Vol. 2, (2000), pp. 195-202. [5] B. Bourqui, A. Huber, C. Moulin, A. Brunetti, Y. Krähenbühl: The first International Congress

of the Extruders' Division of the European Aluminium Association, (2002). [6] Y.A. Khan, H. Valberg, I. Irgens: 12th International ESAFORM Conference on Material

Forming (2009). [7] L. Donati, L. Tomesani: Mater. Sci. Forum Vol. 604-605 (2009), p. 121-131 [8] A.J. den Bakker , W.H. Sillekens and E. Meijers: Aluminium 2000 – 6th World Congress and

Exhibition (2007).


Extrusion Benchmark 2009 Experimental analysis of deflection in extrusion dies

D. Pietzka1,a, N. Ben Khalifa1,b, L. Donati2,c, L. Tomesani2,d and A. E. Tekkaya1,e

1Institute of Forming Technology and Lightweight Construction, TU University Dortmund, Baroperstr. 301, 44227 Dortmund, Germany

2Department of Mechanical Construction Engineering (D.I.E.M.) University of Bologna, V.le Risorgimento 2, 40136 Bologna, Italy

[email protected], [email protected], [email protected] [email protected], [email protected]

Keywords: Extrusion, Benchmark, Die Deformation, Deflection measurements

Abstract. In this paper experimental investigations aimed at measuring the die deformations during

aluminum extrusion process is presented and discussed. A two-holes die generating two U-shape

profiles with different supporting legs was produced and tested under strictly monitored conditions.

The influence of die deformation on the speed, temperature distribution and distortion of the two

profiles is reported and analyzed. AA6082 alloy was used as deforming material while H-13 hot-

work tool steel was selected as die material. The experiments were repeated at least three times in

the same conditions in order to achieve a statistical distribution of the acquired data: such data are

then used as a reference for the 2009 edition of the extrusion benchmark.

Introduction

Still today the design of extrusion dies is mainly based on the experience and skillful of the die

makers. When a new profile has to be manufactured, some trials and prototypes are sometimes

necessary in order to achieve the optimal compromise between die productivity and die life. This

procedure is very costly and also time consuming. Furthermore, the transfer of knowledge between

different generations of die designers or inside the same company between the several employees is

not always given. It is then clear that software tools supporting die design are essential for an

effective and reliable óne step die design´. Therefore in the past years, many papers demonstrated

that FEM simulations are the only feasible way to predict the material flow and the die stress and to

allow, as a consequence, the die optimization [1, 2].

The increasing demand for reliable simulations of the extrusion process has led to the

organization of the biannual international conference, "Extrusion Conference and Benchmark",

specifically related to the optimization of FEM codes for extrusion analysis. In particular, the

Extrusion Benchmark is a conference where the several commercial codes capabilities are analyzed

in deep by the comparison with an extrusion experiment. The event is realized in three main steps:

in the first step an experiment is designed and performed under strictly monitored conditions and

repeated several times in order to provide a statistical significance of the monitored results. The

second step is the process simulation: the organizers provide the information for carrying out the

simulations; then every interested participant (software houses, scientific and industrial users)

performs the simulation before the conference. The third step is the comparison of the results:

during the conference the hidden results of the experiment are disclosed and the different FEM

codes predictions are compared to the experimental data, thus providing an interesting evaluation of

codes capabilities. It is important to note that, due to the complexity of the matter, it would be

useless to consider the benchmark simply as a contest: it is, instead, an opportunity to fix some

points about the everyday simulation practice, each participant with his own particular interest. In

this direction, for example, the software houses can promote their codes capabilities on the basis of

scientific and well monitored experimental data, the industrial users can verify their ability to

Extrusion Benchmark 2009 Experimental analysis of deflection in extrusion dies

D. Pietzka1,a, N. Ben Khalifa1,b, L. Donati2,c, L. Tomesani2,d and A. E. Tekkaya1,e

1Institute of Forming Technology and Lightweight Construction, TU University Dortmund, Baroperstr. 301, 44227 Dortmund, Germany

2Department of Mechanical Construction Engineering (D.I.E.M.) University of Bologna, V.le Risorgimento 2, 40136 Bologna, Italy

[email protected], [email protected], [email protected] [email protected], [email protected]

Keywords: Extrusion, Benchmark, Die Deformation, Deflection measurements

Abstract. In this paper experimental investigations aimed at measuring the die deformations during

aluminum extrusion process is presented and discussed. A two-holes die generating two U-shape

profiles with different supporting legs was produced and tested under strictly monitored conditions.

The influence of die deformation on the speed, temperature distribution and distortion of the two

profiles is reported and analyzed. AA6082 alloy was used as deforming material while H-13 hot-

work tool steel was selected as die material. The experiments were repeated at least three times in

the same conditions in order to achieve a statistical distribution of the acquired data: such data are

then used as a reference for the 2009 edition of the extrusion benchmark.

Introduction

Still today the design of extrusion dies is mainly based on the experience and skillful of the die

makers. When a new profile has to be manufactured, some trials and prototypes are sometimes

necessary in order to achieve the optimal compromise between die productivity and die life. This

procedure is very costly and also time consuming. Furthermore, the transfer of knowledge between

different generations of die designers or inside the same company between the several employees is

not always given. It is then clear that software tools supporting die design are essential for an

effective and reliable óne step die design´. Therefore in the past years, many papers demonstrated

that FEM simulations are the only feasible way to predict the material flow and the die stress and to

allow, as a consequence, the die optimization [1, 2].

The increasing demand for reliable simulations of the extrusion process has led to the

organization of the biannual international conference, "Extrusion Conference and Benchmark",

specifically related to the optimization of FEM codes for extrusion analysis. In particular, the

Extrusion Benchmark is a conference where the several commercial codes capabilities are analyzed

in deep by the comparison with an extrusion experiment. The event is realized in three main steps:

in the first step an experiment is designed and performed under strictly monitored conditions and

repeated several times in order to provide a statistical significance of the monitored results. The

second step is the process simulation: the organizers provide the information for carrying out the

simulations; then every interested participant (software houses, scientific and industrial users)

performs the simulation before the conference. The third step is the comparison of the results:

during the conference the hidden results of the experiment are disclosed and the different FEM

codes predictions are compared to the experimental data, thus providing an interesting evaluation of

codes capabilities. It is important to note that, due to the complexity of the matter, it would be

useless to consider the benchmark simply as a contest: it is, instead, an opportunity to fix some

points about the everyday simulation practice, each participant with his own particular interest. In

this direction, for example, the software houses can promote their codes capabilities on the basis of

scientific and well monitored experimental data, the industrial users can verify their ability to


properly perform a simulation with their own code or even select a code among those participating

the contest. In the 2007 edition of the extrusion benchmark, it could be shown that the FE

simulation of the extrusion process is able to predict all the main process parameters, especially the

press load, profile speed and temperature development [3]. There, it was found that the simulation

of the material flow, in particular by flat dies, can be very accurate if proper thermal conditions are

given.

On the other hand, the increasing complexity of the profiles geometries, often of big size and

small thickness, and the use of porthole dies with very slender mandrels (often multiple) and

supporting legs determines the ever increasing importance of die deflection in determining the

material flow. It is well known that a die can behave in a very different way from what is expected

because of its deformation under process loads. This aspect, together with the problem of die life

was found to be the very first concern among extruders and die makers at the 2007 benchmark

edition [4]. For this reason in the 2009 edition it was chosen to make clear if, and how much, a

simulation code can properly manage this problem.

In the scientific literature, investigations on the die deformation could not be found explicitly.

Only some approaches for measuring the pressure on the die face could be found [5,6]. In

particular, investigations about the influence of the die deflection on the profile distortion, profile

speed and temperature development at the die exit are completely missing. The aim of this work

was then to experimentally measure the die deflection in two different design configurations and to

investigate the effect of the die deflection on the material flow, in order to analyze its influence on

the exiting profiles. The results of the experiment are finally used as reference condition for FEM

codes comparison at Extrusion Benchmark 2009.

Die design

One of the most critical features related to tool deflection for the extrusion dies are the ´tongues ´

that are necessarily adopted in the manufacturing of dies, for example, for U shape profile

extrusion. In this paper, a multiple hole die for the simultaneous extrusion of two U shape profiles

was designed (Fig. 1, up) in order to obtain an effective comparison for different tongue design

strategies. Both profiles have the same dimension (Fig 1, bottom) and feeder in order to balance

material entrance. The two profiles were arranged one upon the other: the bottom one is

characterized by a standard supporting shape while the supporting part of the upper profile was

deeply reduced in order to achieve a measurable die deflection during the process. With this

configuration, a higher deflection of the upper part of the die with the less supported inner profile

contour is expected, thus producing a loss of contact in the bearing zones and an alteration of the

thermal field at the two exits; as a consequence a difference also in material flow and profile

distortions are expected for the two profiles. On the other side, the U-shape of the profiles allows

the accessibility for the laser measuring devices to detect the deflection of the inner tongues along

the extrusion direction, while the length of the U shape (59,3mm) allows an adequate magnification

of the die deflection. The die was made of AISI H-13 hot-working tool steel tempered to 45 HRC

hardness and built by WEFA, Germany.

properly perform a simulation with their own code or even select a code among those participating

the contest. In the 2007 edition of the extrusion benchmark, it could be shown that the FE

simulation of the extrusion process is able to predict all the main process parameters, especially the

press load, profile speed and temperature development [3]. There, it was found that the simulation

of the material flow, in particular by flat dies, can be very accurate if proper thermal conditions are

given.

On the other hand, the increasing complexity of the profiles geometries, often of big size and

small thickness, and the use of porthole dies with very slender mandrels (often multiple) and

supporting legs determines the ever increasing importance of die deflection in determining the

material flow. It is well known that a die can behave in a very different way from what is expected

because of its deformation under process loads. This aspect, together with the problem of die life

was found to be the very first concern among extruders and die makers at the 2007 benchmark

edition [4]. For this reason in the 2009 edition it was chosen to make clear if, and how much, a

simulation code can properly manage this problem.

In the scientific literature, investigations on the die deformation could not be found explicitly.

Only some approaches for measuring the pressure on the die face could be found [5,6]. In

particular, investigations about the influence of the die deflection on the profile distortion, profile

speed and temperature development at the die exit are completely missing. The aim of this work

was then to experimentally measure the die deflection in two different design configurations and to

investigate the effect of the die deflection on the material flow, in order to analyze its influence on

the exiting profiles. The results of the experiment are finally used as reference condition for FEM

codes comparison at Extrusion Benchmark 2009.

Die design

One of the most critical features related to tool deflection for the extrusion dies are the ´tongues ´

that are necessarily adopted in the manufacturing of dies, for example, for U shape profile

extrusion. In this paper, a multiple hole die for the simultaneous extrusion of two U shape profiles

was designed (Fig. 1, up) in order to obtain an effective comparison for different tongue design

strategies. Both profiles have the same dimension (Fig 1, bottom) and feeder in order to balance

material entrance. The two profiles were arranged one upon the other: the bottom one is

characterized by a standard supporting shape while the supporting part of the upper profile was

deeply reduced in order to achieve a measurable die deflection during the process. With this

configuration, a higher deflection of the upper part of the die with the less supported inner profile

contour is expected, thus producing a loss of contact in the bearing zones and an alteration of the

thermal field at the two exits; as a consequence a difference also in material flow and profile

distortions are expected for the two profiles. On the other side, the U-shape of the profiles allows

the accessibility for the laser measuring devices to detect the deflection of the inner tongues along

the extrusion direction, while the length of the U shape (59,3mm) allows an adequate magnification

of the die deflection. The die was made of AISI H-13 hot-working tool steel tempered to 45 HRC

hardness and built by WEFA, Germany.


Fig. 1: Die appearance and design (up) and Profile cross section (enhanced scale)

Experimental setup and conditions

AA6082-O aluminum billets of 140 mm diameter and 300 mm length were used for the

experiments. The experiments were carried out on a 10 MN extrusion press at the laboratory of the

Institute of Forming Technology and Lightweight Construction (IUL) at the TU Dortmund

University. The diameter of the container is 146 mm, so that an upsetting of the billets takes place at

the beginning of the extrusion process.

The die was heated to a target temperature of 400 °C inside the machine. Four holes allowed to

measure the die temperature with thermocouples during extrusion as described in figure 2 (left).

Two thermocouples were required to control the die heating system, while the other two measured

the die temperature during extrusion near the die bearings. The thermocouples were positioned as

close as possible to the bearings, in order to measure temperature variations, in relation to die

deflection and consequently material flow.

Fig. 2: Thermocouple position

The billets were heated up to 450 °C in a furnace, with the billet surface decreasing to 432 °C just

before extrusion: the billet temperature reduction was caused by the billet loading procedure that

took about 1 minute. On the other hand, the temperature of the container press can be considered as

constant and equal to 430 °C due to its high thermal inertia, while the ram temperature was

measured with a contact thermometer at the beginning and end of each cycle and it remained in the

range 365-411°C. Detailed information on temperature evolution are reported in table 1.

The die deflection was measured with two laser beam distance sensors; the sensors operated with

the triangulation method and had an accuracy of 120 m (±60 m accuracy of the laser system

according to the producer).

Fig. 1: Die appearance and design (up) and Profile cross section (enhanced scale)

Experimental setup and conditions

AA6082-O aluminum billets of 140 mm diameter and 300 mm length were used for the

experiments. The experiments were carried out on a 10 MN extrusion press at the laboratory of the

Institute of Forming Technology and Lightweight Construction (IUL) at the TU Dortmund

University. The diameter of the container is 146 mm, so that an upsetting of the billets takes place at

the beginning of the extrusion process.

The die was heated to a target temperature of 400 °C inside the machine. Four holes allowed to

measure the die temperature with thermocouples during extrusion as described in figure 2 (left).

Two thermocouples were required to control the die heating system, while the other two measured

the die temperature during extrusion near the die bearings. The thermocouples were positioned as

close as possible to the bearings, in order to measure temperature variations, in relation to die

deflection and consequently material flow.

Fig. 2: Thermocouple position

The billets were heated up to 450 °C in a furnace, with the billet surface decreasing to 432 °C just

before extrusion: the billet temperature reduction was caused by the billet loading procedure that

took about 1 minute. On the other hand, the temperature of the container press can be considered as

constant and equal to 430 °C due to its high thermal inertia, while the ram temperature was

measured with a contact thermometer at the beginning and end of each cycle and it remained in the

range 365-411°C. Detailed information on temperature evolution are reported in table 1.

The die deflection was measured with two laser beam distance sensors; the sensors operated with

the triangulation method and had an accuracy of 120 m (±60 m accuracy of the laser system

according to the producer).


The working range is between 300 until 500 mm. The application of the laser sensor showed

great advantages if compared to the use of strain gauges or tactile deflection sensors: the laser beam

works without any direct contact with the hot die, they did not require any holes or joining

procedure and nevertheless it provided a continuous measurement of the tool deformation. On the

other side such sensor evidenced also some disadvantages: the sensors were placed out of the die so

the die shape required adequate openings, moreover the beam moved along a complex paths so that

the measured values needs a correction based on their peculiar route (as described later).

The sensors were mounted on a frame in front of the press without contact to the press to prevent

measuring errors which result from a possible deformation of the press during extrusion. As

consequence, the deformation of the press had to be measured too. In order to measure the press

deformation, the two sensors were positioned in the last trials on the die surface near the back-up

plate, thus measuring the rigid displacement of the system backup plate-die. Both sensors were

arranged at a small angle to the profile direction in the inner area of the profile shape. It was

necessary to evaluate the exact angle between tool and sensors, to compensate for the difference

between the diagonal path of the laser sensor and searched die deflection (figure 3). The positions

of the lasers were measured after heating up the extrusion press and the die to discard thermal

effects. In Fig. 3 on the right, the position where the sensors hit the inner profile contours of the die

is shown via the red reflection points on the die surface.

Fig. 3: Determination of the sensors position in relation to the die

Fig. 4: Calculation of the die displacement

The function principle of the laser sensor is based on triangulation method. A deformation of the

inner profile contour (Fig. 4) leads to a changing reflection angle The distance d1 between laser

and die is then automatically calculated by the controller of the laser displacement sensor. The angle

needs to be manually determined by the use of an optical measuring system for instance. The

angle of the right sensor (measuring the deformation of the less supported profile) to the press

The working range is between 300 until 500 mm. The application of the laser sensor showed

great advantages if compared to the use of strain gauges or tactile deflection sensors: the laser beam

works without any direct contact with the hot die, they did not require any holes or joining

procedure and nevertheless it provided a continuous measurement of the tool deformation. On the

other side such sensor evidenced also some disadvantages: the sensors were placed out of the die so

the die shape required adequate openings, moreover the beam moved along a complex paths so that

the measured values needs a correction based on their peculiar route (as described later).

The sensors were mounted on a frame in front of the press without contact to the press to prevent

measuring errors which result from a possible deformation of the press during extrusion. As

consequence, the deformation of the press had to be measured too. In order to measure the press

deformation, the two sensors were positioned in the last trials on the die surface near the back-up

plate, thus measuring the rigid displacement of the system backup plate-die. Both sensors were

arranged at a small angle to the profile direction in the inner area of the profile shape. It was

necessary to evaluate the exact angle between tool and sensors, to compensate for the difference

between the diagonal path of the laser sensor and searched die deflection (figure 3). The positions

of the lasers were measured after heating up the extrusion press and the die to discard thermal

effects. In Fig. 3 on the right, the position where the sensors hit the inner profile contours of the die

is shown via the red reflection points on the die surface.

Fig. 3: Determination of the sensors position in relation to the die

Fig. 4: Calculation of the die displacement

The function principle of the laser sensor is based on triangulation method. A deformation of the

inner profile contour (Fig. 4) leads to a changing reflection angle The distance d1 between laser

and die is then automatically calculated by the controller of the laser displacement sensor. The angle

needs to be manually determined by the use of an optical measuring system for instance. The

angle of the right sensor (measuring the deformation of the less supported profile) to the press


direction was 15.74°, while the corresponding angle of the left sensor was 18.72°. The

deformation of the die along the press axis distance, Δd2, can be then calculated by:

Δd2 =Δd1 * cos

The deformation along the press axis will be compared to the simulation results of the FEM codes

which will take part at the extrusion benchmark.

The profile temperature was continuously measured through a pyrometer only on the upper profile.

The used pyrometer works with two different wavelengths so as to calculate the work piece

temperature impartially from the surface property. The detection point was located 145 mm away

from the die surface as reported in fig. 5. Finally, two laser velocitymeters were used in order to

continuous monitoring the profile speed of both profiles. The velocitymeters work contactless with

lasers beams based on the Doppler principle. Fig. 5 right shows an overview of the whole

arrangement of the used sensors.

Fig. 5: Pyrometer detection point and experimental setup

Two billets were extruded before beginning the experiments, so as to reach almost even thermal

conditions throughout the system. Afterwards, three billets of the same alloy were extruded with

constant process parameters so as to provide a repetition of the process conditions. The 300 mm

long billets were extruded 290 mm to a final 10 mm butt height. Three repetitions were required to

show the possible scattering range of the measured parameters and to evaluate the accuracy of the

results.

Results

Among the repetitions, billet number 4 was chosen as reference condition for the benchmark

comparison: in Fig. 6 the ram force and the temperature evolution for such billet during extrusion

are shown. The extrusion force showed the typical trend of direct extrusion, with 8 MN maximum

load, while for the other two billets the force was 8.04 (billet 3) and 8.51 MN (billet 5) as reported

by the confidence interval at maximum load or in table 1. The profile temperature of the upper

profile (which was less supported) is shown in Fig. 6b. The profile temperature reached a maximum

of 490 °C at the end of the process, continuously increasing during the whole process. At the

beginning the profile temperature was lower than the billet (423°C compared to 432°C), this being

also in relation with die temperature, that at the beginning of the process was 392°C. Indeed, at the

beginning the die was already filled by the aluminum of the billet number 3 and the initial profile

temperature was a balance between billet and die temperature. The maximum profile temperature

for the other repetitions varied between 480 and 493 °C.

direction was 15.74°, while the corresponding angle of the left sensor was 18.72°. The

deformation of the die along the press axis distance, Δd2, can be then calculated by:

Δd2 =Δd1 * cos

The deformation along the press axis will be compared to the simulation results of the FEM codes

which will take part at the extrusion benchmark.

The profile temperature was continuously measured through a pyrometer only on the upper profile.

The used pyrometer works with two different wavelengths so as to calculate the work piece

temperature impartially from the surface property. The detection point was located 145 mm away

from the die surface as reported in fig. 5. Finally, two laser velocitymeters were used in order to

continuous monitoring the profile speed of both profiles. The velocitymeters work contactless with

lasers beams based on the Doppler principle. Fig. 5 right shows an overview of the whole

arrangement of the used sensors.

Fig. 5: Pyrometer detection point and experimental setup

Two billets were extruded before beginning the experiments, so as to reach almost even thermal

conditions throughout the system. Afterwards, three billets of the same alloy were extruded with

constant process parameters so as to provide a repetition of the process conditions. The 300 mm

long billets were extruded 290 mm to a final 10 mm butt height. Three repetitions were required to

show the possible scattering range of the measured parameters and to evaluate the accuracy of the

results.

Results

Among the repetitions, billet number 4 was chosen as reference condition for the benchmark

comparison: in Fig. 6 the ram force and the temperature evolution for such billet during extrusion

are shown. The extrusion force showed the typical trend of direct extrusion, with 8 MN maximum

load, while for the other two billets the force was 8.04 (billet 3) and 8.51 MN (billet 5) as reported

by the confidence interval at maximum load or in table 1. The profile temperature of the upper

profile (which was less supported) is shown in Fig. 6b. The profile temperature reached a maximum

of 490 °C at the end of the process, continuously increasing during the whole process. At the

beginning the profile temperature was lower than the billet (423°C compared to 432°C), this being

also in relation with die temperature, that at the beginning of the process was 392°C. Indeed, at the

beginning the die was already filled by the aluminum of the billet number 3 and the initial profile

temperature was a balance between billet and die temperature. The maximum profile temperature

for the other repetitions varied between 480 and 493 °C.


a) Ram force b) Temperature of the top profile

Fig. 6: Ram force and profile temperature

The speed of both profiles was similar (Fig. 7) even if the bottom profile (the full supported one)

always runs a little faster: at the maximum extrusion load (26mm stroke), the profile on the bottom

ran at 160 mm/sec while the profile on the top ran at 156 mm/sec. At stokes between 50 and 250

mm, the average profile speed for the less supported profile (top profile) stabilized at around 156

mm/sec compared to the 158 mm/sec of the other profile (bottom one). It is worth noting that the

curve of the velocitymeter of the bottom profile showed a lower scatter distribution of the data

compared to the other curve, this being in relation with the velocitymeter models: the velocitymeter

used on the top profile is older than that used on the bottom, thus producing a worse filtering of

acquired data. The difference in profile speeds can be visualized also in term of final profiles

length: the bottom profiles resulted 56mm longer than the upper profile (4196mm respect to

4100mm). Even if the difference is very small all the repetitions showed the same tendencies with

difference of 36mm and 25mm respectively for tests 3 and 5 (Table3).

Fig. 9 shows the recorded die temperatures during the extrusion: both thermocouples were

placed in proximity of the bearing zone, the first on the full supported part of the die (bottom) while

the other on the less supported part (Fig. 3). The initial conditions can be considered homogenous

(392°C for the upper profile, 394°C for the lower) but during the process the temperature of the top

part of the die decreased, while the bottom temperature remained almost constant. At the end of the

process the temperature at the bottom is 394 °C and the temperature at the top is 10 °C lower. The

tendency looks unusual because in this type of press usually the temperature at the bottom part of

the die decrease during the process: the reason can be searched in the die deflections of the upper

tongue and in the resulting decreasing of the friction conditions. It´s worth interesting to note that

the rather small final differences in die temperature are in relation to the distance of the

thermocouples from the bearing surface: larger differences would be found in proximity of bearing

zones thus evidencing the great effect that the changes in friction conditions on the bearings

produce on the thermal field. As previously explained, the laser sensors were placed on a rigid

structure outside the press and fixed to the ground, thus avoiding any displacement related to press

deformation during extrusion.

Fig. 7: Profile speeds (left) and Die temperature (right)

a) Ram force b) Temperature of the top profile

Fig. 6: Ram force and profile temperature

The speed of both profiles was similar (Fig. 7) even if the bottom profile (the full supported one)

always runs a little faster: at the maximum extrusion load (26mm stroke), the profile on the bottom

ran at 160 mm/sec while the profile on the top ran at 156 mm/sec. At stokes between 50 and 250

mm, the average profile speed for the less supported profile (top profile) stabilized at around 156

mm/sec compared to the 158 mm/sec of the other profile (bottom one). It is worth noting that the

curve of the velocitymeter of the bottom profile showed a lower scatter distribution of the data

compared to the other curve, this being in relation with the velocitymeter models: the velocitymeter

used on the top profile is older than that used on the bottom, thus producing a worse filtering of

acquired data. The difference in profile speeds can be visualized also in term of final profiles

length: the bottom profiles resulted 56mm longer than the upper profile (4196mm respect to

4100mm). Even if the difference is very small all the repetitions showed the same tendencies with

difference of 36mm and 25mm respectively for tests 3 and 5 (Table3).

Fig. 9 shows the recorded die temperatures during the extrusion: both thermocouples were

placed in proximity of the bearing zone, the first on the full supported part of the die (bottom) while

the other on the less supported part (Fig. 3). The initial conditions can be considered homogenous

(392°C for the upper profile, 394°C for the lower) but during the process the temperature of the top

part of the die decreased, while the bottom temperature remained almost constant. At the end of the

process the temperature at the bottom is 394 °C and the temperature at the top is 10 °C lower. The

tendency looks unusual because in this type of press usually the temperature at the bottom part of

the die decrease during the process: the reason can be searched in the die deflections of the upper

tongue and in the resulting decreasing of the friction conditions. It´s worth interesting to note that

the rather small final differences in die temperature are in relation to the distance of the

thermocouples from the bearing surface: larger differences would be found in proximity of bearing

zones thus evidencing the great effect that the changes in friction conditions on the bearings

produce on the thermal field. As previously explained, the laser sensors were placed on a rigid

structure outside the press and fixed to the ground, thus avoiding any displacement related to press

deformation during extrusion.

Fig. 7: Profile speeds (left) and Die temperature (right)


As consequence, the tongues deflection measurements include also the deformation of the press. In

order to quantify the press deformation the two sensors were positioned on the die surface near the

back-up plate. The press displacement measured here was about 1 mm at maximum press load and

it decreased linearly with press load decreasing. Figure 8 shows the tongues deflection of the

partially supported (A1, up) and of the full supported (A2, bottom) profile after the subtraction of

the press deformation and the relative displacement of the partially supported tongue respect to fully

support (Δ(A1-A2)). The deflection measured in the bottom tongue was exactly the same like the

press deflection thus producing a negligible purged deflection while the deflection in the top tongue

was 0.4-0.51mm higher than press displacement during the whole stroke as also visible by the

plotting of Δ(A1-A2). So that, after subtracting the press deflection, the bottom tongue did not

deflect while the top one showed an almost constant deflection (Fig. 8). At the end of the trials the

die was cleaned by aluminum by means of caustic soda bath and no permanent deflection of the

tongue was found.

Fig. 8: Deformation of the less supported inner profile contour and curved profile geometry

In order to analyze the influence of the die deflection on the profile geometry more extrusions were

carried out without guiding the exiting profiles. In these experiments, the profile exiting from the

less supported part of the die came out in a pronounced curve (Fig. 8 right), while the other came

out straight. It can be argued that the deformation of the die changes the friction conditions, so that

the material flow locally changes and the material flows unilateral faster.

Conclusions

An original system for monitoring the die deflection was developed and tested on the Extrusion

Benchmark 2009 die. Two U shape profiles were extruded with different tongue supports in order to

allow a controlled deflection of a portion of the die. The selected die design produced a deflection

of 0.4 - 0.5 mm in the upper profile, while almost no deflection in the bottom one. It was found that

the less supported profile always flowed a little slower than the other and it developed also lower

temperatures during the process stroke. As a consequence of the die deflection, when the profiles

were not guided the friction conditions in the less supported hole is strongly altered, thus producing

a bended profile with a large curvature radius.

Acknowledgements

This work was carried out with financial support of the Transregional Collaborative Research

Center SFB/TR10 funded by the German Research Foundation (DFG). The authors would like to

thank WEFA, Germany, for the die manufacturing and POLYTEC for lending laser velocitymeters.

As consequence, the tongues deflection measurements include also the deformation of the press. In

order to quantify the press deformation the two sensors were positioned on the die surface near the

back-up plate. The press displacement measured here was about 1 mm at maximum press load and

it decreased linearly with press load decreasing. Figure 8 shows the tongues deflection of the

partially supported (A1, up) and of the full supported (A2, bottom) profile after the subtraction of

the press deformation and the relative displacement of the partially supported tongue respect to fully

support (Δ(A1-A2)). The deflection measured in the bottom tongue was exactly the same like the

press deflection thus producing a negligible purged deflection while the deflection in the top tongue

was 0.4-0.51mm higher than press displacement during the whole stroke as also visible by the

plotting of Δ(A1-A2). So that, after subtracting the press deflection, the bottom tongue did not

deflect while the top one showed an almost constant deflection (Fig. 8). At the end of the trials the

die was cleaned by aluminum by means of caustic soda bath and no permanent deflection of the

tongue was found.

Fig. 8: Deformation of the less supported inner profile contour and curved profile geometry

In order to analyze the influence of the die deflection on the profile geometry more extrusions were

carried out without guiding the exiting profiles. In these experiments, the profile exiting from the

less supported part of the die came out in a pronounced curve (Fig. 8 right), while the other came

out straight. It can be argued that the deformation of the die changes the friction conditions, so that

the material flow locally changes and the material flows unilateral faster.

Conclusions

An original system for monitoring the die deflection was developed and tested on the Extrusion

Benchmark 2009 die. Two U shape profiles were extruded with different tongue supports in order to

allow a controlled deflection of a portion of the die. The selected die design produced a deflection

of 0.4 - 0.5 mm in the upper profile, while almost no deflection in the bottom one. It was found that

the less supported profile always flowed a little slower than the other and it developed also lower

temperatures during the process stroke. As a consequence of the die deflection, when the profiles

were not guided the friction conditions in the less supported hole is strongly altered, thus producing

a bended profile with a large curvature radius.

Acknowledgements

This work was carried out with financial support of the Transregional Collaborative Research

Center SFB/TR10 funded by the German Research Foundation (DFG). The authors would like to

thank WEFA, Germany, for the die manufacturing and POLYTEC for lending laser velocitymeters.


Table 1: Temperature date and results for the extrusion benchmark

(Billet No. 4 is the benchmark billet which is compared with the results of the FEM codes)

References

[1] T. Kloppenborg, M. Schikorra, M. Schomäcker, A. E. Tekkaya: Numerical Optimization of

Bearing Length in Composite Extrusion Processes, In: Proceedings of International Workshop

and Extrusion Benchmark, Bologna (Italy), Key Engineering Materials Vol. 367, 2008, pp.47-

54.

[2] M. Schikorra, L. Donati, L. Tomesani, M. Kleiner: The role of friction in the extrusion of

AA6060 aluminum alloy, process analysis and monitoring, In: Journal of Materials Processing

Technology, Volume 191, Issues 1-3, 1 August 2007, pp. 288-292

[3] L. Donati, L. Tomesani, M. Schikorra, A. E. Tekkaya, “Extrusion Benchmark 2007 –

Benchmark Experiments: Study on Material Flow Extrusion of a Flat Die”, Proceedings of the

Extrusion Workshop and Benchmark, Key Engineering Materials Vol. 367 (2008) pp. 1-8

[4] N. Ben Khalifa ,L. Donati, L. Tomesani, M. Schikorra, A. E. Tekkaya: Extrusion Benchmark

2009 – A Step Ahead in Virtual Process Optimization, in Light Metal Age, April 2009, pp. 54-

55.

[5] T. Mori, N. Takatsuji, K.Matsuki, T.Aida, K.Murotani, K.Uetoko: Measurement of pressure

distribution on die surface and deformation of extrusion die in hot extrusion of 1050 aluminum

rod, Journal of Materials Processing Technology (2002), p421-425.

[6] W. Assaad, H.J.M. Geijselaers, J.Huétink: 3-D numerical simulation of direct aluminum

extrusion and die deformation (Extrusion Technology, Orlando 2008).

Billet

No.

Ram

Speed

[mm/s]

Ram temp.

[°C]

Billet

Temp.

[°C]

Die

Temp.

[°C]

Max.

Profile

Temp.

[C°]

Max.

ram

Force

[MN]

Profile

Length

[mm]

Max.

Deformation

[mm ] ±0.06

3 10 Start 380

End 408

430 Start

Top 397

Bottom 399

End

Top 389

Bottom 398

493 8.04 Up

4157

Bottom

4193

Supported

profile

(up) 0.49

Less

supported

profile

(bottom)

0

4 10 Start 365

End 411

432 Start

Top 392

Bottom 394

End

Top 384

Bottom 394

490 8 Up

4140

Bottom

4196

Supported

profile

(up) 0.51

Less

supported

profile

(bottom)

0

5 10 Start 377

End 391

410 Start

Top 383

Bottom 388

End

Top 377

Bottom 384

480 8.51 Up

4150

Bottom

4175

Supported

profile

(up) 0.40

Less

supported

profile

(bottom)

0

Table 1: Temperature date and results for the extrusion benchmark

(Billet No. 4 is the benchmark billet which is compared with the results of the FEM codes)

References

[1] T. Kloppenborg, M. Schikorra, M. Schomäcker, A. E. Tekkaya: Numerical Optimization of

Bearing Length in Composite Extrusion Processes, In: Proceedings of International Workshop

and Extrusion Benchmark, Bologna (Italy), Key Engineering Materials Vol. 367, 2008, pp.47-

54.


AA6060 aluminum alloy, process analysis and monitoring, In: Journal of Materials Processing

Technology, Volume 191, Issues 1-3, 1 August 2007, pp. 288-292

[3] L. Donati, L. Tomesani, M. Schikorra, A. E. Tekkaya, “Extrusion Benchmark 2007 –

Benchmark Experiments: Study on Material Flow Extrusion of a Flat Die”, Proceedings of the

Extrusion Workshop and Benchmark, Key Engineering Materials Vol. 367 (2008) pp. 1-8

[4] N. Ben Khalifa ,L. Donati, L. Tomesani, M. Schikorra, A. E. Tekkaya: Extrusion Benchmark

2009 – A Step Ahead in Virtual Process Optimization, in Light Metal Age, April 2009, pp. 54-

55.

[5] T. Mori, N. Takatsuji, K.Matsuki, T.Aida, K.Murotani, K.Uetoko: Measurement of pressure

distribution on die surface and deformation of extrusion die in hot extrusion of 1050 aluminum

rod, Journal of Materials Processing Technology (2002), p421-425.

[6] W. Assaad, H.J.M. Geijselaers, J.Huétink: 3-D numerical simulation of direct aluminum

extrusion and die deformation (Extrusion Technology, Orlando 2008).

Billet

No.

Ram

Speed

[mm/s]

Ram temp.

[°C]

Billet

Temp.

[°C]

Die

Temp.

[°C]

Max.

Profile

Temp.

[C°]

Max.

ram

Force

[MN]

Profile

Length

[mm]

Max.

Deformation

[mm ] ±0.06

3 10 Start 380

End 408

430 Start

Top 397

Bottom 399

End

Top 389

Bottom 398

493 8.04 Up

4157

Bottom

4193

Supported

profile

(up) 0.49

Less

supported

profile

(bottom)

0

4 10 Start 365

End 411

432 Start

Top 392

Bottom 394

End

Top 384

Bottom 394

490 8 Up

4140

Bottom

4196

Supported

profile

(up) 0.51

Less

supported

profile

(bottom)

0

5 10 Start 377

End 391

410 Start

Top 383

Bottom 388

End

Top 377

Bottom 384

480 8.51 Up

4150

Bottom

4175

Supported

profile

(up) 0.40

Less

supported

profile

(bottom)

0


Physically based microstructure modelling of AA6082 during hot extrusion

F. Krumphals1, a, P. Sherstnev1, b, S. Mitsche2, c, S. Randjelovic3, d and C. Sommitsch1, e

1 Christian Doppler Laboratory for Materials Modelling and Simulation, Institute for Materials Science and Welding, Graz University of Technology,

Kopernikusgasse 24, 8010 Graz, Austria 2 Research Institute for Electron Microscopy, Graz University of Technology, Steyrergasse 17,

8010 Graz, Austria

3 Faculty of Mechanical Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia

[email protected], [email protected], [email protected], [email protected], [email protected]

Keywords: AA6082, hot extrusion, FEM, microstructure modelling, dislocation density evolution, nucleation Abstract. Process parameters in aluminium extrusion technology are key points that influence product properties. The precipitation hardening aluminium alloy 6082 is investigated according to different process conditions and the influence onto the final microstructure is simulated as well as experimentally verified. A physical microstructure model based on three dislocation types and three nucleation sites for recrystallization is implemented into the commercial Finite Element package FORGE 2008 to calculate both the microstructure evolution during the extrusion process as well as the recrystallized fraction after the process. The precipitation kinetics during homogenization was investigated using the thermodynamic calculation software MatCalc since the main nucleation mechanism for recrystallization is particle stimulated. The experimental validation was done by miniature extrusion tests and the microstructure was investigated metallographically and by EBSD measurements.

Introduction

It is accepted that the product properties are closely correlated to the final microstructure, i.e. the grain and subgrain structure as well as the precipitation distribution [1]. Hence it is important to consider the influence of the process conditions on the evolution of structure, such as the homogenization treatment both to dissolve particles that are detrimental to the materials formability and to spheroidize plate like particles, respectively. [2,3]. Moreover, the initial microstructure of the billet and extrusion parameters like the extrusion speed, the initial temperature of the billet, container and die, the extrusion ratio, quality of tool surfaces and the die configuration control the materials hardening and softening as well as the substructure evolution during extrusion, which has a great effect on the final grain structure [4,5]. In general the extrudate should have uniform mechanical properties through the thickness and along the length with no surface flaws such as tearing, die lines and coarse grains. These surface imperfections would affect processes like anodising, possibly leading to product rejection. The traditional way to control these properties is the application of empirical knowledge of their complex relationship with forming parameters and metallurgical response. However, there are commercial finite element model (FEM) codes, which can be coupled with sound microstructure models. Controlling the substructure evolution during processing and hence the recrystallization kinetics is a challenging and demanding task for the aluminium extrusion industry. To demonstrate what’s happening during the process and how the final microstructure of the product develops, an FE-simulation of the extrusion process was

Physically based microstructure modelling of AA6082 during hot extrusion

F. Krumphals1, a, P. Sherstnev1, b, S. Mitsche2, c, S. Randjelovic3, d and C. Sommitsch1, e

1 Christian Doppler Laboratory for Materials Modelling and Simulation, Institute for Materials Science and Welding, Graz University of Technology,

Kopernikusgasse 24, 8010 Graz, Austria 2 Research Institute for Electron Microscopy, Graz University of Technology, Steyrergasse 17,

8010 Graz, Austria

3 Faculty of Mechanical Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia


Keywords: AA6082, hot extrusion, FEM, microstructure modelling, dislocation density evolution, nucleation Abstract. Process parameters in aluminium extrusion technology are key points that influence product properties. The precipitation hardening aluminium alloy 6082 is investigated according to different process conditions and the influence onto the final microstructure is simulated as well as experimentally verified. A physical microstructure model based on three dislocation types and three nucleation sites for recrystallization is implemented into the commercial Finite Element package FORGE 2008 to calculate both the microstructure evolution during the extrusion process as well as the recrystallized fraction after the process. The precipitation kinetics during homogenization was investigated using the thermodynamic calculation software MatCalc since the main nucleation mechanism for recrystallization is particle stimulated. The experimental validation was done by miniature extrusion tests and the microstructure was investigated metallographically and by EBSD measurements.

Introduction

It is accepted that the product properties are closely correlated to the final microstructure, i.e. the grain and subgrain structure as well as the precipitation distribution [1]. Hence it is important to consider the influence of the process conditions on the evolution of structure, such as the homogenization treatment both to dissolve particles that are detrimental to the materials formability and to spheroidize plate like particles, respectively. [2,3]. Moreover, the initial microstructure of the billet and extrusion parameters like the extrusion speed, the initial temperature of the billet, container and die, the extrusion ratio, quality of tool surfaces and the die configuration control the materials hardening and softening as well as the substructure evolution during extrusion, which has a great effect on the final grain structure [4,5]. In general the extrudate should have uniform mechanical properties through the thickness and along the length with no surface flaws such as tearing, die lines and coarse grains. These surface imperfections would affect processes like anodising, possibly leading to product rejection. The traditional way to control these properties is the application of empirical knowledge of their complex relationship with forming parameters and metallurgical response. However, there are commercial finite element model (FEM) codes, which can be coupled with sound microstructure models. Controlling the substructure evolution during processing and hence the recrystallization kinetics is a challenging and demanding task for the aluminium extrusion industry. To demonstrate what’s happening during the process and how the final microstructure of the product develops, an FE-simulation of the extrusion process was


performed with FORGE to obtain process boundary conditions, which have a lasting effect onto the microstructure evolution. These data are input parameters for a physical based microstructure model, describing the structure evolution during the forming process and predicting the final microstructure of the product due to various post-treatment conditions. The results produced by the model were experimentally validated by hot extrusion experiments.

Modelling and simulation

FEM model. A software FEM package FORGE 2008® was used to simulate the forward extrusion of hot aluminium with solid sections from a diameter Ø45 to Ø12 mm which means an extrusion ratio of about 14 (Fig.1). As a reason of the high extrusion ratio, a high deformation degree occurs with variable friction coefficients, temperature changes and variable stress and strain rate values (Figs. 2, 3). The data structure of the program includes the governing equations, the mesh of the billet, the rheology of the material, the tool description, the frictional interface and the numerical parameters [6]. The program uses implicit FEM to calculate the hot working parameters: load, strain rate, temperature field and deformation. A Lagrangian method is adopted for the program, which can thus accurately define the material properties, state variables and boundary conditions. To control the degree of remeshing in the areas where high deformation is expected, refinement mesh boxes of the Eulerian type (but maintaining Lagrangian flow) were applied to the billet. The remeshing values are controlled by the average target size of an element and the sharing is specified by mesh-boxes. (Fig.1).

Fig. 1: Mesh box in the area of plastic deformation: The mesh refinement of the billet in the area of maximum deformation can be clearly seen.

The simulation approach is based on a viscoplastic constitutive model, which neglects the elastic behaviour of the metal during deformation process. The meshing is based on two concepts: the quality of the elements and the shape geometry. During the simulation of forward extrusion, large deformations are predominant which require a Lagrangian mesh to be defined, as mentioned above. Thus, complete remeshing is mandatory in areas of excessive deformation of volume. The temperature field in the meridian cross section of the billet (from 549.5°C to 450.6°C on contact surface with tool), die and container indicates their interaction and the heat transfer from billet to tool (Fig. 2a). The strain rate, which shows highest values near the edge of the die, is one of the most important parameters, which illustrates the continual plastic deformation and the quality of the finished part. The transfer radius decisively influences the field of strain rate [7], with values from 1.98s-1 (node 575) to 34.14s-1 at the top of radius of the die (Fig. 2b).

billet

liner

die

mesh box

performed with FORGE to obtain process boundary conditions, which have a lasting effect onto the microstructure evolution. These data are input parameters for a physical based microstructure model, describing the structure evolution during the forming process and predicting the final microstructure of the product due to various post-treatment conditions. The results produced by the model were experimentally validated by hot extrusion experiments.

Modelling and simulation

FEM model. A software FEM package FORGE 2008® was used to simulate the forward extrusion of hot aluminium with solid sections from a diameter Ø45 to Ø12 mm which means an extrusion ratio of about 14 (Fig.1). As a reason of the high extrusion ratio, a high deformation degree occurs with variable friction coefficients, temperature changes and variable stress and strain rate values (Figs. 2, 3). The data structure of the program includes the governing equations, the mesh of the billet, the rheology of the material, the tool description, the frictional interface and the numerical parameters [6]. The program uses implicit FEM to calculate the hot working parameters: load, strain rate, temperature field and deformation. A Lagrangian method is adopted for the program, which can thus accurately define the material properties, state variables and boundary conditions. To control the degree of remeshing in the areas where high deformation is expected, refinement mesh boxes of the Eulerian type (but maintaining Lagrangian flow) were applied to the billet. The remeshing values are controlled by the average target size of an element and the sharing is specified by mesh-boxes. (Fig.1).

Fig. 1: Mesh box in the area of plastic deformation: The mesh refinement of the billet in the area of maximum deformation can be clearly seen.

The simulation approach is based on a viscoplastic constitutive model, which neglects the elastic behaviour of the metal during deformation process. The meshing is based on two concepts: the quality of the elements and the shape geometry. During the simulation of forward extrusion, large deformations are predominant which require a Lagrangian mesh to be defined, as mentioned above. Thus, complete remeshing is mandatory in areas of excessive deformation of volume. The temperature field in the meridian cross section of the billet (from 549.5°C to 450.6°C on contact surface with tool), die and container indicates their interaction and the heat transfer from billet to tool (Fig. 2a). The strain rate, which shows highest values near the edge of the die, is one of the most important parameters, which illustrates the continual plastic deformation and the quality of the finished part. The transfer radius decisively influences the field of strain rate [7], with values from 1.98s-1 (node 575) to 34.14s-1 at the top of radius of the die (Fig. 2b).

billet

liner

die

mesh box


(a) (b) Fig. 2: Mesh of tetrahedral finite elements in the area of plastic deformation. (a) Temperature field

(max.: 549.5°C; min.: 219.9°C) and (b) strain rate distribution near the die radius.

The high change of the zz stress tensor component in the meridian cross section, from – 223 MPa to 28 MPa, indicates the noncontinual stress distributions in the deformation zone (Fig. 3a). The Von Mises equivalent stress range in the materials structure from 3 MPa to 67 MPa near the edge of the die describes the aluminium loading during the process. With three node values of the Von Mises stress (53.4 MPa, 55.3 MPa, 52.8 MPa) the stress conditions in the forming zone can be explained.

(a) (b) Fig. 3: Field of characteristic stresses in the deformation zone: (a) Distribution of zz stress tensor

and (b) distribution of Von Mises stress.

Microstructure model. The extrusion simulation was performed to achieve the local process conditions temperature (Fig. 2a) and strain rate (Fig. 2b), which are input parameters for the physically based microstructure evolution model. This model, based on contemporary understanding of microstructure evolution and the interaction of dislocations with microstructure essentials, gives a reasonable description of the hardening behaviour and accounts adequately for changes of material chemistry, in particular for age-hardened alloys. The used three-internal-variables model (3IVM) consists of a kinetic equation of state and a set of equations for the substructure evolution (mobile dislocations, immobile dislocations in the cell interiors and immobile dislocations in the cell walls) [8]. To predict recrystallization, the 3IVM is coupled with a model describing static recrystallization [9]. If the stored deformation energy increases by generating dislocations and if the dislocation density gradient exceeds a critical value at preferential locations like grain boundaries, triple junctions or particles (>1µm), the material starts to recrystallize.

Physical based microstructure model. For a realistic description of the microstructure evolution during the process and final state, physical based models are adequate that consider dislocations, subgrain boundaries, precipitations and their interactions. The following microstructure processes

(a) (b) Fig. 2: Mesh of tetrahedral finite elements in the area of plastic deformation. (a) Temperature field

(max.: 549.5°C; min.: 219.9°C) and (b) strain rate distribution near the die radius.

The high change of the zz stress tensor component in the meridian cross section, from – 223 MPa to 28 MPa, indicates the noncontinual stress distributions in the deformation zone (Fig. 3a). The Von Mises equivalent stress range in the materials structure from 3 MPa to 67 MPa near the edge of the die describes the aluminium loading during the process. With three node values of the Von Mises stress (53.4 MPa, 55.3 MPa, 52.8 MPa) the stress conditions in the forming zone can be explained.

(a) (b) Fig. 3: Field of characteristic stresses in the deformation zone: (a) Distribution of zz stress tensor

and (b) distribution of Von Mises stress.

Microstructure model. The extrusion simulation was performed to achieve the local process conditions temperature (Fig. 2a) and strain rate (Fig. 2b), which are input parameters for the physically based microstructure evolution model. This model, based on contemporary understanding of microstructure evolution and the interaction of dislocations with microstructure essentials, gives a reasonable description of the hardening behaviour and accounts adequately for changes of material chemistry, in particular for age-hardened alloys. The used three-internal-variables model (3IVM) consists of a kinetic equation of state and a set of equations for the substructure evolution (mobile dislocations, immobile dislocations in the cell interiors and immobile dislocations in the cell walls) [8]. To predict recrystallization, the 3IVM is coupled with a model describing static recrystallization [9]. If the stored deformation energy increases by generating dislocations and if the dislocation density gradient exceeds a critical value at preferential locations like grain boundaries, triple junctions or particles (>1µm), the material starts to recrystallize.

Physical based microstructure model. For a realistic description of the microstructure evolution during the process and final state, physical based models are adequate that consider dislocations, subgrain boundaries, precipitations and their interactions. The following microstructure processes


are considered in the model: § Dislocation evolution by three classes of dislocations; § SRX nucleation at different microstructure sites; § Precipitation kinetics for the calculation of both particle stimulated nucleation by coarse

particles and Zener drag by dispersed precipitations. Stored energy model. During hot forming, subgrains develop by polygonisation and different dislocation classes can be defined [8]: mobile and immobile dislocations in the cell interior as well as dislocations in the cell walls. The mobile dislocations carry the plastic strain:

MLb

t effm1+=≅

∆∆ ρεε

&& (1)

where ε denotes the plastic strain, ε& the strain rate, which was taken from the simulation, ρm the mobile dislocation density, b the Burgers-vector and M the Taylor-factor. Each mobile dislocation is supposed to glide a mean free path, Leff, until it is immobilised or annihilated. This free path depends on the grain size Dg, the dislocation spacing in the cell wall, Lw, and in the cell interior, Li, and the particle spacing of disperse phases, Lp, respectively:

pgw

w

i

i

eff LDLLL111

+++=ββ

, (2)

with iβ and wβ as constants in the order of unit. The mobile dislocation density is reduced by the following mechanisms: dipole formation, formation of Lomer-Cottrel dislocations and annihilation. The immobile dislocations in the cell interior are generated by the formation of Lomer-Cottrel dislocations, whereas the formed dislocation dipoles reach the cell wall and are accumulated there. The immobile dislocations and the dislocations in the cell walls are not able to glide, they are reduced by climb. This recovery process can be explained by following equation:

nd wi

wi

2,

annihilclimb, 2ρ

νρ =−& , (3)

where ρi,w describes the immobile dislocation density as well as the dislocation density in the cell walls, dannihil the critical distance for dislocation annihilation and n the number of active gliding systems. The climbing velocity, vclimb, of the dislocations is diffusion dependent:

ATk

D

B

τν =climb , (4)

with D as the coefficient for self-diffusion, kB denotes the Boltzmann-constant, τ the shear stress and A the activated area. The total dislocation density, ρtot, can finally be calculated as the sum of all dislocation classes:

wwiimtot ff ρρρρ ++= , (5)

where fi and fw are the volume fractions of cell interior and cell walls. The total stored energy per unit volume is approximately [10]:

++−=θθ

δθρρ c

tottotshear

D bb

bGP ln1

2))10ln(1(

1021

2

, (6)

where Gshear is the shear modulus, δ the subgrain size, θ the subgrain misorientation and θc is the critical misorientation for distinguishing between a grain and subgrain boundary (chosen as 15°).

are considered in the model: § Dislocation evolution by three classes of dislocations; § SRX nucleation at different microstructure sites; § Precipitation kinetics for the calculation of both particle stimulated nucleation by coarse

particles and Zener drag by dispersed precipitations. Stored energy model. During hot forming, subgrains develop by polygonisation and different dislocation classes can be defined [8]: mobile and immobile dislocations in the cell interior as well as dislocations in the cell walls. The mobile dislocations carry the plastic strain:

MLb

t effm1+=≅

∆∆ ρεε

&& (1)

where ε denotes the plastic strain, ε& the strain rate, which was taken from the simulation, ρm the mobile dislocation density, b the Burgers-vector and M the Taylor-factor. Each mobile dislocation is supposed to glide a mean free path, Leff, until it is immobilised or annihilated. This free path depends on the grain size Dg, the dislocation spacing in the cell wall, Lw, and in the cell interior, Li, and the particle spacing of disperse phases, Lp, respectively:

pgw

w

i

i

eff LDLLL111

+++=ββ

, (2)

with iβ and wβ as constants in the order of unit. The mobile dislocation density is reduced by the following mechanisms: dipole formation, formation of Lomer-Cottrel dislocations and annihilation. The immobile dislocations in the cell interior are generated by the formation of Lomer-Cottrel dislocations, whereas the formed dislocation dipoles reach the cell wall and are accumulated there. The immobile dislocations and the dislocations in the cell walls are not able to glide, they are reduced by climb. This recovery process can be explained by following equation:

nd wi

wi

2,

annihilclimb, 2ρ

νρ =−& , (3)

where ρi,w describes the immobile dislocation density as well as the dislocation density in the cell walls, dannihil the critical distance for dislocation annihilation and n the number of active gliding systems. The climbing velocity, vclimb, of the dislocations is diffusion dependent:

ATk

D

B

τν =climb , (4)

with D as the coefficient for self-diffusion, kB denotes the Boltzmann-constant, τ the shear stress and A the activated area. The total dislocation density, ρtot, can finally be calculated as the sum of all dislocation classes:

wwiimtot ff ρρρρ ++= , (5)

where fi and fw are the volume fractions of cell interior and cell walls. The total stored energy per unit volume is approximately [10]:

++−=θθ

δθρρ c

tottotshear

D bb

bGP ln1

2))10ln(1(

1021

2

, (6)

where Gshear is the shear modulus, δ the subgrain size, θ the subgrain misorientation and θc is the critical misorientation for distinguishing between a grain and subgrain boundary (chosen as 15°).


ucleation model. For the SRX nucleation the model according to Vatne [9] with three nucleation sites (particle stimulated nucleation, cubic sites and nucleation at grain boundaries) is applied in the following. Particle stimulated nucleation (PSN) is very important recrystallization mechanism of commercial aluminium alloys containing coarse particles (>1µm). The density of PSN nuclei becomes:

−−=

ZDPS!PS! PP

L!C!

γ4exp0 , (7)

where CPS! is a constant and !0 as well as L are particle size distribution parameters. For the calculation of the precipitation parameters the program MatCalc was used [11]. The precipitation kinetics was calculated during heat treatment of AA6082 at 540°C for 3h. The homogenised microstructure shows a relatively high volume fraction of large Al6(Mn,Fe) particles with a mean particle radius of 1-5 µm. Due to the short process time (in comparison to the heat treatment) the calculated precipitation parameters, i.e. volume fraction (fv) and mean radius (r), during extrusion were held constant after homogenization.

The nucleation of the cube recrystallization is considered for multi-step deformation processes, for example rolling. During extrusion, which is a one-step forming process, this recrystallization mechanism can be neglected. Due to accumulation of dislocations during the deformation process, energy is stored at high angle grain boundaries and this energy decreases by the nucleation of new grains during high thermal conditions. The density of grain boundary nuclei becomes hence

( ) ( )[ ]1expexp)1(

+−+−

= εεδ

g

GBcGBGB D

SRC! , (8)

where CGB is a constant and SGB is the density of overcritical nuclei at grain boundaries. The values of the above mentioned parameters and constants are given in Table 1.

Table 1: Numerical values of important parameters which were used in the simulation.

These necessary simulation parameters were partly drawn from literature [9] and experimentally determined at our institute by several compression tests with variable deformation degrees and strain rates. The present model was implemented into the Finite Element program FORGE 2008 and used for the simulation of the microstructure evolution during extrusion of aluminium alloy 6082.

Experimental Investigations

Two different conditions of the post treatment of the material, namely water quenching and air cooling are considered and their influence onto the microstructure of the final state of the extrudate is described. The initial microstructure of the cast billet as well as the homogenized state before the

fw 0.2 -

wi ff −= 1 0.8 -

Gshear Gshear=f(T) Pa b 0.286*10-9 m δ model m θ model - CPS! 0.18 - !0 1*1016 m-3

L 1.3*106 m-1 γ 0.324 J/m2

PZ3 γ⋅ fv⋅

2 r⋅:=

fv=0.032 r=0.12*10-6

- m

CGB 0.09 - RC 0.215 - SGB SGB=f(strain) - D Modell m

ucleation model. For the SRX nucleation the model according to Vatne [9] with three nucleation sites (particle stimulated nucleation, cubic sites and nucleation at grain boundaries) is applied in the following. Particle stimulated nucleation (PSN) is very important recrystallization mechanism of commercial aluminium alloys containing coarse particles (>1µm). The density of PSN nuclei becomes:

−−=

ZDPS!PS! PP

L!C!

γ4exp0 , (7)

where CPS! is a constant and !0 as well as L are particle size distribution parameters. For the calculation of the precipitation parameters the program MatCalc was used [11]. The precipitation kinetics was calculated during heat treatment of AA6082 at 540°C for 3h. The homogenised microstructure shows a relatively high volume fraction of large Al6(Mn,Fe) particles with a mean particle radius of 1-5 µm. Due to the short process time (in comparison to the heat treatment) the calculated precipitation parameters, i.e. volume fraction (fv) and mean radius (r), during extrusion were held constant after homogenization.

The nucleation of the cube recrystallization is considered for multi-step deformation processes, for example rolling. During extrusion, which is a one-step forming process, this recrystallization mechanism can be neglected. Due to accumulation of dislocations during the deformation process, energy is stored at high angle grain boundaries and this energy decreases by the nucleation of new grains during high thermal conditions. The density of grain boundary nuclei becomes hence

( ) ( )[ ]1expexp)1(

+−+−

= εεδ

g

GBcGBGB D

SRC! , (8)

where CGB is a constant and SGB is the density of overcritical nuclei at grain boundaries. The values of the above mentioned parameters and constants are given in Table 1.

Table 1: Numerical values of important parameters which were used in the simulation.

These necessary simulation parameters were partly drawn from literature [9] and experimentally determined at our institute by several compression tests with variable deformation degrees and strain rates. The present model was implemented into the Finite Element program FORGE 2008 and used for the simulation of the microstructure evolution during extrusion of aluminium alloy 6082.

Experimental Investigations

Two different conditions of the post treatment of the material, namely water quenching and air cooling are considered and their influence onto the microstructure of the final state of the extrudate is described. The initial microstructure of the cast billet as well as the homogenized state before the

fw 0.2 -

wi ff −= 1 0.8 -

Gshear Gshear=f(T) Pa b 0.286*10-9 m δ model m θ model - CPS! 0.18 - !0 1*1016 m-3

L 1.3*106 m-1 γ 0.324 J/m2

PZ3 γ⋅ fv⋅

2 r⋅:=

fv=0.032 r=0.12*10-6

- m

CGB 0.09 - RC 0.215 - SGB SGB=f(strain) - D Modell m


hot extrusion process were investigated (Fig. 4). The cast billet shows a dendritic structure with large grains with a mean size of 80µm and mainly primary Mg2Si and AlFeSi precipitations. Prior to hot forming processes commonly a homogenization treatment is performed. It can be clearly seen that the plate like particles spheroidize during the homogenization at 540°C for 3 hours (Fig. 4b), which guarantees better forming conditions. After extruding the aluminium at 500°C billet temperature, two different post treatment conditions for the extruded material were compared to investigate the influence of static recrystallization. Therefore extruded material was water quenched after the extrusion process and compared with air cooled material (Fig. 5)

(a) (b)

Fig. 4: (a) Initial structure of the cast as well as (b) the microstructure of the billet after homogenization (540°C, 3h). Remarkable is the change of the precipitation structure.

The black lines in Fig. 5 mark high angle grain boundaries (θ > 15°) and the grey lines are considered as subgrain boundaries (θ < 15°). The microstructure investigation of the air cooled condition (Fig. 5b) results in a mean subgrain size of about 7µm and the according simulation result is 8µm. The grain structure shows large grains, extending the EBSD-image, which could be some hundred microns long, and smaller grains also showing elongated structure. To compare that with the simulation, an equal circle diameter of the grains was calculated, which amounts to 52µm and this can be compared with the simulation, which resulted in a grain size of about 70µm according to similar experimental thermo-mechanical loads (Fig 6).

The extrudates generally show an elongated grain structure, they are more than some hundred microns long in extrusion direction and relatively small in width, which is typical for extruded products. The quenched sample exhibits a distinct subgrain structure with high stored deformation energy, coarse elongated grains and small subgrains whereas the air cooled sample shows a coarsened subgrain structure and new formed high angle grain boundaries during static recrystallization.

hot extrusion process were investigated (Fig. 4). The cast billet shows a dendritic structure with large grains with a mean size of 80µm and mainly primary Mg2Si and AlFeSi precipitations. Prior to hot forming processes commonly a homogenization treatment is performed. It can be clearly seen that the plate like particles spheroidize during the homogenization at 540°C for 3 hours (Fig. 4b), which guarantees better forming conditions. After extruding the aluminium at 500°C billet temperature, two different post treatment conditions for the extruded material were compared to investigate the influence of static recrystallization. Therefore extruded material was water quenched after the extrusion process and compared with air cooled material (Fig. 5)

(a) (b)

Fig. 4: (a) Initial structure of the cast as well as (b) the microstructure of the billet after homogenization (540°C, 3h). Remarkable is the change of the precipitation structure.

The black lines in Fig. 5 mark high angle grain boundaries (θ > 15°) and the grey lines are considered as subgrain boundaries (θ < 15°). The microstructure investigation of the air cooled condition (Fig. 5b) results in a mean subgrain size of about 7µm and the according simulation result is 8µm. The grain structure shows large grains, extending the EBSD-image, which could be some hundred microns long, and smaller grains also showing elongated structure. To compare that with the simulation, an equal circle diameter of the grains was calculated, which amounts to 52µm and this can be compared with the simulation, which resulted in a grain size of about 70µm according to similar experimental thermo-mechanical loads (Fig 6).

The extrudates generally show an elongated grain structure, they are more than some hundred microns long in extrusion direction and relatively small in width, which is typical for extruded products. The quenched sample exhibits a distinct subgrain structure with high stored deformation energy, coarse elongated grains and small subgrains whereas the air cooled sample shows a coarsened subgrain structure and new formed high angle grain boundaries during static recrystallization.


(a) (b)

Fig. 5: Grain structure EBSD image of the AA6082 according to different post treatments: (a) Water quenched and (b) air cooled sample after the extrusion process. The influene of static

recrystallization can be clearly seen.

The recrystallized fraction of the air cooled sample was determined by EBSD measurements and resulted in 15%, where the simulation output for the recrystallized area yields to 17% at an approximately similar distance of the rod with equal thermal history.

The subgrain size of the water quenched sample is locally extremely fine (lower than one micron) with a generally coarse grain structure with less than 3% recrystallized area, which was also verified by the simulation. The grains in extrusion direction are more than some hundred microns long and relatively small in width, which is typical for extruded products.

(a) (b)

Fig. 6: (a) Subgrain size [m] as well as (b) grain size [m] evolution in the extrudate. The marked areas define the regions, which were compared with the experimental investigations.

Hence the comparison of simulations and experiments show a good correspondence with regard to grain and grain and subgrain size (compare Fig. 5b and Fig. 6) of the air cooled condition. The water quenched specimen was not easy to characterize due to its fine substructure (Fig. 5a), however the difference between these two states has been numerically simulated and the expected tendency was verified.

(a) (b)

Fig. 5: Grain structure EBSD image of the AA6082 according to different post treatments: (a) Water quenched and (b) air cooled sample after the extrusion process. The influene of static

recrystallization can be clearly seen.

The recrystallized fraction of the air cooled sample was determined by EBSD measurements and resulted in 15%, where the simulation output for the recrystallized area yields to 17% at an approximately similar distance of the rod with equal thermal history.

The subgrain size of the water quenched sample is locally extremely fine (lower than one micron) with a generally coarse grain structure with less than 3% recrystallized area, which was also verified by the simulation. The grains in extrusion direction are more than some hundred microns long and relatively small in width, which is typical for extruded products.

(a) (b)

Fig. 6: (a) Subgrain size [m] as well as (b) grain size [m] evolution in the extrudate. The marked areas define the regions, which were compared with the experimental investigations.

Hence the comparison of simulations and experiments show a good correspondence with regard to grain and grain and subgrain size (compare Fig. 5b and Fig. 6) of the air cooled condition. The water quenched specimen was not easy to characterize due to its fine substructure (Fig. 5a), however the difference between these two states has been numerically simulated and the expected tendency was verified.


Summary

A finite element simulation of an aluminium extrusion process was performed to obtain process parameters, which influence the microstructure evolution. Furthermore a physical based model was introduced, to calculate the microstructure evolution during the extrusion process and subsequent post treatments. The combination of all theoretical approaches, namely extrusion process simulation with FORGETM, precipitation calculation with MatCalcTM and dislocation density evolution calculations with the three-internal-variables model, enables a sound prediction of the final microstructure of the product, i.e. recrystallized fraction and grains size, which was compared and verified with experimental investigations.

References

[1] X. Duan, T. Sheppard, “Simulation and control of microstructure evolution during hot extrusion aluminium alloys”, Materials Science and Engineering, vol. A351 (2003) pp. 282-292.

[2] C. Poletti, P. Sherstnev, M. Schöbel, C. Sommitsch, “Substructure development of AA6082 during hot deformation”, Aluminium Alloys, Their Physical and Mechanical Properties, J. Hirsch et al. (Eds.), DGM, Wiley-VCH, vol.1 (2008) pp. 691-697.

[3] X. Duan, T. Sheppard, “Computation of substructural strengthening by the integration of metallurgical models into the finite element code”, Computational Materials Science, vol. 27 (2003) pp. 250-258.

[4] T. Sheppard and X. Duan, “Modelling of static recrystallisation by combining finite element methods with empirical models”. Journal of Materials Processing Technology, vol. 130-131 (2002) pp. 250-253.

[5] F. Krumphals, I. Flitta, S. Mitsche, T. Wlanis, A. Jahn, C. Sommitsch, “Comparison of experimental and Finite Element Modelling of the extrusion of AA6082 on both tools and extrudate as a function of process parameters”, Proc. 11th International Esaform Conference on Material Forming, Lyon, France (2008).

[6] I. Flitta, T. Sheppard, “Nature of friction in extrusion process and its effect on material flow”, Materials Science and Technology, vol. 19 No. 5, (2003) pp. 837-846.

[7] Schikorra M, Tekkaya A. E, Donati L, Tomesani L, “Effect of Pocket Shape in the Extrusion of Aluminium Profiles”, Aluminium Alloys, Their Physical and Mechanical Properties, Hirsch, J, Skrotzki, B, Gottstein, G (eds.) vol. 1, (2008) pp. 1387-1393

[8] F. Roters, D. Raabe, G. Gottstein, “Work hardening in heterogeneous Al-alloys – A microstructural approach based on three internal state variables”, Acta Materialia, vol. 48 (2000) pp. 4181-4189.

[9] H.E. Vatne, T. Furu, R. Orsund, E. Nes, “Modelling recrystallization after hot deformation of aluminium”, Acta Materialia, vol. 44 (1996) pp. 4463-4473.

[10] C.M. Sellars, Q. Zhu, “Microstructural modelling of aluminium alloys during thermomechanical processing”, Mater. Sci. Eng., vol. A280 (2000) pp. 1-7.

[11] E. Kozeschnik, J. Svoboda, P. Fratzl, F.D. Fischer, “Modelling of kinetics in multi-component multi-phase systems with spherical precipitates: II: Numerical solution and application”, Materials Science and Engineering, vol. A385 (2004) pp. 157-165.

Summary

A finite element simulation of an aluminium extrusion process was performed to obtain process parameters, which influence the microstructure evolution. Furthermore a physical based model was introduced, to calculate the microstructure evolution during the extrusion process and subsequent post treatments. The combination of all theoretical approaches, namely extrusion process simulation with FORGETM, precipitation calculation with MatCalcTM and dislocation density evolution calculations with the three-internal-variables model, enables a sound prediction of the final microstructure of the product, i.e. recrystallized fraction and grains size, which was compared and verified with experimental investigations.

References

[1] X. Duan, T. Sheppard, “Simulation and control of microstructure evolution during hot extrusion aluminium alloys”, Materials Science and Engineering, vol. A351 (2003) pp. 282-292.

[2] C. Poletti, P. Sherstnev, M. Schöbel, C. Sommitsch, “Substructure development of AA6082 during hot deformation”, Aluminium Alloys, Their Physical and Mechanical Properties, J. Hirsch et al. (Eds.), DGM, Wiley-VCH, vol.1 (2008) pp. 691-697.

[3] X. Duan, T. Sheppard, “Computation of substructural strengthening by the integration of metallurgical models into the finite element code”, Computational Materials Science, vol. 27 (2003) pp. 250-258.

[4] T. Sheppard and X. Duan, “Modelling of static recrystallisation by combining finite element methods with empirical models”. Journal of Materials Processing Technology, vol. 130-131 (2002) pp. 250-253.

[5] F. Krumphals, I. Flitta, S. Mitsche, T. Wlanis, A. Jahn, C. Sommitsch, “Comparison of experimental and Finite Element Modelling of the extrusion of AA6082 on both tools and extrudate as a function of process parameters”, Proc. 11th International Esaform Conference on Material Forming, Lyon, France (2008).

[6] I. Flitta, T. Sheppard, “Nature of friction in extrusion process and its effect on material flow”, Materials Science and Technology, vol. 19 No. 5, (2003) pp. 837-846.

[7] Schikorra M, Tekkaya A. E, Donati L, Tomesani L, “Effect of Pocket Shape in the Extrusion of Aluminium Profiles”, Aluminium Alloys, Their Physical and Mechanical Properties, Hirsch, J, Skrotzki, B, Gottstein, G (eds.) vol. 1, (2008) pp. 1387-1393

[8] F. Roters, D. Raabe, G. Gottstein, “Work hardening in heterogeneous Al-alloys – A microstructural approach based on three internal state variables”, Acta Materialia, vol. 48 (2000) pp. 4181-4189.

[9] H.E. Vatne, T. Furu, R. Orsund, E. Nes, “Modelling recrystallization after hot deformation of aluminium”, Acta Materialia, vol. 44 (1996) pp. 4463-4473.

[10] C.M. Sellars, Q. Zhu, “Microstructural modelling of aluminium alloys during thermomechanical processing”, Mater. Sci. Eng., vol. A280 (2000) pp. 1-7.

[11] E. Kozeschnik, J. Svoboda, P. Fratzl, F.D. Fischer, “Modelling of kinetics in multi-component multi-phase systems with spherical precipitates: II: Numerical solution and application”, Materials Science and Engineering, vol. A385 (2004) pp. 157-165.


An Assessment of the Grain Structure Evolution during Hot Forward

Extrusion of Aluminum Alloy 7020

A. Foydl1,a, N. Ben Khalifa1,b, A. Brosius1,c and A.E. Tekkaya1,d 1Institute of Forming Technology and Lightweight Construction (IUL),

Technische Universität Dortmund, Germany

[email protected], [email protected], [email protected], [email protected]

Keywords: Extrusion, Aluminum, Microstructure, Finite Element Analysis

Abstract. The current investigation is concerned with the grain structure evolution in an Al-Zn

alloy (EN AW-7020) during the hot forward extrusion process. In order to analyze that, a miniature

hot forward extrusion setup was designed which allows the quenching of the extrusion butt

immediately after extrusion. In order to gain a better understanding of the process, the shape of the

deformed grains was analyzed and the process was simulated. The shape of these grains was

indentified in two directions in the different grain zones, e.g. dead metal zone and shear zone. The

FE simulations showing the different grain zones were also illustrated. Simulation results and the

micrographs were quite promising to find parameters for simulation models in order to predict grain

sizes with the method presented in the current research work.

Introduction

The extrusion process is an old technique to manufacture profiles from light metals (e.g.

aluminum or magnesium). The forming occurs at high temperatures and pressures. The preheating

and the generated heat during the process, together with the deformations, change the

microstructure of the workpiece (e.g. changes in grain size and precipitations). The well-directed

adjustment of the formed microstructure with the help of process parameters is a typical aim in

manufacturing profiles to get optimized properties of strength and ductility. Therefore, it is

necessary to understand how recrystallization occurs or rather how the grain size and grain shape

change during the extrusion process.

In [1] it is described that the process parameters influence the recrystallization of the grains and

thereafter they are then responsible for both the microstructure and the mechanical properties of a

profile. Concerning the different distributions of strain, strain rate and temperature within the

workpiece, there are distinctive deformation zones to be observed. In the shear zone, the grains are

elongated and thin. In the dead metal zone, on the other hand, they are still equiaxed and not

deformed [2].

Recrystallization occurs during and after forming operations at elevated temperatures. The

mechanisms during the process are called dynamic or first, after the process static or second

recrystallization. Therefore, for the well-directed adjustment of the microstructure it is necessary to

investigate the evolution of grains not only at the end of the process, but also during the process.

Aluminum is a high stacking fault energy (HSFE) material. According to Mecking and Kocks [3],

the change of the ratio between the dislocation density and the true strain is dependent on the work

hardening and the dynamic recovery. Since the dislocations are very mobile in aluminum alloys,

they can easily recover and so the change of the ratio will never reach a critical value in order to

start recrystallization. This observation prevents the occurrence of discontinuous (classical)

dynamic recrystallization (dDRX). For HSFE materials such as aluminum the evolution of

microstructure is explained with continuous (cDRX) and geometric (gDRX) dynamic

recrystallization and the dynamic recovery (DRV) theories in the literature.

The DRV theory is described in [4, 5] by McQueen et al.. The subgrains have a constant size

during forming, and the wall and internal dislocation densities are also constant. While the grains

An Assessment of the Grain Structure Evolution during Hot Forward

Extrusion of Aluminum Alloy 7020

A. Foydl1,a, N. Ben Khalifa1,b, A. Brosius1,c and A.E. Tekkaya1,d 1Institute of Forming Technology and Lightweight Construction (IUL),

Technische Universität Dortmund, Germany


Keywords: Extrusion, Aluminum, Microstructure, Finite Element Analysis

Abstract. The current investigation is concerned with the grain structure evolution in an Al-Zn

alloy (EN AW-7020) during the hot forward extrusion process. In order to analyze that, a miniature

hot forward extrusion setup was designed which allows the quenching of the extrusion butt

immediately after extrusion. In order to gain a better understanding of the process, the shape of the

deformed grains was analyzed and the process was simulated. The shape of these grains was

indentified in two directions in the different grain zones, e.g. dead metal zone and shear zone. The

FE simulations showing the different grain zones were also illustrated. Simulation results and the

micrographs were quite promising to find parameters for simulation models in order to predict grain

sizes with the method presented in the current research work.

Introduction

The extrusion process is an old technique to manufacture profiles from light metals (e.g.

aluminum or magnesium). The forming occurs at high temperatures and pressures. The preheating

and the generated heat during the process, together with the deformations, change the

microstructure of the workpiece (e.g. changes in grain size and precipitations). The well-directed

adjustment of the formed microstructure with the help of process parameters is a typical aim in

manufacturing profiles to get optimized properties of strength and ductility. Therefore, it is

necessary to understand how recrystallization occurs or rather how the grain size and grain shape

change during the extrusion process.

In [1] it is described that the process parameters influence the recrystallization of the grains and

thereafter they are then responsible for both the microstructure and the mechanical properties of a

profile. Concerning the different distributions of strain, strain rate and temperature within the

workpiece, there are distinctive deformation zones to be observed. In the shear zone, the grains are

elongated and thin. In the dead metal zone, on the other hand, they are still equiaxed and not

deformed [2].

Recrystallization occurs during and after forming operations at elevated temperatures. The

mechanisms during the process are called dynamic or first, after the process static or second

recrystallization. Therefore, for the well-directed adjustment of the microstructure it is necessary to

investigate the evolution of grains not only at the end of the process, but also during the process.

Aluminum is a high stacking fault energy (HSFE) material. According to Mecking and Kocks [3],

the change of the ratio between the dislocation density and the true strain is dependent on the work

hardening and the dynamic recovery. Since the dislocations are very mobile in aluminum alloys,

they can easily recover and so the change of the ratio will never reach a critical value in order to

start recrystallization. This observation prevents the occurrence of discontinuous (classical)

dynamic recrystallization (dDRX). For HSFE materials such as aluminum the evolution of

microstructure is explained with continuous (cDRX) and geometric (gDRX) dynamic

recrystallization and the dynamic recovery (DRV) theories in the literature.

The DRV theory is described in [4, 5] by McQueen et al.. The subgrains have a constant size

during forming, and the wall and internal dislocation densities are also constant. While the grains


are elongated, the subgrains are still equiaxed, this leads to an increasing length of high angle

boundaries and that the subgrains are continually rearranged. The cDRX, on the other hand, is

described by Gourdet and Montheillet [6] as an alternative theory for the development of subgrains.

During deformation, the number of low angle boundaries increase, in contrast to DRV, because of

transformation from low to high angle boundaries. These occur inside the grains. According to the

development of new grains, Blum at al. [7] show a purely geometrical approach, which is called

gDRX. The gDRX theory claims that elongated grains become serrated and spin off, with the result

that new grains have been formed.

The well-directed adjustment of the microstructure, as mentioned above, could be easier with the

help of finite element analysis, because at present the adjustment is done by experiences and trial

and error. In this connection, a simulation could be a tool to predict the changes in grain sizes. The

increasing capacity of the calculation resources has induced the utilization of finite element

simulations in metal forming analysis, especially in the extrusion sector. Questions of the friction

behavior inside the container [8, 9] and the material flow in two or three dimensions [10] are only

two examples of the simulation activities of the last years. The simulation is also used to optimize

the material flow or the longitudinal seam welds [11], where the numerical analysis of the

composite extrusion process is shown.

In [2] Schikorra et al. present an experimental method to evaluate parameters for a

microstructure model of Avrami, which allows the simulation of the grain size as a post variable by

the use of the DEFORM code. The experimental set up was backward extrusion equipment, and by

linear regression techniques between experimental data and FEM simulations, some temperature-

dependent material parameters were found. The simulation was carried out in two stages: first the

grain deformation was computed, thus providing a good agreement in terms of grain thickness

prediction, and then the heat treatment of the alloy was performed and computed. The results after

heat treatment was less accurate due to the lack of computation of some phenomena like spherical

coarse grains (PCG). The results from backward extrusion (microcups) trials were then extended to

the computation of the grain size for a hot extrusion process. The predictions were good in the dead

metal zone, in the shear zone and in the inner part of the profile while they were unacceptable on

the profile surface (absence of PCG computation) and inside the billet rest (inaccurate static

recrystallization prediction). Another explanation for the inaccuracy could be related to the

differences between the experimental set ups (backward in microcups, forward in billet extrusion).

To improve the model, in the present research work, a miniature hot forward extrusion press has

been designed to be closer to the real forward extrusion process the parameters will be determined

for. The new set up allows testing different alloys with different extrusion ratios, temperatures, and

speeds and quenching the pressed specimen immediately, which is imported to analyze the grains

during the process. This paper examines the shape of the grains in the different extrusion zones for

one alloy. Further, it investigates experimentally the structure of the dynamically recrystallized

grains during hot forward extrusion.

Experimental procedure

Material. The aluminum alloy which was used in this study is a commercial EN AW-7020, whose

chemical composition is shown in Table 1. The alloy is used in aerospace industry.

Table 1: Chemical composition of the EN AW-7020

Si Fe Cu Mn Mg Cr Zn Ti Ni

7020 [%] 0.113 0.174 0.0405 0.145 1.19 0.107 4.37 0.0323 0.0037

In order to assess the change of the grains during the process, it is important to explore the initial

grains in a not deformed billet. An initial billet has been investigated in longitudinal and radial

are elongated, the subgrains are still equiaxed, this leads to an increasing length of high angle

boundaries and that the subgrains are continually rearranged. The cDRX, on the other hand, is

described by Gourdet and Montheillet [6] as an alternative theory for the development of subgrains.

During deformation, the number of low angle boundaries increase, in contrast to DRV, because of

transformation from low to high angle boundaries. These occur inside the grains. According to the

development of new grains, Blum at al. [7] show a purely geometrical approach, which is called

gDRX. The gDRX theory claims that elongated grains become serrated and spin off, with the result

that new grains have been formed.

The well-directed adjustment of the microstructure, as mentioned above, could be easier with the

help of finite element analysis, because at present the adjustment is done by experiences and trial

and error. In this connection, a simulation could be a tool to predict the changes in grain sizes. The

increasing capacity of the calculation resources has induced the utilization of finite element

simulations in metal forming analysis, especially in the extrusion sector. Questions of the friction

behavior inside the container [8, 9] and the material flow in two or three dimensions [10] are only

two examples of the simulation activities of the last years. The simulation is also used to optimize

the material flow or the longitudinal seam welds [11], where the numerical analysis of the

composite extrusion process is shown.

In [2] Schikorra et al. present an experimental method to evaluate parameters for a

microstructure model of Avrami, which allows the simulation of the grain size as a post variable by

the use of the DEFORM code. The experimental set up was backward extrusion equipment, and by

linear regression techniques between experimental data and FEM simulations, some temperature-

dependent material parameters were found. The simulation was carried out in two stages: first the

grain deformation was computed, thus providing a good agreement in terms of grain thickness

prediction, and then the heat treatment of the alloy was performed and computed. The results after

heat treatment was less accurate due to the lack of computation of some phenomena like spherical

coarse grains (PCG). The results from backward extrusion (microcups) trials were then extended to

the computation of the grain size for a hot extrusion process. The predictions were good in the dead

metal zone, in the shear zone and in the inner part of the profile while they were unacceptable on

the profile surface (absence of PCG computation) and inside the billet rest (inaccurate static

recrystallization prediction). Another explanation for the inaccuracy could be related to the

differences between the experimental set ups (backward in microcups, forward in billet extrusion).

To improve the model, in the present research work, a miniature hot forward extrusion press has

been designed to be closer to the real forward extrusion process the parameters will be determined

for. The new set up allows testing different alloys with different extrusion ratios, temperatures, and

speeds and quenching the pressed specimen immediately, which is imported to analyze the grains

during the process. This paper examines the shape of the grains in the different extrusion zones for

one alloy. Further, it investigates experimentally the structure of the dynamically recrystallized

grains during hot forward extrusion.

Experimental procedure

Material. The aluminum alloy which was used in this study is a commercial EN AW-7020, whose

chemical composition is shown in Table 1. The alloy is used in aerospace industry.

Table 1: Chemical composition of the EN AW-7020

Si Fe Cu Mn Mg Cr Zn Ti Ni

7020 [%] 0.113 0.174 0.0405 0.145 1.19 0.107 4.37 0.0323 0.0037

In order to assess the change of the grains during the process, it is important to explore the initial

grains in a not deformed billet. An initial billet has been investigated in longitudinal and radial


direction. The initial structure was completely recrystallized with an equiaxed grain size of 182 m,

measured with software of DHS solution, which shows that the pretreatment, especially the

annealing, was done well. The initial grain shape is provided as a basis for further investigations.

Set-up. The extrusion test was done with a miniature hot extrusion press (Fig. 1). The extrusion

ratio for this investigation was 11.11, the other process parameters are given in Fig. 1. The billet

was heated up together with the die and the container in an oven. The cooling agent was water.

Fig. 1: Set up and process parameters

Characterization. The specimen was analyzed in three directions, twice along the axis and once

transversely to it. For this, it was ground polished up to 2400 silicon carbide grinding paper, electro

polished with an acid composed of 78 ml perchloric acid, 90 ml H2O, 730 ml ethanol and 100 ml

butoxy ethanol (10 sec at 26 V), and etched in a Barker’s reagent [12] (90 sec at 20V). For electro

polishing and etching, the LectroPol-5 machine of Struers was used. As an electrical contact is

required for electro polishing, the specimen must be well prepared. The investigations showed that

an embedded specimen which still has a direct contact to the anode is the best solution. If the

specimens had not been embedded, the corner would have become round, because the side of

specimen would also be polished and etched. The microstructure was investigated by using the

polarized optical microscopy AxioImager.M1m of Zeiss.

Fig. 2 and 3 show an overview about the microstructure of the specimen. First the micrograph in

Fig. 2 was polished, etched and shot. After that, the grinding was done transversely to that area. It

was stopped at five different points (Fig. 3), marked from A to E in Fig. 2. The overview supports

the conclusion of an axial material flow. Long, thin grains are visible in the shear zone and in the

strand. Also the dead metal zone with its equiaxed grains is visible. Measurements of these grains

have shown that the grain size here is like the initial grain size. At last the strand was polished and

etched. It is remarkable that the grains are finer in the surface layer than in the middle of the profile.

The grains look very destructed. Accordingly, no static recrystallization has occurred.

direction. The initial structure was completely recrystallized with an equiaxed grain size of 182 m,

measured with software of DHS solution, which shows that the pretreatment, especially the

annealing, was done well. The initial grain shape is provided as a basis for further investigations.

Set-up. The extrusion test was done with a miniature hot extrusion press (Fig. 1). The extrusion

ratio for this investigation was 11.11, the other process parameters are given in Fig. 1. The billet

was heated up together with the die and the container in an oven. The cooling agent was water.

Fig. 1: Set up and process parameters

Characterization. The specimen was analyzed in three directions, twice along the axis and once

transversely to it. For this, it was ground polished up to 2400 silicon carbide grinding paper, electro

polished with an acid composed of 78 ml perchloric acid, 90 ml H2O, 730 ml ethanol and 100 ml

butoxy ethanol (10 sec at 26 V), and etched in a Barker’s reagent [12] (90 sec at 20V). For electro

polishing and etching, the LectroPol-5 machine of Struers was used. As an electrical contact is

required for electro polishing, the specimen must be well prepared. The investigations showed that

an embedded specimen which still has a direct contact to the anode is the best solution. If the

specimens had not been embedded, the corner would have become round, because the side of

specimen would also be polished and etched. The microstructure was investigated by using the

polarized optical microscopy AxioImager.M1m of Zeiss.

Fig. 2 and 3 show an overview about the microstructure of the specimen. First the micrograph in

Fig. 2 was polished, etched and shot. After that, the grinding was done transversely to that area. It

was stopped at five different points (Fig. 3), marked from A to E in Fig. 2. The overview supports

the conclusion of an axial material flow. Long, thin grains are visible in the shear zone and in the

strand. Also the dead metal zone with its equiaxed grains is visible. Measurements of these grains

have shown that the grain size here is like the initial grain size. At last the strand was polished and

etched. It is remarkable that the grains are finer in the surface layer than in the middle of the profile.

The grains look very destructed. Accordingly, no static recrystallization has occurred.


Fig. 2: Overview: Cross section polish of the specimen (EN AW-7020)


Fig. 4: Micrograph of the strand (EN AW-7020)



Fig. 4: Micrograph of the strand (EN AW-7020)


Simulation. The internal variables like strain, strain rate and temperature were calculated in

DEFORM 3D. The container, the die, and the ram were modeled as rigid bodies in the simulation.

A rigid-plastic material was assigned for the plastic flow behavior of the billet. Tetrahedron

elements were used and remeshing was active. The numbers of elements changed from 8,000 at the

beginning up to 18,000 at the end of the process. Mesh windows saved a constant element size in

the forming zone.

Fig. 5: a) Distribution of strain, b) Distribution of strain rate [1/s]

The maximum effective strain rate was 10 per second, the effective strain was 5. Fig.s 5a and 6

show the distribution of strain after the extrusion process. The dead metal zone is identifiable. In the

corner, both the strain and the strain rate (Fig 5) are zero. Further it becomes clear that the strain is

much higher at the surface than in the middle of the strand, while the forming process is finished at

these points.

Fig. 6: Distribution of strain in different sections

Simulation. The internal variables like strain, strain rate and temperature were calculated in

DEFORM 3D. The container, the die, and the ram were modeled as rigid bodies in the simulation.

A rigid-plastic material was assigned for the plastic flow behavior of the billet. Tetrahedron

elements were used and remeshing was active. The numbers of elements changed from 8,000 at the

beginning up to 18,000 at the end of the process. Mesh windows saved a constant element size in

the forming zone.

Fig. 5: a) Distribution of strain, b) Distribution of strain rate [1/s]

The maximum effective strain rate was 10 per second, the effective strain was 5. Fig.s 5a and 6

show the distribution of strain after the extrusion process. The dead metal zone is identifiable. In the

corner, both the strain and the strain rate (Fig 5) are zero. Further it becomes clear that the strain is

much higher at the surface than in the middle of the strand, while the forming process is finished at

these points.

Fig. 6: Distribution of strain in different sections


Fig. 7: Distribution of strain rate [1/s] in different sections

Results and Discussion

There are different rings to be identified in the cross micrograph of the strand (Fig. 4). The

grains at the surface layer are small. The size increases in the direction of the axis of the profile. In

the axis the calculated strain is between 2.5 and 3.33 and at the layer up to 5 (Fig. 5a). By

comparing of these two Fig.s, a connection between grain size and strain can be found. Different

forming zones and the material flow can be observed in both the micrographs (Fig. 2, 3) and the

calculated strain rate (Fig 5b, 7). Accordingly, a connection between grain size and strain rate can

also be found. These conclusions will help to find parameters for a grain size calculation model in

future.

The small differences between micrographs and simulation Fig.s could have different reasons.

The preparation of the specimens could be a little bevel, so the mid surface was not hit at all. Or the

cause is to be found in the simulation, because the rigid tools were calculated without thermal

effects.

A look at the grain shape reveals that the grains in the dead metal zone are still equiaxed. The

shape of the grains in the shear zone becomes more and more elongated and thin. The view of the

three directions of the micrographs allows the conclusion that the grains more and more take on the

pattern of spaghetti.

The extrusion ratio of 11.11 in this experiment was very small. For this reason no gDRX could

be observed, because strain and strain rate were not high enough. In order to produce smaller

grains, that means with the mechanism of gDRX, it is useful to increase the extrusion ratio, because

in this way the strain and the strain rate decreases.

Conclusion

A method was presented to investigate dynamically recrystallized grains during hot forward

extrusion. For this purpose a miniature press was designed. The design of the set up was explained

in detail. One specimen was investigated in three directions; hence the shape and the size of the

grains could be well analyzed. The method gives the possibility to work on the evolution of

microstructure during hot forward extrusion. The experimental investigations and numerical

calculations showed the potential to improve grain size calculation models which are available in

literature and to predict the grain size.

Fig. 7: Distribution of strain rate [1/s] in different sections


There are different rings to be identified in the cross micrograph of the strand (Fig. 4). The

grains at the surface layer are small. The size increases in the direction of the axis of the profile. In

the axis the calculated strain is between 2.5 and 3.33 and at the layer up to 5 (Fig. 5a). By

comparing of these two Fig.s, a connection between grain size and strain can be found. Different

forming zones and the material flow can be observed in both the micrographs (Fig. 2, 3) and the

calculated strain rate (Fig 5b, 7). Accordingly, a connection between grain size and strain rate can

also be found. These conclusions will help to find parameters for a grain size calculation model in

future.

The small differences between micrographs and simulation Fig.s could have different reasons.

The preparation of the specimens could be a little bevel, so the mid surface was not hit at all. Or the

cause is to be found in the simulation, because the rigid tools were calculated without thermal

effects.

A look at the grain shape reveals that the grains in the dead metal zone are still equiaxed. The

shape of the grains in the shear zone becomes more and more elongated and thin. The view of the

three directions of the micrographs allows the conclusion that the grains more and more take on the

pattern of spaghetti.

The extrusion ratio of 11.11 in this experiment was very small. For this reason no gDRX could

be observed, because strain and strain rate were not high enough. In order to produce smaller

grains, that means with the mechanism of gDRX, it is useful to increase the extrusion ratio, because

in this way the strain and the strain rate decreases.

Conclusion

A method was presented to investigate dynamically recrystallized grains during hot forward

extrusion. For this purpose a miniature press was designed. The design of the set up was explained

in detail. One specimen was investigated in three directions; hence the shape and the size of the

grains could be well analyzed. The method gives the possibility to work on the evolution of

microstructure during hot forward extrusion. The experimental investigations and numerical

calculations showed the potential to improve grain size calculation models which are available in

literature and to predict the grain size.


Acknowledgments

This work was carried out with the financial support of the Researcher Group 922 (FOR 922),

funded by the German Research Foundation (DFG). This support is greatly acknowledged.

References

[1] E. D. Sweet et al.: Effects of Extrusion Parameters on Coarse Grain Surfache Layer in 6xxx

Series Extrusions, ET 2004;

[2] M. Schikorra, L. Donati, L. Tomesani, A.E. Tekkaya: Microstructure analysis of aluminum

extrusion: Prediction of microstructure on AA6060 alloy, Journal of Materials Processing

Technology, Volume 201 (2008), pp. 156-162;

[3] H. Mecking , U.F. Kocks: Kinetics of flow and strain-hardening, Acta Metallurgica, Volume 29

(1981), pp. 1865-1875;

[4] H.J. McQueen, W. Blum: Dynamic recovery: sufficient mechanism in the hot deformation of

Al (<99.99), Materials Science and Engineering A, Volume 290(2000), pp 95-107;

[5] H.J. McQueen: Deficiencies in Continuous DRX Hypothesis as a Substitute for DRX Theory,

Materials Forum, Volume 28 (2004), pp. 351-356;

[6] S. Gourdet, F. Montheillet: A model of continuous dynamic recrystallization, Acta Materialia,

Volume 51 (2003), pp. 2685-2699;

[7] W. Blum, Q. Zhu, R. Merkel, H.J. McQueen: Geometric dynamic recrystallization in hot

torsion of Al-5Mg-0.6Mn (AA5083), Materials Science and Engineering A, Volume 205

(1996), pp. 23-30;

[8] M. Bakhshi-Jooybari: A theoretical and experimental study of friction in metal forming by the

use of the forward extrusion process, Journal of Materials Processing Technology, Volume

125-126 (2002), pp. 369-374;


AA6060 aluminum alloy, process analysis and monitoring, Journal of Materials Processing

Technology, Volume 191 (2007), pp. 288-292

[10] S. Kalz: Numerische Simulation des Strangpresse mit Hilfe der Methode der finiten Elemente,

Dr.-Ing. Dissertation, Institut für bildsame Formgebung, Aachen, IBSN 3-8265-9718-4 (2001)

[11] T. Kloppenborg, M. Schikorra, M. Schomäcker, A.E. Tekkaya: Numerical Optimization of

Bearing Length in Composite Extrusion Processes, Proceedings of International Workshop and

Extrusion Benchmark, Bologna (Italy), 20.-21.Sept. 2007, Zürich: Trans Tech Publications Ltd

(2008), pp. 47-54. - ISBN 0-87849-467-7;

[12] G. Petzow: Metallographisches, Keramographisches, Plastographisches Ätzen, 6. überarbeitete

Auflage, Nachdruck, September 2006, Borntraeger, p. 72, IBSN 013000170;

Acknowledgments

This work was carried out with the financial support of the Researcher Group 922 (FOR 922),

funded by the German Research Foundation (DFG). This support is greatly acknowledged.

References

[1] E. D. Sweet et al.: Effects of Extrusion Parameters on Coarse Grain Surfache Layer in 6xxx

Series Extrusions, ET 2004;

[2] M. Schikorra, L. Donati, L. Tomesani, A.E. Tekkaya: Microstructure analysis of aluminum

extrusion: Prediction of microstructure on AA6060 alloy, Journal of Materials Processing

Technology, Volume 201 (2008), pp. 156-162;

[3] H. Mecking , U.F. Kocks: Kinetics of flow and strain-hardening, Acta Metallurgica, Volume 29

(1981), pp. 1865-1875;

[4] H.J. McQueen, W. Blum: Dynamic recovery: sufficient mechanism in the hot deformation of

Al (<99.99), Materials Science and Engineering A, Volume 290(2000), pp 95-107;

[5] H.J. McQueen: Deficiencies in Continuous DRX Hypothesis as a Substitute for DRX Theory,

Materials Forum, Volume 28 (2004), pp. 351-356;

[6] S. Gourdet, F. Montheillet: A model of continuous dynamic recrystallization, Acta Materialia,

Volume 51 (2003), pp. 2685-2699;

[7] W. Blum, Q. Zhu, R. Merkel, H.J. McQueen: Geometric dynamic recrystallization in hot

torsion of Al-5Mg-0.6Mn (AA5083), Materials Science and Engineering A, Volume 205

(1996), pp. 23-30;

[8] M. Bakhshi-Jooybari: A theoretical and experimental study of friction in metal forming by the

use of the forward extrusion process, Journal of Materials Processing Technology, Volume

125-126 (2002), pp. 369-374;


AA6060 aluminum alloy, process analysis and monitoring, Journal of Materials Processing

Technology, Volume 191 (2007), pp. 288-292

[10] S. Kalz: Numerische Simulation des Strangpresse mit Hilfe der Methode der finiten Elemente,

Dr.-Ing. Dissertation, Institut für bildsame Formgebung, Aachen, IBSN 3-8265-9718-4 (2001)

[11] T. Kloppenborg, M. Schikorra, M. Schomäcker, A.E. Tekkaya: Numerical Optimization of

Bearing Length in Composite Extrusion Processes, Proceedings of International Workshop and

Extrusion Benchmark, Bologna (Italy), 20.-21.Sept. 2007, Zürich: Trans Tech Publications Ltd

(2008), pp. 47-54. - ISBN 0-87849-467-7;

[12] G. Petzow: Metallographisches, Keramographisches, Plastographisches Ätzen, 6. überarbeitete

Auflage, Nachdruck, September 2006, Borntraeger, p. 72, IBSN 013000170;


Modeling and Simulation of Microstructure Evolution in Extruded Aluminum Profiles

F. Parvizian1, a, T. Kayser1, b , B. Svendsen1, c 1Institute of Mechanics, Dortmund University of Technology, Leonhard-Euler-Str. 5, D-44227,

Dortmund, Germany

a [email protected], b [email protected], c [email protected]

Keywords: Aluminum alloys, Extrusion, Microstructure, Functionally-graded material (FGM), Simulation.

Abstract. The purpose of this work is to predict the microstructure evolution of aluminum alloys

during hot metal forming processes using the Finite Element Method (FEM). Here, the focus will be

on the extrusion process of aluminum alloys. Several micromechanical mechanisms such as

diffusion, recovery, recrystallization and grain growth are involved in various subsequent stages of

the extrusion and the cooling process afterward. The evolution of microstructure parameters is

motivated by plastic deformation and temperature. A number of thermomechanical aspects such as

plastic deformation, heat transfer between the material and the container, heat generated by friction,

and cooling process after the extrusion are involved in the extrusion process and result in changes in

temperature and microstructure parameters subsequently. Therefore a thermomechanically coupled

modeling and simulation which includes all of these aspects is required for an accurate prediction of

the microstructure evolution. A brief explanation of the isotropic thermoelastic viscoplastic material

model including some of the simulation results of this model, which is implemented as a user

material (UMAT) in the FEM software ABAQUS, will be given. The microstructure variables are

thereby modeled as internal state variables. The simulation results are finally compared with some

experimental results.

Introduction

Extruded aluminum profiles with low density and high ductility are widely used in the automobile

and aircraft industry. The structural behavior of extruded profiles can be optimized with help of

functionally-graded material (FGM) properties according to the design requirements of the final

product. In other words, the microstructure properties of such profiles are locally varied so that the

desired material behavior for different parts of the profile is achieved.

Functionally graded material properties can be obtained in two steps during the extrusion

process: at first reorientation of grains in extrusion direction, dynamic recovery and geometric

dynamic recrystallization (GDX) during the extrusion process, and secondly grain growth and static

recrystallization during cooling and annealing process. These processes can generate a

heterogeneous microstructure distribution in the profile. The evolution of microstructure variables

can be controlled by process parameters like temperature, extrusion rate and the velocity of the

process as well as the cooling and annealing conditions.

The development of microstructure parameters such as grain size, dislocation density and

misorientation angle is caused by plastic deformation and temperature. The stored energy which

provides the source for all the property changes that are typical of deformed metals is derived from

point defects and dislocations that are generated during the deformation. At higher temperatures

most of the stored energy is derived from the accumulation of dislocations, hence, the density,

distribution and arrangement of dislocations are significant for the prediction of microstructure

evolution. The stored energy is distributed heterogeneously in the material.

Therefore to predict the microstructure evolution during the cooling and annealing process, it is

important to determine the distribution of the defects resulting from deformation [1].

Modeling and Simulation of Microstructure Evolution in Extruded Aluminum Profiles

F. Parvizian1, a, T. Kayser1, b , B. Svendsen1, c 1Institute of Mechanics, Dortmund University of Technology, Leonhard-Euler-Str. 5, D-44227,

Dortmund, Germany


Keywords: Aluminum alloys, Extrusion, Microstructure, Functionally-graded material (FGM), Simulation.

Abstract. The purpose of this work is to predict the microstructure evolution of aluminum alloys

during hot metal forming processes using the Finite Element Method (FEM). Here, the focus will be

on the extrusion process of aluminum alloys. Several micromechanical mechanisms such as

diffusion, recovery, recrystallization and grain growth are involved in various subsequent stages of

the extrusion and the cooling process afterward. The evolution of microstructure parameters is

motivated by plastic deformation and temperature. A number of thermomechanical aspects such as

plastic deformation, heat transfer between the material and the container, heat generated by friction,

and cooling process after the extrusion are involved in the extrusion process and result in changes in

temperature and microstructure parameters subsequently. Therefore a thermomechanically coupled

modeling and simulation which includes all of these aspects is required for an accurate prediction of

the microstructure evolution. A brief explanation of the isotropic thermoelastic viscoplastic material

model including some of the simulation results of this model, which is implemented as a user

material (UMAT) in the FEM software ABAQUS, will be given. The microstructure variables are

thereby modeled as internal state variables. The simulation results are finally compared with some

experimental results.

Introduction

Extruded aluminum profiles with low density and high ductility are widely used in the automobile

and aircraft industry. The structural behavior of extruded profiles can be optimized with help of

functionally-graded material (FGM) properties according to the design requirements of the final

product. In other words, the microstructure properties of such profiles are locally varied so that the

desired material behavior for different parts of the profile is achieved.

Functionally graded material properties can be obtained in two steps during the extrusion

process: at first reorientation of grains in extrusion direction, dynamic recovery and geometric

dynamic recrystallization (GDX) during the extrusion process, and secondly grain growth and static

recrystallization during cooling and annealing process. These processes can generate a

heterogeneous microstructure distribution in the profile. The evolution of microstructure variables

can be controlled by process parameters like temperature, extrusion rate and the velocity of the

process as well as the cooling and annealing conditions.

The development of microstructure parameters such as grain size, dislocation density and

misorientation angle is caused by plastic deformation and temperature. The stored energy which

provides the source for all the property changes that are typical of deformed metals is derived from

point defects and dislocations that are generated during the deformation. At higher temperatures

most of the stored energy is derived from the accumulation of dislocations, hence, the density,

distribution and arrangement of dislocations are significant for the prediction of microstructure

evolution. The stored energy is distributed heterogeneously in the material.

Therefore to predict the microstructure evolution during the cooling and annealing process, it is

important to determine the distribution of the defects resulting from deformation [1].


Material Model

From a phenomenological viewpoint, the behavior of polycrystalline aluminum alloys during

technological processes like extrusion is fundamentally thermoelastic and viscoplastic in nature. For

simplicity, we begin by assuming that the material behavior is isotropic. More generally, the

distribution of grain orientation, grain size, and grain shape, will result in anisotropic behavior. For

the time being, we assume that the high homologous temperatures involved result in a reduction of

the strength of anisotropy due to these factors. In this case, the stress state in the material can be

modeled via the thermoelastic Hooke form

for the Kirchhoff stress in terms of the elastic left logarithmic stretch . Here, represents

the elastic bulk modulus, the elastic shear moduli, the thermal expansion, and the heat

capacity, all at the reference temperature . In addition, is the absolute temperature. Further,

is the deviatoric part of . Neglecting any deformation-dependent

damage and assuming inelastically incompressible von-Mises flow, the evolution of is given

by the (objective) associated flow rule

in terms of the inelastic right Cauchy-Green deformation and accumulated equivalent inelastic

deformation . Here, is the von Mises effective stress measure

determined by the Kirchhoff stress. In the current thermodynamic approach, this determines the

evolution of via the Zener-Holloman form

[2] in terms of the Zener-Holloman parameter . The evolution of drives in

turn that of the (non-dimensional) dislocation density via the experimentally-

established Voce form , where represents the saturation value of the

dislocation density . In this case, varies between 0 and 1 at a rate determined by .

Likewise, the development of the (non-dimensional) subgrain size is given by the

experimentally-established [2] Holt relation , where is the saturation value.

On this basis, decreases from its initial value to 1 at a rate determined by .

Parameter values used for Al 6060 in the current work are , ,

, , , , ,

, , , , , . In addition, for the

temperature equation, we require the value of the coefficient of thermal conductivity

for the Fourier model, as well as that of the heat capacity. In

addition, the rate of heating is given by in terms of the continuum

rate of deformation via the Taylor-Quinney approximation and Taylor-Quinney coefficient . In

the current work, is assumed. It has been shown in [3] that is in fact not a constant but

rather depends on strain and strain-rate to varying degrees. In the following, this coefficient will be

(1)

(2)

(3)

Material Model

From a phenomenological viewpoint, the behavior of polycrystalline aluminum alloys during

technological processes like extrusion is fundamentally thermoelastic and viscoplastic in nature. For

simplicity, we begin by assuming that the material behavior is isotropic. More generally, the

distribution of grain orientation, grain size, and grain shape, will result in anisotropic behavior. For

the time being, we assume that the high homologous temperatures involved result in a reduction of

the strength of anisotropy due to these factors. In this case, the stress state in the material can be

modeled via the thermoelastic Hooke form

for the Kirchhoff stress in terms of the elastic left logarithmic stretch . Here, represents

the elastic bulk modulus, the elastic shear moduli, the thermal expansion, and the heat

capacity, all at the reference temperature . In addition, is the absolute temperature. Further,

is the deviatoric part of . Neglecting any deformation-dependent

damage and assuming inelastically incompressible von-Mises flow, the evolution of is given

by the (objective) associated flow rule

in terms of the inelastic right Cauchy-Green deformation and accumulated equivalent inelastic

deformation . Here, is the von Mises effective stress measure

determined by the Kirchhoff stress. In the current thermodynamic approach, this determines the

evolution of via the Zener-Holloman form

[2] in terms of the Zener-Holloman parameter . The evolution of drives in

turn that of the (non-dimensional) dislocation density via the experimentally-

established Voce form , where represents the saturation value of the

dislocation density . In this case, varies between 0 and 1 at a rate determined by .

Likewise, the development of the (non-dimensional) subgrain size is given by the

experimentally-established [2] Holt relation , where is the saturation value.

On this basis, decreases from its initial value to 1 at a rate determined by .

Parameter values used for Al 6060 in the current work are , ,

, , , , ,

, , , , , . In addition, for the

temperature equation, we require the value of the coefficient of thermal conductivity

for the Fourier model, as well as that of the heat capacity. In

addition, the rate of heating is given by in terms of the continuum

rate of deformation via the Taylor-Quinney approximation and Taylor-Quinney coefficient . In

the current work, is assumed. It has been shown in [3] that is in fact not a constant but

rather depends on strain and strain-rate to varying degrees. In the following, this coefficient will be

(1)

(2)

(3)


treated as constant as there is no experimental data relevant to the determination of for the

materials of interest here.

Simulation Aspects:

Several numerical aspects should be considered for the accurate simulation of the extrusion process

[4]. Element distortion due to the large deformation of material can be prevented by using an

adaptive remeshing. The approach which is applied in this work is based on new meshing of the

deformed geometry after each step of the simulation. In contrast to mesh refinement, this method

helps us to improve the quality of mesh and decrease the number of elements during the simulation.

After each remeshing step, the solution of the old mesh including all the internal state variables

should be transferred to the new mesh. An interpolation scheme is used for the solution mapping. In

contrast to refinement, remeshing does not change the element density in the new mesh. This means

less interpolation of the result is required and therefore the accuracy of the final solution will be

higher.

Realistic boundary conditions such as friction and thermal contact have a significant influence on

the deformation of material and on the evolution of microstructure parameters during the simulation

of the extrusion process.

The heat transfer between the contacted surfaces is modeled as

,

where is the gap conductance between two surfaces and and are the surface temperatures.

The gap conductance can be defined as

,

where is the average of the temperatures at surfaces A and B, is the spacing between A

and B, is the contact pressure transmitted across the interface between A and B and is

the average of any predefined field variable at A and B. This model is applied for heat transfer

between material and container and also between the extruded profile and the air during the cooling

process. The convection and surface radiation are not considered in this work.

The contact simulation in this work is based on surface-to-surface method which provides a

more physical contact condition compared to node-to-surface contact.

Results

The simulation is performed with the commercial FEM software ABAQUS Standard with the

element type CAX4RT which has temperature as one degree of freedom and is suitable for the

coupled temperature-displacement simulations. The geometry of the axisymmetric model is

described in Fig. 1. As it is shown, die, ram and container are all meshed and considered as

deformable. The ram moves with 5 mm/s and forces the material block to pass through the die. Here

the initial temperature of the block is 673 °K whereas the temperature of the die and container is

573 °K and the ratio of the block diameter to extruded profile diameter is .

The described material model is implemented as user material (UMAT) in the FEM software

ABAQUS. Fig. 2 shows the different zones of deformation from experimental results [5]. As it can

be seen there are three different zones distinguishable: main deformation zone (MDZ), shear

intensive zone (SIZ) and dead material zone (DMZ).

(4)

(5)

treated as constant as there is no experimental data relevant to the determination of for the

materials of interest here.

Simulation Aspects:

Several numerical aspects should be considered for the accurate simulation of the extrusion process

[4]. Element distortion due to the large deformation of material can be prevented by using an

adaptive remeshing. The approach which is applied in this work is based on new meshing of the

deformed geometry after each step of the simulation. In contrast to mesh refinement, this method

helps us to improve the quality of mesh and decrease the number of elements during the simulation.

After each remeshing step, the solution of the old mesh including all the internal state variables

should be transferred to the new mesh. An interpolation scheme is used for the solution mapping. In

contrast to refinement, remeshing does not change the element density in the new mesh. This means

less interpolation of the result is required and therefore the accuracy of the final solution will be

higher.

Realistic boundary conditions such as friction and thermal contact have a significant influence on

the deformation of material and on the evolution of microstructure parameters during the simulation

of the extrusion process.

The heat transfer between the contacted surfaces is modeled as

,

where is the gap conductance between two surfaces and and are the surface temperatures.

The gap conductance can be defined as

,

where is the average of the temperatures at surfaces A and B, is the spacing between A

and B, is the contact pressure transmitted across the interface between A and B and is

the average of any predefined field variable at A and B. This model is applied for heat transfer

between material and container and also between the extruded profile and the air during the cooling

process. The convection and surface radiation are not considered in this work.

The contact simulation in this work is based on surface-to-surface method which provides a

more physical contact condition compared to node-to-surface contact.

Results

The simulation is performed with the commercial FEM software ABAQUS Standard with the

element type CAX4RT which has temperature as one degree of freedom and is suitable for the

coupled temperature-displacement simulations. The geometry of the axisymmetric model is

described in Fig. 1. As it is shown, die, ram and container are all meshed and considered as

deformable. The ram moves with 5 mm/s and forces the material block to pass through the die. Here

the initial temperature of the block is 673 °K whereas the temperature of the die and container is

573 °K and the ratio of the block diameter to extruded profile diameter is .

The described material model is implemented as user material (UMAT) in the FEM software

ABAQUS. Fig. 2 shows the different zones of deformation from experimental results [5]. As it can

be seen there are three different zones distinguishable: main deformation zone (MDZ), shear

intensive zone (SIZ) and dead material zone (DMZ).

(4)

(5)


Fig. 1: Geometry and configuration of the model for simulation with the FEM software ABAQUS.

In Fig. 2 (left) the displacement vector of the material during the simulation is presented. As it

can be seen in the corner of the container the displacement vectors have less density and are smaller

compared to the middle of the block. These zones represent the dead material zone and main

deformation zone, respectively.

Fig. 2: Displacement vector of material during simulation of the extrusion process (left) and

different zones of deformation from experiment (right).

Fig. 3 shows the distribution of equivalent plastic strain (left) and the non-dimensional grain size

(right) in the simulation of extrusion. The equivalent plastic strain has higher values in the die exit

area where the material undergoes a larger deformation and also close to the corner of the container

due to friction and sticking of the material.

Material block

Ram

Die

Container

r

R

Fig. 3: Distribution of equivalent plastic strain (left) and distribution of non-dimensional grain size

(right).

coarser subgrain

finer subgrain

I: Dead zone

II: Shear zone

III: Deformation zone

IV: Die exit

Fig. 1: Geometry and configuration of the model for simulation with the FEM software ABAQUS.

In Fig. 2 (left) the displacement vector of the material during the simulation is presented. As it

can be seen in the corner of the container the displacement vectors have less density and are smaller

compared to the middle of the block. These zones represent the dead material zone and main

deformation zone, respectively.

Fig. 2: Displacement vector of material during simulation of the extrusion process (left) and

different zones of deformation from experiment (right).

Fig. 3 shows the distribution of equivalent plastic strain (left) and the non-dimensional grain size

(right) in the simulation of extrusion. The equivalent plastic strain has higher values in the die exit

area where the material undergoes a larger deformation and also close to the corner of the container

due to friction and sticking of the material.

Material block

Ram

Die

Container

r

R

Fig. 3: Distribution of equivalent plastic strain (left) and distribution of non-dimensional grain size

(right).

coarser subgrain

finer subgrain

I: Dead zone

II: Shear zone

III: Deformation zone

IV: Die exit


The distribution of non-dimensional grain size in Fig. 3 (right) shows that in the areas where the

deformation is smaller (in DMZ and in the middle of the block close to the ram) the grain size is not

changing during the extrusion and has almost the original grain size of the material before

deformation, whereas in the die exit, MDZ and SIZ, the size of grains gets smaller. This distribution

is non-dimensional and is qualitatively comparable with the experiment.

In Fig. 4 and Fig. 5 the evolution of the equivalent plastic strain, temperature and non-

dimensional subgrain size in die exit, DMZ and MDZ for two different contact conditions are

shown. Comparing these two cases shows the different behavior of the microstructure evolution due

to friction effect. Fig. 4 (a) demonstrates that the equivalent plastic strain is mainly developed in die

exit area and in MDZ whereas in the dead material zone it remains almost zero. The evolution of

equivalent plastic strain results in the evolution of temperature and state dependent variables such as

subgrain size. It can be seen from Fig. 4 (b) that the temperature raises mostly in the die exit area

with higher equivalent plastic strain. In the DMZ the temperature decreases due to thermal contact

of the material block with the container and die with lower temperatures. The non-dimensional

subgrain size decreases rapidly in the die exit area and saturates faster than other areas. In the MDZ

the non-dimensional subgrain size decreases with a smoother rate and ends at a higher saturation

value compared to the die exit area. The evolution of non-dimensional subgrain size in the DMZ is

very slow and the size of grains remains almost unchanged.

The evolution of equivalent plastic strain in case of no friction shown in Fig. 5 (a) in the die exit

area is relatively faster compared to Fig. 4 (a) in presence of friction. In absence of friction, there is

less resistance against material movement and material can move faster and this increases the rate

of evolution of equivalent plastic strain. This can be seen even in the corner of the container

(DMZ). The temperature raise in both cases follows a similar pattern, in the MDZ the temperature

raises due to plastic deformation and in the DMZ the temperature decreases because of the heat flux

from material to container and die. The size of grains in absence of friction decreases rapidly in the

DMZ which is in contrast to the experimental results in Fig. 2.

Summary and conclusion:

Thermomechanically coupled simulation of extrusion process with help of a thermo-elastic visco-

plastic model and new remeshing method is presented in this work. This model includes the

microstructure variables as internal state dependent variables. The significant influence of boundary

conditions on the evolution of microstructure parameters in different areas of the material block

during the extrusion process is shown. The simulation results are in qualitative agreement with

experimental results. A quantitative comparison requires more knowledge of experimental

parameters and will be presented in upcoming works.

Acknowledgement

The authors would like to appreciate the financial support of Transregional Collaborative Research

Center (TRR30) funded by the German Research Foundation (DFG).

The distribution of non-dimensional grain size in Fig. 3 (right) shows that in the areas where the

deformation is smaller (in DMZ and in the middle of the block close to the ram) the grain size is not

changing during the extrusion and has almost the original grain size of the material before

deformation, whereas in the die exit, MDZ and SIZ, the size of grains gets smaller. This distribution

is non-dimensional and is qualitatively comparable with the experiment.

In Fig. 4 and Fig. 5 the evolution of the equivalent plastic strain, temperature and non-

dimensional subgrain size in die exit, DMZ and MDZ for two different contact conditions are

shown. Comparing these two cases shows the different behavior of the microstructure evolution due

to friction effect. Fig. 4 (a) demonstrates that the equivalent plastic strain is mainly developed in die

exit area and in MDZ whereas in the dead material zone it remains almost zero. The evolution of

equivalent plastic strain results in the evolution of temperature and state dependent variables such as

subgrain size. It can be seen from Fig. 4 (b) that the temperature raises mostly in the die exit area

with higher equivalent plastic strain. In the DMZ the temperature decreases due to thermal contact

of the material block with the container and die with lower temperatures. The non-dimensional

subgrain size decreases rapidly in the die exit area and saturates faster than other areas. In the MDZ

the non-dimensional subgrain size decreases with a smoother rate and ends at a higher saturation

value compared to the die exit area. The evolution of non-dimensional subgrain size in the DMZ is

very slow and the size of grains remains almost unchanged.

The evolution of equivalent plastic strain in case of no friction shown in Fig. 5 (a) in the die exit

area is relatively faster compared to Fig. 4 (a) in presence of friction. In absence of friction, there is

less resistance against material movement and material can move faster and this increases the rate

of evolution of equivalent plastic strain. This can be seen even in the corner of the container

(DMZ). The temperature raise in both cases follows a similar pattern, in the MDZ the temperature

raises due to plastic deformation and in the DMZ the temperature decreases because of the heat flux

from material to container and die. The size of grains in absence of friction decreases rapidly in the

DMZ which is in contrast to the experimental results in Fig. 2.

Summary and conclusion:

Thermomechanically coupled simulation of extrusion process with help of a thermo-elastic visco-

plastic model and new remeshing method is presented in this work. This model includes the

microstructure variables as internal state dependent variables. The significant influence of boundary

conditions on the evolution of microstructure parameters in different areas of the material block

during the extrusion process is shown. The simulation results are in qualitative agreement with

experimental results. A quantitative comparison requires more knowledge of experimental

parameters and will be presented in upcoming works.

Acknowledgement

The authors would like to appreciate the financial support of Transregional Collaborative Research

Center (TRR30) funded by the German Research Foundation (DFG).


Fig. 4: Evolution of (a) equivalent plastic strain, (b) temperature and (c) non-dimensional grain size

in die exit area (point 3 in Fig. 2 right), dead material zone (point 1 in Fig. 2 right) and main

deformation zone (point 2 in Fig. 2 right), during the extrusion process simulation with considering

friction in contact simulation.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Eq

uiv

ale

nt

pla

sti

c s

tra

in

die Exit

DMZ

MDZ

550

600

650

700

750

800

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Te

mp

era

ture

(K

)

die exit

DMZ

MDZ

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

No

n-d

ime

ns

ion

al g

rain

siz

e

die exit

DMZ

MDZ

(a)

(b)

(c)



deformation zone (point 2 in Fig. 2 right), during the extrusion process simulation with considering

friction in contact simulation.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Eq

uiv

ale

nt

pla

sti

c s

tra

in

die Exit

DMZ

MDZ

550

600

650

700

750

800

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Te

mp

era

ture

(K

)

die exit

DMZ

MDZ

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

No

n-d

ime

ns

ion

al g

rain

siz

e

die exit

DMZ

MDZ

(a)

(b)

(c)




deformation zone (point 2 in Fig. 2 right) during the extrusion process simulation without

considering friction in contact simulation.

References

[1] F.J. Humphreys and M. Hatherly: Recrystallization and Related Annealing Phenomena,

ELSEVIER, Second Edition (2004).

[2] C. M. Sellars and Q. Zhu: Microstructural modelling of aluminium alloys during

thermomechanical processing, Materials Science and Engineering A, Vol. 280 (2000), pp. 1-7.

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Eq

uiv

ale

nt

pla

sti

c s

tra

in

die exit

DMZ

MDZ

550

600

650

700

750

800

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Te

mp

era

ture

(K

)

die exit

DMZ

MDZ

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

No

n-d

ime

ns

ion

al g

rain

siz

e

die exit

DMZ

MDZ

(a)

(b)

(c)



deformation zone (point 2 in Fig. 2 right) during the extrusion process simulation without

considering friction in contact simulation.

References

[1] F.J. Humphreys and M. Hatherly: Recrystallization and Related Annealing Phenomena,

ELSEVIER, Second Edition (2004).

[2] C. M. Sellars and Q. Zhu: Microstructural modelling of aluminium alloys during

thermomechanical processing, Materials Science and Engineering A, Vol. 280 (2000), pp. 1-7.

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Eq

uiv

ale

nt

pla

sti

c s

tra

in

die exit

DMZ

MDZ

550

600

650

700

750

800

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Te

mp

era

ture

(K

)

die exit

DMZ

MDZ

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

No

n-d

ime

ns

ion

al g

rain

siz

e

die exit

DMZ

MDZ

(a)

(b)

(c)


[3] P. Rosakis, A. J. Rosakis, G. Ravichandran, J. Hodowany: A thermodynamic internal variable

model for the partition of plastic work into heat and stored energy in metals, Journal of the

Mechanics and Physics of Solids, Vol. 48, Issue 3 (2000), pp. 581-607.

[4] F. Parvizian, T. Kayser, C. Hortig, B. Svendsen: Thermomechanical modeling and simulation

of aluminumalloy behavior during extrusion and cooling, Journal of Materials Processing

Technology, Vol. 209, Issue 2 (2009), pp. 876-883.

[5] M. Schikorra, L. Donati, L. Tomesani, E. Tekkaya: Microstructure analysis of aluminum

extrusion: grain size distribution in AA6060, AA6082 and AA7075 alloys, Journal of

Mechanical Science and Technology, Vol. 21 (2007), pp. 1445-1451.

[3] P. Rosakis, A. J. Rosakis, G. Ravichandran, J. Hodowany: A thermodynamic internal variable

model for the partition of plastic work into heat and stored energy in metals, Journal of the

Mechanics and Physics of Solids, Vol. 48, Issue 3 (2000), pp. 581-607.

[4] F. Parvizian, T. Kayser, C. Hortig, B. Svendsen: Thermomechanical modeling and simulation

of aluminumalloy behavior during extrusion and cooling, Journal of Materials Processing

Technology, Vol. 209, Issue 2 (2009), pp. 876-883.

[5] M. Schikorra, L. Donati, L. Tomesani, E. Tekkaya: Microstructure analysis of aluminum

extrusion: grain size distribution in AA6060, AA6082 and AA7075 alloys, Journal of

Mechanical Science and Technology, Vol. 21 (2007), pp. 1445-1451.


Simulation of the Quench Sensitivity of the Aluminum Alloy 6082

A. Güzel1,a, A. Jäger1,b, N. Ben Khalifa1,c , and A. E. Tekkaya1,d 1TU Dortmund, Institute of Forming Technology and Lightweight Construction (IUL), Germany


Keywords: Aluminum, Jominy End-Quench Test, Finite Element Analysis. Abstract. A method for the numerical estimation of the final hardness distribution of heat treated aluminum alloys was developed and implemented into a commercial finite element (FE) tool. Jominy end-quench tests were carried out in order to determine the quench sensitivity of the aluminum alloy EN AW-6082. The hardness distribution of the alloy after end-quenching was related to the corresponding cooling rates. The derived relation was tested for an industrial application by investigating the local heat treatment of a prototype crash absorbing structure. Numerical estimations were validated with experimental measurements. Effectiveness of the derived method and possible improvements were discussed.

Introduction

Energy shortage and the subsequent environmental issues increased the importance of using light weight structures, especially in the automotive industry. Extruded products made of hardenable aluminum alloys of the type Al-Mg-Si are widely used as light weight construction profiles in vehicles. These materials achieve the desired values of their mechanical properties by heat treatment after the semi-finished material production. For the aluminum alloy under consideration, mechanical properties can be enhanced by a finely grained microstructure and a dispersion of Mg2Si in the lattice structure. Hardening by precipitation takes place in the stages of heat treatment, such as solution annealing, quenching and aging [1]. After a hot metal forming operation, quenching followed by an aging operation yields fine grains with supersaturated solutions, which have a direct influence on the final mechanical properties such as yield strength and hardness.

In order to determine the hardenability of a material, an experimental method known as Jominy end-quench test is widely used. The test involves heating a standard cylindrical bar up to solution soaking temperature and then transferring it to a quenching fixture where the specimen is held vertically and through which a jet of water is directed against the bottom of the specimen. This results in a gradually varied cooling rate along the length of the specimen, with the maximum at the bottom. After the specimen has been fully quenched, it is aged in order to achieve the maximally attainable hardness values of the material. Finally, hardness measurements are performed along the length of the specimen’s surface [2]. The method has been designed for ferrous alloys. Therefore, up to now this method has found only little application for non-ferrous materials such as aluminum. Robinson and Tanner [3] have implemented the Jominy end-quench technique in order to determine the residual stresses in quenched high strength aluminum forgings. Steele et al. [4] studied the susceptibility of 6XXX alloys to grain boundary precipitation during quenching. Cavazos and Colás [5] and Dolan et al. [2] implemented the method and presented a continuous cooling property diagram for aluminum alloys 6063 and 7000 series, respectively.

The present research work aims at relating the hardness distribution of the aluminum alloy 6082 after quenching to the corresponding rates of cooling. This relation was formulized and parameterized for the alloy under consideration and implemented into the commercial FE tool DEFORMTM. The effectiveness of the developed strategy was tested by the application of an industrial problem.

Simulation of the Quench Sensitivity of the Aluminum Alloy 6082

A. Güzel1,a, A. Jäger1,b, N. Ben Khalifa1,c , and A. E. Tekkaya1,d 1TU Dortmund, Institute of Forming Technology and Lightweight Construction (IUL), Germany


Keywords: Aluminum, Jominy End-Quench Test, Finite Element Analysis. Abstract. A method for the numerical estimation of the final hardness distribution of heat treated aluminum alloys was developed and implemented into a commercial finite element (FE) tool. Jominy end-quench tests were carried out in order to determine the quench sensitivity of the aluminum alloy EN AW-6082. The hardness distribution of the alloy after end-quenching was related to the corresponding cooling rates. The derived relation was tested for an industrial application by investigating the local heat treatment of a prototype crash absorbing structure. Numerical estimations were validated with experimental measurements. Effectiveness of the derived method and possible improvements were discussed.

Introduction

Energy shortage and the subsequent environmental issues increased the importance of using light weight structures, especially in the automotive industry. Extruded products made of hardenable aluminum alloys of the type Al-Mg-Si are widely used as light weight construction profiles in vehicles. These materials achieve the desired values of their mechanical properties by heat treatment after the semi-finished material production. For the aluminum alloy under consideration, mechanical properties can be enhanced by a finely grained microstructure and a dispersion of Mg2Si in the lattice structure. Hardening by precipitation takes place in the stages of heat treatment, such as solution annealing, quenching and aging [1]. After a hot metal forming operation, quenching followed by an aging operation yields fine grains with supersaturated solutions, which have a direct influence on the final mechanical properties such as yield strength and hardness.

In order to determine the hardenability of a material, an experimental method known as Jominy end-quench test is widely used. The test involves heating a standard cylindrical bar up to solution soaking temperature and then transferring it to a quenching fixture where the specimen is held vertically and through which a jet of water is directed against the bottom of the specimen. This results in a gradually varied cooling rate along the length of the specimen, with the maximum at the bottom. After the specimen has been fully quenched, it is aged in order to achieve the maximally attainable hardness values of the material. Finally, hardness measurements are performed along the length of the specimen’s surface [2]. The method has been designed for ferrous alloys. Therefore, up to now this method has found only little application for non-ferrous materials such as aluminum. Robinson and Tanner [3] have implemented the Jominy end-quench technique in order to determine the residual stresses in quenched high strength aluminum forgings. Steele et al. [4] studied the susceptibility of 6XXX alloys to grain boundary precipitation during quenching. Cavazos and Colás [5] and Dolan et al. [2] implemented the method and presented a continuous cooling property diagram for aluminum alloys 6063 and 7000 series, respectively.

The present research work aims at relating the hardness distribution of the aluminum alloy 6082 after quenching to the corresponding rates of cooling. This relation was formulized and parameterized for the alloy under consideration and implemented into the commercial FE tool DEFORMTM. The effectiveness of the developed strategy was tested by the application of an industrial problem.


Table 1: Chemical composition of EN AW-6082.

Mg Si Mn Fe Cr Cu Other

6082 (wt.%) 0.6-1.2 0.7-1.3 0.4-1.0 ≤ 0.50 ≤ 0.25 ≤ 0.10 ≤ 0.50

Experimental Procedure

Jominy End-Quench Test. For the purpose of the current research work, the Jominy end-quench test was used. The test specimen was prepared from an EN AW-6082 press block in accordance with DIN EN ISO 642 [6]. The chemical composition of the alloy used in the experiment is tabulated in Table 1.

The Jominy specimen and the experimental setup for the end-quenching are illustrated in Fig. 1. In order to record the cooling history during quenching, three thermocouples of type K with a diameter of 0.5 mm were placed in the holes drilled at 3, 38, and 78 mm from the quench end of the specimen. The thermocouples were inserted up to the central axis of the specimen. A measuring amplifier of HBM with a frequency of 5 Hz was used in order to enrich the sensitivity of the measurements. Fig. 2 shows the measured and simulated cooling rate of the specimen.

The specimen was placed in an air circulating laboratory furnace and solution heat treated for 2 h at 550°C. The specimen was then removed from the furnace and placed into the quench rig. It remained in the quench rig for about 5 min to allow sufficient time to cool to the room temperature. In order to reach the maximum hardness of the alloy, the Jominy specimen was then artificially aged using a T6 type temper. It was heated from room temperature to 180°C and then held for 3 h before being allowed to air cool. For the hardness measurements, a flat surface was machined on one side of the specimen. Vickers hardness was then measured at 1.5 to 5 mm intervals along the length of the specimen. Hardness measurements were done using a Struers Duramin microhardness tester with a 500 N load. Measurements of 25 material points were recorded. An average of five measurements was used for each location. Measured and simulated hardness values are illustrated in Fig. 2.

r

Supporting arm

Jominy test specimen

Water jet

Water pipe

3 mm 25 mm

100 mm

36 mm

3 mm

78 mm

Z

Positions of thermocouples

Fig. 1: (Left) Jominy specimen. (Right) Jominy end-quench test setup.

Table 1: Chemical composition of EN AW-6082.

Mg Si Mn Fe Cr Cu Other

6082 (wt.%) 0.6-1.2 0.7-1.3 0.4-1.0 ≤ 0.50 ≤ 0.25 ≤ 0.10 ≤ 0.50

Experimental Procedure

Jominy End-Quench Test. For the purpose of the current research work, the Jominy end-quench test was used. The test specimen was prepared from an EN AW-6082 press block in accordance with DIN EN ISO 642 [6]. The chemical composition of the alloy used in the experiment is tabulated in Table 1.

The Jominy specimen and the experimental setup for the end-quenching are illustrated in Fig. 1. In order to record the cooling history during quenching, three thermocouples of type K with a diameter of 0.5 mm were placed in the holes drilled at 3, 38, and 78 mm from the quench end of the specimen. The thermocouples were inserted up to the central axis of the specimen. A measuring amplifier of HBM with a frequency of 5 Hz was used in order to enrich the sensitivity of the measurements. Fig. 2 shows the measured and simulated cooling rate of the specimen.

The specimen was placed in an air circulating laboratory furnace and solution heat treated for 2 h at 550°C. The specimen was then removed from the furnace and placed into the quench rig. It remained in the quench rig for about 5 min to allow sufficient time to cool to the room temperature. In order to reach the maximum hardness of the alloy, the Jominy specimen was then artificially aged using a T6 type temper. It was heated from room temperature to 180°C and then held for 3 h before being allowed to air cool. For the hardness measurements, a flat surface was machined on one side of the specimen. Vickers hardness was then measured at 1.5 to 5 mm intervals along the length of the specimen. Hardness measurements were done using a Struers Duramin microhardness tester with a 500 N load. Measurements of 25 material points were recorded. An average of five measurements was used for each location. Measured and simulated hardness values are illustrated in Fig. 2.

r

Supporting arm

Jominy test specimen

Water jet

Water pipe

3 mm 25 mm

100 mm

36 mm

3 mm

78 mm

Z

Positions of thermocouples

Fig. 1: (Left) Jominy specimen. (Right) Jominy end-quench test setup.


umerical Analyses. In order to predict the rates of cooling at every location along the length of the specimen, an FE analysis of the Jominy end-quench test was carried out using the commercial FE tool DEFORMTM. A two dimensional model for the heat transfer analysis was built due to the axial symmetry. The model was discretized using 4-noded quadrilateral elements. After carrying out a mesh convergence study, the specimen was meshed using 1332 elements with a maximum element length of 1.1 mm. Cooling curves measured at three different points of the Jominy end-quench test specimen were used as the main boundary condition for FE simulation and they determined the thermal properties of the workpiece with the following parameters:

6 2( ) 147 44.8x10k T T−= + , (1)

where k [ /(sec ) K⋅ ] is the thermal conductivity of the alloy as a function of temperature, and

6 2.7( ) 9 4.93x10h T T−= + , (2)

where h is the convection heat transfer coefficient of the water jet as a function of temperature. Convection heat transfer coefficient between ambient air and the specimen was taken to be constant with a value h=0.05 /(sec ) mm C⋅ ⋅ ° . Finally, the specific heat capacity of the material is

c=2.443 2/( ) mm C⋅ ° . Concerning the rate of cooling during quenching, a good agreement between the experimental

and numerical results was obtained (Fig. 2, left). Such an agreement between the experiment and the simulation at three measurement points was quite encouraging to determine the cooling rate of the rest of the specimen using simulation results.

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100

Time [sec]

Tem

pera

ture

[°C

]

Exp. 78 mmExp. 38 mmExp. 3 mmSim. 78 mmSim. 38 mmSim. 3 mm 80

120

0 20 40 60 80 100Distance from the quench-end [mm]

Vic

kers

Har

dnes

s[H

V]

Experiment

Simulation

Fig. 2: (Left) Cooling curves of the 3 measurement points and the corresponding simulation results. (Right) Hardness measurements and simulated hardness values along the Jominy specimen.

After determining the cooling history of the Jominy end-quench model via numerical simulations

and measuring the hardness values along the surface of the specimen experimentally, a relation between the hardness of any material point and its rate of cooling can be found. It has been assumed that during the quenching of the alloy under investigation, precipitations occur within a critical temperature range from 400°C to 200°C. Linear averages of the cooling rates along the specimen were calculated. Therefore, a single rate of cooling of a material point within the critical temperature range was related to the corresponding hardness value. An example of such a calculation is illustrated in Fig. 3 (left) for a point on the specimen which is 35 mm away from the quench-end. The relationship between the linearized rates of cooling and the hardness measurements is also illustrated in Fig. 3 (right).

umerical Analyses. In order to predict the rates of cooling at every location along the length of the specimen, an FE analysis of the Jominy end-quench test was carried out using the commercial FE tool DEFORMTM. A two dimensional model for the heat transfer analysis was built due to the axial symmetry. The model was discretized using 4-noded quadrilateral elements. After carrying out a mesh convergence study, the specimen was meshed using 1332 elements with a maximum element length of 1.1 mm. Cooling curves measured at three different points of the Jominy end-quench test specimen were used as the main boundary condition for FE simulation and they determined the thermal properties of the workpiece with the following parameters:

6 2( ) 147 44.8x10k T T−= + , (1)

where k [ /(sec ) K⋅ ] is the thermal conductivity of the alloy as a function of temperature, and

6 2.7( ) 9 4.93x10h T T−= + , (2)

where h is the convection heat transfer coefficient of the water jet as a function of temperature. Convection heat transfer coefficient between ambient air and the specimen was taken to be constant with a value h=0.05 /(sec ) mm C⋅ ⋅ ° . Finally, the specific heat capacity of the material is

c=2.443 2/( ) mm C⋅ ° . Concerning the rate of cooling during quenching, a good agreement between the experimental

and numerical results was obtained (Fig. 2, left). Such an agreement between the experiment and the simulation at three measurement points was quite encouraging to determine the cooling rate of the rest of the specimen using simulation results.

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100

Time [sec]

Tem

pera

ture

[°C

]

Exp. 78 mmExp. 38 mmExp. 3 mmSim. 78 mmSim. 38 mmSim. 3 mm 80

120

0 20 40 60 80 100Distance from the quench-end [mm]

Vic

kers

Har

dnes

s[H

V]

Experiment

Simulation

Fig. 2: (Left) Cooling curves of the 3 measurement points and the corresponding simulation results. (Right) Hardness measurements and simulated hardness values along the Jominy specimen.

After determining the cooling history of the Jominy end-quench model via numerical simulations

and measuring the hardness values along the surface of the specimen experimentally, a relation between the hardness of any material point and its rate of cooling can be found. It has been assumed that during the quenching of the alloy under investigation, precipitations occur within a critical temperature range from 400°C to 200°C. Linear averages of the cooling rates along the specimen were calculated. Therefore, a single rate of cooling of a material point within the critical temperature range was related to the corresponding hardness value. An example of such a calculation is illustrated in Fig. 3 (left) for a point on the specimen which is 35 mm away from the quench-end. The relationship between the linearized rates of cooling and the hardness measurements is also illustrated in Fig. 3 (right).


200

240

280

320

360

400

0 10 20 30 40 50

Time [sec]

Tem

pera

ture

[°C

]

Material point at Z=35 mm

Linear behaviour

at Z=35 mm5.55 /secT C= °&

Tα = &

70

80

90

100

110

120

0 25 50 75 100 125

Rate of cooling [°C/s]

Vic

kers

Har

dnes

s[H

V]

Fig. 3: (Left) Sample calculation for linear rate of cooling assumption for a point 35 mm away from the quench-end. (Right) The relationship between the rate of cooling and Vickers hardness.

In order to implement such a relationship into the FE analysis, entries of the Fig. 3 (right) were fitted to the following exponential formula:

( ) expb

HV T aT c

= + +

&&

, (3)

where HV is the Vickers Hardness, T& is the rate of cooling, a, b and c are the constants with the values of 4.79864, -1.60084, and 0.17402, respectively. Equation (3) was implemented as a user subroutine into the FE tool DEFORMTM-2D. An FE simulation for the same quenching experiment was then carried out once more for the calculation of Vickers hardness values. Fig. 2 (right) illustrates the numerical prediction of the hardness distribution along the Jominy end-quench test specimen.

Application of the method in an industrial problem

Having demonstrated the simulation of the hardness evolution of a Jominy test specimen during end-quenching, it is interesting to see the performance of the method for the estimation of the final mechanical properties of a construction element. For this purpose, the heat treatment of a prototype crash absorbing structure was analyzed.

It has been investigated that the energy absorption characteristics of a crash element (i.e. crash-box) can be influenced by introducing a functional grading along that element [7]. Functionally graded materials can be characterized by the variation in composition and structure gradually over volume, resulting in corresponding changes in the properties of a material [8]. In order to control the buckling modes of the energy absorbing structures, having a portion in the structure for concentrating stress, weakening or strengthening some portions are the existing strategies. Considering the prototype crash absorbing profile, the idea of generating a gradient in the mechanical properties was realized by applying a graded heat treatment along the profile. The technology for the integration of this partial quenching strategy in the process chain of extrusion was explained in [9] in detail (see Fig. 4). The aim was to achieve different solution conditions of Mg and Si in the alloy over the profile’s volume, especially through its length. Such a difference in solution conditions yields a difference in the hardness through the profile’s length as well. The distribution of the Vickers hardness along the length of the extruded profile after this special quenching strategy is illustrated in Fig. 5.

200

240

280

320

360

400

0 10 20 30 40 50

Time [sec]

Tem

pera

ture

[°C

]

Material point at Z=35 mm

Linear behaviour

at Z=35 mm5.55 /secT C= °&

Tα = &

70

80

90

100

110

120

0 25 50 75 100 125

Rate of cooling [°C/s]

Vic

kers

Har

dnes

s[H

V]

Fig. 3: (Left) Sample calculation for linear rate of cooling assumption for a point 35 mm away from the quench-end. (Right) The relationship between the rate of cooling and Vickers hardness.

In order to implement such a relationship into the FE analysis, entries of the Fig. 3 (right) were fitted to the following exponential formula:

( ) expb

HV T aT c

= + +

&&

, (3)

where HV is the Vickers Hardness, T& is the rate of cooling, a, b and c are the constants with the values of 4.79864, -1.60084, and 0.17402, respectively. Equation (3) was implemented as a user subroutine into the FE tool DEFORMTM-2D. An FE simulation for the same quenching experiment was then carried out once more for the calculation of Vickers hardness values. Fig. 2 (right) illustrates the numerical prediction of the hardness distribution along the Jominy end-quench test specimen.

Application of the method in an industrial problem

Having demonstrated the simulation of the hardness evolution of a Jominy test specimen during end-quenching, it is interesting to see the performance of the method for the estimation of the final mechanical properties of a construction element. For this purpose, the heat treatment of a prototype crash absorbing structure was analyzed.

It has been investigated that the energy absorption characteristics of a crash element (i.e. crash-box) can be influenced by introducing a functional grading along that element [7]. Functionally graded materials can be characterized by the variation in composition and structure gradually over volume, resulting in corresponding changes in the properties of a material [8]. In order to control the buckling modes of the energy absorbing structures, having a portion in the structure for concentrating stress, weakening or strengthening some portions are the existing strategies. Considering the prototype crash absorbing profile, the idea of generating a gradient in the mechanical properties was realized by applying a graded heat treatment along the profile. The technology for the integration of this partial quenching strategy in the process chain of extrusion was explained in [9] in detail (see Fig. 4). The aim was to achieve different solution conditions of Mg and Si in the alloy over the profile’s volume, especially through its length. Such a difference in solution conditions yields a difference in the hardness through the profile’s length as well. The distribution of the Vickers hardness along the length of the extruded profile after this special quenching strategy is illustrated in Fig. 5.


Fig. 4: (Left) Process integrated quench design. (Right) Corresponding temperature distribution

during quenching [9]. In order to estimate the final hardness distribution of the profile, the method shown in the

previous part of the current study was implemented for the simulation of partial quenching of the extruded profile. Due to the symmetry, a half of the geometry was modeled. The three-dimensional (3D) model was discretized using 3480 8-noded hexahedral elements. The user subroutine developed for the estimation of the Vickers hardness of Jominy end-quench was converted into 3D and implemented in DEFORMTM-3D. Fig. 5 shows the predicted hardness distribution of the profile as well as the experimental measurements.

Fig. 5: Hardness distribution through the length of the locally quenched profile.

Discussion

As it can be seen from Fig. 5 (right), the numerical simulation derived from the Jominy end-quench test can reflect the graded behavior of the hardness distribution along the length of the partially quenched profile. Considering the upper and the lower bounds of the measured hardness values, FE estimations are also quite promising. Nevertheless, the transition trend within the neighborhood of the quench area shows a slight difference in the simulation compared to the experiments. The sharper transition observed in the simulation can be attributed to the difference in the cooling rates between Jominy end-quench test and partial quenching of the hollow profile. Namely, the rate of cooling varies between 106.5 and 3.84 °C/sec in end-quench testing. On the other hand, the interval of the rate of cooling is 100.6 to 1.58 °C/sec during the local quenching of the extruded profile.

Vickers Hardness [HV]

120 80

Fig. 4: (Left) Process integrated quench design. (Right) Corresponding temperature distribution

during quenching [9]. In order to estimate the final hardness distribution of the profile, the method shown in the

previous part of the current study was implemented for the simulation of partial quenching of the extruded profile. Due to the symmetry, a half of the geometry was modeled. The three-dimensional (3D) model was discretized using 3480 8-noded hexahedral elements. The user subroutine developed for the estimation of the Vickers hardness of Jominy end-quench was converted into 3D and implemented in DEFORMTM-3D. Fig. 5 shows the predicted hardness distribution of the profile as well as the experimental measurements.

Fig. 5: Hardness distribution through the length of the locally quenched profile.

Discussion

As it can be seen from Fig. 5 (right), the numerical simulation derived from the Jominy end-quench test can reflect the graded behavior of the hardness distribution along the length of the partially quenched profile. Considering the upper and the lower bounds of the measured hardness values, FE estimations are also quite promising. Nevertheless, the transition trend within the neighborhood of the quench area shows a slight difference in the simulation compared to the experiments. The sharper transition observed in the simulation can be attributed to the difference in the cooling rates between Jominy end-quench test and partial quenching of the hollow profile. Namely, the rate of cooling varies between 106.5 and 3.84 °C/sec in end-quench testing. On the other hand, the interval of the rate of cooling is 100.6 to 1.58 °C/sec during the local quenching of the extruded profile.

Vickers Hardness [HV]

120 80


Exponential form of the equation used in the hardness prediction (see Eq. 3), based on the end-quench testing, does not permit to be extrapolated for cooling rates smaller than 3.84. Therefore, the minimum value of the attainable hardness of the alloy is reached when the cooling rate is 3.84. In order to have better estimations, the equation used for the calculation of the hardness distribution during quenching has to be better parameterized by extending the range of the cooling rates. This can simply be achieved by elongating the Jominy end-quench test sample.

In the current method, since the cooling rate is taken to be constant within the critical temperature interval, the nonlinear behavior of the cooling curves has no influence on the final hardness distribution. Therefore, an improvement on the physical equation can be achieved by introducing temperature as a second variable on which the evolution of hardness depends.

The critical temperature range, where precipitation is most likely to occur, can be further analyzed, and better assumptions can be made. The effect of the deformation history on precipitations or the characteristic of the quench medium (i.e. water jet or water spray) must also be analyzed in order to have better models for the numerical estimation of the hardness values. Acknowledgments This work was carried out with the financial support of the Transregional Collaborative Research Center/TR30 (Sub-project A2) funded by the German Research Foundation (DFG). This support is greatly acknowledged.

References

[1] Totten G. E., Mackenzie D. S., “Handbook of Aluminum”, CRC Press, New York, 2003.

[2] Dolan G.P., Flynn R.J., Tanner D.A., Robinson J.S., Quench factor analysis of aluminum alloys using the Jominy end quench technique, Mater. Sci. Eng. 21 (6) (2005), pp. 687–691.

[3] Tanner D.A., Robinson J.S., Effect of precipitation during quenching on the mechanical properties of the aluminium alloy 7010 in the W-temper, Journal of Materials Processing Technology, 153-154 (2004), pp. 998-1004.

[4] Steele D., Evans D., Nolan P., Lloyd D.J., Quantification of grain boundary precipitation and the influence of quench rate in 6XXX aluminum alloys, Materials Characterization, Volume 58, Issue 1, January 2007, pp. 40-45.

[5] Cavazos J.L., Colas R., Quench sensitivity of a heat treatable aluminum alloy, Mater. Sci. Eng. A: Struct. Mater. Properties Microstruct. Process. 363 (1–2) (2003), pp. 171–178.

[6] Deutsches Institut für Normung e.V.: DIN EN ISO 642:2000-01 Stirnabschreckversuch (Jominy-Versuch). Deutsche Fassung EN ISO 642:1999 Beuth Verlag, Berlin 2000.

[7] Güzel A., Jäger A., Schikorra M., Tekkaya A.E., Crushing energy absorption of functionally graded aluminum extruded profiles, Steel Res. Int. 79(2008), Vol.2, pp. 312-316.

[8] Hirai, T.: Functional Gradient Materials. Processing of Ceramics, pt. 2, vol. 17B, Richard J. Brook, et al., eds., Weinheim, New York, NY, 1996, pp. 293-341.

[9] Jäger A., Güzel A., Schikorra M., Tekkaya A.E., Production of functionally graded aluminum EN AW-6082 profiles by extrusion with a subsequent quenching strategy, Steel Res. Int. 79(2008), Vol.2, pp. 842-846.

Exponential form of the equation used in the hardness prediction (see Eq. 3), based on the end-quench testing, does not permit to be extrapolated for cooling rates smaller than 3.84. Therefore, the minimum value of the attainable hardness of the alloy is reached when the cooling rate is 3.84. In order to have better estimations, the equation used for the calculation of the hardness distribution during quenching has to be better parameterized by extending the range of the cooling rates. This can simply be achieved by elongating the Jominy end-quench test sample.

In the current method, since the cooling rate is taken to be constant within the critical temperature interval, the nonlinear behavior of the cooling curves has no influence on the final hardness distribution. Therefore, an improvement on the physical equation can be achieved by introducing temperature as a second variable on which the evolution of hardness depends.

The critical temperature range, where precipitation is most likely to occur, can be further analyzed, and better assumptions can be made. The effect of the deformation history on precipitations or the characteristic of the quench medium (i.e. water jet or water spray) must also be analyzed in order to have better models for the numerical estimation of the hardness values. Acknowledgments This work was carried out with the financial support of the Transregional Collaborative Research Center/TR30 (Sub-project A2) funded by the German Research Foundation (DFG). This support is greatly acknowledged.

References

[1] Totten G. E., Mackenzie D. S., “Handbook of Aluminum”, CRC Press, New York, 2003.

[2] Dolan G.P., Flynn R.J., Tanner D.A., Robinson J.S., Quench factor analysis of aluminum alloys using the Jominy end quench technique, Mater. Sci. Eng. 21 (6) (2005), pp. 687–691.

[3] Tanner D.A., Robinson J.S., Effect of precipitation during quenching on the mechanical properties of the aluminium alloy 7010 in the W-temper, Journal of Materials Processing Technology, 153-154 (2004), pp. 998-1004.

[4] Steele D., Evans D., Nolan P., Lloyd D.J., Quantification of grain boundary precipitation and the influence of quench rate in 6XXX aluminum alloys, Materials Characterization, Volume 58, Issue 1, January 2007, pp. 40-45.

[5] Cavazos J.L., Colas R., Quench sensitivity of a heat treatable aluminum alloy, Mater. Sci. Eng. A: Struct. Mater. Properties Microstruct. Process. 363 (1–2) (2003), pp. 171–178.

[6] Deutsches Institut für Normung e.V.: DIN EN ISO 642:2000-01 Stirnabschreckversuch (Jominy-Versuch). Deutsche Fassung EN ISO 642:1999 Beuth Verlag, Berlin 2000.

[7] Güzel A., Jäger A., Schikorra M., Tekkaya A.E., Crushing energy absorption of functionally graded aluminum extruded profiles, Steel Res. Int. 79(2008), Vol.2, pp. 312-316.

[8] Hirai, T.: Functional Gradient Materials. Processing of Ceramics, pt. 2, vol. 17B, Richard J. Brook, et al., eds., Weinheim, New York, NY, 1996, pp. 293-341.

[9] Jäger A., Güzel A., Schikorra M., Tekkaya A.E., Production of functionally graded aluminum EN AW-6082 profiles by extrusion with a subsequent quenching strategy, Steel Res. Int. 79(2008), Vol.2, pp. 842-846.


Simulation of gas and spray quenching during extrusion of aluminium alloys

M. Reich1, S. Schöne1, O. Keßler1, M. Nowak2, O. Grydin2, F. Nürnberger2, M. Schaper2 1Universität Rostock, Fakultät für Maschinenbau und Schiffstechnik,

Lehrstuhl für Werkstofftechnik, [email protected] 2Leibniz Universität Hannover, Institut für Werkstoffkunde, [email protected]

Keywords: Aluminium alloy, quenching simulation, gas quenching, spray quenching

Abstract. After the extrusion process most aluminium alloy profiles don´t satisfy the necessary strength requirements. An increase of strength can be obtained by age hardening of hardenable aluminium alloys. Age hardening includes the three steps of solution annealing, quenching and aging and is usually carried out in a separate process after extrusion. The integration of the sub-steps solution annealing and quenching in the extrusion process results in a marked reduction of the complete process chain. The applicability of this integration depends primarily on the quenching power of the cooling module and on the quench sensitivity of the aluminium alloy. Using the finite element method the non-steady-state process of quenching the profiles after leaving the extrusion press has been simulated. The boundary conditions for quenching are varied for a gas nozzle field and a spray cooling using heat transfer coefficients based on experiments. The simulation results support the design of gas nozzle fields or spray cooling for the extrusion process of different aluminium alloys.

Introduction

Heat treatment of aluminium alloys. Aluminium wrought alloys of the systems Al-Zn-Mg or Al-Mg-Si are heat treated by age hardening, i.e. solution annealing, quenching and ageing. Extruded aluminium profiles can be age hardened either in a separate process after extrusion or integrated into the extrusion process. Most of the 6XXX alloys are quenched directly after the extrusion, followed by either a natural or artificial aging sequence. Direct quenching is a method of combining the extrusion process and the solution annealing offering the potential of economic savings [1]. Fig. 1 shows a schematic temperature profile of a typically heat treatment for age-hardenable aluminium alloys in comparison to the temperature profile due to extrusion.

Fig. 1: Temperature profile for age hardening of aluminium alloys compared to

temperature profile during extrusion (schematic)

quenching (water)

supersaturated solid solution

solution annealing (about 540 °C)

aging (150 °C to 200 °C)

press quenching (T5)

tem

per

atu

re

time

extrusion followed by separate heat treatment (T6)

air cooling

extrusiondirect

Simulation of gas and spray quenching during extrusion of aluminium alloys

M. Reich1, S. Schöne1, O. Keßler1, M. Nowak2, O. Grydin2, F. Nürnberger2, M. Schaper2 1Universität Rostock, Fakultät für Maschinenbau und Schiffstechnik,

Lehrstuhl für Werkstofftechnik, [email protected] 2Leibniz Universität Hannover, Institut für Werkstoffkunde, [email protected]

Keywords: Aluminium alloy, quenching simulation, gas quenching, spray quenching

Abstract. After the extrusion process most aluminium alloy profiles don´t satisfy the necessary strength requirements. An increase of strength can be obtained by age hardening of hardenable aluminium alloys. Age hardening includes the three steps of solution annealing, quenching and aging and is usually carried out in a separate process after extrusion. The integration of the sub-steps solution annealing and quenching in the extrusion process results in a marked reduction of the complete process chain. The applicability of this integration depends primarily on the quenching power of the cooling module and on the quench sensitivity of the aluminium alloy. Using the finite element method the non-steady-state process of quenching the profiles after leaving the extrusion press has been simulated. The boundary conditions for quenching are varied for a gas nozzle field and a spray cooling using heat transfer coefficients based on experiments. The simulation results support the design of gas nozzle fields or spray cooling for the extrusion process of different aluminium alloys.

Introduction

Heat treatment of aluminium alloys. Aluminium wrought alloys of the systems Al-Zn-Mg or Al-Mg-Si are heat treated by age hardening, i.e. solution annealing, quenching and ageing. Extruded aluminium profiles can be age hardened either in a separate process after extrusion or integrated into the extrusion process. Most of the 6XXX alloys are quenched directly after the extrusion, followed by either a natural or artificial aging sequence. Direct quenching is a method of combining the extrusion process and the solution annealing offering the potential of economic savings [1]. Fig. 1 shows a schematic temperature profile of a typically heat treatment for age-hardenable aluminium alloys in comparison to the temperature profile due to extrusion.

Fig. 1: Temperature profile for age hardening of aluminium alloys compared to

temperature profile during extrusion (schematic)

quenching (water)

supersaturated solid solution

solution annealing (about 540 °C)

aging (150 °C to 200 °C)

press quenching (T5)

tem

per

atu

re

time

extrusion followed by separate heat treatment (T6)

air cooling

extrusiondirect


Conventional quenching methods are the standing water wave quench and the water quenching in bath. These methods allow the fastest cooling, but are leading to large thermal stresses and, thus, to residual stresses and distortion due to the high temperature gradients [2]. The quenching by gas or two phase spray quenching allows the reduction of residual stresses and distortion due to the possibility of controlling the local surface heat transfer [2,3,13]. The achievable heat transfer coefficients for two-phase spray quenching are in between those for the standing water wave quenching and those for the forced air quenching. The heat transfer coefficients for air cooling range from 100 W/m2K to 300 W/m2K [4,5] and the heat transfer coefficients for water spraying reach up to 1000 W/m2K [5]. The local heat transfer can be configured by variation of the pressure, the nozzle-to-profile distance and the type of the nozzle, e.g. round or flat spray, thus allowing quenching of profiles with unequal wall thicknesses. Using spray quenching for the direct quenching adds another advantage, the directed quenching of the profiles.

Extreme variety of extruded profiles form and wide spectrum of used aluminium alloys reduce the efficiency of experimental research methods and usability of their results. The most effective and convenient tool for extrusion process analysis is numerical simulation. It allows to examine process parameters at large and to select the optimal of them in relative shot terms. The two-phase spray cooling of extruded aluminum alloy was already investigated by means of mathematical simulation [2,5,7]. Hall et al. have analyzed the temperature changing at water-air flow cooling of L-profile of aluminum alloy Al 2024. It was suggested to describe with some equations the dependence of heat flux from the temperature and its distribution on the sprayed area. The model has been implemented as a user subroutine in the FEM software ABAQUS and verified on the own experimental results. In the works of Järvsträt etc. and Bratland etc. the thermal task, precipitation kinetic, distortion [7] and prediction of mechanical properties [5] on example of alloy AW-6082 were modelled. Regrettably in both of the mentioned papers the heat transfer coefficients were simplified, although the importance of taking into account of this was concluded.

Characteristics of gas and spray quenching. As mentioned before the spray quenching allows the directed quenching of parts to reduce residual stresses and distortion. But in order to properly adjust the local heat transfer one must know the characteristics of the used spray, i.e. the heat transfer coefficient against the temperature, the admission on the surface and the size and velocity of the droplets. In [2,3] different sprays have been characterized. The size and velocity have been investigated by Phase-Doppler-Anemometer (PDA) and the water admission by patternator investigations. The heat transfer coefficients have been measured indirectly using a thermographic (IR) camera. Round samples have been heated up and subsequently sprayed from one side, whilst the temperature has been measured on the other side [2]. This has been carried out for different pressures of water (W) and of air (A), measured in bar. The analysis of the thermographic images has been carried out using a series expansion according to Hamed [5].

While the heat transfer coefficient for gas cooling can be assumed approximately as constant relating to a material’s surface temperature for a specific set of process parameters, heat transfer coefficients for two-phase sprays based on water and air are frequently temperature dependent. Besides, parameters affecting the heat transfer during spray cooling are the cooled material itself and the spray’s local properties that vary e.g. with the diameter of the atomizing cone. Furthermore, the application of two-phase quenching directly into the extrusion process requires considering extrusion related parameters like profile geometry, profile exit velocity, profile exit temperature and distance between die exit and the quenching module as well as the overall area of the quenched surface that is connected to the length of the quench module. Typically heat transfer coefficients related to surface temperatures for three different sprays with varying water and air pressures (W/A) are given in Fig. 2 [1,2]. The determination of the heat transfer coefficients is based on thermographic measurements of temperature courses during spray cooling of thin metal plates as described e.g. by [3] using calculation methods specified elsewhere [4,5]. For the spray quenching

Conventional quenching methods are the standing water wave quench and the water quenching in bath. These methods allow the fastest cooling, but are leading to large thermal stresses and, thus, to residual stresses and distortion due to the high temperature gradients [2]. The quenching by gas or two phase spray quenching allows the reduction of residual stresses and distortion due to the possibility of controlling the local surface heat transfer [2,3,13]. The achievable heat transfer coefficients for two-phase spray quenching are in between those for the standing water wave quenching and those for the forced air quenching. The heat transfer coefficients for air cooling range from 100 W/m2K to 300 W/m2K [4,5] and the heat transfer coefficients for water spraying reach up to 1000 W/m2K [5]. The local heat transfer can be configured by variation of the pressure, the nozzle-to-profile distance and the type of the nozzle, e.g. round or flat spray, thus allowing quenching of profiles with unequal wall thicknesses. Using spray quenching for the direct quenching adds another advantage, the directed quenching of the profiles.

Extreme variety of extruded profiles form and wide spectrum of used aluminium alloys reduce the efficiency of experimental research methods and usability of their results. The most effective and convenient tool for extrusion process analysis is numerical simulation. It allows to examine process parameters at large and to select the optimal of them in relative shot terms. The two-phase spray cooling of extruded aluminum alloy was already investigated by means of mathematical simulation [2,5,7]. Hall et al. have analyzed the temperature changing at water-air flow cooling of L-profile of aluminum alloy Al 2024. It was suggested to describe with some equations the dependence of heat flux from the temperature and its distribution on the sprayed area. The model has been implemented as a user subroutine in the FEM software ABAQUS and verified on the own experimental results. In the works of Järvsträt etc. and Bratland etc. the thermal task, precipitation kinetic, distortion [7] and prediction of mechanical properties [5] on example of alloy AW-6082 were modelled. Regrettably in both of the mentioned papers the heat transfer coefficients were simplified, although the importance of taking into account of this was concluded.

Characteristics of gas and spray quenching. As mentioned before the spray quenching allows the directed quenching of parts to reduce residual stresses and distortion. But in order to properly adjust the local heat transfer one must know the characteristics of the used spray, i.e. the heat transfer coefficient against the temperature, the admission on the surface and the size and velocity of the droplets. In [2,3] different sprays have been characterized. The size and velocity have been investigated by Phase-Doppler-Anemometer (PDA) and the water admission by patternator investigations. The heat transfer coefficients have been measured indirectly using a thermographic (IR) camera. Round samples have been heated up and subsequently sprayed from one side, whilst the temperature has been measured on the other side [2]. This has been carried out for different pressures of water (W) and of air (A), measured in bar. The analysis of the thermographic images has been carried out using a series expansion according to Hamed [5].

While the heat transfer coefficient for gas cooling can be assumed approximately as constant relating to a material’s surface temperature for a specific set of process parameters, heat transfer coefficients for two-phase sprays based on water and air are frequently temperature dependent. Besides, parameters affecting the heat transfer during spray cooling are the cooled material itself and the spray’s local properties that vary e.g. with the diameter of the atomizing cone. Furthermore, the application of two-phase quenching directly into the extrusion process requires considering extrusion related parameters like profile geometry, profile exit velocity, profile exit temperature and distance between die exit and the quenching module as well as the overall area of the quenched surface that is connected to the length of the quench module. Typically heat transfer coefficients related to surface temperatures for three different sprays with varying water and air pressures (W/A) are given in Fig. 2 [1,2]. The determination of the heat transfer coefficients is based on thermographic measurements of temperature courses during spray cooling of thin metal plates as described e.g. by [3] using calculation methods specified elsewhere [4,5]. For the spray quenching


of the described aluminium alloys the spray 3W6A in Fig. 2 is suitable because of the high heat transfer coefficients in the temperature range of precipitation between 500 °C and 200 °C.

Fig. 2: Temperature dependent heat transfer coefficients in several spray centers for varying pressures of water and air calculated using thermographic measured cooling curves of spray-cooled metal plates

[8,9]; round spray nozzles of the type SUJ22B 1/8JJAU, Spraying Systems, air nozzle PAJ73160, water nozzle PFJ2850

The area quenched by spray cooling is related to the number of spray nozzles. It has to be accounted for that the heat transfer coefficient α generated by a round spray nozzle is not constant on the materials surface but decreases with the radius r of the spray cone (Fig. 3). Such dependence can be approximated e.g. using a simple formula like given by equation 1:

α = αcentre · (1-(k·r/R)n) , (1)

where αcentre is the heat transfer coefficient at the spray’s centre, R the overall radius of the spray cone, k a constant and n an exponent.

Fig. 3: Dependence of the heat transfer coefficient related to the radius r of the spray cone; measuring

data depicted by points according to [8,9]; lines approximated using equation 1 (R = 30 mm, n = 0.9, k = 0.55)

0

5000

10000

15000

0 200 400 600

temperature [°C]

hea

t tr

ansf

erco

effi

cien

t[W

/m2

K] 3W 3A

3W 6A

6W 6A

W: water pressure [bar]A: air pressure [bar]

0

4000

8000

12000

50 150 250 350

hea

t tr

ansf

erco

effi

cien

t[W

/m2

K]

temperature [°C]

r = 20 mm

r = 10 mm

spray centre

of the described aluminium alloys the spray 3W6A in Fig. 2 is suitable because of the high heat transfer coefficients in the temperature range of precipitation between 500 °C and 200 °C.

Fig. 2: Temperature dependent heat transfer coefficients in several spray centers for varying pressures of water and air calculated using thermographic measured cooling curves of spray-cooled metal plates

[8,9]; round spray nozzles of the type SUJ22B 1/8JJAU, Spraying Systems, air nozzle PAJ73160, water nozzle PFJ2850

The area quenched by spray cooling is related to the number of spray nozzles. It has to be accounted for that the heat transfer coefficient α generated by a round spray nozzle is not constant on the materials surface but decreases with the radius r of the spray cone (Fig. 3). Such dependence can be approximated e.g. using a simple formula like given by equation 1:

α = αcentre · (1-(k·r/R)n) , (1)

where αcentre is the heat transfer coefficient at the spray’s centre, R the overall radius of the spray cone, k a constant and n an exponent.

Fig. 3: Dependence of the heat transfer coefficient related to the radius r of the spray cone; measuring

data depicted by points according to [8,9]; lines approximated using equation 1 (R = 30 mm, n = 0.9, k = 0.55)

0

5000

10000

15000

0 200 400 600

temperature [°C]

hea

t tr

ansf

erco

effi

cien

t[W

/m2

K] 3W 3A

3W 6A

6W 6A

W: water pressure [bar]A: air pressure [bar]

0

4000

8000

12000

50 150 250 350

hea

t tr

ansf

erco

effi

cien

t[W

/m2

K]

temperature [°C]

r = 20 mm

r = 10 mm

spray centre


Modelling of Gas and Spray Quenching

Material properties. Table 1 summarizes the thermal properties of some aluminium wrought alloys. These have to be known when carrying out a finite element simulation of the quenching. Furthermore, information on the quenching characteristics, i.e. the critical cooling rate and the temperature range of precipitation, are given. To determine the critical cooling rate T6-heat treatments (Fig. 1) were carried out with several samples to age harden the samples with varying cooling rates. The hardness of each sample was determined and the critical cooling rate determined by indentifying the cooling rate which did not result in a further increase of the hardness. For the following investigations the aluminium alloy EN AW-6082 with a critical cooling rate of about 12 K/s has been examined. In order to identify the temperature range of precipitation experiments with differential scanning calorimetry (DSC) have been carried out [13].

Table 1: Thermal properties and precipitation characteristics for some aluminum wrought alloys [14,15,16,17]

Simulation Environments and Model Characteristics. The transient quenching of two cylindrical profiles with diameters of 20 mm and 30 mm has been simulated using the finite element software Sysweld® as well as ASYS®. Both software environments feature coupled thermal-mechanical simulations to calculate temperature fields as well as residual stresses and distortion though in this paper presented investigations focus on thermal calculations. The profiles’ die exit temperatures were set constant and heating of the profile due to deformation heat not considered. Table 2 gives an overview about the model characteristics implemented. The spray quenching was simulated with ASYS® and the gas quenching with Sysweld®. The maximum heat transfer coefficient for gas quenching is assumed as about 2,200 W/(m²K) [18]. For this method heat transfer coefficients in a range between 100 and 3,000 W/(m²K) were simulated.

Table 2: Model characteristics for gas and spray quenching

parameters gas quenching spray quenching software Sysweld® ANSYS® model 2D-axially symmetrical full 3D profiles diameters 20 mm and 30 mm diameters 20 mm and 30 mm element types bilinear 2D-elements

linear 1D-elements (surface) 3D 10-Node tetrahedral elements

element numbers 50,000 (diameter 20 mm) 75,000 (diameter 30 mm) 5,010 (surface)

46,000 (diameter 20 mm) 70,500 – 150,000 (diameter 30 mm)

heat transfer homogenous, constant temperature dependent heat transfer coefficient

100 W/(m2K) to 3000 W/(m2K), 20 W/(m2K) between die exit and cooling field

coefficient according to water-air- spray 3W6A (Fig. 2)

medium temperature

20 °C 23 °C

die exit temperature

540 °C (constant) 550 °C (constant)

E! AW-critical

cooling rate [K/s]

temperature range of

precipitation [°C]6060 (Al MgSi) 0.8 ca. 200-4706063 (Al Mg0.7Si) 1.7 200-4706005A (Al SiMg(A)) 6.3 220-5006082 (Al Si1MgMn) 12 200-540

density [kg /m³]

thermal conductivity

[W/mK]

specific heat capacity [J/kgK]ca. 900

900

170-220205-2202.70

896ca. 900

200-2202.702.70

2.70

200-220

Modelling of Gas and Spray Quenching

Material properties. Table 1 summarizes the thermal properties of some aluminium wrought alloys. These have to be known when carrying out a finite element simulation of the quenching. Furthermore, information on the quenching characteristics, i.e. the critical cooling rate and the temperature range of precipitation, are given. To determine the critical cooling rate T6-heat treatments (Fig. 1) were carried out with several samples to age harden the samples with varying cooling rates. The hardness of each sample was determined and the critical cooling rate determined by indentifying the cooling rate which did not result in a further increase of the hardness. For the following investigations the aluminium alloy EN AW-6082 with a critical cooling rate of about 12 K/s has been examined. In order to identify the temperature range of precipitation experiments with differential scanning calorimetry (DSC) have been carried out [13].

Table 1: Thermal properties and precipitation characteristics for some aluminum wrought alloys [14,15,16,17]

Simulation Environments and Model Characteristics. The transient quenching of two cylindrical profiles with diameters of 20 mm and 30 mm has been simulated using the finite element software Sysweld® as well as ASYS®. Both software environments feature coupled thermal-mechanical simulations to calculate temperature fields as well as residual stresses and distortion though in this paper presented investigations focus on thermal calculations. The profiles’ die exit temperatures were set constant and heating of the profile due to deformation heat not considered. Table 2 gives an overview about the model characteristics implemented. The spray quenching was simulated with ASYS® and the gas quenching with Sysweld®. The maximum heat transfer coefficient for gas quenching is assumed as about 2,200 W/(m²K) [18]. For this method heat transfer coefficients in a range between 100 and 3,000 W/(m²K) were simulated.

Table 2: Model characteristics for gas and spray quenching

parameters gas quenching spray quenching software Sysweld® ANSYS® model 2D-axially symmetrical full 3D profiles diameters 20 mm and 30 mm diameters 20 mm and 30 mm element types bilinear 2D-elements

linear 1D-elements (surface) 3D 10-Node tetrahedral elements

element numbers 50,000 (diameter 20 mm) 75,000 (diameter 30 mm) 5,010 (surface)

46,000 (diameter 20 mm) 70,500 – 150,000 (diameter 30 mm)

heat transfer homogenous, constant temperature dependent heat transfer coefficient

100 W/(m2K) to 3000 W/(m2K), 20 W/(m2K) between die exit and cooling field

coefficient according to water-air- spray 3W6A (Fig. 2)

medium temperature

20 °C 23 °C

die exit temperature

540 °C (constant) 550 °C (constant)

E! AW-critical

cooling rate [K/s]

temperature range of

precipitation [°C]6060 (Al MgSi) 0.8 ca. 200-4706063 (Al Mg0.7Si) 1.7 200-4706005A (Al SiMg(A)) 6.3 220-5006082 (Al Si1MgMn) 12 200-540

density [kg /m³]

thermal conductivity

[W/mK]

specific heat capacity [J/kgK]ca. 900

900

170-220205-2202.70

896ca. 900

200-2202.702.70

2.70

200-220


wrought alloy EN AW-6082 EN AW-6082 profile velocities 1.5 m/min to 6 m/min 5 m/min to 11 m/min. spray field size characterization

length of cooling field spray cooled surface

time step size up to 1 s 0.2 s calculated characteristics

maximum cooling rate in the core temperature in the core when leaving the cooling field

temperature in the core when leaving the cooling field

The calculated maximum cooling rate in the profile’s core and the temperature in the core when leaving the cooling module have been considered as main simulation results since the maximum cooling rate gives an estimation whether a required cooling rate could be achieved and the temperature in the core provides information whether the length of the cooling field is sufficient for the chosen extrusion speed. For the sensitivity study of quenching profiles by a two-phase spray, instead of a locally varying spray cone area a homogenous quenched area has been investigated. This makes the simulation results independent of the used spray nozzles and the result can easily be used for the design of the cooling module.


Gas quenching. In table 3 the temperatures in the core when leaving the cooling module and the maximum cooling rates during quenching are given for a radius of 10 mm, an cooling field lengths of 500 and varying heat transfer coefficients α as well as extrusion speed vextr

Table 3: Maximum cooling rates and temperatures (TEnd) in the core of a cylindrical EN AW-6082 profile (ø 20 mm) at the end of a gas cooling field with a length of 500 mm for different extrusion speeds and heat transfer coefficients

Dark grey cells represent cooling conditions where the maximum cooling rate is lower than the required one and precipitations can not be suppressed. A cylindrical profile of EN AW-6082 with a diameter of 20 mm requires a cooling field that provides at least a heat transfer coefficient of about 500 W/(m²K) to obtain the required cooling rate at least temporarily. A light grey cell means that the temperature when leaving the cooling field is still inside the temperature range of precipitation although the required cooling rate is given. In this case a higher heat transfer coefficient could remedy or the cooling duration has to be increased by a lower extrusion speed or a higher cooling field length.

Fig. 4 depicts that for a heat transfer coefficient of 500 W/(m²K) the required cooling rate is achieved for a relative short period of time only. Thus cooling rates are insufficient at the lower part of the temperature range of precipitation. On the contrary, a heat transfer coefficient of 1,000 W/(m²K) should be sufficient to suppress precipitations.

Investigations of a profile with a radius of 15 mm show that higher heat transfer coefficients are inevitable to achieve acceptable cooling rates, also longer cooling durations are necessary, since the profiles’ thermal behavior is comparatively slower.

simulationresults 100 500 1000 1500 2000 3000

TEnd: 436 °C 230 °C 108 °C 57 °C 36 °C 23,15 °Cmax. cooling rate: 4,11 K/s 19,84 K/s 38,16 K/s 55,33 K/s 72,06 K/s 104,56 K/s



heat transfer coefficient α [W/m²K]vextr [mm/s]

100

50

25

wrought alloy EN AW-6082 EN AW-6082 profile velocities 1.5 m/min to 6 m/min 5 m/min to 11 m/min. spray field size characterization

length of cooling field spray cooled surface

time step size up to 1 s 0.2 s calculated characteristics

maximum cooling rate in the core temperature in the core when leaving the cooling field

temperature in the core when leaving the cooling field

The calculated maximum cooling rate in the profile’s core and the temperature in the core when leaving the cooling module have been considered as main simulation results since the maximum cooling rate gives an estimation whether a required cooling rate could be achieved and the temperature in the core provides information whether the length of the cooling field is sufficient for the chosen extrusion speed. For the sensitivity study of quenching profiles by a two-phase spray, instead of a locally varying spray cone area a homogenous quenched area has been investigated. This makes the simulation results independent of the used spray nozzles and the result can easily be used for the design of the cooling module.


Gas quenching. In table 3 the temperatures in the core when leaving the cooling module and the maximum cooling rates during quenching are given for a radius of 10 mm, an cooling field lengths of 500 and varying heat transfer coefficients α as well as extrusion speed vextr

Table 3: Maximum cooling rates and temperatures (TEnd) in the core of a cylindrical EN AW-6082 profile (ø 20 mm) at the end of a gas cooling field with a length of 500 mm for different extrusion speeds and heat transfer coefficients

Dark grey cells represent cooling conditions where the maximum cooling rate is lower than the required one and precipitations can not be suppressed. A cylindrical profile of EN AW-6082 with a diameter of 20 mm requires a cooling field that provides at least a heat transfer coefficient of about 500 W/(m²K) to obtain the required cooling rate at least temporarily. A light grey cell means that the temperature when leaving the cooling field is still inside the temperature range of precipitation although the required cooling rate is given. In this case a higher heat transfer coefficient could remedy or the cooling duration has to be increased by a lower extrusion speed or a higher cooling field length.

Fig. 4 depicts that for a heat transfer coefficient of 500 W/(m²K) the required cooling rate is achieved for a relative short period of time only. Thus cooling rates are insufficient at the lower part of the temperature range of precipitation. On the contrary, a heat transfer coefficient of 1,000 W/(m²K) should be sufficient to suppress precipitations.

Investigations of a profile with a radius of 15 mm show that higher heat transfer coefficients are inevitable to achieve acceptable cooling rates, also longer cooling durations are necessary, since the profiles’ thermal behavior is comparatively slower.

simulationresults 100 500 1000 1500 2000 3000




heat transfer coefficient α [W/m²K]vextr [mm/s]

100

50

25


Fig. 4: Cooling rate depending on temperature for some combinations of parameters

According to table 1 the thermal properties of the alloys of the EN AW-6XXX series are quite similar, thus, thermal behavior can be assumed as similar, too. However, these alloys make different demands on cooling. Fig. 5 represent the possible working area for AW-6082 and AW-6005A with higher quenching requirements.

Fig. 5: Possible working area, heat transfer coefficient and duration in cooling module of a profile

cross section, for AW-6082 and AW-6005A with diameter 20 mm

Spray Quenching. Figs. 6 and 7 depict the simulated profile’s core temperature for a round profile after leaving the cooling module subject to the profile’s exit velocity and the cooling area. The simulation was carried out for a round profile with a diameter of 30 mm (cf. Fig. 6) and 20 mm (cf. Fig. 7) respectively.

Fig. 6 depicts that the critical temperature for a round profile with a diameter of 30 mm can be achieved for a cooling area of 0.04 m² and moderate profile velocities of maximum 6 m/min. For round-spray nozzles as used in [8,9] this would result in an approximated length of the spray field of 550 mm.

As can be seen in Fig. 7, for a round profile with diameter 20 mm the critical temperature can be attained even for high profile velocities and a smaller cooling area, resulting in a smaller length of the quenching module. Even for relatively high profile velocities the critical temperature can be achieved in a quenching module of 500 mm length of round spray nozzles as described in [1,2].

Conclusion and outlook

The simulation results support the design of gas or spray cooling fields for extrusion processes of the investigated profiles. For the less quench sensitive alloys 6060, 6063 and 6005A heat transfer coefficients of 500 W/(m²K) might be sufficient to prevent precipitation during quenching from the

cooling rate - temperature, EN AW-6082, R10, L=500 mm, v=25 mm/s

-100

-80

-60

-40

-20

00 100 200 300 400 500 T [°C]

∆T

/∆t

[K/s

] 100 W/m²K

500 W/m²K

temperature range of precipitation

1500 W/m²K

α = 1000 W/m²K

2000 W/m²K

3000 W/m²K

0

1000

2000

4000

0 10 20 30

duration [s]

hea

t tr

ansf

erco

effi

cien

t[W

/m2

K]

3000

AW-6005A

AW-6082

Fig. 4: Cooling rate depending on temperature for some combinations of parameters

According to table 1 the thermal properties of the alloys of the EN AW-6XXX series are quite similar, thus, thermal behavior can be assumed as similar, too. However, these alloys make different demands on cooling. Fig. 5 represent the possible working area for AW-6082 and AW-6005A with higher quenching requirements.

Fig. 5: Possible working area, heat transfer coefficient and duration in cooling module of a profile

cross section, for AW-6082 and AW-6005A with diameter 20 mm

Spray Quenching. Figs. 6 and 7 depict the simulated profile’s core temperature for a round profile after leaving the cooling module subject to the profile’s exit velocity and the cooling area. The simulation was carried out for a round profile with a diameter of 30 mm (cf. Fig. 6) and 20 mm (cf. Fig. 7) respectively.

Fig. 6 depicts that the critical temperature for a round profile with a diameter of 30 mm can be achieved for a cooling area of 0.04 m² and moderate profile velocities of maximum 6 m/min. For round-spray nozzles as used in [8,9] this would result in an approximated length of the spray field of 550 mm.

As can be seen in Fig. 7, for a round profile with diameter 20 mm the critical temperature can be attained even for high profile velocities and a smaller cooling area, resulting in a smaller length of the quenching module. Even for relatively high profile velocities the critical temperature can be achieved in a quenching module of 500 mm length of round spray nozzles as described in [1,2].

Conclusion and outlook

The simulation results support the design of gas or spray cooling fields for extrusion processes of the investigated profiles. For the less quench sensitive alloys 6060, 6063 and 6005A heat transfer coefficients of 500 W/(m²K) might be sufficient to prevent precipitation during quenching from the

cooling rate - temperature, EN AW-6082, R10, L=500 mm, v=25 mm/s

-100

-80

-60

-40

-20

00 100 200 300 400 500 T [°C]

∆T

/∆t

[K/s

] 100 W/m²K

500 W/m²K

temperature range of precipitation

1500 W/m²K

α = 1000 W/m²K

2000 W/m²K

3000 W/m²K

0

1000

2000

4000

0 10 20 30

duration [s]

hea

t tr

ansf

erco

effi

cien

t[W

/m2

K]

3000

AW-6005A

AW-6082


extrusion heat, provided that the material is cooled for a sufficient time. For the more quench sensitive alloy 6082 at least twice as high heat transfer coefficients are necessary. It has to be clarified whether reduced cooling rates in the lower part of the temperature range of precipitation during gas quenching are temporarily acceptable.

Simulation results indicate that solid profiles of diameters up to 30 mm can be quenched below the critical temperature range of precipitation using quenching modules with a size of about 500 mm or less. Within future works these results will be examined in comparison with experimental investigations.

Furthermore, microstructure and property changes, residual stresses and distortion caused by quenching shall be a future subject of numerical calculations. Using the finite element method these can be predicted though there still is a lack of materials data suited for numerical simulations. For example, thermophysical and mechanical properties depending on temperature are only available in the literature to a certain extent. Finally, the simulation results shall be verified by experimental heat treatments for a successfully realization of integrated gas or spray quenching at the extrusion process.

Fig. 6: Profile’s core temperature after quenching for a round profile with diameter 30 mm

Fig. 7: Profile’s core temperature after quenching for round profile with diameter 20 mm

5 6 7 8 9 10 110.01

0.02

0.0370

90

110

130150

170

190

210

230250

270290

310

330350

370390

410 430

coo

ling

area

[m²]

profile velocity [m/min]

5 6 7 8 9 10 110.01

0.02

0.03

0.04


200220

240260 280

300320

340

360

380

400

420

440

460480 500

coo

ling

area

[m²]

extrusion heat, provided that the material is cooled for a sufficient time. For the more quench sensitive alloy 6082 at least twice as high heat transfer coefficients are necessary. It has to be clarified whether reduced cooling rates in the lower part of the temperature range of precipitation during gas quenching are temporarily acceptable.

Simulation results indicate that solid profiles of diameters up to 30 mm can be quenched below the critical temperature range of precipitation using quenching modules with a size of about 500 mm or less. Within future works these results will be examined in comparison with experimental investigations.

Furthermore, microstructure and property changes, residual stresses and distortion caused by quenching shall be a future subject of numerical calculations. Using the finite element method these can be predicted though there still is a lack of materials data suited for numerical simulations. For example, thermophysical and mechanical properties depending on temperature are only available in the literature to a certain extent. Finally, the simulation results shall be verified by experimental heat treatments for a successfully realization of integrated gas or spray quenching at the extrusion process.

Fig. 6: Profile’s core temperature after quenching for a round profile with diameter 30 mm

Fig. 7: Profile’s core temperature after quenching for round profile with diameter 20 mm

5 6 7 8 9 10 110.01

0.02

0.0370

90

110

130150

170

190

210

230250

270290

310

330350

370390

410 430

coo

ling

area

[m²]


5 6 7 8 9 10 110.01

0.02

0.03

0.04


200220

240260 280

300320

340

360

380

400

420

440

460480 500

coo

ling

area

[m²]


Acknowledgements

The authors gratefully acknowledge funding of this work by the Deutsche Forschungsgemeinschaft, Forschergruppe 922, projects KE616/13-1 and SCHA 1484/7-1.

References

[1] T. Sheppard: Extrusion of Aluminium Alloys, Kluwer Academic Publishers, Dordrecht, 1999

[2] D.D. Hall, I. Mudawar, R.E. Morgan, S.L. Ehlers: Validation of a Systematic Approach to Modeling Spray Quenching of Aluminum Alloy Extrusions, Composites, and Continuous Castings, in: JMEPEG vol. 6, 1997, pp. 77-92

[3] T.A. Deiters, I. Mudawar: Optimization of Spray quenching for Aluminum Extrusion, Forging, or Continuous Casting, in: J. Heat Treat. Vol. 7, 1989, pp. 9-18

[4] C. Kramer, M. Becker: Device for Cooling Extruded Profiles, US Patent 6,216,485 B1, 2001

[5] D.H. Bratland, O. Grong, H. Shercliff, O.R. Myhr, S. Tjotta: Modelling of Precipitation Reactions in Industrial Processing, in: Acta mater. Vol. 45, 1997, pp. 1-22

[6] C. Kramer: Strangabkühlung, in: J. Baumgarten: Strangpressen, DGM-Informationsges.-Verl., 1990, Oberursel, pp. 119-129

[7] N. Jaervstraet, S. Tjotta: A Process Modell for On-Line Quenching of Aluminium Alloys, in: Mateallurgical and Materials Transactions B vol. 27B, 1996, pp. 501-508

[8] C. Krause, E. Wulf, F. Nürnberger, F.-W. Bach: Wärmeübergangs- und Tropfencharakteristik für eine Spraykühlung im Temperaturbereich von 900-100 °C, in: Forsch Ingenieurwes vol. 72 (2008), pp.163-173

[9] C. Krause: Randschichtvergüten verzahnter Bauteile mittels einer Wasser-Luft-Spraykühlung, Dissertation, Leibniz Universität Hannover (2008)

[10] F. Puschmann: Experimentelle Untersuchung der Spraykühlung zur Qualitätsverbesserung durch definierte Einstellung des Wärmeübergangs, Dissertation, Otto-von-Guericke-Universität Magdeburg (2003)

[11] J.P. Holman: Heat Transfer, McGraw-Hill, New York, 2002

[12] M.S Hamed: Evaluation of Heat Transfer Coefficients in Water Spray Quenching Systems, 20th Heat Treating Conf. Proc., 2000, ASM International, Vol. II, pp. 785

[13] B. Milkereit, O. Kessler, C. Schick: Recording of continuous cooling precipitation diagrams of aluminium alloys, in: Thermochimica Acta, Vol. 492, Elsevier Science (2009), pp. 73-78

[14] C. Kammer: Aluminium-Taschenbuch, edition 15, Aluminium-Verlag (1998)

[15] W. Hesse, Key to Aluminium, Aluminium-Verlag (2006)

[16] B. Milkereit, C. Schick, O. Kessler: Continuous cooling precipitation diagrams of aluminium-magnesium-silicon alloys, in: J. Hirsch, B. Skrotzki, G. Gottstein (Eds), 11th International Conference on Aluminium Alloys, Deutsche Gesellschaft für Materialkunde e.V., WILEY-VCH Weinheim, Aachen, Germany, (2008), pp. 1232-1237

[17] R. von Bargen, O. Kessler, H.-W. Zoch: Kontinuierliche Zeit-Ausscheidungs-Diagramme der Aluminiumlegierungen E AW-7020 und E AW-7050, in: HTM Z. Werkst. Wärmebeh. Fertigung 62 (2007) 6 pp. 285-293

[18] M. Narazaki, M. Kogawara, M. Qin, Y. Watanabe: Measurement and Database Construction of Heat Transfer Coefficient of Gas Quenching, edited by H.-W. Zoch, Th. Lübben, Proc. 2nd Int. Conf. on Distortion Engineering, 17-19.09.08, Bremen, Germany, 2008, pp. 327-334.

Acknowledgements

The authors gratefully acknowledge funding of this work by the Deutsche Forschungsgemeinschaft, Forschergruppe 922, projects KE616/13-1 and SCHA 1484/7-1.

References

[1] T. Sheppard: Extrusion of Aluminium Alloys, Kluwer Academic Publishers, Dordrecht, 1999

[2] D.D. Hall, I. Mudawar, R.E. Morgan, S.L. Ehlers: Validation of a Systematic Approach to Modeling Spray Quenching of Aluminum Alloy Extrusions, Composites, and Continuous Castings, in: JMEPEG vol. 6, 1997, pp. 77-92

[3] T.A. Deiters, I. Mudawar: Optimization of Spray quenching for Aluminum Extrusion, Forging, or Continuous Casting, in: J. Heat Treat. Vol. 7, 1989, pp. 9-18

[4] C. Kramer, M. Becker: Device for Cooling Extruded Profiles, US Patent 6,216,485 B1, 2001

[5] D.H. Bratland, O. Grong, H. Shercliff, O.R. Myhr, S. Tjotta: Modelling of Precipitation Reactions in Industrial Processing, in: Acta mater. Vol. 45, 1997, pp. 1-22

[6] C. Kramer: Strangabkühlung, in: J. Baumgarten: Strangpressen, DGM-Informationsges.-Verl., 1990, Oberursel, pp. 119-129

[7] N. Jaervstraet, S. Tjotta: A Process Modell for On-Line Quenching of Aluminium Alloys, in: Mateallurgical and Materials Transactions B vol. 27B, 1996, pp. 501-508

[8] C. Krause, E. Wulf, F. Nürnberger, F.-W. Bach: Wärmeübergangs- und Tropfencharakteristik für eine Spraykühlung im Temperaturbereich von 900-100 °C, in: Forsch Ingenieurwes vol. 72 (2008), pp.163-173

[9] C. Krause: Randschichtvergüten verzahnter Bauteile mittels einer Wasser-Luft-Spraykühlung, Dissertation, Leibniz Universität Hannover (2008)

[10] F. Puschmann: Experimentelle Untersuchung der Spraykühlung zur Qualitätsverbesserung durch definierte Einstellung des Wärmeübergangs, Dissertation, Otto-von-Guericke-Universität Magdeburg (2003)

[11] J.P. Holman: Heat Transfer, McGraw-Hill, New York, 2002

[12] M.S Hamed: Evaluation of Heat Transfer Coefficients in Water Spray Quenching Systems, 20th Heat Treating Conf. Proc., 2000, ASM International, Vol. II, pp. 785

[13] B. Milkereit, O. Kessler, C. Schick: Recording of continuous cooling precipitation diagrams of aluminium alloys, in: Thermochimica Acta, Vol. 492, Elsevier Science (2009), pp. 73-78

[14] C. Kammer: Aluminium-Taschenbuch, edition 15, Aluminium-Verlag (1998)

[15] W. Hesse, Key to Aluminium, Aluminium-Verlag (2006)

[16] B. Milkereit, C. Schick, O. Kessler: Continuous cooling precipitation diagrams of aluminium-magnesium-silicon alloys, in: J. Hirsch, B. Skrotzki, G. Gottstein (Eds), 11th International Conference on Aluminium Alloys, Deutsche Gesellschaft für Materialkunde e.V., WILEY-VCH Weinheim, Aachen, Germany, (2008), pp. 1232-1237

[17] R. von Bargen, O. Kessler, H.-W. Zoch: Kontinuierliche Zeit-Ausscheidungs-Diagramme der Aluminiumlegierungen E AW-7020 und E AW-7050, in: HTM Z. Werkst. Wärmebeh. Fertigung 62 (2007) 6 pp. 285-293

[18] M. Narazaki, M. Kogawara, M. Qin, Y. Watanabe: Measurement and Database Construction of Heat Transfer Coefficient of Gas Quenching, edited by H.-W. Zoch, Th. Lübben, Proc. 2nd Int. Conf. on Distortion Engineering, 17-19.09.08, Bremen, Germany, 2008, pp. 327-334.


An Approach to Simulate Shape Distortion due to Cooling in Aluminum Extrusion

S. Bikass1, 2,a , B. Andersson1,b, X. Ma1,c 1 SINTEF Material and Chemistry, PB 124 Blindern, 0134 Oslo, Norway

2University of Oslo, Faculty of Mathematics and Natural Sciences [email protected], [email protected], [email protected]

Keywords: Extrusion, Cooling, FEM, Boundary Condition

Abstract. Cooling subsequent to extrusion is a crucial process in aluminum extrusion value chain. Non-uniform cooling-induced shape distortion, such as deflection, twisting and etc., is a challenge for extrusion profile manufacturers. Temperature management is therefore a key to the aluminum extrusion process. Appropriate modeling, using both physical and numerical methods, can help us achieve a better temperature control in extrusion plants. In this work, finite element (FE) method was used to simulate shape distortion due to cooling and the most important challenge was to make FE models compatible to real conditions in plants. The effects of three important items I) mechanical boundary condition II) cooling source type and III) effective cooling length were examined. It was shown that for compatible prediction of distortions it was necessary to define these items similar to real life. It was also revealed that with a suitable definition of boundary conditions it is possible to use a short lab scale sample to understand mechanisms in real life profiles.

Introduction

Aluminum extrusion is capable for the production of long solid or hollow sections with complex cross-section geometries [1]. A wide range of applications can therefore be found in automotives and aircraft manufacturing, as well as for lightweight constructions [2]. Cooling subsequent to extrusion is crucial both for strength and shape. The strength increases

significantly with increasing quenching rate. When rapid cooling is intended, there is no medium better than water that is cheaper and easier to use. Heat transfer coefficient is highly temperature dependent. Its variations are generally classified into four different regimes, i.e. film boiling, transition boiling, nucleate boiling and natural convection [3,4]. However, the distortion due to non-homogeneous distribution of cooling regime is inevitable, so

shape corrections are needed [5]. It is a challenge for extrusion profile manufacturers to reduce shape changes to be within close tolerances at low cost. The costs of the production optimization can be lowered significantly by using numerical

simulation to reduce costly time-consuming trial and error experiments. It can also help understand governing mechanisms. The finite element (FE) modeling is a powerful numerical tool for analyzing of non-linear, thermo-mechanical coupled cases with plastic distortions. It could be utilized to predict distortion induced by water quenching during cooling. The effects of process parameters and distortion mechanisms could also be investigated. The accuracy of the FE simulation, however, depends on the proper definition of boundary conditions at interfaces. It is particular important for the cooling simulation as there are several constrains and variable conditions. In this paper, the main goal was to prepare a capable FE model which is manageable but still

representative for a realistic industrial case.

An Approach to Simulate Shape Distortion due to Cooling in Aluminum Extrusion

S. Bikass1, 2,a , B. Andersson1,b, X. Ma1,c 1 SINTEF Material and Chemistry, PB 124 Blindern, 0134 Oslo, Norway

2University of Oslo, Faculty of Mathematics and Natural Sciences [email protected], [email protected], [email protected]

Keywords: Extrusion, Cooling, FEM, Boundary Condition

Abstract. Cooling subsequent to extrusion is a crucial process in aluminum extrusion value chain. Non-uniform cooling-induced shape distortion, such as deflection, twisting and etc., is a challenge for extrusion profile manufacturers. Temperature management is therefore a key to the aluminum extrusion process. Appropriate modeling, using both physical and numerical methods, can help us achieve a better temperature control in extrusion plants. In this work, finite element (FE) method was used to simulate shape distortion due to cooling and the most important challenge was to make FE models compatible to real conditions in plants. The effects of three important items I) mechanical boundary condition II) cooling source type and III) effective cooling length were examined. It was shown that for compatible prediction of distortions it was necessary to define these items similar to real life. It was also revealed that with a suitable definition of boundary conditions it is possible to use a short lab scale sample to understand mechanisms in real life profiles.

Introduction

Aluminum extrusion is capable for the production of long solid or hollow sections with complex cross-section geometries [1]. A wide range of applications can therefore be found in automotives and aircraft manufacturing, as well as for lightweight constructions [2]. Cooling subsequent to extrusion is crucial both for strength and shape. The strength increases

significantly with increasing quenching rate. When rapid cooling is intended, there is no medium better than water that is cheaper and easier to use. Heat transfer coefficient is highly temperature dependent. Its variations are generally classified into four different regimes, i.e. film boiling, transition boiling, nucleate boiling and natural convection [3,4]. However, the distortion due to non-homogeneous distribution of cooling regime is inevitable, so

shape corrections are needed [5]. It is a challenge for extrusion profile manufacturers to reduce shape changes to be within close tolerances at low cost. The costs of the production optimization can be lowered significantly by using numerical

simulation to reduce costly time-consuming trial and error experiments. It can also help understand governing mechanisms. The finite element (FE) modeling is a powerful numerical tool for analyzing of non-linear, thermo-mechanical coupled cases with plastic distortions. It could be utilized to predict distortion induced by water quenching during cooling. The effects of process parameters and distortion mechanisms could also be investigated. The accuracy of the FE simulation, however, depends on the proper definition of boundary conditions at interfaces. It is particular important for the cooling simulation as there are several constrains and variable conditions. In this paper, the main goal was to prepare a capable FE model which is manageable but still

representative for a realistic industrial case.


Finite Element Modeling

Material and Process Parameters The material used was AA6082. Physical properties of this alloy were given in Table 1 and these were assumed to be independent on temperature. Some mechanical properties in solute condition are temperature dependent as shown in Figure 1. Extrusion process parameters were selected as in real process in plants (Table 2).

The profile section was a rectangle with width of 200 mm and thickness of 3 mm (where thickness is along z direction). The length was different in cases (5m or 10m), as will be discussed in case design section. The top side was cooled by water spraying and the bottom side of profile by air flow. Heat transfer coefficients for air cooling and water spray cooling were dependent on temperature. As it was mentioned before, heat transfer during cooling will typically occur through four regimes. These four regimes were simplified here; the first and fourth regimes were assumed to have constant heat transfer while it declines with increasing temperature in the second and third regimes. Transition boiling and nucleate boiling were merged together and these zones are considered as straight lines instead of concave and convex shapes (Fig. 2).

Table 1. Physical properties of AA6082 Table 2. Extrusion process parameters Density [Kg/m3] 2700

Exit Velocity [m/sec] 0.25 Expansion Coefficient [/˚C] 2.55e-05 Outlet Temperature [˚C] 550 Conductivity [W/ m.˚K] 200 Water Temperature [˚C] 17 Specific Heat [J/(Kg.˚C)] 900 Ambient Temperature [˚C] 17

Finite Element parameters The 3D finite element simulations were carried out for cooling operation by means of ABAQUS/Standard software which performs coupled temperature-displacement modeling in a well established way. The brick element type, C3D20T, was used to model the extrudate. This is a hexahedral solid element with 20 nodes and with the quadratic displacement interpolation which is formulated for plastic deformation. Four elements were used in the thickness direction and the width and length were both selected equal to 100 mm.

Case design In this study the most important challenge was to make FE models compatible to real conditions in plants. Generally cooling process consists of a die, a puller and a quench box which is shown schematically in Fig. 3. The die and the puller were defined by mechanical boundary conditions and the quench box was considered as a cooling source. Mechanical boundary condition, cooling source type and effective cooling length “L” (distance between the die and the puller) are three important items affecting simulation results. Various types of boundary conditions and cooling sources beside of the two values for length were considered.

Boundary Condition: The die side was completely constrained by the die cavity and implemented in FE models. The constraint due to the puller can be strong or weak in reality. Therefore, only two boundary conditions (partial and full constraints) need to be considered. In the first one, the puller side was constrained partially (only at y and z directions when x, y and z were extrusion direction, width direction and thickness direction, respectively). In the second one, the puller side was constrained completely, too. Cooling Source Type: It could be defined in two types. The first one was stationary which can be considered also as a slow extrusion and the cooling zone (into the quench box) would be quenched completely. The second one was a moving type and had a constant velocity (similar to real life) relative to the profile. Effective cooling length: In real life, the length of the extruded profile varies from 5 m to 20 m but in modeling it seemed to be difficult to change the length during the process. Consequently it was decided to select two lengths: I) 5m; the quench box length and the distance between the die and the quench box are 4 m and 1 m, respectively, and II) 10 m. It was shown in Fig. 3. Type I could show

Finite Element Modeling

Material and Process Parameters The material used was AA6082. Physical properties of this alloy were given in Table 1 and these were assumed to be independent on temperature. Some mechanical properties in solute condition are temperature dependent as shown in Figure 1. Extrusion process parameters were selected as in real process in plants (Table 2).

The profile section was a rectangle with width of 200 mm and thickness of 3 mm (where thickness is along z direction). The length was different in cases (5m or 10m), as will be discussed in case design section. The top side was cooled by water spraying and the bottom side of profile by air flow. Heat transfer coefficients for air cooling and water spray cooling were dependent on temperature. As it was mentioned before, heat transfer during cooling will typically occur through four regimes. These four regimes were simplified here; the first and fourth regimes were assumed to have constant heat transfer while it declines with increasing temperature in the second and third regimes. Transition boiling and nucleate boiling were merged together and these zones are considered as straight lines instead of concave and convex shapes (Fig. 2).

Table 1. Physical properties of AA6082 Table 2. Extrusion process parameters Density [Kg/m3] 2700

Exit Velocity [m/sec] 0.25 Expansion Coefficient [/˚C] 2.55e-05 Outlet Temperature [˚C] 550 Conductivity [W/ m.˚K] 200 Water Temperature [˚C] 17 Specific Heat [J/(Kg.˚C)] 900 Ambient Temperature [˚C] 17

Finite Element parameters The 3D finite element simulations were carried out for cooling operation by means of ABAQUS/Standard software which performs coupled temperature-displacement modeling in a well established way. The brick element type, C3D20T, was used to model the extrudate. This is a hexahedral solid element with 20 nodes and with the quadratic displacement interpolation which is formulated for plastic deformation. Four elements were used in the thickness direction and the width and length were both selected equal to 100 mm.

Case design In this study the most important challenge was to make FE models compatible to real conditions in plants. Generally cooling process consists of a die, a puller and a quench box which is shown schematically in Fig. 3. The die and the puller were defined by mechanical boundary conditions and the quench box was considered as a cooling source. Mechanical boundary condition, cooling source type and effective cooling length “L” (distance between the die and the puller) are three important items affecting simulation results. Various types of boundary conditions and cooling sources beside of the two values for length were considered.

Boundary Condition: The die side was completely constrained by the die cavity and implemented in FE models. The constraint due to the puller can be strong or weak in reality. Therefore, only two boundary conditions (partial and full constraints) need to be considered. In the first one, the puller side was constrained partially (only at y and z directions when x, y and z were extrusion direction, width direction and thickness direction, respectively). In the second one, the puller side was constrained completely, too. Cooling Source Type: It could be defined in two types. The first one was stationary which can be considered also as a slow extrusion and the cooling zone (into the quench box) would be quenched completely. The second one was a moving type and had a constant velocity (similar to real life) relative to the profile. Effective cooling length: In real life, the length of the extruded profile varies from 5 m to 20 m but in modeling it seemed to be difficult to change the length during the process. Consequently it was decided to select two lengths: I) 5m; the quench box length and the distance between the die and the quench box are 4 m and 1 m, respectively, and II) 10 m. It was shown in Fig. 3. Type I could show


effect of cooling at the beginning of cooling and type II was long enough to show effects of length. The designed cases intended to reveal the effects of these parameters were listed in Table 3.

0

10

20

30

40

50

60

70

80

0 100 200 300 400 500 600Temperature( ˚C)

You

ng's

Mod

ulus

(GP

a)

0.34

0.35

0.36

0.37

0.38

0 100 200 300 400 500 600Temperature( ˚C)

Poi

sson

Rat

io

(a) (b)

0

10

20

30

40

50

60

70

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Strain()

Stre

ss(M

Pa)

(c)

Fig.: 1. Mechanical properties of Al6082 depending on the temperature variation: a) Elastic Module, b) Poisson ratio, c) Stress – Strain curve

T=20˚C

T=200˚C

T=225˚

T=250˚

T=275˚

T=325˚

T=375˚

T=400˚C

T=500˚C

effect of cooling at the beginning of cooling and type II was long enough to show effects of length. The designed cases intended to reveal the effects of these parameters were listed in Table 3.

0

10

20

30

40

50

60

70

80

0 100 200 300 400 500 600Temperature( ˚C)

You

ng's

Mod

ulus

(GP

a)

0.34

0.35

0.36

0.37

0.38

0 100 200 300 400 500 600Temperature( ˚C)

Poi

sson

Rat

io

(a) (b)

0

10

20

30

40

50

60

70

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Strain()

Stre

ss(M

Pa)

(c)

Fig.: 1. Mechanical properties of Al6082 depending on the temperature variation: a) Elastic Module, b) Poisson ratio, c) Stress – Strain curve

T=20˚C

T=200˚C

T=225˚

T=250˚

T=275˚

T=325˚

T=375˚

T=400˚C

T=500˚C


0

2000

4000

6000

8000

10000

12000

0 100 200 300 400 500 600

Temperature( ˚C)

h(W

/m2 se

c)

02468

10121416

0 100 200 300 400 500 600Temperature( ˚C)

h(W

/m2 se

c)

(a) (b)

Fig.: 2. Heat transfer coefficient (h) variation for: a) Water spray b) Air cooling

Fig. 3: Schematic of cooling process defined in extrusion process


Simulation results demonstrated the effects of cooling source and boundary conditions on the deflection for short (5 m) and long (10 m) samples, as illustrated in Fig. 4 (a) and (b). For the short sample, the induced distortion by the stationary cooling source and weak constraint in puller side (WS5) was in opposite direction to the short sample with a moving cooling source (WM5). The same result was seen for the long sample even when both sides completely constrained (BS10 and BM10). The most interesting result was that the distortion shape (banana shape distortion) of the short sample (BM5) was similar to the long one (BM10). In addition, the maximum deflection for the short sample was larger. This implies that the short sample can be used as an upper bound prediction of the magnitude of deflection. It also saves the calculation time greatly. Therefore, an effective cooling length of 5 m for rectangular sections is acceptable. However, a lab scale model is needed in order to verify hypothesis of mechanisms by direct

comparing with experiment results. The simulation results in Fig. 5 show that the deflection curvature of selected lab scale model with a length of 0.35 m after cooling are different from a full size model in Fig. 4 (BM10 and BM5). This difference might be eliminated by defining the lab scale sample as a small element of real scale one (as shown in Fig. 6). For this representative element, boundary conditions are not the same as real scale and they should be defined properly. By using of this idea, results (except distortion along length such as banana shape) can be applied to real life. However, absolute values of real scale distortion, especially along length, should be calculated by its full size model; because lab scale length is very small relative to real length and its distortion in z direction is not sensible.

workpiece

1m

Puller

Quench Box

Die 4m

z x

0

2000

4000

6000

8000

10000

12000

0 100 200 300 400 500 600

Temperature( ˚C)

h(W

/m2 se

c)

02468

10121416

0 100 200 300 400 500 600Temperature( ˚C)

h(W

/m2 se

c)

(a) (b)

Fig.: 2. Heat transfer coefficient (h) variation for: a) Water spray b) Air cooling

Fig. 3: Schematic of cooling process defined in extrusion process


Simulation results demonstrated the effects of cooling source and boundary conditions on the deflection for short (5 m) and long (10 m) samples, as illustrated in Fig. 4 (a) and (b). For the short sample, the induced distortion by the stationary cooling source and weak constraint in puller side (WS5) was in opposite direction to the short sample with a moving cooling source (WM5). The same result was seen for the long sample even when both sides completely constrained (BS10 and BM10). The most interesting result was that the distortion shape (banana shape distortion) of the short sample (BM5) was similar to the long one (BM10). In addition, the maximum deflection for the short sample was larger. This implies that the short sample can be used as an upper bound prediction of the magnitude of deflection. It also saves the calculation time greatly. Therefore, an effective cooling length of 5 m for rectangular sections is acceptable. However, a lab scale model is needed in order to verify hypothesis of mechanisms by direct

comparing with experiment results. The simulation results in Fig. 5 show that the deflection curvature of selected lab scale model with a length of 0.35 m after cooling are different from a full size model in Fig. 4 (BM10 and BM5). This difference might be eliminated by defining the lab scale sample as a small element of real scale one (as shown in Fig. 6). For this representative element, boundary conditions are not the same as real scale and they should be defined properly. By using of this idea, results (except distortion along length such as banana shape) can be applied to real life. However, absolute values of real scale distortion, especially along length, should be calculated by its full size model; because lab scale length is very small relative to real length and its distortion in z direction is not sensible.

workpiece

1m

Puller

Quench Box

Die 4m

z x


Table 3. Case study in FEM

Case 0ame Boundary condition Cooling source Length(m) WS5 Weak constraint at the puller side Stationary 5 WM5 Weak constraint at the puller side Moving 5 BS5 Both sides completely constrained Stationary 5 BM5 Both sides completely constrained Moving 5 WS10 Weak constraint at the puller side Stationary 10 BS10 Both sides completely constrained Stationary 10 BM10 Both sides completely constrained Moving 10

-0.06

-0.03

0

0.03

0 1 2 3 4 5Length (m)

Def

lect

ion

(m)

WS5WM5BS5BM5

-0.06

-0.03

0

0.03

0.06

0.09

0 1 2 3 4 5 6 7 8 9 10

Length (m)

Def

lect

ion

(m)

WS10BS10BM10

(a) (b)

Fig. 4: Effects of cooling source and boundary condition on deflection for a) L=5m b) L=10m

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0 0.1 0.2 0.3 0.4

Length(m)

Def

lect

ion(

mm

)

Fig. 5: Deflection of lab scale sample with real life boundary condition

Fig. 6: Schematic of new idea assumes lab scale sample as a small element of real scale sample

workpiece

Puller

Quench Box

Die

Lab scale sample

Die Puller Puller Die

Die Side Puller Side

Table 3. Case study in FEM

Case 0ame Boundary condition Cooling source Length(m) WS5 Weak constraint at the puller side Stationary 5 WM5 Weak constraint at the puller side Moving 5 BS5 Both sides completely constrained Stationary 5 BM5 Both sides completely constrained Moving 5 WS10 Weak constraint at the puller side Stationary 10 BS10 Both sides completely constrained Stationary 10 BM10 Both sides completely constrained Moving 10

-0.06

-0.03

0

0.03

0 1 2 3 4 5Length (m)

Def

lect

ion

(m)

WS5WM5BS5BM5

-0.06

-0.03

0

0.03

0.06

0.09

0 1 2 3 4 5 6 7 8 9 10

Length (m)

Def

lect

ion

(m)

WS10BS10BM10

(a) (b)

Fig. 4: Effects of cooling source and boundary condition on deflection for a) L=5m b) L=10m

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0 0.1 0.2 0.3 0.4

Length(m)

Def

lect

ion(

mm

)

Fig. 5: Deflection of lab scale sample with real life boundary condition

Fig. 6: Schematic of new idea assumes lab scale sample as a small element of real scale sample

workpiece

Puller

Quench Box

Die

Lab scale sample

Die Puller Puller Die

Die Side Puller Side


Conclusion

Finite element modeling of cooling process of extrudates was performed and the simulation results illustrated that defining cooling source and boundary condition is very important. In order to predict distortions properly:

• Boundary conditions should be defined similar to real life. • Cooling source must be moving type as in plants. • It is not necessary to define effective cooling length as same as real profile length. An effective cooling length of 5 m for rectangular sections is acceptable.

• With an appropriate definition of boundary condition, it is possible to use a short lab scale sample which represents a small element of a real product section.

Acknowledgements

This work is part of a project run by Hydro in cooperation with SINTEF Materials and Chemistry. The work is partly funded by the Research Council of Norway (RCN). The authors would like to acknowledge their supports greatly. References

[1] T. Hatzenbichler, B. Buchmayra and A. Umgeherb: Journal of Materials Processing Technology Vol. 182 (2007), p. 73.

[2] F. Parvizian, T. Kayser, C. Hortig and B. Svendsen: Journal of Materials Processing Technology Vol. 209 (2009), p. 876.

[3] M. Kristoffersen: Studies of Shape Variations during Cooling of Flat Extruded Sections, PhD Thesis, University of Oslo (2004).

[4] T. Walle: Shape variations due to cooling, PhD Thesis, University of Oslo (2007). [5] M. Imose: Transactions of the Iron and Steel Institute of Japan Vol. 25 (1985), p. 911.

Conclusion

Finite element modeling of cooling process of extrudates was performed and the simulation results illustrated that defining cooling source and boundary condition is very important. In order to predict distortions properly:

• Boundary conditions should be defined similar to real life. • Cooling source must be moving type as in plants. • It is not necessary to define effective cooling length as same as real profile length. An effective cooling length of 5 m for rectangular sections is acceptable.

• With an appropriate definition of boundary condition, it is possible to use a short lab scale sample which represents a small element of a real product section.

Acknowledgements

This work is part of a project run by Hydro in cooperation with SINTEF Materials and Chemistry. The work is partly funded by the Research Council of Norway (RCN). The authors would like to acknowledge their supports greatly. References

[1] T. Hatzenbichler, B. Buchmayra and A. Umgeherb: Journal of Materials Processing Technology Vol. 182 (2007), p. 73.

[2] F. Parvizian, T. Kayser, C. Hortig and B. Svendsen: Journal of Materials Processing Technology Vol. 209 (2009), p. 876.

[3] M. Kristoffersen: Studies of Shape Variations during Cooling of Flat Extruded Sections, PhD Thesis, University of Oslo (2004).

[4] T. Walle: Shape variations due to cooling, PhD Thesis, University of Oslo (2007). [5] M. Imose: Transactions of the Iron and Steel Institute of Japan Vol. 25 (1985), p. 911.


Analysis of polypropylene deformation in a 135° ECAE die: experiments and three-dimensional finite element simulations

B. Aour1,a, F. Zaïri2,b, M. Naït-Abdelaziz2, J.M. Gloaguen3, J.M. Lefebvre3 1ENSET d'Oran, Laboratoire de recherche en Technologie de l’Environnement, Département de

Mécanique, BP1523 El'Mnaour 31000, Algeria 2Université Lille 1 Sciences et Technologies, Laboratoire de Mécanique de Lille (UMR CNRS

8107) Avenue P. Langevin, 59655 Villeneuve d’Ascq Cedex, France 3Université Lille 1 Sciences et Technologies, Laboratoire de Structure et Propriétés de l’Etat Solide

(UMR CNRS 8008), Bât. C6, 59655 Villeneuve d’Ascq Cedex, France [email protected], [email protected]

Keywords: Polypropylene; ECAE; Experiments; Finite element analysis. Abstract. Plastic deformation of polypropylene (PP) resulting from equal channel angular extrusion (ECAE) process was investigated in a 135° die. A phenomenological elastic-viscoplastic constitutive model was identified and coupled with the three-dimensional finite element (FE) method in order to predict the different processing parameters governing the deformation behaviour of PP during the extrusion. An optimal agreement between FE results and experimental data was obtained for a friction coefficient of 0.2. A detailed three-dimensional FE analysis of stress-strain field distribution was then carried out. The effects of both the number of extrusion passes and the processing routes were experimentally highlighted. The results show that the pressing force decreases with the increase of the number of extrusion passes and reaches its saturation state rapidly for routes A and C while, for routes BA and BC, it requires a high number of passes.

Introduction

Equal channel angular extrusion (ECAE) is a method for deforming materials to very high plastic deformations without changing the sample cross-section. The general principle of this process is shown in Fig. 1. The tool is a block with two intersecting channels of identical cross-sections. The sample is placed in the vertical channel and then extruded around the bend into the second channel. Furthermore, by varying the orientation of the sample between consecutive passes, very different microstructures can be expected. Indeed, four fundamental ECAE routes (Fig. 1b) were defined in the literature [1]. Route A: the sample is re-extruded in the same orientation as the previous pass. Route BA: the sample is rotated alternatively by +90° and -90° around the longitudinal axis of the sample between two successive passes. Route BC: the sample is rotated by +90° after each pass. Route C: the sample is rotated by 180° and then re-extruded.

The main investigations and developments on ECAE were achieved on metallic alloys [1-5]. Indeed, although 200 papers per year are published on ECAE, those only concerning polymers are much less numerous [6-18]. According to our knowledge, the first work on polymers extrusion was reported by Sue and Li [6]. They showed that the ECAE process is effective in altering the morphology in low density polyethylene (LDPE). Later, for polycarbonate (PC), Sue et al. [7] pointed out that the extrusion temperature requires to be slightly below the glass transition in order to improve the effectiveness of the ECAE process. Li et al. [8] examined the effects of the number of extrusion passes and the processing routes on the mechanical properties of PC. The effect of molecular anisotropy on the impact strength of PC was examined by Xia et al. [9]. It was found that PC samples processed via routes A and C have higher impact strength than that of the reference material. Xia et al. [10] found that the crystallinity and the molecular orientation are the major factors affecting the dynamic mechanical properties of semicrystalline polyethylene terephthalate (PET) extruded by ECAE. It was shown that the extruded PET has higher bending and torsional

Analysis of polypropylene deformation in a 135° ECAE die: experiments and three-dimensional finite element simulations

B. Aour1,a, F. Zaïri2,b, M. Naït-Abdelaziz2, J.M. Gloaguen3, J.M. Lefebvre3 1ENSET d'Oran, Laboratoire de recherche en Technologie de l’Environnement, Département de

Mécanique, BP1523 El'Mnaour 31000, Algeria 2Université Lille 1 Sciences et Technologies, Laboratoire de Mécanique de Lille (UMR CNRS

8107) Avenue P. Langevin, 59655 Villeneuve d’Ascq Cedex, France 3Université Lille 1 Sciences et Technologies, Laboratoire de Structure et Propriétés de l’Etat Solide

(UMR CNRS 8008), Bât. C6, 59655 Villeneuve d’Ascq Cedex, France [email protected], [email protected]

Keywords: Polypropylene; ECAE; Experiments; Finite element analysis. Abstract. Plastic deformation of polypropylene (PP) resulting from equal channel angular extrusion (ECAE) process was investigated in a 135° die. A phenomenological elastic-viscoplastic constitutive model was identified and coupled with the three-dimensional finite element (FE) method in order to predict the different processing parameters governing the deformation behaviour of PP during the extrusion. An optimal agreement between FE results and experimental data was obtained for a friction coefficient of 0.2. A detailed three-dimensional FE analysis of stress-strain field distribution was then carried out. The effects of both the number of extrusion passes and the processing routes were experimentally highlighted. The results show that the pressing force decreases with the increase of the number of extrusion passes and reaches its saturation state rapidly for routes A and C while, for routes BA and BC, it requires a high number of passes.

Introduction

Equal channel angular extrusion (ECAE) is a method for deforming materials to very high plastic deformations without changing the sample cross-section. The general principle of this process is shown in Fig. 1. The tool is a block with two intersecting channels of identical cross-sections. The sample is placed in the vertical channel and then extruded around the bend into the second channel. Furthermore, by varying the orientation of the sample between consecutive passes, very different microstructures can be expected. Indeed, four fundamental ECAE routes (Fig. 1b) were defined in the literature [1]. Route A: the sample is re-extruded in the same orientation as the previous pass. Route BA: the sample is rotated alternatively by +90° and -90° around the longitudinal axis of the sample between two successive passes. Route BC: the sample is rotated by +90° after each pass. Route C: the sample is rotated by 180° and then re-extruded.

The main investigations and developments on ECAE were achieved on metallic alloys [1-5]. Indeed, although 200 papers per year are published on ECAE, those only concerning polymers are much less numerous [6-18]. According to our knowledge, the first work on polymers extrusion was reported by Sue and Li [6]. They showed that the ECAE process is effective in altering the morphology in low density polyethylene (LDPE). Later, for polycarbonate (PC), Sue et al. [7] pointed out that the extrusion temperature requires to be slightly below the glass transition in order to improve the effectiveness of the ECAE process. Li et al. [8] examined the effects of the number of extrusion passes and the processing routes on the mechanical properties of PC. The effect of molecular anisotropy on the impact strength of PC was examined by Xia et al. [9]. It was found that PC samples processed via routes A and C have higher impact strength than that of the reference material. Xia et al. [10] found that the crystallinity and the molecular orientation are the major factors affecting the dynamic mechanical properties of semicrystalline polyethylene terephthalate (PET) extruded by ECAE. It was shown that the extruded PET has higher bending and torsional


storage moduli than those of the reference material at temperatures above the glass transition. More recently, the evolution of microstructure in extruded PET was examined by Wang et al. [11] using X-ray scattering. Two-dimensional finite element (FE) analyses were recently conducted to examine the effects of tool geometry, friction, extrusion velocity, extrusion temperature, number of extrusion passes and processing routes on the deformation behaviour of polymers during ECAE process [12-18].

(a) (b)

Fig. 1. Schematic illustration of (a) a typical ECAE facility (in this work: Φ = 135° and θ = 34°) and (b) the different processing routes.

In this work, the deformation behaviour of polypropylene (PP) is examined in a 135° ECAE die.

The angular extrusion tests were carried out on prismatic samples with square cross-sections, which allow an analysis of all the possible routes by rotation of the samples around its longitudinal axis. The experimental results in terms of the force-displacement response are compared with those obtained by three-dimensional FE simulations. Then, a detailed analysis of stress-strain field distribution in the bulk of the sample was carried out. Finally, the effects of the number of extrusion passes and the processing routes on the pressing force were investigated as well.

Experiments

The experiments were conducted using a semicrystalline PP material provided by the Goodfellow Company (United Kingdom) with a weight-average molar weight of 180 kg/mol. Its thermal properties were obtained by differential scanning calorimetry (DSC) analysis. A crystal content of about 55% was found.

The mechanical measurements were achieved at room temperature on an electromechanical Instron© testing machine. The testing temperature (ambient) being between the glass transition temperature (about -20°C) and the melting temperature (about 170°C), the amorphous phase is therefore in the rubbery state.

The ECAE samples were machined along the same direction from a compression molded plate, then surfaced simultaneously on the cutting facets and polished. The ECAE samples have a cross-section of approximately 10×10 mm2 and a length of 70 mm. Extrusion tests were performed on a 135° die without lubrication. To characterize the plastic flow behaviour of PP material and to derive

Route A

Route C

Route Bc: rotated by +90°

180°

90°

0°

Route BA: rotated alternatively by +90° and -90°

Sample rotation direction

Φ

θ

Top surface

Bottom surface

storage moduli than those of the reference material at temperatures above the glass transition. More recently, the evolution of microstructure in extruded PET was examined by Wang et al. [11] using X-ray scattering. Two-dimensional finite element (FE) analyses were recently conducted to examine the effects of tool geometry, friction, extrusion velocity, extrusion temperature, number of extrusion passes and processing routes on the deformation behaviour of polymers during ECAE process [12-18].

(a) (b)

Fig. 1. Schematic illustration of (a) a typical ECAE facility (in this work: Φ = 135° and θ = 34°) and (b) the different processing routes.

In this work, the deformation behaviour of polypropylene (PP) is examined in a 135° ECAE die.

The angular extrusion tests were carried out on prismatic samples with square cross-sections, which allow an analysis of all the possible routes by rotation of the samples around its longitudinal axis. The experimental results in terms of the force-displacement response are compared with those obtained by three-dimensional FE simulations. Then, a detailed analysis of stress-strain field distribution in the bulk of the sample was carried out. Finally, the effects of the number of extrusion passes and the processing routes on the pressing force were investigated as well.

Experiments

The experiments were conducted using a semicrystalline PP material provided by the Goodfellow Company (United Kingdom) with a weight-average molar weight of 180 kg/mol. Its thermal properties were obtained by differential scanning calorimetry (DSC) analysis. A crystal content of about 55% was found.

The mechanical measurements were achieved at room temperature on an electromechanical Instron© testing machine. The testing temperature (ambient) being between the glass transition temperature (about -20°C) and the melting temperature (about 170°C), the amorphous phase is therefore in the rubbery state.

The ECAE samples were machined along the same direction from a compression molded plate, then surfaced simultaneously on the cutting facets and polished. The ECAE samples have a cross-section of approximately 10×10 mm2 and a length of 70 mm. Extrusion tests were performed on a 135° die without lubrication. To characterize the plastic flow behaviour of PP material and to derive

Route A

Route C

Route Bc: rotated by +90°

180°

90°

0°

Route BA: rotated alternatively by +90° and -90°

Sample rotation direction

Φ

θ

Top surface

Bottom surface


the required constitutive law for FE analyses, compression tests were also achieved. To this end, cylindrical samples of 10 mm length and 5 mm diameter were machined as well.

Three-dimensional FE simulations

Three-dimensional FE simulations were carried out using the software MSC.Marc© to predict the deformation behaviour of PP samples during ECAE process. The die and the ram were assumed to be rigid. The sample was meshed with 7000 eight-node isoparametric hexahedral elements. The die geometry, the sample dimensions and the processing conditions were taken according to those used in the experimental study.

Elastic-viscoplastic constitutive model

The constitutive equations governing the deformation behaviour of solid polymers under ECAE process must take into account complex phenomena such as viscoplasticity, hardening, relaxation and strain memory effect. These phenomena were studied by many scientists and especially in the recent years, basing on physical [19-20] or purely phenomenological [21-23] considerations. In the present work, a phenomenological elastic-viscoplastic constitutive model, based on the Norton-Hoff flow rule, was used to describe the specific behaviour of PP material. The constitutive equations of the model under isothermal conditions are summarized in Table 1. Table 1. Constitutive model used in the FE simulations.

Strain rate tensor e vp= +D D D • Elastic part 1e −=D C σ%

• Viscoplastic part ( )32

vp pJ

′ ′−=

−σ X

Dσ X

& with ( ) ( ) ( )1 2

3:

2J ′ ′ ′ ′− = − −

σ X σ X σ X

Elastic modulus tensor ( ) ( ) 22 1 1 2

νδ δ δ δ δ δν ν

= + + + − ijkl ik jl il jk ij kl

EC

Equivalent plastic strain rate ( ) − −

=&n

J R k

Kp

σ - X

Isotropic hardening rate ( )1R b R R p= −& &

Kinematic hardening rate ( ) γ= − −+

& & &C

p pR k

X σ X X

In Table 1, X′ is the deviatoric part of the kinematic hardening tensor X , ′σ is the deviatoric part of the stress tensor σ , %σ is the Jaumann derivative of σ , the brackets are defined by ( )=w wH w

where ( )H w is the Heaviside function ( ( ) 0=H w if 0<w , ( ) 1=H w if 0≥w ), ( )−J σ X is the

equivalent value of −σ X , k is the initial yield stress, K is the viscoplastic resistance, n is the rate sensitivity coefficient, b , 1R , C and γ are hardening parameters, E is the Young’s modulus, ν is the Poisson’s ratio and δ is the Kronecker-delta symbol.

Results and discussion

Compression stress-strain curves. The material constants of the elastic-viscoplastic constitutive model were determined from a least-squares regression fitting of the compression tests data. The values of material constants are listed in Table 2.

the required constitutive law for FE analyses, compression tests were also achieved. To this end, cylindrical samples of 10 mm length and 5 mm diameter were machined as well.

Three-dimensional FE simulations

Three-dimensional FE simulations were carried out using the software MSC.Marc© to predict the deformation behaviour of PP samples during ECAE process. The die and the ram were assumed to be rigid. The sample was meshed with 7000 eight-node isoparametric hexahedral elements. The die geometry, the sample dimensions and the processing conditions were taken according to those used in the experimental study.

Elastic-viscoplastic constitutive model

The constitutive equations governing the deformation behaviour of solid polymers under ECAE process must take into account complex phenomena such as viscoplasticity, hardening, relaxation and strain memory effect. These phenomena were studied by many scientists and especially in the recent years, basing on physical [19-20] or purely phenomenological [21-23] considerations. In the present work, a phenomenological elastic-viscoplastic constitutive model, based on the Norton-Hoff flow rule, was used to describe the specific behaviour of PP material. The constitutive equations of the model under isothermal conditions are summarized in Table 1. Table 1. Constitutive model used in the FE simulations.

Strain rate tensor e vp= +D D D • Elastic part 1e −=D C σ%

• Viscoplastic part ( )32

vp pJ

′ ′−=

−σ X

Dσ X

& with ( ) ( ) ( )1 2

3:

2J ′ ′ ′ ′− = − −

σ X σ X σ X

Elastic modulus tensor ( ) ( ) 22 1 1 2

νδ δ δ δ δ δν ν

= + + + − ijkl ik jl il jk ij kl

EC

Equivalent plastic strain rate ( ) − −

=&n

J R k

Kp

σ - X

Isotropic hardening rate ( )1R b R R p= −& &

Kinematic hardening rate ( ) γ= − −+

& & &C

p pR k

X σ X X

In Table 1, X′ is the deviatoric part of the kinematic hardening tensor X , ′σ is the deviatoric part of the stress tensor σ , %σ is the Jaumann derivative of σ , the brackets are defined by ( )=w wH w

where ( )H w is the Heaviside function ( ( ) 0=H w if 0<w , ( ) 1=H w if 0≥w ), ( )−J σ X is the

equivalent value of −σ X , k is the initial yield stress, K is the viscoplastic resistance, n is the rate sensitivity coefficient, b , 1R , C and γ are hardening parameters, E is the Young’s modulus, ν is the Poisson’s ratio and δ is the Kronecker-delta symbol.


Compression stress-strain curves. The material constants of the elastic-viscoplastic constitutive model were determined from a least-squares regression fitting of the compression tests data. The values of material constants are listed in Table 2.


As shown in Fig. 2, a quite good agreement over two decades is observed between experimental data in compression and the constitutive model. Indeed, the model is able to reproduce three main features of the behaviour: the linear elastic response, the rollover to yield and the post-yield response. Table 2. Values of material constants of PP.

E (MPa)

ν k (MPa)

K (MPa)

n b 1R (MPa)

C (MPa)

γ

1100 0.4 10 30.26 6.9 65 18 30 -3.2

0

20

40

60

80

0 0,1 0,2 0,3 0,4 0,5Strain

Stress (M

Pa)

Experimental results

Constitutive model

10-2s-1

10-3s-1

10-4s-1

Fig. 2. Stress-strain curves of PP at different strain rates.

Pressing force-displacement curves during ECAE. In order to make a comparison between the ECAE experiments and simulations, the evolution of the pressing force as a function of the ram displacement is plotted in Fig. 3. The PP samples were extruded through 135° die at a ram speed of 0.07 mm/s. The friction conditions between the tooling and the samples were modelled using the Coulomb's friction law with different values of friction coefficients. It can be seen in Fig. 3 that the best results provided by the FE simulations are obtained with a friction coefficient of 0.2, for which a good estimation of the maximum pressing force is obtained.

0

400

800

1200

1600

0 10 20 30 40 50 60 70Ram displacement (mm)

Pressing

force (N

)

ExperimentalFE (f = 0.0)FE (f = 0.1)FE (f = 0.2)

800

1000

1200

1400

6 8 10 12 14 16

Fig. 3. Comparison between experimental and simulated force-displacement curves.

As shown in Fig. 2, a quite good agreement over two decades is observed between experimental data in compression and the constitutive model. Indeed, the model is able to reproduce three main features of the behaviour: the linear elastic response, the rollover to yield and the post-yield response. Table 2. Values of material constants of PP.

E (MPa)

ν k (MPa)

K (MPa)

n b 1R (MPa)

C (MPa)

γ

1100 0.4 10 30.26 6.9 65 18 30 -3.2

0

20

40

60

80

0 0,1 0,2 0,3 0,4 0,5Strain

Stress (M

Pa)


Constitutive model

10-2s-1

10-3s-1

10-4s-1

Fig. 2. Stress-strain curves of PP at different strain rates.

Pressing force-displacement curves during ECAE. In order to make a comparison between the ECAE experiments and simulations, the evolution of the pressing force as a function of the ram displacement is plotted in Fig. 3. The PP samples were extruded through 135° die at a ram speed of 0.07 mm/s. The friction conditions between the tooling and the samples were modelled using the Coulomb's friction law with different values of friction coefficients. It can be seen in Fig. 3 that the best results provided by the FE simulations are obtained with a friction coefficient of 0.2, for which a good estimation of the maximum pressing force is obtained.

0

400

800

1200

1600

0 10 20 30 40 50 60 70Ram displacement (mm)

Pressing

force (N

)

ExperimentalFE (f = 0.0)FE (f = 0.1)FE (f = 0.2)

800

1000

1200

1400

6 8 10 12 14 16

Fig. 3. Comparison between experimental and simulated force-displacement curves.


Estimation of the equivalent plastic strain. In order to obtain proper information regarding the plastic deformation distribution in the PP sample, the equivalent plastic strain in the bulk of the extruded sample was analyzed as shown in Figs. 4 and 5. It can be observed that the plastic strain is not uniform across the sample width (Fig. 5a), however, there is a steady flow region where the plastic strain is quite uniform along the longitudinal direction except the edges (Fig. 5b). In this steady state region, deformation gradient exists along the transverse direction and the local plastic strain decreases from the top surface to the bottom surface of the sample as shown in the selected cutting planes (Fig. 5). This can be attributed to the bending mechanisms. Furthermore, the plastic deformation is relatively more homogeneous at the medium planes (P2 to P6) compared to that of the edges which have undergone a low level of plastic deformation. This is due mainly to the fact that only a portion of the extrudate is slightly sheared at the beginning and at the end of the ECAE process.

Fig. 4. Plastic strain contour in PP sample.

0

0,1

0,2

0,3

0,4

0,5

0,6

0 2 4 6 8 10Transverse direction from the bottom (mm)

Equ

ivalent p

lastic strain

At plane P6

At plane P4

At plane P20

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 100 200 300 400 500 600 700Longitudinal direction from the left (mm)

Equ

ivalent p

lastic strain

BottomMediumTop

(a) (b)

Fig. 5. Plastic strain distribution in PP sample along (a) transverse and (b) longitudinal directions. Estimation of the equivalent stress. In order to give more information on the deformation pattern during ECAE process, the equivalent von Mises stress along the sample is plotted in Fig. 6. According to this figure, the magnitude of the equivalent von Mises stress is higher at the top and the bottom regions of the sample, while the middle longitudinal region displays a lower equivalent

P7

P6

P3

P4

P1

P2

P5

Top Medium Bottom

Longitudinal directions

Estimation of the equivalent plastic strain. In order to obtain proper information regarding the plastic deformation distribution in the PP sample, the equivalent plastic strain in the bulk of the extruded sample was analyzed as shown in Figs. 4 and 5. It can be observed that the plastic strain is not uniform across the sample width (Fig. 5a), however, there is a steady flow region where the plastic strain is quite uniform along the longitudinal direction except the edges (Fig. 5b). In this steady state region, deformation gradient exists along the transverse direction and the local plastic strain decreases from the top surface to the bottom surface of the sample as shown in the selected cutting planes (Fig. 5). This can be attributed to the bending mechanisms. Furthermore, the plastic deformation is relatively more homogeneous at the medium planes (P2 to P6) compared to that of the edges which have undergone a low level of plastic deformation. This is due mainly to the fact that only a portion of the extrudate is slightly sheared at the beginning and at the end of the ECAE process.

Fig. 4. Plastic strain contour in PP sample.

0

0,1

0,2

0,3

0,4

0,5

0,6

0 2 4 6 8 10Transverse direction from the bottom (mm)

Equ

ivalent p

lastic strain

At plane P6

At plane P4

At plane P20

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 100 200 300 400 500 600 700Longitudinal direction from the left (mm)

Equ

ivalent p

lastic strain

BottomMediumTop

(a) (b)

Fig. 5. Plastic strain distribution in PP sample along (a) transverse and (b) longitudinal directions. Estimation of the equivalent stress. In order to give more information on the deformation pattern during ECAE process, the equivalent von Mises stress along the sample is plotted in Fig. 6. According to this figure, the magnitude of the equivalent von Mises stress is higher at the top and the bottom regions of the sample, while the middle longitudinal region displays a lower equivalent

P7

P6

P3

P4

P1

P2

P5

Top Medium Bottom

Longitudinal directions


stress as clearly shown in cutting planes. Moreover, the maximum value is located at the vicinity of the inner corner (about 50 MPa).

Estimation of the hydrostatic stress. Fig. 7 shows the contour plots of the hydrostatic stress for an intermediate state of ECAE process. It can be seen that the hydrostatic stress is negative (compressive state) around the inner corner of the die and along the surface in contact with the bottom of the die wall.

Fig. 6. Equivalent von Mises stress distribution in PP sample.

Due to the concavity created by the outer corner gap, the hydrostatic stress is positive (tensile state) at the vicinity of the outer corner of the die and along the top surface of the sample except the end part of the extruded sample. At the inner corner, the hydrostatic stress is negative due to the convexity imposed by the inner round corner. Furthermore, an interesting observation is the whitening experimentally observed at the bottom and above the inner corner regions as shown in Fig. 7b. This whitening may be attributed to the cavitation damage induced by positive hydrostatic stress. In order to trim down this phenomenon, it is advised to use a back-pressure at the end of the sample in the exit channel [16].

(a) (b) Fig. 7. (a) Hydrostatic stress distribution in PP sample. (b) Photography of PP sample inside the

135° ECAE die.

Top

Bottom

Middle

Whitening of the sample

stress as clearly shown in cutting planes. Moreover, the maximum value is located at the vicinity of the inner corner (about 50 MPa).

Estimation of the hydrostatic stress. Fig. 7 shows the contour plots of the hydrostatic stress for an intermediate state of ECAE process. It can be seen that the hydrostatic stress is negative (compressive state) around the inner corner of the die and along the surface in contact with the bottom of the die wall.

Fig. 6. Equivalent von Mises stress distribution in PP sample.

Due to the concavity created by the outer corner gap, the hydrostatic stress is positive (tensile state) at the vicinity of the outer corner of the die and along the top surface of the sample except the end part of the extruded sample. At the inner corner, the hydrostatic stress is negative due to the convexity imposed by the inner round corner. Furthermore, an interesting observation is the whitening experimentally observed at the bottom and above the inner corner regions as shown in Fig. 7b. This whitening may be attributed to the cavitation damage induced by positive hydrostatic stress. In order to trim down this phenomenon, it is advised to use a back-pressure at the end of the sample in the exit channel [16].

(a) (b) Fig. 7. (a) Hydrostatic stress distribution in PP sample. (b) Photography of PP sample inside the

135° ECAE die.

Top

Bottom

Middle

Whitening of the sample


Effects of number of extrusion passes and processing routes. The advantage of ECAE process, in addition to maintaining constant sample cross-section, is that it is possible to generate various microstructures if multiple passes with a suitable selection of processing routes are carried out. In this subsection, the samples were processed via four ECAE processing routes using 135° die at a ram speed of 0.7 mm/s. In order to make a comparison between the different routes, the evolution of the maximum pressing force versus the number of passes is plotted in Fig. 8. According to the results obtained by the routes A and C, it can be seen that the pressing force decreases with the increase of the number of passes. By contrast, a random variation is highlighted for the routes BA and BC. This aspect can be allotted to the strength variation created by the mobility of the crystalline lamellae inside the bulk material with respect to ECAE loading. Moreover, it can be observed that, routes A and C reach rapidly their saturation values (after about four passes uniquely) compared to routes BA and BC, which require a high number of passes to reach their steady states.

0

200

400

600

800

1000

1200

1400

0 4 8 12 16 20Number of passes

Maxim

um fo

rce (N

)

Route ARoute CRoute BARoute BC

Fig. 8. Variation of the maximum force versus the number of passes for different routes.

In order to quantify the warping effect, Fig. 9 shows photography of PP samples that have

undergone sixteen passes of ECAE by different processing routes outlined above (see Fig. 1). The maximum curvature of the sample was quantified by measuring the height of the sample before and after ECAE deformation. It can be remarked that the significant reduction of warping is obtained by using the routes BC and C; however the maximum warping is obtained with the route A.

(a) (b)

(c) (d)

Fig. 9. PP samples after 16 passes of ECAE with different processing routes: (a) route A, (b) route C, (c) route BA, (d) route BC (dimensions in mm).

The warping may be due to the existence of residual stress and the concurrent stress relaxation

process on the extruded samples. Sue et al. [7] anticipate that the higher the extrusion temperature, but below the glass transition, the less residual stress will build up in the extruded sample.

17.2

13.5

13.25

13.15

Effects of number of extrusion passes and processing routes. The advantage of ECAE process, in addition to maintaining constant sample cross-section, is that it is possible to generate various microstructures if multiple passes with a suitable selection of processing routes are carried out. In this subsection, the samples were processed via four ECAE processing routes using 135° die at a ram speed of 0.7 mm/s. In order to make a comparison between the different routes, the evolution of the maximum pressing force versus the number of passes is plotted in Fig. 8. According to the results obtained by the routes A and C, it can be seen that the pressing force decreases with the increase of the number of passes. By contrast, a random variation is highlighted for the routes BA and BC. This aspect can be allotted to the strength variation created by the mobility of the crystalline lamellae inside the bulk material with respect to ECAE loading. Moreover, it can be observed that, routes A and C reach rapidly their saturation values (after about four passes uniquely) compared to routes BA and BC, which require a high number of passes to reach their steady states.

0

200

400

600

800

1000

1200

1400

0 4 8 12 16 20Number of passes

Maxim

um fo

rce (N

)

Route ARoute CRoute BARoute BC

Fig. 8. Variation of the maximum force versus the number of passes for different routes.

In order to quantify the warping effect, Fig. 9 shows photography of PP samples that have

undergone sixteen passes of ECAE by different processing routes outlined above (see Fig. 1). The maximum curvature of the sample was quantified by measuring the height of the sample before and after ECAE deformation. It can be remarked that the significant reduction of warping is obtained by using the routes BC and C; however the maximum warping is obtained with the route A.

(a) (b)

(c) (d)

Fig. 9. PP samples after 16 passes of ECAE with different processing routes: (a) route A, (b) route C, (c) route BA, (d) route BC (dimensions in mm).

The warping may be due to the existence of residual stress and the concurrent stress relaxation

process on the extruded samples. Sue et al. [7] anticipate that the higher the extrusion temperature, but below the glass transition, the less residual stress will build up in the extruded sample.

17.2

13.5

13.25

13.15


Unfortunately, their study was only limited to a PC extruded using route A. However, in the case of PP a slight reduction of warping was observed as the extrusion temperature is increased [18]. Hence, it is advised to test other parameters such as the geometry of the exit channel and the use of back-pressure which will represent an improvement of the ECAE device in a near future. It is also of interest to complete this study by mechanical and morphological characterization of the material after ECAE deformation.

References

[1] Y. Iwahashi, Z. Horita, M. Nemoto and T.G. Langdon: Acta Mater. Vol. 46 (1998) p. 3317.

[2] V.M. Segal: Mater. Sci. Eng. A Vol. 197 (1995) p. 157.

[3] H.S. Kim: Mater. Sci. Eng. A Vol. 382 (2002) p. 317.

[4] R.Z. Valiev and T.G. Langdon: Prog. Mater. Sci. Vol. 51 (2006) p. 881.

[5] I.J. Beyerlein and L.S. Toth: Prog. Mater. Sci. Vol. 54 (2009) p. 427.

[6] H.J. Sue and C.K.Y. Li: J. Mater. Sci. Lett. Vol. 17 (1998) p. 853.

[7] H.J. Sue, H. Dilan and C.K.Y. Li: Polym. Eng. Sci. Vol. 39 (1999) p. 2505.

[8] C.K.Y. Li, Z.Y. Xia and H.J. Sue: Polym. Vol. 41 (2000) p. 6285.

[9] Z. Xia, H.J. Sue and A.J. Hsieh: J. Appl. Polym. Sci. Vol. 79 (2001) p. 2060.

[10] Z. Xia, H.J. Sue, A.J. Hsieh and J.W.L. Huang: J. Polym. Sci. Part B: Polym. Phys. Vol. 39 (2001) p. 1394.

[11] Z.G. Wang, Z.Y. Xia, Z.Q. Yu, E.Q. Chen, H.J. Sue, C.C. Han and B.S. Hsiao: Macromol. Vol. 39 (2006) p. 2930.

[12] B. Aour, F. Zaïri, J.M. Gloaguen, M. Naït-Abdelaziz and J.M. Lefebvre: Comp. Mater. Sci. Vol. 37 (2006) p. 491.

[13] F. Zaïri, B. Aour, J.M. Gloaguen, M. Naït-Abdelaziz and J.M. Lefebvre: Comp. Mater. Sci. Vol. 38 (2006) p. 202.

[14] F. Zaïri, B. Aour, J.M. Gloaguen, M. Naït-Abdelaziz and J.M. Lefebvre: Scripta Mater. Vol. 56 (2007) p. 105.

[15] B. Aour, F. Zaïri, M. Naït-Abdelaziz, J.M. Gloaguen, O. Rahmani and J.M. Lefebvre: Inter. J. Mech. Sci. Vol. 50 (2008) p. 589.

[16] F. Zaïri, B. Aour, J.M. Gloaguen, M. Naït-Abdelaziz and J.M. Lefebvre: Polym. Eng. Sci. Vol. 48 (2008) p. 1015.

[17] B. Aour, F. Zaïri, M. Naït-Abdelaziz, J.M. Gloaguen and J.M. Lefebvre: J. Manuf. Sci. Eng. Vol. 131 (2009) p. 31016.

[18] B. Aour, F. Zaïri, R. Boulahia, M. Naït-Abdelaziz, J.M. Gloaguen and J.M. Lefebvre: Comp. Mater. Sci. Vol. 45 (2009) p. 646.

[19] M.C. Boyce, D.M. Parks and A.S. Argon: Mech. Mater. Vol. 7 (1988) p. 15.

[20] S. Ahzi, A. Makradi, R.V. Gregory and D.D. Edie: Mech. Mater. Vol. 35 (2003) p. 1139.

[21] O.U. Colak: Int. J. Plast. Vol. 21 (2005) p. 145.

[22] F. Zaïri, K. Woznica and M. Naït-Abdelaziz: Comp. R. Mec. Vol. 333 (2005) p. 359.

[23] F. Zaïri, M. Naït-Abdelaziz, K. Woznica and J.M. Gloaguen: J. Eng. Mater. Tech. Vol. 129 (2007) p. 29.

Unfortunately, their study was only limited to a PC extruded using route A. However, in the case of PP a slight reduction of warping was observed as the extrusion temperature is increased [18]. Hence, it is advised to test other parameters such as the geometry of the exit channel and the use of back-pressure which will represent an improvement of the ECAE device in a near future. It is also of interest to complete this study by mechanical and morphological characterization of the material after ECAE deformation.

References

[1] Y. Iwahashi, Z. Horita, M. Nemoto and T.G. Langdon: Acta Mater. Vol. 46 (1998) p. 3317.

[2] V.M. Segal: Mater. Sci. Eng. A Vol. 197 (1995) p. 157.

[3] H.S. Kim: Mater. Sci. Eng. A Vol. 382 (2002) p. 317.

[4] R.Z. Valiev and T.G. Langdon: Prog. Mater. Sci. Vol. 51 (2006) p. 881.

[5] I.J. Beyerlein and L.S. Toth: Prog. Mater. Sci. Vol. 54 (2009) p. 427.

[6] H.J. Sue and C.K.Y. Li: J. Mater. Sci. Lett. Vol. 17 (1998) p. 853.

[7] H.J. Sue, H. Dilan and C.K.Y. Li: Polym. Eng. Sci. Vol. 39 (1999) p. 2505.

[8] C.K.Y. Li, Z.Y. Xia and H.J. Sue: Polym. Vol. 41 (2000) p. 6285.

[9] Z. Xia, H.J. Sue and A.J. Hsieh: J. Appl. Polym. Sci. Vol. 79 (2001) p. 2060.

[10] Z. Xia, H.J. Sue, A.J. Hsieh and J.W.L. Huang: J. Polym. Sci. Part B: Polym. Phys. Vol. 39 (2001) p. 1394.

[11] Z.G. Wang, Z.Y. Xia, Z.Q. Yu, E.Q. Chen, H.J. Sue, C.C. Han and B.S. Hsiao: Macromol. Vol. 39 (2006) p. 2930.

[12] B. Aour, F. Zaïri, J.M. Gloaguen, M. Naït-Abdelaziz and J.M. Lefebvre: Comp. Mater. Sci. Vol. 37 (2006) p. 491.

[13] F. Zaïri, B. Aour, J.M. Gloaguen, M. Naït-Abdelaziz and J.M. Lefebvre: Comp. Mater. Sci. Vol. 38 (2006) p. 202.

[14] F. Zaïri, B. Aour, J.M. Gloaguen, M. Naït-Abdelaziz and J.M. Lefebvre: Scripta Mater. Vol. 56 (2007) p. 105.

[15] B. Aour, F. Zaïri, M. Naït-Abdelaziz, J.M. Gloaguen, O. Rahmani and J.M. Lefebvre: Inter. J. Mech. Sci. Vol. 50 (2008) p. 589.

[16] F. Zaïri, B. Aour, J.M. Gloaguen, M. Naït-Abdelaziz and J.M. Lefebvre: Polym. Eng. Sci. Vol. 48 (2008) p. 1015.

[17] B. Aour, F. Zaïri, M. Naït-Abdelaziz, J.M. Gloaguen and J.M. Lefebvre: J. Manuf. Sci. Eng. Vol. 131 (2009) p. 31016.

[18] B. Aour, F. Zaïri, R. Boulahia, M. Naït-Abdelaziz, J.M. Gloaguen and J.M. Lefebvre: Comp. Mater. Sci. Vol. 45 (2009) p. 646.

[19] M.C. Boyce, D.M. Parks and A.S. Argon: Mech. Mater. Vol. 7 (1988) p. 15.

[20] S. Ahzi, A. Makradi, R.V. Gregory and D.D. Edie: Mech. Mater. Vol. 35 (2003) p. 1139.

[21] O.U. Colak: Int. J. Plast. Vol. 21 (2005) p. 145.

[22] F. Zaïri, K. Woznica and M. Naït-Abdelaziz: Comp. R. Mec. Vol. 333 (2005) p. 359.

[23] F. Zaïri, M. Naït-Abdelaziz, K. Woznica and J.M. Gloaguen: J. Eng. Mater. Tech. Vol. 129 (2007) p. 29.


Analysis of Joint Quality along Welding Plane

E. Ceretti1, L. Filice2, L. Fratini3, F. Gagliardi2, C. Giardini4, D. La Spisa3 1University of Brescia, Department of Mech. and Ind. Engineering

2University of Calabria, Mechanical Department

3University of Palermo, Dept. of Mechanical Technology Production and Management

4University of Bergamo, Department of Design and Technologies

[email protected], [email protected], [email protected], [email protected], [email protected], [email protected]

Keywords: FEM, Extrusion, Welding Line. Abstract. Porthole die extrusion is an always more important process for industrial applications. It is, however, characterized by a considerable complexity; in fact, different parameters have to be carefully set for improving the final part.

A critical zone that strongly influences the goodness of the extruded component is the so called “welding plane”. It is the junction area where material flows converge inside the welding chamber. The variables that have to be controlled for improving the material characteristics in this zone are the effective stress, the pressure and the time that the material takes to cross the welding chamber. Moreover, material temperature is another fundamental issue that influences both the quality and the typology of the final joint.

However, especially for complex parts, the material can follow diverse directions to get out from the die; this means that the deformation history can be different, thus influencing the quality of the final jont.

In the study here proposed, the property of the welding plane was highlighted for an industrial component that was cut through a profile cross section carrying out both metallurgical and mechanical investigations. More in detail, specimens, derived from the extruded part, were mounted, polished and etched with Keller reagent and observed by a light microscopy. Then, macro and micro observation were developed highlighting the welding line position. Moreover, local values of the average grain size of the material were measured showing the microstructural evolutions undergone by the material due to the extrusion process. As far as mechanical tests are regarded, micro-hardness tests were executed nearby the welding line; in this way, correlations between material metallurgical evolutions and subsequent local mechanical performances were highlighted.

Furthermore, a 3D numerical study was developed in order to point out the numerical ability to predict the welding line position for complex parts; finally, a welding criterion was used in order to locally validate the experimental observations. All these aspects are accurately analyzed and discussed in the paper.

Introduction

The extrusion of hollow or semi hollow profiles is increasingly used for industrial applications in order to produce parts characterized by always more different shapes. In this manufacture typology, the material is divided according to the number of mandrel legs; afterwards, a welding chamber is used to rejoin the material [1]. In order to guarantee good quality of the final components, great attention has to be put on the choice of the right process parameters.

From this point of view, several papers giving suitable inputs for the identification of the better process conditions are recognizable in technical literature [2-3]. More in particular, the height of the

Analysis of Joint Quality along Welding Plane

E. Ceretti1, L. Filice2, L. Fratini3, F. Gagliardi2, C. Giardini4, D. La Spisa3 1University of Brescia, Department of Mech. and Ind. Engineering

2University of Calabria, Mechanical Department

3University of Palermo, Dept. of Mechanical Technology Production and Management

4University of Bergamo, Department of Design and Technologies

[email protected], [email protected], [email protected], [email protected], [email protected], [email protected]

Keywords: FEM, Extrusion, Welding Line. Abstract. Porthole die extrusion is an always more important process for industrial applications. It is, however, characterized by a considerable complexity; in fact, different parameters have to be carefully set for improving the final part.

A critical zone that strongly influences the goodness of the extruded component is the so called “welding plane”. It is the junction area where material flows converge inside the welding chamber. The variables that have to be controlled for improving the material characteristics in this zone are the effective stress, the pressure and the time that the material takes to cross the welding chamber. Moreover, material temperature is another fundamental issue that influences both the quality and the typology of the final joint.

However, especially for complex parts, the material can follow diverse directions to get out from the die; this means that the deformation history can be different, thus influencing the quality of the final jont.

In the study here proposed, the property of the welding plane was highlighted for an industrial component that was cut through a profile cross section carrying out both metallurgical and mechanical investigations. More in detail, specimens, derived from the extruded part, were mounted, polished and etched with Keller reagent and observed by a light microscopy. Then, macro and micro observation were developed highlighting the welding line position. Moreover, local values of the average grain size of the material were measured showing the microstructural evolutions undergone by the material due to the extrusion process. As far as mechanical tests are regarded, micro-hardness tests were executed nearby the welding line; in this way, correlations between material metallurgical evolutions and subsequent local mechanical performances were highlighted.

Furthermore, a 3D numerical study was developed in order to point out the numerical ability to predict the welding line position for complex parts; finally, a welding criterion was used in order to locally validate the experimental observations. All these aspects are accurately analyzed and discussed in the paper.

Introduction

The extrusion of hollow or semi hollow profiles is increasingly used for industrial applications in order to produce parts characterized by always more different shapes. In this manufacture typology, the material is divided according to the number of mandrel legs; afterwards, a welding chamber is used to rejoin the material [1]. In order to guarantee good quality of the final components, great attention has to be put on the choice of the right process parameters.

From this point of view, several papers giving suitable inputs for the identification of the better process conditions are recognizable in technical literature [2-3]. More in particular, the height of the


welding chamber, the bridge width, the ram speed and the billet and die temperature were some of the geometrical and process variables investigated in the works above cited. It has to be highlighted that weakness zones for this extruded profiles are observed close to the welding planes; in fact, cracks usually appear in proximity of the welding lines [2]. Different variables have to be monitored for the improvement of the final parts; more in detail, the effective stress, the pressure and the time that the material takes to cross the welding chamber are the principal greatnesses to consider [3].

Modified die shape, for example, have been proposed in literature [4] in order to obtain larger welding pressure. Anyway, die shape is just one of the variables that strongly affects the welding strength of the joint lines; in fact, many other parameters have to be considered, too, like: extrusion ratio, portholes number, extrusion speed, bearing length and billet temperature [5]. Regarding the variables above listed, different welding criteria were proposed in order to assess welding quality [6]; concerning this aspect, the authors already proved how the conditions to obtain a good welding plane depend also on the temperature at which the contact between the material flows takes place [7].

However, even the material flow inside the welding chamber plays a fundamental role for the goodness of the final junction; this is a variable to take into account above all when the welding chamber is characterized by a complex shape. From this point of view, in the last two decades, at least, few studies were presented regarding the process mechanics of such complex extrusions [8–11]. The developed research was based on the analysis of an extruded profile that was obtained using a particular welding chamber. The joint quality was studied both by metallurgical and mechanical investigation; more in detail, the welding line was deeply observed in order to find differences on its quality.

FEM analysis was, even, carried out using Deform 3D; this study was useful, first of all, to highlight the code ability in the prediction of welding line position for a complex porthole extrusion. Moreover, the numerical results were useful to show locally the influence that the different material flow can have on the quality of final joint.

Experimental investigations

As it was said before, the section of a typical extruded workpiece (Fig. 1) was examined macroscopically and microscopically in order to highlight differences in grain size and hardness all along the welding line typical of this processes. The part was obtained starting from an extruded AA6061 Aluminum Alloy.

Fig. 1: Section of the analyzed profile

In this way, the specimens were mounted on a resin support, they were burnished with a polishing machine, then etched with an acid solution (9% HF, 13% HCl, 78% H2O) for about 1 min. Then the etched surface was observed both with a camera (macro observations) and with a light microscope (micro observations); the resulting macro images are reported in the next Fig. 2. It should be observed that – especially in the upper side of the specimen – the bonding line of two opposite

welding chamber, the bridge width, the ram speed and the billet and die temperature were some of the geometrical and process variables investigated in the works above cited. It has to be highlighted that weakness zones for this extruded profiles are observed close to the welding planes; in fact, cracks usually appear in proximity of the welding lines [2]. Different variables have to be monitored for the improvement of the final parts; more in detail, the effective stress, the pressure and the time that the material takes to cross the welding chamber are the principal greatnesses to consider [3].

Modified die shape, for example, have been proposed in literature [4] in order to obtain larger welding pressure. Anyway, die shape is just one of the variables that strongly affects the welding strength of the joint lines; in fact, many other parameters have to be considered, too, like: extrusion ratio, portholes number, extrusion speed, bearing length and billet temperature [5]. Regarding the variables above listed, different welding criteria were proposed in order to assess welding quality [6]; concerning this aspect, the authors already proved how the conditions to obtain a good welding plane depend also on the temperature at which the contact between the material flows takes place [7].

However, even the material flow inside the welding chamber plays a fundamental role for the goodness of the final junction; this is a variable to take into account above all when the welding chamber is characterized by a complex shape. From this point of view, in the last two decades, at least, few studies were presented regarding the process mechanics of such complex extrusions [8–11]. The developed research was based on the analysis of an extruded profile that was obtained using a particular welding chamber. The joint quality was studied both by metallurgical and mechanical investigation; more in detail, the welding line was deeply observed in order to find differences on its quality.

FEM analysis was, even, carried out using Deform 3D; this study was useful, first of all, to highlight the code ability in the prediction of welding line position for a complex porthole extrusion. Moreover, the numerical results were useful to show locally the influence that the different material flow can have on the quality of final joint.

Experimental investigations

As it was said before, the section of a typical extruded workpiece (Fig. 1) was examined macroscopically and microscopically in order to highlight differences in grain size and hardness all along the welding line typical of this processes. The part was obtained starting from an extruded AA6061 Aluminum Alloy.

Fig. 1: Section of the analyzed profile

In this way, the specimens were mounted on a resin support, they were burnished with a polishing machine, then etched with an acid solution (9% HF, 13% HCl, 78% H2O) for about 1 min. Then the etched surface was observed both with a camera (macro observations) and with a light microscope (micro observations); the resulting macro images are reported in the next Fig. 2. It should be observed that – especially in the upper side of the specimen – the bonding line of two opposite


material flows at the considered section of the extruded part is highlighted. The latter is not straight and its position actually depends on the different velocities of the material coming from the different sides of the welding chamber. Overall it can be stated that for smaller sections of the chamber and of the bearing of the porthole die, larger values of the material velocity are expected and observed, as in this case.

a b

Fig. 2: Macroimages of the welding line In order to investigate the local values of the material grain size and micro-hardness, the highlighted bonding line was divided into three different areas, namely A, B and C, as indicated in Fig. 2b, being A zone the nearest to the hole in the section of the specimen. First of all the attention was focused on the microstructural analysis of the junction. A Leica optical microscope was used and the micrographs of the welding zones are printed with a zooming of 62.5X. In the next Fig. 3 and Fig. 4 the material microstucture is shown for zone A and zone B-C, respectively. It should be observed that, even if the material grains are clearly discernable just a slight difference of the average grain size is measurable: actually material in zona A (average grain size: 10µm) showed an average grain size just a bit larger than in zone B-C (6µm).

Fig. 3: Material microstructure in zone A

Fig. 4: Material microstructure in zone B-C

Further investigations are needed in order to determine clear relations between the different material paths and the local values of the average grain size. The second stage of the experimental investigation was aimed to measure the micro-hardness values of the material in the different zones of the bonding line. In particular Vickers tests were carried out with a load of 100g and using a lens zoom of 40X.

material flows at the considered section of the extruded part is highlighted. The latter is not straight and its position actually depends on the different velocities of the material coming from the different sides of the welding chamber. Overall it can be stated that for smaller sections of the chamber and of the bearing of the porthole die, larger values of the material velocity are expected and observed, as in this case.

a b

Fig. 2: Macroimages of the welding line In order to investigate the local values of the material grain size and micro-hardness, the highlighted bonding line was divided into three different areas, namely A, B and C, as indicated in Fig. 2b, being A zone the nearest to the hole in the section of the specimen. First of all the attention was focused on the microstructural analysis of the junction. A Leica optical microscope was used and the micrographs of the welding zones are printed with a zooming of 62.5X. In the next Fig. 3 and Fig. 4 the material microstucture is shown for zone A and zone B-C, respectively. It should be observed that, even if the material grains are clearly discernable just a slight difference of the average grain size is measurable: actually material in zona A (average grain size: 10µm) showed an average grain size just a bit larger than in zone B-C (6µm).

Fig. 3: Material microstructure in zone A

Fig. 4: Material microstructure in zone B-C

Further investigations are needed in order to determine clear relations between the different material paths and the local values of the average grain size. The second stage of the experimental investigation was aimed to measure the micro-hardness values of the material in the different zones of the bonding line. In particular Vickers tests were carried out with a load of 100g and using a lens zoom of 40X.


The measured data are reported in the next Fig. 5: it results that the hardness increases along the welding line from zone A towards to zone C, i.e. from the circular hole in the extruded part to the external side of the component.

20

30

40

50

60

70

80

Zone

Hv

A

BC

Fig. 5: Microhardness vs. material zones

Furthermore, the hardness values measured in the different points all along the bonding line - starting from the hole towards the leg – are reported in Table 1.

Table 1: Micro-hardness values

[Hv] 50,7 45,79 51,33 53,84 69,6 64,21 65,93 67,73

Overall it can be then concluded that different material paths determine different mechanical characteristics in the final transverse section of the extruded part.

$umerical analysis

The commercial code DEFORM 3D [12] was utilized for the numerical analyses. The plastic behaviour of the AA6061 Aluminium Alloy was obtained from the FE code library. Thermo-mechanical analyses were set and material emissivity was extracted from literature [9]; the initial billet temperature was set equal to 475 °C while the punch and die were set to 450 °C. The billet, according to the experimental extrusion, has a diameter equal to 240mm and an initial height of 100 mm.

A fine billet discretization was utilized; in fact, 60,000 solid tetrahedral elements were used and, moreover, a cylindrical mesh box was introduced to refine the mesh in correspondence to the gate of welding chamber.

Moreover, the die and the punch were modeled as rigid bodies in order to reduce the simulation time. The heat transfer coefficient between the objects in contact was set equal to 11X103 W/m2 K [12]. The friction forces were predicted through the shear model; more in detail, according to the die element–material interface friction factors in a range between 0.7-0.8 were used [5,13]. Inside the welding chamber, instead, adhesion was considered. The punch movement was set in order to reach a material velocity, along the welding line, of about 9 mm/s, reproducing the actual industrial conditions. Finally, taking advantage of two symmetry planes, just a quarter of the whole extrusion process was analyzed. The initial model is reported in Fig. °6.

The measured data are reported in the next Fig. 5: it results that the hardness increases along the welding line from zone A towards to zone C, i.e. from the circular hole in the extruded part to the external side of the component.

20

30

40

50

60

70

80

Zone

Hv

A

BC

Fig. 5: Microhardness vs. material zones

Furthermore, the hardness values measured in the different points all along the bonding line - starting from the hole towards the leg – are reported in Table 1.

Table 1: Micro-hardness values

[Hv] 50,7 45,79 51,33 53,84 69,6 64,21 65,93 67,73

Overall it can be then concluded that different material paths determine different mechanical characteristics in the final transverse section of the extruded part.

$umerical analysis

The commercial code DEFORM 3D [12] was utilized for the numerical analyses. The plastic behaviour of the AA6061 Aluminium Alloy was obtained from the FE code library. Thermo-mechanical analyses were set and material emissivity was extracted from literature [9]; the initial billet temperature was set equal to 475 °C while the punch and die were set to 450 °C. The billet, according to the experimental extrusion, has a diameter equal to 240mm and an initial height of 100 mm.

A fine billet discretization was utilized; in fact, 60,000 solid tetrahedral elements were used and, moreover, a cylindrical mesh box was introduced to refine the mesh in correspondence to the gate of welding chamber.

Moreover, the die and the punch were modeled as rigid bodies in order to reduce the simulation time. The heat transfer coefficient between the objects in contact was set equal to 11X103 W/m2 K [12]. The friction forces were predicted through the shear model; more in detail, according to the die element–material interface friction factors in a range between 0.7-0.8 were used [5,13]. Inside the welding chamber, instead, adhesion was considered. The punch movement was set in order to reach a material velocity, along the welding line, of about 9 mm/s, reproducing the actual industrial conditions. Finally, taking advantage of two symmetry planes, just a quarter of the whole extrusion process was analyzed. The initial model is reported in Fig. °6.


Fig. 6: Starting model used for numerical analysis.

Considerations on numerical results

The investigated component it is characterized by a very complex shape; a die sketch is reported in Fig. °7.

Fig. 7: Section of the utilized welding chamber.

Four welding lines are generated to achieve the final part; a good correspondence between predicted and real position can be observed (Fig. °8).

Mesh Box

Fig. 6: Starting model used for numerical analysis.

Considerations on numerical results

The investigated component it is characterized by a very complex shape; a die sketch is reported in Fig. °7.

Fig. 7: Section of the utilized welding chamber.

Four welding lines are generated to achieve the final part; a good correspondence between predicted and real position can be observed (Fig. °8).

Mesh Box


Fig. 8: a) real and b) predicted position of welding lines. According to this result, it is possible to state that even for complex die and, consequently,

complex flow material, the numerical simulation can be used to find the right position of the welding lines. Moreover, processing of numerical results allowed to highlight, even, the influence that the shape of the welding chamber can have on the welding quality of joint surface. More in detail, different material flows where observed calculating the value of the welding criterion for different solder zones.

Amongst the criteria proposed for representing the conditions at which solid state welding occurs, the one introduced by Pivnik and Plata [14] was utilized for the study here proposed. This criterion calculates a field variable (w) as the integral on time of the contact pressure (p), rated to the actual material effective tress (σeff) acting on the self-contact material surfaces:

∫=t

eff

dtp

0.

σσ (1)

Like a general rule, when the so defined parameter reaches a limit value (wlim) the material

welds; obviously, greater is w when the material gets out from the welding chamber and better is the quality of the final weld. In order to locally calculate this variable, a specific user-subroutine was implemented inside the commercial code and, so, it was possible to record, step by step, its variations. The positions of the investigated points, and their flow inside the welding chamber, are shown in Fig. °9.

Welding zones

a) b)

Welding lines

Fig. 8: a) real and b) predicted position of welding lines. According to this result, it is possible to state that even for complex die and, consequently,

complex flow material, the numerical simulation can be used to find the right position of the welding lines. Moreover, processing of numerical results allowed to highlight, even, the influence that the shape of the welding chamber can have on the welding quality of joint surface. More in detail, different material flows where observed calculating the value of the welding criterion for different solder zones.

Amongst the criteria proposed for representing the conditions at which solid state welding occurs, the one introduced by Pivnik and Plata [14] was utilized for the study here proposed. This criterion calculates a field variable (w) as the integral on time of the contact pressure (p), rated to the actual material effective tress (σeff) acting on the self-contact material surfaces:

∫=t

eff

dtp

0.

σσ (1)

Like a general rule, when the so defined parameter reaches a limit value (wlim) the material

welds; obviously, greater is w when the material gets out from the welding chamber and better is the quality of the final weld. In order to locally calculate this variable, a specific user-subroutine was implemented inside the commercial code and, so, it was possible to record, step by step, its variations. The positions of the investigated points, and their flow inside the welding chamber, are shown in Fig. °9.

Welding zones

a) b)

Welding lines


Fig. 9: Material flow inside the welding chamber for different points.

The values of Pivnik and Plata parameter for the different points are reported in Table 2. Table 2: Different values of Pivnik and Plata parameter

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 w 2.36 1.95 1.62 1.32 1.00 0.80 0.86 0.95 0.92 0.40

It is possible to note how the obtained values change significantly depending on the point position; according to this numerical observation, the difference on joint quality can be physically understood. Obviously, homogeneity of the solder line can be improved trying to design welding chamber where material flow is more uniform.

Conclusions

In the present paper the results of experimental and numerical investigations on parts extruded through a porthole die are reported. In particular the fully three-dimensional material flow occurring for the considered part is taken into account and through a FE commercial code the evolution of the Pivnik and Plata criterion is considered for several material points. The obtained results show that different welding conditions are reached by the flowing material for different points of an actual welding line occurring in extruded part. Such result is confirmed by the experiments: the micro-hardness values measured all along welding line corresponding to the one considered in the numerical simulations demonstrated the different mechanical characteristics of the material for different zones of the welding line.

Further investigations are needed in order also to highlight the material metallurgical evolutions occurring in the different zones of the welding line at the varying of the welding conditions and to relate them to the material flow towards the welding zone.

Overall the relevance of an automatic numerical procedure implementing an effective welding criterion based on a specific material characterization and able to highlight the actual bonding mechanics occurring in the porthole die is stressed.

Fig. 9: Material flow inside the welding chamber for different points.

The values of Pivnik and Plata parameter for the different points are reported in Table 2. Table 2: Different values of Pivnik and Plata parameter

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 w 2.36 1.95 1.62 1.32 1.00 0.80 0.86 0.95 0.92 0.40

It is possible to note how the obtained values change significantly depending on the point position; according to this numerical observation, the difference on joint quality can be physically understood. Obviously, homogeneity of the solder line can be improved trying to design welding chamber where material flow is more uniform.

Conclusions

In the present paper the results of experimental and numerical investigations on parts extruded through a porthole die are reported. In particular the fully three-dimensional material flow occurring for the considered part is taken into account and through a FE commercial code the evolution of the Pivnik and Plata criterion is considered for several material points. The obtained results show that different welding conditions are reached by the flowing material for different points of an actual welding line occurring in extruded part. Such result is confirmed by the experiments: the micro-hardness values measured all along welding line corresponding to the one considered in the numerical simulations demonstrated the different mechanical characteristics of the material for different zones of the welding line.

Further investigations are needed in order also to highlight the material metallurgical evolutions occurring in the different zones of the welding line at the varying of the welding conditions and to relate them to the material flow towards the welding zone.

Overall the relevance of an automatic numerical procedure implementing an effective welding criterion based on a specific material characterization and able to highlight the actual bonding mechanics occurring in the porthole die is stressed.


Acknowledgement

This work has been performed with funding from MIUR (Italian Ministry for Instruction, University and Research).

References

[1] H. Valberg: Int. J. Mater. and Product Technol. Vol.17 No. 7 (2002), p. 497

[2] H. Valberg, T. Loeken, M. Hval, B. Nyhus and C. Thaulow: Int. J. Mater. and Product Technol. Vol.10 (1995), p. 222

[3] L. Donati and L.Tomesani: J. Mater. Process. Technol. Vol.153-154 (2004), p. 366

[4] K.J. Kim, C.H. Lee and D.Y. Yang: J. Mater. Process. Technol. Vol. 130–131 (2002), p. 426

[5] H.H. Jo, C.S. Jeong, S.K. Lee and B.M. Kim: J. Mater. Process. Technol. Vol. 139 (2003), p. 428

[6] L. Donati and T. Tomesani: Mater. Sci. Forum Vol. 604-605 (2009), p. 121

[7] E. Ceretti, L. Fratini, F. Gagliardi and C. Giardini: CIRP Annals – Manufac. Technol. (2009), in press.

[8] M. Kiuchi, J. Yanagimoto and M. Victor: CIRP Annals– Manufac. Technol. Vol 45(1) (1996), p.235

[9] D.Y. Yang and Y.S. Kang: CIRP Annals– Manufac. Technol. Vol.45(1) (1996), p.239.

[10] Y. Kim, K. Ikeda, T. Murakami: Int. J. Mater. Product Technol. Vol. 121 (2002), p.107

[11] D.Y. Yang: CIRP Annals– Manufac. Technol. Vol. 43(1) (1994), p.229

[12] DEFORM 3D Version 6.1(sp3), User’s Manual, (2008).

[13] L. Donati, L. Tomesani and G. Minak: Int. J. Mater. Product.Technol. Vol. 191 (2007), p.127

[14] M. Plata and J. Piwnik, in: Seventh Int. Aluminum Extrusion Technol.Seminar, USA, Chicago Vol. I (2000), p.205

Acknowledgement

This work has been performed with funding from MIUR (Italian Ministry for Instruction, University and Research).

References


[2] H. Valberg, T. Loeken, M. Hval, B. Nyhus and C. Thaulow: Int. J. Mater. and Product Technol. Vol.10 (1995), p. 222

[3] L. Donati and L.Tomesani: J. Mater. Process. Technol. Vol.153-154 (2004), p. 366


[5] H.H. Jo, C.S. Jeong, S.K. Lee and B.M. Kim: J. Mater. Process. Technol. Vol. 139 (2003), p. 428

[6] L. Donati and T. Tomesani: Mater. Sci. Forum Vol. 604-605 (2009), p. 121

[7] E. Ceretti, L. Fratini, F. Gagliardi and C. Giardini: CIRP Annals – Manufac. Technol. (2009), in press.

[8] M. Kiuchi, J. Yanagimoto and M. Victor: CIRP Annals– Manufac. Technol. Vol 45(1) (1996), p.235

[9] D.Y. Yang and Y.S. Kang: CIRP Annals– Manufac. Technol. Vol.45(1) (1996), p.239.

[10] Y. Kim, K. Ikeda, T. Murakami: Int. J. Mater. Product Technol. Vol. 121 (2002), p.107

[11] D.Y. Yang: CIRP Annals– Manufac. Technol. Vol. 43(1) (1994), p.229

[12] DEFORM 3D Version 6.1(sp3), User’s Manual, (2008).

[13] L. Donati, L. Tomesani and G. Minak: Int. J. Mater. Product.Technol. Vol. 191 (2007), p.127

[14] M. Plata and J. Piwnik, in: Seventh Int. Aluminum Extrusion Technol.Seminar, USA, Chicago Vol. I (2000), p.205


Accurate Welding Line Prediction in Extrusion Processes

T. Kloppenborg1, a, N. Ben Khalifa1, b, A. E. Tekkaya1,c 1Institute of Forming Technology and Lightweight Construction,

Technische Universität Dortmund, Germany [email protected], [email protected]

[email protected]

Keywords: Extrusion, Welding Line, Seam Weld, Finite Element Method Abstract. In contrast to conventional extrusion processes, where a lot of research is done on in the welding quality, in composite extrusion, research is investigated into the welding line positioning. As a result of the process principle, the reinforcing elements are embedded into the longitudinal welding line. Hence, an undefined material flow inside the welding chamber induces reinforcement deflection, which can lead to reduced mechanical properties, as momentum of inertia. Therefore and to reduce costly experimental investigations, a new method of an automated numerical welding line prediction was developed. The results form HyperXtrude finite element calculations are used for special particle tracing simulations to predict the welding line in the profile cross section accurately. The procedures of segmentation and characteristic extraction are presented to approximate the welding line by cubic spline functions. The method was fully programmed in the Java program language, and works well for all HyperXtrude process models consisting of tetrahedral elements.

Introduction

Porthole die extrusion leads to longitudinal seam welds in the manufactured profiles. Die bridges divide the billet material into different feeders before the metal streams are rejoined around the mandrel and in the welding chamber. The welding line extends over the whole profile length. In general, these types of dies are used for the manufacturing of hollow profiles (Fig. 1i). Advanced and innovative extrusion processes have been developed to extend the requirements of the bridges. In composite extrusion, the bridges are not only utilized to fix the mandrel in the material flow, but also to feed high strength wires in-between the material streams to embed them in the welding chamber at the moment of material rejoining. The supply of the endless wires in the same profile makes additional bridges necessary, which lead to a more complex material flow and to additional seam welds (Fig. 1ii).

Fig. 1: Comparison of: i) Conventional bridge die ii) Composite bridge die

Accurate Welding Line Prediction in Extrusion Processes

T. Kloppenborg1, a, N. Ben Khalifa1, b, A. E. Tekkaya1,c 1Institute of Forming Technology and Lightweight Construction,

Technische Universität Dortmund, Germany [email protected], [email protected]

[email protected]

Keywords: Extrusion, Welding Line, Seam Weld, Finite Element Method Abstract. In contrast to conventional extrusion processes, where a lot of research is done on in the welding quality, in composite extrusion, research is investigated into the welding line positioning. As a result of the process principle, the reinforcing elements are embedded into the longitudinal welding line. Hence, an undefined material flow inside the welding chamber induces reinforcement deflection, which can lead to reduced mechanical properties, as momentum of inertia. Therefore and to reduce costly experimental investigations, a new method of an automated numerical welding line prediction was developed. The results form HyperXtrude finite element calculations are used for special particle tracing simulations to predict the welding line in the profile cross section accurately. The procedures of segmentation and characteristic extraction are presented to approximate the welding line by cubic spline functions. The method was fully programmed in the Java program language, and works well for all HyperXtrude process models consisting of tetrahedral elements.

Introduction

Porthole die extrusion leads to longitudinal seam welds in the manufactured profiles. Die bridges divide the billet material into different feeders before the metal streams are rejoined around the mandrel and in the welding chamber. The welding line extends over the whole profile length. In general, these types of dies are used for the manufacturing of hollow profiles (Fig. 1i). Advanced and innovative extrusion processes have been developed to extend the requirements of the bridges. In composite extrusion, the bridges are not only utilized to fix the mandrel in the material flow, but also to feed high strength wires in-between the material streams to embed them in the welding chamber at the moment of material rejoining. The supply of the endless wires in the same profile makes additional bridges necessary, which lead to a more complex material flow and to additional seam welds (Fig. 1ii).

Fig. 1: Comparison of: i) Conventional bridge die ii) Composite bridge die


In extrusion industry the interest is focused on the welding line position and on the seam weld quality. The seam weld position is only taken into consideration when an aesthetical aspect for the application of the profiles becomes necessary. In this case, the die is generally designed to weld the material streams in the profile curvatures to achieve an accurate profile surface. More important for the extrusion industry is the seam weld quality. Bad welding between the two metal streams can result in profile defects, as cracks, and complete failure of the structure under load. Hence, much research has been investigated in recent decades to understand the welding [1-6].

For the composite extrusion process the welding line position is as well important as the welding quality. The material flow in the welding chamber is not usually accurate enough for a well positioning of the reinforcing elements in the final extrusion product. However, with the insertion of reinforcement, a problem can occur which is negligible in the conventional extrusion process. Namely, depending on the material flow conditions in the die, reinforcing elements are deflected horizontally and vertically in relation to the supply position, which yields a change in the mechanical properties like moment of inertia (Fig. 2).

Fig. 2: Reinforcement deflection in composite extrusion

In [7] Schomäcker analyzed the main effects of the positioning failures. He examined the process

experimentally and found out that the position of the elements is mainly influenced by the press on, the temperature distribution, the forming velocity, the die design and the position of the supply channels. It is obvious that the degree of difficulty to predict the material flow rises with the complexity of the die. Hence, for high-quality die designing, technical know-how is necessary, which has to be acquired over a long time. But the process comprehension is limited so that cost intensive trial-and-error experiments are often essential. For composite extrusion, Schomäcker established that an experimental analysis of all influencing parameters on reinforcement positioning exceeds the economic efficiency of the die development process.

For this reason, the use of numerical simulations becomes more interesting [8]. Especially the process conditions in the inaccessible die, such as distribution of the material flow, temperature, and pressure, can be visualized [9]. In [10] Schikorra presented two methods to predict the longitudinal seam weld. It could be shown that the effective strain rate or the equivalent strain and the particle tracings are the criteria for the welding line position (Fig. 3) and concluded that these criteria can be helpful to improve reinforcement positioning. However, the determination of the seam weld position was mainly performed optically and thus implies a more qualitative character. In order to substantiate these criteria, it is necessary to predict the longitudinal seam weld more accurately and in an automated way. Especially in case of an automated process optimization, it can be helpful to approximate the weld line, for example, by polynomials. The polynomials can then be useful as an optimization criterion.

Fig. 3: Criteria to predict the weld line formation in composite extrusion [3]

In extrusion industry the interest is focused on the welding line position and on the seam weld quality. The seam weld position is only taken into consideration when an aesthetical aspect for the application of the profiles becomes necessary. In this case, the die is generally designed to weld the material streams in the profile curvatures to achieve an accurate profile surface. More important for the extrusion industry is the seam weld quality. Bad welding between the two metal streams can result in profile defects, as cracks, and complete failure of the structure under load. Hence, much research has been investigated in recent decades to understand the welding [1-6].

For the composite extrusion process the welding line position is as well important as the welding quality. The material flow in the welding chamber is not usually accurate enough for a well positioning of the reinforcing elements in the final extrusion product. However, with the insertion of reinforcement, a problem can occur which is negligible in the conventional extrusion process. Namely, depending on the material flow conditions in the die, reinforcing elements are deflected horizontally and vertically in relation to the supply position, which yields a change in the mechanical properties like moment of inertia (Fig. 2).

Fig. 2: Reinforcement deflection in composite extrusion

In [7] Schomäcker analyzed the main effects of the positioning failures. He examined the process

experimentally and found out that the position of the elements is mainly influenced by the press on, the temperature distribution, the forming velocity, the die design and the position of the supply channels. It is obvious that the degree of difficulty to predict the material flow rises with the complexity of the die. Hence, for high-quality die designing, technical know-how is necessary, which has to be acquired over a long time. But the process comprehension is limited so that cost intensive trial-and-error experiments are often essential. For composite extrusion, Schomäcker established that an experimental analysis of all influencing parameters on reinforcement positioning exceeds the economic efficiency of the die development process.

For this reason, the use of numerical simulations becomes more interesting [8]. Especially the process conditions in the inaccessible die, such as distribution of the material flow, temperature, and pressure, can be visualized [9]. In [10] Schikorra presented two methods to predict the longitudinal seam weld. It could be shown that the effective strain rate or the equivalent strain and the particle tracings are the criteria for the welding line position (Fig. 3) and concluded that these criteria can be helpful to improve reinforcement positioning. However, the determination of the seam weld position was mainly performed optically and thus implies a more qualitative character. In order to substantiate these criteria, it is necessary to predict the longitudinal seam weld more accurately and in an automated way. Especially in case of an automated process optimization, it can be helpful to approximate the weld line, for example, by polynomials. The polynomials can then be useful as an optimization criterion.

Fig. 3: Criteria to predict the weld line formation in composite extrusion [3]


In the present paper, an automated detection of the welding line position using particle tracings is presented. The method was programmed in java code and is applicable on any extrusion models calculated with HyperXtrude Software. The program works only on unstructured tetrahedral grids in Euclidean 3D- Space. The method is illustrated on a double-T shaped profile and validated on experimental investigations.

Particle tracing

In many scientific areas as well as in technical applications, finite element simulation is of central importance. The results of numerical calculations are data sets which usually describe the flow behavior in a 3D-environment. To understand the flow characteristics of the simulated process, a meaningful visualization of the data is necessary. The raw data are defined on a discrete structure, a finite element mesh. In the nodes of the mesh the velocity and other results, e.g. temperature, stresses and strains, are stored. In particle tracing individual material particle traces are generated based on the velocity vector field. For the calculation of the flow lines numerical integration of an ordinary differential equation (ODE) is essential [11].

dp( t )

v( p( t ))dt

=r

r r (1)

where p( t )

r represents the position of the particle at time t , starting at time 0t at position 0p

r.

For the initial vector 0pr

is essential that:

0 0p( t ) p=r r

(2) For fixed time steps 0 1 nt ,t ,...,t , the positions 0 1 np , p ,..., p can be calculated, which are a set of

particle positions to generate the flow line. In Computational Fluid Dynamics (CFD) time dependent and time independent velocity fields

are differentiated. Latter, the velocity field is also time dependent. For the simulation of the extrusion process using the Euler-Flow-Formulation, the velocity vectors are time independent, which is why following the explanations are focused only on this problem. Nevertheless, many aspects described later are valid as well for time dependent velocity fields. Darmofal et al. [12] gives a detailed overview of both types of flow fields.

Particle tracing is valid for two-dimensional as well as three-dimensional problems. The technique described in the following is referred to 3D finite element models but for a better understanding two dimensional examples are shown.

Numerical integration is a standard procedure for solving Eq. 1. For the implementation of particle tracing, additional procedures are necessary. These are element localization, velocity interpolation and integration. For each procedure, many methods are known, while in the following only the implemented ones are given. The basic algorithm for particle tracing is shown in Fig. 4 as pseudo code.

while end while

Define an element which contains the starting point element localization particle in the element do calculate the velocity at the actual position velocity interpolation calculate the new position integration calculate the element at the new position element localization

Fig. 4: Particle tracing in pseudo code [13]

In the present paper, an automated detection of the welding line position using particle tracings is presented. The method was programmed in java code and is applicable on any extrusion models calculated with HyperXtrude Software. The program works only on unstructured tetrahedral grids in Euclidean 3D- Space. The method is illustrated on a double-T shaped profile and validated on experimental investigations.

Particle tracing

In many scientific areas as well as in technical applications, finite element simulation is of central importance. The results of numerical calculations are data sets which usually describe the flow behavior in a 3D-environment. To understand the flow characteristics of the simulated process, a meaningful visualization of the data is necessary. The raw data are defined on a discrete structure, a finite element mesh. In the nodes of the mesh the velocity and other results, e.g. temperature, stresses and strains, are stored. In particle tracing individual material particle traces are generated based on the velocity vector field. For the calculation of the flow lines numerical integration of an ordinary differential equation (ODE) is essential [11].

dp( t )

v( p( t ))dt

=r

r r (1)

where p( t )

r represents the position of the particle at time t , starting at time 0t at position 0p

r.

For the initial vector 0pr

is essential that:

0 0p( t ) p=r r

(2) For fixed time steps 0 1 nt ,t ,...,t , the positions 0 1 np , p ,..., p can be calculated, which are a set of

particle positions to generate the flow line. In Computational Fluid Dynamics (CFD) time dependent and time independent velocity fields

are differentiated. Latter, the velocity field is also time dependent. For the simulation of the extrusion process using the Euler-Flow-Formulation, the velocity vectors are time independent, which is why following the explanations are focused only on this problem. Nevertheless, many aspects described later are valid as well for time dependent velocity fields. Darmofal et al. [12] gives a detailed overview of both types of flow fields.

Particle tracing is valid for two-dimensional as well as three-dimensional problems. The technique described in the following is referred to 3D finite element models but for a better understanding two dimensional examples are shown.

Numerical integration is a standard procedure for solving Eq. 1. For the implementation of particle tracing, additional procedures are necessary. These are element localization, velocity interpolation and integration. For each procedure, many methods are known, while in the following only the implemented ones are given. The basic algorithm for particle tracing is shown in Fig. 4 as pseudo code.

while end while

Define an element which contains the starting point element localization particle in the element do calculate the velocity at the actual position velocity interpolation calculate the new position integration calculate the element at the new position element localization

Fig. 4: Particle tracing in pseudo code [13]


Element localization. Firstly, the element in which the particle point is provided has to be identified before an interpolation of the velocity vectors of the element nodes can be realized. This operation has to be evaluated at the beginning of the particle tracing simulation as well as in every flow line generation loop. The finite element mesh for extrusion simulation is mostly unstructured as a result of different element shapes, element dimensions and element types. For this case, Ren et al. [14] presented an efficient element identification. Here, the characteristic of shared element planes is utilized. This is feasible for all elements except the elements on the model surface. It is helpful to consider that for small time steps, the new position of the particles is in one of the direct finite element neighbors. Based hereon, a heuristic search method can be useful to detect the element of the new particle position.

Ren et al. restricted the method to tetrahedral elements and recommended that other element types should be deconstructed into tetrahedral elements. The deconstruction can result in highly distorted tetrahedral elements, in which the interpolation error increases. Hence, hexahedral elements should be prevented.

To check if the particles are inside the element, the normal vectors of the element faces can be used. This method is usable for every element type. For every element face s the normal vector in

r

is calculated. The orientation of the vector is directed normal to the element. Every element face is considered as plane which divides the space into two parts. The part which is positive concerning the normal vector includes no particles that are inside the element. In converse argumentation, the particles inside the elements are on the negative side of all element planes. Hence, it is sufficient to check if the normal vector for every element plane has a positive portion. This can be calculated with the vector product. sp

r stands for any particle point on the element face s . The method is

useable for tetrahedral and convex hexahedral elements

0s s( p p ) n− ⋅ >r r r

(3) For the determination of the initial position the described heuristical method is inefficient.

Alternatively, at the beginning of the particle tracing every element is checked systematically to find the elements in which the particle is placed. The complete search is only executed once, so that the computational time is acceptable. For the subsequent element detections the more time efficient heuristical method is used. This search algorithm also uses the point test. Is a particle at time t located at the position p( t )

r in element E is firstly tested if the particle is also in element E at

position 1p( t )+r

. In case of a failure of the point test at element plane s, the point test is recursively conducted for the neighbor element on face s . This procedure is continued until the element is found in which 1p( t )+

r is allocated or no further neighbor element is found. Finally, the particle

leaves the finite element model. Fig. 5 demonstrates the procedure for the two-dimensional case.

Fig. 5: Principle of neighbor element search:

(i) Point pr is located in element A , no normal vector is directed in direction p

r;

(ii) Normal vector 2nr

is directed in pr, the search is accomplished in element C ;

(iii) Normal vector 3nr

is directed in pr, the search is accomplished in element D ;

(iv) Normal vector 1nr and 2n

r are directed in p

r, the search is accomplished in B or C

Element localization. Firstly, the element in which the particle point is provided has to be identified before an interpolation of the velocity vectors of the element nodes can be realized. This operation has to be evaluated at the beginning of the particle tracing simulation as well as in every flow line generation loop. The finite element mesh for extrusion simulation is mostly unstructured as a result of different element shapes, element dimensions and element types. For this case, Ren et al. [14] presented an efficient element identification. Here, the characteristic of shared element planes is utilized. This is feasible for all elements except the elements on the model surface. It is helpful to consider that for small time steps, the new position of the particles is in one of the direct finite element neighbors. Based hereon, a heuristic search method can be useful to detect the element of the new particle position.

Ren et al. restricted the method to tetrahedral elements and recommended that other element types should be deconstructed into tetrahedral elements. The deconstruction can result in highly distorted tetrahedral elements, in which the interpolation error increases. Hence, hexahedral elements should be prevented.

To check if the particles are inside the element, the normal vectors of the element faces can be used. This method is usable for every element type. For every element face s the normal vector in

r

is calculated. The orientation of the vector is directed normal to the element. Every element face is considered as plane which divides the space into two parts. The part which is positive concerning the normal vector includes no particles that are inside the element. In converse argumentation, the particles inside the elements are on the negative side of all element planes. Hence, it is sufficient to check if the normal vector for every element plane has a positive portion. This can be calculated with the vector product. sp

r stands for any particle point on the element face s . The method is

useable for tetrahedral and convex hexahedral elements

0s s( p p ) n− ⋅ >r r r

(3) For the determination of the initial position the described heuristical method is inefficient.

Alternatively, at the beginning of the particle tracing every element is checked systematically to find the elements in which the particle is placed. The complete search is only executed once, so that the computational time is acceptable. For the subsequent element detections the more time efficient heuristical method is used. This search algorithm also uses the point test. Is a particle at time t located at the position p( t )

r in element E is firstly tested if the particle is also in element E at

position 1p( t )+r

. In case of a failure of the point test at element plane s, the point test is recursively conducted for the neighbor element on face s . This procedure is continued until the element is found in which 1p( t )+

r is allocated or no further neighbor element is found. Finally, the particle

leaves the finite element model. Fig. 5 demonstrates the procedure for the two-dimensional case.

Fig. 5: Principle of neighbor element search:

(i) Point pr is located in element A , no normal vector is directed in direction p

r;

(ii) Normal vector 2nr

is directed in pr, the search is accomplished in element C ;

(iii) Normal vector 3nr

is directed in pr, the search is accomplished in element D ;

(iv) Normal vector 1nr and 2n

r are directed in p

r, the search is accomplished in B or C


Interpolation. The velocity vectors are only known at the nodes of the finite elements. At every other point in the mesh a velocity vector has to be interpolated. Within the element identification it is known in which element the particle point is positioned and which nodes are to be used for the interpolation. Dependent on the element types, Sardajoen et al. described different methods [13]. The interpolation is not only used for the velocity vectors but also for values of temperature and stress along the flow lines. In the following, the interpolation of tetrahedron elements which were implemented is shown.

For the interpolation in a tetrahedron, the volume weighting is used which is based on volume weights. Let p

r be a point in a tetrahedron consisting of nodes 0 1 2 3x ,x ,x ,x

r r r r. Then the tetrahedron can

be subdivided into four sub-tetrahedrons, in all of which pr is a corner node. The weight for each

node of the main tetrahedron is the ratio of the volume of the sub-tetrahedron to the volume of the main tetrahedron (Eq.4) [13]. The interpolated velocity is than calculated as a sum of the weight multiplicated with the corresponding velocity vector (Eq.5). In Fig. 6i the principle is presented for a 2-dimensional triangle element.

123 023 013 0120 1 2 3

0123 0123 0123 0123

p p p pv v v v

w w w wv v v v

= = = = (4)

0 0 1 1 2 2 3 3pv w v w v w v w v= + + +r r r r r

(5)

Integration. The solution of the basic equation of the particle tracing (Eq. 1) is conventionally solved by numerical methods. Many integration methods are known in the literature, ranging from the simple first-order Euler scheme to the fourth-order Runge-Kutta scheme or even higher-order methods, applied with fixed or variable time steps. An extensive analysis of different integration algorithms and the applicability in particle tracing is proposed in [12]. In the following, the implemented second order Runge-Kutta scheme is shortly presented. The integration method was chosen in order to gain a good agreement between accuracy and calculation time. The second-order Runge-Kutta scheme is also known as Heun’s scheme. Starting from position ip

r at time it t= , the

position 1ip +

r at time 1it t += is calculated in two steps.

1

1 1

12

*i i i

*i i i i

p p v( p ) t

p p ( v( p ) v( p )) t

+

+ +

= + ⋅

= + + ⋅ ⋅

r r r r

r r r r r r (6)

(7)

The integration principle is shown in Fig. 6ii. There are further numerical methods with higher accuracy in literature. In [11] such a method is presented for tetrahedron element meshes.

Fig. 6: i) Area weighting [13]; ii) Second order Runge-Kutta schema

Additional features. The results from the finite element calculations with commercial code HyperXtrude are not error free. The errors are affecting on the particle tracing results. In dead zones for example as well on the contact area no material flow is present. In the ideal case, here the

Interpolation. The velocity vectors are only known at the nodes of the finite elements. At every other point in the mesh a velocity vector has to be interpolated. Within the element identification it is known in which element the particle point is positioned and which nodes are to be used for the interpolation. Dependent on the element types, Sardajoen et al. described different methods [13]. The interpolation is not only used for the velocity vectors but also for values of temperature and stress along the flow lines. In the following, the interpolation of tetrahedron elements which were implemented is shown.

For the interpolation in a tetrahedron, the volume weighting is used which is based on volume weights. Let p

r be a point in a tetrahedron consisting of nodes 0 1 2 3x ,x ,x ,x

r r r r. Then the tetrahedron can

be subdivided into four sub-tetrahedrons, in all of which pr is a corner node. The weight for each

node of the main tetrahedron is the ratio of the volume of the sub-tetrahedron to the volume of the main tetrahedron (Eq.4) [13]. The interpolated velocity is than calculated as a sum of the weight multiplicated with the corresponding velocity vector (Eq.5). In Fig. 6i the principle is presented for a 2-dimensional triangle element.

123 023 013 0120 1 2 3

0123 0123 0123 0123

p p p pv v v v

w w w wv v v v

= = = = (4)

0 0 1 1 2 2 3 3pv w v w v w v w v= + + +r r r r r

(5)

Integration. The solution of the basic equation of the particle tracing (Eq. 1) is conventionally solved by numerical methods. Many integration methods are known in the literature, ranging from the simple first-order Euler scheme to the fourth-order Runge-Kutta scheme or even higher-order methods, applied with fixed or variable time steps. An extensive analysis of different integration algorithms and the applicability in particle tracing is proposed in [12]. In the following, the implemented second order Runge-Kutta scheme is shortly presented. The integration method was chosen in order to gain a good agreement between accuracy and calculation time. The second-order Runge-Kutta scheme is also known as Heun’s scheme. Starting from position ip

r at time it t= , the

position 1ip +

r at time 1it t += is calculated in two steps.

1

1 1

12

*i i i

*i i i i

p p v( p ) t

p p ( v( p ) v( p )) t

+

+ +

= + ⋅

= + + ⋅ ⋅

r r r r

r r r r r r (6)

(7)

The integration principle is shown in Fig. 6ii. There are further numerical methods with higher accuracy in literature. In [11] such a method is presented for tetrahedron element meshes.

Fig. 6: i) Area weighting [13]; ii) Second order Runge-Kutta schema

Additional features. The results from the finite element calculations with commercial code HyperXtrude are not error free. The errors are affecting on the particle tracing results. In dead zones for example as well on the contact area no material flow is present. In the ideal case, here the


velocity field is zero, but the experience has shown that velocity remains due to numerical errors. The velocity vectors are small but arbitrarily directed, for example contrary to the extrusion direction. Within the dead zones, for example, circulation of the particle traces can occur. Here, the flow lines run on cyclic tracks and can not leave the area. In such a case, it is convenient to restrict the length of the flow line.

Method for numerical weld line prediction

In the following, the method is presented which can be used to predict the longitudinal seam weld position in the final profile cross section more accurately and in an automated way. In Fig. 7 a simplified 2-dimensional extrusion model is shown. Based on the velocity vectors particle traces have been calculated starting from different die feeder positions, running through the welding chamber into the extruded profile. It is obvious that the material which forms the longitudinal seam weld position is diagrammed by tracings which have started next to the mandrel.

Fig. 7: Schematic illustration of the seam weld formation

A 3-dimensional extrusion process model was set-up for weld line prediction. It is based on

experimental investigations on a 2.5 MN press. The model was implemented in the commercial implicit finite element code HyperXtrude from Altair to calculate the velocity vectors for particle tracing. The container, the die and the leaking profile are illustrated together with the profile cross section and the used parameters in Fig. 8. A full model was considered in spite of the symmetrical character.

Fig. 8: i) Initial extrusion process model ii) Cross-section of the profile and simulation parameters The billet, made of AA-6060, is preheated to 480°C and then extruded with a punch velocity of

1 mm/s. A Coulomb friction coefficient of 0.577 was utilized on the die and the container wall. Here, the friction shear stress is limited by the shear yield point so that the static friction implements von Mises shear friction with a friction value of 1. The model consists of 809.926 four-node

velocity field is zero, but the experience has shown that velocity remains due to numerical errors. The velocity vectors are small but arbitrarily directed, for example contrary to the extrusion direction. Within the dead zones, for example, circulation of the particle traces can occur. Here, the flow lines run on cyclic tracks and can not leave the area. In such a case, it is convenient to restrict the length of the flow line.

Method for numerical weld line prediction

In the following, the method is presented which can be used to predict the longitudinal seam weld position in the final profile cross section more accurately and in an automated way. In Fig. 7 a simplified 2-dimensional extrusion model is shown. Based on the velocity vectors particle traces have been calculated starting from different die feeder positions, running through the welding chamber into the extruded profile. It is obvious that the material which forms the longitudinal seam weld position is diagrammed by tracings which have started next to the mandrel.

Fig. 7: Schematic illustration of the seam weld formation

A 3-dimensional extrusion process model was set-up for weld line prediction. It is based on

experimental investigations on a 2.5 MN press. The model was implemented in the commercial implicit finite element code HyperXtrude from Altair to calculate the velocity vectors for particle tracing. The container, the die and the leaking profile are illustrated together with the profile cross section and the used parameters in Fig. 8. A full model was considered in spite of the symmetrical character.

Fig. 8: i) Initial extrusion process model ii) Cross-section of the profile and simulation parameters The billet, made of AA-6060, is preheated to 480°C and then extruded with a punch velocity of

1 mm/s. A Coulomb friction coefficient of 0.577 was utilized on the die and the container wall. Here, the friction shear stress is limited by the shear yield point so that the static friction implements von Mises shear friction with a friction value of 1. The model consists of 809.926 four-node


tetrahedral elements with linear shape functions. In order to reduce the calculation time, the analysis type was set to steady-state extrusion.

The calculated velocities on the nodes of each element were used to simulate particle tracing lines through the numerical model. In Fig. 9 the basic procedure is demonstrated. The particle start position and the resulting position of the particles in the final cross-section are demonstrated. The traces follow the material flow, starting in the feeders at the die entrance. Then they cross the bearing area and terminate on a predefined cross section. For seam weld detection, only the particle tracings around the feeders have been calculated.

Fig. 9: Method for welding line prediction

Due to the friction on the die wall, particles have started with a small border distance. An undersized border distance indicates that particles leave the model. Thus, the number of dots in the final cross section decreases and the detection of the seam weld position becomes difficult. Contrary to this, an oversized border distance will increase the distance between the flow lines in the final cross section. Therefore, the border distance was sequentially increased until the longitudinal seam weld was well visualized. Neglecting the particle dots on the profile surface, it can easily be seen that the method indicates an accurate reference value for the detection of longitudinal seam weld formation. Segmentation. The emphasized contour of the seam weld can be used to extract a continuous seam weld characteristic with the help of a pattern matching method. Therefore particles which do not belong to the seam weld have to be deleted. These are positioned on the profile surface or somewhere in the profile cross section due to modelling defects. However, all particles that fall below a predefined distance value to the profile surface are not further considered. Thus, exclusive particles remain that illustrate the seam weld and result from modelling defects. For extrusion process models with multiple feeders, a welding of the material out of two different feeders results in one segment of the weld line. For the identification of every segment, particles out of the same feeder are assigned with the same index. In the profile cross-section every particle point neighbors are checked to characterize the different weld line segments. If there is no neighbor the particle contains out of modeling defects and is deleted. In Fig.10 the particle points before (i) and after (ii) the segmentation procedure are opposed. The five weld line segments are uniformly displayed in terms of color. Characteristic extraction. A continuous weld line can be derived based on segmented particle points. The aim of the procedure is to describe the welding line by a curve for quantitative estimation. Through the segmentation procedure the particle points are already the part segments of the welding line assigned. The approximation is conducted for every weld line segment and than combined to an continuous weld line. The flexible curve character is approximated by cubic spline functions. In contrast to a characteristic polynomial, any curves can be approximated in this way. Fig. 10 iii) shows the results of the characteristic extraction.

tetrahedral elements with linear shape functions. In order to reduce the calculation time, the analysis type was set to steady-state extrusion.

The calculated velocities on the nodes of each element were used to simulate particle tracing lines through the numerical model. In Fig. 9 the basic procedure is demonstrated. The particle start position and the resulting position of the particles in the final cross-section are demonstrated. The traces follow the material flow, starting in the feeders at the die entrance. Then they cross the bearing area and terminate on a predefined cross section. For seam weld detection, only the particle tracings around the feeders have been calculated.

Fig. 9: Method for welding line prediction

Due to the friction on the die wall, particles have started with a small border distance. An undersized border distance indicates that particles leave the model. Thus, the number of dots in the final cross section decreases and the detection of the seam weld position becomes difficult. Contrary to this, an oversized border distance will increase the distance between the flow lines in the final cross section. Therefore, the border distance was sequentially increased until the longitudinal seam weld was well visualized. Neglecting the particle dots on the profile surface, it can easily be seen that the method indicates an accurate reference value for the detection of longitudinal seam weld formation. Segmentation. The emphasized contour of the seam weld can be used to extract a continuous seam weld characteristic with the help of a pattern matching method. Therefore particles which do not belong to the seam weld have to be deleted. These are positioned on the profile surface or somewhere in the profile cross section due to modelling defects. However, all particles that fall below a predefined distance value to the profile surface are not further considered. Thus, exclusive particles remain that illustrate the seam weld and result from modelling defects. For extrusion process models with multiple feeders, a welding of the material out of two different feeders results in one segment of the weld line. For the identification of every segment, particles out of the same feeder are assigned with the same index. In the profile cross-section every particle point neighbors are checked to characterize the different weld line segments. If there is no neighbor the particle contains out of modeling defects and is deleted. In Fig.10 the particle points before (i) and after (ii) the segmentation procedure are opposed. The five weld line segments are uniformly displayed in terms of color. Characteristic extraction. A continuous weld line can be derived based on segmented particle points. The aim of the procedure is to describe the welding line by a curve for quantitative estimation. Through the segmentation procedure the particle points are already the part segments of the welding line assigned. The approximation is conducted for every weld line segment and than combined to an continuous weld line. The flexible curve character is approximated by cubic spline functions. In contrast to a characteristic polynomial, any curves can be approximated in this way. Fig. 10 iii) shows the results of the characteristic extraction.


Fig. 10: i) Simulated particle points; ii) Particle points after segmentation; iii) Approximated weld line

Experimental verification

In Fig. 11 the numerical results are compared to experimental investigations. It can be shown that there is a sufficient correlation between the experimentally determined welding line position and the simulated one. The differences are based on the numerical errors and/or modeling errors from the finite element calculation.

Fig. 11: Comparison of simulated welding line and experimental results

Conclusion and Outlook

In this paper a method for an automated welding line prediction is presented. The results from HyperXtrude calculations are used for the simulation of particle tracing that form the weld line in the profile cross-section. The procedures of segmentation and characteristic extraction are presented to approximate the weld line with cubic spline function. The method was fully programmed in the Java program language and works well for all HyperXtrude process models consisting of tetrahedral elements.

In case of composite extrusion, the method can be a helpful tool to optimize the reinforcement position numerically. In further investigations the method will by implemented in a closed loop algorithm to optimize the welding line regarding a predefined optimal weld line.

Acknowledgment

This paper is based on investigations within the scope of the Transregional Collaborative Research Center/ TR10 and is kindly supported by the German Research Foundation (DFG).

References

[1] R. Akeret: Eigenschaften von Pressschweißnähten in Strangpressprofilen aus Aluminiumlegierungen, Special Report, Deutsche Gesellschaft für Metallkunde, Oberursal, Germany (1974), (extended version of Ref.1 in German)

[2] M. Plata and J. Piwnik: Theoretical And Experimental Analysis Of Seam Weld Formation In Hot Extrusion Of Aluminum Alloys, Proceedings of the Seventh International Aluminum Extrusion Technology Seminar ET 2000, Vol. I, 205-211.

Fig. 10: i) Simulated particle points; ii) Particle points after segmentation; iii) Approximated weld line

Experimental verification

In Fig. 11 the numerical results are compared to experimental investigations. It can be shown that there is a sufficient correlation between the experimentally determined welding line position and the simulated one. The differences are based on the numerical errors and/or modeling errors from the finite element calculation.

Fig. 11: Comparison of simulated welding line and experimental results

Conclusion and Outlook

In this paper a method for an automated welding line prediction is presented. The results from HyperXtrude calculations are used for the simulation of particle tracing that form the weld line in the profile cross-section. The procedures of segmentation and characteristic extraction are presented to approximate the weld line with cubic spline function. The method was fully programmed in the Java program language and works well for all HyperXtrude process models consisting of tetrahedral elements.

In case of composite extrusion, the method can be a helpful tool to optimize the reinforcement position numerically. In further investigations the method will by implemented in a closed loop algorithm to optimize the welding line regarding a predefined optimal weld line.

Acknowledgment

This paper is based on investigations within the scope of the Transregional Collaborative Research Center/ TR10 and is kindly supported by the German Research Foundation (DFG).

References

[1] R. Akeret: Eigenschaften von Pressschweißnähten in Strangpressprofilen aus Aluminiumlegierungen, Special Report, Deutsche Gesellschaft für Metallkunde, Oberursal, Germany (1974), (extended version of Ref.1 in German)

[2] M. Plata and J. Piwnik: Theoretical And Experimental Analysis Of Seam Weld Formation In Hot Extrusion Of Aluminum Alloys, Proceedings of the Seventh International Aluminum Extrusion Technology Seminar ET 2000, Vol. I, 205-211.


[3] L. Donati, L. Tomesani, G. Minak, Characterization of seam weld quality in AA6082 extruded profiles Journal of Materials Processing Technology 191 (2007) pp. 127–131

[4] H. Valberg: The mechanics of two-dimensional aluminium extrusion welding investigated by FEM-analysis with experiment, ICTP 2008 (The 9th International Conference on Technology of Plasticity)

[5] K.J. Kim, C.H. Lee and D.Y. Yang, Investigation into the Improvement of Welding Strength in Three-dimensional Extrusion of Tubes Using Porthole Dies, International Journal of Materials & Product Technology 130-131 (2002), pp. 426–431

[6] A. Fratini: A new approach to study material bonding in extrusion porthole dies CIRP Annals - Manufacturing Technology 58 (2009) 259–262

[7] M. Schomäcker: Verbundstrangpressen von Aluminiumprofilen mit endlosen metallischen Verstärkungselementen, Dr.-Ing. Dissertation, Institute of Forming Technology and Lightweight Construction, Shaker Verlag, ISBN 978-3-8322-6039-2, 2007, Dortmund, Germany

[8] M. Kleiner, A. Klaus, M. Schomäcker: Composite Extrusion – Determination of the Influencing Factors on the Positioning of the Reinforcing Elements, Advanced Materials Research: Flexible Manufacture of Lightweight Frame Structures, Vol.10, 2006, p.13-22

[9] G. Liu, J. Zhou, J. Duszczyk: FE Analysis of metal flow and weld seam formation in a porthole die during the extension of a magnesium alloy into a square tube and the effect of ram speed on weld strength, JMPT 200, 2008, p.185-198

[10] M. Schikorra, M. Kleiner: Simulation-Based Analysis of Composite Extrusion Processes, CIRP Annals, Vol.56/1, 2007, General Assembly, Dresden, Germany

[11] P. Kipfer, F. Reck and G. Greiner: Local Exact Particle Tracing on Unstructured Grids. Computer Graphics Forum, 22(2):133–142, 2003.

[12] D. L. Darmofal and R. Haimes: An analysis of 3D particle path integration algorithms. J. Comput. Phys., 123(1):182–195, 1996.

[13] I. Ari Sadarjoen, Theo van Walsum, Andrea J. S. Him and Frits H. Post: Practicle Tracing Algorithms for 3D Curvilinear Grids. In: Scientific Visualization, Overviews, Methodologies, and Techniques, Seiten 311–335, Washington, DC, USA, 1994. IEEE Computer Society.

[14] Ren, Jicheng, Guangzhou Zeng and Shenquan Liu: Interactive Particle TracingAlgorithm for Unstructured Grids. In: ICSC ’95: Proceedings of the Third International Computer Science Conference on Image Analysis Applications and Computer Graphics, pp. 59–65, London, UK, 1995. Springer-Verlag.

[3] L. Donati, L. Tomesani, G. Minak, Characterization of seam weld quality in AA6082 extruded profiles Journal of Materials Processing Technology 191 (2007) pp. 127–131

[4] H. Valberg: The mechanics of two-dimensional aluminium extrusion welding investigated by FEM-analysis with experiment, ICTP 2008 (The 9th International Conference on Technology of Plasticity)

[5] K.J. Kim, C.H. Lee and D.Y. Yang, Investigation into the Improvement of Welding Strength in Three-dimensional Extrusion of Tubes Using Porthole Dies, International Journal of Materials & Product Technology 130-131 (2002), pp. 426–431

[6] A. Fratini: A new approach to study material bonding in extrusion porthole dies CIRP Annals - Manufacturing Technology 58 (2009) 259–262

[7] M. Schomäcker: Verbundstrangpressen von Aluminiumprofilen mit endlosen metallischen Verstärkungselementen, Dr.-Ing. Dissertation, Institute of Forming Technology and Lightweight Construction, Shaker Verlag, ISBN 978-3-8322-6039-2, 2007, Dortmund, Germany

[8] M. Kleiner, A. Klaus, M. Schomäcker: Composite Extrusion – Determination of the Influencing Factors on the Positioning of the Reinforcing Elements, Advanced Materials Research: Flexible Manufacture of Lightweight Frame Structures, Vol.10, 2006, p.13-22

[9] G. Liu, J. Zhou, J. Duszczyk: FE Analysis of metal flow and weld seam formation in a porthole die during the extension of a magnesium alloy into a square tube and the effect of ram speed on weld strength, JMPT 200, 2008, p.185-198

[10] M. Schikorra, M. Kleiner: Simulation-Based Analysis of Composite Extrusion Processes, CIRP Annals, Vol.56/1, 2007, General Assembly, Dresden, Germany

[11] P. Kipfer, F. Reck and G. Greiner: Local Exact Particle Tracing on Unstructured Grids. Computer Graphics Forum, 22(2):133–142, 2003.

[12] D. L. Darmofal and R. Haimes: An analysis of 3D particle path integration algorithms. J. Comput. Phys., 123(1):182–195, 1996.

[13] I. Ari Sadarjoen, Theo van Walsum, Andrea J. S. Him and Frits H. Post: Practicle Tracing Algorithms for 3D Curvilinear Grids. In: Scientific Visualization, Overviews, Methodologies, and Techniques, Seiten 311–335, Washington, DC, USA, 1994. IEEE Computer Society.

[14] Ren, Jicheng, Guangzhou Zeng and Shenquan Liu: Interactive Particle TracingAlgorithm for Unstructured Grids. In: ICSC ’95: Proceedings of the Third International Computer Science Conference on Image Analysis Applications and Computer Graphics, pp. 59–65, London, UK, 1995. Springer-Verlag.


Simulation of Porthole Die Extrusion Process comparing NEM

and FEM modelling

I. Alfaro1a*, F. Gagliardi2b, E. Cueto1c, L. Filice2d, F. Chinesta3e 1 I3A, University of Zaragoza, Spain,

2 Dept. of Mech. Engineer., Univers. of Calabria, Italy

3 EADS Corp. Intern- Chair. Ecole Centrale de Nantes, France

[email protected], [email protected], [email protected], [email protected],

[email protected]

Keywords: NEM, FEM, Extrusion, meshless methods.

Abstract. Porthole die extrusion is a process typology that can give great advantages in the forming

processes. Due to the complexity of the die assembly, experimental analyses are often carried out in

order to investigate the parameter influence on the quality of the final parts.

Finite Element Analyses, however, have been often used for the cost reducing and for a better local

investigation of variables like pressure and effective stress inside the welding chamber.

In spite of that, up to now, commercial FE codes present a “structural” limit during the welding

phase due to the impossibility to simulate element joining when material reaches the required

process conditions.

From this point of view, the Natural Element Method (NEM) provides significant advantages; in

fact, the meshless characteristic of NEM is “natively” able to simulate joining of free surfaces, as it

occurs during porthole die extrusion, simulating the welding line formation inside the welding

chamber.

In this paper, using experimental tests recognizable in literature, the authors tried to validate the

effectiveness of this technique; moreover, even a comparison between NEM and FEM results was

carried out.

More in detail, different geometries of the welding chamber were analyzed; in some cases, the

process conditions were suitable to guarantee material welding while, in other cases, the material

came out from the porthole die without joint formation. The variable that was used to verify the

process goodness is the maximum pressure inside the welding chamber.

Furthermore, to evaluate the effectiveness of 2D analyses, even in a complex shape, a significant

section was extrapolated for each die, performing a NEM vs. FEM assessment of the results.

A good comparison was obtained between the two different methods that, moreover, were in

agreement with the experimental tests.

Introduction

Extrusion welding is a process that generally is characterized by co-extrusion of two or more metals

[1] or, even, by different flows of the same metal. In the last case, the material undergoes an initial

splitting phase due to a suitable porthole and, subsequently, a joining phase inside a so called

welding chamber. The process, usually, is conducted at elevated temperature not only to improve

welding, but even to reduce the required pressure inside this chamber.

Different aluminum alloys have been worked through this technique; at now, in fact, the

investigated process is physically possible with all wrought aluminum [2].

Diverse geometrical and process parameters have to be, however, considered in order to improve

the quality of the welding lines and, consequently, the goodness of the worked parts. In the

technical literature, several works have been carried out to highlight the influence that die design

has on the extrusion process [3-4]. From this point of view, the analysis of the metal flow in the

Simulation of Porthole Die Extrusion Process comparing NEM

and FEM modelling

I. Alfaro1a*, F. Gagliardi2b, E. Cueto1c, L. Filice2d, F. Chinesta3e 1 I3A, University of Zaragoza, Spain,

2 Dept. of Mech. Engineer., Univers. of Calabria, Italy

3 EADS Corp. Intern- Chair. Ecole Centrale de Nantes, France

[email protected], [email protected], [email protected], [email protected],

[email protected]

Keywords: NEM, FEM, Extrusion, meshless methods.

Abstract. Porthole die extrusion is a process typology that can give great advantages in the forming

processes. Due to the complexity of the die assembly, experimental analyses are often carried out in

order to investigate the parameter influence on the quality of the final parts.

Finite Element Analyses, however, have been often used for the cost reducing and for a better local

investigation of variables like pressure and effective stress inside the welding chamber.

In spite of that, up to now, commercial FE codes present a “structural” limit during the welding

phase due to the impossibility to simulate element joining when material reaches the required

process conditions.

From this point of view, the Natural Element Method (NEM) provides significant advantages; in

fact, the meshless characteristic of NEM is “natively” able to simulate joining of free surfaces, as it

occurs during porthole die extrusion, simulating the welding line formation inside the welding

chamber.

In this paper, using experimental tests recognizable in literature, the authors tried to validate the

effectiveness of this technique; moreover, even a comparison between NEM and FEM results was

carried out.

More in detail, different geometries of the welding chamber were analyzed; in some cases, the

process conditions were suitable to guarantee material welding while, in other cases, the material

came out from the porthole die without joint formation. The variable that was used to verify the

process goodness is the maximum pressure inside the welding chamber.

Furthermore, to evaluate the effectiveness of 2D analyses, even in a complex shape, a significant

section was extrapolated for each die, performing a NEM vs. FEM assessment of the results.

A good comparison was obtained between the two different methods that, moreover, were in

agreement with the experimental tests.

Introduction

Extrusion welding is a process that generally is characterized by co-extrusion of two or more metals

[1] or, even, by different flows of the same metal. In the last case, the material undergoes an initial

splitting phase due to a suitable porthole and, subsequently, a joining phase inside a so called

welding chamber. The process, usually, is conducted at elevated temperature not only to improve

welding, but even to reduce the required pressure inside this chamber.

Different aluminum alloys have been worked through this technique; at now, in fact, the

investigated process is physically possible with all wrought aluminum [2].

Diverse geometrical and process parameters have to be, however, considered in order to improve

the quality of the welding lines and, consequently, the goodness of the worked parts. In the

technical literature, several works have been carried out to highlight the influence that die design

has on the extrusion process [3-4]. From this point of view, the analysis of the metal flow in the


porthole die extrusion results to be fundamental and its optimization can lead to an high process

performance [5].

Different variables have been taken into account in order to predict the quality of welding line;

however, substantially, the effective stress, the pressure and the time that the material spends to

cross the welding chamber are the greatnesses usually monitored [6].

Moreover, the temperature is another important variable that has to be properly considered; from

this point of view, a relationship between temperature and limit welding values was proposed [7]

using the Pivnik and Plata criterion [8] for representing the conditions at which solid state welding

occurs.

To optimize the process, experimental and numerical studies have been carried out [9-11].

However, due to the porthole die complexity, experimental analyses usually require time

consuming for the equipment construction and, besides, it results to be expensive to verify different

geometrical solutions. From this point of view, simplified equipments were proposed in literature

[12].

On the other part, the FE simulations can overcome the above presented limitations but, due to

the great mesh distortions, the obtained results can be deeply affected from remeshing phases.

Furthermore, at now, the joining phase cannot be simulated using commercial codes and this aspect

represents an important limitation for the process analysis.

The natural element methods (NEM) can be adequately used in this context according to the

highlighted issues. This technique, in fact, presents those advantages, such as no remeshing

requirements for the accuracy of the approximation and capacity to simulate the creation and

joining of free surfaces, fundamental for welding extrusion. Moreover, it is also possible to detect

and simulate the formation of welding lines checking if the process conditions are enough to

guarantee the welding conditions.

In the study here proposed, experimental and numerical comparison was proposed. More in

detail, experimental data, found in literature [13], were used in order to validate the numerical

results.

Both FE and NE methods were used in order to simulate the process starting from 2D analyses; for

this investigation, a significant section was extrapolated by the complete die.

Finally, even a 3D numerical study was carried out and the comparison of results was reported.

The Experimental Data

The production of special H profiles was taken into account. The used die was reported in Fig. 1.

Fig. 1: Geometry used in the experimental analysis.

porthole die extrusion results to be fundamental and its optimization can lead to an high process

performance [5].

Different variables have been taken into account in order to predict the quality of welding line;

however, substantially, the effective stress, the pressure and the time that the material spends to

cross the welding chamber are the greatnesses usually monitored [6].

Moreover, the temperature is another important variable that has to be properly considered; from

this point of view, a relationship between temperature and limit welding values was proposed [7]

using the Pivnik and Plata criterion [8] for representing the conditions at which solid state welding

occurs.

To optimize the process, experimental and numerical studies have been carried out [9-11].

However, due to the porthole die complexity, experimental analyses usually require time

consuming for the equipment construction and, besides, it results to be expensive to verify different

geometrical solutions. From this point of view, simplified equipments were proposed in literature

[12].

On the other part, the FE simulations can overcome the above presented limitations but, due to

the great mesh distortions, the obtained results can be deeply affected from remeshing phases.

Furthermore, at now, the joining phase cannot be simulated using commercial codes and this aspect

represents an important limitation for the process analysis.

The natural element methods (NEM) can be adequately used in this context according to the

highlighted issues. This technique, in fact, presents those advantages, such as no remeshing

requirements for the accuracy of the approximation and capacity to simulate the creation and

joining of free surfaces, fundamental for welding extrusion. Moreover, it is also possible to detect

and simulate the formation of welding lines checking if the process conditions are enough to

guarantee the welding conditions.

In the study here proposed, experimental and numerical comparison was proposed. More in

detail, experimental data, found in literature [13], were used in order to validate the numerical

results.

Both FE and NE methods were used in order to simulate the process starting from 2D analyses; for

this investigation, a significant section was extrapolated by the complete die.

Finally, even a 3D numerical study was carried out and the comparison of results was reported.

The Experimental Data

The production of special H profiles was taken into account. The used die was reported in Fig. 1.

Fig. 1: Geometry used in the experimental analysis.


The experimental investigations were carried out by Valberg et al. [13] for the manufacturing of

the demonstrated profile with different welding chamber dimensions. Several geometries were

considered in order to modify the process conditions along the welding plane; in this way, the

material joining was more or less favoured.

For the work here proposed, just four die designs were investigated trying to analyze both cases that

lead to sound and unsound parts. More in particular, the tests numbered with 1, 4, 7, and 9 were

taken into account; their geometrical differences were reported in Table 1.

Table 1: Geometrical differences and results of the analyzed experiments [6]

Experiment

No.

Tongue

h/b/angle

Extrusion

ratio

Optical analysis Welding

chamber

1 17/5/90° 25.6 - Fill

4 17/5/45° 25.6 - Fill

7 10/3/90° 28.9 No welded No Filling

9 10/3/45° 28.9 Unwelded stripes Gas Pocket

The other geometrical variables and process conditions were, instead, fixed and their influences

were not discussed in the work.

The study was carried out extruding an AA6082, an aluminium alloy that presents relevant

industrial applications.

Numerical Analyses

Both FEM and NEM results were conducted and their results were compared with the

experimental ones. In this phase, isothermal analyses were carried out in order to reduce the

computational time fixing the billet temperature to 510°C; the model simplification can be justified

considering that along the welding plane the material presents a narrow temperature variation.

An equation relating the hyperbolic sine of flow stress to the temperature modified strain rate was

used to describe the AA6082 flow behavior [14].

The effectiveness of NEM analyses from this process typology was tested starting from a 2D study

(Fig. 2).

Fig. 2: 2D section extracted by 3D model.

This analysis typology, obviously, cannot be used for a comparison with the experimental data

due to the complexity of the 3D model; however, the extrapolated results are meaningful for

validating NEM goodness in 2D studies. The successive 3D simulations, in fact, result to have a

more truthful physical meaning but, obviously, to detriment of computational time.

2D section

The experimental investigations were carried out by Valberg et al. [13] for the manufacturing of

the demonstrated profile with different welding chamber dimensions. Several geometries were

considered in order to modify the process conditions along the welding plane; in this way, the

material joining was more or less favoured.

For the work here proposed, just four die designs were investigated trying to analyze both cases that

lead to sound and unsound parts. More in particular, the tests numbered with 1, 4, 7, and 9 were

taken into account; their geometrical differences were reported in Table 1.

Table 1: Geometrical differences and results of the analyzed experiments [6]

Experiment

No.

Tongue

h/b/angle

Extrusion

ratio

Optical analysis Welding

chamber

1 17/5/90° 25.6 - Fill

4 17/5/45° 25.6 - Fill

7 10/3/90° 28.9 No welded No Filling

9 10/3/45° 28.9 Unwelded stripes Gas Pocket

The other geometrical variables and process conditions were, instead, fixed and their influences

were not discussed in the work.

The study was carried out extruding an AA6082, an aluminium alloy that presents relevant

industrial applications.

Numerical Analyses

Both FEM and NEM results were conducted and their results were compared with the

experimental ones. In this phase, isothermal analyses were carried out in order to reduce the

computational time fixing the billet temperature to 510°C; the model simplification can be justified

considering that along the welding plane the material presents a narrow temperature variation.

An equation relating the hyperbolic sine of flow stress to the temperature modified strain rate was

used to describe the AA6082 flow behavior [14].

The effectiveness of NEM analyses from this process typology was tested starting from a 2D study

(Fig. 2).

Fig. 2: 2D section extracted by 3D model.

This analysis typology, obviously, cannot be used for a comparison with the experimental data

due to the complexity of the 3D model; however, the extrapolated results are meaningful for

validating NEM goodness in 2D studies. The successive 3D simulations, in fact, result to have a

more truthful physical meaning but, obviously, to detriment of computational time.

2D section


The 3D study was, moreover, conducted taking advantage of a symmetry plane that let to study just

½ of the real geometry.

Furthermore, for an additional simulation time reduction, just the billet was meshed while punch,

porthole die and welding chamber were considered like rigid bodies. Finally, adhesion was

considered between dies and forming material [6]. So doing, the shear stresses are probably over-

estimated at low values of contact pressure, but, this condition was adequately validated [15].

FE Analyses. The numerical analyses were carried out using the commercial code numerical

SFTC Deform. The 2D and 3D simulations were set with the extruded billet which was meshed

using suitable mesh boxes in order to reduce the element dimensions close to the die edges and

inside the welding chamber (Fig. 3).

Fig. 3: a) 2D and b) 3D model used for FE analyses.

NE Analyses. The principal characteristic of this method is that it is a Galerkin procedure that

relies on natural neighbor interpolation to construct the trial and characteristic test functions.

The starting point is a model composed by a cloud of points N = n1, n2,…,nm Rd, for which the

space decomposition into regions is unique; more in detail, each point within these regions is closer

to the node to which the region is associated than to any other in the cloud. This decomposition is

known as Voronoi diagrams of the cloud of points; each Voronoi cell is formally defined as Eq.1:

.),(),(: IJxxdxxdRxT JI

d

I (1)

In Eq.1 d(., .) is the Euclidean distance function; two nodes that share a facet of their Voronoi cell

are called natural neighbours.

The dual structure of the Voronoi diagram is the Delaunay triangulation; nodes that share with a

specific node an edge of a Delaunay triangle (2D) or tetrahedron (3D) are defined its natural

neighbours.

In the NEM framework, different interpolants have been proposed. The original version of the

method [16] employed natural neighbour (Sibson) interpolation [17]. This one is very well-known

in the approximation community as a high-quality interpolation scheme with a lot of advantages

[18]. Sukumar [19], subsequently, proposed the use of Laplace (also known as non-Sibsonian)

interpolation [20]. The last one, used in this paper, is considerably less costly than the original

Sibson interpolation, although somewhat less smooth.

The extrusion of hollow profiles presents further difficulties for NEM due to free surface flows;

in fact, for a correct process study results to be fundamental to track accurately the surface position.

Since meshless methods only use clouds of nodes, shape constructors, which are geometrical

entities that give a continuous shape to a discrete cloud of nodes, have to be introduced. One of

a) b)

The 3D study was, moreover, conducted taking advantage of a symmetry plane that let to study just

½ of the real geometry.

Furthermore, for an additional simulation time reduction, just the billet was meshed while punch,

porthole die and welding chamber were considered like rigid bodies. Finally, adhesion was

considered between dies and forming material [6]. So doing, the shear stresses are probably over-

estimated at low values of contact pressure, but, this condition was adequately validated [15].

FE Analyses. The numerical analyses were carried out using the commercial code numerical

SFTC Deform. The 2D and 3D simulations were set with the extruded billet which was meshed

using suitable mesh boxes in order to reduce the element dimensions close to the die edges and

inside the welding chamber (Fig. 3).

Fig. 3: a) 2D and b) 3D model used for FE analyses.

NE Analyses. The principal characteristic of this method is that it is a Galerkin procedure that

relies on natural neighbor interpolation to construct the trial and characteristic test functions.

The starting point is a model composed by a cloud of points N = n1, n2,…,nm Rd, for which the

space decomposition into regions is unique; more in detail, each point within these regions is closer

to the node to which the region is associated than to any other in the cloud. This decomposition is

known as Voronoi diagrams of the cloud of points; each Voronoi cell is formally defined as Eq.1:

.),(),(: IJxxdxxdRxT JI

d

I (1)

In Eq.1 d(., .) is the Euclidean distance function; two nodes that share a facet of their Voronoi cell

are called natural neighbours.

The dual structure of the Voronoi diagram is the Delaunay triangulation; nodes that share with a

specific node an edge of a Delaunay triangle (2D) or tetrahedron (3D) are defined its natural

neighbours.

In the NEM framework, different interpolants have been proposed. The original version of the

method [16] employed natural neighbour (Sibson) interpolation [17]. This one is very well-known

in the approximation community as a high-quality interpolation scheme with a lot of advantages

[18]. Sukumar [19], subsequently, proposed the use of Laplace (also known as non-Sibsonian)

interpolation [20]. The last one, used in this paper, is considerably less costly than the original

Sibson interpolation, although somewhat less smooth.

The extrusion of hollow profiles presents further difficulties for NEM due to free surface flows;

in fact, for a correct process study results to be fundamental to track accurately the surface position.

Since meshless methods only use clouds of nodes, shape constructors, which are geometrical

entities that give a continuous shape to a discrete cloud of nodes, have to be introduced. One of

a) b)


such constructors, used in the proposed models, is the family of -shapes [21]. The use of a proper

-shape for the definition of the domain ensures the linear interpolation of the essential field along

the boundary [22].

The 2D and 3D models used for NE analyses are reported in Fig. 4.

Fig. 4: a) 2D and b) 3D model used for NE analyses.

Result Comparison

The variable that was taken into account in order to judge the quality of the obtained results was the

maximum pressure inside the welding chamber. This is the criterium proposed by Akeret [23] that

is the easiest and, perhaps, clearest criterion, to evaluate the weld quality; it states that if the

monitored pressure exceeds a critical value, obtained by experimental tests, the welding can be

considered correct.

2D Numerical Results. FE and NE comparison for the chosen section are shown in Fig. °5.

Fig. 5: Pressure distribution inside a section of welding chamber for a) FE and b) NE analyses.

The range of pressure inside the welding chamber, predicted by two different analyses, shows a

good comparison; more in detail, along the welding plane, the pressure results to be slightly slow

for the NE analysis. Besides, it is important to highlight how in the NE representation, there is not a

separation line between the two material flows that, instead, it is present in the FE analysis.

To tell the truth, in literature, a special procedure was illustrated in order to guarantee the element

joining for FE method [24]; it uses geometrical considerations and, for 3D real case, it was, at now,

still never implemented due to its complexity.

a) b) Separation line

a) b)

such constructors, used in the proposed models, is the family of -shapes [21]. The use of a proper

-shape for the definition of the domain ensures the linear interpolation of the essential field along

the boundary [22].

The 2D and 3D models used for NE analyses are reported in Fig. 4.

Fig. 4: a) 2D and b) 3D model used for NE analyses.

Result Comparison

The variable that was taken into account in order to judge the quality of the obtained results was the

maximum pressure inside the welding chamber. This is the criterium proposed by Akeret [23] that

is the easiest and, perhaps, clearest criterion, to evaluate the weld quality; it states that if the

monitored pressure exceeds a critical value, obtained by experimental tests, the welding can be

considered correct.

2D Numerical Results. FE and NE comparison for the chosen section are shown in Fig. °5.

Fig. 5: Pressure distribution inside a section of welding chamber for a) FE and b) NE analyses.

The range of pressure inside the welding chamber, predicted by two different analyses, shows a

good comparison; more in detail, along the welding plane, the pressure results to be slightly slow

for the NE analysis. Besides, it is important to highlight how in the NE representation, there is not a

separation line between the two material flows that, instead, it is present in the FE analysis.

To tell the truth, in literature, a special procedure was illustrated in order to guarantee the element

joining for FE method [24]; it uses geometrical considerations and, for 3D real case, it was, at now,

still never implemented due to its complexity.

a) b) Separation line

a) b)


Fig. °5 is referred to the experiment n°4, but the some consideration can be done even for the other

investigated cases. From this point of view, it resulted to be very interesting the comparison among

the pressure variations obtained by NEM for the four different geometries (Fig. 6).

The predicted trends seem to be, qualitatively, close to the experimental results; in fact, the high

value was observed for the section extracted from die 4 while the worst condition was recorded for

the section refereed to the small welding chamber (die 7). The others two geometries, instead,

showed an halfway distribution that can be comparable.

Fig. 6: Pressure distribution inside welding chamber for section extracted from a) 1, b) 4, c) 7 and

d) 9 experimental tests.

3D Numerical Results. In order to compare the results derived from the different FE and NE

analyses, even for the 3D cases, the experiment 4 was taken into account (Fig.8).

Fig. 8: Pressure distribution (exp. 4) inside the welding chamber for a) FE and b) NE study.

a) b)

c) d)

a) Jagged Surface b)

Fig. °5 is referred to the experiment n°4, but the some consideration can be done even for the other

investigated cases. From this point of view, it resulted to be very interesting the comparison among

the pressure variations obtained by NEM for the four different geometries (Fig. 6).

The predicted trends seem to be, qualitatively, close to the experimental results; in fact, the high

value was observed for the section extracted from die 4 while the worst condition was recorded for

the section refereed to the small welding chamber (die 7). The others two geometries, instead,

showed an halfway distribution that can be comparable.

Fig. 6: Pressure distribution inside welding chamber for section extracted from a) 1, b) 4, c) 7 and

d) 9 experimental tests.

3D Numerical Results. In order to compare the results derived from the different FE and NE

analyses, even for the 3D cases, the experiment 4 was taken into account (Fig.8).

Fig. 8: Pressure distribution (exp. 4) inside the welding chamber for a) FE and b) NE study.

a) b)

c) d)

a) Jagged Surface b)


The pressure range inside the welding chamber showed a good comparison. However, for 3D study,

the importance of element joining has to be more emphasized; in fact, for the finite element code

the interaction between two material flows is very complicated to manage and, even using a suitable

billet discretization, the welding zone is characterized by jagged surfaces (Fig. 8) that make, in

these zones, the results rather arguable.

The pressure distribution for the two die geometry characterized by larger tongue (b=5mm) were

compared in Fig. 9. The other two cases, due to the narrower die gate, require a finer billet

discretization; for this reason, their results will be proposed in a future work.

Fig. 9: Pressure distribution inside welding chamber respectively for a) 1 and b) 4 experimental

tests.

The results obtained from 2D analyses were qualitatively confirmed for the reported 3D analyses; in

fact, an higher pressure was recorded for the die related to experiment 4. Furthermore, the

experimental data were validated, too; in fact, the pressure in the welding chamber changes passing

from about 80 MPa for the experiment 1 to about 110 MPa for the most suitable die (experiment 4).

This variable, actually, presents a certain variability; more in detail, the punctual value was

established taking into account the zone below to the die bearing.

Conclusions

A comparison between FE and NE results was carried out analyzing a porthole die extrusion

process. The investigated material was an aluminum alloy, AA 6082, that presents great industrial

relevance; in order to validate the obtained results, an experimental campaign, found in literature,

was utilized.

A good agreement between the two different numerical analyses was observed and, for the 3D

study, an acceptable correspondence with the experimental data was registered.

The great advantage of NEM is, above all, due to the material flow joining that allows a welding

plane formation carrying out numerical analyses closer to the real process.

Moreover, due to this aspects, the results in this zone are no influenced by frequent remeshing and

jagged surfaces that are, instead, typical for a FE analysis.

Different problems, however, have to be still tackled for increasing the NE potentiality; in fact, at

now, the long simulation time and its set-up complexity represent significant drawbacks that have

to be considered and improved for considering the NE techniques useful for forming process

optimization.

Acknowledgement

The authors want to thank the University of Palermo (Italy) for the performed 3D FE analyses.

The pressure range inside the welding chamber showed a good comparison. However, for 3D study,

the importance of element joining has to be more emphasized; in fact, for the finite element code

the interaction between two material flows is very complicated to manage and, even using a suitable

billet discretization, the welding zone is characterized by jagged surfaces (Fig. 8) that make, in

these zones, the results rather arguable.

The pressure distribution for the two die geometry characterized by larger tongue (b=5mm) were

compared in Fig. 9. The other two cases, due to the narrower die gate, require a finer billet

discretization; for this reason, their results will be proposed in a future work.

Fig. 9: Pressure distribution inside welding chamber respectively for a) 1 and b) 4 experimental

tests.

The results obtained from 2D analyses were qualitatively confirmed for the reported 3D analyses; in

fact, an higher pressure was recorded for the die related to experiment 4. Furthermore, the

experimental data were validated, too; in fact, the pressure in the welding chamber changes passing

from about 80 MPa for the experiment 1 to about 110 MPa for the most suitable die (experiment 4).

This variable, actually, presents a certain variability; more in detail, the punctual value was

established taking into account the zone below to the die bearing.

Conclusions

A comparison between FE and NE results was carried out analyzing a porthole die extrusion

process. The investigated material was an aluminum alloy, AA 6082, that presents great industrial

relevance; in order to validate the obtained results, an experimental campaign, found in literature,

was utilized.

A good agreement between the two different numerical analyses was observed and, for the 3D

study, an acceptable correspondence with the experimental data was registered.

The great advantage of NEM is, above all, due to the material flow joining that allows a welding

plane formation carrying out numerical analyses closer to the real process.

Moreover, due to this aspects, the results in this zone are no influenced by frequent remeshing and

jagged surfaces that are, instead, typical for a FE analysis.

Different problems, however, have to be still tackled for increasing the NE potentiality; in fact, at

now, the long simulation time and its set-up complexity represent significant drawbacks that have

to be considered and improved for considering the NE techniques useful for forming process

optimization.

Acknowledgement

The authors want to thank the University of Palermo (Italy) for the performed 3D FE analyses.


References

[1] Deformation Welding, in: Solid State Welding Processes, edited by J.R. Davis, second edition of

Metals Handbook, part, 4, The Materials Information Society (1998).

[2] R. Akeret: Proc. 5th

Int. Al. Extr. Techn. Sem.Vol. 1 (1992), p.319

[3] L. Donati and L.Tomesani: J. Mater. Process. Technol. Vol. 164–165 (2005), p. 1025

[4] J. M. Lee, K. Byung Min and K. Chung Gil, Mater. and Design Vol. 26 (2005), p. 327

[5] K.Young-Tae, I. Keisuke and M.Tadasu: J. Mater. Process. Technol. Vol. 121 (2002), p. 107

[6] L. Donati and L.Tomesani: J. Mater. Process. Technol.: Vol.153-154 (2004), p. 366

[7] E. Ceretti, L. Fratini, F. Gagliardi and C. Giardini: CIRP Annals – Manufac. Technol. (2009), in

press.

[8] M. Plata and J. Piwnik: Proc. 7th

Int. Al. Extr. Technol. Vol. I (2000), p. 205



[11] L. Filice, F. Gagliardi and F. Micari: Key Eng. Mater. Vol. 367, p. 137 (Trans Tech

Publications, Switzerland 2007).

[12] L. Filice, F. Gagliardi and F. Micari: Proc. Metal Form. Conf. Vol. 2 (2008), p. 870

[13] H. Valberg, T. Loeken, M. Hval, B. Nyhus and C. Thaulow: Int. J. Mater. and Product

Technol. Vol.10 (1995), p. 222

[14] C. Bruni, A. Forcellese and F. Gabrielli: Proc.VI Int. Conf. Adv. Manufac. Syst. and Technol.

(2002), p. 367

[15] T. Chanda, J. Zhou and J. Duszczyk: Proc. 7th


[16] J. Braun and M. Sambridge: Nature Vol. 376 (1995), p.655

[17] R. Sibson: Math. Proc. Cambridge Philosoph. Society Vol. 87 (1980), p.151

[18] H. Hiyoshi, in: International Symposium on Voronoi diagrams in Science and Engineering,.

edited by K. Sugihara, Japan, Tokio (2004), p.1

[19] N. Sukumar, B. Moran, A. Yu Semenov, and V. V. Belikov: Int. J. Num. Meth. Eng. Vol.

50(1) (2001), p.1

[20] H. Hiyoshi and K. Sugihara: Int. J. Shape Modeling Vol. 5(2) (1999), p.219

[21] H. Edelsbrunner and E. Mücke: ACM Transactions on Graphics Vol. 13 (1994), p.43

[22] E. Cueto, M. Doblarè and L. Gracia: Int. J. Num. Meth. Eng. Vol. 49-4 (2000), p. 519

[23] R. Akeret: J. Inst. Met. Vol.10 (1972), p. 202

[24] E.Ceretti and C.Giardini, in: 1st Int. Conf. On Sustainable Manufacturing, Canada, Montreal

(2007), p.125

References

[1] Deformation Welding, in: Solid State Welding Processes, edited by J.R. Davis, second edition of

Metals Handbook, part, 4, The Materials Information Society (1998).

[2] R. Akeret: Proc. 5th

Int. Al. Extr. Techn. Sem.Vol. 1 (1992), p.319

[3] L. Donati and L.Tomesani: J. Mater. Process. Technol. Vol. 164–165 (2005), p. 1025

[4] J. M. Lee, K. Byung Min and K. Chung Gil, Mater. and Design Vol. 26 (2005), p. 327

[5] K.Young-Tae, I. Keisuke and M.Tadasu: J. Mater. Process. Technol. Vol. 121 (2002), p. 107

[6] L. Donati and L.Tomesani: J. Mater. Process. Technol.: Vol.153-154 (2004), p. 366

[7] E. Ceretti, L. Fratini, F. Gagliardi and C. Giardini: CIRP Annals – Manufac. Technol. (2009), in

press.

[8] M. Plata and J. Piwnik: Proc. 7th




[11] L. Filice, F. Gagliardi and F. Micari: Key Eng. Mater. Vol. 367, p. 137 (Trans Tech

Publications, Switzerland 2007).

[12] L. Filice, F. Gagliardi and F. Micari: Proc. Metal Form. Conf. Vol. 2 (2008), p. 870

[13] H. Valberg, T. Loeken, M. Hval, B. Nyhus and C. Thaulow: Int. J. Mater. and Product

Technol. Vol.10 (1995), p. 222

[14] C. Bruni, A. Forcellese and F. Gabrielli: Proc.VI Int. Conf. Adv. Manufac. Syst. and Technol.

(2002), p. 367

[15] T. Chanda, J. Zhou and J. Duszczyk: Proc. 7th


[16] J. Braun and M. Sambridge: Nature Vol. 376 (1995), p.655

[17] R. Sibson: Math. Proc. Cambridge Philosoph. Society Vol. 87 (1980), p.151

[18] H. Hiyoshi, in: International Symposium on Voronoi diagrams in Science and Engineering,.

edited by K. Sugihara, Japan, Tokio (2004), p.1

[19] N. Sukumar, B. Moran, A. Yu Semenov, and V. V. Belikov: Int. J. Num. Meth. Eng. Vol.

50(1) (2001), p.1

[20] H. Hiyoshi and K. Sugihara: Int. J. Shape Modeling Vol. 5(2) (1999), p.219

[21] H. Edelsbrunner and E. Mücke: ACM Transactions on Graphics Vol. 13 (1994), p.43

[22] E. Cueto, M. Doblarè and L. Gracia: Int. J. Num. Meth. Eng. Vol. 49-4 (2000), p. 519

[23] R. Akeret: J. Inst. Met. Vol.10 (1972), p. 202

[24] E.Ceretti and C.Giardini, in: 1st Int. Conf. On Sustainable Manufacturing, Canada, Montreal

(2007), p.125


Numerical Analysis of Aluminum Alloys Extrusion Through Porthole Dies

J. Zasadziński1,a, A. Rękas1,b, W. Libura1,c, J. Richert1,d, D. Leśniak1,e 1AGH - University of Science and Technology, Faculty of Non-Ferrous Metals,

A. Mickiewicza 30 Ave., 30-059 Krakow, Poland [email protected], [email protected], [email protected], [email protected]

[email protected]

Keywords: extrusion, porthole dies, welding chamber, aluminum alloys, numerical calculations Abstract. In the work the distribution of stresses and strains as well as temperature field within the welding chamber of the porthole die were determined. The analysis was performed by the use of the computer program DEFORM based on a finite element method. The direct hot extrusion of 2024 aluminum alloy was investigated with the use of the porthole dies of different geometry. Particularly, a different height of the welding chamber was adopted in calculations. The calculations allowed determining both pressure and temperature levels and their distributions within the welding chamber leading to the best welding conditions for the alloy tested.

Introduction

Hot extrusion through porthole dies is the most common method of manufacturing hollow sections from aluminum and its alloys. In this method the extruded billet is split on a die’s bridge into separate streams. These streams of metal that flow through the inlet ports join together in a welding chamber surrounding the mandrel. The deformed metal exits from the die through the gap between a mandrel and the die land as a hollow shape [1-2]. As a result, several seams occur on the cross-section of hollow profiles. The number of seam welds depends of the porthole die construction [3-4]. The method is used for manufacturing hollow shapes from easy to deform aluminum alloys, mainly of 6XXX serie, which demonstrate very good deformability. Hard aluminum alloys, such as 2XXX (AlCuMg) series, manifest both poor deformability and weldability in the standard extrusion practise; therefore they are not extruded through the porthole dies [5]. Low weldability also show 5XXX and 7XXX series alloys. However, taking into account the growing needs for complex shapes of high strength it is reasonable to search of the conditions enabling application of porthole dies for these alloys [6-7]. In order to receive the high-strength welds and high quality of the hollow extrusions, the correct conditions in the welding chamber have to be satisfied, i.e. appropriate high temperature, possibly high pressure and the suitably high value of shear strains in the area of welds formation. The lower these parameters (temperature, pressure) the easily the material can be welded in the extrusion conditions.

In design of extrusion technology of the hollow section from hard deformable aluminum alloys the exact conditions required to occur in the welding chamber must be determined. This can be obtained by numerical analysi, which includes distribution of the state of stresses and strains, the temperature field within the welding chamber and particularly in the seam region.

Simulation details

This article presents the results of the numerical calculations of the extrusion of 2024 aluminum alloy through the porthole dies. The analysis is based on the calculated distributions of stresses and strains and the temperature for various heights of welding chamber and different billet temperature. To solve this task a computer program Deform 3D was applied based on the finite elements method. A rigid-plastic model of deformed material was adopted in calculations. For simplicity, in the first stage of calculations the analysis of welding solid section of rectangular shape was conducted

Numerical Analysis of Aluminum Alloys Extrusion Through Porthole Dies

J. Zasadziński1,a, A. Rękas1,b, W. Libura1,c, J. Richert1,d, D. Leśniak1,e 1AGH - University of Science and Technology, Faculty of Non-Ferrous Metals,

A. Mickiewicza 30 Ave., 30-059 Krakow, Poland [email protected], [email protected], [email protected], [email protected]

[email protected]

Keywords: extrusion, porthole dies, welding chamber, aluminum alloys, numerical calculations Abstract. In the work the distribution of stresses and strains as well as temperature field within the welding chamber of the porthole die were determined. The analysis was performed by the use of the computer program DEFORM based on a finite element method. The direct hot extrusion of 2024 aluminum alloy was investigated with the use of the porthole dies of different geometry. Particularly, a different height of the welding chamber was adopted in calculations. The calculations allowed determining both pressure and temperature levels and their distributions within the welding chamber leading to the best welding conditions for the alloy tested.

Introduction

Hot extrusion through porthole dies is the most common method of manufacturing hollow sections from aluminum and its alloys. In this method the extruded billet is split on a die’s bridge into separate streams. These streams of metal that flow through the inlet ports join together in a welding chamber surrounding the mandrel. The deformed metal exits from the die through the gap between a mandrel and the die land as a hollow shape [1-2]. As a result, several seams occur on the cross-section of hollow profiles. The number of seam welds depends of the porthole die construction [3-4]. The method is used for manufacturing hollow shapes from easy to deform aluminum alloys, mainly of 6XXX serie, which demonstrate very good deformability. Hard aluminum alloys, such as 2XXX (AlCuMg) series, manifest both poor deformability and weldability in the standard extrusion practise; therefore they are not extruded through the porthole dies [5]. Low weldability also show 5XXX and 7XXX series alloys. However, taking into account the growing needs for complex shapes of high strength it is reasonable to search of the conditions enabling application of porthole dies for these alloys [6-7]. In order to receive the high-strength welds and high quality of the hollow extrusions, the correct conditions in the welding chamber have to be satisfied, i.e. appropriate high temperature, possibly high pressure and the suitably high value of shear strains in the area of welds formation. The lower these parameters (temperature, pressure) the easily the material can be welded in the extrusion conditions.

In design of extrusion technology of the hollow section from hard deformable aluminum alloys the exact conditions required to occur in the welding chamber must be determined. This can be obtained by numerical analysi, which includes distribution of the state of stresses and strains, the temperature field within the welding chamber and particularly in the seam region.

Simulation details

This article presents the results of the numerical calculations of the extrusion of 2024 aluminum alloy through the porthole dies. The analysis is based on the calculated distributions of stresses and strains and the temperature for various heights of welding chamber and different billet temperature. To solve this task a computer program Deform 3D was applied based on the finite elements method. A rigid-plastic model of deformed material was adopted in calculations. For simplicity, in the first stage of calculations the analysis of welding solid section of rectangular shape was conducted


according to the model presented in Fig. 1. A discretization of the whole billet with varied size of elements was used and a mesh of higher density in the area of maximal deformation was generated (Fig. 1). Only a quarter of the extrusion setting is shown when considering symmetry of the problem.

Fig. 1: Model for extrusion of a flat section with the use of porthole die

The flat rectangular section of 60 x 6 mm was extruded with the extrusion ratio R = 31.4 and the welding chamber of height hz = 10, 20 and 40 mm was applied. The calculations were conducted for the billes of temperatures 400 and 500°C.

In the second stage of this study the welding parameters for a hollow profile of dimensions 30 x 30 x 3 mm were determined (Fig. 2). The cross-section of the profile was equal to the cross-section of the solid profile analyzed in the first stage of calculations, so that the extrusion ratio would be the same in the both cases. In this stage the billet temperature of 400°C and height of the welding chamber hz of 20 and 40 mm were assumed. In the calculation the tool temperature was 250°C, the ram speed was 1 mm/s, the billet was 200 mm in length and the container was 125 mm in diameter. The constant friction conditions at the tools - billet interface were also assumed ( m = 0.7). The rheological data for the alloy used in this study and characteristics of the H13 tool steel were taken from the DRFORM database.

Fig. 2: Model for extrusion of hollow profile through a porthole die

according to the model presented in Fig. 1. A discretization of the whole billet with varied size of elements was used and a mesh of higher density in the area of maximal deformation was generated (Fig. 1). Only a quarter of the extrusion setting is shown when considering symmetry of the problem.

Fig. 1: Model for extrusion of a flat section with the use of porthole die

The flat rectangular section of 60 x 6 mm was extruded with the extrusion ratio R = 31.4 and the welding chamber of height hz = 10, 20 and 40 mm was applied. The calculations were conducted for the billes of temperatures 400 and 500°C.

In the second stage of this study the welding parameters for a hollow profile of dimensions 30 x 30 x 3 mm were determined (Fig. 2). The cross-section of the profile was equal to the cross-section of the solid profile analyzed in the first stage of calculations, so that the extrusion ratio would be the same in the both cases. In this stage the billet temperature of 400°C and height of the welding chamber hz of 20 and 40 mm were assumed. In the calculation the tool temperature was 250°C, the ram speed was 1 mm/s, the billet was 200 mm in length and the container was 125 mm in diameter. The constant friction conditions at the tools - billet interface were also assumed ( m = 0.7). The rheological data for the alloy used in this study and characteristics of the H13 tool steel were taken from the DRFORM database.

Fig. 2: Model for extrusion of hollow profile through a porthole die



First, the analysis concerned extrusion of the solid flat section will be presented. To demonstrate the simulation results of the extrusion process the distributions of state of stresses and strains as well as temperature fields are presented. The distributions of the effective strains on the axial plane of the billet show the region of welding of the metal streams flowing to the die orifice (Fig. 3 and 4). The calculations have shown that the radial compressive stresses have the greatest participation in the effective stress values within the welding region.

Fig. 3: Distribution of the effective strains on the billet axial plane for billet temperature 400°C and

for various welding chamber height hz



As can be seen from Fig. 3 and 4, the maximal effective strain occurs within the region of die orifice. The intensity of deformation depends on both height of the welding chamber and the initial billet temperature. It was found higher for the lower height hz and for lower billet temperature. The observed state of strains corresponds with the effective stress distribution visible in Figs 5 and 6. The exact analysis of the state of stresses indicates that as the height of the welding chamber hz decreases the more varying distribution of the effective stress occurs on the profile width and the higher effective stress value exists within the die orifice and at the half of the height hz (Figs 5 and 6). The results presented in Figs 5 and 6 indicate that the optimal height of the welding chamber is when the effective stress is relatively high and rises towards the die orifice.


First, the analysis concerned extrusion of the solid flat section will be presented. To demonstrate the simulation results of the extrusion process the distributions of state of stresses and strains as well as temperature fields are presented. The distributions of the effective strains on the axial plane of the billet show the region of welding of the metal streams flowing to the die orifice (Fig. 3 and 4). The calculations have shown that the radial compressive stresses have the greatest participation in the effective stress values within the welding region.





As can be seen from Fig. 3 and 4, the maximal effective strain occurs within the region of die orifice. The intensity of deformation depends on both height of the welding chamber and the initial billet temperature. It was found higher for the lower height hz and for lower billet temperature. The observed state of strains corresponds with the effective stress distribution visible in Figs 5 and 6. The exact analysis of the state of stresses indicates that as the height of the welding chamber hz decreases the more varying distribution of the effective stress occurs on the profile width and the higher effective stress value exists within the die orifice and at the half of the height hz (Figs 5 and 6). The results presented in Figs 5 and 6 indicate that the optimal height of the welding chamber is when the effective stress is relatively high and rises towards the die orifice.


Fig. 5: Distribution of effective stress on the billet axial plane for the billet temperature 400°C and




Especially interesting is a distribution of the effective stress along the welding chamber height (Fig. 7). The most favorable conditions for welding occur at the half of the height of the welding chamber. At the same time as the metal flows towards the die orifice the conditions for welding vary. It was found that the value of the effective stress decreases as the billet temperature rises (Figs 5 and 6). Assuming a criterion in which the effective stress will be high enough and increasing towards the die orifice, it was possible to determine the optimal height of the welding chamber hz = 20 mm and billet temperature Tw = 500°C (Fig. 7).

Fig. 7: Effective stress distribution along the height of welding chamber





Especially interesting is a distribution of the effective stress along the welding chamber height (Fig. 7). The most favorable conditions for welding occur at the half of the height of the welding chamber. At the same time as the metal flows towards the die orifice the conditions for welding vary. It was found that the value of the effective stress decreases as the billet temperature rises (Figs 5 and 6). Assuming a criterion in which the effective stress will be high enough and increasing towards the die orifice, it was possible to determine the optimal height of the welding chamber hz = 20 mm and billet temperature Tw = 500°C (Fig. 7).

Fig. 7: Effective stress distribution along the height of welding chamber


The temperature distributions presented in Figs 8 and 9 indicate the temperature concentration within the seam region, which is advantageous for welding, particularly for the billet temperature 500°C and height hz = 20 mm.

Fig. 8: Temperature distribution on the billet axial plane for the billet temperature 400°C and for various welding chamber height hz


In this part of the study we will discuss the welding parameters during extrusion of the hollow

profile from the 2024 aluminum alloy. In the assumed model (Fig. 2) two welding regions occur on the profile cross-section. In the simulations the temperature of the billet was 400°C and the heights of welding chamber were 20 and 40 mm. The obtained distributions of stresses, strains and temperature for the hollow profile shown in Fig. 10, 11 and 12 are comparable to these for the flat solid profile (Fig. 3, 5 and 7). In the case of height hz = 20 mm there is a very advantageous strain concentration in the welding region (Fig. 10a). Similar results were obtained for the effective stresses (Fig. 11a). In addition, the rise of temperature (Fig. 12a) facilitates joining of the metal streams flowing to the welding chamber.

When the height of the welding chamber hz = 40 mm was adopted the conditions for welding were disadvantageous as results from the presented distributions of stresses, strains and temperature (Fig. 10b, 11b and 12b).

The temperature distributions presented in Figs 8 and 9 indicate the temperature concentration within the seam region, which is advantageous for welding, particularly for the billet temperature 500°C and height hz = 20 mm.



In this part of the study we will discuss the welding parameters during extrusion of the hollow

profile from the 2024 aluminum alloy. In the assumed model (Fig. 2) two welding regions occur on the profile cross-section. In the simulations the temperature of the billet was 400°C and the heights of welding chamber were 20 and 40 mm. The obtained distributions of stresses, strains and temperature for the hollow profile shown in Fig. 10, 11 and 12 are comparable to these for the flat solid profile (Fig. 3, 5 and 7). In the case of height hz = 20 mm there is a very advantageous strain concentration in the welding region (Fig. 10a). Similar results were obtained for the effective stresses (Fig. 11a). In addition, the rise of temperature (Fig. 12a) facilitates joining of the metal streams flowing to the welding chamber.

When the height of the welding chamber hz = 40 mm was adopted the conditions for welding were disadvantageous as results from the presented distributions of stresses, strains and temperature (Fig. 10b, 11b and 12b).


Fig. 10: Distribution of effective strain during extrusion of hollow profile for various height of the

welding chamber hz


welding chamber hz

Fig. 12: Temperature distribution during extrusion of hollow profile for various height of the welding chamber hz

Conclusions

Design of extrusion technology for the hollow profiles from the hard aluminum alloys is connected with the establishing welding conditions and with the decreasing force parameters of the process. Particularly important is information that the pressure required for welding depends on the height of


welding chamber hz


welding chamber hz

Fig. 12: Temperature distribution during extrusion of hollow profile for various height of the welding chamber hz

Conclusions

Design of extrusion technology for the hollow profiles from the hard aluminum alloys is connected with the establishing welding conditions and with the decreasing force parameters of the process. Particularly important is information that the pressure required for welding depends on the height of


the welding chamber and on the initial billet temperature. The calculations have indicated that the best conditions for welding of the 2024 aluminum alloy occur for the optimal height of the welding chamber hz = 20 mm and for the billet temperature 500°C. The obtained numerical data will be validated soon in the industrial testing.

References

[1] J. Wantuchowski, J. Zasadziński, J. Richert: Badania nad zastosowaniem matryc mostkowych w praktyce wyciskania na gorąco aluminium i jego stopów, AGH University of Science and Technology Publications, Metallurgy and Foundry, 438, 59 (1974), pp. 259-273 (in Polish).

[2] H. Valberg: Extrusion Welding in Porthole Die Extrusion, Proc. 6th Int. Aluminum Extrusion Technology Seminar, vol. II, Chicago 1996, pp. 213-224.

[3] J. Gąsiorczyk, J. Richert: Application of FEM modeling to simulate metal flow through porthole dies, Proc. 7th Int. Aluminum Extrusion Technology Seminar, vol. I, Chicago 2000, pp. 195-202.

[4] L. Donati, L. Tomesani: Evaluation of mew FEM criterion for seam welds quality prediction in aluminum extruded profiles, Proc. 8th Int. Aluminum Extrusion Technology Seminar, vol. 2, 2004, pp. 221-234.

[5] W. Libura: Metal flow in extrusion, AGH University of Science and Technology Publications, Kraków 2008 (in Polish).

[6] G. Liu, J. Zhou, K. Huang, J. Duszczyk: Analysis of Metal Flow through a Porthole Die to Produce a Rectangular Hollow Profile with Longitudinal Weld Seams, Key Engineering Materials Vol. 367 (2008) pp. 145-152.

[7] G. Liu, J. Zhou, J. Duszczyk: FE analysis of metal flow and weld seam formation in a porthole die during the extrusion of a magnesium alloy into a square tube and the effect of ram speed on weld strength, Journal of Materials Processing Technology Vol. 200 (2008) pp. 185-198.

the welding chamber and on the initial billet temperature. The calculations have indicated that the best conditions for welding of the 2024 aluminum alloy occur for the optimal height of the welding chamber hz = 20 mm and for the billet temperature 500°C. The obtained numerical data will be validated soon in the industrial testing.

References

[1] J. Wantuchowski, J. Zasadziński, J. Richert: Badania nad zastosowaniem matryc mostkowych w praktyce wyciskania na gorąco aluminium i jego stopów, AGH University of Science and Technology Publications, Metallurgy and Foundry, 438, 59 (1974), pp. 259-273 (in Polish).

[2] H. Valberg: Extrusion Welding in Porthole Die Extrusion, Proc. 6th Int. Aluminum Extrusion Technology Seminar, vol. II, Chicago 1996, pp. 213-224.

[3] J. Gąsiorczyk, J. Richert: Application of FEM modeling to simulate metal flow through porthole dies, Proc. 7th Int. Aluminum Extrusion Technology Seminar, vol. I, Chicago 2000, pp. 195-202.

[4] L. Donati, L. Tomesani: Evaluation of mew FEM criterion for seam welds quality prediction in aluminum extruded profiles, Proc. 8th Int. Aluminum Extrusion Technology Seminar, vol. 2, 2004, pp. 221-234.

[5] W. Libura: Metal flow in extrusion, AGH University of Science and Technology Publications, Kraków 2008 (in Polish).

[6] G. Liu, J. Zhou, K. Huang, J. Duszczyk: Analysis of Metal Flow through a Porthole Die to Produce a Rectangular Hollow Profile with Longitudinal Weld Seams, Key Engineering Materials Vol. 367 (2008) pp. 145-152.

[7] G. Liu, J. Zhou, J. Duszczyk: FE analysis of metal flow and weld seam formation in a porthole die during the extrusion of a magnesium alloy into a square tube and the effect of ram speed on weld strength, Journal of Materials Processing Technology Vol. 200 (2008) pp. 185-198.


Simulation of the co-extrusion of hybrid Mg/Al profiles

J. Muehlhause1,a, S. Gall1,b, S. Mueller1, c 1Extrusion Research and Development Center, Chair Metallic Materials, TU Berlin, Gustav-Meyer-

Allee 25, Sekr. TIB 4/1-2, 13355 Berlin, Germany [email protected], [email protected], c [email protected]

Keywords: Magnesium, Aluminum, Co-extrusion, Material flow, Extrusion seams Abstract. Extrusion of composite materials can offer big advantages. In this work the manufacturing of a hybrid metal profile in a single production step was investigated. A porthole die was used, thus producing profiles with extrusion seams. Along the seams a material mix up was visible. The extrusion process was simulated with the Finite Element Method to investigate the material flow in die and welding chamber in order to understand the cause for the defects at the seams. Introduction

The latest efforts in reducing the CO2 emissions and with that the increasing interest of the automotive and transportation industries in light-weight constructions have caused a new era for magnesium alloys as a construction material. But as of today the use of magnesium alloys in high-volume production cars is very limited. Besides some other influences this is also due to the poor corrosion resistance of most wrought magnesium alloys [1]. So in order to increase the use of magnesium profiles the corrosion resistance needs to be improved. This can be achieved by coating the profiles after the extrusion. But this would result in an extra production step and thus additional costs and time. A coating in the same step as the extrusion could overcome this problem. Therefore, the idea is to use the commonly used light metal aluminum EN-AW 6060 as a „coating“ for AZ 31 magnesium profiles. The profiles are manufactured by direct extrusion from specially prepared hybrid Mg/Al billets. Hence light magnesium profiles with a corrosion resistant aluminum coating can be produced in a single production step. In order to investigate further parameters in the coextrusion process a model of a hollow profile with a hybrid billet was simulated using the Finite Element Method (FEM). Preceding simulations of Mg and Al single alloy profiles have shown significant differences in pressure, velocity and deformation resistance that inhibit a homogenous flow of the hybrid material components. Simulation of the coextrusion with a hybrid Mg/Al billet should bring a better understanding of the mutual influences of both materials in terms of material flow. For the simulation of the co-extrusion process a model with a Al-skin and a Mg-core and a hollow profile was chosen.

Experiments

For the coextrusion of hollow profiles as base material the magnesium alloy AZ31 and the aluminum alloy EN-AW 6060 as coating material were used. The specially prepared billets for the coextrusion process consist of an AZ31 core and an EN-AW 6060 shell. The aluminum shell thickness was 12 mm, respectively the magnesium core was 83 mm. The aluminum shell thickness is equivalent to 21 % of the billet diameter. The billet length was 150 mm. By direct extrusion hollow profiles with one chamber were manufactured. Figure 1 schematically depicts the deformation process. To produce the hollow profile a porthole die with four die recesses was used. The extrusion seams for the profile were positioned in the corners (Figure 2). The use of porthole dies causes an unseaming of the material in the die recess and a seaming of the material in welding chamber. This

Simulation of the co-extrusion of hybrid Mg/Al profiles

J. Muehlhause1,a, S. Gall1,b, S. Mueller1, c 1Extrusion Research and Development Center, Chair Metallic Materials, TU Berlin, Gustav-Meyer-

Allee 25, Sekr. TIB 4/1-2, 13355 Berlin, Germany [email protected], [email protected], c [email protected]

Keywords: Magnesium, Aluminum, Co-extrusion, Material flow, Extrusion seams Abstract. Extrusion of composite materials can offer big advantages. In this work the manufacturing of a hybrid metal profile in a single production step was investigated. A porthole die was used, thus producing profiles with extrusion seams. Along the seams a material mix up was visible. The extrusion process was simulated with the Finite Element Method to investigate the material flow in die and welding chamber in order to understand the cause for the defects at the seams. Introduction

The latest efforts in reducing the CO2 emissions and with that the increasing interest of the automotive and transportation industries in light-weight constructions have caused a new era for magnesium alloys as a construction material. But as of today the use of magnesium alloys in high-volume production cars is very limited. Besides some other influences this is also due to the poor corrosion resistance of most wrought magnesium alloys [1]. So in order to increase the use of magnesium profiles the corrosion resistance needs to be improved. This can be achieved by coating the profiles after the extrusion. But this would result in an extra production step and thus additional costs and time. A coating in the same step as the extrusion could overcome this problem. Therefore, the idea is to use the commonly used light metal aluminum EN-AW 6060 as a „coating“ for AZ 31 magnesium profiles. The profiles are manufactured by direct extrusion from specially prepared hybrid Mg/Al billets. Hence light magnesium profiles with a corrosion resistant aluminum coating can be produced in a single production step. In order to investigate further parameters in the coextrusion process a model of a hollow profile with a hybrid billet was simulated using the Finite Element Method (FEM). Preceding simulations of Mg and Al single alloy profiles have shown significant differences in pressure, velocity and deformation resistance that inhibit a homogenous flow of the hybrid material components. Simulation of the coextrusion with a hybrid Mg/Al billet should bring a better understanding of the mutual influences of both materials in terms of material flow. For the simulation of the co-extrusion process a model with a Al-skin and a Mg-core and a hollow profile was chosen.

Experiments

For the coextrusion of hollow profiles as base material the magnesium alloy AZ31 and the aluminum alloy EN-AW 6060 as coating material were used. The specially prepared billets for the coextrusion process consist of an AZ31 core and an EN-AW 6060 shell. The aluminum shell thickness was 12 mm, respectively the magnesium core was 83 mm. The aluminum shell thickness is equivalent to 21 % of the billet diameter. The billet length was 150 mm. By direct extrusion hollow profiles with one chamber were manufactured. Figure 1 schematically depicts the deformation process. To produce the hollow profile a porthole die with four die recesses was used. The extrusion seams for the profile were positioned in the corners (Figure 2). The use of porthole dies causes an unseaming of the material in the die recess and a seaming of the material in welding chamber. This


matter of fact creates a complex material flow in the die, especially after the bridges in the welding chamber. The specially prepared billets were then direct extruded on the 8 MN horizontal rod and tube press of the Extrusion Research and Development Center of the TU Berlin. The extrusion ratio of the die was 11:1, container and billet temperature were set to 300°C, the temperature of the die was 330°C, ram speed was 1.5 mm s-1.

Results

Extrusion Trials. In contrast to the extrusion with a mandrel, where seamless profiles are produced, the extrusion of more complicated profiles using a porthole die leads to defects in the Al coating in the area of the extrusion seams. Figure 3 shows the hybrid profile. The inner material is Mg that is coated by the Al. In the corners the seams are clearly recognizable. Therefore, special interest was paid to the areas of the extrusion seams. As it can be seen from Fig. 4 there is a material mix up in the area of the extrusion seam. Thus, the magnesium does not stay in the inner part of the profile but stretched along the extrusion seam to the profile surface. This is definitely unwanted because the aluminum coating is an anticorrosion layer for the magnesium. In order to understand how the material mixes up, the material left in the die (Fig. 5) was investigated. Seams are visible in the welding chamber. The view of the inflow of the die shows that core and coating material have not mixed up then (Fig. 6). For further investigation the inner material was cut into several parts. Whereas in Fig. 8 the material distribution in the welding chamber in the area of the extrusion seams can be seen, Fig. 7 is taken from an area between two extrusion seams. The analysis of the material left in the die after the extrusion shows that the magnesium coming from the core material encloses the Al from the coating.

Fig. 2: Position of the extrusion seams

Fig. 3: Hybrid Mg/Al profile Fig. 4: Detail of material distribution in the seam area of the profile

Fig. 1: Manufacturing of a coated profile

matter of fact creates a complex material flow in the die, especially after the bridges in the welding chamber. The specially prepared billets were then direct extruded on the 8 MN horizontal rod and tube press of the Extrusion Research and Development Center of the TU Berlin. The extrusion ratio of the die was 11:1, container and billet temperature were set to 300°C, the temperature of the die was 330°C, ram speed was 1.5 mm s-1.

Results

Extrusion Trials. In contrast to the extrusion with a mandrel, where seamless profiles are produced, the extrusion of more complicated profiles using a porthole die leads to defects in the Al coating in the area of the extrusion seams. Figure 3 shows the hybrid profile. The inner material is Mg that is coated by the Al. In the corners the seams are clearly recognizable. Therefore, special interest was paid to the areas of the extrusion seams. As it can be seen from Fig. 4 there is a material mix up in the area of the extrusion seam. Thus, the magnesium does not stay in the inner part of the profile but stretched along the extrusion seam to the profile surface. This is definitely unwanted because the aluminum coating is an anticorrosion layer for the magnesium. In order to understand how the material mixes up, the material left in the die (Fig. 5) was investigated. Seams are visible in the welding chamber. The view of the inflow of the die shows that core and coating material have not mixed up then (Fig. 6). For further investigation the inner material was cut into several parts. Whereas in Fig. 8 the material distribution in the welding chamber in the area of the extrusion seams can be seen, Fig. 7 is taken from an area between two extrusion seams. The analysis of the material left in the die after the extrusion shows that the magnesium coming from the core material encloses the Al from the coating.

Fig. 2: Position of the extrusion seams

Fig. 3: Hybrid Mg/Al profile Fig. 4: Detail of material distribution in the seam area of the profile

Fig. 1: Manufacturing of a coated profile


From the Fig. 5 to Fig. 8 it can be deducted that during the extrusion of the hybrid Al/Mg billet the material flow is homogeneous until it reaches the welding chamber. In the welding chamber the magnesium core is pushed through the open extrusion seams to the outside and thus the magnesium encloses the aluminum in the welding chamber (Fig. 8). After the magnesium is pushed through the open extrusion seams it then flows to the dead metal zone in the welding chamber. There the magnesium is held back and does not take part in the material flow anymore so that only in the area of the extrusion seams magnesium can be found on the profile surface (Fig. 7).

Simulation. The common tool for computer aided analysis for the extrusion process is the Finite Element Method (FEM). Although several FEM software solutions exist that support modeling, meshing, solving and/or post processing only a few specialize on the simulation of metal extrusion. A realistic reproduction of the metal extrusion process challenges the software tools by demanding consideration of highly detailed physical characteristics on the one hand and a possibly high level of abstraction in order to gain computational efficiency on the other hand. However the relevant physical influences as well as the appropriate ways to model these are subject of ongoing research. Thus different software solutions accomplish the essential requirements by implementing different ways of solving the simulation processes. For lack of a comprehensive standard for the modeling of the relevant parameters each software solution offers its very own way of handling the calculation of the extrusion process parameters. Accordingly each solution comes with different strengths and weaknesses and therefore - in the worst case - with varying results for the simulation of the same process.

Fig. 7: Enclosed Al in the welding chamber, cut through the material left in the die

Fig. 8: Enclosed Al in the welding area, outer surface of material left in the die

Fig. 5: Inner material, die, welding chamber, profile

Fig. 6: Inner material, inflow of the die

From the Fig. 5 to Fig. 8 it can be deducted that during the extrusion of the hybrid Al/Mg billet the material flow is homogeneous until it reaches the welding chamber. In the welding chamber the magnesium core is pushed through the open extrusion seams to the outside and thus the magnesium encloses the aluminum in the welding chamber (Fig. 8). After the magnesium is pushed through the open extrusion seams it then flows to the dead metal zone in the welding chamber. There the magnesium is held back and does not take part in the material flow anymore so that only in the area of the extrusion seams magnesium can be found on the profile surface (Fig. 7).

Simulation. The common tool for computer aided analysis for the extrusion process is the Finite Element Method (FEM). Although several FEM software solutions exist that support modeling, meshing, solving and/or post processing only a few specialize on the simulation of metal extrusion. A realistic reproduction of the metal extrusion process challenges the software tools by demanding consideration of highly detailed physical characteristics on the one hand and a possibly high level of abstraction in order to gain computational efficiency on the other hand. However the relevant physical influences as well as the appropriate ways to model these are subject of ongoing research. Thus different software solutions accomplish the essential requirements by implementing different ways of solving the simulation processes. For lack of a comprehensive standard for the modeling of the relevant parameters each software solution offers its very own way of handling the calculation of the extrusion process parameters. Accordingly each solution comes with different strengths and weaknesses and therefore - in the worst case - with varying results for the simulation of the same process.

Fig. 7: Enclosed Al in the welding chamber, cut through the material left in the die

Fig. 8: Enclosed Al in the welding area, outer surface of material left in the die

Fig. 5: Inner material, die, welding chamber, profile

Fig. 6: Inner material, inflow of the die


In [2] the different methods used by the most common FEM software solutions were compared. Most obvious differences are the applied models for continuum mechanics, where primarily Eulerian and Lagrangian formulations are used. Given the mesh based models used for FEM simulations depending on the applied formulations the mesh deformation is either not modeled at all (Eulerian) or may lead to heavy mesh distortions that impede the simulation (Lagrangian). These drawbacks are counteracted with combined formulations as the Arbitrary Lagrangian-Eulerian (ALE) formulation and/or by repeatedly remeshing the model during the simulation. Both approaches affect the simulation time because they can only be handled with an increased computational effort. Further differences affect the applied models for friction, material flow and thermal behavior. Each of the differences being a potential cause for diverging results. Yet another difference of the FEM software solutions is the way how they handle the representation of tool and material. Whereas some require a model for each, in order to simulate relevant parts of the tool as it affects and interacts with the material, other solutions expect the model to represent the inner material of the extrusion tool, from billet to profile. While both approaches are almost equal in modeling costs, the former has to struggle with more complex mesh deformations, while the latter is especially inefficient when it comes to coextrusion. Since the simulation starts with a model that has filled die and profile the model should actually include the progress of the coating as well - considering the fact that the hybrid billet was equally wrapped with the coat. But exactly the material flow of the billet coating is focus of interest and hence hard to model a priori. A first step towards simulation of co-extrusion processes was taken when bi-metal rod coextrusion processes were investigated [3]. In contrary to the experiments this paper is based on, the extrusion of rods has different demands in comparison to the co-extrusion of hollow hybrid profiles. The material flow during the extrusion of a rod usually is linear during the whole extrusion process. Whereas the coating material as well as the core underly heavy distortions of the material flow when put through a die for a hollow profile. Thus realistic simulation results exist for rod extrusion [3] while the simulation of co-extrusion with porthole dies show artifacts. In order to investigate the disturbed material flow in the welding chambers of the die various FEM simulations with the commercial software code HyperXtrude of the extrusion process have

been performed. The model is shown in Fig. 9. According to the demands of the used FEM software the model represents the hybrid billet and die, welding chamber and profile. The initial geometries of the model were taken from the hybrid billet used for the experiments. The material in the die recess, welding chamber and billet was modeled solely with the core material being Mg. Because in experimental extrusions the first part of the profile is uncoated magnesium due to the faster material flow in the center of the billet. For the coating Al was used. Thus the initial setup for the simulation

Fig. 9: Model for simulation of coextrusion with hybrid Mg/Al

In [2] the different methods used by the most common FEM software solutions were compared. Most obvious differences are the applied models for continuum mechanics, where primarily Eulerian and Lagrangian formulations are used. Given the mesh based models used for FEM simulations depending on the applied formulations the mesh deformation is either not modeled at all (Eulerian) or may lead to heavy mesh distortions that impede the simulation (Lagrangian). These drawbacks are counteracted with combined formulations as the Arbitrary Lagrangian-Eulerian (ALE) formulation and/or by repeatedly remeshing the model during the simulation. Both approaches affect the simulation time because they can only be handled with an increased computational effort. Further differences affect the applied models for friction, material flow and thermal behavior. Each of the differences being a potential cause for diverging results. Yet another difference of the FEM software solutions is the way how they handle the representation of tool and material. Whereas some require a model for each, in order to simulate relevant parts of the tool as it affects and interacts with the material, other solutions expect the model to represent the inner material of the extrusion tool, from billet to profile. While both approaches are almost equal in modeling costs, the former has to struggle with more complex mesh deformations, while the latter is especially inefficient when it comes to coextrusion. Since the simulation starts with a model that has filled die and profile the model should actually include the progress of the coating as well - considering the fact that the hybrid billet was equally wrapped with the coat. But exactly the material flow of the billet coating is focus of interest and hence hard to model a priori. A first step towards simulation of co-extrusion processes was taken when bi-metal rod coextrusion processes were investigated [3]. In contrary to the experiments this paper is based on, the extrusion of rods has different demands in comparison to the co-extrusion of hollow hybrid profiles. The material flow during the extrusion of a rod usually is linear during the whole extrusion process. Whereas the coating material as well as the core underly heavy distortions of the material flow when put through a die for a hollow profile. Thus realistic simulation results exist for rod extrusion [3] while the simulation of co-extrusion with porthole dies show artifacts. In order to investigate the disturbed material flow in the welding chambers of the die various FEM simulations with the commercial software code HyperXtrude of the extrusion process have

been performed. The model is shown in Fig. 9. According to the demands of the used FEM software the model represents the hybrid billet and die, welding chamber and profile. The initial geometries of the model were taken from the hybrid billet used for the experiments. The material in the die recess, welding chamber and billet was modeled solely with the core material being Mg. Because in experimental extrusions the first part of the profile is uncoated magnesium due to the faster material flow in the center of the billet. For the coating Al was used. Thus the initial setup for the simulation

Fig. 9: Model for simulation of coextrusion with hybrid Mg/Al


differed from the initial setup in the experiment, since in the experimental process die and welding chamber were not filled until the extrusion process started. The Al-material properties of the model were taken from the simulation software‘s database. The properties of the Mg-material were deducted from experimental data and added to the FEM software. Initially the co-extrusion process was simulated for monomaterial models for both materials. The model shown in Fig. 9 was used, but instead of the coating a model of the billet with an accordingly bigger diameter was used. Region of interest were the areas in the die and the welding area. The process parameters of interest were the pressure distribution and the velocity. The simulation results showed two determining factors for the material mix up. First of all the simulation results revealed a much higher deformation pressure for the Mg (Fig. 10a and 10b). The pressure distribution in the die during the extrusion of only the EN-AW 6060 and only the AZ31 alloy showed that the pressure in the welding chamber for the AZ31 is about 50% higher than that of the EN-AW 6060. The analysis of the velocities in the welding chambers shows that the speed decreases from the center of the die to the border. The velocities thereby are practically the same for both materials (Fig. 11). Due to the different velocities in the welding chamber the aluminum on the outside of the billet is held back, in part the velocity is even 0, which means this material does not take part in the extrusion anymore.

Thus the velocity and the different deformation resistance of the Mg and the Al alloy are influencing the material flow in the die. The higher pressure in combination with the disturbed material flow leads to the material mix up in the weld seams [4]. The coating material is held back due to the friction on the surface between billet and die.

Accordingly first the magnesium from the core fills up the die recess. Furthermore the slower flowing aluminum coating material is easily pushed away as long as the seam is not closed. Thus the magnesium which was pushed through the open seams is accumulated in the dead metal zones of the welding chamber (Fig. 7 and Fig. 12).

Fig. 10a: Pressure distribution in the die during the extrusion of EN-AW 6060

Fig. 10b: Pressure distribution in the die during the extrusion of AZ31

Fig. 11: Velocity distribution in the welding chamber of the die

differed from the initial setup in the experiment, since in the experimental process die and welding chamber were not filled until the extrusion process started. The Al-material properties of the model were taken from the simulation software‘s database. The properties of the Mg-material were deducted from experimental data and added to the FEM software. Initially the co-extrusion process was simulated for monomaterial models for both materials. The model shown in Fig. 9 was used, but instead of the coating a model of the billet with an accordingly bigger diameter was used. Region of interest were the areas in the die and the welding area. The process parameters of interest were the pressure distribution and the velocity. The simulation results showed two determining factors for the material mix up. First of all the simulation results revealed a much higher deformation pressure for the Mg (Fig. 10a and 10b). The pressure distribution in the die during the extrusion of only the EN-AW 6060 and only the AZ31 alloy showed that the pressure in the welding chamber for the AZ31 is about 50% higher than that of the EN-AW 6060. The analysis of the velocities in the welding chambers shows that the speed decreases from the center of the die to the border. The velocities thereby are practically the same for both materials (Fig. 11). Due to the different velocities in the welding chamber the aluminum on the outside of the billet is held back, in part the velocity is even 0, which means this material does not take part in the extrusion anymore.

Thus the velocity and the different deformation resistance of the Mg and the Al alloy are influencing the material flow in the die. The higher pressure in combination with the disturbed material flow leads to the material mix up in the weld seams [4]. The coating material is held back due to the friction on the surface between billet and die.

Accordingly first the magnesium from the core fills up the die recess. Furthermore the slower flowing aluminum coating material is easily pushed away as long as the seam is not closed. Thus the magnesium which was pushed through the open seams is accumulated in the dead metal zones of the welding chamber (Fig. 7 and Fig. 12).

Fig. 10a: Pressure distribution in the die during the extrusion of EN-AW 6060

Fig. 10b: Pressure distribution in the die during the extrusion of AZ31

Fig. 11: Velocity distribution in the welding chamber of the die


The simulation of the co-extrusion process, with both materials being used in the model, phenomenologically confirms this material flow. Again the velocity in the coating areas, i. e. at the outer borders of the billet, tends to zero whereas the core material is moved. Thus the simulation shows that the core material passes the coating and therefore fills the dead zones in the die and the welding chamber. While the Mg from the core is pushed into the die the Al-coating slowly drifts into the die afterwards (Fig. 12 and Fig. 13). Accordingly the coating has to be pushed through the magnesium in order to reach the surface of the profile. Especially when the seam has not been closed in the welding chamber the higher pressure in the magnesium leads to a breakthroughof the Mg through the Al-coating. Accordingly the core material can be found on the surface of the profile. Though phenomenologically the simulation results fit the observed characteristics of the

experiment a further comparison of simulation and experimental results reveal, as the simulation proceeds, more and more artifacts. Especially the complex material flow in the welding chamber can only be simulated roughly. Most realistic results were obtained for the first seconds of the process.

Fig. 12: Simulated material flow in the co-extrusion process

Fig. 13: Simulated velocity in the co-extrusion process

The simulation of the co-extrusion process, with both materials being used in the model, phenomenologically confirms this material flow. Again the velocity in the coating areas, i. e. at the outer borders of the billet, tends to zero whereas the core material is moved. Thus the simulation shows that the core material passes the coating and therefore fills the dead zones in the die and the welding chamber. While the Mg from the core is pushed into the die the Al-coating slowly drifts into the die afterwards (Fig. 12 and Fig. 13). Accordingly the coating has to be pushed through the magnesium in order to reach the surface of the profile. Especially when the seam has not been closed in the welding chamber the higher pressure in the magnesium leads to a breakthroughof the Mg through the Al-coating. Accordingly the core material can be found on the surface of the profile. Though phenomenologically the simulation results fit the observed characteristics of the

experiment a further comparison of simulation and experimental results reveal, as the simulation proceeds, more and more artifacts. Especially the complex material flow in the welding chamber can only be simulated roughly. Most realistic results were obtained for the first seconds of the process.

Fig. 12: Simulated material flow in the co-extrusion process

Fig. 13: Simulated velocity in the co-extrusion process


Summary

Manufacturing of hybrid profiles with co-extrusion through a porthole die produces a coated profile. Welding seams are visible and reveal a material mix up where the coating is penetrated with the core material. With FEM simulation the material flow in the die and the welding chamber could be reproduced. The velocity in the coating area tends towards zero and deformation pressures are much higher in the core. Thus the magnesium advances into the die and the Al-coating has to be pushed against that higher pressure through the core material in order to reach the surface of the profile. The simulation results confirm the observations made in cuts through the materials left in die recess and welding chamber after the extrusion process. Still, the simulation results show artifacts that can not be observed in the experiments, especially when run longer. Therefore the FEM models have to be refined. A first step will be the further investigation of the physical and geometrical models that produce the material flow with the focus in the mutual impacts of the used alloys.

References

[1] G. S. Cole: Issues that influences Magnesiums’s use in the Automotive Industry, Materials Science Forum, 419-422, (2003), pp. 43-50;

[2] M. Schikorra: Modellierung und simulationsgestützte Analyse der Verbundstrangpressens, Reihe Dortmunder Umformtechnik, Shaker Verlag, Aachen (2006)

[3] P. Kazanowski, M.E. Epler, W. Z. Misiolek: Bi-metal rod extrusion - process and product optimization, Materials Science and Engineering A369 (2004), pp. 170-180

[4] S. Mueller, S. Gall, W. Reimers: Extrusion of hybrid aluminum magnesium profiles, International Symposium on Plasticity 2009, (2009), CD

Summary

Manufacturing of hybrid profiles with co-extrusion through a porthole die produces a coated profile. Welding seams are visible and reveal a material mix up where the coating is penetrated with the core material. With FEM simulation the material flow in the die and the welding chamber could be reproduced. The velocity in the coating area tends towards zero and deformation pressures are much higher in the core. Thus the magnesium advances into the die and the Al-coating has to be pushed against that higher pressure through the core material in order to reach the surface of the profile. The simulation results confirm the observations made in cuts through the materials left in die recess and welding chamber after the extrusion process. Still, the simulation results show artifacts that can not be observed in the experiments, especially when run longer. Therefore the FEM models have to be refined. A first step will be the further investigation of the physical and geometrical models that produce the material flow with the focus in the mutual impacts of the used alloys.

References

[1] G. S. Cole: Issues that influences Magnesiums’s use in the Automotive Industry, Materials Science Forum, 419-422, (2003), pp. 43-50;

[2] M. Schikorra: Modellierung und simulationsgestützte Analyse der Verbundstrangpressens, Reihe Dortmunder Umformtechnik, Shaker Verlag, Aachen (2006)

[3] P. Kazanowski, M.E. Epler, W. Z. Misiolek: Bi-metal rod extrusion - process and product optimization, Materials Science and Engineering A369 (2004), pp. 170-180

[4] S. Mueller, S. Gall, W. Reimers: Extrusion of hybrid aluminum magnesium profiles, International Symposium on Plasticity 2009, (2009), CD


Effect of tube wall thickness in Joining of Aluminum Tube and Holed Rib by Extrusion

T. Moroi1, a, T. Kuboki1, a and M. Murata1, a 1 The University of Electro-Communications, Department of Mechanical Engineering and Intelligent

Systems, Tokyo, 182-8585, Japan [email protected]

Keywords: New extrusion method, Finite element method, Joining, Guide position, Tube wall thickness Abstract. Existence of some holes at internal ribs enhances the function and value of the tubes. A new extrusion method is proposed here for the forming of this shape by extrusion with joining. The method involves the use of a unique mandrel that has a slit along its axis and two guides at the slit exit. A holed sheet is fed through the slit and joined with the inner surface of extrude tube. Effect of two parameters, that are tube-wall thickness and guide position h which is distance from guide top to die surface were clarified by FEA. Two kinds of three-dimensional analysis models were prepared. One of the analysis models treats the rib as rigid body to examine a gap between rib and tube. Another model treats the rib as the elasto-plasticity body as well as the billet to examine the effect of the guide position and the tube wall thickness on the rib deformation. The series of analyses was carried out with emphasis on the metal flow. The gap between tube and rib is able to be suppressed small and joining condition becomes satisfactory when guide position rose or tube wall was thin. When the guide position rose further, or the tube wall thickness was excessively thinner, the amount of the deformation of the rib increases, and it causes defects.

Introduction

Extrusion has been used as a forming method for the long product with the same cross section so far. Extrusion is known as a suitable manufacturing method of aluminium tubes as shown in Fig. 1(a), particularly those with complex cross-sectional shapes, having internal ribs inside as shown in Fig. 1(b). These extruded tubes include structural components, radiator, and impact absorbers used in automobiles. Recently, cars are requested to be lighter considering environmental problems. Using these materials can reduce car weight. If these tubes with the holed rib are used as structural components, the following effects can be expected (Fig. 1(c)). (1) If there are holes at the appropriate position of ribs, structural component could be lighter without

reducing strength. (2) Installation of such tubes into shock absorption units could stabilize buckling behaviour. (3) Installation in a radiator would improve its heat exchange performance. While tubes with uniform cross section as in Fig.s 1(a) and (b) can be formed by conventional extrusion, the tube, which has variable cross section in longitudinal direction, cannot be formed conventionally. Although a method was proposed for changing inside diameter of circular tube axial direction[1], the method can not form the shape like Fig. 1(c) where tube has holes. Then, the authors have proposed a method that extrudes tube joining with a ready made rib. The rib is a machined sheet metal with holes. While the tube is extruded, the rib is fed through a slit of mandrel. Tube and sheet are joined at the same time of extrusion. Steel wire reinforced aluminum tube is also a kind of joining extrusion[2]. This research focuses upon a joining extrusion whereby a holed sheet is joined with the inner surface of extrude tube. The authors showed that the shape can be formed using aluminium as material in the experiment [3].

Effect of tube wall thickness in Joining of Aluminum Tube and Holed Rib by Extrusion

T. Moroi1, a, T. Kuboki1, a and M. Murata1, a 1 The University of Electro-Communications, Department of Mechanical Engineering and Intelligent

Systems, Tokyo, 182-8585, Japan [email protected]

Keywords: New extrusion method, Finite element method, Joining, Guide position, Tube wall thickness Abstract. Existence of some holes at internal ribs enhances the function and value of the tubes. A new extrusion method is proposed here for the forming of this shape by extrusion with joining. The method involves the use of a unique mandrel that has a slit along its axis and two guides at the slit exit. A holed sheet is fed through the slit and joined with the inner surface of extrude tube. Effect of two parameters, that are tube-wall thickness and guide position h which is distance from guide top to die surface were clarified by FEA. Two kinds of three-dimensional analysis models were prepared. One of the analysis models treats the rib as rigid body to examine a gap between rib and tube. Another model treats the rib as the elasto-plasticity body as well as the billet to examine the effect of the guide position and the tube wall thickness on the rib deformation. The series of analyses was carried out with emphasis on the metal flow. The gap between tube and rib is able to be suppressed small and joining condition becomes satisfactory when guide position rose or tube wall was thin. When the guide position rose further, or the tube wall thickness was excessively thinner, the amount of the deformation of the rib increases, and it causes defects.

Introduction

Extrusion has been used as a forming method for the long product with the same cross section so far. Extrusion is known as a suitable manufacturing method of aluminium tubes as shown in Fig. 1(a), particularly those with complex cross-sectional shapes, having internal ribs inside as shown in Fig. 1(b). These extruded tubes include structural components, radiator, and impact absorbers used in automobiles. Recently, cars are requested to be lighter considering environmental problems. Using these materials can reduce car weight. If these tubes with the holed rib are used as structural components, the following effects can be expected (Fig. 1(c)). (1) If there are holes at the appropriate position of ribs, structural component could be lighter without

reducing strength. (2) Installation of such tubes into shock absorption units could stabilize buckling behaviour. (3) Installation in a radiator would improve its heat exchange performance. While tubes with uniform cross section as in Fig.s 1(a) and (b) can be formed by conventional extrusion, the tube, which has variable cross section in longitudinal direction, cannot be formed conventionally. Although a method was proposed for changing inside diameter of circular tube axial direction[1], the method can not form the shape like Fig. 1(c) where tube has holes. Then, the authors have proposed a method that extrudes tube joining with a ready made rib. The rib is a machined sheet metal with holes. While the tube is extruded, the rib is fed through a slit of mandrel. Tube and sheet are joined at the same time of extrusion. Steel wire reinforced aluminum tube is also a kind of joining extrusion[2]. This research focuses upon a joining extrusion whereby a holed sheet is joined with the inner surface of extrude tube. The authors showed that the shape can be formed using aluminium as material in the experiment [3].


The joining strength was improved by controlling metal flow for increasing contact area between rib and tube walls.

However, these experiments were carried out with the same wall thickness. The applicability of the new extrusion method should be examined for the wider range of tube wall thickness. Because components for transportation vehicles are demanded to be lighter considering environmental issues and reduce costs, thinner walled tubes would be preferable in some parts of industry. On the other hand, thicker walled tube would also be needed as some structural components in other area. In this research, results of Finite Element Method and experiment which showed satisfactory state of joining would be realized under appropriate working conditions corresponding to the tube wall thickness.

(a) Tube (conventional method).

(b) Tube with rib (conventional method).

(c) Tube with holed rib (new method).

Fig. 1: Variable of extruded tube.

Principle of extrusion

Fig. 2 shows the principle of the extrusion processing. The billet is hollow because a mandrel is used to extrude the tube. Mandrel has a slit to insert the holed sheet. Two guides, which cover and protect the holed sheet from the pressure of metal, are equipped at the exit of mandrel. The authors showed that this guide is useful for joining by comparison with conventional straight mandrel [4]. The metal flow of billet was once divided by the guide before coming together again to join with the sheet. Guide position h, which is the distance from the guide top to die surface, is one of important factor for the control of metal flow.

Fig. 3 shows schematic of metal flow. When guide position rises, metal flow under the guide changes. When the guide position rises, the metal enters into the space under the guide. As a result, the "guide mark" shrinks and that would increase the joining strength. Fig. 4(a) shows cross section of X-X section of Fig. 2 under the condition that sheet is not supplied. These cross sections are located at the area denoted by dashed line in Fig. 3. Fig. 4(b), (c) and (d) shows variation of extruded tube cross section attendant upon the guide position h. The cross section of the tube would be classified into one of the following three states: (1) The guide position is the same as the level of die surface (Fig. 4(b)).

A metal flow at the lower part of the guide does not occur in horizontal direction. As the guide mark becomes the same shape of the guide, metal does not contact with sheet.

(2) The guide position is in the upper part from the die surface (Fig. 4(c)). Width and depth of the guide mark become smaller than those in the state (1).

(3) The guide position is higher in the upper part than that in (2) (Fig. 4(d)). Before a metal flow reaches the die bearing, a metal flow at the lower part of the guide fills up.

In the state (1), joining is impossible because dimension of guide mark become larger than that of sheet. In the state (2) and (3), tube and sheet can be joined.

The joining strength was improved by controlling metal flow for increasing contact area between rib and tube walls.

However, these experiments were carried out with the same wall thickness. The applicability of the new extrusion method should be examined for the wider range of tube wall thickness. Because components for transportation vehicles are demanded to be lighter considering environmental issues and reduce costs, thinner walled tubes would be preferable in some parts of industry. On the other hand, thicker walled tube would also be needed as some structural components in other area. In this research, results of Finite Element Method and experiment which showed satisfactory state of joining would be realized under appropriate working conditions corresponding to the tube wall thickness.

(a) Tube (conventional method).

(b) Tube with rib (conventional method).

(c) Tube with holed rib (new method).

Fig. 1: Variable of extruded tube.

Principle of extrusion

Fig. 2 shows the principle of the extrusion processing. The billet is hollow because a mandrel is used to extrude the tube. Mandrel has a slit to insert the holed sheet. Two guides, which cover and protect the holed sheet from the pressure of metal, are equipped at the exit of mandrel. The authors showed that this guide is useful for joining by comparison with conventional straight mandrel [4]. The metal flow of billet was once divided by the guide before coming together again to join with the sheet. Guide position h, which is the distance from the guide top to die surface, is one of important factor for the control of metal flow.

Fig. 3 shows schematic of metal flow. When guide position rises, metal flow under the guide changes. When the guide position rises, the metal enters into the space under the guide. As a result, the "guide mark" shrinks and that would increase the joining strength. Fig. 4(a) shows cross section of X-X section of Fig. 2 under the condition that sheet is not supplied. These cross sections are located at the area denoted by dashed line in Fig. 3. Fig. 4(b), (c) and (d) shows variation of extruded tube cross section attendant upon the guide position h. The cross section of the tube would be classified into one of the following three states: (1) The guide position is the same as the level of die surface (Fig. 4(b)).

A metal flow at the lower part of the guide does not occur in horizontal direction. As the guide mark becomes the same shape of the guide, metal does not contact with sheet.

(2) The guide position is in the upper part from the die surface (Fig. 4(c)). Width and depth of the guide mark become smaller than those in the state (1).

(3) The guide position is higher in the upper part than that in (2) (Fig. 4(d)). Before a metal flow reaches the die bearing, a metal flow at the lower part of the guide fills up.

In the state (1), joining is impossible because dimension of guide mark become larger than that of sheet. In the state (2) and (3), tube and sheet can be joined.


Container

BilletMandrel

Guide position h

Slit

Die bea

ring

Fig. 2: Principle of extrusion joining.

Guide

Guide

Guide

h

Die

. (a)h=0mm. (b)h=2.0mm. (c)h=3.0mm.

Fig. 3: Illustration of metal flow.

Fig. 4: Cross section of extruded tube.

Analysis model

Estimation of the gap between tube and rib, and the deformation of rib hole by 3D model. Finite element analysis is conducted using a commercial code ELFEN [5], which was developed by Rockfield Software Limited, in Swansea, U.K. There are some papers on metal forming by using ELFEN[6,7]. A quarter of the geometry was considered due to the symmetry as shown in Fig. 5. The rib and tools were defined as rigid body in the FEM. The billet is elasto-plastic material. Billet and sheet are elasto-plastic material and they obey Von Mises yield criterion, which was defined by the mechanical properties of 1100 Aluminum at 370 degree Celsius. Yield stress of the billet is 11.0 MPa, Young’s modulus is 69.0 GPa and Poisson’s ratio is 0.33. Container, mandrel, punch and die are defined as rigid body. Mesh is divided by tetrahedral solid element.

Mandrel top diameter is 10mm and die hole diameter is from 14 to 20mm. The tube wall thickness is set by adjusting the die hole diameter. Inside diameter, outside diameter and length of the billet are 20mm, 40mm and 20mm respectively. Two kinds of analysis models were prepared. One of the analysis models treats the rib as rigid body to examine a gap between rib and tube. Another model treats the rib as the elasto-plasticity body same as the billet to examine the effect of the guide position and the tube wall thickness on the rib deformation. Sheet thickness, sheet width, sheet hole diameter and distance between hole centers are 1.0mm, 15mm, 6mm and 10mm. The sheet is fed through the slit inside the mandrel.

Container

BilletMandrel

Guide position h

Slit

Die bea

ring

Fig. 2: Principle of extrusion joining.

Guide

Guide

Guide

h

Die

. (a)h=0mm. (b)h=2.0mm. (c)h=3.0mm.

Fig. 3: Illustration of metal flow.

Fig. 4: Cross section of extruded tube.

Analysis model

Estimation of the gap between tube and rib, and the deformation of rib hole by 3D model. Finite element analysis is conducted using a commercial code ELFEN [5], which was developed by Rockfield Software Limited, in Swansea, U.K. There are some papers on metal forming by using ELFEN[6,7]. A quarter of the geometry was considered due to the symmetry as shown in Fig. 5. The rib and tools were defined as rigid body in the FEM. The billet is elasto-plastic material. Billet and sheet are elasto-plastic material and they obey Von Mises yield criterion, which was defined by the mechanical properties of 1100 Aluminum at 370 degree Celsius. Yield stress of the billet is 11.0 MPa, Young’s modulus is 69.0 GPa and Poisson’s ratio is 0.33. Container, mandrel, punch and die are defined as rigid body. Mesh is divided by tetrahedral solid element.

Mandrel top diameter is 10mm and die hole diameter is from 14 to 20mm. The tube wall thickness is set by adjusting the die hole diameter. Inside diameter, outside diameter and length of the billet are 20mm, 40mm and 20mm respectively. Two kinds of analysis models were prepared. One of the analysis models treats the rib as rigid body to examine a gap between rib and tube. Another model treats the rib as the elasto-plasticity body same as the billet to examine the effect of the guide position and the tube wall thickness on the rib deformation. Sheet thickness, sheet width, sheet hole diameter and distance between hole centers are 1.0mm, 15mm, 6mm and 10mm. The sheet is fed through the slit inside the mandrel.


The effect of guide position and tube thickness on metal flow by 2D model. The metal flow in the vicinity of the guide dominates the gap between tube and rib, and the rib-hole deformation. The less the gap, the joining strength would increase, and the less deformation of rib-hole is preferable. It is necessary to expand the range of the analysis condition to clarify the behavior of the metal flow. However, the computing time becomes a huge amount as for doing a lot of conditions. Moreover, the calculation might stop in a severe condition of the thickness 2mm or less with a high extrusion ratio. Then, a simple two dimension axial model was conFig.d as the basic research for the study of metal flow. Two dimensional simple models can be calculated more promptly and more stably than the three-dimensional model. Although this 2d model can not describe actual deformation, it is suitable for the evaluation of the metal flow behavior.

Fig. 5 Quarter model of FEM for extrusion

Analysis results

3D analysis using rigid rib. A series of analyses was carried out with emphasis on the metal flow, in particular, the gap between tube inner surface and the rib surface after extrusion. It was assumed that smaller gap in analysis would be interpreted as better joining state in real phenomena [3], [4]. The effect of guide position on this gap was examined and the results were shown in Fig. 6. The gap becomes small as guide position h rises. In this Fig., gx and gy are the gap between rib and tube in x and y direction, i.e. rib width and thickness directions respectively. Results for each tube wall thickness of t =2, 3, 5 mm were shown in this Fig.. When the guide position is constant, the gaps become small with decrease of tube wall thickness due to the metal flow. This is because thin tube wall raises the extrusion ratio so that a large amount of metal might flow toward the center of cylinder. On the other hand, it would also be supposed that excessive metal flow in x-direction might cause rib collapse during joining. As a result of these analyses, it was predicted that lower guide position would be suitable for thinner tube wall. The minimum bare gap height, which could reduce the gap gy in thickness direction less than 0.1 mm, is assumed to be the optimum condition. For the optimum joining, i.e. the gap is less than 0.1mm, guide position h should be 3.5, 2.0, 1.5mm for the tube wall thickness t of 5, 3 and 2mm respectively. The deformation of the rib is analyzed in next section based on this result. 3D analysis using deformable rib. Result of 4.1 forecasts that the gap between the tube and the rib is small, and the joining condition became satisfactory when the guide position rises, but too high a guide position causes the collapse of the rib. In this section, the model with a deformable rib was used to clarify the influence of the guide position and the tube wall thickness on the deformation of the rib. Elongation of the rib hole along extrusion direction (DL) is shown in Fig. 7. Reduction of the rib hole in width direction (DW) is shown in Fig. 8. The effect of the guide position on the rib thickness (TR) is shown in Fig. 9. The amount of rib thickness is measured at the center of the tube. In Fig. 7, rib hole

The effect of guide position and tube thickness on metal flow by 2D model. The metal flow in the vicinity of the guide dominates the gap between tube and rib, and the rib-hole deformation. The less the gap, the joining strength would increase, and the less deformation of rib-hole is preferable. It is necessary to expand the range of the analysis condition to clarify the behavior of the metal flow. However, the computing time becomes a huge amount as for doing a lot of conditions. Moreover, the calculation might stop in a severe condition of the thickness 2mm or less with a high extrusion ratio. Then, a simple two dimension axial model was conFig.d as the basic research for the study of metal flow. Two dimensional simple models can be calculated more promptly and more stably than the three-dimensional model. Although this 2d model can not describe actual deformation, it is suitable for the evaluation of the metal flow behavior.

Fig. 5 Quarter model of FEM for extrusion

Analysis results

3D analysis using rigid rib. A series of analyses was carried out with emphasis on the metal flow, in particular, the gap between tube inner surface and the rib surface after extrusion. It was assumed that smaller gap in analysis would be interpreted as better joining state in real phenomena [3], [4]. The effect of guide position on this gap was examined and the results were shown in Fig. 6. The gap becomes small as guide position h rises. In this Fig., gx and gy are the gap between rib and tube in x and y direction, i.e. rib width and thickness directions respectively. Results for each tube wall thickness of t =2, 3, 5 mm were shown in this Fig.. When the guide position is constant, the gaps become small with decrease of tube wall thickness due to the metal flow. This is because thin tube wall raises the extrusion ratio so that a large amount of metal might flow toward the center of cylinder. On the other hand, it would also be supposed that excessive metal flow in x-direction might cause rib collapse during joining. As a result of these analyses, it was predicted that lower guide position would be suitable for thinner tube wall. The minimum bare gap height, which could reduce the gap gy in thickness direction less than 0.1 mm, is assumed to be the optimum condition. For the optimum joining, i.e. the gap is less than 0.1mm, guide position h should be 3.5, 2.0, 1.5mm for the tube wall thickness t of 5, 3 and 2mm respectively. The deformation of the rib is analyzed in next section based on this result. 3D analysis using deformable rib. Result of 4.1 forecasts that the gap between the tube and the rib is small, and the joining condition became satisfactory when the guide position rises, but too high a guide position causes the collapse of the rib. In this section, the model with a deformable rib was used to clarify the influence of the guide position and the tube wall thickness on the deformation of the rib. Elongation of the rib hole along extrusion direction (DL) is shown in Fig. 7. Reduction of the rib hole in width direction (DW) is shown in Fig. 8. The effect of the guide position on the rib thickness (TR) is shown in Fig. 9. The amount of rib thickness is measured at the center of the tube. In Fig. 7, rib hole


elongates in the extrusion direction. This is because the rib is stretch along extrusion direction attendant upon velocity differential of metal flow.

In Fig. 8, rib hole compress to rib width direction. This is caused by the metal flow in the rib width direction. In Fig. 9, rib thickness increases because rib is compressed in the rib width direction. As excessive thickness increase in analysis would be interpreted as buckling in real experimental phenomena, less increase of thickness is more preferable. To summarize our interpretation of the results, it can be explained that the rib deforms largely with increase of guide position or decrease of tube wall. The rib thickness increases because the amount of the compression in the width direction is larger than that of the axial elongation. 2D axisymmetric analysis. It was shown that the joining condition becomes satisfactory by reducing the gap between tube and rib in section 4.1. In section 4.2, it was shown that defective deformations: hole elongation and excessive thickening, appear when the gap is too small. In fact, it is necessary to set the guide at a proper position for the tube and the rib to joint without the gap and to suppress the defective deformation of the rib at the minimum. However, it has been understood that the proper value is different according to the tube wall thickness.

It is important to examine the fundamental effect of the guide position and tube wall thickness on the metal flow, which would determine the joining strength and defective deformation. This examination is conducted in a concise 2D axisymmetric analysis in this section. The amount of change metal flow is evaluated by metal flow angle. Fig. 10 shows an analytical model. The mechanical properties are the same as the 3-dimensional analyses. The effects of the guide position and the tube wall thickness on the metal flow angle θ are shown in Fig.s 11 and 12. Amount of metal toward mandrel center grows as metal flow angle is large. The maximum angle of θ is 90 degree, and the metal flow angle increases linearly with the increase of the guide position. On the other hand, metal flow angle changes exponentially with the decrease of the tube wall thickness. In above mention, it was clarified that metal flow is affected by the tube wall thickness more than the guide position. Metal flow angle at t=5mm can be controlled within the wider range of 35 degree (from 25 to 60 degree). In case of t=2mm, metal flow angle can be controlled within the narrower range of 15 degree (from 75 to 90 degree). The controllable range of flow angle is much wider for thick wall tube than that for thin wall tube. Because the extrusion ratio rises when the tube wall thickness is thins, too high an extrusion ratio makes it difficult to control the metal flow by the guide position. It is necessary to reduce the billet diameter or expand the flow guide that decreases the extrusion ratio for effective usage of the guide position in the case of thin-walled tube extrusion.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5Guide position h / mm

Gap of rib and tu

be g / mm

t2gyt2gx16gy16gx20gy20gx

t 2g y

t 2g x

t 3g y

t 3g x

t 5g y

t 5g x

Fig. 6 Effect of guide position on gap between rib and tube corresponding to wall thickness

elongates in the extrusion direction. This is because the rib is stretch along extrusion direction attendant upon velocity differential of metal flow.

In Fig. 8, rib hole compress to rib width direction. This is caused by the metal flow in the rib width direction. In Fig. 9, rib thickness increases because rib is compressed in the rib width direction. As excessive thickness increase in analysis would be interpreted as buckling in real experimental phenomena, less increase of thickness is more preferable. To summarize our interpretation of the results, it can be explained that the rib deforms largely with increase of guide position or decrease of tube wall. The rib thickness increases because the amount of the compression in the width direction is larger than that of the axial elongation. 2D axisymmetric analysis. It was shown that the joining condition becomes satisfactory by reducing the gap between tube and rib in section 4.1. In section 4.2, it was shown that defective deformations: hole elongation and excessive thickening, appear when the gap is too small. In fact, it is necessary to set the guide at a proper position for the tube and the rib to joint without the gap and to suppress the defective deformation of the rib at the minimum. However, it has been understood that the proper value is different according to the tube wall thickness.

It is important to examine the fundamental effect of the guide position and tube wall thickness on the metal flow, which would determine the joining strength and defective deformation. This examination is conducted in a concise 2D axisymmetric analysis in this section. The amount of change metal flow is evaluated by metal flow angle. Fig. 10 shows an analytical model. The mechanical properties are the same as the 3-dimensional analyses. The effects of the guide position and the tube wall thickness on the metal flow angle θ are shown in Fig.s 11 and 12. Amount of metal toward mandrel center grows as metal flow angle is large. The maximum angle of θ is 90 degree, and the metal flow angle increases linearly with the increase of the guide position. On the other hand, metal flow angle changes exponentially with the decrease of the tube wall thickness. In above mention, it was clarified that metal flow is affected by the tube wall thickness more than the guide position. Metal flow angle at t=5mm can be controlled within the wider range of 35 degree (from 25 to 60 degree). In case of t=2mm, metal flow angle can be controlled within the narrower range of 15 degree (from 75 to 90 degree). The controllable range of flow angle is much wider for thick wall tube than that for thin wall tube. Because the extrusion ratio rises when the tube wall thickness is thins, too high an extrusion ratio makes it difficult to control the metal flow by the guide position. It is necessary to reduce the billet diameter or expand the flow guide that decreases the extrusion ratio for effective usage of the guide position in the case of thin-walled tube extrusion.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5Guide position h / mm

Gap of rib and tu

be g / mm

t2gyt2gx16gy16gx20gy20gx

t 2g y

t 2g x

t 3g y

t 3g x

t 5g y

t 5g x

Fig. 6 Effect of guide position on gap between rib and tube corresponding to wall thickness


0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Guide position h / mm

Rib hole elongatio

n ∆D

L / m

m

161820

t =3t =4t =5

Fig. 7: Amount of rib hole compress

0

0.5

1

1.5

2

0 1 2 3 4 5


Rib hole compress ∆D

W / mm

161820

t =3t =4t =5

Fig. 8: Amount of rib hole elongation

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


Rib th

ickness ∆T R / mm 16

1820

t =3t =4t =5

Fig. 9: Amount of rib thickness increment

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5


Rib hole elongatio

n ∆D

L / m

m

161820

t =3t =4t =5

Fig. 7: Amount of rib hole compress

0

0.5

1

1.5

2

0 1 2 3 4 5


Rib hole compress ∆D

W / mm

161820

t =3t =4t =5

Fig. 8: Amount of rib hole elongation

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


Rib th

ickness ∆T R / mm 16

1820

t =3t =4t =5

Fig. 9: Amount of rib thickness increment


h

t

θ

Fig. 10: two dimension symmetrical analysis model

0

20

40

60

80

100

0123456

Tube wall thickness t /mm

Metal flow

ang

le θ/ d

eg

h=0.5 mmh=1h=2h=3h=4

h =0.5 mmh =1.0h =2.0h =3.0h =4.0

Fig. 11: Relationship between guide position and metal flow angle

0

20

40

60

80

100

0 1 2 3 4 5

Guide position h /mm

Metal flow

ang

le θ/ d

eg

t=1 mmt=2t=3t=4t=5

t =1 mmt =2t =3t =4t =5

Fig. 12: Relationship between tube wall thickness and metal flow angle

Conclusions

The rib and the tube are joined with the metal that flow through the space between the guide and the die. As a result, control of metal flow is very important. The conclusions are as follows.

h

t

θ

Fig. 10: two dimension symmetrical analysis model

0

20

40

60

80

100

0123456

Tube wall thickness t /mm

Metal flow

ang

le θ/ d

eg

h=0.5 mmh=1h=2h=3h=4

h =0.5 mmh =1.0h =2.0h =3.0h =4.0

Fig. 11: Relationship between guide position and metal flow angle

0

20

40

60

80

100

0 1 2 3 4 5

Guide position h /mm

Metal flow

ang

le θ/ d

eg

t=1 mmt=2t=3t=4t=5

t =1 mmt =2t =3t =4t =5

Fig. 12: Relationship between tube wall thickness and metal flow angle

Conclusions

The rib and the tube are joined with the metal that flow through the space between the guide and the die. As a result, control of metal flow is very important. The conclusions are as follows.


・ The gap between tube and rib becomes small and joining condition gets into satisfactory when guide position rises or tube wall is thin.

・ When the guide position rises further, or the tube wall thickness is excessively thinner, the amount of the deformation of the rib increases, and it causes defects.

・ The setting of the guide position is difficult for the tube wall thickness to thin. The effect of the guide position is small for the thin wall-tube extrusion.

・ When the thin-wall tube is extruded, it is necessary to improve device to reduce the extrusion ratio for enhancing the efficiency of guide position control.

References

[1] Takahiro Makiyama and Makoto Murata: “Controlling Inside Diameter of Circular Tube by Extrusion”, Materials Science Forum Vol. 396-402, (2002), 513-518

[2] Katsuyoshi Saito and Katsumi Watanabe: “Co-extruded aluminum composites”, Journal of Japan Institute of Light Metals, 35-5, (1985), 297-303

[3] T. Moroi, T. Kuboki and M. Murata: “Effect of temperature on tube extrusion and joining holed rib”, Steel research international, Vol.79, No.11, 2008, pp. 677-682

[4] T. Moroi, T. Kuboki and M. Murata: “A new extrusion method joining tube and sheet with holed rib”, Journal of Mechanical Science and Technology, Vol.21, No. 10, October 2007, pp. 1548-1552

[5] Rockfield Software Limited: ELFEN User Manual ver.3.0, Rockfield Software Limited (2000), 1.1-13.8.

[6] Turk, R., Perus, I. & Tercelj, M.: “New starting points for the prediction of tool wear in hot forging”, International Journal of Machine Tools and Manufacture, 44-12-13, (2004), 1319-1331

[7] Browne, M. T. and Hillery, M. T.: “Optimising the variables when deep-drawing C.R.1 cups”, Journal of Material Processing Technology, 136-1-3, (2003), 64-71

・ The gap between tube and rib becomes small and joining condition gets into satisfactory when guide position rises or tube wall is thin.

・ When the guide position rises further, or the tube wall thickness is excessively thinner, the amount of the deformation of the rib increases, and it causes defects.

・ The setting of the guide position is difficult for the tube wall thickness to thin. The effect of the guide position is small for the thin wall-tube extrusion.

・ When the thin-wall tube is extruded, it is necessary to improve device to reduce the extrusion ratio for enhancing the efficiency of guide position control.

References

[1] Takahiro Makiyama and Makoto Murata: “Controlling Inside Diameter of Circular Tube by Extrusion”, Materials Science Forum Vol. 396-402, (2002), 513-518

[2] Katsuyoshi Saito and Katsumi Watanabe: “Co-extruded aluminum composites”, Journal of Japan Institute of Light Metals, 35-5, (1985), 297-303

[3] T. Moroi, T. Kuboki and M. Murata: “Effect of temperature on tube extrusion and joining holed rib”, Steel research international, Vol.79, No.11, 2008, pp. 677-682

[4] T. Moroi, T. Kuboki and M. Murata: “A new extrusion method joining tube and sheet with holed rib”, Journal of Mechanical Science and Technology, Vol.21, No. 10, October 2007, pp. 1548-1552

[5] Rockfield Software Limited: ELFEN User Manual ver.3.0, Rockfield Software Limited (2000), 1.1-13.8.

[6] Turk, R., Perus, I. & Tercelj, M.: “New starting points for the prediction of tool wear in hot forging”, International Journal of Machine Tools and Manufacture, 44-12-13, (2004), 1319-1331

[7] Browne, M. T. and Hillery, M. T.: “Optimising the variables when deep-drawing C.R.1 cups”, Journal of Material Processing Technology, 136-1-3, (2003), 64-71


Numerical and experimental investigations of the production processes of coextruded Al/Mg- compounds and the strength of the interface

K. Kittner1,a, B. Awiszus1,b 1Chemnitz University of Technology, Institute of Machine Tools and Production Processes, -

Department of Virtual Production Engineering-, Reichenhainer Str. 70, 09126 Chemnitz, Germany [email protected], [email protected]

Keywords: Aluminium-magnesium compound, coextrusion, bonding strength, finite element method.

Introduction

Due to a changing environmental awareness and the improved use of resources, the application of light-weight materials, such as aluminium and magnesium, becomes increasingly important and partially substitutes the utilisation of conventional materials such as steel. However, a widespread application demands a better understanding of these materials. This concerns production processes of semi-finished products and the products itself. Coextruded aluminium-magnesium compounds are investigated in the subproject B3 (“Experimental and numerical investigations of the interface behavior of Al-Mg compounds”) which is part of the special research area 692 – HALS at the Chemnitz University of Technology. These compounds are characterized by a very good weight-strength-ratio and allow a wide field of application, for example in automotive industry. The compounds are manufactured in extrusion processes. The interface which is developed during the production is of special interest and the investigation of it is a shared aim of the Department of Experimental Mechanics and the Department of Virtual Production Processes. The two main tasks are the extrusion process optimisation and the microstructural, mechanical and thermal examination of the semi-finished product. The following paper gives an overview of the performed investigations in this subproject.

Investigation and analysis of compound extrusion processes

The focus is on the interface between both compound materials, which is developed during the extrusion process. The strength of the interface has an influence on the strength of the whole compound. It is necessary that the quality of the interface is impeccable, without cracks, and the strength is determinable. Therefore, it is possible to make a failure prediction of the compound particularly with regard to the interface for following forming processes as well as for the strength requirements of the part. In the hydrostatic extrusion process a punch imposes an indirect pressure on the billet with a

hydrostatic medium (castor oil). Thus, the billet is pressed through an extrusion die. A reduced abrasion, an improved surface quality and the possibility of higher plastic strain are achieved by fluid friction between billet and die as well as between container and billet. The difference compared to conventional extrusion processes is that the billet is tapered in order

to press it against the conical die. Thus, the latter is sealed and the hydrostatic medium can be compress. In addition to the description of the process, the procedural principle is depicted in Fig. 1. Müller et al. [1] explain the processes in detail.

Numerical and experimental investigations of the production processes of coextruded Al/Mg- compounds and the strength of the interface

K. Kittner1,a, B. Awiszus1,b 1Chemnitz University of Technology, Institute of Machine Tools and Production Processes, -

Department of Virtual Production Engineering-, Reichenhainer Str. 70, 09126 Chemnitz, Germany [email protected], [email protected]

Keywords: Aluminium-magnesium compound, coextrusion, bonding strength, finite element method.

Introduction

Due to a changing environmental awareness and the improved use of resources, the application of light-weight materials, such as aluminium and magnesium, becomes increasingly important and partially substitutes the utilisation of conventional materials such as steel. However, a widespread application demands a better understanding of these materials. This concerns production processes of semi-finished products and the products itself. Coextruded aluminium-magnesium compounds are investigated in the subproject B3 (“Experimental and numerical investigations of the interface behavior of Al-Mg compounds”) which is part of the special research area 692 – HALS at the Chemnitz University of Technology. These compounds are characterized by a very good weight-strength-ratio and allow a wide field of application, for example in automotive industry. The compounds are manufactured in extrusion processes. The interface which is developed during the production is of special interest and the investigation of it is a shared aim of the Department of Experimental Mechanics and the Department of Virtual Production Processes. The two main tasks are the extrusion process optimisation and the microstructural, mechanical and thermal examination of the semi-finished product. The following paper gives an overview of the performed investigations in this subproject.

Investigation and analysis of compound extrusion processes

The focus is on the interface between both compound materials, which is developed during the extrusion process. The strength of the interface has an influence on the strength of the whole compound. It is necessary that the quality of the interface is impeccable, without cracks, and the strength is determinable. Therefore, it is possible to make a failure prediction of the compound particularly with regard to the interface for following forming processes as well as for the strength requirements of the part. In the hydrostatic extrusion process a punch imposes an indirect pressure on the billet with a

hydrostatic medium (castor oil). Thus, the billet is pressed through an extrusion die. A reduced abrasion, an improved surface quality and the possibility of higher plastic strain are achieved by fluid friction between billet and die as well as between container and billet. The difference compared to conventional extrusion processes is that the billet is tapered in order

to press it against the conical die. Thus, the latter is sealed and the hydrostatic medium can be compress. In addition to the description of the process, the procedural principle is depicted in Fig. 1. Müller et al. [1] explain the processes in detail.


Fig. 1: procedural principle of the hydrostatic extrusion process (HSP)

The hydrostatic extrusion compounds are produced by CEP Corporation in Freiberg, Saxony, the indirect extrusion by the Extrusion Research and Development Center at the TU Berlin. In addition to the billet and the die, the container and dummy block can also be heated in the indirect extrusion process. Among other things, the difference between both processes is noticeable in the force displacement curves.

Fig. 2: force displacement curves of extrusion processes

Fig. 2 shows the comparison of force displacement curves of the hydrostatic extrusion, in the following short-named as HSP and indirect extrusion process, in the following short-named as ISP. The three lower curves show the hydrostatic process with different process parameters, such as heating temperature (450°C and 300°C) and plastic strain (2.77 and 4.16). It is noticeable that the force rises during the process. This fact is well founded in the cooling of the billet. For this reason the yield stress is increasing and therefore the force is increasing, too. In the opposite the curve on the top reflected a constant force level during the indirect extrusion process ( plastic strain 3.2). As can be seen, an important parameter is the temperature. The numerical simulation reflected

this fact for the hydrostatic extrusion process. The temperature range is from 325 °C at the beginning to 285°C at the end of the process. In Fig. 3 you can see the comparison of the force displacement curves between the real process and the numerical simulation. The force levels correspond over the whole process. Fig. 4 shows the temperature field in the region of the die, on the left hand side at the beginning and on the right hand side at the end of the process.

Fig. 1: procedural principle of the hydrostatic extrusion process (HSP)

The hydrostatic extrusion compounds are produced by CEP Corporation in Freiberg, Saxony, the indirect extrusion by the Extrusion Research and Development Center at the TU Berlin. In addition to the billet and the die, the container and dummy block can also be heated in the indirect extrusion process. Among other things, the difference between both processes is noticeable in the force displacement curves.

Fig. 2: force displacement curves of extrusion processes

Fig. 2 shows the comparison of force displacement curves of the hydrostatic extrusion, in the following short-named as HSP and indirect extrusion process, in the following short-named as ISP. The three lower curves show the hydrostatic process with different process parameters, such as heating temperature (450°C and 300°C) and plastic strain (2.77 and 4.16). It is noticeable that the force rises during the process. This fact is well founded in the cooling of the billet. For this reason the yield stress is increasing and therefore the force is increasing, too. In the opposite the curve on the top reflected a constant force level during the indirect extrusion process ( plastic strain 3.2). As can be seen, an important parameter is the temperature. The numerical simulation reflected

this fact for the hydrostatic extrusion process. The temperature range is from 325 °C at the beginning to 285°C at the end of the process. In Fig. 3 you can see the comparison of the force displacement curves between the real process and the numerical simulation. The force levels correspond over the whole process. Fig. 4 shows the temperature field in the region of the die, on the left hand side at the beginning and on the right hand side at the end of the process.


Fig. 3: comparison of force curves (HSP)

a) b) Fig. 4: a) temperature field in the region of the die at the beginning (HSP); b) temperature field at

the end of the process (HSP) In the hydrostatic extrusion process high quality strands, compounds made of Al99.5/AZ31 and Al99.5/Mg, could be achieved without cracks. For partially bonded compounds (AlMgSi1/AZ31) some areas of the interface were showing cracks, Fig. 5 [2]. The numerical analysis shows high shear stress in the interface in the region of the die, Fig. 6. If the stress becomes too high, the interface cannot transmit the stress and so cracks are induced. The shear stress is based on the die geometry, the different flow behaviour of the materials and on tribology conditions. With the possibility of changing the die design the shear stress can be reduced. The hydrostatic extrusion process provides better lubrication conditions, due to the fact that the castor oil flows into the die and decreases the friction stress between die and billet. For the indirect extrusion process it is more complicated to adapt the die design for reducing the friction. In the next working steps, this problem will be examined more closely and measures will be adopted that improve the strand quality.

Fig. 3: comparison of force curves (HSP)

a) b) Fig. 4: a) temperature field in the region of the die at the beginning (HSP); b) temperature field at

the end of the process (HSP) In the hydrostatic extrusion process high quality strands, compounds made of Al99.5/AZ31 and Al99.5/Mg, could be achieved without cracks. For partially bonded compounds (AlMgSi1/AZ31) some areas of the interface were showing cracks, Fig. 5 [2]. The numerical analysis shows high shear stress in the interface in the region of the die, Fig. 6. If the stress becomes too high, the interface cannot transmit the stress and so cracks are induced. The shear stress is based on the die geometry, the different flow behaviour of the materials and on tribology conditions. With the possibility of changing the die design the shear stress can be reduced. The hydrostatic extrusion process provides better lubrication conditions, due to the fact that the castor oil flows into the die and decreases the friction stress between die and billet. For the indirect extrusion process it is more complicated to adapt the die design for reducing the friction. In the next working steps, this problem will be examined more closely and measures will be adopted that improve the strand quality.


a) b) c)

Fig. 5: a) axial cut of compound piece; b) micrograph of the interface with cracks, c) dye penetrant test indicates cracks in the interface (ISP)

a) b)

Fig. 6: a) shear stress in the region of the die (HSP); b) detail picture of shear stress (HSP)

Analysis and determination of the interface strength

In addition to the previous investigations, the Department of Experimental Mechanics developed loading tests for the compounds within the project [2]. These tests allow the determination of the compound strength and they revealed that the latter, and in particular the interface strength, is high which means that it is approximately as high as the flow stress of the softer compound material. These tests are a push-out-test and a bending test, Fig.7.

a) b)

Fig. 7: a) schematic sketch – push-out test; b) schematic sketch – bending test

a) b) c)

Fig. 5: a) axial cut of compound piece; b) micrograph of the interface with cracks, c) dye penetrant test indicates cracks in the interface (ISP)

a) b)

Fig. 6: a) shear stress in the region of the die (HSP); b) detail picture of shear stress (HSP)

Analysis and determination of the interface strength

In addition to the previous investigations, the Department of Experimental Mechanics developed loading tests for the compounds within the project [2]. These tests allow the determination of the compound strength and they revealed that the latter, and in particular the interface strength, is high which means that it is approximately as high as the flow stress of the softer compound material. These tests are a push-out-test and a bending test, Fig.7.

a) b)

Fig. 7: a) schematic sketch – push-out test; b) schematic sketch – bending test


The first approach was to describe the interface behaviour with macromechanical damage criteria [3], but this is especially insufficient for alloyed compounds (AlMgSi1/AZ31). Therefore, the new approach was to visualize the behaviour with a separation criterion: the contact normal stress/ shear stress. The advantage is that the separation stress can be obtained directly from the loading tests and that it is independent from the loading test or the following forming process. If the separation stress is reached, a crack is induced in the interface. However, it is not possible to carry out loading tests for every compound and application part.

Additionally, the bond strength can differ in a single process. Thus, the aim is to determine the strength based on the extrusion process parameters, e.g. by using bond strength models. So far models according to Vaidyanath [4,5], Eq. 1 and Bay [6,5] have been analyzed. Both are developed for rolling processes and compute a bond strength value between the compound materials. A significant factor is the enlargement of the contact surface during the extrusion process as new

bondable surfaces are generated. If these new surfaces touch, a bond is created, whose strength can be computed according to the above-mentioned models. The objective is to apply these models to the extrusion process and to compute the interface strength. This seems to be appropriate since the computed bond strength values based on given parameters taken from the below-mentioned literature and the extrusion process are very close to the experimental values from the loading tests [3]. Fig. 8 illustrates the comparison of the computed interface strength values and the experimental values of unalloyed (Al99.5/Mg) and alloyed compounds (AlMgSi1/AZ31). The following equation demonstrates the computation of the interface strength according to Vaidyanath for a hydrostatic extrusion process (unalloyed compound Al99.5/Mg; plastic strain equals 2.77).

( ) solidVaiweld RR σσ ⋅−⋅=− 2 . 1

01

AAA

R−

= . (1)

Contact surface before extrusion process: A0 = 47100 mm² Contact surface after the process (whole geometry plastic strain 2.77): A1 = 188400 mm² yield stress of aluminium (Al99.5): σsolid = 95 "/mm²

²/89 mm"Vaiweld =−σ .

Fig. 8: a) comparison of interface strength; b) application of the interface strength value as separation value in a push out test

The aim is to compute the interface strength during the simulation of the hydrostatic extrusion process using an implemented user subroutine. The surface/ interface surface expansion is not directly computable. With the analysis of the plastic strains in spatial direction it is possible to determine the surface plastic strain and subsequently the surface expansion. This is applicable in the bond strength models, in example in the model according to Vaidyanath, Fig. 9, Eq. 2.

The first approach was to describe the interface behaviour with macromechanical damage criteria [3], but this is especially insufficient for alloyed compounds (AlMgSi1/AZ31). Therefore, the new approach was to visualize the behaviour with a separation criterion: the contact normal stress/ shear stress. The advantage is that the separation stress can be obtained directly from the loading tests and that it is independent from the loading test or the following forming process. If the separation stress is reached, a crack is induced in the interface. However, it is not possible to carry out loading tests for every compound and application part.

Additionally, the bond strength can differ in a single process. Thus, the aim is to determine the strength based on the extrusion process parameters, e.g. by using bond strength models. So far models according to Vaidyanath [4,5], Eq. 1 and Bay [6,5] have been analyzed. Both are developed for rolling processes and compute a bond strength value between the compound materials. A significant factor is the enlargement of the contact surface during the extrusion process as new

bondable surfaces are generated. If these new surfaces touch, a bond is created, whose strength can be computed according to the above-mentioned models. The objective is to apply these models to the extrusion process and to compute the interface strength. This seems to be appropriate since the computed bond strength values based on given parameters taken from the below-mentioned literature and the extrusion process are very close to the experimental values from the loading tests [3]. Fig. 8 illustrates the comparison of the computed interface strength values and the experimental values of unalloyed (Al99.5/Mg) and alloyed compounds (AlMgSi1/AZ31). The following equation demonstrates the computation of the interface strength according to Vaidyanath for a hydrostatic extrusion process (unalloyed compound Al99.5/Mg; plastic strain equals 2.77).

( ) solidVaiweld RR σσ ⋅−⋅=− 2 . 1

01

AAA

R−

= . (1)

Contact surface before extrusion process: A0 = 47100 mm² Contact surface after the process (whole geometry plastic strain 2.77): A1 = 188400 mm² yield stress of aluminium (Al99.5): σsolid = 95 "/mm²

²/89 mm"Vaiweld =−σ .

Fig. 8: a) comparison of interface strength; b) application of the interface strength value as separation value in a push out test

The aim is to compute the interface strength during the simulation of the hydrostatic extrusion process using an implemented user subroutine. The surface/ interface surface expansion is not directly computable. With the analysis of the plastic strains in spatial direction it is possible to determine the surface plastic strain and subsequently the surface expansion. This is applicable in the bond strength models, in example in the model according to Vaidyanath, Fig. 9, Eq. 2.


yysurface

surface

surfacegentialaxial

radialgentialaxial

rr

uu

ll

ϕϕ

ϕ

ϕϕϕ

ϕϕϕ

=

=

=+

=

+

+

=++

38.1

0lnlnln

0

tan

0

1

0

1

0

1

tan

l0 (x) - Length of billet before forming l1 (x) - Length of strand after forming u0 (z) - Circumference of magnesium before forming u1 (z) - Circumference of magnesium after forming r0 (y) - Radius of magnesium before forming r1 (y) - Radius of magnesium after forming

Fig. 9: Schematic diagram of deformation zone and partial plastic strain in the hydrostatic

extrusion process (HSP)

solidVaiweld yyyy eeσσ ϕϕ ⋅

−−⋅

−=−

112

11 . (2)

Fig. 10 shows the computed interface strength in the hydrostatic extrusion process. It is noticeable that the interface strength is increasing with the increasing of the equivalent plastic strain. This figure also shows the shear stress in the region of the die. In the area 1, 2 and 3 the radius is changing and in these areas the shear stress is especially high. As noted above, if the shear stress becomes too high in particular in area 1, then damaging of this region of the interface is possible.

Fig.10: developing of the interface strength, plastic strain and shear stress in the region of die (HSP)

yysurface

surface

surfacegentialaxial

radialgentialaxial

rr

uu

ll

ϕϕ

ϕ

ϕϕϕ

ϕϕϕ

=

=

=+

=

+

+

=++

38.1

0lnlnln

0

tan

0

1

0

1

0

1

tan

l0 (x) - Length of billet before forming l1 (x) - Length of strand after forming u0 (z) - Circumference of magnesium before forming u1 (z) - Circumference of magnesium after forming r0 (y) - Radius of magnesium before forming r1 (y) - Radius of magnesium after forming

Fig. 9: Schematic diagram of deformation zone and partial plastic strain in the hydrostatic

extrusion process (HSP)

solidVaiweld yyyy eeσσ ϕϕ ⋅

−−⋅

−=−

112

11 . (2)

Fig. 10 shows the computed interface strength in the hydrostatic extrusion process. It is noticeable that the interface strength is increasing with the increasing of the equivalent plastic strain. This figure also shows the shear stress in the region of the die. In the area 1, 2 and 3 the radius is changing and in these areas the shear stress is especially high. As noted above, if the shear stress becomes too high in particular in area 1, then damaging of this region of the interface is possible.

Fig.10: developing of the interface strength, plastic strain and shear stress in the region of die (HSP)


Fig.11 shows the computed interface strength according to Vaidyanath in the numerical simulation. The model was implemented by a user subroutine.

Fig.11: computed interface strength according to Vaidyanath in the numerical model (HSP)

Summary

The presented work in the framework of the subproject B3 as part of the special research area 692 - HALS - showed the investigations of the compound extrusion process. The significant parameters temperature and shear stress were analyzed. Furthermore it was discussed to apply bond strength models in extrusion processes in order to compute the interface strength between the aluminium and the magnesium. The computed interface values are corresponding to the experimental values. Thus in the next steps the models were further developed and implemented in the numerical

model by means of user subroutines.

References

[1] Müller, K. et al.: Fundamentals of Extrusion Technology, Giesel Verlag, Isernhagen, 2004.

[2] Awiszus, B.; Naumann, J; Stockmann, M.; Kittner, K.; Lehmann, T.: Experimentelle und numerische Untersuchungen zur Grenzschicht von Al/Mg-Werkstoffverbunden, 1. SFB 692 Kolloquium, Schriftenreihe: Werkstoffe und Werkstofftechnische Anwendungen, Band 25, Eigenverlag Chemnitz, 2007, p. 55-64.

[3] Awiszus, B.; Kittner, K.: Examinations and simulation of the interface of an aluminium- magnesium compound. Tagungsband zur 9th International Conference on Technology of Plasticity (9th ICTP 2008), Gyeongju, Korea, September 7- 11 2008, p.258-259.

[4] Vaidyanath, L.R.; Nicholas, M.G.; Milner, D.R.: Pressure welding by rolling, British Welding Journal, 1959, 1, 13-28.

[5] Bay, N.: Bond Strength in Cold Roll Bonding, Annals of the CIRP, 1985, 34 N.1, p.221-224.

[6] Schmidtchen, M.; Hajduk, D.; Simecek P.: Die Haftfestigkeit von Walzplattierungen, deren Bestimmung und Simulation. Tagungsband MEFORM, Freiberg 2004, p. 81-110.

Fig.11 shows the computed interface strength according to Vaidyanath in the numerical simulation. The model was implemented by a user subroutine.

Fig.11: computed interface strength according to Vaidyanath in the numerical model (HSP)

Summary

The presented work in the framework of the subproject B3 as part of the special research area 692 - HALS - showed the investigations of the compound extrusion process. The significant parameters temperature and shear stress were analyzed. Furthermore it was discussed to apply bond strength models in extrusion processes in order to compute the interface strength between the aluminium and the magnesium. The computed interface values are corresponding to the experimental values. Thus in the next steps the models were further developed and implemented in the numerical

model by means of user subroutines.

References

[1] Müller, K. et al.: Fundamentals of Extrusion Technology, Giesel Verlag, Isernhagen, 2004.

[2] Awiszus, B.; Naumann, J; Stockmann, M.; Kittner, K.; Lehmann, T.: Experimentelle und numerische Untersuchungen zur Grenzschicht von Al/Mg-Werkstoffverbunden, 1. SFB 692 Kolloquium, Schriftenreihe: Werkstoffe und Werkstofftechnische Anwendungen, Band 25, Eigenverlag Chemnitz, 2007, p. 55-64.

[3] Awiszus, B.; Kittner, K.: Examinations and simulation of the interface of an aluminium- magnesium compound. Tagungsband zur 9th International Conference on Technology of Plasticity (9th ICTP 2008), Gyeongju, Korea, September 7- 11 2008, p.258-259.

[4] Vaidyanath, L.R.; Nicholas, M.G.; Milner, D.R.: Pressure welding by rolling, British Welding Journal, 1959, 1, 13-28.

[5] Bay, N.: Bond Strength in Cold Roll Bonding, Annals of the CIRP, 1985, 34 N.1, p.221-224.

[6] Schmidtchen, M.; Hajduk, D.; Simecek P.: Die Haftfestigkeit von Walzplattierungen, deren Bestimmung und Simulation. Tagungsband MEFORM, Freiberg 2004, p. 81-110.


The use of extruded profiles as filling material in Friction Stir Welding (FSW)

L. Donati1, a and L. Tomesani1,b 1University of Bologna, DIEM Department, Viale Risorgimento 2, 40136 Bologna, Italy

[email protected], [email protected]

Keywords: Friction Stir Welding, AA6082, filling material, extruded profile. Abstract. In this paper, an innovative approach is presented for joining two sheets with an extruded profile all made by AA6082-T6 aluminum alloy. The tested configuration is the T-joint and the innovation presented in this paper is the use of a specially design appendix of the extruded profile as filler material during the friction welding. In particular three configurations were analyzed: without appendix, with I appendix and with T appendix. In the experiments, several process parameters and PIN shapes were investigated in order to determine optimal processing conditions able to produce an effective sound weld. Specimens were extracted from the joint and tensile tests were performed along the sheet direction thus allowing a comparison of the welded sections respect to the base material. It was found that the appendixes of the extrude profile are able to effectively fill the distance between the sheets and, in particular with the T shape, a gap up to 1,7 mm on the retreating side was successfully welded.

Introduction

The friction stir welding (FSW) joining technology is a process developed in 1991 by TWI [1] and since its development it had been object of deep investigation and advance worldwide. The great interest around this technology is mainly related to its intrinsic simplicity thus allowing remarkable energy savings from one side and very good joint proprieties on the other one.

The technology. In the FSW a tool named PIN is rotated at elevated speed (n, rpm) and moved along the path to be welded (fig. 1) with a particular feeding rate (vf, mm/min). The tool -in its more basic configuration- is characterized by the collet, the shoulder and the probe. The collet is used to connect the PIN to the machine mandrel while the probe –that in the most recent configurations may assume very complex shapes with flutes or grooves- stirs the material under welding. Finally, the shoulder produces the greatest amount of heat of the process by means of friction. Seldom, the PIN plunges and welds the material with a straight angle (90°) while more often a tilt angle is used, hence producing a higher compression stress state in the trailing edge of the PIN (fig. 1). In the most recent and dedicated machines the pinch force applied to the tool is independently controlled and it is used to regulate the contact between the tools shoulder and the workpiece surface thus changing the friction extent. The FSW is a solid-state joining process, thus meaning that the metal is heated during the process but it never melts. This is very useful for metals where the melted phase produces relevant defects during welding like for some aluminum alloys. As consequence the process is primarily used on aluminum alloys, or combinations of different alloys but it is also applied on copper (and its alloys), titanium (and its alloys), magnesium alloys, plastics, mild steels and C-Mn steels or stainless steel (austenitic, martensitic and duplex) [2].

Another interesting aspect of the process is the joint asymmetry; the combination of rotation speed and feeding rate always produce two separate edge of the joint: the advancing side (A.S.) and the retreating one (R.S.). In the advancing side the component of the rotation speed has the same direction of the feeding rate, while in the retreating such velocities are opposed. As visible in micrographs [3] the final effect is an asymmetric joint with the bonding surface always located on the advancing side of the junction.

The use of extruded profiles as filling material in Friction Stir Welding (FSW)

L. Donati1, a and L. Tomesani1,b 1University of Bologna, DIEM Department, Viale Risorgimento 2, 40136 Bologna, Italy

[email protected], [email protected]

Keywords: Friction Stir Welding, AA6082, filling material, extruded profile. Abstract. In this paper, an innovative approach is presented for joining two sheets with an extruded profile all made by AA6082-T6 aluminum alloy. The tested configuration is the T-joint and the innovation presented in this paper is the use of a specially design appendix of the extruded profile as filler material during the friction welding. In particular three configurations were analyzed: without appendix, with I appendix and with T appendix. In the experiments, several process parameters and PIN shapes were investigated in order to determine optimal processing conditions able to produce an effective sound weld. Specimens were extracted from the joint and tensile tests were performed along the sheet direction thus allowing a comparison of the welded sections respect to the base material. It was found that the appendixes of the extrude profile are able to effectively fill the distance between the sheets and, in particular with the T shape, a gap up to 1,7 mm on the retreating side was successfully welded.

Introduction

The friction stir welding (FSW) joining technology is a process developed in 1991 by TWI [1] and since its development it had been object of deep investigation and advance worldwide. The great interest around this technology is mainly related to its intrinsic simplicity thus allowing remarkable energy savings from one side and very good joint proprieties on the other one.

The technology. In the FSW a tool named PIN is rotated at elevated speed (n, rpm) and moved along the path to be welded (fig. 1) with a particular feeding rate (vf, mm/min). The tool -in its more basic configuration- is characterized by the collet, the shoulder and the probe. The collet is used to connect the PIN to the machine mandrel while the probe –that in the most recent configurations may assume very complex shapes with flutes or grooves- stirs the material under welding. Finally, the shoulder produces the greatest amount of heat of the process by means of friction. Seldom, the PIN plunges and welds the material with a straight angle (90°) while more often a tilt angle is used, hence producing a higher compression stress state in the trailing edge of the PIN (fig. 1). In the most recent and dedicated machines the pinch force applied to the tool is independently controlled and it is used to regulate the contact between the tools shoulder and the workpiece surface thus changing the friction extent. The FSW is a solid-state joining process, thus meaning that the metal is heated during the process but it never melts. This is very useful for metals where the melted phase produces relevant defects during welding like for some aluminum alloys. As consequence the process is primarily used on aluminum alloys, or combinations of different alloys but it is also applied on copper (and its alloys), titanium (and its alloys), magnesium alloys, plastics, mild steels and C-Mn steels or stainless steel (austenitic, martensitic and duplex) [2].

Another interesting aspect of the process is the joint asymmetry; the combination of rotation speed and feeding rate always produce two separate edge of the joint: the advancing side (A.S.) and the retreating one (R.S.). In the advancing side the component of the rotation speed has the same direction of the feeding rate, while in the retreating such velocities are opposed. As visible in micrographs [3] the final effect is an asymmetric joint with the bonding surface always located on the advancing side of the junction.


Fig. 1. FSW process in butt joint configuration Joint configurations. In the FSW usually two sheets are joined by means of described in literature or patents [1require the joining of three or more bodies in order to realize a structural componentthe bodies assume a configurations like in fig. joint or corner welds, and very often they authors will evaluate the quality of joints performed between two thin sheets and a thick extruded profile in the T-joint configuration. profiles show almost the same mechanical proprieties of rolled sheets extruded to a desired shape (L shape, C shape, I shape with or without appendix)sheets have to be properly bended in order to can be extruded at almost every kind of shaperolled sheets), thus allowing an optimized oriented design of the stru

Fig. 2. Joints configurations: (a)(e)Multiple-lap-joint; (f)T-lap-joint; Applications. The FSW technology is today applied in the manufacturing of components in the transportation industry such as trains, airplanes and ships because it allows to replace older technologies like mechanical fasteners or rivets, or to improve joint quality and energy efficiency of the former joining technologies like MIG, TIG or laser welding. The disadvantages of traditional technologies are well known: fasteners usually require sheets overlapping thus producing heterogeneous distribution of the stressassistance, and the achievable mechanical proprieties are lower than 50% of the base material due to the transition of metal to the liquid phase. Finally,technologies in joint manufacturing is usallows great advantages: process efficiency is near to 100%, no gas assistance and filling material are required and the joint quality can achieve a resistance up to the 80% of base material. Nevertheless, the extensive application of this technology in industrial production is strongly limited due to several reasons. First of allfor the selection of proper welding parameters and any changesthickness or tool shape require a new process parameter optimization. Thenfirmly constrained and clamped during the whole process strokeand consequently the presence of voids in the junction. specific ‘clamping devices’ that enforce the manufacturing of the joint on dedicated machines rather than directly on the f

FSW process in butt joint configuration and PIN shape.

In the FSW usually two sheets are joined by means of ed in literature or patents [1,3,4]. Nevertheless, some industrial applications of this process

require the joining of three or more bodies in order to realize a structural componentthe bodies assume a configurations like in fig. 2(f) or 2(c), these types of joint are usually

very often they are realized by joining three sheets [evaluate the quality of joints performed between two thin sheets and a thick extruded

joint configuration. The advantages of this approach are numerous: extruded almost the same mechanical proprieties of rolled sheets but they

(L shape, C shape, I shape with or without appendix)to be properly bended in order to assume the required final geometry.

almost every kind of shape at very low production costs (comparable to , thus allowing an optimized oriented design of the structural component.

Joints configurations: (a)Butt-Joint; (b)Edge-butt; (c)T-butt-joint;

joint; (g) Fillet-joint .

technology is today applied in the manufacturing of tion industry such as trains, airplanes and ships because it allows to

replace older technologies like mechanical fasteners or rivets, or to improve joint quality and energy technologies like MIG, TIG or laser welding. The disadvantages of

traditional technologies are well known: fasteners usually require sheets overlapping thus producing heterogeneous distribution of the stress, whereas thermal processes need filling materialassistance, and the achievable mechanical proprieties are lower than 50% of the base material due to the transition of metal to the liquid phase. Finally, an overall low energy efficientechnologies in joint manufacturing is usually observed. In this direction the FSW technology allows great advantages: process efficiency is near to 100%, no gas assistance and filling material are required and the joint quality can achieve a resistance up to the 80% of base material.

s, the extensive application of this technology in industrial production is strongly First of all, the process has a low flexibility: it requires lots of trials

for the selection of proper welding parameters and any changes like in material composition, or thickness or tool shape require a new process parameter optimization. Then

during the whole process stroke in order to avoid sheets separation of voids in the junction. Such problems are produce also a precise positioning of the sheets

the manufacturing of the joint on dedicated machines rather than directly on the f

In the FSW usually two sheets are joined by means of the rotating PIN as Nevertheless, some industrial applications of this process

require the joining of three or more bodies in order to realize a structural component (fig. 2). When hese types of joint are usually called T-

are realized by joining three sheets [5]. In this work the evaluate the quality of joints performed between two thin sheets and a thick extruded

The advantages of this approach are numerous: extruded but they can be directly

(L shape, C shape, I shape with or without appendix), while rolled geometry. Indeed, a profile

at very low production costs (comparable to simple ctural component.

joint; (d)Overlap-joint;

technology is today applied in the manufacturing of lightweight tion industry such as trains, airplanes and ships because it allows to


traditional technologies are well known: fasteners usually require sheets overlapping thus producing whereas thermal processes need filling material and/or gas

assistance, and the achievable mechanical proprieties are lower than 50% of the base material due to an overall low energy efficiency of traditional

n this direction the FSW technology allows great advantages: process efficiency is near to 100%, no gas assistance and filling material are required and the joint quality can achieve a resistance up to the 80% of base material.

s, the extensive application of this technology in industrial production is strongly the process has a low flexibility: it requires lots of trials

in material composition, or thickness or tool shape require a new process parameter optimization. Then, the sheets must be

in order to avoid sheets separation avoided by the use of

precise positioning of the sheets but they finally the manufacturing of the joint on dedicated machines rather than directly on the final

Fig. 1. FSW process in butt joint configuration Joint configurations. In the FSW usually two sheets are joined by means of described in literature or patents [1require the joining of three or more bodies in order to realize a structural componentthe bodies assume a configurations like in fig. joint or corner welds, and very often they authors will evaluate the quality of joints performed between two thin sheets and a thick extruded profile in the T-joint configuration. profiles show almost the same mechanical proprieties of rolled sheets extruded to a desired shape (L shape, C shape, I shape with or without appendix)sheets have to be properly bended in order to can be extruded at almost every kind of shaperolled sheets), thus allowing an optimized oriented design of the stru

Fig. 2. Joints configurations: (a)(e)Multiple-lap-joint; (f)T-lap-joint; Applications. The FSW technology is today applied in the manufacturing of components in the transportation industry such as trains, airplanes and ships because it allows to replace older technologies like mechanical fasteners or rivets, or to improve joint quality and energy efficiency of the former joining technologies like MIG, TIG or laser welding. The disadvantages of traditional technologies are well known: fasteners usually require sheets overlapping thus producing heterogeneous distribution of the stressassistance, and the achievable mechanical proprieties are lower than 50% of the base material due to the transition of metal to the liquid phase. Finally,technologies in joint manufacturing is usallows great advantages: process efficiency is near to 100%, no gas assistance and filling material are required and the joint quality can achieve a resistance up to the 80% of base material. Nevertheless, the extensive application of this technology in industrial production is strongly limited due to several reasons. First of allfor the selection of proper welding parameters and any changesthickness or tool shape require a new process parameter optimization. Thenfirmly constrained and clamped during the whole process strokeand consequently the presence of voids in the junction. specific ‘clamping devices’ that enforce the manufacturing of the joint on dedicated machines rather than directly on the f

FSW process in butt joint configuration and PIN shape.

In the FSW usually two sheets are joined by means of ed in literature or patents [1,3,4]. Nevertheless, some industrial applications of this process

require the joining of three or more bodies in order to realize a structural componentthe bodies assume a configurations like in fig. 2(f) or 2(c), these types of joint are usually

very often they are realized by joining three sheets [evaluate the quality of joints performed between two thin sheets and a thick extruded

joint configuration. The advantages of this approach are numerous: extruded almost the same mechanical proprieties of rolled sheets but they

(L shape, C shape, I shape with or without appendix)to be properly bended in order to assume the required final geometry.

almost every kind of shape at very low production costs (comparable to , thus allowing an optimized oriented design of the structural component.

Joints configurations: (a)Butt-Joint; (b)Edge-butt; (c)T-butt-joint;

joint; (g) Fillet-joint .

technology is today applied in the manufacturing of tion industry such as trains, airplanes and ships because it allows to


traditional technologies are well known: fasteners usually require sheets overlapping thus producing heterogeneous distribution of the stress, whereas thermal processes need filling materialassistance, and the achievable mechanical proprieties are lower than 50% of the base material due to the transition of metal to the liquid phase. Finally, an overall low energy efficientechnologies in joint manufacturing is usually observed. In this direction the FSW technology allows great advantages: process efficiency is near to 100%, no gas assistance and filling material are required and the joint quality can achieve a resistance up to the 80% of base material.

s, the extensive application of this technology in industrial production is strongly First of all, the process has a low flexibility: it requires lots of trials

for the selection of proper welding parameters and any changes like in material composition, or thickness or tool shape require a new process parameter optimization. Then

during the whole process stroke in order to avoid sheets separation of voids in the junction. Such problems are produce also a precise positioning of the sheets

the manufacturing of the joint on dedicated machines rather than directly on the f

In the FSW usually two sheets are joined by means of the rotating PIN as Nevertheless, some industrial applications of this process

require the joining of three or more bodies in order to realize a structural component (fig. 2). When hese types of joint are usually called T-

are realized by joining three sheets [5]. In this work the evaluate the quality of joints performed between two thin sheets and a thick extruded

The advantages of this approach are numerous: extruded but they can be directly

(L shape, C shape, I shape with or without appendix), while rolled geometry. Indeed, a profile

at very low production costs (comparable to simple ctural component.

joint; (d)Overlap-joint;

technology is today applied in the manufacturing of lightweight tion industry such as trains, airplanes and ships because it allows to


traditional technologies are well known: fasteners usually require sheets overlapping thus producing whereas thermal processes need filling material and/or gas

assistance, and the achievable mechanical proprieties are lower than 50% of the base material due to an overall low energy efficiency of traditional

n this direction the FSW technology allows great advantages: process efficiency is near to 100%, no gas assistance and filling material are required and the joint quality can achieve a resistance up to the 80% of base material.

s, the extensive application of this technology in industrial production is strongly the process has a low flexibility: it requires lots of trials

in material composition, or thickness or tool shape require a new process parameter optimization. Then, the sheets must be

in order to avoid sheets separation avoided by the use of

precise positioning of the sheets but they finally the manufacturing of the joint on dedicated machines rather than directly on the final


product (while this is possible with older technologies). As a consequence the FSW technology is today rarely applied and mostly in the production of very long and repetitive junction like in train, airplanes or ship construction.

In order to overcome the limitations latter described, the authors decided to study the application of the FSW technology in the welding of aluminum sheets on extrude profiles in the T-joint configuration. In particular they introduced an appendix on the top surface of the extrudate in order to use such appendix as filling material during the welding stroke. Several sheet distances, PIN shapes and process parameters were investigated in order to verify the consistent enlargement of the process tolerances. Three profile shape configurations were investigated as reported in figure 3: no appendix, I appendix and T appendix.

Fig. 3. Profile shapes, without appendix, I appendix and T appendix

Experimental Trials

All the specimens were produced by welding AA6082-T6 500x100x3mm rolled strips (MicroVikers Hardness 114HV) to an AA6082-T6 extruded profile (97 HV) by means of a rotating PIN made by AISI H-11 tempered tool steel (48 HRC). Tensile tests performed on the transverse rolling direction on the sheets evidenced a proof strength of 300MPa, an Ultimate Tensile Strength-UTS equal to 330MPa, and an elongation e%=11, while for the extruded profile an UTS equal to 310Mpa and e%=10 was found. The FSW processes were carried out on a CAMU FU35 milling machine with discrete adjustment of the rotating speed and feeding rate.

Fig 4. Pin shape and tilt angle effect o appendix Tests. Five different tool shapes were evaluated, as reported in fig.(5); all the PINs were characterized by a shoulder of 20 mm diameter and a global length of the probe of 8mm. The main difference between the several tools was the probe shape: conical, straight and reversed conical were applied with the aim of evaluating the behavior of metal flow. The first PIN (referred to as CL in the following) had a conical shape with the diameter decreasing from 6mm at the shoulder to 4mm at the tip. The second one (SS) had a cylindrical surface of 6mm diameter with a

vf

product (while this is possible with older technologies). As a consequence the FSW technology is today rarely applied and mostly in the production of very long and repetitive junction like in train, airplanes or ship construction.

In order to overcome the limitations latter described, the authors decided to study the application of the FSW technology in the welding of aluminum sheets on extrude profiles in the T-joint configuration. In particular they introduced an appendix on the top surface of the extrudate in order to use such appendix as filling material during the welding stroke. Several sheet distances, PIN shapes and process parameters were investigated in order to verify the consistent enlargement of the process tolerances. Three profile shape configurations were investigated as reported in figure 3: no appendix, I appendix and T appendix.

Fig. 3. Profile shapes, without appendix, I appendix and T appendix

Experimental Trials

All the specimens were produced by welding AA6082-T6 500x100x3mm rolled strips (MicroVikers Hardness 114HV) to an AA6082-T6 extruded profile (97 HV) by means of a rotating PIN made by AISI H-11 tempered tool steel (48 HRC). Tensile tests performed on the transverse rolling direction on the sheets evidenced a proof strength of 300MPa, an Ultimate Tensile Strength-UTS equal to 330MPa, and an elongation e%=11, while for the extruded profile an UTS equal to 310Mpa and e%=10 was found. The FSW processes were carried out on a CAMU FU35 milling machine with discrete adjustment of the rotating speed and feeding rate.

Fig 4. Pin shape and tilt angle effect o appendix Tests. Five different tool shapes were evaluated, as reported in fig.(5); all the PINs were characterized by a shoulder of 20 mm diameter and a global length of the probe of 8mm. The main difference between the several tools was the probe shape: conical, straight and reversed conical were applied with the aim of evaluating the behavior of metal flow. The first PIN (referred to as CL in the following) had a conical shape with the diameter decreasing from 6mm at the shoulder to 4mm at the tip. The second one (SS) had a cylindrical surface of 6mm diameter with a

vf


spherical end. Three more pin geometries were then realized with a reverse conical shape (RC), with 6mm diameter at the shoulder increasing to 8mm and a 0,4 connecting radius. RC.1 was characterized by a spherical end, RC.2 by an inclination of the PIN shoulder equal to the tilt angle (3°) while the RC.3 presented a flat probe end. The guidelines for PIN design were mainly based on the requirements of heat generation inside the extruded profile. In fact, it is usually recognized that the heat generated by the shoulder is mainly kept inside the strips, so that the temperatures of the extrude profiles remains too low. The design of a straight PIN or a reverse conical one is aimed to generate more heat by friction near the probe tip.

Table 1. No appendix experimental plan.

# Test PI n [rpm]

vf [mm/min]

Tilt [°]

UTS-average [MPa]

Elong. av. [%]

1 CL 1380 92 0° 188 16,3 2 CL 1380 92 3° 116 5,5 3 CL 1380 92 3° 135 9,9 4 CL 1380 58 3° 173 12 5 CL 1380 125 3° 196 15 6 CL 1380 92 3° 169 11,1 7 SS 1380 92 3° 131 6,6 8 RC. 1 1380 92 3° 75 3,4 9 RC. 2 1380 92 3° - - 10 RC. 3 1380 92 3° - -

In Table 1 the tested conditions are summarized: the feeding rate was varied in the range of 58-

128 mm/min while a high spindle speeds (1380 rpm) was generally used; a 3° tilt angle was applied in almost all the conditions, as suggested by Fratini et alii. [3]. During the tests many problems arose in sheets clamping: sometimes the sheets were distanced by the probe action during the process stroke thus generating voids or the tunnel defect while other times the sheets were lifted from the profile surface due to thermal dilatations. The joined elements were then sectioned in specimens of 30mm thickness and named as X.1 to X.13 moving from the inlet to the outlet. The cross section of each specimen was then grinded to 1,6 Ra, in order to allow the analysis of the section. Finally, selected specimens were tensile tested on a servo-hydraulic Instron machine at a speed of 0,01mm/sec.

I appendix Tests. In order to allow wider tolerances between the bodies, the configuration of the joint was modified with an appendix of 5x3mm placed on the upper zone of the extruded profile, as shown in fig.3. The small volume of material of the appendix was deformed during the FSW stroke and consequently acted as filler material between the sheets. In the experimental trials, two different PIN shapes and several process parameters were investigated in order to produce a sound weld. Different sheets positioning ranging from no distance up to 2 mm distance from the appendix were used in order to verify if the shortage of material can be overcome by the process. The used pin shapes are presented in figure 5: both shapes had a shoulder radius of 2mm. The pins were inclined by the tilt angle θ of 3° and 1,8°. The pin B was characterized by a bigger shoulder diameter, so as to increase the heat flux, and by a shoulder angle of 8°, in order to amplify the tilt angle effect. A summary of the tested conditions and process parameters are reported in table 2: the sheets distances were measured from the appendix (see fig. 3) and different values were used in the advancing side with respect to the retreating one, due to joint asymmetry. The initial processing conditions were chosen as they were optimized from the previous phase, and then modified in relation to joint aspect, process monitoring analysis and tensile test results. In particular the trials performed with PIN A evidenced a very poor strength. Micrographs showed that such PIN was unable to stir both the sheets properly thus being in relation with the small probe diameter (φ6-4mm) compared to the similar sheets distance (6mm). As a consequence a new pin was designed (PIN B) with increased probe diameter. In the trials some problems arose also on sheets clamping:

spherical end. Three more pin geometries were then realized with a reverse conical shape (RC), with 6mm diameter at the shoulder increasing to 8mm and a 0,4 connecting radius. RC.1 was characterized by a spherical end, RC.2 by an inclination of the PIN shoulder equal to the tilt angle (3°) while the RC.3 presented a flat probe end. The guidelines for PIN design were mainly based on the requirements of heat generation inside the extruded profile. In fact, it is usually recognized that the heat generated by the shoulder is mainly kept inside the strips, so that the temperatures of the extrude profiles remains too low. The design of a straight PIN or a reverse conical one is aimed to generate more heat by friction near the probe tip.

Table 1. No appendix experimental plan.

# Test PI n [rpm]

vf [mm/min]

Tilt [°]

UTS-average [MPa]

Elong. av. [%]

1 CL 1380 92 0° 188 16,3 2 CL 1380 92 3° 116 5,5 3 CL 1380 92 3° 135 9,9 4 CL 1380 58 3° 173 12 5 CL 1380 125 3° 196 15 6 CL 1380 92 3° 169 11,1 7 SS 1380 92 3° 131 6,6 8 RC. 1 1380 92 3° 75 3,4 9 RC. 2 1380 92 3° - - 10 RC. 3 1380 92 3° - -

In Table 1 the tested conditions are summarized: the feeding rate was varied in the range of 58-

128 mm/min while a high spindle speeds (1380 rpm) was generally used; a 3° tilt angle was applied in almost all the conditions, as suggested by Fratini et alii. [3]. During the tests many problems arose in sheets clamping: sometimes the sheets were distanced by the probe action during the process stroke thus generating voids or the tunnel defect while other times the sheets were lifted from the profile surface due to thermal dilatations. The joined elements were then sectioned in specimens of 30mm thickness and named as X.1 to X.13 moving from the inlet to the outlet. The cross section of each specimen was then grinded to 1,6 Ra, in order to allow the analysis of the section. Finally, selected specimens were tensile tested on a servo-hydraulic Instron machine at a speed of 0,01mm/sec.

I appendix Tests. In order to allow wider tolerances between the bodies, the configuration of the joint was modified with an appendix of 5x3mm placed on the upper zone of the extruded profile, as shown in fig.3. The small volume of material of the appendix was deformed during the FSW stroke and consequently acted as filler material between the sheets. In the experimental trials, two different PIN shapes and several process parameters were investigated in order to produce a sound weld. Different sheets positioning ranging from no distance up to 2 mm distance from the appendix were used in order to verify if the shortage of material can be overcome by the process. The used pin shapes are presented in figure 5: both shapes had a shoulder radius of 2mm. The pins were inclined by the tilt angle θ of 3° and 1,8°. The pin B was characterized by a bigger shoulder diameter, so as to increase the heat flux, and by a shoulder angle of 8°, in order to amplify the tilt angle effect. A summary of the tested conditions and process parameters are reported in table 2: the sheets distances were measured from the appendix (see fig. 3) and different values were used in the advancing side with respect to the retreating one, due to joint asymmetry. The initial processing conditions were chosen as they were optimized from the previous phase, and then modified in relation to joint aspect, process monitoring analysis and tensile test results. In particular the trials performed with PIN A evidenced a very poor strength. Micrographs showed that such PIN was unable to stir both the sheets properly thus being in relation with the small probe diameter (φ6-4mm) compared to the similar sheets distance (6mm). As a consequence a new pin was designed (PIN B) with increased probe diameter. In the trials some problems arose also on sheets clamping:


in particular the sheets had the tendency to lift from the surface of the extrude profile in proximity of weld centerline, as consequence of thermal dilatation.

Fig. 5. Modified PIN shape and appendix deformation during the welding stroke (PIN A).

Table 2: I shape appendix experimental plan.

# Test

PI n [rpm]

vf [mm/min]

Tilt [°]

Sheet distance [mm] d1[A.S.] d2[R.S.]

Temperature range in the extrudate [°C]

UTS [MPa]

1 A 1380 92 3° 1 1 300-350 52.9 2 A 1380 92 3° 1 1 350-380 42.3 3 A 1380 92 3° 1 1 350-380 37.4 4 A 950 92 3° 0 0 350 130 5 A 680 92 3° 0 0 300-350 134.5 6 A 1380 92 3° 0 1 350-380 73.1 7 A 950 58 3° 0 1 350-400 115.6 8 B 680 92 3° 1 2 270-390 147.8 9 B 460 30 1.8° 1 2 410-450 95.0 10 B 460 58 1.8° 1 2 400-350 207.6 11 B 460 92 1.8° 1 2 400-340 150.6 12 B 460 125 1.8° 1 2 400-240 195.6

T appendix Tests. In order to overcome the clamping problems but at the same time to allow wider tolerances between the bodies, the configuration of the appendix was modified again towards a T-shape as shown in fig.3. From a production point of view the T shape does not increase production costs (because it’s obtained directly by extrusion) on the other hand it was able to produce the double effect of sheet clamping and material filling. In particular, the developed configuration of the T appendix allows compensating differences in sheet thickness through the 9° bottom angle, while the 1mm thick upper part of the T shape provides an adequate amount of material for welds filling. Moreover, it’s interesting to note that such a shape can be easily designed on the basis of the specific applications: if narrow tolerances are available the T thickness and bottom angle can be reduced, while if the assembly process requires high tolerances (like welding directly on the final product for example) such dimensions can be increased together with probe dimensions. In the trials only one configuration of the PIN was used (fig 6). A double step conical probe was designed: the thicker part (φ7-9mm) aimed in stirring the sheets located at 4,3mm distance and the smaller one (φ1,7-3) with rounded tip so as to smooth the progress of material flow in the extruded profile. A φ22m shoulder, characterized by a 7° relieve angle was then used in order to facilitate appendix deformation during the process stroke in combination with the tilt angle.

in particular the sheets had the tendency to lift from the surface of the extrude profile in proximity of weld centerline, as consequence of thermal dilatation.

Fig. 5. Modified PIN shape and appendix deformation during the welding stroke (PIN A).

Table 2: I shape appendix experimental plan.

# Test

PI n [rpm]

vf [mm/min]

Tilt [°]

Sheet distance [mm] d1[A.S.] d2[R.S.]


UTS [MPa]

1 A 1380 92 3° 1 1 300-350 52.9 2 A 1380 92 3° 1 1 350-380 42.3 3 A 1380 92 3° 1 1 350-380 37.4 4 A 950 92 3° 0 0 350 130 5 A 680 92 3° 0 0 300-350 134.5 6 A 1380 92 3° 0 1 350-380 73.1 7 A 950 58 3° 0 1 350-400 115.6 8 B 680 92 3° 1 2 270-390 147.8 9 B 460 30 1.8° 1 2 410-450 95.0 10 B 460 58 1.8° 1 2 400-350 207.6 11 B 460 92 1.8° 1 2 400-340 150.6 12 B 460 125 1.8° 1 2 400-240 195.6

T appendix Tests. In order to overcome the clamping problems but at the same time to allow wider tolerances between the bodies, the configuration of the appendix was modified again towards a T-shape as shown in fig.3. From a production point of view the T shape does not increase production costs (because it’s obtained directly by extrusion) on the other hand it was able to produce the double effect of sheet clamping and material filling. In particular, the developed configuration of the T appendix allows compensating differences in sheet thickness through the 9° bottom angle, while the 1mm thick upper part of the T shape provides an adequate amount of material for welds filling. Moreover, it’s interesting to note that such a shape can be easily designed on the basis of the specific applications: if narrow tolerances are available the T thickness and bottom angle can be reduced, while if the assembly process requires high tolerances (like welding directly on the final product for example) such dimensions can be increased together with probe dimensions. In the trials only one configuration of the PIN was used (fig 6). A double step conical probe was designed: the thicker part (φ7-9mm) aimed in stirring the sheets located at 4,3mm distance and the smaller one (φ1,7-3) with rounded tip so as to smooth the progress of material flow in the extruded profile. A φ22m shoulder, characterized by a 7° relieve angle was then used in order to facilitate appendix deformation during the process stroke in combination with the tilt angle.


Fig. 6: Modified PIN shape and appendix deformation during the welding stroke

Table 3: T shape appendix experimental plan.

# Test PI n

[rpm] Vf

[mm/min] Tilt

6 17 680 92 7 17 680 125 8 17 680 250

10 17 680 125 12 17 680 92,125,250 13 17 680 125 14 17 680 250 16 17 680 125 17 17 680 250 18 17 680 300 19 17 680 420 20 17 680 600 21 17 680 125 22 17 680 250 23 17 680 300

24 17 680 420 A summary of the tested experimental conditions is reported in table 3. Initially the sheets were placed in contact with the appendix (0,6mm distance)verify if the lack of material can be overcome by the shoulder angle, different tilt angles were tested ranging from 3° up to 5°. Imaximum feeding rates were obtained for a tilt angle of 5°. No problems on sheets clamping or sheets opening were now evidenced thus verifying the functionality of the T shape appendix.


Selected specimens were tested along the sheets dirpresented in fig. 7 for the 3 different configuratidotted lines the resistance of the base material

In the configuration characterized by the absence of appendix, optimal conditions were obtained in test 5 (PIN CL, n=1380rpm, vf

resistance was obtained when the minor amount of heat was generated. After this consideration a thermal control of the extruded profile was performedelsewhere [6,7]. A resistance

shape and appendix deformation during the welding stroke


Tilt Angle [°]

Sheet distance [mm]


Start-end A.S. R.S.

4 0.6 0.6 375-385 3 0.6 0.6 385-370 3 0.6 0.6 400-300 3 0.6 1.5 400-330 4 0.6 1.5 420-300 4 0.6 1.7 380-400 4 0.6 1.7 330-330 5 0.6 1.7 375-330 5 0.6 1.7 300-310 5 0.6 1.7 355-325 5 0.6 1.7 310-260 5 0.6 1.7 310-240 3 0.6 1.7 375-375 3 0.6 1.7 375-350 3 0.6 1.7 350-310

3 0.6 1.7 345-240

A summary of the tested experimental conditions is reported in table 3. Initially the sheets were with the appendix (0,6mm distance) then a distance of 1,7mm was used of material can be overcome by the appendix deformation.

shoulder angle, different tilt angles were tested ranging from 3° up to 5°. Ifeeding rates were obtained for a tilt angle of 5°. No problems on sheets clamping or

sheets opening were now evidenced thus verifying the functionality of the T shape appendix.

sted along the sheets direction. UTS was recorded, the rfor the 3 different configurations of the appendix. In figure 7

dotted lines the resistance of the base material of extruded profile and of the shIn the configuration characterized by the absence of appendix, optimal conditions were obtained

f=125 and 3° tilt angle). In particular, it was evidenced that the best resistance was obtained when the minor amount of heat was generated. After this consideration a thermal control of the extruded profile was performed in subsequent trials as better described

resistance of around 200MPa was found in optimized conditions


Temperature range in the UTS [Mpa]

135-187 199-284 118-255 158-186 208-249 180-252 139-226 218-230 186-254 256-271 133-238

13-18 186-219 99-185 60-159

85-110

A summary of the tested experimental conditions is reported in table 3. Initially the sheets were then a distance of 1,7mm was used in order to

. Due to the particular shoulder angle, different tilt angles were tested ranging from 3° up to 5°. It was found that the

feeding rates were obtained for a tilt angle of 5°. No problems on sheets clamping or sheets opening were now evidenced thus verifying the functionality of the T shape appendix.

UTS was recorded, the results being ons of the appendix. In figure 7 are also reported in

the sheets. In the configuration characterized by the absence of appendix, optimal conditions were obtained

it was evidenced that the best resistance was obtained when the minor amount of heat was generated. After this consideration a

in subsequent trials as better described was found in optimized conditions that

Fig. 6: Modified PIN shape and appendix deformation during the welding stroke


# Test PI n

[rpm] Vf

[mm/min] Tilt

6 17 680 92 7 17 680 125 8 17 680 250

10 17 680 125 12 17 680 92,125,250 13 17 680 125 14 17 680 250 16 17 680 125 17 17 680 250 18 17 680 300 19 17 680 420 20 17 680 600 21 17 680 125 22 17 680 250 23 17 680 300

24 17 680 420 A summary of the tested experimental conditions is reported in table 3. Initially the sheets were placed in contact with the appendix (0,6mm distance)verify if the lack of material can be overcome by the shoulder angle, different tilt angles were tested ranging from 3° up to 5°. Imaximum feeding rates were obtained for a tilt angle of 5°. No problems on sheets clamping or sheets opening were now evidenced thus verifying the functionality of the T shape appendix.


Selected specimens were tested along the sheets dirpresented in fig. 7 for the 3 different configuratidotted lines the resistance of the base material

In the configuration characterized by the absence of appendix, optimal conditions were obtained in test 5 (PIN CL, n=1380rpm, vf

resistance was obtained when the minor amount of heat was generated. After this consideration a thermal control of the extruded profile was performedelsewhere [6,7]. A resistance



Tilt Angle [°]

Sheet distance [mm]


Start-end A.S. R.S.

4 0.6 0.6 375-385 3 0.6 0.6 385-370 3 0.6 0.6 400-300 3 0.6 1.5 400-330 4 0.6 1.5 420-300 4 0.6 1.7 380-400 4 0.6 1.7 330-330 5 0.6 1.7 375-330 5 0.6 1.7 300-310 5 0.6 1.7 355-325 5 0.6 1.7 310-260 5 0.6 1.7 310-240 3 0.6 1.7 375-375 3 0.6 1.7 375-350 3 0.6 1.7 350-310

3 0.6 1.7 345-240

A summary of the tested experimental conditions is reported in table 3. Initially the sheets were with the appendix (0,6mm distance) then a distance of 1,7mm was used of material can be overcome by the appendix deformation.

shoulder angle, different tilt angles were tested ranging from 3° up to 5°. Ifeeding rates were obtained for a tilt angle of 5°. No problems on sheets clamping or

sheets opening were now evidenced thus verifying the functionality of the T shape appendix.

sted along the sheets direction. UTS was recorded, the rfor the 3 different configurations of the appendix. In figure 7

dotted lines the resistance of the base material of extruded profile and of the shIn the configuration characterized by the absence of appendix, optimal conditions were obtained

f=125 and 3° tilt angle). In particular, it was evidenced that the best resistance was obtained when the minor amount of heat was generated. After this consideration a thermal control of the extruded profile was performed in subsequent trials as better described

resistance of around 200MPa was found in optimized conditions


Temperature range in the UTS [Mpa]

135-187 199-284 118-255 158-186 208-249 180-252 139-226 218-230 186-254 256-271 133-238

13-18 186-219 99-185 60-159

85-110

A summary of the tested experimental conditions is reported in table 3. Initially the sheets were then a distance of 1,7mm was used in order to

. Due to the particular shoulder angle, different tilt angles were tested ranging from 3° up to 5°. It was found that the

feeding rates were obtained for a tilt angle of 5°. No problems on sheets clamping or sheets opening were now evidenced thus verifying the functionality of the T shape appendix.

UTS was recorded, the results being ons of the appendix. In figure 7 are also reported in

the sheets. In the configuration characterized by the absence of appendix, optimal conditions were obtained

it was evidenced that the best resistance was obtained when the minor amount of heat was generated. After this consideration a

in subsequent trials as better described was found in optimized conditions that


corresponds to the 60% of the sheets base material resistance, but, on the other end, in some conditions elongations bigger than the base materialwill be explained shortly and it’s related to the loss of tempered condition of the alloy.

Fig 7. Tensile test results: (c) T shape appendix configuration

In the I shape appendix configuration, as already described, the t

with the PIN A; it generally produced stable conditions but with poor values of UTS, this being related with a limited deformation of the sheets when high sheet distance were usedof the probe). The PIN B, instead, produced higher UTS values, but with related to the very high temperatures produced by the bigger shoulder of temperatures were obtained (below 350°C), high resistance welds were produced. The UTS data of tests 8-12 are not so defective material). With this configurationn=460rpm, vf=58 and 125, respectively and 1,8in the range of 300-350°C.

In the T shape appendix configurationmoreover it was evidenced a limited scattering of the data.to the 7° relieve angle of the PIN shouconfiguration a maximum feeding rate of 600mm/min was achieved without any visible defects but with a very poor UTS resistance (below 20 MPa18 (n=680rpm, vf=300 5° tilt angle) being produced in a range of temperature between 325 and 355°C.

In butt joints obtained by FSW, a resistance In the tests performed here, tensile strengths ranged 40-82% of the base material resistance but with an elongation bigger than the base material oneexplained by considering that the T6 treatment (solubilisation, quenching and aging) of the three

a)

corresponds to the 60% of the sheets base material resistance, but, on the other end, in some conditions elongations bigger than the base material were found. The meaning of this phenomenon

ined shortly and it’s related to the loss of tempered condition of the alloy.

: (a) no appendix configuration, (b) I shape appendix

configuration and (d) specimen under testing.

In the I shape appendix configuration, as already described, the trials from 1 to 7 were performed A; it generally produced stable conditions but with poor values of UTS, this being

related with a limited deformation of the sheets when high sheet distance were usedB, instead, produced higher UTS values, but with a greater dispersion: this is

related to the very high temperatures produced by the bigger shoulder of PIN temperatures were obtained (below 350°C), high resistance welds were produced. The UTS data of

12 are not so defective compared to the base material (up to 75% of UTS of the base ). With this configuration, optimal conditions were obtained in test 10 and 12 (

respectively and 1,8° tilt angle) that produced the weld at a temperature

T shape appendix configuration the highest values of resistance were now found, moreover it was evidenced a limited scattering of the data. In particular it was found that, in relation to the 7° relieve angle of the PIN shoulder, a optimized 5° tilt angle was found. configuration a maximum feeding rate of 600mm/min was achieved without any visible defects but with a very poor UTS resistance (below 20 MPa, test 20). Optimal conditions were obtained in test

tilt angle) being produced in a range of temperature between 325 and

d by FSW, a resistance up to 100% of the base material , tensile strengths ranged instead between 140-270

% of the base material resistance but with an elongation in some conditions one. The decrease in UTS and the increase the T6 treatment (solubilisation, quenching and aging) of the three

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6

UT

S [M

pa

]

Test

UTS

Extr. Prof. Base material

Sheets base material

d) c)

b)

corresponds to the 60% of the sheets base material resistance, but, on the other end, in some . The meaning of this phenomenon


(a) no appendix configuration, (b) I shape appendix,

rials from 1 to 7 were performed A; it generally produced stable conditions but with poor values of UTS, this being

related with a limited deformation of the sheets when high sheet distance were used (small diameter a greater dispersion: this is

B. Again, when lower temperatures were obtained (below 350°C), high resistance welds were produced. The UTS data of

75% of UTS of the base re obtained in test 10 and 12 (PIN B,

tilt angle) that produced the weld at a temperature

es of resistance were now found, In particular it was found that, in relation

5° tilt angle was found. For this configuration a maximum feeding rate of 600mm/min was achieved without any visible defects but

Optimal conditions were obtained in test tilt angle) being produced in a range of temperature between 325 and

ase material can be achieved [5]. 70MPa corresponding to

in some conditions up to 17%, much in elongation can be

the T6 treatment (solubilisation, quenching and aging) of the three

7 8 9 10 11 12 13

corresponds to the 60% of the sheets base material resistance, but, on the other end, in some conditions elongations bigger than the base materialwill be explained shortly and it’s related to the loss of tempered condition of the alloy.

Fig 7. Tensile test results: (c) T shape appendix configuration

In the I shape appendix configuration, as already described, the t

with the PIN A; it generally produced stable conditions but with poor values of UTS, this being related with a limited deformation of the sheets when high sheet distance were usedof the probe). The PIN B, instead, produced higher UTS values, but with related to the very high temperatures produced by the bigger shoulder of temperatures were obtained (below 350°C), high resistance welds were produced. The UTS data of tests 8-12 are not so defective material). With this configurationn=460rpm, vf=58 and 125, respectively and 1,8in the range of 300-350°C.

In the T shape appendix configurationmoreover it was evidenced a limited scattering of the data.to the 7° relieve angle of the PIN shouconfiguration a maximum feeding rate of 600mm/min was achieved without any visible defects but with a very poor UTS resistance (below 20 MPa18 (n=680rpm, vf=300 5° tilt angle) being produced in a range of temperature between 325 and 355°C.

In butt joints obtained by FSW, a resistance In the tests performed here, tensile strengths ranged 40-82% of the base material resistance but with an elongation bigger than the base material oneexplained by considering that the T6 treatment (solubilisation, quenching and aging) of the three

a)

corresponds to the 60% of the sheets base material resistance, but, on the other end, in some conditions elongations bigger than the base material were found. The meaning of this phenomenon


: (a) no appendix configuration, (b) I shape appendix

configuration and (d) specimen under testing.

In the I shape appendix configuration, as already described, the trials from 1 to 7 were performed A; it generally produced stable conditions but with poor values of UTS, this being

related with a limited deformation of the sheets when high sheet distance were usedB, instead, produced higher UTS values, but with a greater dispersion: this is

related to the very high temperatures produced by the bigger shoulder of PIN temperatures were obtained (below 350°C), high resistance welds were produced. The UTS data of

12 are not so defective compared to the base material (up to 75% of UTS of the base ). With this configuration, optimal conditions were obtained in test 10 and 12 (

respectively and 1,8° tilt angle) that produced the weld at a temperature

T shape appendix configuration the highest values of resistance were now found, moreover it was evidenced a limited scattering of the data. In particular it was found that, in relation to the 7° relieve angle of the PIN shoulder, a optimized 5° tilt angle was found. configuration a maximum feeding rate of 600mm/min was achieved without any visible defects but with a very poor UTS resistance (below 20 MPa, test 20). Optimal conditions were obtained in test

tilt angle) being produced in a range of temperature between 325 and

d by FSW, a resistance up to 100% of the base material , tensile strengths ranged instead between 140-270

% of the base material resistance but with an elongation in some conditions one. The decrease in UTS and the increase the T6 treatment (solubilisation, quenching and aging) of the three

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6

UT

S [M

pa

]

Test

UTS

Extr. Prof. Base material

Sheets base material

d) c)

b)

corresponds to the 60% of the sheets base material resistance, but, on the other end, in some . The meaning of this phenomenon


(a) no appendix configuration, (b) I shape appendix,

rials from 1 to 7 were performed A; it generally produced stable conditions but with poor values of UTS, this being

related with a limited deformation of the sheets when high sheet distance were used (small diameter a greater dispersion: this is

B. Again, when lower temperatures were obtained (below 350°C), high resistance welds were produced. The UTS data of

75% of UTS of the base re obtained in test 10 and 12 (PIN B,

tilt angle) that produced the weld at a temperature

es of resistance were now found, In particular it was found that, in relation

5° tilt angle was found. For this configuration a maximum feeding rate of 600mm/min was achieved without any visible defects but

Optimal conditions were obtained in test tilt angle) being produced in a range of temperature between 325 and

ase material can be achieved [5]. 70MPa corresponding to

in some conditions up to 17%, much in elongation can be

the T6 treatment (solubilisation, quenching and aging) of the three

7 8 9 10 11 12 13


welding elements is partially modified by the alloy re-precipitation determined by the heat cycle determined by the FSW thermo-mechanical process. The consequence is a decrease in the UTS of the joint with an increase of its elongation: a condition that can be represented by a T3 or T4 tempering was also evidenced by microhardnesses performed on the specimens [7].

Conclusions

In this paper, an innovative use of specially design appendix of an extruded profile as filler material during the friction welding of AA6082-T6 aluminum alloy was presented and discussed. In particular three configurations were analyzed: without appendix, with I appendix and with T appendix. In the experiments, several process parameters and PIN shapes were investigated in order to determine optimal processing conditions able to produce an effective sound weld. A temperature control of the process allowed to determine optimal range of manufacturing temperatures (330-350°C) in relation to the lost of temper proprieties from one side and effective bonding on the other one. Specimens were extracted from the joint and tensile tests were performed along the sheet direction thus providing a resistance in the range of 60-82% of the base material depending on the used configuration. It was found that the appendixes of the extrude profile are able to effectively fill the distance between the sheets and, in particular with the T shape, a gap up to 1,7mm on the retreating side was successfully welded.

Acknowledgments

This work was carried out with the financial support of the University of Bologna (STRA06-Strategic Project Founding) which is acknowledged.

References

[1] W Thomas, WM; Nicholas, ED; Needham, JC; Murch, MG;Temple-Smith, P;Dawes, CJ. Friction-stir butt welding, GB Patent No. 9125978.8, International patent application No. PCT/GB92/02203, (1991) TWI, UK

[2] http://www.twi.co.uk/content/fswmat.html

[3] A. Barcellona, G. Buffa, L. Fratini, Process parameters analysis in friction stir welding of AA6082-T6 sheets, Proceedings of VIIth Esaform 2004 Conference (ed. S. Stören), Trondhaim, Norway, pp.371-374, May 28-30, 2004

[4] N. Oiwa, S. Iwaki, T. Okada, N. Eguchi, S. Tanaka, K. Namba, Studies on characteristics of friction stir welded joints in structural thin aluminium alloys part 1: Imperfections in friction stir welded zones and their precision non-destructive testing, Welding in the World, 49, no. 3-4, March/April, 76-82, 2005

[5] L. Fratini, F. Micari, A. Squillace, G. Giorleo, Experimental characterization of FSW T-joints of light alloys, Key Engineering Materials, 344, pp. 751-758, 2007.

[6] L. Donati, L. Tomesani, G. Minak, Friction Stir Welding Between Sheets and Extruded Profiles, Steel Research International, 79, Special Edition Metal Forming Conference 2008, Vol. 1, pp.671-676, 2008.

[7] L. Donati, L. Tomesani, A. Morri ”Structural T-joint produced by means of Friction Stir Welding (FSW) with filling material” under publishing on AIP Conference Proceedings (2009).

welding elements is partially modified by the alloy re-precipitation determined by the heat cycle determined by the FSW thermo-mechanical process. The consequence is a decrease in the UTS of the joint with an increase of its elongation: a condition that can be represented by a T3 or T4 tempering was also evidenced by microhardnesses performed on the specimens [7].

Conclusions

In this paper, an innovative use of specially design appendix of an extruded profile as filler material during the friction welding of AA6082-T6 aluminum alloy was presented and discussed. In particular three configurations were analyzed: without appendix, with I appendix and with T appendix. In the experiments, several process parameters and PIN shapes were investigated in order to determine optimal processing conditions able to produce an effective sound weld. A temperature control of the process allowed to determine optimal range of manufacturing temperatures (330-350°C) in relation to the lost of temper proprieties from one side and effective bonding on the other one. Specimens were extracted from the joint and tensile tests were performed along the sheet direction thus providing a resistance in the range of 60-82% of the base material depending on the used configuration. It was found that the appendixes of the extrude profile are able to effectively fill the distance between the sheets and, in particular with the T shape, a gap up to 1,7mm on the retreating side was successfully welded.

Acknowledgments

This work was carried out with the financial support of the University of Bologna (STRA06-Strategic Project Founding) which is acknowledged.

References

[1] W Thomas, WM; Nicholas, ED; Needham, JC; Murch, MG;Temple-Smith, P;Dawes, CJ. Friction-stir butt welding, GB Patent No. 9125978.8, International patent application No. PCT/GB92/02203, (1991) TWI, UK

[2] http://www.twi.co.uk/content/fswmat.html

[3] A. Barcellona, G. Buffa, L. Fratini, Process parameters analysis in friction stir welding of AA6082-T6 sheets, Proceedings of VIIth Esaform 2004 Conference (ed. S. Stören), Trondhaim, Norway, pp.371-374, May 28-30, 2004

[4] N. Oiwa, S. Iwaki, T. Okada, N. Eguchi, S. Tanaka, K. Namba, Studies on characteristics of friction stir welded joints in structural thin aluminium alloys part 1: Imperfections in friction stir welded zones and their precision non-destructive testing, Welding in the World, 49, no. 3-4, March/April, 76-82, 2005

[5] L. Fratini, F. Micari, A. Squillace, G. Giorleo, Experimental characterization of FSW T-joints of light alloys, Key Engineering Materials, 344, pp. 751-758, 2007.

[6] L. Donati, L. Tomesani, G. Minak, Friction Stir Welding Between Sheets and Extruded Profiles, Steel Research International, 79, Special Edition Metal Forming Conference 2008, Vol. 1, pp.671-676, 2008.

[7] L. Donati, L. Tomesani, A. Morri ”Structural T-joint produced by means of Friction Stir Welding (FSW) with filling material” under publishing on AIP Conference Proceedings (2009).


Analysis of metal flow of aluminum through long choked die channels

Henry Valberg1,a 1Norwegian University of Science and Technology, Department of Engineering Design and

Materials, Richard Birkelands vei 2b, 7491, Trondheim, Norway [email protected]

Keywords: Metal flow, die channel, contact conditions, shear layer, plug flow. Abstract. The mechanics of metal flow through long choked die channels have been investigated in unlubricated hot aluminum extrusion. Experiments were performed in a laboratory press at an earlier occasion by letting a grid pattern introduced into the billet flow down into the choked die channel to appear adjacent to the channel wall. The grid pattern was then revealed to characterize the metal flow in the channel. A 2D-model of the extrusion process was made. The model was applied to study the conditions in the extrusion experiments and in this model good similarity was obtained with the experiment. New knowledge regarding the metal flow through a choked die channel have been obtained this way, such as; contact conditions, presence of sticking and sliding zones, friction conditions in the sliding contact zone and the velocity profile over the cross-section of the channel.

Introduction

Throughout the years much attention has been paid to the tribo-mechanical conditions on the bearing surface [1, 2], i.e., the die land, of extrusion dies. The die land is considered very important in extrusion of aluminum and other metals, because the shape and the dimension of the extruded product are strongly influenced by the conditions at this surface. In industrial extrusion practice the die land is gradually altered through die correction until the profile satisfies the geometrical requirements of the user. The outer skin of the profile is formed in this region, and the surface appearance of the extrusion thus is determined by the tribo-mechanical processes taking place here. The interaction between the tool steel, the atmosphere, and the aluminum flowing past the bearing causes wear, and determines when the die has to be reworked or substituted. Moreover, the friction forces transferred to the bearing by the metal flowing over the die bearing generates heat. Generated heat increases with increasing extrusion speed until the speed-limiting conditions are obtained. Above the speed limit, unacceptable profile quality results since surface defects form, unacceptable recrystallization takes place, or other limiting phenomena occur. Finally, the bearing surface influences the extrusion force and the mechanical power consumed in extrusion.

Methods previously applied for study of contact conditions on the die land

The existing knowledge of metal flow and the tribo-mechanical conditions at the bearing surface is yet far from complete. Most of published information refers to extrusion dies of simple geometry as axisymmetric dies or dies for extrusion of rectangular sections. It is generally recognized that contact conditions at the bearing surface strongly depend on the

angle of inclination of the bearing surface. When the bearing angle is gradually changed [1-4] from a negative (choke) to a positive value (relief) a sudden change in contact conditions occurs in the range from -0.5 to +0.5°. With choke there are intimate contact between the work material and the die bearing, resulting in high contact stresses. With relief the contact stresses drop to zero, indicating no contact at all. In the range -0.5 to +0.5° the contact conditions change rather suddenly. Because the metal fills the die channel, in-situ visual inspection of the contact between the die

and the workpiece during extrusion is impossible. When the contact conditions at the bearing surface have been investigated various approaches have been used:

Analysis of metal flow of aluminum through long choked die channels

Henry Valberg1,a 1Norwegian University of Science and Technology, Department of Engineering Design and

Materials, Richard Birkelands vei 2b, 7491, Trondheim, Norway [email protected]

Keywords: Metal flow, die channel, contact conditions, shear layer, plug flow. Abstract. The mechanics of metal flow through long choked die channels have been investigated in unlubricated hot aluminum extrusion. Experiments were performed in a laboratory press at an earlier occasion by letting a grid pattern introduced into the billet flow down into the choked die channel to appear adjacent to the channel wall. The grid pattern was then revealed to characterize the metal flow in the channel. A 2D-model of the extrusion process was made. The model was applied to study the conditions in the extrusion experiments and in this model good similarity was obtained with the experiment. New knowledge regarding the metal flow through a choked die channel have been obtained this way, such as; contact conditions, presence of sticking and sliding zones, friction conditions in the sliding contact zone and the velocity profile over the cross-section of the channel.

Introduction

Throughout the years much attention has been paid to the tribo-mechanical conditions on the bearing surface [1, 2], i.e., the die land, of extrusion dies. The die land is considered very important in extrusion of aluminum and other metals, because the shape and the dimension of the extruded product are strongly influenced by the conditions at this surface. In industrial extrusion practice the die land is gradually altered through die correction until the profile satisfies the geometrical requirements of the user. The outer skin of the profile is formed in this region, and the surface appearance of the extrusion thus is determined by the tribo-mechanical processes taking place here. The interaction between the tool steel, the atmosphere, and the aluminum flowing past the bearing causes wear, and determines when the die has to be reworked or substituted. Moreover, the friction forces transferred to the bearing by the metal flowing over the die bearing generates heat. Generated heat increases with increasing extrusion speed until the speed-limiting conditions are obtained. Above the speed limit, unacceptable profile quality results since surface defects form, unacceptable recrystallization takes place, or other limiting phenomena occur. Finally, the bearing surface influences the extrusion force and the mechanical power consumed in extrusion.

Methods previously applied for study of contact conditions on the die land

The existing knowledge of metal flow and the tribo-mechanical conditions at the bearing surface is yet far from complete. Most of published information refers to extrusion dies of simple geometry as axisymmetric dies or dies for extrusion of rectangular sections. It is generally recognized that contact conditions at the bearing surface strongly depend on the

angle of inclination of the bearing surface. When the bearing angle is gradually changed [1-4] from a negative (choke) to a positive value (relief) a sudden change in contact conditions occurs in the range from -0.5 to +0.5°. With choke there are intimate contact between the work material and the die bearing, resulting in high contact stresses. With relief the contact stresses drop to zero, indicating no contact at all. In the range -0.5 to +0.5° the contact conditions change rather suddenly. Because the metal fills the die channel, in-situ visual inspection of the contact between the die

and the workpiece during extrusion is impossible. When the contact conditions at the bearing surface have been investigated various approaches have been used:


1) The axial shear force transferred to the die bearing is determined [5] by comparing the extrusion force in extrusion experiments performed with different lengths of the die bearing. 2) Shear stresses and forces transferred to the bearing are determined [6] by comparing indirect

and direct extrusion experiments in dies with constant reduction ratio and bearing length, but varying numbers of holes. 3) A die with two holes is used where both holes run with equal speeds when they are

geometrically identical. Then keeping one hole constant, the bearing geometry of the other hole is changed; and the effect are evaluated from the speed difference between the profiles [2, 4]. 4) Split dies or dies partitioned after extrusion have been used. The process is stopped after

partial extrusion; the die is then removed and split - and the contact conditions are evaluated by visual inspection of the die land [3]. 5) Direct measurement of the friction force is performed in a modular die consisting of two parts

where the bearing is one part fitted with a sensor to measure the axial force [7].

ew experimental approach for study of contact and flow conditions in the bearing channel

We decided to perform a series of experiments where new methods were to be used [8-9] for study of the contact conditions on the bearing surface of a die channel including metal flow inside the material flowing through the die channel. This work was done many years ago but will be reviewed here in short version. A choked channel was chosen in this case, because it was expected that the contact conditions then would be stable, and that elastic tool bending would not alter the inclination to relief. A rather small reduction ratio (R=10) and a long die channel were chosen, in order to ease use and analysis of a grid pattern flowing through the channel. The method can be listed as method no. 6 in addition to those already mentioned. Radial grid lines were applied on the longitudinal mid-plane of the billet. They were made either

by scratching of lines on a longitudinal cut section of the billet, or by insertion of indicator pins into holes drilled into the billet. During extrusion the lines flowed into the channel where a momentary recording of the pattern was obtained by stopping the extrusion process. The press residue were then removed and sectioned to reveal the appearance of the lines inside the bearing channel.

Experimental study

Industrially cast and homogenized billets of the alloy AA 6063 were extruded in a 100mm diameter container with a ram speed of 10mms-1. A billet temperature of 450° and a container temperature of 430° were used. Altogether 4 billets with radial grid lines made from contrast pins were extruded. The same number of billets were also used but with corresponding scratched grid lines. The line patterns consisted of transverse lines made with 5 or 2mm equidistance inside the initial billet. All experiments were performed in an 8MN vertical laboratory extrusion press. The experiments are described briefly below while additional details are reported in earlier work [8-9]. The die used was made with interchangeable inserts. A new insert was used in each experiment

with one exception. The inlet diameter of the bearing channel was always 31.6mm and the channel had 1° choke. The length of the channel was 50 and 100mm, respectively, and had been ground perpendicular to the extrusion direction. The die inserts were made of ORVAR steel in hardened and annealed temper. The transverse indicator pins were observed to change the metal flow in the middle of the channel. Therefore, this method is not recommended for investigation of flow in the mid-region of the channel. However, in layers adjacent to the bearing this line pattern was observed to provide useful information about metal flow. Use of scratched lines provided reliable information about metal flow in the mid-region of the channel. However, they could not be used to describe metal flow in the layer near to the channel wall, as they were erased there by the severe deformation. The die insert and the metal inside the channels were removed as one piece. It was sectioned and

the insert was removed from the aluminum. After partitioning, the bearing surface and the mating aluminum surface were studied visually. The Al from inside the channel were sectioned or split

1) The axial shear force transferred to the die bearing is determined [5] by comparing the extrusion force in extrusion experiments performed with different lengths of the die bearing. 2) Shear stresses and forces transferred to the bearing are determined [6] by comparing indirect

and direct extrusion experiments in dies with constant reduction ratio and bearing length, but varying numbers of holes. 3) A die with two holes is used where both holes run with equal speeds when they are

geometrically identical. Then keeping one hole constant, the bearing geometry of the other hole is changed; and the effect are evaluated from the speed difference between the profiles [2, 4]. 4) Split dies or dies partitioned after extrusion have been used. The process is stopped after

partial extrusion; the die is then removed and split - and the contact conditions are evaluated by visual inspection of the die land [3]. 5) Direct measurement of the friction force is performed in a modular die consisting of two parts

where the bearing is one part fitted with a sensor to measure the axial force [7].

ew experimental approach for study of contact and flow conditions in the bearing channel

We decided to perform a series of experiments where new methods were to be used [8-9] for study of the contact conditions on the bearing surface of a die channel including metal flow inside the material flowing through the die channel. This work was done many years ago but will be reviewed here in short version. A choked channel was chosen in this case, because it was expected that the contact conditions then would be stable, and that elastic tool bending would not alter the inclination to relief. A rather small reduction ratio (R=10) and a long die channel were chosen, in order to ease use and analysis of a grid pattern flowing through the channel. The method can be listed as method no. 6 in addition to those already mentioned. Radial grid lines were applied on the longitudinal mid-plane of the billet. They were made either

by scratching of lines on a longitudinal cut section of the billet, or by insertion of indicator pins into holes drilled into the billet. During extrusion the lines flowed into the channel where a momentary recording of the pattern was obtained by stopping the extrusion process. The press residue were then removed and sectioned to reveal the appearance of the lines inside the bearing channel.

Experimental study

Industrially cast and homogenized billets of the alloy AA 6063 were extruded in a 100mm diameter container with a ram speed of 10mms-1. A billet temperature of 450° and a container temperature of 430° were used. Altogether 4 billets with radial grid lines made from contrast pins were extruded. The same number of billets were also used but with corresponding scratched grid lines. The line patterns consisted of transverse lines made with 5 or 2mm equidistance inside the initial billet. All experiments were performed in an 8MN vertical laboratory extrusion press. The experiments are described briefly below while additional details are reported in earlier work [8-9]. The die used was made with interchangeable inserts. A new insert was used in each experiment

with one exception. The inlet diameter of the bearing channel was always 31.6mm and the channel had 1° choke. The length of the channel was 50 and 100mm, respectively, and had been ground perpendicular to the extrusion direction. The die inserts were made of ORVAR steel in hardened and annealed temper. The transverse indicator pins were observed to change the metal flow in the middle of the channel. Therefore, this method is not recommended for investigation of flow in the mid-region of the channel. However, in layers adjacent to the bearing this line pattern was observed to provide useful information about metal flow. Use of scratched lines provided reliable information about metal flow in the mid-region of the channel. However, they could not be used to describe metal flow in the layer near to the channel wall, as they were erased there by the severe deformation. The die insert and the metal inside the channels were removed as one piece. It was sectioned and

the insert was removed from the aluminum. After partitioning, the bearing surface and the mating aluminum surface were studied visually. The Al from inside the channel were sectioned or split


along the plane containing the pattern. In this way the appearance of the deformed grid lines inside the bearing channel was revealed.


Appearance of the bearing surface after removal of the extrusion metal. The bearing surface had three regions of different visual appearance; see Fig. 1a). Near the outlet from the channel there were two regions covered with an aluminum-colored adhesion layer. The layer nearest the outlet had a smooth, shiny appearance which extended typically 8-15mm into the channel. It is labeled region A in Fig. 1a. Deeper inside the channel the adhesion layer had a rougher, duller, white appearance; region A1 in the figure. There the layer occurred as a band of varying width around the die land circumference. The boundary between the two regions was sometimes difficult to determine, being less pronounced for the longest channels. The band A1 also had a more stripe-like texture in the extrusion direction than the rest of the adhesion layer.

a) b)

c) d)

Fig. 1: Appearance of bearing surface and stripe patterns inside the bearing channel after extrusion; a) Photo of bearing surface, b) Scratched stripes (marked with broken black lines in the bottom half of the specimen), c) Indicator stripes adjacent the die bearing and d) Indicator stripes inside the channel.

At the inlet side of the channel the overall color was black with clearly visible transverse grooves

due to grinding. This region is labeled B in Fig. 1a). This part of the channel was longer than that with adhesion coating for both channel lengths, especially for the longest channel. Small adhesive flecks of aluminum occurred randomly at this part of the die land. In one case a stripe of adhesive material extended along the whole black region of the bearing surface. This was an experiment

along the plane containing the pattern. In this way the appearance of the deformed grid lines inside the bearing channel was revealed.


Appearance of the bearing surface after removal of the extrusion metal. The bearing surface had three regions of different visual appearance; see Fig. 1a). Near the outlet from the channel there were two regions covered with an aluminum-colored adhesion layer. The layer nearest the outlet had a smooth, shiny appearance which extended typically 8-15mm into the channel. It is labeled region A in Fig. 1a. Deeper inside the channel the adhesion layer had a rougher, duller, white appearance; region A1 in the figure. There the layer occurred as a band of varying width around the die land circumference. The boundary between the two regions was sometimes difficult to determine, being less pronounced for the longest channels. The band A1 also had a more stripe-like texture in the extrusion direction than the rest of the adhesion layer.

a) b)

c) d)

Fig. 1: Appearance of bearing surface and stripe patterns inside the bearing channel after extrusion; a) Photo of bearing surface, b) Scratched stripes (marked with broken black lines in the bottom half of the specimen), c) Indicator stripes adjacent the die bearing and d) Indicator stripes inside the channel.

At the inlet side of the channel the overall color was black with clearly visible transverse grooves

due to grinding. This region is labeled B in Fig. 1a). This part of the channel was longer than that with adhesion coating for both channel lengths, especially for the longest channel. Small adhesive flecks of aluminum occurred randomly at this part of the die land. In one case a stripe of adhesive material extended along the whole black region of the bearing surface. This was an experiment


where removal of the inserts from the metal residue was difficult due to strong bonding between the two. The intensity of the black color of region B varied from one experiment to another in a random way, from lighter black to completely black, probably due to differing degrees of oxidation of the die when kept at ambient extrusion temperature before the experiment. In one of the experiments extrusion was stopped at an earlier stage than in the other experiments. Due to this, the adhesive layer of the bearing surface was less pronounced then than in the other experiments.

Appearance of the indicator line pattern inside the bearing channel. This deformed line pattern in a longitudinal section cut through the extrusion discard from the channel at a partial extrusion stage is shown in Fig. 1d) for one experiment. The line pattern, which initially consisted of alternating light and dark radial stripes inside the billet, now is present in the bearing channel of the die, where it mainly appears as stripes running approximately parallel to the die channel surface. A detail of the pattern adjacent to the outlet from the die channel marked by a small rectangle in Fig.1d), are shown in greater magnification in Fig.1c). The appearance of the pattern in this detail proves that there is sticking contact between the Al

inside the die channel over the major of its length in unlubricated extrusion, i.e., the region labeled B in Fig.1a). At the end of this region, however, there is a point where sticking can not be maintained any longer, and the extrusion metal therefore starts to slide against the channel wall. Because of this, there is radial outward flow of the grid stripes here, so that the stripes appear there with an outwards bow directed towards the die channel. The line patterns were also revealed for other experiments. They had all the same features as

shown in Fig.1c), but in the experiments with the longer channel, the inward curvature of the longitudinal grid lines occurred further away from the die exit. As a matter of fact, this phenomenon occurred always at the same distance away from the exit side of the channel as the adhesion layer A1. This appearance of the grid lines shows that there is a radial, outward-pointed velocity component in this region, corresponding to that observed during flow of plastics in channels where the speed changes from parabolic to uniform axial speed distribution. The points at the die channel where the contact shifted from sticking to sliding – for the die channels of 50mm and 100mm length – were situated ~13mm and ~25mm from the exit of the channel, respectively.

Appearance of the scratched line pattern inside the bearing channel. Three neighboring grid lines of this type, initially being radial lines inside the billet before extrusion, were caught upon passage through the mid-region of die channel at end of extrusion in one experiment, see Fig.1b). The geometry of each line was measured in a microscope; then they were added on top of each other with the vertex coinciding. This showed that all grid lines had approximately the same shape. This was also the case for corresponding grid lines remaining inside the die channel at the end of extrusion in other experiments. That nearly spaced grid lines have the same shape inside the bearing channel, although the first line has flown deeper into the channel than the second line, shows that the lines are in a region of constant axial and zero radial velocity. The material in the middle of the channel therefore must flow like a rigid plug.

Discussion of experimental results

With a parabolic speed distribution more material must be fed forward in the middle of the channel than in the outer circumferential region. At the channel exit, however, an equal amount of material has to be fed to the whole cross-section to deliver a rod of diameter equal to that of the channel. Because of this, and since metal is approximately incompressible, there must be a zone inside the channel at the stick-slip transition point, where material is fed outwards toward the periphery of the rod to provide sufficient supply of material there. From the observation of the depth of the region of divergent flow, the thickness of the sticking layer of Al at the bearing seemed to depend on the channel length. In the short channel this layer had a thickness of ~3mm; in the long channel, a thickness of ~6mm.

where removal of the inserts from the metal residue was difficult due to strong bonding between the two. The intensity of the black color of region B varied from one experiment to another in a random way, from lighter black to completely black, probably due to differing degrees of oxidation of the die when kept at ambient extrusion temperature before the experiment. In one of the experiments extrusion was stopped at an earlier stage than in the other experiments. Due to this, the adhesive layer of the bearing surface was less pronounced then than in the other experiments.

Appearance of the indicator line pattern inside the bearing channel. This deformed line pattern in a longitudinal section cut through the extrusion discard from the channel at a partial extrusion stage is shown in Fig. 1d) for one experiment. The line pattern, which initially consisted of alternating light and dark radial stripes inside the billet, now is present in the bearing channel of the die, where it mainly appears as stripes running approximately parallel to the die channel surface. A detail of the pattern adjacent to the outlet from the die channel marked by a small rectangle in Fig.1d), are shown in greater magnification in Fig.1c). The appearance of the pattern in this detail proves that there is sticking contact between the Al

inside the die channel over the major of its length in unlubricated extrusion, i.e., the region labeled B in Fig.1a). At the end of this region, however, there is a point where sticking can not be maintained any longer, and the extrusion metal therefore starts to slide against the channel wall. Because of this, there is radial outward flow of the grid stripes here, so that the stripes appear there with an outwards bow directed towards the die channel. The line patterns were also revealed for other experiments. They had all the same features as

shown in Fig.1c), but in the experiments with the longer channel, the inward curvature of the longitudinal grid lines occurred further away from the die exit. As a matter of fact, this phenomenon occurred always at the same distance away from the exit side of the channel as the adhesion layer A1. This appearance of the grid lines shows that there is a radial, outward-pointed velocity component in this region, corresponding to that observed during flow of plastics in channels where the speed changes from parabolic to uniform axial speed distribution. The points at the die channel where the contact shifted from sticking to sliding – for the die channels of 50mm and 100mm length – were situated ~13mm and ~25mm from the exit of the channel, respectively.

Appearance of the scratched line pattern inside the bearing channel. Three neighboring grid lines of this type, initially being radial lines inside the billet before extrusion, were caught upon passage through the mid-region of die channel at end of extrusion in one experiment, see Fig.1b). The geometry of each line was measured in a microscope; then they were added on top of each other with the vertex coinciding. This showed that all grid lines had approximately the same shape. This was also the case for corresponding grid lines remaining inside the die channel at the end of extrusion in other experiments. That nearly spaced grid lines have the same shape inside the bearing channel, although the first line has flown deeper into the channel than the second line, shows that the lines are in a region of constant axial and zero radial velocity. The material in the middle of the channel therefore must flow like a rigid plug.

Discussion of experimental results

With a parabolic speed distribution more material must be fed forward in the middle of the channel than in the outer circumferential region. At the channel exit, however, an equal amount of material has to be fed to the whole cross-section to deliver a rod of diameter equal to that of the channel. Because of this, and since metal is approximately incompressible, there must be a zone inside the channel at the stick-slip transition point, where material is fed outwards toward the periphery of the rod to provide sufficient supply of material there. From the observation of the depth of the region of divergent flow, the thickness of the sticking layer of Al at the bearing seemed to depend on the channel length. In the short channel this layer had a thickness of ~3mm; in the long channel, a thickness of ~6mm.


The adhesion layer on the bearing coincided with the bearing area subjected to sliding contact, i.e., the region behind the transition point. The narrow band of adhesive material with dull stripe-like appearance, was coincident with the regiotransition point. The dull adhesion band is thickness/roughness than the rest of the adhesion layer. This adhesion band was only partially present in the long channels, but when present it coincided with the point of transition from sticking to sliding. A probable reason for the buildeither low sliding speeds or low presThe smooth, shiny, thin adhesion layer occurring towards the exit of the chaFig. 1a), is obviously due to transfer of flowing past the bearing surface. When this surface has bwill probably take place between the extruding metal and the adhesion layer itself, corresponding to the description given in [3]. Sliding towards the exit side of the channel is probably complete, i.e., the material shows plug flow and surface layers slide with the same speed as the interior layers and the delivered profile. A less pronounced adhesion layer stopped earlier. This indicates that the buadhesive layer obviously grows in thickness with an increasing amount of matapproximately same location and the same visual appearance of the adhesion layer, including the dull adhesion band, at the bearing in all channels of sameremains in the same position during the course of extrusion and does not move along the bearing surface.

Reproduction of experiments in FEM

A FEM-model of the extrusion experthe software DEFORM-2D. Since a hot forming process is considered, the model was made nonisothermal and included effects of heat transfer from the billet to the surroundmaterial was modeled rigid-plastic and the dies rigid. The model setmodel were largely the same as those in a previous FEM[10]. Inside the bearing channel the nodesspecified to be sticking, while in the sliding zone at the rear end of the bearinwere modeled as Tresca type with the friction factor

Results from the finite element

Some simulation results obtained by the model a row of points is added inside the stripe A-A in the experiment, see Fig.1bstage of extrusion will appear very similar to the experimental stripestick-slip transition point.

Fig. 2: Results of point-tracking in FEM

the bearing surface near the die exit; the regions labeled coincided with the bearing area subjected to sliding contact, i.e., the region behind the transition point. The narrow band of adhesive material with dull Al color, region A1 in Fig.

cident with the region of divergent flow adjacent to the sticktransition point. The dull adhesion band is thought to be an adhesion layer of greater thickness/roughness than the rest of the adhesion layer. This adhesion band was only partially

s, but when present it coincided with the point of transition from sticking to sliding. A probable reason for the build-up of the dull adhesion band near the transition point is

low sliding speeds or low pressure at the end of the sticking region. he smooth, shiny, thin adhesion layer occurring towards the exit of the cha

, is obviously due to transfer of Al onto the bearing caused by the sliding action of metal flowing past the bearing surface. When this surface has been covered with an adhesive film, sliding will probably take place between the extruding metal and the adhesion layer itself, corresponding to

. Sliding towards the exit side of the channel is probably complete, i.e., ial shows plug flow and surface layers slide with the same speed as the interior layers and

A less pronounced adhesion layer was formed in the die land in the experiment. This indicates that the build-up of the adhesion layer is a gradual process

adhesive layer obviously grows in thickness with an increasing amount of matmately same location and the same visual appearance of the adhesion layer, including the

he bearing in all channels of same length, indicate that the transition point remains in the same position during the course of extrusion and does not move along the bearing

Reproduction of experiments in FEM-analysis

l of the extrusion experiments performed in the shorter die channel was created using 2D. Since a hot forming process is considered, the model was made non

isothermal and included effects of heat transfer from the billet to the surroundplastic and the dies rigid. The model set-up and the input data to the

model were largely the same as those in a previous FEM-model of indirect extrusion reported in [10]. Inside the bearing channel the nodes of the workpiece adjacent the sticking zon

to be sticking, while in the sliding zone at the rear end of the bearinwith the friction factor set equal 0.5.

Results from the finite element analysis

Some simulation results obtained by the model are shown in Fig.2 and Fig.3. Fig.2 shows that when added inside the aluminum in the bearing channel, so as to mimic the contrast

in the experiment, see Fig.1b), the predicted appearance of the same points at a later stage of extrusion will appear very similar to the experimental stripe; with an outward bow

tracking in FEM-model mimicking contrast stripe A

regions labeled A and A1 in Fig. 1a), coincided with the bearing area subjected to sliding contact, i.e., the region behind the transition

in Fig. 1a), with a rough gent flow adjacent to the stick-slip an adhesion layer of greater

thickness/roughness than the rest of the adhesion layer. This adhesion band was only partially s, but when present it coincided with the point of transition from sticking

dull adhesion band near the transition point is

he smooth, shiny, thin adhesion layer occurring towards the exit of the channel, i.e., region A in onto the bearing caused by the sliding action of metal

een covered with an adhesive film, sliding will probably take place between the extruding metal and the adhesion layer itself, corresponding to


the experiment where extrusion was r is a gradual process. The

adhesive layer obviously grows in thickness with an increasing amount of material sliding past. The mately same location and the same visual appearance of the adhesion layer, including the

length, indicate that the transition point remains in the same position during the course of extrusion and does not move along the bearing

die channel was created using 2D. Since a hot forming process is considered, the model was made non-

isothermal and included effects of heat transfer from the billet to the surrounding dies. The billet up and the input data to the

model of indirect extrusion reported in of the workpiece adjacent the sticking zone were

to be sticking, while in the sliding zone at the rear end of the bearing channel the friction

Fig.3. Fig.2 shows that when in the bearing channel, so as to mimic the contrast

cted appearance of the same points at a later with an outward bow at the

model mimicking contrast stripe A-A in Fig.1.

The adhesion layer on the bearing coincided with the bearing area subjected to sliding contact, i.e., the region behind the transition point. The narrow band of adhesive material with dull stripe-like appearance, was coincident with the regiotransition point. The dull adhesion band is thickness/roughness than the rest of the adhesion layer. This adhesion band was only partially present in the long channels, but when present it coincided with the point of transition from sticking to sliding. A probable reason for the buildeither low sliding speeds or low presThe smooth, shiny, thin adhesion layer occurring towards the exit of the chaFig. 1a), is obviously due to transfer of flowing past the bearing surface. When this surface has bwill probably take place between the extruding metal and the adhesion layer itself, corresponding to the description given in [3]. Sliding towards the exit side of the channel is probably complete, i.e., the material shows plug flow and surface layers slide with the same speed as the interior layers and the delivered profile. A less pronounced adhesion layer stopped earlier. This indicates that the buadhesive layer obviously grows in thickness with an increasing amount of matapproximately same location and the same visual appearance of the adhesion layer, including the dull adhesion band, at the bearing in all channels of sameremains in the same position during the course of extrusion and does not move along the bearing surface.

Reproduction of experiments in FEM

A FEM-model of the extrusion experthe software DEFORM-2D. Since a hot forming process is considered, the model was made nonisothermal and included effects of heat transfer from the billet to the surroundmaterial was modeled rigid-plastic and the dies rigid. The model setmodel were largely the same as those in a previous FEM[10]. Inside the bearing channel the nodesspecified to be sticking, while in the sliding zone at the rear end of the bearinwere modeled as Tresca type with the friction factor

Results from the finite element

Some simulation results obtained by the model a row of points is added inside the stripe A-A in the experiment, see Fig.1bstage of extrusion will appear very similar to the experimental stripestick-slip transition point.

Fig. 2: Results of point-tracking in FEM

the bearing surface near the die exit; the regions labeled coincided with the bearing area subjected to sliding contact, i.e., the region behind the transition point. The narrow band of adhesive material with dull Al color, region A1 in Fig.

cident with the region of divergent flow adjacent to the sticktransition point. The dull adhesion band is thought to be an adhesion layer of greater thickness/roughness than the rest of the adhesion layer. This adhesion band was only partially

s, but when present it coincided with the point of transition from sticking to sliding. A probable reason for the build-up of the dull adhesion band near the transition point is

low sliding speeds or low pressure at the end of the sticking region. he smooth, shiny, thin adhesion layer occurring towards the exit of the cha

, is obviously due to transfer of Al onto the bearing caused by the sliding action of metal flowing past the bearing surface. When this surface has been covered with an adhesive film, sliding will probably take place between the extruding metal and the adhesion layer itself, corresponding to


A less pronounced adhesion layer was formed in the die land in the experiment. This indicates that the build-up of the adhesion layer is a gradual process

adhesive layer obviously grows in thickness with an increasing amount of matmately same location and the same visual appearance of the adhesion layer, including the

he bearing in all channels of same length, indicate that the transition point remains in the same position during the course of extrusion and does not move along the bearing

Reproduction of experiments in FEM-analysis

l of the extrusion experiments performed in the shorter die channel was created using 2D. Since a hot forming process is considered, the model was made non

isothermal and included effects of heat transfer from the billet to the surroundplastic and the dies rigid. The model set-up and the input data to the

model were largely the same as those in a previous FEM-model of indirect extrusion reported in [10]. Inside the bearing channel the nodes of the workpiece adjacent the sticking zon

to be sticking, while in the sliding zone at the rear end of the bearinwith the friction factor set equal 0.5.

Results from the finite element analysis

Some simulation results obtained by the model are shown in Fig.2 and Fig.3. Fig.2 shows that when added inside the aluminum in the bearing channel, so as to mimic the contrast

in the experiment, see Fig.1b), the predicted appearance of the same points at a later stage of extrusion will appear very similar to the experimental stripe; with an outward bow

tracking in FEM-model mimicking contrast stripe A

regions labeled A and A1 in Fig. 1a), coincided with the bearing area subjected to sliding contact, i.e., the region behind the transition

in Fig. 1a), with a rough gent flow adjacent to the stick-slip an adhesion layer of greater

thickness/roughness than the rest of the adhesion layer. This adhesion band was only partially s, but when present it coincided with the point of transition from sticking

dull adhesion band near the transition point is

he smooth, shiny, thin adhesion layer occurring towards the exit of the channel, i.e., region A in onto the bearing caused by the sliding action of metal

een covered with an adhesive film, sliding will probably take place between the extruding metal and the adhesion layer itself, corresponding to


the experiment where extrusion was r is a gradual process. The

adhesive layer obviously grows in thickness with an increasing amount of material sliding past. The mately same location and the same visual appearance of the adhesion layer, including the

length, indicate that the transition point remains in the same position during the course of extrusion and does not move along the bearing

die channel was created using 2D. Since a hot forming process is considered, the model was made non-

isothermal and included effects of heat transfer from the billet to the surrounding dies. The billet up and the input data to the

model of indirect extrusion reported in of the workpiece adjacent the sticking zone were

to be sticking, while in the sliding zone at the rear end of the bearing channel the friction

Fig.3. Fig.2 shows that when in the bearing channel, so as to mimic the contrast

cted appearance of the same points at a later with an outward bow at the

model mimicking contrast stripe A-A in Fig.1.


a) b) c) d) Fig. 3: FEM-predicted plug flow through mid-region of the channel and intensive shearing in

sticking zone.

A grid pattern of transverse lines were added into the simulation workpiece at a stage of extrusion when the die channel had been completely filled, see Fig.3a). The appearance of the pattern at later stages was then computed by the FEM-model; see Figs.3b) - 3d). As these patterns show plug flow is predicted in the mid-region of the die channel, with a shear layer adjacent to the wall of the die channel characterized by sticking friction. Behind this region the extrusion metal slides against the die channel wall, and the shear layer is no longer present, instead the metal slides with high velocity against the die wall. Because of the friction against the wall, however, there is some retention of the outer layer of the rod in relation to the core. This effect is perhaps best shown by the grid line labeled A in Fig.3c). FEA allows strain rate and strain distributions to be determined for the axial section of the extrusion process. Such distributions are shown in Fig.4 and Fig.5. As these figures depict the strain rate is predicted to be very high right above the die mouth but also in the surface layer of the die channel where there is very intensive shearing. When the levels of these strain rates were examined in more detail they were found to be predicted as high as 0.7-2s-1 above the die mouth, and even higher in the shear layer adjacent the sticking zone on the die channel; ~8 s-1 in the most intensive shear layer. When it comes to strains they are predicted to increase in the extrusion material inside the die channel, in the centre strains are very low in the front end of the extruded rod, but as extrusion proceeds they increase. However, the very highest strains are experienced in the layer of material adjacent the sticking zone on the die channel wall. This material remains as an approximately stationary layer near to the die land because of sticking friction in there. As extrusion continues this layer deforms more and more in shear, so that FEA-predicted strains here soon exceeds an effective strain value of 15, see Fig.5b).

a) b) c) d) Fig. 3: FEM-predicted plug flow through mid-region of the channel and intensive shearing in

sticking zone.

A grid pattern of transverse lines were added into the simulation workpiece at a stage of extrusion when the die channel had been completely filled, see Fig.3a). The appearance of the pattern at later stages was then computed by the FEM-model; see Figs.3b) - 3d). As these patterns show plug flow is predicted in the mid-region of the die channel, with a shear layer adjacent to the wall of the die channel characterized by sticking friction. Behind this region the extrusion metal slides against the die channel wall, and the shear layer is no longer present, instead the metal slides with high velocity against the die wall. Because of the friction against the wall, however, there is some retention of the outer layer of the rod in relation to the core. This effect is perhaps best shown by the grid line labeled A in Fig.3c). FEA allows strain rate and strain distributions to be determined for the axial section of the extrusion process. Such distributions are shown in Fig.4 and Fig.5. As these figures depict the strain rate is predicted to be very high right above the die mouth but also in the surface layer of the die channel where there is very intensive shearing. When the levels of these strain rates were examined in more detail they were found to be predicted as high as 0.7-2s-1 above the die mouth, and even higher in the shear layer adjacent the sticking zone on the die channel; ~8 s-1 in the most intensive shear layer. When it comes to strains they are predicted to increase in the extrusion material inside the die channel, in the centre strains are very low in the front end of the extruded rod, but as extrusion proceeds they increase. However, the very highest strains are experienced in the layer of material adjacent the sticking zone on the die channel wall. This material remains as an approximately stationary layer near to the die land because of sticking friction in there. As extrusion continues this layer deforms more and more in shear, so that FEA-predicted strains here soon exceeds an effective strain value of 15, see Fig.5b).


a) b) Fig. 4: FEM-predicted strain rate distribution in the extrusion process. a) High and b) Low strain

rates.

a) b) Fig. 5: FEM-predictions; a) Low strain rates towards the outlet of the die channel and b) High

strains in the sticking surface layer adjacent the die land.

Conclusion

In long choked die channels, with length to diameter ratio of ~1.6 and ~3.1, it has been shown experimentally that there is a zone near to the inlet side of the channel where the contact conditions between Al and the die bearing is characterized by complete sticking. Deeper inside the channel, at the end of the sticking zone, there is a transition point where the metal starts to slide against the die land. Between the transition point and the die exit, the die land gets covered with an adhesion layer of aluminum that develops gradually throughout an extrusion stroke. In the front end portion of the die channel, characterized by sticking, only minor flecks of adhesive metal occurred when the extrusion metal was removed from the bearing.

a) b) Fig. 4: FEM-predicted strain rate distribution in the extrusion process. a) High and b) Low strain

rates.

a) b) Fig. 5: FEM-predictions; a) Low strain rates towards the outlet of the die channel and b) High

strains in the sticking surface layer adjacent the die land.

Conclusion

In long choked die channels, with length to diameter ratio of ~1.6 and ~3.1, it has been shown experimentally that there is a zone near to the inlet side of the channel where the contact conditions between Al and the die bearing is characterized by complete sticking. Deeper inside the channel, at the end of the sticking zone, there is a transition point where the metal starts to slide against the die land. Between the transition point and the die exit, the die land gets covered with an adhesion layer of aluminum that develops gradually throughout an extrusion stroke. In the front end portion of the die channel, characterized by sticking, only minor flecks of adhesive metal occurred when the extrusion metal was removed from the bearing.


The die lines of the extrudate were observed to form at the very exit end of the choked die channel. This shows that the sliding movement between the aluminum and the adhesion layer behind the transition point is one of intimate contact. The metal flow in the middle of the die channel was determined to conform to plug flow; the metal flowed through without significant plastic deformation. However, in the subsurface layer of Al adjacent to the sticking zone on the die wall, a layer of material remained almost stationary in the channel. Due to this, material flowed radially outwards toward the rod surface at the end of this layer. Knowing how the contact conditions really are at the die land due to the grid pattern techniques used in this study, it has been possible to model the deformation conditions in the bearing by means of FEA with good similarity to the observations in the experiments. Thus FEA confirmed that there is plug flow in the interior of the die channel, and that a heavily shear deformed layer forms adjacent to the sticking zone on the inlet side of the die channel. At the stick-slip transition point behind the sticking zone, however, the material starts to flow approximately like a plug over the whole diameter of the channel, in the sliding contact zone behind this point. However, some small deformations are subjected to the material there in terms of a deformation cross with low strain rates.

References

[1] R. Akeret, Aluminium, Vol. 59, No. 10, 1983, pp. E355-E360

[2] R. Akeret and W. Strehmel, Proc. of the 4th Int'l. Al. Extr. Techn. Sem., Vol. II, April 11-14, 1988, Chicago, pp. 357 - 367.

[3] W. Thedja, K. B. Müller and D. Ruppin, Aluminium, Vol. 69, No. 6, 1993, pp. 543 – 547.

[4] Akeret, R. ; Aluminium, Vol.61, No.3, 1985, pp. E1 66 – E1 69.

[5] G. Lang, Aluminium, Vol. 60, No. 4, 1984, pp. E249-E251.

[6] G. Lang, Aluminium, Vol.57, No. 12, 1981, pp.791 -796.

[7] W. Ziegler and G. Hartmann, Vol. 83, 1977, pp. 2034-2036.

[8] H. Valberg and T. Malvik, Int. J. Mat. Prod. Techn., Vol. 9, Nos. 4/5/6, 1994, pp. 428-463.

[9] H. Valberg and T. Malvik, Proc. 6th Int. Al. Extr. Techn., Sem., Chicago, Vol.2, 1996, p. 17.

[10] H. Valberg and W.Z. Misiolek, Proc. 9th Esaform Conf., Glasgow, 2006, p. 487.

The die lines of the extrudate were observed to form at the very exit end of the choked die channel. This shows that the sliding movement between the aluminum and the adhesion layer behind the transition point is one of intimate contact. The metal flow in the middle of the die channel was determined to conform to plug flow; the metal flowed through without significant plastic deformation. However, in the subsurface layer of Al adjacent to the sticking zone on the die wall, a layer of material remained almost stationary in the channel. Due to this, material flowed radially outwards toward the rod surface at the end of this layer. Knowing how the contact conditions really are at the die land due to the grid pattern techniques used in this study, it has been possible to model the deformation conditions in the bearing by means of FEA with good similarity to the observations in the experiments. Thus FEA confirmed that there is plug flow in the interior of the die channel, and that a heavily shear deformed layer forms adjacent to the sticking zone on the inlet side of the die channel. At the stick-slip transition point behind the sticking zone, however, the material starts to flow approximately like a plug over the whole diameter of the channel, in the sliding contact zone behind this point. However, some small deformations are subjected to the material there in terms of a deformation cross with low strain rates.

References

[1] R. Akeret, Aluminium, Vol. 59, No. 10, 1983, pp. E355-E360

[2] R. Akeret and W. Strehmel, Proc. of the 4th Int'l. Al. Extr. Techn. Sem., Vol. II, April 11-14, 1988, Chicago, pp. 357 - 367.

[3] W. Thedja, K. B. Müller and D. Ruppin, Aluminium, Vol. 69, No. 6, 1993, pp. 543 – 547.

[4] Akeret, R. ; Aluminium, Vol.61, No.3, 1985, pp. E1 66 – E1 69.

[5] G. Lang, Aluminium, Vol. 60, No. 4, 1984, pp. E249-E251.

[6] G. Lang, Aluminium, Vol.57, No. 12, 1981, pp.791 -796.

[7] W. Ziegler and G. Hartmann, Vol. 83, 1977, pp. 2034-2036.

[8] H. Valberg and T. Malvik, Int. J. Mat. Prod. Techn., Vol. 9, Nos. 4/5/6, 1994, pp. 428-463.

[9] H. Valberg and T. Malvik, Proc. 6th Int. Al. Extr. Techn., Sem., Chicago, Vol.2, 1996, p. 17.

[10] H. Valberg and W.Z. Misiolek, Proc. 9th Esaform Conf., Glasgow, 2006, p. 487.


Friction in double action extrusion

Liliang Wang a, Jie Zhou b and Jurek Duszczyk c Department of Materials Science and Engineering, Delft University of Technology,

Mekelweg 2, 2628 CD Delft, The Netherlands [email protected], [email protected], [email protected]

Keywords: Friction; FEM simulation; Extrusion; Aluminum Abstract. A novel extrusion testing method, double action extrusion (DAE), to highlight the effect of friction at the die bearing in aluminum extrusion was developed. It was found that the lengths of the extrudates and extrusion force were indeed sensitive to the die bearing length and thus to the friction. FEM simulations of DAE were carried out to evaluate the shear and Coulomb friction models over a wide range of friction factors/coefficients from 0.2 to 1. The full sticking friction appeared to represent the interfacial contact between hot aluminum and die the best. The friction factor values in the shear friction model over a range of 0.3 to 0.6 commonly used to describe the contact at the billet-die interface in FEM simulation appeared to be too low. The comparison between the experimental and simulation results indicated that the shear friction model at m = 1 predicted the extrusion force the best, while the Coulomb friction model at µ = 1 predicted the extrudate lengths the best. Of the existing friction models and friction factors/coefficients, it is recommended to use the shear friction model at m = 1 to describe the friction at the billet-die interface in FEM simulation.

Introduction

In the FEM analysis of the aluminium extrusion process, the accuracy of the results is strongly influenced by two main factors: (i) the flow stress of the workpiece material as a function of strain, strain rate and temperature and (ii) the friction conditions at the workpiece-tooling interfaces. Obviously, sensible selection of friction model and friction factor is of critical importance for reliable FEM analysis of the aluminum extrusion process [1-4]. The shear (Tresca) friction model has been almost exclusively used in the FEM simulation of the

aluminum extrusion process. The model assumes that the friction stress f is independent of the contact pressure and proportional to the shear flow stress of the workpiece material. The shear friction model is commonly expressed as:

f mk= (1)

where k is the shear flow stress of the softer material and m the friction factor that may vary between 0 and 1. 0m = represents the frictionless contact, while 1m = indicates the full sticking condition. The Coulomb friction model is another friction model that is mostly used in the low contact

pressure conditions. In this model, the friction stress is considered proportional to the contact pressure p:

f pµ= (2)

The friction stress calculated from the Coulomb friction model tends to be higher than the shear flow stress of the workpiece material. Because of the tendency of overestimating the friction stress, the Coulomb friction model is rarely used in the FEM simulation of the aluminum extrusion process, unless the shear flow stress of the workpiece material is taken into consideration [5-6].

Friction in double action extrusion

Liliang Wang a, Jie Zhou b and Jurek Duszczyk c Department of Materials Science and Engineering, Delft University of Technology,

Mekelweg 2, 2628 CD Delft, The Netherlands [email protected], [email protected], [email protected]

Keywords: Friction; FEM simulation; Extrusion; Aluminum Abstract. A novel extrusion testing method, double action extrusion (DAE), to highlight the effect of friction at the die bearing in aluminum extrusion was developed. It was found that the lengths of the extrudates and extrusion force were indeed sensitive to the die bearing length and thus to the friction. FEM simulations of DAE were carried out to evaluate the shear and Coulomb friction models over a wide range of friction factors/coefficients from 0.2 to 1. The full sticking friction appeared to represent the interfacial contact between hot aluminum and die the best. The friction factor values in the shear friction model over a range of 0.3 to 0.6 commonly used to describe the contact at the billet-die interface in FEM simulation appeared to be too low. The comparison between the experimental and simulation results indicated that the shear friction model at m = 1 predicted the extrusion force the best, while the Coulomb friction model at µ = 1 predicted the extrudate lengths the best. Of the existing friction models and friction factors/coefficients, it is recommended to use the shear friction model at m = 1 to describe the friction at the billet-die interface in FEM simulation.

Introduction

In the FEM analysis of the aluminium extrusion process, the accuracy of the results is strongly influenced by two main factors: (i) the flow stress of the workpiece material as a function of strain, strain rate and temperature and (ii) the friction conditions at the workpiece-tooling interfaces. Obviously, sensible selection of friction model and friction factor is of critical importance for reliable FEM analysis of the aluminum extrusion process [1-4]. The shear (Tresca) friction model has been almost exclusively used in the FEM simulation of the

aluminum extrusion process. The model assumes that the friction stress f is independent of the contact pressure and proportional to the shear flow stress of the workpiece material. The shear friction model is commonly expressed as:

f mk= (1)

where k is the shear flow stress of the softer material and m the friction factor that may vary between 0 and 1. 0m = represents the frictionless contact, while 1m = indicates the full sticking condition. The Coulomb friction model is another friction model that is mostly used in the low contact

pressure conditions. In this model, the friction stress is considered proportional to the contact pressure p:

f pµ= (2)

The friction stress calculated from the Coulomb friction model tends to be higher than the shear flow stress of the workpiece material. Because of the tendency of overestimating the friction stress, the Coulomb friction model is rarely used in the FEM simulation of the aluminum extrusion process, unless the shear flow stress of the workpiece material is taken into consideration [5-6].


In nearly all of the FEM simulations of the aluminum extrusion process performed in recent years, the full or nearly full sticking condition at the billet-container interface has been assumed, on the basis of experimental observations and industrial experience [4]. The shear friction model and a friction factor m at or close to 1 have been used in these FEM simulations. At the billet-die interface, however, the contact condition is more complicated and the assumption of a friction condition for FEM simulation has entailed a higher degree of uncertainty. This is because both of a full sticking zone and a sliding zone in the billet-die interface have been experimentally observed [7]. To avoid the complications, the contact has been simplified to be of the sliding type and a constant friction factor ranging between 0.3 and 0.6 used [8-11]. While the friction at the billet-die interface is of crucial importance for the aluminum extrusion process, the contact at this interface is the least confident factor in FEM simulation. General rules guiding the selection of the friction model and friction factor/coefficient have not been established. The fundamental reason is that, in direct extrusion, the contact area between the billet and die bearing is very small, relative to the contact area between the billet and container. Thus, the friction at the billet-die interface accounts for a very small fraction of the total extrusion force measurable. Any variation of the friction tends to be not recognizable in the total extrusion force that is several orders higher and contains a certain degree of inaccuracy and non-reproducibility. In the present research, a novel extrusion process, double action extrusion (DAE), was introduced

to highlight the friction at the billet-die interface so as to aid in identifying the friction mode and determining the friction factor/coefficient. Both of the shear and Coulomb friction models over a wide range of factors/coefficients were evaluated.

Double action extrusion (DAE)

Fig. 1 shows the schematic of DAE and the experimental setup. During the experiments on a Gleeble thermomechanical simulator, an aluminum billet was pressed against two extrusion dies with different bearing lengths (6 and 2 mm) simultaneously. A 15’ chock angle was assigned to the bearing of the dies in order to enhance the effect of the friction on the DAE results. It was expected that the differentiated lengths of the extrudates passing these two bearing channels as well as the extrusion force could be used to characterize the friction at the die bearing.

(a) (b)

Fig. 1: (a) Schematic and (b) experimental setup of double action extrusion (DAE).

Experimental and FEM simulation details

The aluminum alloy AA7475 was used as the billet material. The extrusion tooling, i.e. two extrusion dies with different bearing lengths and one container, was made of the H11 hot-work tool steel. Their physical properties are listed in Table 1. Fig. 2 shows the aluminum billet and extrusion tooling used in the DAE experiments. The dimensions of the billet, extrusion dies and container, together with the main process parameters, are listed in Table 2. The DAE experiments were carried out at 350, 400 and

In nearly all of the FEM simulations of the aluminum extrusion process performed in recent years, the full or nearly full sticking condition at the billet-container interface has been assumed, on the basis of experimental observations and industrial experience [4]. The shear friction model and a friction factor m at or close to 1 have been used in these FEM simulations. At the billet-die interface, however, the contact condition is more complicated and the assumption of a friction condition for FEM simulation has entailed a higher degree of uncertainty. This is because both of a full sticking zone and a sliding zone in the billet-die interface have been experimentally observed [7]. To avoid the complications, the contact has been simplified to be of the sliding type and a constant friction factor ranging between 0.3 and 0.6 used [8-11]. While the friction at the billet-die interface is of crucial importance for the aluminum extrusion process, the contact at this interface is the least confident factor in FEM simulation. General rules guiding the selection of the friction model and friction factor/coefficient have not been established. The fundamental reason is that, in direct extrusion, the contact area between the billet and die bearing is very small, relative to the contact area between the billet and container. Thus, the friction at the billet-die interface accounts for a very small fraction of the total extrusion force measurable. Any variation of the friction tends to be not recognizable in the total extrusion force that is several orders higher and contains a certain degree of inaccuracy and non-reproducibility. In the present research, a novel extrusion process, double action extrusion (DAE), was introduced

to highlight the friction at the billet-die interface so as to aid in identifying the friction mode and determining the friction factor/coefficient. Both of the shear and Coulomb friction models over a wide range of factors/coefficients were evaluated.

Double action extrusion (DAE)

Fig. 1 shows the schematic of DAE and the experimental setup. During the experiments on a Gleeble thermomechanical simulator, an aluminum billet was pressed against two extrusion dies with different bearing lengths (6 and 2 mm) simultaneously. A 15’ chock angle was assigned to the bearing of the dies in order to enhance the effect of the friction on the DAE results. It was expected that the differentiated lengths of the extrudates passing these two bearing channels as well as the extrusion force could be used to characterize the friction at the die bearing.

(a) (b)

Fig. 1: (a) Schematic and (b) experimental setup of double action extrusion (DAE).

Experimental and FEM simulation details

The aluminum alloy AA7475 was used as the billet material. The extrusion tooling, i.e. two extrusion dies with different bearing lengths and one container, was made of the H11 hot-work tool steel. Their physical properties are listed in Table 1. Fig. 2 shows the aluminum billet and extrusion tooling used in the DAE experiments. The dimensions of the billet, extrusion dies and container, together with the main process parameters, are listed in Table 2. The DAE experiments were carried out at 350, 400 and


450°C typical of the temperatures used in aluminum extrusion. The speed of the moving anvils was 1 mm/s. To facilitate the comparison with the extrusion process to produce non-symmetrically shaped

profiles in the future and minimize possible differences caused by different FEM codes, in the present research, DEFORM-3D version 6.1, was employed to analyze the DAE process to produce extrudates in the form of round bars. To save computing time, one-sixteenth of the workpiece and tooling were modeled. The symmetry planes were assumed to be immobile with no material moving across. The materials, geometrical and process parameters used in the FEM simulations were exactly the same as those used in the DAE experiments. Table 1 Physical properties of the AA7475 workpiece and H11 tooling

Property AA 7475 H-11 tool steel

Heat capacity (N/mm2°C) 2.43369 3.2 at 315°C 4.5 at 540°C

Thermal conductivity (W/m°C) 180.181 24

Heat transfer coefficient between tooling and billet (N/°C s mm2) 11 11

Heat transfer coefficient between tooling/billet and air (N/°C s mm2) 0.02 0.02

Emissivity 0.7 0.7

Fig. 2: Aluminum alloy billet and steel tooling used in the DAE experiments. Table 2 Dimensions of the billet and DAE tooling as well as the main process parameters

Billet length (mm) 15 Billet diameter (mm) 9.8 Container inside diameter (mm) 10 Container outside diameter (mm) 20 Die bearing length (mm) 2 and 6 Chock angle (min) 15 Reduction ratio 11 Initial billet temperature (°C) 350, 400 and 450 Initial tooling temperature (°C) 350, 400 and 450 Anvil speed (mm/s) 1

450°C typical of the temperatures used in aluminum extrusion. The speed of the moving anvils was 1 mm/s. To facilitate the comparison with the extrusion process to produce non-symmetrically shaped

profiles in the future and minimize possible differences caused by different FEM codes, in the present research, DEFORM-3D version 6.1, was employed to analyze the DAE process to produce extrudates in the form of round bars. To save computing time, one-sixteenth of the workpiece and tooling were modeled. The symmetry planes were assumed to be immobile with no material moving across. The materials, geometrical and process parameters used in the FEM simulations were exactly the same as those used in the DAE experiments. Table 1 Physical properties of the AA7475 workpiece and H11 tooling

Property AA 7475 H-11 tool steel

Heat capacity (N/mm2°C) 2.43369 3.2 at 315°C 4.5 at 540°C

Thermal conductivity (W/m°C) 180.181 24

Heat transfer coefficient between tooling and billet (N/°C s mm2) 11 11

Heat transfer coefficient between tooling/billet and air (N/°C s mm2) 0.02 0.02

Emissivity 0.7 0.7

Fig. 2: Aluminum alloy billet and steel tooling used in the DAE experiments. Table 2 Dimensions of the billet and DAE tooling as well as the main process parameters

Billet length (mm) 15 Billet diameter (mm) 9.8 Container inside diameter (mm) 10 Container outside diameter (mm) 20 Die bearing length (mm) 2 and 6 Chock angle (min) 15 Reduction ratio 11 Initial billet temperature (°C) 350, 400 and 450 Initial tooling temperature (°C) 350, 400 and 450 Anvil speed (mm/s) 1


The materials of the aluminium billet and extrusion tooling were considered to behave as thermo-viscoplastic and thermo-rigid ones, respectively, and the elastic behavior of the materials was neglected. The flow stress/strain data of the AA7475 alloy were determined from hot compression tests using a Gleeble 3800 thermomechanical simulator, after flow stresses at high strain rates were corrected for deformational heating [12]. Flow stress–strain data over a temperature range of 250 – 500°C and a strain rate range of 0.01 – 180 s-1 were imported into DEFORM as the material model of the AA7475 alloy. All the objects in the FEM model were meshed with tetrahedral elements. To enhance the

efficiency of the FEM simulations and the accuracy in the areas of particular interest, a number of mesh windows with an increased element density were applied around the die orifices to generate local finer elements. A relative interference depth of 0.2 was defined to trigger the remeshing procedure. The friction at the billet-container and billet-die face interfaces was considered to be of shear type

and a friction factor m = 1 used. Friction windows were applied at the workpiece-die bearing interface to make the friction boundary condition adjustable. Both the shear friction model and the Coulomb friction model with friction factors/coefficients ranging from 0.2 to 1 were used in the FEM simulations to evaluate these friction models and determine the friction factor/coefficient. In DEFORM 3D version 6.1, to avoid the overestimation of the friction stress, the value of the friction stress calculated from the Coulomb friction model was compared with the shear flow stress of the workpiece material at each iteration step and automatically changed to the shear flow stress, if the calculated friction stress was larger than the shear flow stress. In this way, the Coulomb friction model could be used in the FEM simulation of the aluminum extrusion process at elevated temperatures.


The DAE experiments. Fig. 3 shows the extrudates with different lengths at different ram displacements. During the DAE experiments, the aluminum billet was pressed against two extrusion dies and extrusion in the indirect mode took place simultaneously through these two dies. The friction force for the extrudate to flow through the die with a bearing length of 6 mm was greater than that through the die with a bearing length of 2 mm, as soon as the extrudate flew through the die with a shorter bearing channel. As a result, the lengths of the extrudates were significantly different due to the sensitivity of extrusion speed to the friction force at the die bearing.

Fig. 3: Extrudates at different ram displacements from the DAE experiments.

Fig. 4 shows the extrusion forces measured, when DAE was performed at 350, 400 and 450 0C. As can be seen, the extrusion forces decrease markedly with increasing temperature, mainly due to decreasing flow stress of the workpiece material with rising temperature. The extrusion forces at these temperatures show a similar trend, i.e. a small plateau at the very early stage, followed by a sharp increase in extrusion force and then a gentle decrease as the process proceeded further. The small plateau corresponds to the initiation of extrusion toward both of the die (upsetting) and the sharp force increase corresponds to breakthrough. In DAE, there is no friction between the billet and container and therefore the extrusion force in the steady state reflects the dynamic balance of the billet material (work hardening and dynamic restoration) which is governed by temperature and influenced by the temperature evolution during DAE.

The materials of the aluminium billet and extrusion tooling were considered to behave as thermo-viscoplastic and thermo-rigid ones, respectively, and the elastic behavior of the materials was neglected. The flow stress/strain data of the AA7475 alloy were determined from hot compression tests using a Gleeble 3800 thermomechanical simulator, after flow stresses at high strain rates were corrected for deformational heating [12]. Flow stress–strain data over a temperature range of 250 – 500°C and a strain rate range of 0.01 – 180 s-1 were imported into DEFORM as the material model of the AA7475 alloy. All the objects in the FEM model were meshed with tetrahedral elements. To enhance the

efficiency of the FEM simulations and the accuracy in the areas of particular interest, a number of mesh windows with an increased element density were applied around the die orifices to generate local finer elements. A relative interference depth of 0.2 was defined to trigger the remeshing procedure. The friction at the billet-container and billet-die face interfaces was considered to be of shear type

and a friction factor m = 1 used. Friction windows were applied at the workpiece-die bearing interface to make the friction boundary condition adjustable. Both the shear friction model and the Coulomb friction model with friction factors/coefficients ranging from 0.2 to 1 were used in the FEM simulations to evaluate these friction models and determine the friction factor/coefficient. In DEFORM 3D version 6.1, to avoid the overestimation of the friction stress, the value of the friction stress calculated from the Coulomb friction model was compared with the shear flow stress of the workpiece material at each iteration step and automatically changed to the shear flow stress, if the calculated friction stress was larger than the shear flow stress. In this way, the Coulomb friction model could be used in the FEM simulation of the aluminum extrusion process at elevated temperatures.


The DAE experiments. Fig. 3 shows the extrudates with different lengths at different ram displacements. During the DAE experiments, the aluminum billet was pressed against two extrusion dies and extrusion in the indirect mode took place simultaneously through these two dies. The friction force for the extrudate to flow through the die with a bearing length of 6 mm was greater than that through the die with a bearing length of 2 mm, as soon as the extrudate flew through the die with a shorter bearing channel. As a result, the lengths of the extrudates were significantly different due to the sensitivity of extrusion speed to the friction force at the die bearing.

Fig. 3: Extrudates at different ram displacements from the DAE experiments.

Fig. 4 shows the extrusion forces measured, when DAE was performed at 350, 400 and 450 0C. As can be seen, the extrusion forces decrease markedly with increasing temperature, mainly due to decreasing flow stress of the workpiece material with rising temperature. The extrusion forces at these temperatures show a similar trend, i.e. a small plateau at the very early stage, followed by a sharp increase in extrusion force and then a gentle decrease as the process proceeded further. The small plateau corresponds to the initiation of extrusion toward both of the die (upsetting) and the sharp force increase corresponds to breakthrough. In DAE, there is no friction between the billet and container and therefore the extrusion force in the steady state reflects the dynamic balance of the billet material (work hardening and dynamic restoration) which is governed by temperature and influenced by the temperature evolution during DAE.


0 1 2 3 4 5 60

10

20

30

40

50

60

70

400oC350oC

450oC

Extrusion force (kN)

Ram displacement (mm)

Fig. 4: Extrusion forces measured during the DAE experiments at different temperatures.

Extrudate lengths. Fig. 5 shows the comparison in the lengths of the extrudates between the DAE experiments and FEM simulations. As can be seen, the relative lengths of the extrudates are not really sensitive to the temperature. As soon as the extrudate is out of the 2 mm long die bearing, the extrudate lengths start to diverge. In other words, with the extrusion process proceeding, the difference in extrudate length becomes greater. Obviously, the friction force at the bearing channel plays a decisive role in the DAE process. In this figure, the FEM predictions of the extrudate lengths based on the shear and Coulomb friction models over a range of friction factors/coefficients are superimposed onto the experimental data. At these three extrusion temperatures, the Coulomb friction model at µ = 1 gives the best predictions of the extrudate lengths. The predictions of the shear friction model at m = 1 are quite accurate as well, although small deviations from the experimental measurements can be found at the high temperatures (Fig. 5b and c). These deviations may be partly caused by the errors of numerical iterations. Nevertheless, the results of the present research clearly indicate that a friction factor in the range from 0.3 to 0.6 often assumed at the die bearing during aluminum extrusion may be too low and the friction in the die bearing channel may be better represented by using the sticking boundary condition. Steady-state extrusion force. Fig. 6 shows the steady-state extrusion forces at different extrusion temperatures. The extrusion force decreases with increasing temperature as a result of material softening at higher temperatures. Of more interest is the comparison in the experimentally measured extrusion forces and those predicted on the basis of the shear and Coulomb friction models at different friction factors/coefficients. It can be seen that both of the models show the same trend as the experimental results in terms of the effect of temperature on the extrusion force. However, the extrusion forces predicted vary over a wide range, as a result of different friction conditions assigned. From Fig. 6, it appears that the shear friction model at m = 1 yields the extrusion forces the closest to the experimental measurements, although a deviation of 7.7% at 350°C exists. The results of the Coulomb friction model at µ = 1 with a deviation of 12.2% or smaller from the experimental results may still be acceptable. At the other friction conditions, however, the predicted extrusion forces are all much lower than the experimental results, having deviations greater than 25%. It is clear that the steady-state extrusion force is indeed highly sensitive to the friction at the die bearing in DAE. The shear friction model with a large friction factor (m = 1) describes the friction boundary condition at the die bearing the best.

0 1 2 3 4 5 60

10

20

30

40

50

60

70

400oC350oC

450oC

Extrusion force (kN)

Ram displacement (mm)

Fig. 4: Extrusion forces measured during the DAE experiments at different temperatures.

Extrudate lengths. Fig. 5 shows the comparison in the lengths of the extrudates between the DAE experiments and FEM simulations. As can be seen, the relative lengths of the extrudates are not really sensitive to the temperature. As soon as the extrudate is out of the 2 mm long die bearing, the extrudate lengths start to diverge. In other words, with the extrusion process proceeding, the difference in extrudate length becomes greater. Obviously, the friction force at the bearing channel plays a decisive role in the DAE process. In this figure, the FEM predictions of the extrudate lengths based on the shear and Coulomb friction models over a range of friction factors/coefficients are superimposed onto the experimental data. At these three extrusion temperatures, the Coulomb friction model at µ = 1 gives the best predictions of the extrudate lengths. The predictions of the shear friction model at m = 1 are quite accurate as well, although small deviations from the experimental measurements can be found at the high temperatures (Fig. 5b and c). These deviations may be partly caused by the errors of numerical iterations. Nevertheless, the results of the present research clearly indicate that a friction factor in the range from 0.3 to 0.6 often assumed at the die bearing during aluminum extrusion may be too low and the friction in the die bearing channel may be better represented by using the sticking boundary condition. Steady-state extrusion force. Fig. 6 shows the steady-state extrusion forces at different extrusion temperatures. The extrusion force decreases with increasing temperature as a result of material softening at higher temperatures. Of more interest is the comparison in the experimentally measured extrusion forces and those predicted on the basis of the shear and Coulomb friction models at different friction factors/coefficients. It can be seen that both of the models show the same trend as the experimental results in terms of the effect of temperature on the extrusion force. However, the extrusion forces predicted vary over a wide range, as a result of different friction conditions assigned. From Fig. 6, it appears that the shear friction model at m = 1 yields the extrusion forces the closest to the experimental measurements, although a deviation of 7.7% at 350°C exists. The results of the Coulomb friction model at µ = 1 with a deviation of 12.2% or smaller from the experimental results may still be acceptable. At the other friction conditions, however, the predicted extrusion forces are all much lower than the experimental results, having deviations greater than 25%. It is clear that the steady-state extrusion force is indeed highly sensitive to the friction at the die bearing in DAE. The shear friction model with a large friction factor (m = 1) describes the friction boundary condition at the die bearing the best.


(a)

(b)

(c)

Fig. 5: Comparison in the extrudate lengths from DAE at (a) 350, (b) 400 and (c) 450°C between the experiments and FEM simulations.

(a)

(b)

(c)

Fig. 5: Comparison in the extrudate lengths from DAE at (a) 350, (b) 400 and (c) 450°C between the experiments and FEM simulations.


Fig. 6: Steady-state extrusion forces at different extrusion temperatures.

Summary

The DAE experiments and FEM simulations were carried out. It was confirmed that the measurable parameters of the DAE experiments, i.e. extrudate lengths and extrusion force, were both sensitive to the friction at the die bearing. The comparisons between the FEM simulation and DAE experimental results indicated that the commonly assumed friction factor values over a range of 0.3 to 0.6 in the shear friction model at the billet-die bearing interface might be inappropriate and the full sticking condition would represent the interfacial contact better. In terms of the extrudate lengths, the Coulomb model at µ = 1 yielded the results the closest to the experimental measurements. In terms of the steady-state extrusion force, the shear friction model at m = 1 was in agreement with the experiments reasonably well. Of the existing friction models and friction factors/coefficients, the shear model at m = 1 is recommended to describe the friction condition at the die bearing in FEM simulation of the aluminum extrusion process.

Acknowledgements

The authors express their appreciation to Prof. Gang Liu, Mr. Lambert Schipperheijn, Mr. Hans Hofman and Mr. Floris Slooff for their help in the DAE experiments.

References

[1] I. Flitta and T. Sheppard: Nature of friction in extrusion process and its effect on material flow, Mater. Sci. Technol. Vol. 19 (2003), p. 837.

[2] L. Wang, Y. He, J. Zhou and J. Duszczyk: Modelling of plowing and shear friction coefficients during high-temperature ball-on-disc tests, Tribol. Int. Vol. 42 (2009) p. 15.

[3] L. Wang, Y. He, J. Zhou and J. Duszczyk: Effect of temperature on the frictional behaviour of an aluminium alloy sliding against steel during ball-on-disc tests, Tribol. Int. (2009), in press.

Fig. 6: Steady-state extrusion forces at different extrusion temperatures.

Summary

The DAE experiments and FEM simulations were carried out. It was confirmed that the measurable parameters of the DAE experiments, i.e. extrudate lengths and extrusion force, were both sensitive to the friction at the die bearing. The comparisons between the FEM simulation and DAE experimental results indicated that the commonly assumed friction factor values over a range of 0.3 to 0.6 in the shear friction model at the billet-die bearing interface might be inappropriate and the full sticking condition would represent the interfacial contact better. In terms of the extrudate lengths, the Coulomb model at µ = 1 yielded the results the closest to the experimental measurements. In terms of the steady-state extrusion force, the shear friction model at m = 1 was in agreement with the experiments reasonably well. Of the existing friction models and friction factors/coefficients, the shear model at m = 1 is recommended to describe the friction condition at the die bearing in FEM simulation of the aluminum extrusion process.

Acknowledgements

The authors express their appreciation to Prof. Gang Liu, Mr. Lambert Schipperheijn, Mr. Hans Hofman and Mr. Floris Slooff for their help in the DAE experiments.

References

[1] I. Flitta and T. Sheppard: Nature of friction in extrusion process and its effect on material flow, Mater. Sci. Technol. Vol. 19 (2003), p. 837.

[2] L. Wang, Y. He, J. Zhou and J. Duszczyk: Modelling of plowing and shear friction coefficients during high-temperature ball-on-disc tests, Tribol. Int. Vol. 42 (2009) p. 15.

[3] L. Wang, Y. He, J. Zhou and J. Duszczyk: Effect of temperature on the frictional behaviour of an aluminium alloy sliding against steel during ball-on-disc tests, Tribol. Int. (2009), in press.


[4] M. Schikorra, L. Donati, L. Tomesani and M. Kleiner: The role of friction in the extrusion of AA6060 aluminum alloy, process analysis and monitoring, J. Mater. Process. Technol. Vol. 191 (2007), p. 292.

[5] E. Orowan: The calculation of roll pressure in hot and cold flat rolling, in: Proceedings of the Institution of Mechanical Engineers Vol. 150 (1943), p. 140.

[6] T. Wanheim, N. Bay, A. S. Petersen: A theoretically determined model for friction in metal working processes, Wear Vol. 28 (1974), p. 251.

[7] S. Tverlid: Modeling of Friction in the Bearing Channel of Dies for Extrusion of Aluminum Sections (PhD Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 1997).

[8] L. Li, J. Zhou and J. Duszczyk: Prediction of temperature evolution during the extrusion of 7075 aluminium alloy at various ram speeds by means of 3D FEM simulation, J. Mater. Process. Technol. Vol. 145 (2004), p. 360.

[9] I. Flitta, T. Sheppard and Z. Peng: FEM analysis to predict development of structure during extrusion and subsequent solution soak cycle, Mater. Sci. Technol. Vol. 23 (2007), p. 582-592.

[10] X. Duan, X. Velay and T. Sheppard: Application of finite element method in the hot extrusion of aluminium alloys, Mater. Sci. Eng. Vol. 369 (2004), p. 66.

[11] G. Fang, J. Zhou and J. Duszczyk: Extrusion of 7075 aluminium alloy through double-pocket dies to manufacture a complex profile, J. Mater. Process. Technol. Vol. 209 (2009), p. 3050.

[12] G.J. Pluijms: Flow Stress Characterization of Aluminum Alloys in Warm and Hot Working Conditions (Master’s Thesis, Delft University of Technology, Delft, the Netherlands, November 2008).

[4] M. Schikorra, L. Donati, L. Tomesani and M. Kleiner: The role of friction in the extrusion of AA6060 aluminum alloy, process analysis and monitoring, J. Mater. Process. Technol. Vol. 191 (2007), p. 292.

[5] E. Orowan: The calculation of roll pressure in hot and cold flat rolling, in: Proceedings of the Institution of Mechanical Engineers Vol. 150 (1943), p. 140.

[6] T. Wanheim, N. Bay, A. S. Petersen: A theoretically determined model for friction in metal working processes, Wear Vol. 28 (1974), p. 251.

[7] S. Tverlid: Modeling of Friction in the Bearing Channel of Dies for Extrusion of Aluminum Sections (PhD Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 1997).

[8] L. Li, J. Zhou and J. Duszczyk: Prediction of temperature evolution during the extrusion of 7075 aluminium alloy at various ram speeds by means of 3D FEM simulation, J. Mater. Process. Technol. Vol. 145 (2004), p. 360.

[9] I. Flitta, T. Sheppard and Z. Peng: FEM analysis to predict development of structure during extrusion and subsequent solution soak cycle, Mater. Sci. Technol. Vol. 23 (2007), p. 582-592.

[10] X. Duan, X. Velay and T. Sheppard: Application of finite element method in the hot extrusion of aluminium alloys, Mater. Sci. Eng. Vol. 369 (2004), p. 66.

[11] G. Fang, J. Zhou and J. Duszczyk: Extrusion of 7075 aluminium alloy through double-pocket dies to manufacture a complex profile, J. Mater. Process. Technol. Vol. 209 (2009), p. 3050.

[12] G.J. Pluijms: Flow Stress Characterization of Aluminum Alloys in Warm and Hot Working Conditions (Master’s Thesis, Delft University of Technology, Delft, the Netherlands, November 2008).


A new cone-friction test for evaluating friction phenomena in extrusion processes

C. Karadogan1, a, R. Grueebler1, b and P. Hora1, c 1ETH Zurich, Institute of virtual manufacturing, Tannenstr. 3, 8092 Zurich, Switzerland [email protected], [email protected], [email protected]

Keywords: Friction modeling, Aluminum extrusion

Abstract. Friction is one of the most influential parameters in extrusion processes. The flow distribution is controlled using the effect of friction lengths on the extrusion dies. A comparison between multi-hole die aluminum extrusion experiments and simulations [1] necessitated studies on numerical and physical modeling of friction during aluminum extrusion. In order to measure the friction under conditions similar to extrusion processes a new experimental setup is proposed.

Introduction and Motivation

Extrusion process is highly sensitive to frictional effects. This was shown by the multi-hole die extrusion experiments of the IVP benchmark 2005 [1, 2]. The die (Fig. 1 left) had 5 cylindrical outlets: One of them being central, the others lie on the same central circle, where the only difference among the holes is their diameters. The different profile lengths demonstrate that even small deviations in the shape of channels have significant influence on the velocity distribution. The presented FEM simulations at that time mostly failed to predict this sensitive behavior correctly (Fig. 1 right). The reason was not only the lack of correct friction coefficients, which led to the use of constant values for friction together with conventional friction modeling like the Coulomb, shear or shear-limited-Coulomb, but a too simplified FEM implementation of the friction models as well. These results triggered a study on the development of new friction model implementations for extrusion process simulations, which are published in [3]. The recent goal is to specify the friction coefficient as a function of temperature, pressure and relative velocity. This study aims to develop an experimental setup to investigate such relations.

Fig. 1: Benchmark Extrusion Zurich 2005. Cooperators: SPZ- TU-Berlin & WEFA Test Die 1.15.

A new cone-friction test for evaluating friction phenomena in extrusion processes

C. Karadogan1, a, R. Grueebler1, b and P. Hora1, c 1ETH Zurich, Institute of virtual manufacturing, Tannenstr. 3, 8092 Zurich, Switzerland [email protected], [email protected], [email protected]

Keywords: Friction modeling, Aluminum extrusion

Abstract. Friction is one of the most influential parameters in extrusion processes. The flow distribution is controlled using the effect of friction lengths on the extrusion dies. A comparison between multi-hole die aluminum extrusion experiments and simulations [1] necessitated studies on numerical and physical modeling of friction during aluminum extrusion. In order to measure the friction under conditions similar to extrusion processes a new experimental setup is proposed.

Introduction and Motivation

Extrusion process is highly sensitive to frictional effects. This was shown by the multi-hole die extrusion experiments of the IVP benchmark 2005 [1, 2]. The die (Fig. 1 left) had 5 cylindrical outlets: One of them being central, the others lie on the same central circle, where the only difference among the holes is their diameters. The different profile lengths demonstrate that even small deviations in the shape of channels have significant influence on the velocity distribution. The presented FEM simulations at that time mostly failed to predict this sensitive behavior correctly (Fig. 1 right). The reason was not only the lack of correct friction coefficients, which led to the use of constant values for friction together with conventional friction modeling like the Coulomb, shear or shear-limited-Coulomb, but a too simplified FEM implementation of the friction models as well. These results triggered a study on the development of new friction model implementations for extrusion process simulations, which are published in [3]. The recent goal is to specify the friction coefficient as a function of temperature, pressure and relative velocity. This study aims to develop an experimental setup to investigate such relations.

Fig. 1: Benchmark Extrusion Zurich 2005. Cooperators: SPZ- TU-Berlin & WEFA Test Die 1.15.


Friction behavior and mathematical models

Most of the finite element codes make use of the classical Coulomb friction model with npµτ = ,

or shear friction model with Ymστ = . In both cases, the friction parameters µ and m are assumed to be constant. The Coulomb friction model has the incorrect limits of 0=τ for 0=np , and ∞=τ

for ∞=np . Shear friction model has again the lower limit of 0=τ for the vanishing strain rate, 0=γ& , which is not correct either. The observed contamination on the aluminum extrusion dies are all clues for the sticking of the

material. Additionally the friction has to be described as a function of pressure, temperature and effective relative velocity ),,( relvTpττ = (1) Fig. 2 shows the boundary region of the profile, where complex friction and thermal conditions are active. Recent studies [4, 5] have confirmed the dependence of the friction coefficients on the process parameters pressure, temperature and velocity.

Fig. 2: Assumed frictional behavior during hot aluminum extrusion.

Experimental methods

In the above mentioned aspects, neither the pin-on-disk setup, Fig. 3, nor the ring upsetting technique [6] provides physically dependable values for the friction modeling used in extrusion process simulations. High pressure also produces side effects in the pin-on-disk investigation. Furthermore, the nature of contact attained in the pin-on-disk setup is not similar to that of extrusion. The achieved relative velocities in a ring upsetting test are much lower than the values attained in extrusion. Furthermore, the pressure, for which the corresponding friction coefficient is measured, is averaged to a greater extent in a ring upsetting test.

Fig. 3: High temperature pin-on-disk tribometer.

Friction behavior and mathematical models

Most of the finite element codes make use of the classical Coulomb friction model with npµτ = ,

or shear friction model with Ymστ = . In both cases, the friction parameters µ and m are assumed to be constant. The Coulomb friction model has the incorrect limits of 0=τ for 0=np , and ∞=τ

for ∞=np . Shear friction model has again the lower limit of 0=τ for the vanishing strain rate, 0=γ& , which is not correct either. The observed contamination on the aluminum extrusion dies are all clues for the sticking of the

material. Additionally the friction has to be described as a function of pressure, temperature and effective relative velocity ),,( relvTpττ = (1) Fig. 2 shows the boundary region of the profile, where complex friction and thermal conditions are active. Recent studies [4, 5] have confirmed the dependence of the friction coefficients on the process parameters pressure, temperature and velocity.

Fig. 2: Assumed frictional behavior during hot aluminum extrusion.

Experimental methods

In the above mentioned aspects, neither the pin-on-disk setup, Fig. 3, nor the ring upsetting technique [6] provides physically dependable values for the friction modeling used in extrusion process simulations. High pressure also produces side effects in the pin-on-disk investigation. Furthermore, the nature of contact attained in the pin-on-disk setup is not similar to that of extrusion. The achieved relative velocities in a ring upsetting test are much lower than the values attained in extrusion. Furthermore, the pressure, for which the corresponding friction coefficient is measured, is averaged to a greater extent in a ring upsetting test.

Fig. 3: High temperature pin-on-disk tribometer.


Cone-friction test

To investigate the friction behavior in the extrusion process a new friction test setup has been developed. The setup uses a torsion testing machine as the testing facility, Fig. 4 left, and consists of a conical inner-tool in a conical aluminum ring (specimen) lying in an exterior-tool having a conical shape, Fig. 4 right. A schematic layout of the tool assembly is shown in Fig. 5. This assembly is then axially and rotationally loaded on the torsion testing machine, so that the ring plastifies under these loading conditions. The axial loading on the equipment is kept constant for each test. This is realized by first pressing the assembly axially up to a specified axial force. Then, keeping this axial force constant during the whole test, relative rotation is given to the assembly with a specified velocity. The required torque is then measured during the whole test. The system could be heated and kept at a specific temperature and the torque could be measured

for different pressures and (rotational) velocities, allowing the friction to be expressed as a function of pressure, temperature and velocity. Fig. 6 shows the finite element computation of the pressure distribution, before the beginning of the rotational loading, on the inner-tool interface for a relatively long specimen. This distribution will tend to a uniform distribution after some rotations. Even for the shown pressure distribution, the pressure fluctuation is less than 10 % for the majority of the contact surface. The experimental observations show that the inner contact interface tends to slip early. Therefore

all the analytical computation of the friction is based on the inner contact interface. After an amount of relative rotation the axial force balance is due only to normal stresses on the conical surface. This leads to the following relation

αsinaxial

FF = (2)

where F is the total normal force on the contact interface, Faxial is the axial force loaded by the plastometer, and α is the angle of conicity. Furthermore, the moment balance is expressed by

ave RFM µ= (3)

where the torque M measured by the torsion testing machine is a function of normal force, friction coefficient, µ, and the average radius, Rave of the inner cone. Combining (2) and (3) in one equation

Fig. 4: Torsion testing machine, three tool-couples with different coatings and the specimen.

Cone-friction test

To investigate the friction behavior in the extrusion process a new friction test setup has been developed. The setup uses a torsion testing machine as the testing facility, Fig. 4 left, and consists of a conical inner-tool in a conical aluminum ring (specimen) lying in an exterior-tool having a conical shape, Fig. 4 right. A schematic layout of the tool assembly is shown in Fig. 5. This assembly is then axially and rotationally loaded on the torsion testing machine, so that the ring plastifies under these loading conditions. The axial loading on the equipment is kept constant for each test. This is realized by first pressing the assembly axially up to a specified axial force. Then, keeping this axial force constant during the whole test, relative rotation is given to the assembly with a specified velocity. The required torque is then measured during the whole test. The system could be heated and kept at a specific temperature and the torque could be measured

for different pressures and (rotational) velocities, allowing the friction to be expressed as a function of pressure, temperature and velocity. Fig. 6 shows the finite element computation of the pressure distribution, before the beginning of the rotational loading, on the inner-tool interface for a relatively long specimen. This distribution will tend to a uniform distribution after some rotations. Even for the shown pressure distribution, the pressure fluctuation is less than 10 % for the majority of the contact surface. The experimental observations show that the inner contact interface tends to slip early. Therefore

all the analytical computation of the friction is based on the inner contact interface. After an amount of relative rotation the axial force balance is due only to normal stresses on the conical surface. This leads to the following relation

αsinaxial

FF = (2)

where F is the total normal force on the contact interface, Faxial is the axial force loaded by the plastometer, and α is the angle of conicity. Furthermore, the moment balance is expressed by

ave RFM µ= (3)

where the torque M measured by the torsion testing machine is a function of normal force, friction coefficient, µ, and the average radius, Rave of the inner cone. Combining (2) and (3) in one equation

Fig. 4: Torsion testing machine, three tool-couples with different coatings and the specimen.


Fig. 5: Schematic layout of the friction test.

Fig. 6: Pressure distribution on the inner contact interface.

aveaxial RFM α

µsin

= (4)

gives the friction coefficient. This value of the coefficient is valid for the specified temperature, velocity and normal pressure at inner contact interface. An average value for the normal pressure could be computed either analytically using F , or using a finite element computation. Since global balance equations are in either case fulfilled, both give the same result.


Selecting different materials (for the tools and specimen) and coatings, this test setup makes it possible to measure different influences on the friction. For the current study, the influence of coatings was investigated. Experiments for an uncoated tool and two different coatings have been performed. In Figures 7 & 8 the resulting torque is shown for two different axial pressing forces. The fluctuations in the torque measurements are due to the small misalignment of the inner and exterior tools. The uncoated tool results in the highest torque whereas the coatings 1 and 2 results in lower torques depending of the pressing forces. Details of the materials and the coatings are given in [7], another publication of this conference by our industrial collaboration partner WEFA.

Fig. 5: Schematic layout of the friction test.

Fig. 6: Pressure distribution on the inner contact interface.

aveaxial RFM α

µsin

= (4)

gives the friction coefficient. This value of the coefficient is valid for the specified temperature, velocity and normal pressure at inner contact interface. An average value for the normal pressure could be computed either analytically using F , or using a finite element computation. Since global balance equations are in either case fulfilled, both give the same result.


Selecting different materials (for the tools and specimen) and coatings, this test setup makes it possible to measure different influences on the friction. For the current study, the influence of coatings was investigated. Experiments for an uncoated tool and two different coatings have been performed. In Figures 7 & 8 the resulting torque is shown for two different axial pressing forces. The fluctuations in the torque measurements are due to the small misalignment of the inner and exterior tools. The uncoated tool results in the highest torque whereas the coatings 1 and 2 results in lower torques depending of the pressing forces. Details of the materials and the coatings are given in [7], another publication of this conference by our industrial collaboration partner WEFA.


Fig. 7: Measurements for the tested cases.

Fig. 8: Dependency of friction on temperature and axial force.

Conclusions

The new cone-friction test enables the control of temperature, pressure and relative velocity, yielding the measurement of friction dependent on these process parameters. Compared to conventional friction test setups, conditions similar to extrusion are better represented. This makes the information obtained from a cone-friction test valued especially for design of extrusion tools. The presented experimental results show the applicability of this new test for further investigations. As a complementary study, the results of these and further tests will be used in extrusion simulations for which the comparison with the reality is available.

References

[1] P. Hora, C. Karadogan, L. Tong: umerische Modellierung thermischer und tribologischer Randbedingungen, Conference Proceedings: Extrusion Zurich (2005)

[2] C. Karadogan, F. Vanini, L. Tong, P. Hora: State of the Art and Potential Development of Digital Extrusion Modeling, Light Metal Age, Volume 63 (May 2005), No. 3, pp. 40-43.

Fig. 7: Measurements for the tested cases.

Fig. 8: Dependency of friction on temperature and axial force.

Conclusions

The new cone-friction test enables the control of temperature, pressure and relative velocity, yielding the measurement of friction dependent on these process parameters. Compared to conventional friction test setups, conditions similar to extrusion are better represented. This makes the information obtained from a cone-friction test valued especially for design of extrusion tools. The presented experimental results show the applicability of this new test for further investigations. As a complementary study, the results of these and further tests will be used in extrusion simulations for which the comparison with the reality is available.

References

[1] P. Hora, C. Karadogan, L. Tong: umerische Modellierung thermischer und tribologischer Randbedingungen, Conference Proceedings: Extrusion Zurich (2005)

[2] C. Karadogan, F. Vanini, L. Tong, P. Hora: State of the Art and Potential Development of Digital Extrusion Modeling, Light Metal Age, Volume 63 (May 2005), No. 3, pp. 40-43.


[3] C. Karadogan; L. Tong, P. Hora: An Improved Modeling of Friction for Extrusion Simulations, 10TH ESAFORM CONFERENCE ON MATERIAL FORMING. AIP Conference Proceedings, Volume 907 (2007), pp. 1325-1330.

[4] B. Post-Pedersen; T. Wanheim, N. Bay, Verification of a friction test for warm and hot forging, ICFT '98, (1998), Issue: 3 pp. 253-261

[5] O. Cora, M. Akkok, H. Darendeliler, Modelling of variable friction in cold forging, Proceedings of the institution of Mechanical Engineers Part J-Journal of Engineering Tribology (2008), Volume 222 Issue: J7 Pages: 899-908

[6] K. Lange, Handbook of metal forming, McGraw-Hill Int. Book Company, USA (1985)

[7] Joachim Maier, CVD Coated Aluminium Extrusion Dies, Conference Proceedings: Extrusion Workshop (2009), Dortmund

[3] C. Karadogan; L. Tong, P. Hora: An Improved Modeling of Friction for Extrusion Simulations, 10TH ESAFORM CONFERENCE ON MATERIAL FORMING. AIP Conference Proceedings, Volume 907 (2007), pp. 1325-1330.

[4] B. Post-Pedersen; T. Wanheim, N. Bay, Verification of a friction test for warm and hot forging, ICFT '98, (1998), Issue: 3 pp. 253-261

[5] O. Cora, M. Akkok, H. Darendeliler, Modelling of variable friction in cold forging, Proceedings of the institution of Mechanical Engineers Part J-Journal of Engineering Tribology (2008), Volume 222 Issue: J7 Pages: 899-908

[6] K. Lange, Handbook of metal forming, McGraw-Hill Int. Book Company, USA (1985)

[7] Joachim Maier, CVD Coated Aluminium Extrusion Dies, Conference Proceedings: Extrusion Workshop (2009), Dortmund


Modelling of thermo-mechanical Behaviour of Magnesium Alloys during Indirect Extrusion

S. Ertürk1, a, D. Steglich1, b, J. Bohlen1, c, D.Letzig1, d and W. Brocks2, e 1 GKSS Research Centre, Institute of Materials Research, 21502 Geesthacht, Germany 2 Christian-Albrechts-University of Kiel, Faculty of Engineering, 24143 Kiel, Germany


Keywords: Rate-dependent-J3 plasticity, Fully thermo-mechanical coupled analysis, Extrusion, Magnesium alloys Abstract. A yield function for hexagonal closed packed (hcp) metals was modified with respect to strain rate and temperature and developed to capture the material behaviour during extrusion. Magnesium alloy ZEK100 was extruded indirectly at 300°C into a round bar. Compression tests were carried out at various strain rates, temperatures and sample orientation to characterise the material flow. These data were used as input data for fully thermo-mechanical coupled simulations of indirect extrusion. A successful prediction of the extrusion force and the temperature increase during extrusion is presented.

Introduction

Magnesium and its alloys have become promising materials saving structural weight and reducing fuel consumption especially for transportation industry, due to being the lightest metal for structural applications. One of the established production methods for semi-finished products is extrusion. For magnesium and its alloys, this technology is available today, but there is still a fundamental lack in understanding the factors that determine the development of microstructure and mechanical properties during the process. Such alloys show unusual mechanical characteristics such as deformation anisotropy and asymmetry in tension-compression, which originate from the hexagonal closed packed (hcp) crystallographic structure and the distinct textures that develop during massive deformation such as extrusion. A phenomenological model derived by Cazacu and Barlat [1] accounts for the complexity in the yielding behaviour of magnesium and its alloys such as anisotropy and asymmetry in tension-compression. However, the capabilities of this model for simulation of extrusion, where complex thermo-mechanical loading exists, are limited since strain rate and temperature dependency on flow behaviour are not considered. Modifications including these phenomena were derived [2] and implemented as user defined subroutine, VUMAT, into the commercial Finite Element (FE) software, ABAQUS/Explicit [3].

Material Model

In order to capture strain rate and temperature dependence on plastic yielding, the yield function, f, is written as a function of three internal state variables, namely equivalent plastic strain, plε , plastic strain rate, plε& , and temperature, θ ,

( ) ),,()()( 33

2/3

2 θεετεε plply

plpl JJf &oo −−= , (1)

where o2J and

o3J are generalisations of the second and third invariant of the stress deviator. In

order to describe the strain hardening of the material, the invariants are assumed to be dependent on the equivalent plastic strain by a saturating exponential law.

Modelling of thermo-mechanical Behaviour of Magnesium Alloys during Indirect Extrusion

S. Ertürk1, a, D. Steglich1, b, J. Bohlen1, c, D.Letzig1, d and W. Brocks2, e 1 GKSS Research Centre, Institute of Materials Research, 21502 Geesthacht, Germany 2 Christian-Albrechts-University of Kiel, Faculty of Engineering, 24143 Kiel, Germany


Keywords: Rate-dependent-J3 plasticity, Fully thermo-mechanical coupled analysis, Extrusion, Magnesium alloys Abstract. A yield function for hexagonal closed packed (hcp) metals was modified with respect to strain rate and temperature and developed to capture the material behaviour during extrusion. Magnesium alloy ZEK100 was extruded indirectly at 300°C into a round bar. Compression tests were carried out at various strain rates, temperatures and sample orientation to characterise the material flow. These data were used as input data for fully thermo-mechanical coupled simulations of indirect extrusion. A successful prediction of the extrusion force and the temperature increase during extrusion is presented.

Introduction

Magnesium and its alloys have become promising materials saving structural weight and reducing fuel consumption especially for transportation industry, due to being the lightest metal for structural applications. One of the established production methods for semi-finished products is extrusion. For magnesium and its alloys, this technology is available today, but there is still a fundamental lack in understanding the factors that determine the development of microstructure and mechanical properties during the process. Such alloys show unusual mechanical characteristics such as deformation anisotropy and asymmetry in tension-compression, which originate from the hexagonal closed packed (hcp) crystallographic structure and the distinct textures that develop during massive deformation such as extrusion. A phenomenological model derived by Cazacu and Barlat [1] accounts for the complexity in the yielding behaviour of magnesium and its alloys such as anisotropy and asymmetry in tension-compression. However, the capabilities of this model for simulation of extrusion, where complex thermo-mechanical loading exists, are limited since strain rate and temperature dependency on flow behaviour are not considered. Modifications including these phenomena were derived [2] and implemented as user defined subroutine, VUMAT, into the commercial Finite Element (FE) software, ABAQUS/Explicit [3].

Material Model

In order to capture strain rate and temperature dependence on plastic yielding, the yield function, f, is written as a function of three internal state variables, namely equivalent plastic strain, plε , plastic strain rate, plε& , and temperature, θ ,

( ) ),,()()( 33

2/3

2 θεετεε plply

plpl JJf &oo −−= , (1)

where o2J and

o3J are generalisations of the second and third invariant of the stress deviator. In

order to describe the strain hardening of the material, the invariants are assumed to be dependent on the equivalent plastic strain by a saturating exponential law.


Cowper-Symonds’ overstress model [4] was chosen to capture the rate dependency of plastic deformation. The yield stress under quasi-static conditions is linked to “dynamic” yield stress via 2 model parameters: reference strain rate, D, and exponent, n, respectively as

1)(

)(/1

+

=

′ θ

θε

σ

σ npl

y

y

D

&, (2)

where D and n are defined as functions of temperature in order to take the variation of the rate dependence with temperature into account.

Compression Tests

Compression tests on cylindrical specimen with 10 mm of diameter and 15 mm of height machined from as-cast ZEK100 magnesium alloy were performed at different test temperatures (i.e. 300, 400, 500°C) and strain rates (i.e. 0.1, 1, 10 s-1) and different directions in order to study the metal flow. FE simulations were executed to regenerate the experimental results. The pair of parameters, i.e. D and n, was identified for each test temperature, evidencing that the rate dependency depends on the test temperature. As a result, a single pair of the model parameters is not sufficient to capture whole rate dependency seen in Fig. 1.

0 1 2 3 4 5 60

4

8

12

16

Experiment @ Strain rate=0.1s-1

Experiment @ Strain rate=1s-1


Simulations @ D=800s-1 & n=3

Force [kN]

displacement [mm]

ZEK100θ=300°C

0 1 2 3 4 5 60

4

8

12

16 Experiment @ Strain rate=0.1s-1




ZEK100θ=400°C

Force [kN]

displacement [mm]

Fig. 1: The experimental and simulation results of compression tests at 300°C (left) and 400°C (right)

In order to capture deformation anisotropy in compression, the tests were performed on specimens prepared at different orientations, namely extrusion (L) and transverse directions (T). Fig. 2 shows the yield loci drawn with set of parameters, CaBaExpo2, together with experiments. The parameters embedded in o

2J and o3J were identified by minimizing the difference between

model predictions and experimental results.

Cowper-Symonds’ overstress model [4] was chosen to capture the rate dependency of plastic deformation. The yield stress under quasi-static conditions is linked to “dynamic” yield stress via 2 model parameters: reference strain rate, D, and exponent, n, respectively as

1)(

)(/1

+

=

′ θ

θε

σ

σ npl

y

y

D

&, (2)

where D and n are defined as functions of temperature in order to take the variation of the rate dependence with temperature into account.

Compression Tests

Compression tests on cylindrical specimen with 10 mm of diameter and 15 mm of height machined from as-cast ZEK100 magnesium alloy were performed at different test temperatures (i.e. 300, 400, 500°C) and strain rates (i.e. 0.1, 1, 10 s-1) and different directions in order to study the metal flow. FE simulations were executed to regenerate the experimental results. The pair of parameters, i.e. D and n, was identified for each test temperature, evidencing that the rate dependency depends on the test temperature. As a result, a single pair of the model parameters is not sufficient to capture whole rate dependency seen in Fig. 1.

0 1 2 3 4 5 60

4

8

12

16

Experiment @ Strain rate=0.1s-1




Force [kN]

displacement [mm]

ZEK100θ=300°C

0 1 2 3 4 5 60

4

8

12

16 Experiment @ Strain rate=0.1s-1




ZEK100θ=400°C

Force [kN]

displacement [mm]

Fig. 1: The experimental and simulation results of compression tests at 300°C (left) and 400°C (right)

In order to capture deformation anisotropy in compression, the tests were performed on specimens prepared at different orientations, namely extrusion (L) and transverse directions (T). Fig. 2 shows the yield loci drawn with set of parameters, CaBaExpo2, together with experiments. The parameters embedded in o

2J and o3J were identified by minimizing the difference between

model predictions and experimental results.


-125 -100 -75 -50 -25 0 25-125

-100

-75

-50

-25

0

25 εpl=0.000

εpl=0.015

εpl=0.030

εpl=0.050

εpl=0.080

εpl=0.100

εpl=0.160

εpl=0.200

εpl=0.250

εpl=0.350

εpl=0.450

CaBaExpo2

σT [MPa]

σL [MPa]

isostrain contours:

Fig. 2: Compression test results with the corresponding yield loci and hardening behaviour drawn

by parameter set CaBaExpo2

Indirect Extrusion

Indirect extrusion was carried out at on the billet machined down to a diameter of 93 mm and a length of 300 mm at billet temperature of 300°C. The extrusion ratio is 1:30. During extrusion, a round bar with 17 mm diameter was produced with a profile speed of 10 m/min.

A fully coupled thermo-mechanical analysis, in which the temperature is assumed as an additional degree of freedom, was used in extrusion simulations for calculation of the temperature field by considering heat fluxes and heat generated due to plastic deformation. In the simulations, so-called Arbitrary Lagrangian-Eulerian (ALE) [5] formulation was used. In the Lagrangian (material) description, a material point is focussed, whereas a stationary spatial reference frame is observed during deformation in the Eulerian (spatial) formulation. The combination of both limits forms ALE. This eliminates the problems of mesh distortions that can occur in a pure Lagrangian approach. The metal flow was considered via Eulerian boundary condition. On the other hand, Lagrangian boundary conditions were applied to the die and the container. The problem is assumed to be axi-symmetric. In order to keep reasonable computational cost, the container and the die were considered as

analytical rigid surface, hence no deformation or temperature fields are able to be monitored on these surface. Since there is no relative displacement between the billet and the container, friction between the billet and the container does not exist in indirect extrusion. Therefore, the contact between the billet and the container was established without friction. The contact area with the die, on the other hand, was described by Coulomb friction. The friction coefficient is estimated in literature varying between 0.1 and 1 for different metallic materials [6, 7]. In this study, it was assumed as 0.5. The die is equipped with a thermocouple at the inner surface. This enables the measurement of

the profile temperature during the extrusion process. The temperature measurements seen in Fig. 3 were used to calibrate heat transfer properties between the billet and the die. Fig. 3 shows the agreement between the experiments and simulations in the case of both temperature and reaction force.

-125 -100 -75 -50 -25 0 25-125

-100

-75

-50

-25

0

25 εpl=0.000

εpl=0.015

εpl=0.030

εpl=0.050

εpl=0.080

εpl=0.100

εpl=0.160

εpl=0.200

εpl=0.250

εpl=0.350

εpl=0.450

CaBaExpo2

σT [MPa]

σL [MPa]

isostrain contours:

Fig. 2: Compression test results with the corresponding yield loci and hardening behaviour drawn

by parameter set CaBaExpo2

Indirect Extrusion

Indirect extrusion was carried out at on the billet machined down to a diameter of 93 mm and a length of 300 mm at billet temperature of 300°C. The extrusion ratio is 1:30. During extrusion, a round bar with 17 mm diameter was produced with a profile speed of 10 m/min.

A fully coupled thermo-mechanical analysis, in which the temperature is assumed as an additional degree of freedom, was used in extrusion simulations for calculation of the temperature field by considering heat fluxes and heat generated due to plastic deformation. In the simulations, so-called Arbitrary Lagrangian-Eulerian (ALE) [5] formulation was used. In the Lagrangian (material) description, a material point is focussed, whereas a stationary spatial reference frame is observed during deformation in the Eulerian (spatial) formulation. The combination of both limits forms ALE. This eliminates the problems of mesh distortions that can occur in a pure Lagrangian approach. The metal flow was considered via Eulerian boundary condition. On the other hand, Lagrangian boundary conditions were applied to the die and the container. The problem is assumed to be axi-symmetric. In order to keep reasonable computational cost, the container and the die were considered as

analytical rigid surface, hence no deformation or temperature fields are able to be monitored on these surface. Since there is no relative displacement between the billet and the container, friction between the billet and the container does not exist in indirect extrusion. Therefore, the contact between the billet and the container was established without friction. The contact area with the die, on the other hand, was described by Coulomb friction. The friction coefficient is estimated in literature varying between 0.1 and 1 for different metallic materials [6, 7]. In this study, it was assumed as 0.5. The die is equipped with a thermocouple at the inner surface. This enables the measurement of

the profile temperature during the extrusion process. The temperature measurements seen in Fig. 3 were used to calibrate heat transfer properties between the billet and the die. Fig. 3 shows the agreement between the experiments and simulations in the case of both temperature and reaction force.


0 50 100 150 200 250 3000

1

2

3

4

Experiment Simulation-CaBaExpo2

νP=10m/min

Force [MN]

displacement [mm]

ZEK100

0 50 100 150 200 250 300250

300

350

400

450

500

Experiment Simulation-CaBaExpo2νP=10m/min

Temperature [°C]

displacement [mm]

ZEK100

Fig. 3: Experimental and simulation results of indirect extrusion: force vs. displacement (left) and

temperature vs. displacement (right)

Fig. 4 shows the von Mises stress and temperature distributions at ram displacement=300mm.

Fig. 4: von Mises stress (left) and temperature (right) distributions

It is predicted that the higher-stress-region is located where metal flow is in contact with the dead

metal zone and container. The temperature at the die exit where large deformation takes place is predicted as the highest. The region close to the container heat transfer causes cooling down of the extrudate.

Summary

Compression tests were executed at different punch velocities and test temperatures in order to describe the rate dependency on deformation. Simulations of upsetting tests were performed to fit model parameters for rate dependency, temperature dependency and anisotropic yielding by

0 50 100 150 200 250 3000

1

2

3

4

Experiment Simulation-CaBaExpo2

νP=10m/min

Force [MN]

displacement [mm]

ZEK100

0 50 100 150 200 250 300250

300

350

400

450

500

Experiment Simulation-CaBaExpo2νP=10m/min

Temperature [°C]

displacement [mm]

ZEK100

Fig. 3: Experimental and simulation results of indirect extrusion: force vs. displacement (left) and

temperature vs. displacement (right)

Fig. 4 shows the von Mises stress and temperature distributions at ram displacement=300mm.

Fig. 4: von Mises stress (left) and temperature (right) distributions

It is predicted that the higher-stress-region is located where metal flow is in contact with the dead

metal zone and container. The temperature at the die exit where large deformation takes place is predicted as the highest. The region close to the container heat transfer causes cooling down of the extrudate.

Summary

Compression tests were executed at different punch velocities and test temperatures in order to describe the rate dependency on deformation. Simulations of upsetting tests were performed to fit model parameters for rate dependency, temperature dependency and anisotropic yielding by


comparing with the corresponding experimental results and then to use as input data for simulations of indirect extrusion. The simulations of indirect extrusion show good agreement between experimental results.

References

[1] O. Cazacu and F. Barlat: International Journal of Plasticity Vol. 20 (2004), p. 2027-2045

[2] S. Ertürk, D. Steglich, J. Bohlen, D. Letzig and W. Brocks: International Journal of Material Forming (2009), in press

[3] Abaqus, ABAQUS User Subroutines Reference Manual (2006)

[4] G.R. Cowper and P.S. Symonds: (Brown University, 1957)

[5] Abaqus, ABAQUS Analysis User's Manual (2006)

[6] M. Arentoft, Z. Gronostajski, A. Niechajowicz and T. Wanheim: Journal of Materials Processing Technology Vol. 106 (2000), p. 2-7

[7] R.Y., Lapovok, M.R. Barnett and C.H.J. Davies: Journal of Materials Processing Technology Vol. 146, (2004) p. 408-414

comparing with the corresponding experimental results and then to use as input data for simulations of indirect extrusion. The simulations of indirect extrusion show good agreement between experimental results.

References

[1] O. Cazacu and F. Barlat: International Journal of Plasticity Vol. 20 (2004), p. 2027-2045

[2] S. Ertürk, D. Steglich, J. Bohlen, D. Letzig and W. Brocks: International Journal of Material Forming (2009), in press

[3] Abaqus, ABAQUS User Subroutines Reference Manual (2006)

[4] G.R. Cowper and P.S. Symonds: (Brown University, 1957)

[5] Abaqus, ABAQUS Analysis User's Manual (2006)

[6] M. Arentoft, Z. Gronostajski, A. Niechajowicz and T. Wanheim: Journal of Materials Processing Technology Vol. 106 (2000), p. 2-7

[7] R.Y., Lapovok, M.R. Barnett and C.H.J. Davies: Journal of Materials Processing Technology Vol. 146, (2004) p. 408-414


Numerical Analysis of Four-Hole Extrusion of Aluminum Alloys

W. Libura1, a, A. Rękas1,b, D. Leśniak1,c 1AGH - University of Science and Technology, Faculty of Non-Ferrous Metals,

A. Mickiewicza 30 Ave., 30-059 Krakow, Poland [email protected], [email protected], [email protected]

Keywords: extrusion, metal flow, four-hole die, aluminum alloys, numerical calculations Abstract. The work presents the results of FEM simulations of extrusion process with the use of four – hole dies of various geometry. The traditional flat dies and pocket dies were adopted for comparison. The calculations were conducted for indirect extrusion of rods of 14 mm in diameter from the 6061 aluminium alloy. The distributions of strains, stresses, metal velocities and temperature within the deformation zone were the basis for metal flow analysis. Based on the conducted calculations the die configuration, leading to the best product quality was recommended. The product quality was evaluated by the flow direction of rods from the die orifices.

Introduction

Today the hot extrusion is one of the principal methods of producing solid sections from aluminium alloys. The demands for aluminium extrusions grow despite economical crisis and high production costs. Extruded aluminium is the material of choice for many applications. Such products are preferably used in building industry, in means of transportation, including aircraft, aerospace and automotive industry. Low effectiveness causes significant production problems, especially, when the traditional one-hole dies are used. The use of multi-hole dies is an effective way for improving the process output. The advantage of technology utilizing the multi-hole dies is also a lower extrusion force. However, due to the complicated metal flow during extrusion through such dies, the correct die design is still a crucial challenge. The incorrect die design may generate unfavorable metal flow causing distortion of the extruded product. It is a well known that the mode of the metal flow in extrusion strongly affects the product quality. Next, the important factors influencing the metal flow are; the interface friction between the billet and the tools, the extrusion speed, the extrusion ratio, the material temperature and the die geometry. Finally, the homogeneous deformation and uniform metal velocity in the die orifice at the stable exit temperature are necessary conditions for obtaining a product of acceptable quality [1-5]. Peng and Sheppard have reported that the material flow can be more homogeneous than normal extrusion if an appropriate pocket die design is applied [6].

The subject of the study is a numerical analysis of the hot extrusion of solid sections from 6061 aluminium alloy through the four-hole dies. The influence of the die geometry including layout of the orifices, on the product quality, extrusion force and the metal flow was analysed.

Simulation details

The three-dimensional FEM simulations of the indirect extrusion of 6061 alloy were conducted using the DEFORM program. The rigid-plastic model of the material was assumed. The extrudates in the form of rods of 14 mm in diameter and the symmetrical arrangement of the holes were established in calculations. The model assumed allows discretization of the whole billet volume in which a mesh of a higher density is generated within the region of maximal deformations, as visible in fig 1. Only a quarter of the extrusion setting is shown when considering the symmetry of the problem.

Numerical Analysis of Four-Hole Extrusion of Aluminum Alloys

W. Libura1, a, A. Rękas1,b, D. Leśniak1,c 1AGH - University of Science and Technology, Faculty of Non-Ferrous Metals,

A. Mickiewicza 30 Ave., 30-059 Krakow, Poland [email protected], [email protected], [email protected]

Keywords: extrusion, metal flow, four-hole die, aluminum alloys, numerical calculations Abstract. The work presents the results of FEM simulations of extrusion process with the use of four – hole dies of various geometry. The traditional flat dies and pocket dies were adopted for comparison. The calculations were conducted for indirect extrusion of rods of 14 mm in diameter from the 6061 aluminium alloy. The distributions of strains, stresses, metal velocities and temperature within the deformation zone were the basis for metal flow analysis. Based on the conducted calculations the die configuration, leading to the best product quality was recommended. The product quality was evaluated by the flow direction of rods from the die orifices.

Introduction

Today the hot extrusion is one of the principal methods of producing solid sections from aluminium alloys. The demands for aluminium extrusions grow despite economical crisis and high production costs. Extruded aluminium is the material of choice for many applications. Such products are preferably used in building industry, in means of transportation, including aircraft, aerospace and automotive industry. Low effectiveness causes significant production problems, especially, when the traditional one-hole dies are used. The use of multi-hole dies is an effective way for improving the process output. The advantage of technology utilizing the multi-hole dies is also a lower extrusion force. However, due to the complicated metal flow during extrusion through such dies, the correct die design is still a crucial challenge. The incorrect die design may generate unfavorable metal flow causing distortion of the extruded product. It is a well known that the mode of the metal flow in extrusion strongly affects the product quality. Next, the important factors influencing the metal flow are; the interface friction between the billet and the tools, the extrusion speed, the extrusion ratio, the material temperature and the die geometry. Finally, the homogeneous deformation and uniform metal velocity in the die orifice at the stable exit temperature are necessary conditions for obtaining a product of acceptable quality [1-5]. Peng and Sheppard have reported that the material flow can be more homogeneous than normal extrusion if an appropriate pocket die design is applied [6].

The subject of the study is a numerical analysis of the hot extrusion of solid sections from 6061 aluminium alloy through the four-hole dies. The influence of the die geometry including layout of the orifices, on the product quality, extrusion force and the metal flow was analysed.

Simulation details

The three-dimensional FEM simulations of the indirect extrusion of 6061 alloy were conducted using the DEFORM program. The rigid-plastic model of the material was assumed. The extrudates in the form of rods of 14 mm in diameter and the symmetrical arrangement of the holes were established in calculations. The model assumed allows discretization of the whole billet volume in which a mesh of a higher density is generated within the region of maximal deformations, as visible in fig 1. Only a quarter of the extrusion setting is shown when considering the symmetry of the problem.


Fig. 1: The model of indirect extrusion assumed in calculations.

The rheological properties of the alloy within the temperature range of 300 ÷ 500°C and the characteristics of H13 tool steel where taken from the program database. In all the simulation runs the following process parameters were established: billet temperature T0 = 340°C, tools temperature Tt = 340°C, exit speed ve = 8 m/min, billet dimensions – 123 mm in diameter and 150 mm in length. The friction conditions at the tools - billet interface were also assumed constant (friction factor m = 0.7).

The calculations were performed for the traditional flat dies and for the pocket dies, having the same bearing lands. In case of flat dies the influence of the orifices layout on the product quality was analysed. It was assumed that the orifices’ arrangement depends on the factor k describing the relationship between the die surface AD and the surface Ad of the circle described at the centers of orifices, according to relations (1) and (2) (fig.2).

d

dD

AAA

k−

= (1)

2

22

ddD

k−

= (2)

The factor k values were assumed equal to 1, 3, 5 and 9, respectively. The layout of the orifices, defined by diameter d of the circle described at the product axes was found from the relations (3) (fig.2).

1

2

+=

kD

d (3)

Fig.. 2: Scheme of four-hole die

Fig. 1: The model of indirect extrusion assumed in calculations.

The rheological properties of the alloy within the temperature range of 300 ÷ 500°C and the characteristics of H13 tool steel where taken from the program database. In all the simulation runs the following process parameters were established: billet temperature T0 = 340°C, tools temperature Tt = 340°C, exit speed ve = 8 m/min, billet dimensions – 123 mm in diameter and 150 mm in length. The friction conditions at the tools - billet interface were also assumed constant (friction factor m = 0.7).

The calculations were performed for the traditional flat dies and for the pocket dies, having the same bearing lands. In case of flat dies the influence of the orifices layout on the product quality was analysed. It was assumed that the orifices’ arrangement depends on the factor k describing the relationship between the die surface AD and the surface Ad of the circle described at the centers of orifices, according to relations (1) and (2) (fig.2).

d

dD

AAA

k−

= (1)

2

22

ddD

k−

= (2)

The factor k values were assumed equal to 1, 3, 5 and 9, respectively. The layout of the orifices, defined by diameter d of the circle described at the product axes was found from the relations (3) (fig.2).

1

2

+=

kD

d (3)

Fig.. 2: Scheme of four-hole die


The modelling of extrusion with the use of pocket dies was conducted for three geometrical

variants. In the first case the local pockets at each hole were used (fig. 3a) with different pocket heights h = 2, 5 and 7 mm. In the second variant a large central pocket was adopted with the height of 7 mm, surrounding all holes (fig. 3b). Based on the flow analysis obtained for the previous variants the third die was designed with the ring shaped pocket of 2 mm height (fig. 3c). For all dies with pockets the factor k was equal to 9.

Fig.. 3: Dies with the pockets, a) local, b) central, c) ring shaped

On the basis of the metal flow analysis within the deformation zone and distributions of strains, stresses, velocities and temperature; the influence of the die geometry on the product quality was discussed. Particularly, as a deciding factor describing the product quality the direction of metal exit from the orifices was assumed. The identification of the mode of metal flow allows correct designing of the die geometry in terms of product quality.


In the design of multi-hole dies the important aspects guaranteeing a good product quality are the number of orifices and their location (fig.4). Only a half of the setting is shown in fig. 5 because of symmetry of the process. When the flat dies are used, depending on the distance of orifices from the die center axis, a distortion (bending) of a product may occur towards the axis (fig. 4a, b, c) or to the outer side direction (fig. 4d), which makes receiving of extrudates on the run-out table impossible. This feature is the result of inhomogeneous metal flow from the die orifice and along the deformation zone as well. In addition, in the case of closely localized orifices, the interference of the local deformation areas at each orifice takes 0ccurs.

Fig. 4: The image of products extruded with different factor k describing the layout of orifices

The modelling of extrusion with the use of pocket dies was conducted for three geometrical

variants. In the first case the local pockets at each hole were used (fig. 3a) with different pocket heights h = 2, 5 and 7 mm. In the second variant a large central pocket was adopted with the height of 7 mm, surrounding all holes (fig. 3b). Based on the flow analysis obtained for the previous variants the third die was designed with the ring shaped pocket of 2 mm height (fig. 3c). For all dies with pockets the factor k was equal to 9.

Fig.. 3: Dies with the pockets, a) local, b) central, c) ring shaped

On the basis of the metal flow analysis within the deformation zone and distributions of strains, stresses, velocities and temperature; the influence of the die geometry on the product quality was discussed. Particularly, as a deciding factor describing the product quality the direction of metal exit from the orifices was assumed. The identification of the mode of metal flow allows correct designing of the die geometry in terms of product quality.


In the design of multi-hole dies the important aspects guaranteeing a good product quality are the number of orifices and their location (fig.4). Only a half of the setting is shown in fig. 5 because of symmetry of the process. When the flat dies are used, depending on the distance of orifices from the die center axis, a distortion (bending) of a product may occur towards the axis (fig. 4a, b, c) or to the outer side direction (fig. 4d), which makes receiving of extrudates on the run-out table impossible. This feature is the result of inhomogeneous metal flow from the die orifice and along the deformation zone as well. In addition, in the case of closely localized orifices, the interference of the local deformation areas at each orifice takes 0ccurs.

Fig. 4: The image of products extruded with different factor k describing the layout of orifices


The analysis of metal flow for various factor k values (fig. 5) in connection with the metal

velocity distribution (fig. 6) enabled evaluation of the effect of the orifices layout on the extrudate quality. When the orifices are located close to the die center axis (k = 9), the outer part of the billet flow faster in comparison to the billet core which results in bending of the extrudates towards the die center axis. For the lower k values (5 and 3) some improvements in the metal flow can be observed. In the case when the ring surface AD – Ad is equal Ad (k = 1) the inner part of the billet flows faster than the outer layer. The way of extrudate exit direction is like this presented in fig. 4d.

Fig. 5: The metal flow for different factor k applied

Fig. 6: Velocity fields for different factor k applied The variation in strain distribution is shown in fig. 7, where the change of the shape of the deformation zone in dependence on the orifices location is visible. These changes affect also temperature distribution on the extrudate cross-section (fig. 8). The best extrudate quality in the analysed variants was obtained for the factor k = 3 (figs 7 and 8).

Due to the complicated mode of the metal flow when extruding through the four-hole traditional flat dies, the process control by the simple regulation of the orifice location is very difficult. The pocket dies are considered to have a beneficial effect on the metal flow control within the deformation zone. In fig. 9 a velocity distributions for the pocket dies applied is presented, whereas fig. 10 shows an effective strain distributions for these dies. As it was mentioned above, the four-hole die with the individual pockets at each orifice does not improve the metal flow satisfactorily (fig. 9a, b, c). For the die with a one large central pocket the metal flow is still inhomogeneous; the outer layer flows faster compared to the core (figs 9d, 10d). The above results enabled designing a

The analysis of metal flow for various factor k values (fig. 5) in connection with the metal

velocity distribution (fig. 6) enabled evaluation of the effect of the orifices layout on the extrudate quality. When the orifices are located close to the die center axis (k = 9), the outer part of the billet flow faster in comparison to the billet core which results in bending of the extrudates towards the die center axis. For the lower k values (5 and 3) some improvements in the metal flow can be observed. In the case when the ring surface AD – Ad is equal Ad (k = 1) the inner part of the billet flows faster than the outer layer. The way of extrudate exit direction is like this presented in fig. 4d.

Fig. 5: The metal flow for different factor k applied

Fig. 6: Velocity fields for different factor k applied The variation in strain distribution is shown in fig. 7, where the change of the shape of the deformation zone in dependence on the orifices location is visible. These changes affect also temperature distribution on the extrudate cross-section (fig. 8). The best extrudate quality in the analysed variants was obtained for the factor k = 3 (figs 7 and 8).

Due to the complicated mode of the metal flow when extruding through the four-hole traditional flat dies, the process control by the simple regulation of the orifice location is very difficult. The pocket dies are considered to have a beneficial effect on the metal flow control within the deformation zone. In fig. 9 a velocity distributions for the pocket dies applied is presented, whereas fig. 10 shows an effective strain distributions for these dies. As it was mentioned above, the four-hole die with the individual pockets at each orifice does not improve the metal flow satisfactorily (fig. 9a, b, c). For the die with a one large central pocket the metal flow is still inhomogeneous; the outer layer flows faster compared to the core (figs 9d, 10d). The above results enabled designing a


die with the ring shaped pocket (figs 9e, 10e). Such variant provided uniform flow towards the die orifices and more homogeneous deformation within the deformation zone.

Fig. 7: Effective strains for different factor k applied

Fig. 8: Temperature distribution for different factor k applied

die with the ring shaped pocket (figs 9e, 10e). Such variant provided uniform flow towards the die orifices and more homogeneous deformation within the deformation zone.

Fig. 7: Effective strains for different factor k applied

Fig. 8: Temperature distribution for different factor k applied


Fig. 9: Velocity fields for different dies with the pockets

Fig. 10: Effective strains for different dies with the pockets

Conclusions

The extrusion through the four-hole dies requires correct location of the orifices with respect to the die center axis and correct selection of bearing lands. The results demonstrate that for the traditional flat dies the most favourable case occurs when the factor k regulating location of the orifices was equal to 3. The velocity field (fig 6) is the most uniform both with respect to the die axial symmetry and the orifices’ axes. The similar situation is observed in case of effective strain (fig.7) and temperature distributions (fig. 8).

Balanced metal flow can be achieved by applying the pocket dies of the correct geometry. The pocket acts as a flow regulator influencing behavior of the metal within the deformation zone. The best results were obtained for the ring shaped pocket. Such variant provided uniform metal flow

Fig. 9: Velocity fields for different dies with the pockets

Fig. 10: Effective strains for different dies with the pockets

Conclusions

The extrusion through the four-hole dies requires correct location of the orifices with respect to the die center axis and correct selection of bearing lands. The results demonstrate that for the traditional flat dies the most favourable case occurs when the factor k regulating location of the orifices was equal to 3. The velocity field (fig 6) is the most uniform both with respect to the die axial symmetry and the orifices’ axes. The similar situation is observed in case of effective strain (fig.7) and temperature distributions (fig. 8).

Balanced metal flow can be achieved by applying the pocket dies of the correct geometry. The pocket acts as a flow regulator influencing behavior of the metal within the deformation zone. The best results were obtained for the ring shaped pocket. Such variant provided uniform metal flow


towards the die orifices and more homogeneous deformation within the deformation zone. The product is straight after exiting the die orifice. This is the result of uniform distribution of metal velocity within the deformation zone (fig. 9e) and the effective strain field as well (fig. 10). The advantageous is also the fact the optimal pocket height is only 2 mm, what minimizes the material loss.

References

[1] W. Libura: Metal flow in extrusion, in Metallurgy on the turn of the 20th century, Krakow, AKAPIT Publication, (2002) pp. 391-412.

[2] K. Nakanishi, S. Kamitani, T. Yang. H. Takio, M. Nakayoshi: Material flow characteristics in hot extrusion of aluminium alloy controlled by the flow guide and die bearing, Proc. 7th ICTP, vol. 1 (2002) pp. 409-414.

[3] Y. T. Kim, K. Ikeda, T. Murakami: Metal flow in porthole die extrusion of aluminum, Journal of Materials Processing Technology, vol. 121 (2002) pp. 107-115.

[4] W. Libura, D. Leśniak, A. Rękas, J. Zasadziński: Physical and numerical modelling of extrusion of flat sections from hard deformable aluminium alloys, Proc. of the 8th International Conference on Technology of Plasticity ICTP, Verona (2005) pp. 219-220.

[5] W. Libura: Płynięcie metalu w procesie wyciskania, AGH University of Science and Technology Publications, Kraków 2008 (in Polish).

[6] Z. Peng, T. Sheppard, Effect of die pockets on multi-hole extrusion, Materials Science and Engineering, A 407 (2005) pp. 89-97.

towards the die orifices and more homogeneous deformation within the deformation zone. The product is straight after exiting the die orifice. This is the result of uniform distribution of metal velocity within the deformation zone (fig. 9e) and the effective strain field as well (fig. 10). The advantageous is also the fact the optimal pocket height is only 2 mm, what minimizes the material loss.

References

[1] W. Libura: Metal flow in extrusion, in Metallurgy on the turn of the 20th century, Krakow, AKAPIT Publication, (2002) pp. 391-412.

[2] K. Nakanishi, S. Kamitani, T. Yang. H. Takio, M. Nakayoshi: Material flow characteristics in hot extrusion of aluminium alloy controlled by the flow guide and die bearing, Proc. 7th ICTP, vol. 1 (2002) pp. 409-414.

[3] Y. T. Kim, K. Ikeda, T. Murakami: Metal flow in porthole die extrusion of aluminum, Journal of Materials Processing Technology, vol. 121 (2002) pp. 107-115.

[4] W. Libura, D. Leśniak, A. Rękas, J. Zasadziński: Physical and numerical modelling of extrusion of flat sections from hard deformable aluminium alloys, Proc. of the 8th International Conference on Technology of Plasticity ICTP, Verona (2005) pp. 219-220.

[5] W. Libura: Płynięcie metalu w procesie wyciskania, AGH University of Science and Technology Publications, Kraków 2008 (in Polish).

[6] Z. Peng, T. Sheppard, Effect of die pockets on multi-hole extrusion, Materials Science and Engineering, A 407 (2005) pp. 89-97.


Computer-Aided Simulation of Metal Flow through Curved Die for Extrusion of Square Section from Square Billet

K. P. Maity1, a, A. K. Rout1, b, Kalu Majhi1, c 1Department of Mechanical Engineering, National Institute of Technology, Rourkela-769008,

Orissa, INDIA

a [email protected], b [email protected],c [email protected]

Keywords: Extrusion, cosine die, Dual stream function, Upper-Bound, Square section

Abstract. Extrusion through mathematically contoured die plays a critical role in improvement of

surface integrity of extruded product. There is gradual deformation which results in the uniform

microstructure. In the present investigation non-dimensional extrusion pressure and optimum die

length for cosine die profile has been obtained by three dimensional upper bound method using dual

stream function method for different reductions. The theoretical modeling has been validated with

experiments. The experimental results are found to be compatible with the theory.

Introduction

The geometry of die profile plays a significant role for smooth flow of material resulting in the

evolution of uniform microstructure in extruded product with improved mechanical properties and

reduction in extrusion pressure. Recently the process design involving mathematically contoured

die profile has drawn the attention of various researchers to improve not only dimensional accuracy

but also quality of products. Richmond and Devenpeck [1] first conceptualized an ideal die of

perfect efficiency and developed the governing equations for metal flow. Later on, Richmond and

Morrision [2] used the above concept to design stream-lined wire-drawing dies of minimum length

with sigmoidal die shape. The total work of deformation is equal to that for homogeneous

compression with redundant work at entry and exit equal to zero. However, due to difficulty in the

manufacture of sigmoidal dies, those have found very little application in actual extrusion/drawing

of metals. On the other hand alternative die profiles such as cosine, parabolic, hyperbolic etc. have

been preferred because of ease of manufacture. A number of investigations have been carried out in

the past to predict the deformation load for extrusion through curved die. Slipline field solution for

extrusion through cosine shaped die has been postulated by Samanta [3]. Upper bound solutions for

extrusion through axisymmetric curved dies have been proposed by Chen and Ling [4] and Chang

and Choi [5]. Upper bound solutions with experimental flow studies through different axisymmetric

curved dies have also been reported by Frisch and Mata-Pietri [6,7]. Narayansamy et. al [8] carried

out an upper bound solution to extrusion of circular billet to circular shape through cosine dies. But

adequate literature is not available for three-dimensional extrusion through mathematically

contoured dies because of difficulty in predicting kinematically admissible velocity fields. Maity

et.al [8] investigated three dimensional upper bound methods for extrusion of square sections from

square billet using general dual stream function method to determine kinematically admissible

velocity field. Ponalagusamy et al. [9] investigated computer aided metal flow in stream lined

extrusion dies. Lee et. al [10] designed an optimal Bezier shaped die profile that yielded more

uniform microstructure. Rani Kainew et al. [11] carried out finite element analysis of copper

extrusion process in both flat faced and converging dies. In the present investigation a three-

dimensional upper bound analysis using dual stream function has been carried out for extrusion of

square section from square billet using cosine die profile. The metal flows tangentially at the exit

and entry to the die-wall resulting the redundant work at entry and exit equal to zero. The mode of

deformation is very gradual resulting uniform microstructure. The kinematically admissible velocity

field has been obtained from dual stream function method. Because of symmetry of the deformation

zone, only one quadrant of deformation zone has been chosen. The two stream functions are chosen

Computer-Aided Simulation of Metal Flow through Curved Die for Extrusion of Square Section from Square Billet

K. P. Maity1, a, A. K. Rout1, b, Kalu Majhi1, c 1Department of Mechanical Engineering, National Institute of Technology, Rourkela-769008,

Orissa, INDIA

a [email protected], b [email protected],c [email protected]

Keywords: Extrusion, cosine die, Dual stream function, Upper-Bound, Square section

Abstract. Extrusion through mathematically contoured die plays a critical role in improvement of

surface integrity of extruded product. There is gradual deformation which results in the uniform

microstructure. In the present investigation non-dimensional extrusion pressure and optimum die

length for cosine die profile has been obtained by three dimensional upper bound method using dual

stream function method for different reductions. The theoretical modeling has been validated with

experiments. The experimental results are found to be compatible with the theory.

Introduction

The geometry of die profile plays a significant role for smooth flow of material resulting in the

evolution of uniform microstructure in extruded product with improved mechanical properties and

reduction in extrusion pressure. Recently the process design involving mathematically contoured

die profile has drawn the attention of various researchers to improve not only dimensional accuracy

but also quality of products. Richmond and Devenpeck [1] first conceptualized an ideal die of

perfect efficiency and developed the governing equations for metal flow. Later on, Richmond and

Morrision [2] used the above concept to design stream-lined wire-drawing dies of minimum length

with sigmoidal die shape. The total work of deformation is equal to that for homogeneous

compression with redundant work at entry and exit equal to zero. However, due to difficulty in the

manufacture of sigmoidal dies, those have found very little application in actual extrusion/drawing

of metals. On the other hand alternative die profiles such as cosine, parabolic, hyperbolic etc. have

been preferred because of ease of manufacture. A number of investigations have been carried out in

the past to predict the deformation load for extrusion through curved die. Slipline field solution for

extrusion through cosine shaped die has been postulated by Samanta [3]. Upper bound solutions for

extrusion through axisymmetric curved dies have been proposed by Chen and Ling [4] and Chang

and Choi [5]. Upper bound solutions with experimental flow studies through different axisymmetric

curved dies have also been reported by Frisch and Mata-Pietri [6,7]. Narayansamy et. al [8] carried

out an upper bound solution to extrusion of circular billet to circular shape through cosine dies. But

adequate literature is not available for three-dimensional extrusion through mathematically

contoured dies because of difficulty in predicting kinematically admissible velocity fields. Maity

et.al [8] investigated three dimensional upper bound methods for extrusion of square sections from

square billet using general dual stream function method to determine kinematically admissible

velocity field. Ponalagusamy et al. [9] investigated computer aided metal flow in stream lined

extrusion dies. Lee et. al [10] designed an optimal Bezier shaped die profile that yielded more

uniform microstructure. Rani Kainew et al. [11] carried out finite element analysis of copper

extrusion process in both flat faced and converging dies. In the present investigation a three-

dimensional upper bound analysis using dual stream function has been carried out for extrusion of

square section from square billet using cosine die profile. The metal flows tangentially at the exit

and entry to the die-wall resulting the redundant work at entry and exit equal to zero. The mode of

deformation is very gradual resulting uniform microstructure. The kinematically admissible velocity

field has been obtained from dual stream function method. Because of symmetry of the deformation

zone, only one quadrant of deformation zone has been chosen. The two stream functions are chosen


in such a way that automatically satisfies the boundary condition. The velocity and strain rate

components determined from stream functions have been used to determine the internal work and

the work against the velocity discontinuities. This has been achieved with the help of a 5-point

Gauss-Legendre quadrature alogarithm for volume and surface integral. The constant friction factor

is assumed at the die-billet interface with constant flow stress of rigid plastic material. A

FORTRAN main programme with a number of sub-programs and subroutine has been developed to

compute total power of deformation and extrusion pressure. The total power of deformation has

been minimized with respect to die length to determine optimum die length and extrusion pressure

from upper bound method. The velocity and strain rate distributions have been determined in the

deformation zone. The curved die with optimum cosine die profile was manufactured. The

experimental investigation has been carried for hot-work operation using telerium-lead for

extruding square section from square billet. The extrusion pressure computed from the upper bound

theory was found to be compatible with the experiment using the above boundary condition.

Upper bound method

The upper bound theorem states that the power estimated from kinematically-admissible velocity

fields (KAVF) is always higher than the actual one. Amongst all kinematically-admissible velocity

fields the actual one minimizes the expression:

i

ii

iSD

SD

SDii

S

S

V

ijij dSVm

dSVdVJ

333

2 000

(1)

Where J is the power of dissipation rate, σ0 is the flow stress; εij is the derived strain-rate tensor,

iSV

is the velocity discontinuity at the entry and exit surfaces Si, iSD

V is the velocity discontinuity at

the die-metal interfaces SDi and m is the friction factor.

The kinematically admissible velocity field has been obtained using dual stream function

method.

According to Yih [13], the velocity components can be derived from these stream functions using

the equations.

zyzyVx

2112 (2a)

xzxzVy

2112 (2b)

yxyxVz 2112

(2c)

To derive the dual stream functions for the present problem, the geometry shown in Fig.1

with prescribed reference system is considered. Because of symmetry about two mutually

perpendicular axes, only one quadrant of the actual deformation zone is considered, F(z) is the die-

profile function such that the die faces in the x-z and y-z planes are represented by x=F(z) and

y=F(z) respectively. The function F (z) must satisfy the conditions that F (z)=W at z=0 and F(z)=A

at x=L, where W and A are the semi width of billet and product respectively and L is the die length.

The dual stream functions 1 and 2 are chosen as shown below

in such a way that automatically satisfies the boundary condition. The velocity and strain rate

components determined from stream functions have been used to determine the internal work and

the work against the velocity discontinuities. This has been achieved with the help of a 5-point

Gauss-Legendre quadrature alogarithm for volume and surface integral. The constant friction factor

is assumed at the die-billet interface with constant flow stress of rigid plastic material. A

FORTRAN main programme with a number of sub-programs and subroutine has been developed to

compute total power of deformation and extrusion pressure. The total power of deformation has

been minimized with respect to die length to determine optimum die length and extrusion pressure

from upper bound method. The velocity and strain rate distributions have been determined in the

deformation zone. The curved die with optimum cosine die profile was manufactured. The

experimental investigation has been carried for hot-work operation using telerium-lead for

extruding square section from square billet. The extrusion pressure computed from the upper bound

theory was found to be compatible with the experiment using the above boundary condition.

Upper bound method

The upper bound theorem states that the power estimated from kinematically-admissible velocity

fields (KAVF) is always higher than the actual one. Amongst all kinematically-admissible velocity

fields the actual one minimizes the expression:

i

ii

iSD

SD

SDii

S

S

V

ijij dSVm

dSVdVJ

333

2 000

(1)

Where J is the power of dissipation rate, σ0 is the flow stress; εij is the derived strain-rate tensor,

iSV

is the velocity discontinuity at the entry and exit surfaces Si, iSD

V is the velocity discontinuity at

the die-metal interfaces SDi and m is the friction factor.

The kinematically admissible velocity field has been obtained using dual stream function

method.

According to Yih [13], the velocity components can be derived from these stream functions using

the equations.

zyzyVx

2112 (2a)

xzxzVy

2112 (2b)

yxyxVz 2112

(2c)

To derive the dual stream functions for the present problem, the geometry shown in Fig.1

with prescribed reference system is considered. Because of symmetry about two mutually

perpendicular axes, only one quadrant of the actual deformation zone is considered, F(z) is the die-

profile function such that the die faces in the x-z and y-z planes are represented by x=F(z) and

y=F(z) respectively. The function F (z) must satisfy the conditions that F (z)=W at z=0 and F(z)=A

at x=L, where W and A are the semi width of billet and product respectively and L is the die length.

The dual stream functions 1 and 2 are chosen as shown below


zF

x1 (3a)

zF

yVW b

2

2 (3b)

Fig. 1(a). Profile of a curved die with Fig. 1(b). One quadrant of the deformation zone the axes

of reference.

where V b is the billet velocity. It can be easily verified that (i) Ψ=0 on the plane x=0 and ) Ψ1= -1

on the die surface plane x=F (z); and (ii) Ψ2= 0 on the plane y=0 and Ψ2= W2Vb (which is a

constant) on the die surface y=F (z). Such constant values ensure that surfaces x=0, x=F (z), y=0

and y=F (z) are stream surfaces, and as such velocity components normal to those surface vanish.

Thus, Ψ1 and Ψ2 defined in the above-mentioned manner satisfy all velocity boundary

conditions. Hence they are valid boundary conditions. Hence, they are valid stream functions to

generate a kinematically-admissible velocity field. Substituting Eq. (3) into Eq. (2) and simplifying,

the velocity components in the deformation region are:

3

2

F

FxVWV b

x

(4a)

3

2

F

FyVWV b

y

(4b)

2

2

F

VWV b

z (4c)

Where F = F (z) and F ' = dF/dz

The strain-rate components εij are derived from the velocity components using the relationship:

j

i

i

j

ijx

V

x

V

2

1 (5)

The strain-rate components for the proposed flow field are as follows by substituting Eq. (4) in Eq.

(5)

zF

x1 (3a)

zF

yVW b

2

2 (3b)

Fig. 1(a). Profile of a curved die with Fig. 1(b). One quadrant of the deformation zone the axes

of reference.

where V b is the billet velocity. It can be easily verified that (i) Ψ=0 on the plane x=0 and ) Ψ1= -1

on the die surface plane x=F (z); and (ii) Ψ2= 0 on the plane y=0 and Ψ2= W2Vb (which is a

constant) on the die surface y=F (z). Such constant values ensure that surfaces x=0, x=F (z), y=0

and y=F (z) are stream surfaces, and as such velocity components normal to those surface vanish.

Thus, Ψ1 and Ψ2 defined in the above-mentioned manner satisfy all velocity boundary

conditions. Hence they are valid boundary conditions. Hence, they are valid stream functions to

generate a kinematically-admissible velocity field. Substituting Eq. (3) into Eq. (2) and simplifying,

the velocity components in the deformation region are:

3

2

F

FxVWV b

x

(4a)

3

2

F

FyVWV b

y

(4b)

2

2

F

VWV b

z (4c)

Where F = F (z) and F ' = dF/dz

The strain-rate components εij are derived from the velocity components using the relationship:

j

i

i

j

ijx

V

x

V

2

1 (5)

The strain-rate components for the proposed flow field are as follows by substituting Eq. (4) in Eq.

(5)


3

'2

F

FVW bxx

3

'2

F

FVW byy

3

'22

F

FVW b

zz

0 yxxy

4

2'

3

''2 3

2

1

F

F

F

FyVW bzyyz

4

2'

3

''2 3

2

1

F

F

F

FxVW bxzzx (6)

where 22'' / dzFdF

From equation (6), it is evident that velocity field satisfy incompressibility condition. Using Eq. (6),

J can be evaluated from Eq. (1) when the die-profile function, F, is known. For any reduction and

friction factor m, J then can be minimized with respect to appropriate parameters to yield the best

upper bound.

Die-profile function The die geometry examined in the present investigation is shown in Fig. (1).

Referring to this Fig., it may be seen that the die profile function F (z) is similar in both x- and y-

direction. The die profile function is given as:

(7)

The die profile function satisfies the boundary condition such that at z=0, x=W and z=L, x=A. The

exit and entry angles are non-zero angles. The velocity-discontinuity surfaces are normal to the

axial flow directions.

Computation

An integrated FORTRAN code was developed to compute the upper bound extrusion load using

Eq. (1). For any reduction R and friction factor m, the program first calculates the velocity

components and the strain rate components using Eq. (4) and (5) respectively and then evaluates

the upper-bound on power Eq.(1) by numerical integration using the 5-point Gauss-Legendre

quadrature algorithm. The total power of deformation has been minimized using a multivariable

optimization technique [12].

L

zAWAWzFyx

cos

22)(

3

'2

F

FVW bxx

3

'2

F

FVW byy

3

'22

F

FVW b

zz

0 yxxy

4

2'

3

''2 3

2

1

F

F

F

FyVW bzyyz

4

2'

3

''2 3

2

1

F

F

F

FxVW bxzzx (6)

where 22'' / dzFdF

From equation (6), it is evident that velocity field satisfy incompressibility condition. Using Eq. (6),

J can be evaluated from Eq. (1) when the die-profile function, F, is known. For any reduction and

friction factor m, J then can be minimized with respect to appropriate parameters to yield the best

upper bound.

Die-profile function The die geometry examined in the present investigation is shown in Fig. (1).

Referring to this Fig., it may be seen that the die profile function F (z) is similar in both x- and y-

direction. The die profile function is given as:

(7)

The die profile function satisfies the boundary condition such that at z=0, x=W and z=L, x=A. The

exit and entry angles are non-zero angles. The velocity-discontinuity surfaces are normal to the

axial flow directions.

Computation

An integrated FORTRAN code was developed to compute the upper bound extrusion load using

Eq. (1). For any reduction R and friction factor m, the program first calculates the velocity

components and the strain rate components using Eq. (4) and (5) respectively and then evaluates

the upper-bound on power Eq.(1) by numerical integration using the 5-point Gauss-Legendre

quadrature algorithm. The total power of deformation has been minimized using a multivariable

optimization technique [12].

L

zAWAWzFyx

cos

22)(



The variation of non-dimensional extrusion pressure with respect to reductions are shown in Fig.2

for different friction factor (m=0.0 to 1.0). It is observed that there is an increase in extrusion

pressure with increase in reduction and friction factor. At low reduction, R=30% the extrusion

pressure varies from 0.5σ0 to 1.5σ0 whereas at high reduction R=90%, it varies from 2.0σ0 to 6.2σ0.

It is interesting to note that the effect of friction is more significant at higher reduction compared to

lower reduction. Hence, the role of lubricant at larger reduction is more effective in reducing the

extrusion pressure.

The present modeling is validated with experiments. The extrusion was carried with lead specimens

using set up as shown in Fig.3 and Fig.4. The dry and wet friction conditions at the die-billet

interface corresponds to constant friction factor m=0.75 and m=0.38 respectively, which was

determined by ring compression test. The flow stress of the work material determined using uni-

axial compression test was found to be 52.5 N/mm2. On lubricated condition, the variation of

extrusion loads with ram travel as obtained from the experiments for 30% and 60% reductions are

shown in Fig.6. The computed results for different area reductions are shown in Table 1. The non-

dimensional extrusion pressure as obtained from experiment is compared with that of theoretical

solution in Fig.5. It seems that the present modeling agrees well with the experimental

investigations.

Table 1. Comparison of experimental and computed resultsa (Cosine Die)

Reduction (%) Punch Pav (N/mm2) σ0 (N/mm

2) Pav/σ0 Error (%)

Load (N)

Dry (m=0.38) Exp. Computed

30 70x103 43.75 52.5 0.8333 0.903 7.718

60 150x103 93.75 52.5 1.785 1.830 2.459

a Area of the extrusion chamber = 16.00 cm

2 = 1600 mm

2

Fig. 2: Variation of the non-dimensional extrusion pressure with percentage reduction.


The variation of non-dimensional extrusion pressure with respect to reductions are shown in Fig.2

for different friction factor (m=0.0 to 1.0). It is observed that there is an increase in extrusion

pressure with increase in reduction and friction factor. At low reduction, R=30% the extrusion

pressure varies from 0.5σ0 to 1.5σ0 whereas at high reduction R=90%, it varies from 2.0σ0 to 6.2σ0.

It is interesting to note that the effect of friction is more significant at higher reduction compared to

lower reduction. Hence, the role of lubricant at larger reduction is more effective in reducing the

extrusion pressure.

The present modeling is validated with experiments. The extrusion was carried with lead specimens

using set up as shown in Fig.3 and Fig.4. The dry and wet friction conditions at the die-billet

interface corresponds to constant friction factor m=0.75 and m=0.38 respectively, which was

determined by ring compression test. The flow stress of the work material determined using uni-

axial compression test was found to be 52.5 N/mm2. On lubricated condition, the variation of

extrusion loads with ram travel as obtained from the experiments for 30% and 60% reductions are

shown in Fig.6. The computed results for different area reductions are shown in Table 1. The non-

dimensional extrusion pressure as obtained from experiment is compared with that of theoretical

solution in Fig.5. It seems that the present modeling agrees well with the experimental

investigations.

Table 1. Comparison of experimental and computed resultsa (Cosine Die)

Reduction (%) Punch Pav (N/mm2) σ0 (N/mm

2) Pav/σ0 Error (%)

Load (N)

Dry (m=0.38) Exp. Computed

30 70x103 43.75 52.5 0.8333 0.903 7.718

60 150x103 93.75 52.5 1.785 1.830 2.459

a Area of the extrusion chamber = 16.00 cm

2 = 1600 mm

2

Fig. 2: Variation of the non-dimensional extrusion pressure with percentage reduction.


Fig. 3: The experimental equipment with assembled set-up.

Fig. 4: Extrusion Die

Conclusion

A three dimensional upper bound method has been used to metal deformation process for the

extrusion of square section from square billet using a cosine die profile. The dual stream function

method has been used to determine kinematically admissible velocity field. The theoretically

solution agrees with the experimental.

Fig. 5: Comparison of Theory with experiments

Fig. 3: The experimental equipment with assembled set-up.

Fig. 4: Extrusion Die

Conclusion

A three dimensional upper bound method has been used to metal deformation process for the

extrusion of square section from square billet using a cosine die profile. The dual stream function

method has been used to determine kinematically admissible velocity field. The theoretically

solution agrees with the experimental.

Fig. 5: Comparison of Theory with experiments


Fig. 6: Punch load vs. punch travel

References

[1] O. Richmond, M.L. Devenpick: A Die Profile for maximum efficiency in strip drawing. Proc.

4th

U.S. Congr. Appl. Mech., ASME (1962), p.1053

[2] O. Richmond, H.L. Morrison: Streamlined wire drawing dies of minimum length. Journal of

Mech. Phy. Solids Vol.15 (1967), p.195.

[3] S.K. Samanta: Slipline field for extrusion through cosine shaped dies. Journal of Mech. Phy.

Solids Vol.18 (1970), p. 311.

[4] C. T. Chen, F. F. Ling: Upper bound solutions to axisymmetric extrusion problems. Int. Journal

of Mechanical Science Vol. 10 (1970), p. 311.

[5] K. T. Chang, J.C. Choi: Upper bound solutions to axisymmetric extrusion problems through

curve die. Proc. the 12th

Midwestern Mech. Conf. Univ of Notre dame (1971).

[6] E. Meta-Pietri, J. Friach: Metal flow through various mathematically contoured extrusion dies.

Proceedings, North Amer. Metal-working Research Conf. Vol. 5 (1977).

[7] J. Friach, E. Mata-Pietric: Experiments and the upper bound solution in axisymmetric

extrusion. Proc. IMTDR conference Vol. 18 (1977), p. 55.

[8] K.P. Maity, P. K. Kar and N.S. Das: A class of Upper-bound Solutions for the extrusion of

square shapes from square billets through curved dies. Jourrnal of Materials Processing

Technology Vol. 62 (1996), pp.185-190.

[9] R. Narayanasamy, R. Ponalagusamy, R. Venkatesan and P. Srinivasan: An Upper Bound

Solution to Extrusion of Circular Billet to Circular Shape through cosine dies. Journal of

Material and Design Vol. 27 (2006), pp. 411-415.

[10] S.K. Lee, D. C. Ko and B.M. Kim: Optimal die profile design for uniform microstructure in hot

extruded product. International Journal of Machine Tools & Manufacture Vol. 40 (2000),

pp.1457-1478.

Fig. 6: Punch load vs. punch travel

References

[1] O. Richmond, M.L. Devenpick: A Die Profile for maximum efficiency in strip drawing. Proc.

4th

U.S. Congr. Appl. Mech., ASME (1962), p.1053

[2] O. Richmond, H.L. Morrison: Streamlined wire drawing dies of minimum length. Journal of

Mech. Phy. Solids Vol.15 (1967), p.195.

[3] S.K. Samanta: Slipline field for extrusion through cosine shaped dies. Journal of Mech. Phy.

Solids Vol.18 (1970), p. 311.

[4] C. T. Chen, F. F. Ling: Upper bound solutions to axisymmetric extrusion problems. Int. Journal

of Mechanical Science Vol. 10 (1970), p. 311.

[5] K. T. Chang, J.C. Choi: Upper bound solutions to axisymmetric extrusion problems through

curve die. Proc. the 12th

Midwestern Mech. Conf. Univ of Notre dame (1971).

[6] E. Meta-Pietri, J. Friach: Metal flow through various mathematically contoured extrusion dies.

Proceedings, North Amer. Metal-working Research Conf. Vol. 5 (1977).

[7] J. Friach, E. Mata-Pietric: Experiments and the upper bound solution in axisymmetric

extrusion. Proc. IMTDR conference Vol. 18 (1977), p. 55.

[8] K.P. Maity, P. K. Kar and N.S. Das: A class of Upper-bound Solutions for the extrusion of

square shapes from square billets through curved dies. Jourrnal of Materials Processing

Technology Vol. 62 (1996), pp.185-190.

[9] R. Narayanasamy, R. Ponalagusamy, R. Venkatesan and P. Srinivasan: An Upper Bound

Solution to Extrusion of Circular Billet to Circular Shape through cosine dies. Journal of

Material and Design Vol. 27 (2006), pp. 411-415.

[10] S.K. Lee, D. C. Ko and B.M. Kim: Optimal die profile design for uniform microstructure in hot

extruded product. International Journal of Machine Tools & Manufacture Vol. 40 (2000),

pp.1457-1478.


[11] T. Reinikainen, K. Andersson, S. Kivivuori and A. S. Korhonen: Finite-element analysis of

copper extrusion processes. Journal of Materials Processing Technology Vol. 34 (1992),

pp.101-108.

[12] J. L. Kuester, J. H. Mize: Optimization Techniques with Fortran. McGraw Hill Book Company.

[13] C.S. Yih: Stream Functions in Three-Dimensional Flow. La Haulle Blanche Vol.12 (1957),

p.445.

[11] T. Reinikainen, K. Andersson, S. Kivivuori and A. S. Korhonen: Finite-element analysis of

copper extrusion processes. Journal of Materials Processing Technology Vol. 34 (1992),

pp.101-108.

[12] J. L. Kuester, J. H. Mize: Optimization Techniques with Fortran. McGraw Hill Book Company.

[13] C.S. Yih: Stream Functions in Three-Dimensional Flow. La Haulle Blanche Vol.12 (1957),

p.445.


THREE DIMENSIONAL UPPER BOUND MODELLING FOR EXTRUSION OF ROUND-TO-OCTAGON SECTION USING

LINEARLY CONVERGING DIE

K P Maity1, a, A. K. Rout2, b 1Department of Mechanical Engineering, National Institute of Technology, Rourkela, Orissa, INDIA

a [email protected] ; [email protected]

Keywords: SERR, Round, Octagon, Extrusion, Die Abstract. The extrusion of section from round billet poses a great challenge for theoretical modeling of the process using upper bound method. The greatest difficulty in three-dimensional upper bound method is to determine kinematically admissible velocity field. The SERR (Spatial Elementary Rigid Region) technique is fairly applicable for analyzing extrusion of sections having re-entrant corners. A modified version of SERR technique has been used for extrusion of octagon sections from round billet through a linearly converging die. The circular cross section of the round billet is approximated by a regular polygon of equal area. The extrusion pressure has been computed for different boundary condition at the die billet interface. The optimum die geometry has been determined.

Introduction

Extrusion is a massive deformation process not only to produce cylindrical bars or hollow tubes but a large variety of irregular cross sections. It is one of the fastest growing metal working methods having definite advantages over other metal deformation process like rolling for the production of complicated and re-entrant sections (section with no convexity like I,T, Channel, etc.). For the extrusion of sections, linearly converging dies with lubricants are more preferred to square dies, as the former provide a gradual change in shape and reduction of area simultaneously resulting uniform microstructure. It is highly desirable to study the mechanics of metal deformation in order to optimize the process. Very often, many empirical rules are followed to determine process parameters, extrusion load and geometries of die profile. However, empirical relations have limited applications and can not be applied universally under various conditions. The upper-bound technique appears to be an approximate tool for investigating 3D metal forming problems which is having some specific advantage over finite element method as well as slip-line field method. This is more applicable when the objective of such an analysis is limited to prediction of the deformation load and study of metal flow during the process. This is so because the classical slipline field solution is only applicable to the plane strain mode of deformation and the finite element method (FEM) is constrained by computational difficulties to achieve accuracy in these cases. The only difficulty in three dimensional upper bound method is to predict kinematically admissible velocity field. To formulate kinematically admissible velocity fields in case of three-dimensional metal deformation processes, three different techniques have been employed: the dual stream function method due to Nagpal and Altan [1], the conformal transformation technique due to Yang and Lee [2], the generalized velocity field due to Han, Yang and Kiuchi [3]. The first two methods are used when section symmetry exists in the deformation zone where as the third method is applicable to any general situation. A fourth method based on discretisation of the deformation zone into rigid tetrahedral blocks using discontinuous velocity field has also been proposed by Gato and Giardo [4]. However, this is applicable to problems where the die walls are planar in nature with similar product and billet sections. Of course it is possible to predict an admissible velocity field by guessing the form of the streamlines. This has been used by Hoshino and Gunasekara [5] to predict load for extrusion through curved stream lined dies. Kar and Das [6] modified the technique proposed by Gatto and Giarda [4] to solve problems with dissimilar billet and product sections. Kar

THREE DIMENSIONAL UPPER BOUND MODELLING FOR EXTRUSION OF ROUND-TO-OCTAGON SECTION USING

LINEARLY CONVERGING DIE

K P Maity1, a, A. K. Rout2, b 1Department of Mechanical Engineering, National Institute of Technology, Rourkela, Orissa, INDIA

a [email protected] ; [email protected]

Keywords: SERR, Round, Octagon, Extrusion, Die Abstract. The extrusion of section from round billet poses a great challenge for theoretical modeling of the process using upper bound method. The greatest difficulty in three-dimensional upper bound method is to determine kinematically admissible velocity field. The SERR (Spatial Elementary Rigid Region) technique is fairly applicable for analyzing extrusion of sections having re-entrant corners. A modified version of SERR technique has been used for extrusion of octagon sections from round billet through a linearly converging die. The circular cross section of the round billet is approximated by a regular polygon of equal area. The extrusion pressure has been computed for different boundary condition at the die billet interface. The optimum die geometry has been determined.

Introduction

Extrusion is a massive deformation process not only to produce cylindrical bars or hollow tubes but a large variety of irregular cross sections. It is one of the fastest growing metal working methods having definite advantages over other metal deformation process like rolling for the production of complicated and re-entrant sections (section with no convexity like I,T, Channel, etc.). For the extrusion of sections, linearly converging dies with lubricants are more preferred to square dies, as the former provide a gradual change in shape and reduction of area simultaneously resulting uniform microstructure. It is highly desirable to study the mechanics of metal deformation in order to optimize the process. Very often, many empirical rules are followed to determine process parameters, extrusion load and geometries of die profile. However, empirical relations have limited applications and can not be applied universally under various conditions. The upper-bound technique appears to be an approximate tool for investigating 3D metal forming problems which is having some specific advantage over finite element method as well as slip-line field method. This is more applicable when the objective of such an analysis is limited to prediction of the deformation load and study of metal flow during the process. This is so because the classical slipline field solution is only applicable to the plane strain mode of deformation and the finite element method (FEM) is constrained by computational difficulties to achieve accuracy in these cases. The only difficulty in three dimensional upper bound method is to predict kinematically admissible velocity field. To formulate kinematically admissible velocity fields in case of three-dimensional metal deformation processes, three different techniques have been employed: the dual stream function method due to Nagpal and Altan [1], the conformal transformation technique due to Yang and Lee [2], the generalized velocity field due to Han, Yang and Kiuchi [3]. The first two methods are used when section symmetry exists in the deformation zone where as the third method is applicable to any general situation. A fourth method based on discretisation of the deformation zone into rigid tetrahedral blocks using discontinuous velocity field has also been proposed by Gato and Giardo [4]. However, this is applicable to problems where the die walls are planar in nature with similar product and billet sections. Of course it is possible to predict an admissible velocity field by guessing the form of the streamlines. This has been used by Hoshino and Gunasekara [5] to predict load for extrusion through curved stream lined dies. Kar and Das [6] modified the technique proposed by Gatto and Giarda [4] to solve problems with dissimilar billet and product sections. Kar


and Sahoo [7] used the reformulated spatial elementary rigid region (SERR) technique for the analysis of round-to-square extrusion by approximating the circle into a polygon and successively increasing the number of sides of this approximating polygon until the extrusion pressure converged for square die. The present investigation is based on 3D upper bound method using SERR technique for the analysis of round-to-octagon extrusion through a converging die. The linear converging die is having some specific advantage over the flat faced die in respect of low friction, less redundant work and more uniform grain structure [10,11,12]. For the sake of the present analysis, it is assumed that the centroid of die aperture lies on the billet axis. This assumption is necessary so that the product remains straight as it comes out of the die orifice. The curved surfaces are approximated to the planar surfaces to apply SERR technique. A comprehensive computational model was developed to determine the normalized extrusion pressure using a multivariate unconstrained optimization technique [9]. The extrusion pressure has been computed for various semi-cone angles with different reductions and friction factors. The theoretical results are compared with experimental investigations. These results can be used to predict the forming load and optimal die shape for designing the sectioned die assuming the frictional condition.

The SERR Technique

In the SERR technique, the deformation zone is envisaged to consist of tetrahedral rigid blocks, each block separated from others by planes of velocity discontinuity. Each rigid region has its own internal velocity vector consistent with the boundary conditions. Thus, if there are N rigid blocks, then the number of unknown internal velocity vectors is also N (thus, 3N spatial velocity components). The velocity at entry to the deformation zone (the billet velocity) is considered to be prescribed and the velocity at the exit has a single component since its direction is known from the physical description of the problem. Therefore the total number of unknown velocity components in the global level becomes 3N+1. All these unknown velocity components can be uniquely determined if an equal number of equations are generated. This is done applying the mass continuity condition to the bounding faces of all the tetrahedral rigid blocks taken together. It may be noted that the set of velocity equations so generated becomes consistent and determinate if and only if the SERR blocks are tetrahedral in shape, so that, the number of triangular bounding faces automatically becomes 3N+1. To illustrate the application of the above principles, let the ith bounding face in the assembly of tetrahedrons be in the plane

01),,( 321 =+++≡ zayaxazyx iiiφ (1)

The coefficients ai1, ai2 and ai3 in Eq. (1) above can be determined by specifying the co-ordinates of the three vertices of this triangular face. Then the unit normal vector to this face is

φφ

∇∇

=n (2)

If V1 and V2 are the velocity vectors on both sides of the ith face, the condition for continuity is

21 .ˆ.ˆ VnVn ii = (3) A determinate set of velocity equations is generated by applying Eq. (3) to all the bounding faces in the assembly of tetrahedrons. The boundary conditions on the velocity field are also enforced through this equation. For example, if a face lies on a plane of symmetry then the right-hand side of Eq. (3) is made zero to admit the condition that no mass flow occurs normal to these faces.

Application to the present problem. For the sake of the present analysis, it is assumed that the centroid of the die aperture lies on the billet axis, this assumption being necessary so that the product remains straight as it comes out of the die orifice.

and Sahoo [7] used the reformulated spatial elementary rigid region (SERR) technique for the analysis of round-to-square extrusion by approximating the circle into a polygon and successively increasing the number of sides of this approximating polygon until the extrusion pressure converged for square die. The present investigation is based on 3D upper bound method using SERR technique for the analysis of round-to-octagon extrusion through a converging die. The linear converging die is having some specific advantage over the flat faced die in respect of low friction, less redundant work and more uniform grain structure [10,11,12]. For the sake of the present analysis, it is assumed that the centroid of die aperture lies on the billet axis. This assumption is necessary so that the product remains straight as it comes out of the die orifice. The curved surfaces are approximated to the planar surfaces to apply SERR technique. A comprehensive computational model was developed to determine the normalized extrusion pressure using a multivariate unconstrained optimization technique [9]. The extrusion pressure has been computed for various semi-cone angles with different reductions and friction factors. The theoretical results are compared with experimental investigations. These results can be used to predict the forming load and optimal die shape for designing the sectioned die assuming the frictional condition.

The SERR Technique

In the SERR technique, the deformation zone is envisaged to consist of tetrahedral rigid blocks, each block separated from others by planes of velocity discontinuity. Each rigid region has its own internal velocity vector consistent with the boundary conditions. Thus, if there are N rigid blocks, then the number of unknown internal velocity vectors is also N (thus, 3N spatial velocity components). The velocity at entry to the deformation zone (the billet velocity) is considered to be prescribed and the velocity at the exit has a single component since its direction is known from the physical description of the problem. Therefore the total number of unknown velocity components in the global level becomes 3N+1. All these unknown velocity components can be uniquely determined if an equal number of equations are generated. This is done applying the mass continuity condition to the bounding faces of all the tetrahedral rigid blocks taken together. It may be noted that the set of velocity equations so generated becomes consistent and determinate if and only if the SERR blocks are tetrahedral in shape, so that, the number of triangular bounding faces automatically becomes 3N+1. To illustrate the application of the above principles, let the ith bounding face in the assembly of tetrahedrons be in the plane

01),,( 321 =+++≡ zayaxazyx iiiφ (1)

The coefficients ai1, ai2 and ai3 in Eq. (1) above can be determined by specifying the co-ordinates of the three vertices of this triangular face. Then the unit normal vector to this face is

φφ

∇∇

=n (2)

If V1 and V2 are the velocity vectors on both sides of the ith face, the condition for continuity is

21 .ˆ.ˆ VnVn ii = (3) A determinate set of velocity equations is generated by applying Eq. (3) to all the bounding faces in the assembly of tetrahedrons. The boundary conditions on the velocity field are also enforced through this equation. For example, if a face lies on a plane of symmetry then the right-hand side of Eq. (3) is made zero to admit the condition that no mass flow occurs normal to these faces.

Application to the present problem. For the sake of the present analysis, it is assumed that the centroid of the die aperture lies on the billet axis, this assumption being necessary so that the product remains straight as it comes out of the die orifice.


As mentioned earlier, the SERR technique can be applied where there are plane boundaries. Hence, the curved surface is to be replaced by planar surfaces so as to accommodate the SERR analysis. For the present analysis the round billet is approximated by a regular polygon with 24 sides (as there is a negligible change of final computed value by further increasing the sides). To approximate the circular cross-section of the billet into a regular polygon, the cross-sectional areas of the billet and the approximating polygon must be maintained equal, this condition being written as:

=Π24

1 22 θCotLMR (4)

where: θ is the internal angle of the M-sided regular polygon; and L is length of each side of the approximating polygon. Since the octagon section has two-fold symmetry, only one-fourth of the deformation zone is considered for the analysis. Following the principles laid down in reference [6], the sub-zones of deformation are delineated in the domain of interest by taking a suitably located floating point. For illustration, Fig. 1 shows one-fourth of the deformation zone (in this case the round cross-section is approximated by 24 sides for clear demonstration) with a single floating point on the extrusion axis at a distance from origin, all the corner points being joined to it. The resulting pyramid and tetrahedrons are the ultimate deformation sub-zone for the SERR formulation. The single-point formulation (round cross-section approximated by 24 sides) gives rise to three pyramidal sub-zones and four tetrahedral sub-zones (for the present zone of interest i.e. one-fourth of the deformation zone). Hence, it results in ten tetrahedrons, with the number of global schemes of discretisation being four. All these sub-zones are interconnected and have common triangular faces. Thus the basic SERR blocks in their totality have 31 bounding faces, so that as all these bounding faces are triangular in shape, by applying Eq. (3) 31velocity equations can be obtained. When these equations are solved, an equal number of velocity components can be obtained for this formulation (the discretisation details are summarized in Table 1). Similarly, if the round cross-section is approximated by 48 sides, it gives rise to three pyramidal sub-zones and nine tetrahedral sub zones for one-fourth of the deformation zone. Application of the upper-bound theorem. The upper-bound theorem predicts the power necessary to perform the desired metal forming at the prescribed velocities. However, since the velocity field for a given problem is generally not known, the power for any velocity field as calculated by the upper-bound theorem is greater than or equal to the actual power. The development also applies to any velocity field which satisfies the boundary and plasticity requirements. Thus for any possible velocity field there also exists an associated total power. The actual velocity field is that which minimizes the associated total power and the actual total power is the minimum associated total power. The formal statement of the upper-bound theorem is that amongst all kinematically admissible velocity fields, the actual field minimizes the work-function J, where: 321 JJJJ ++= (5)

In the present formulation with a discontinuous velocity field the strain rate components ijε , are all zero inside the rigid blocks. Hence, J1 =0 Since, velocity discontinuities iV∆ and jV∆ are constant over all of the faces:

fjjii AVm

AVJ ∫∫ ∆

+∆=

3300 σσ (6)

The mean non-dimensional average extrusion pressure is determined from the relation

02

0 σσ b

av

VWJp

= (7)

As mentioned earlier, the SERR technique can be applied where there are plane boundaries. Hence, the curved surface is to be replaced by planar surfaces so as to accommodate the SERR analysis. For the present analysis the round billet is approximated by a regular polygon with 24 sides (as there is a negligible change of final computed value by further increasing the sides). To approximate the circular cross-section of the billet into a regular polygon, the cross-sectional areas of the billet and the approximating polygon must be maintained equal, this condition being written as:

=Π24

1 22 θCotLMR (4)

where: θ is the internal angle of the M-sided regular polygon; and L is length of each side of the approximating polygon. Since the octagon section has two-fold symmetry, only one-fourth of the deformation zone is considered for the analysis. Following the principles laid down in reference [6], the sub-zones of deformation are delineated in the domain of interest by taking a suitably located floating point. For illustration, Fig. 1 shows one-fourth of the deformation zone (in this case the round cross-section is approximated by 24 sides for clear demonstration) with a single floating point on the extrusion axis at a distance from origin, all the corner points being joined to it. The resulting pyramid and tetrahedrons are the ultimate deformation sub-zone for the SERR formulation. The single-point formulation (round cross-section approximated by 24 sides) gives rise to three pyramidal sub-zones and four tetrahedral sub-zones (for the present zone of interest i.e. one-fourth of the deformation zone). Hence, it results in ten tetrahedrons, with the number of global schemes of discretisation being four. All these sub-zones are interconnected and have common triangular faces. Thus the basic SERR blocks in their totality have 31 bounding faces, so that as all these bounding faces are triangular in shape, by applying Eq. (3) 31velocity equations can be obtained. When these equations are solved, an equal number of velocity components can be obtained for this formulation (the discretisation details are summarized in Table 1). Similarly, if the round cross-section is approximated by 48 sides, it gives rise to three pyramidal sub-zones and nine tetrahedral sub zones for one-fourth of the deformation zone. Application of the upper-bound theorem. The upper-bound theorem predicts the power necessary to perform the desired metal forming at the prescribed velocities. However, since the velocity field for a given problem is generally not known, the power for any velocity field as calculated by the upper-bound theorem is greater than or equal to the actual power. The development also applies to any velocity field which satisfies the boundary and plasticity requirements. Thus for any possible velocity field there also exists an associated total power. The actual velocity field is that which minimizes the associated total power and the actual total power is the minimum associated total power. The formal statement of the upper-bound theorem is that amongst all kinematically admissible velocity fields, the actual field minimizes the work-function J, where: 321 JJJJ ++= (5)

In the present formulation with a discontinuous velocity field the strain rate components ijε , are all zero inside the rigid blocks. Hence, J1 =0 Since, velocity discontinuities iV∆ and jV∆ are constant over all of the faces:

fjjii AVm

AVJ ∫∫ ∆

+∆=

3300 σσ (6)

The mean non-dimensional average extrusion pressure is determined from the relation

02

0 σσ b

av

VWJp

= (7)


The optimization parameters

For the single-point formulation, the floating point lies on the extrusion axis. Thus, the formulation has one undetermined co-ordinate, which serves as the optimization parameter to minimise the extrusion pressure for this formulation. Here, it is to be noted that the length of the die is taken as per the equivalent semi cone angle. The equivalent semi-cone angle is defined as the semi-cone angle of a conical die where the reduction in area is the same as that of the polygonal sections.


Computations were carried out for all eight schemes of octagonal section and the scheme giving the least upper-bound was identified. The discretised deformation zone corresponding to the least upper-bound is named here as the optimum configuration. This optimum configuration is utilised for computation of the variation of the normalized extrusion pressure with equivalent semi-cone angle (in degrees) and the percentage area reduction, for different friction factors (Fig. 2). It is clear from these Fig.s that the optimal semi-cone angle that secures the minimum extrusion pressure increases with the increase of friction. These results can be used to predict the forming stress and optimal die shape for designing the sectioned die, assuming the frictional condition either in an empirical way or by means of a simulation test. Comparison of the present solution is also made with the solution proposed by Gunasekera et al. [8] (Fig. 3). The present solution yields higher extrusion pressure. Table 1 Summary of discretisation schemes (Single-point formulation)

Type of sub-zones 3 pyramids ; 4 tetrahedrons

Total number of SERR blocks 2+2+2+1+1+1+1=10

Number of discretisation schemes 2x2x2=8

Number of triangular faces 31

No. of velocity components 10x3=30 for 10 SERR and 1 at exit, Total=31

The optimization parameters

For the single-point formulation, the floating point lies on the extrusion axis. Thus, the formulation has one undetermined co-ordinate, which serves as the optimization parameter to minimise the extrusion pressure for this formulation. Here, it is to be noted that the length of the die is taken as per the equivalent semi cone angle. The equivalent semi-cone angle is defined as the semi-cone angle of a conical die where the reduction in area is the same as that of the polygonal sections.


Computations were carried out for all eight schemes of octagonal section and the scheme giving the least upper-bound was identified. The discretised deformation zone corresponding to the least upper-bound is named here as the optimum configuration. This optimum configuration is utilised for computation of the variation of the normalized extrusion pressure with equivalent semi-cone angle (in degrees) and the percentage area reduction, for different friction factors (Fig. 2). It is clear from these Fig.s that the optimal semi-cone angle that secures the minimum extrusion pressure increases with the increase of friction. These results can be used to predict the forming stress and optimal die shape for designing the sectioned die, assuming the frictional condition either in an empirical way or by means of a simulation test. Comparison of the present solution is also made with the solution proposed by Gunasekera et al. [8] (Fig. 3). The present solution yields higher extrusion pressure. Table 1 Summary of discretisation schemes (Single-point formulation)

Type of sub-zones 3 pyramids ; 4 tetrahedrons

Total number of SERR blocks 2+2+2+1+1+1+1=10

Number of discretisation schemes 2x2x2=8

Number of triangular faces 31

No. of velocity components 10x3=30 for 10 SERR and 1 at exit, Total=31


Fig. 1(a). One-fourth of the deformation sub-zone

Z

2 3 4

5

6

7

8

9 1

1

13

12 11

110

Y

X

Fig. 1(a). One-fourth of the deformation sub-zone

Z

2 3 4

5

6

7

8

9 1

1

13

12 11

110

Y

X


Fig. 1 (b). One-fourth of the deformation sub-zone (plan view)

Conclusions

1. Using this solution, the optimal die-geometry (the equivalent semi-cone angle) that requires the minimum forming stress can be obtained for different reductions of area and friction conditions. 2. Comparison made with existing theoretical results shows that the present solution can predict reasonable upper-bound extrusion pressures. 3. The present method can be extended to obtain the solution of generalised problems of non-axisymmetric extrusion or drawing through converging dies.

Reduction of area =40%

00.5

11.5

22.5

33.5

44.5

0 10 20 30 40 50

Equivalent semi cone angle, Degree

&on

dim

ensi

onal

ex

trus

ion

pres

sure

m=0.0

m=0.1

m=0.2

m=0.3

m=0.4

Fig.2.: Effect of friction on the extrusion pressure with variation in the die angle

2

3 4

7

13

8

10,15,1 14 9

X

5

6

12 11

Y

Fig. 1 (b). One-fourth of the deformation sub-zone (plan view)

Conclusions

1. Using this solution, the optimal die-geometry (the equivalent semi-cone angle) that requires the minimum forming stress can be obtained for different reductions of area and friction conditions. 2. Comparison made with existing theoretical results shows that the present solution can predict reasonable upper-bound extrusion pressures. 3. The present method can be extended to obtain the solution of generalised problems of non-axisymmetric extrusion or drawing through converging dies.

Reduction of area =40%

00.5

11.5

22.5

33.5

44.5

0 10 20 30 40 50

Equivalent semi cone angle, Degree

&on

dim

ensi

onal

ex

trus

ion

pres

sure

m=0.0

m=0.1

m=0.2

m=0.3

m=0.4

Fig.2.: Effect of friction on the extrusion pressure with variation in the die angle

2

3 4

7

13

8

10,15,1 14 9

X

5

6

12 11

Y


Fig. 3: Comparison with ref. [8] for the extrusion of octagonal section

References

[1] V. Nagpal, T Altan: Analysis of the three dimensional metal flow in extrusion of shapes with the use of dual stream function in: Proceedings of the third North American Metal Research Conference on Pittsburgh, Pennsylvania, (1975), p. 26.

[2] D. Y. Yang, C. H. Lee: Analysis of three dimensional extrusion of sections through curved dies by conformal transformation. International Journal of Mechanical Sciences, Vol. 29 (1978), pp. 541-549.

[3] C. H. Han, D.Y. Yang, M. Kiuchi: A new formulation for three-dimensional extrusion and its application to extrusion of clover sections. International Journal of Mechanical Science, Vol. 28 (1986), p. 201.

[4] F. Gatto, A Giardo: The characteristics of three-dimensional analysis of plastic deformation according to the SERR method. International Journal of Mechanical Science, Vol.23 (1981), pp. 129-138.

[5] S. Hoshino, J. S. Gunasekara: An upper bound solution for extrusion of square section from round bar through converging dies. Proceedings of the 20th International Machine and Tool Design Research Conference, Vol. 21 (1980), p. 97.

[6] P. K. Kar, N. S. Das: Upper bound analysis of extrusion of I-section bars from square/rectangular billets through square dies. International Journal of Mechanical Science, Vol. 39 (1997), pp. 925-934.

[7] P. K. Kar, R. K. Sahoo: An application of the SERR technique to the analysis of extrusion of sections from round billets. Journal of Institution of Engineers (India), Vol.78 (1977), pp. 151-154.

[8] J. S. Gunasekera, S. Hosino: Analysis of extrusion or drawing of polygonal sections through straightly conversing dies. J. Eng. Ind. Trans, ASME, Vol. 104 (1982), pp. 38–45.

[9] J. L. Kuester, J. H. Mize: Optimization Techniques with Fortran. McGraw Hill Book Company. [10] K. P. Maity, P. K. Kar, N. S. Das: A class of U-B solutions for the extrusion of square shapes from square billets through curved dies. Int. J. of Materials Processing Technology, Vol. 62 (1996), pp. 185-190.

8

Fig. 3: Comparison with ref. [8] for the extrusion of octagonal section

References

[1] V. Nagpal, T Altan: Analysis of the three dimensional metal flow in extrusion of shapes with the use of dual stream function in: Proceedings of the third North American Metal Research Conference on Pittsburgh, Pennsylvania, (1975), p. 26.

[2] D. Y. Yang, C. H. Lee: Analysis of three dimensional extrusion of sections through curved dies by conformal transformation. International Journal of Mechanical Sciences, Vol. 29 (1978), pp. 541-549.

[3] C. H. Han, D.Y. Yang, M. Kiuchi: A new formulation for three-dimensional extrusion and its application to extrusion of clover sections. International Journal of Mechanical Science, Vol. 28 (1986), p. 201.

[4] F. Gatto, A Giardo: The characteristics of three-dimensional analysis of plastic deformation according to the SERR method. International Journal of Mechanical Science, Vol.23 (1981), pp. 129-138.

[5] S. Hoshino, J. S. Gunasekara: An upper bound solution for extrusion of square section from round bar through converging dies. Proceedings of the 20th International Machine and Tool Design Research Conference, Vol. 21 (1980), p. 97.

[6] P. K. Kar, N. S. Das: Upper bound analysis of extrusion of I-section bars from square/rectangular billets through square dies. International Journal of Mechanical Science, Vol. 39 (1997), pp. 925-934.

[7] P. K. Kar, R. K. Sahoo: An application of the SERR technique to the analysis of extrusion of sections from round billets. Journal of Institution of Engineers (India), Vol.78 (1977), pp. 151-154.

[8] J. S. Gunasekera, S. Hosino: Analysis of extrusion or drawing of polygonal sections through straightly conversing dies. J. Eng. Ind. Trans, ASME, Vol. 104 (1982), pp. 38–45.

[9] J. L. Kuester, J. H. Mize: Optimization Techniques with Fortran. McGraw Hill Book Company. [10] K. P. Maity, P. K. Kar, N. S. Das: A class of U-B solutions for the extrusion of square shapes from square billets through curved dies. Int. J. of Materials Processing Technology, Vol. 62 (1996), pp. 185-190.

8


[11] R. Ponalagusamy, R. Narayanasamy P. Srinivasan: Design & Development of streamlined extrusion dies a Bezier curve approach. Int. J. of Materials Processing Technology, Vol. 161 (2005), pp. 375-380.

[12] R. Narayanasamy, R. Ponalagusamy, R. Venkatesan, P. Srinivasan: An upper bound solution to extrusion of circular billet to circular shape through cosine dies. Int. J. of Materials and Design, Vol. 27 ( 2006), pp. 411-415.

[11] R. Ponalagusamy, R. Narayanasamy P. Srinivasan: Design & Development of streamlined extrusion dies a Bezier curve approach. Int. J. of Materials Processing Technology, Vol. 161 (2005), pp. 375-380.

[12] R. Narayanasamy, R. Ponalagusamy, R. Venkatesan, P. Srinivasan: An upper bound solution to extrusion of circular billet to circular shape through cosine dies. Int. J. of Materials and Design, Vol. 27 ( 2006), pp. 411-415.


Measuring the Deformation of a Flat Die by Applying a Laser Beam on a Reflecting Surface

W. Assaad1, a, H.J.M. Geijselaers2,b and K.E.Nilsen3,c 1Materials Innovation Institute, The Netherlands

2Faculty of Engineering Technology, University of Twente, The Netherlands 3Boal Beheer B.V, De Lier, The Netherlands

[email protected], [email protected], [email protected]

Keywords: extrusion, deformation, decoupled, die. Abstract. The design of extrusion dies depends on the experience of the designer. After the die has been manufactured, it is tested during an extrusion process and machined several times until it works properly. The die is designed by a trial and error method which is expensive interms of time consumption and the amount of scrap. Research is going on to replace the trial pressing with finite element simulations that concentrate on material and tool analysis. In order to validate the tool simulations, an experiment is required for measuring the deformation of the die. Measuring the deformation of the die is faced with two main obstacles: high temperature and little free space. To overcome these obstacles a method is tried, which works by applying a laser beam on a reflecting surface. This cheap method is simple, robust and gives good results. This paper describes measuring the deformation of a flat die used to extrude a single U shape profile. In addition, finite element calculation of the die is performed. Finally, a comparison is performed between experimental and numerical results.

Introduction

In a direct aluminum extrusion process the die is subjected to two types of loads: mechanical and thermal loads. These loads cause the die face to deform in a concave shape. Consequently, the section is extruded non uniformly through the deformed die where it is thinner at the middle and thicker at the edges. Therefore, the dimensions of the extruded section may not be as specified. The die must be corrected in order to extrude a profile with the specified dimensions. Prediction of how the die deforms helps in decreasing the number of trial pressings and die corrections. In fact finite element simulations are used in predicting the deformation of the die. Moreover, these simulations require experiments in order to be validated. Therefore, an experiment is conducted for measuring the deformation of a flat die used in the extrusion of a U shape profile. Measuring the die deformation or the pressure on the die face is a challenging task especially in an industrial extrusion environment. In literature different approaches were applied for measuring the pressure on the die face and deformation of the die. In [1] the pressure distribution on the die face and deformation of the die in the extrusion of 1050 aluminum rod were measured by the use of a semi conductor strain gauge pressure sensor and a laser displacement meter respectively. The measurements were performed on a 400 tons vertical laboratory press. The pressure sensor was inserted in a hole drilled through the die and its holder such that the contact between the sensor and the metal would take place. The measurement of the die deformation was performed by measuring the deflection of the bar attached to the die at a specified position. In [2] cylindrical flat steel capsule which deforms linearly was inserted in the die face. The capsule was connected to a deformation measurement system with a bar inserted in a hole drilled through the tool stack. In [3] a technique was designed for measuring the pressure on the die face with the application of Capacitec capacitive probes. This type of sensors was chosen due to their small size and functionality at temperatures above 400 C˚. In [3] and [4] the technique was applied successfully in measuring the pressure on the die face during

Measuring the Deformation of a Flat Die by Applying a Laser Beam on a Reflecting Surface

W. Assaad1, a, H.J.M. Geijselaers2,b and K.E.Nilsen3,c 1Materials Innovation Institute, The Netherlands

2Faculty of Engineering Technology, University of Twente, The Netherlands 3Boal Beheer B.V, De Lier, The Netherlands


Keywords: extrusion, deformation, decoupled, die. Abstract. The design of extrusion dies depends on the experience of the designer. After the die has been manufactured, it is tested during an extrusion process and machined several times until it works properly. The die is designed by a trial and error method which is expensive interms of time consumption and the amount of scrap. Research is going on to replace the trial pressing with finite element simulations that concentrate on material and tool analysis. In order to validate the tool simulations, an experiment is required for measuring the deformation of the die. Measuring the deformation of the die is faced with two main obstacles: high temperature and little free space. To overcome these obstacles a method is tried, which works by applying a laser beam on a reflecting surface. This cheap method is simple, robust and gives good results. This paper describes measuring the deformation of a flat die used to extrude a single U shape profile. In addition, finite element calculation of the die is performed. Finally, a comparison is performed between experimental and numerical results.

Introduction

In a direct aluminum extrusion process the die is subjected to two types of loads: mechanical and thermal loads. These loads cause the die face to deform in a concave shape. Consequently, the section is extruded non uniformly through the deformed die where it is thinner at the middle and thicker at the edges. Therefore, the dimensions of the extruded section may not be as specified. The die must be corrected in order to extrude a profile with the specified dimensions. Prediction of how the die deforms helps in decreasing the number of trial pressings and die corrections. In fact finite element simulations are used in predicting the deformation of the die. Moreover, these simulations require experiments in order to be validated. Therefore, an experiment is conducted for measuring the deformation of a flat die used in the extrusion of a U shape profile. Measuring the die deformation or the pressure on the die face is a challenging task especially in an industrial extrusion environment. In literature different approaches were applied for measuring the pressure on the die face and deformation of the die. In [1] the pressure distribution on the die face and deformation of the die in the extrusion of 1050 aluminum rod were measured by the use of a semi conductor strain gauge pressure sensor and a laser displacement meter respectively. The measurements were performed on a 400 tons vertical laboratory press. The pressure sensor was inserted in a hole drilled through the die and its holder such that the contact between the sensor and the metal would take place. The measurement of the die deformation was performed by measuring the deflection of the bar attached to the die at a specified position. In [2] cylindrical flat steel capsule which deforms linearly was inserted in the die face. The capsule was connected to a deformation measurement system with a bar inserted in a hole drilled through the tool stack. In [3] a technique was designed for measuring the pressure on the die face with the application of Capacitec capacitive probes. This type of sensors was chosen due to their small size and functionality at temperatures above 400 C˚. In [3] and [4] the technique was applied successfully in measuring the pressure on the die face during


the extrusion of a rod and thin strip with an experimental vertical extrusion press. But it was not a complete success in [5] in measuring the pressure on the die face in an industrial U shape profile extrusion due to failure of the sensors. Two different ideas were utilized in the above mentioned experiments. First, the deflection of the die is measured by measuring the deflection of a bar connected to the die face. Second, the deformation of the die is measured by sensors integrated in the die. Moreover, a special die is required to be designed and manufactured for mounting the sensors and their connectors to the measurement system. In addition calibration is a demand before measurement.

Since the experiment is carried out on a press owned by an extrusion company, modification to the tool stack is limited. Therefore, the application of the second idea is difficult in this case. Finally, a new approach is deduced from the first idea and followed by applying a laser beam on a reflecting surface. A reflecting surface is mounted on the die face. The experiment is carried out successfully in two rounds which guarantee its repeatability. The experimental results of the first round are compared with finite element simulations where a decoupled analysis is applied. The finite element simulations are performed by the in-house implicit FE-program DiekA.

Experiment setup

The measurement is done on the deformation of a flat die used in producing a single U shape profile shown in Fig. 1. To avoid interrupting the beam during the experiment, the saw and the stretcher are switched off. The die, backer and ring are mounted together as shown in Fig. 2. Fig.3 illustrates the experiment setup, where a laser beam is emitted from a laser source towards a reflecting surface which reflects the beam on a white screen. The laser source is placed out side the run-out table and far from the press because it works at room temperature.

Fig.1: profile (Dimensions in mm) Fig.2: tool (Dimensions in mm)

Fig.3: experiment setup

Fig.4: production of the stainless steel flat mirror

the extrusion of a rod and thin strip with an experimental vertical extrusion press. But it was not a complete success in [5] in measuring the pressure on the die face in an industrial U shape profile extrusion due to failure of the sensors. Two different ideas were utilized in the above mentioned experiments. First, the deflection of the die is measured by measuring the deflection of a bar connected to the die face. Second, the deformation of the die is measured by sensors integrated in the die. Moreover, a special die is required to be designed and manufactured for mounting the sensors and their connectors to the measurement system. In addition calibration is a demand before measurement.

Since the experiment is carried out on a press owned by an extrusion company, modification to the tool stack is limited. Therefore, the application of the second idea is difficult in this case. Finally, a new approach is deduced from the first idea and followed by applying a laser beam on a reflecting surface. A reflecting surface is mounted on the die face. The experiment is carried out successfully in two rounds which guarantee its repeatability. The experimental results of the first round are compared with finite element simulations where a decoupled analysis is applied. The finite element simulations are performed by the in-house implicit FE-program DiekA.

Experiment setup

The measurement is done on the deformation of a flat die used in producing a single U shape profile shown in Fig. 1. To avoid interrupting the beam during the experiment, the saw and the stretcher are switched off. The die, backer and ring are mounted together as shown in Fig. 2. Fig.3 illustrates the experiment setup, where a laser beam is emitted from a laser source towards a reflecting surface which reflects the beam on a white screen. The laser source is placed out side the run-out table and far from the press because it works at room temperature.

Fig.1: profile (Dimensions in mm) Fig.2: tool (Dimensions in mm)

Fig.3: experiment setup

Fig.4: production of the stainless steel flat mirror


Reflecting surface. A stainless steel flat mirror is attached to the tongue of the die as shown in Fig. 6. Stainless steel is chosen as a reflecting material, because it withstands high temperature and preserves its reflectivity during the experiment. An inclined reflecting surface is designed because the laser source must be placed outside the run-out table. Its angle is determined from the position of the laser source, position of the screen and opening in the pressure ring. The small size and the angle of the reflecting surface are the main obstacles in the polishing stage during its production. Finally, after several trials it was produced in the following manner as shown in Fig. 4: (1) embedding a stainless steel piece in "Bakelite", (2) polishing, (3) cutting the mirror from the middle of the piece by eroding in order to get the best flatness.

Laser source. The laser source is chosen such that the diameter of the spot is less than the length of the side of the reflecting surface. Therefore, a laser source is selected with the following specifications:

1. Green dot laser with 532nm wavelength 2. Output power: 20mW. 3. Divergence: 0.1mrad. 4. Dot diameter varies between 0.4mm and 3mm.

Backer. A new backer displayed in Fig. 5 is produced to accommodate the incident beam, reflected beam and the stainless steel mirror.

Fig.5: front and section view of the backer [mm] Fig.6: fixation of the mirror

Screen. The reflected beam is projected on a screen. The screen has a white background with four reference points. The reference points are used in calculating the movement of the reflected spot through a bilinear transformation.

Billets. Billets with 92mm diameter and 360mm length are extruded. Their material is AA6060

with 0.40% Si and 0.45% Mg.

Experiment procedure

The following points summarize the procedure of the experiment: 1. Fix the mirror on the die with two M3 bolts as shown in Fig. 6. 2. Assemble the tool parts such as die, backer, and ring. 3. Put the tool in the oven and heat it up to 460C˚. 4. Place the laser source and screen. 5. Two cameras are placed in two different positions. Camera “A” is positioned in front of the

control panel, and camera “B” in front of the screen. 6. As soon as the temperature of the tool reaches the desired one, it is removed from the oven

and placed in the press. 7. Turn on the laser source, aim it at the mirror and adjust the position of the screen until the

reflected spot can be seen on it. 8. Turn on the two video cameras and start pressing 9. The locations of the laser source and screen are measured.

Reflecting surface. A stainless steel flat mirror is attached to the tongue of the die as shown in Fig. 6. Stainless steel is chosen as a reflecting material, because it withstands high temperature and preserves its reflectivity during the experiment. An inclined reflecting surface is designed because the laser source must be placed outside the run-out table. Its angle is determined from the position of the laser source, position of the screen and opening in the pressure ring. The small size and the angle of the reflecting surface are the main obstacles in the polishing stage during its production. Finally, after several trials it was produced in the following manner as shown in Fig. 4: (1) embedding a stainless steel piece in "Bakelite", (2) polishing, (3) cutting the mirror from the middle of the piece by eroding in order to get the best flatness.

Laser source. The laser source is chosen such that the diameter of the spot is less than the length of the side of the reflecting surface. Therefore, a laser source is selected with the following specifications:

1. Green dot laser with 532nm wavelength 2. Output power: 20mW. 3. Divergence: 0.1mrad. 4. Dot diameter varies between 0.4mm and 3mm.

Backer. A new backer displayed in Fig. 5 is produced to accommodate the incident beam, reflected beam and the stainless steel mirror.

Fig.5: front and section view of the backer [mm] Fig.6: fixation of the mirror

Screen. The reflected beam is projected on a screen. The screen has a white background with four reference points. The reference points are used in calculating the movement of the reflected spot through a bilinear transformation.

Billets. Billets with 92mm diameter and 360mm length are extruded. Their material is AA6060

with 0.40% Si and 0.45% Mg.

Experiment procedure

The following points summarize the procedure of the experiment: 1. Fix the mirror on the die with two M3 bolts as shown in Fig. 6. 2. Assemble the tool parts such as die, backer, and ring. 3. Put the tool in the oven and heat it up to 460C˚. 4. Place the laser source and screen. 5. Two cameras are placed in two different positions. Camera “A” is positioned in front of the

control panel, and camera “B” in front of the screen. 6. As soon as the temperature of the tool reaches the desired one, it is removed from the oven

and placed in the press. 7. Turn on the laser source, aim it at the mirror and adjust the position of the screen until the

reflected spot can be seen on it. 8. Turn on the two video cameras and start pressing 9. The locations of the laser source and screen are measured.



The two movies are analyzed and the data are extracted for the first four billets. The ram speed, seal pressure and main cylinder pressure are taken out from movie “A”. The seal pressure gives the information about locking up the container to the tool. The cylinder pressure is the pressure applied on the ram to extrude the billet. The cylinder pressure and the seal pressure are plotted in Fig.7. After loading the billet in the container, the seal pressure is increased to 210 bars in order to lock up the container to the tool, and then the cylinder pressure is increased to 50 bars in order to compress the billet until it fills the container which is 95mm diameter. Then the cylinder pressure is decreased to zero and the container is moved backward to allow the hot gas to escape from the container. This procedure is known as "Burp". Soon afterward the container is closed again and cylinder pressure is increased to 120 bars and extruding the current billet is started. During extrusion the cylinder pressure decreases slightly exponentially due to friction between the billet and the container as described in [6]. After extruding the current billet, the container is moved backward and part of the oil from the hydraulic circuit is passed to shear off the butt end. As shown in Fig 7, the profile of the cylinder pressure during the extrusion of the first billet is different from that of the successor billets because part of the first billet fills the die and the baffle. The extrusion force is calculated from the cylinder pressure and the diameter of the cylinder and displayed in Fig.8. The extrusion force profiles for the third and fourth billets are higher than that of the second billet because of cooling down. The ram speed with a nominal value of 5.3mm/sec is exhibited in Fig.9. The extruded billet length is calculated by integrating the ram speed in time. Table 1 shows that 20% of the first billet is lost in filling the die and the baffle.

Billet 1 2 3 4 Extruded length [mm] 250 310 310 310

Table 1: Extruded billet length

Fig.7: pressure versus time

Fig.8: extrusion force versus time Fig.9: ram speed versus time

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350 400 450 500 550 600

Delta t [sec]

Ram

spe

ed [m

m/s

ec]

Ram speed

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400 450 500 550 600

Delta t [sec]

Pre

ssur

e [b

ar]

Cylinder pressure

Seal pressure

0

50

100

150

200

250

300

300 350 400

Delta t [sec]

Pre

ssur

e [b

ar]

Cylinder pressure

Seal pressure

extruding 2nd billet

cutting butt endburp

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250 300 350 400 450 500 550 600

Delta t [sec]

Ext

rusi

on fo

rce

[M#

]

Extrusion force


The two movies are analyzed and the data are extracted for the first four billets. The ram speed, seal pressure and main cylinder pressure are taken out from movie “A”. The seal pressure gives the information about locking up the container to the tool. The cylinder pressure is the pressure applied on the ram to extrude the billet. The cylinder pressure and the seal pressure are plotted in Fig.7. After loading the billet in the container, the seal pressure is increased to 210 bars in order to lock up the container to the tool, and then the cylinder pressure is increased to 50 bars in order to compress the billet until it fills the container which is 95mm diameter. Then the cylinder pressure is decreased to zero and the container is moved backward to allow the hot gas to escape from the container. This procedure is known as "Burp". Soon afterward the container is closed again and cylinder pressure is increased to 120 bars and extruding the current billet is started. During extrusion the cylinder pressure decreases slightly exponentially due to friction between the billet and the container as described in [6]. After extruding the current billet, the container is moved backward and part of the oil from the hydraulic circuit is passed to shear off the butt end. As shown in Fig 7, the profile of the cylinder pressure during the extrusion of the first billet is different from that of the successor billets because part of the first billet fills the die and the baffle. The extrusion force is calculated from the cylinder pressure and the diameter of the cylinder and displayed in Fig.8. The extrusion force profiles for the third and fourth billets are higher than that of the second billet because of cooling down. The ram speed with a nominal value of 5.3mm/sec is exhibited in Fig.9. The extruded billet length is calculated by integrating the ram speed in time. Table 1 shows that 20% of the first billet is lost in filling the die and the baffle.

Billet 1 2 3 4 Extruded length [mm] 250 310 310 310

Table 1: Extruded billet length

Fig.7: pressure versus time

Fig.8: extrusion force versus time Fig.9: ram speed versus time

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350 400 450 500 550 600

Delta t [sec]

Ram

spe

ed [m

m/s

ec]

Ram speed

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400 450 500 550 600

Delta t [sec]

Pre

ssur

e [b

ar]

Cylinder pressure

Seal pressure

0

50

100

150

200

250

300

300 350 400

Delta t [sec]

Pre

ssur

e [b

ar]

Cylinder pressure

Seal pressure

extruding 2nd billet

cutting butt endburp

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250 300 350 400 450 500 550 600

Delta t [sec]

Ext

rusi

on fo

rce

[M#

]

Extrusion force


The movement of the reflected spot is determined from movie “B”. A program is implemented using image processing toolbox in order to read movie “B” and to calculate the position of the spot during the extrusion process. Moreover, the angular deflection of the tongue is determined from Fig.10 and equations 1 and 2.

Fig.10: sketch for calculating the angular deflection of the tongue

(1)

(2)

Where θ = angular displacement of the reflected beam, θM = angular deflection of the tongue, d= total displacement of the spot in mm, L = 3376 mm, D1= 810 mm, α= 12 degrees.

The angular deflection of the tongue is displayed in Fig.11 which shows that it is increasing during the extrusion because the binding force (Fb) shown in Fig.12 between the container and the tool decreases with decreasing the friction force between the container and the billet as depicted in [1]. The angular deflection of the tongue reaches a value of 8 mrad and 7 mrad at the end of the extrusion of the first and the successor billets respectively. The flexibility of the die during the extrusion of the first billet leads to higher angular deflection of the tongue. After the first and second rounds of the experiment, the die is checked and 0.03 mm deviation in the bearing is detected. This amount is equivalent to 0.6mrad angular deflection of the tongue. The reason of this amount of plastic deformation has not been clarified yet. It may be a production defect or occur during the extrusion of the first billet. Finally a rigid body motion of the tool is detected during shearing off the butt end because it is free.

Fig.11: tongue angular deflection versus time Fig.12: loads on the tool

#umerical analysis

The decoupled analysis [7] is applied where the billet and the tool are studied separately. First, a 3D isothermal numerical simulation for the billet is performed by applying an Eulerian formulation to over come the problem of large deformation. In fact, a transient calculation which consumes large calculation times is required to evaluate the extrusion pressure at the corresponding ram position. Therefore, a steady state solution of the problem is computed at a specified ram position for avoiding large calculation time. For example in the current simulation, the ram position is defined at

-2

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350 400 450 500 550 600

Delta t [sec]

Ang

ular

def

lect

ion

[mra

d]

Angular deflection about x

The movement of the reflected spot is determined from movie “B”. A program is implemented using image processing toolbox in order to read movie “B” and to calculate the position of the spot during the extrusion process. Moreover, the angular deflection of the tongue is determined from Fig.10 and equations 1 and 2.

Fig.10: sketch for calculating the angular deflection of the tongue

(1)

(2)

Where θ = angular displacement of the reflected beam, θM = angular deflection of the tongue, d= total displacement of the spot in mm, L = 3376 mm, D1= 810 mm, α= 12 degrees.

The angular deflection of the tongue is displayed in Fig.11 which shows that it is increasing during the extrusion because the binding force (Fb) shown in Fig.12 between the container and the tool decreases with decreasing the friction force between the container and the billet as depicted in [1]. The angular deflection of the tongue reaches a value of 8 mrad and 7 mrad at the end of the extrusion of the first and the successor billets respectively. The flexibility of the die during the extrusion of the first billet leads to higher angular deflection of the tongue. After the first and second rounds of the experiment, the die is checked and 0.03 mm deviation in the bearing is detected. This amount is equivalent to 0.6mrad angular deflection of the tongue. The reason of this amount of plastic deformation has not been clarified yet. It may be a production defect or occur during the extrusion of the first billet. Finally a rigid body motion of the tool is detected during shearing off the butt end because it is free.

Fig.11: tongue angular deflection versus time Fig.12: loads on the tool

#umerical analysis

The decoupled analysis [7] is applied where the billet and the tool are studied separately. First, a 3D isothermal numerical simulation for the billet is performed by applying an Eulerian formulation to over come the problem of large deformation. In fact, a transient calculation which consumes large calculation times is required to evaluate the extrusion pressure at the corresponding ram position. Therefore, a steady state solution of the problem is computed at a specified ram position for avoiding large calculation time. For example in the current simulation, the ram position is defined at

-2

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350 400 450 500 550 600

Delta t [sec]

Ang

ular

def

lect

ion

[mra

d]

Angular deflection about x


the end of its stroke which corresponds to 50 mm of the billet’s analyzed length. This length is obtained by the summation of the baffle’s length and the butt end length. Moreover, the temperature of the analyzed billet is set similar to the temperature of the extrudate which is about 520 Cº. In addition, a rigid die is assumed where the influence of the die deformation on the material flow is neglected. As soon as the analysis reaches the steady state, the reaction forces in the contact zone between die and billet are calculated and transferred to the die face. Next a 3D isothermal numerical simulation for the tool including die, backer and bolster is performed by applying Updated Lagrangian formulation.

Material models. The behaviour of aluminum alloy (AA6060) is described by von Mises viscoplastic material model. The relation between the flow stress and the equivalent viscoplastic strain rate is described by Sellars-Tegart law in Eq.3 [6]. Since the material constants for (AA6060) are not available and the amounts of Mg and Si in the alloy are in the range of that in (AA6063). Then material constants for (AA6063) listed in Table 2 [8] are used. The tool material (AISIH-13 steel) is described by elasto-plastic material model in which Voce hardening is used to describe the plastic behavior. The material properties at temperatures of 460 Cº are listed in Table 3 [9].

(3)

N Q [J/mol] A[s-1] R[J/K.mol] α[MPa-1] T[K] 5.4 140000 6.0E09 8.314 0.04 793 Table 2: Constants used in Sellars-Tegart law

Young’s Modulus [N/mm2] Yield Stress [N/mm2] Poisson’s ratio

1.75E05 850 0.29 Table 3: Material properties of the tool steel at 460 Cº Boundary conditions. Since the numerical model has a large number of degrees of freedom, then the usage of contact boundary conditions increases its complexity. Therefore, the contact boundary conditions must be simplified to fully slip, stick or connecting degrees of freedom between the parts. Moreover, a special attention must be given in applying the right boundary conditions on the right surface; otherwise the model will be too stiff or too flexible. Concerning the billet, the following boundary conditions are applied as shown in Fig.13:

(1) Stick at cylinder-billet contact zone and die-billet contact zone (2) Prescribed velocity of 5.3 mm/sec at the inflow. (3) Free in the extrusion direction at the outflow. (4) A constraint equation is determined at each corner node between its displacement

components in order to satisfy the material conservation condition [10].

Concerning the tool, the following boundary conditions are applied as shown in Fig.14:

Fig.13: billet’s boundaries Fig.14: tool’s boundaries

the end of its stroke which corresponds to 50 mm of the billet’s analyzed length. This length is obtained by the summation of the baffle’s length and the butt end length. Moreover, the temperature of the analyzed billet is set similar to the temperature of the extrudate which is about 520 Cº. In addition, a rigid die is assumed where the influence of the die deformation on the material flow is neglected. As soon as the analysis reaches the steady state, the reaction forces in the contact zone between die and billet are calculated and transferred to the die face. Next a 3D isothermal numerical simulation for the tool including die, backer and bolster is performed by applying Updated Lagrangian formulation.

Material models. The behaviour of aluminum alloy (AA6060) is described by von Mises viscoplastic material model. The relation between the flow stress and the equivalent viscoplastic strain rate is described by Sellars-Tegart law in Eq.3 [6]. Since the material constants for (AA6060) are not available and the amounts of Mg and Si in the alloy are in the range of that in (AA6063). Then material constants for (AA6063) listed in Table 2 [8] are used. The tool material (AISIH-13 steel) is described by elasto-plastic material model in which Voce hardening is used to describe the plastic behavior. The material properties at temperatures of 460 Cº are listed in Table 3 [9].

(3)

N Q [J/mol] A[s-1] R[J/K.mol] α[MPa-1] T[K] 5.4 140000 6.0E09 8.314 0.04 793 Table 2: Constants used in Sellars-Tegart law

Young’s Modulus [N/mm2] Yield Stress [N/mm2] Poisson’s ratio

1.75E05 850 0.29 Table 3: Material properties of the tool steel at 460 Cº Boundary conditions. Since the numerical model has a large number of degrees of freedom, then the usage of contact boundary conditions increases its complexity. Therefore, the contact boundary conditions must be simplified to fully slip, stick or connecting degrees of freedom between the parts. Moreover, a special attention must be given in applying the right boundary conditions on the right surface; otherwise the model will be too stiff or too flexible. Concerning the billet, the following boundary conditions are applied as shown in Fig.13:

(1) Stick at cylinder-billet contact zone and die-billet contact zone (2) Prescribed velocity of 5.3 mm/sec at the inflow. (3) Free in the extrusion direction at the outflow. (4) A constraint equation is determined at each corner node between its displacement

components in order to satisfy the material conservation condition [10].

Concerning the tool, the following boundary conditions are applied as shown in Fig.14:

Fig.13: billet’s boundaries Fig.14: tool’s boundaries


(1) Suppress the downstream end of the bolster in the extrusion direction. (2) The influence of the ring on the die deformation is neglected. (3) Forces are applied at the nodes belonging to die-billet contact zone. (4) The degrees of freedom of the contact nodes in the tool parts are connected in the

following manner: nodes in the Bolster-Backer contact zone are connected in extrusion direction only, nodes in the Backer-Die contact zone are connected in three possibilities: in extrusion direction only, in all directions and in all directions except the tongue in the extrusion direction. Finally, the results from the three possibilities are compared.

Finite element models. The billet and the tool are discretized by a 10 node tetrahedron element. Each node has three translational degrees of freedom. They are discretized simultaneously to produce node-to-node contact. But the important point is the choice of how many elements per profile thickness to give sufficient results. Three meshes are checked with 2, 3 and 4 elements per profile thickness. Moreover, the use of more elements is limited with the solver or the computer capacity.

#umerical results. The angular deflection of the tongue of the mesh with 2 elements per profile thickness with three connection possibilities is summarized in table 4. In comparison with the experimental results, it is deduced that the last connection possibility is the most realistic one. In addition, Fig.15 confirms that only slip will occur between the die and the backer at the tongue. Regarding the three meshes, the results summarized in table 5 shows that three elements per profile thickness are sufficient to give accurate results. The three meshes are compared in number of degrees of freedom and not in calculation time because different solvers, direct and iterative are applied in these simulations. Finally, the deflection of the tool in the extrusion direction is exhibited in Fig.16. The relative linear displacement between points A and B in the extrusion direction is about 0.4 mm where the bearing length is 3mm. Table 4: angular deflection of the tongue of the three connection possibilities

Connection possibility of D.o.F Angular deflection of tongue [mrad] In extrusion direction 10 In all directions 5.25 In all directions except tongue in extrusion direction 7

Table 5: number of degrees of freedom, extrusion force and angular deflection of the tongue for the finite element models

Elements per thickness

Number of D.o.F Extrusion force [MN] Angular deflection of tongue [mrad]

Two elements 40131 1.03 7 Three elements 104031 0.96 6.0 Four elements 175914 0.96 6.0

Fig.15: back side of the die Fig.16: deflection of the tool in the extrusion direction [mm]

A

B

(1) Suppress the downstream end of the bolster in the extrusion direction. (2) The influence of the ring on the die deformation is neglected. (3) Forces are applied at the nodes belonging to die-billet contact zone. (4) The degrees of freedom of the contact nodes in the tool parts are connected in the

following manner: nodes in the Bolster-Backer contact zone are connected in extrusion direction only, nodes in the Backer-Die contact zone are connected in three possibilities: in extrusion direction only, in all directions and in all directions except the tongue in the extrusion direction. Finally, the results from the three possibilities are compared.

Finite element models. The billet and the tool are discretized by a 10 node tetrahedron element. Each node has three translational degrees of freedom. They are discretized simultaneously to produce node-to-node contact. But the important point is the choice of how many elements per profile thickness to give sufficient results. Three meshes are checked with 2, 3 and 4 elements per profile thickness. Moreover, the use of more elements is limited with the solver or the computer capacity.

#umerical results. The angular deflection of the tongue of the mesh with 2 elements per profile thickness with three connection possibilities is summarized in table 4. In comparison with the experimental results, it is deduced that the last connection possibility is the most realistic one. In addition, Fig.15 confirms that only slip will occur between the die and the backer at the tongue. Regarding the three meshes, the results summarized in table 5 shows that three elements per profile thickness are sufficient to give accurate results. The three meshes are compared in number of degrees of freedom and not in calculation time because different solvers, direct and iterative are applied in these simulations. Finally, the deflection of the tool in the extrusion direction is exhibited in Fig.16. The relative linear displacement between points A and B in the extrusion direction is about 0.4 mm where the bearing length is 3mm. Table 4: angular deflection of the tongue of the three connection possibilities

Connection possibility of D.o.F Angular deflection of tongue [mrad] In extrusion direction 10 In all directions 5.25 In all directions except tongue in extrusion direction 7

Table 5: number of degrees of freedom, extrusion force and angular deflection of the tongue for the finite element models

Elements per thickness

Number of D.o.F Extrusion force [MN] Angular deflection of tongue [mrad]

Two elements 40131 1.03 7 Three elements 104031 0.96 6.0 Four elements 175914 0.96 6.0

Fig.15: back side of the die Fig.16: deflection of the tool in the extrusion direction [mm]

A

B


Conclusion

Finally, it is concluded that the cheap and simple experiment succeeded in measuring the deformation of a flat die. It emphasizes that the die deforms elastically during the extrusion of the successors of the first billet while the origin of the plastic deformation that is found has not been yet clarified because the die is not tested directly after production. Concerning the numerical analysis, underestimated extrusion force and the angular deflection of the tongue are found in the comparison with the experimental results. The reason of the difference comes from the assumptions of aluminum material constants and isothermal analysis.

Acknowledgement

This research was carried out under project number MC4.05221A in the framework of the Material innovation institute research program in the Netherlands.

References

[1] T. Mori, N. Takatsuji, K.Matsuki, T.Aida, K.Murotani, K.Uetoko: Measurement of pressure distribution on die surface and deformation of extrusion die in hot extrusion of 1050 aluminum rod, Journal of Materials Processing Technology (2002), p421-425.

[2] B. Bourqui, A. Huber, C.Moulin, A.Brunetti, Y.Krähenbühl: Improved weld seam quality using 3D FEM simulation in correlation with practice (The First EAA Extruders Division Congress, Brescia 2002).

[3] P.T.Moe, S.Støren: A techniques for measuring pressure on the die face during extrusion ( Esaform, Kraków, 2002).

[4] M.Lefstad, P.T.Moe, S.Støren, R.Flatval: Thin strip aluminum extrusion – pressure, temperature and deflection recordings of the extrusion die (Esaform, Kraków, 2002).

[5] P.T.Moe: Pressure and Strain Measurement During Hot Extrusion of Aluminum (2005), p106-112.

[6] T. Sheppard: Extrusion of Aluminum Alloys, Kluwer Academic Publishers (1999).

[7] W. Assaad, H.J.M. Geijselaers, J.Huétink: 3-D numerical simulation of direct aluminum extrusion and die deformation (Extrusion Technology, Orlando 2008).

[8] J.Lof: Developments in finite element simulations of aluminum extrusion (2000), p. 86

[9] H. Mooi: Finite element simulations of aluminum extrusion (1996), p. 127

[10] W. Assaad, H.J.M. Geijselaers, J.Huétink: Boundary conditions applied on bearing corner in direct aluminum extrusion (Esaform, Enschede 2009).

Conclusion

Finally, it is concluded that the cheap and simple experiment succeeded in measuring the deformation of a flat die. It emphasizes that the die deforms elastically during the extrusion of the successors of the first billet while the origin of the plastic deformation that is found has not been yet clarified because the die is not tested directly after production. Concerning the numerical analysis, underestimated extrusion force and the angular deflection of the tongue are found in the comparison with the experimental results. The reason of the difference comes from the assumptions of aluminum material constants and isothermal analysis.

Acknowledgement

This research was carried out under project number MC4.05221A in the framework of the Material innovation institute research program in the Netherlands.

References

[1] T. Mori, N. Takatsuji, K.Matsuki, T.Aida, K.Murotani, K.Uetoko: Measurement of pressure distribution on die surface and deformation of extrusion die in hot extrusion of 1050 aluminum rod, Journal of Materials Processing Technology (2002), p421-425.

[2] B. Bourqui, A. Huber, C.Moulin, A.Brunetti, Y.Krähenbühl: Improved weld seam quality using 3D FEM simulation in correlation with practice (The First EAA Extruders Division Congress, Brescia 2002).

[3] P.T.Moe, S.Støren: A techniques for measuring pressure on the die face during extrusion ( Esaform, Kraków, 2002).

[4] M.Lefstad, P.T.Moe, S.Støren, R.Flatval: Thin strip aluminum extrusion – pressure, temperature and deflection recordings of the extrusion die (Esaform, Kraków, 2002).

[5] P.T.Moe: Pressure and Strain Measurement During Hot Extrusion of Aluminum (2005), p106-112.

[6] T. Sheppard: Extrusion of Aluminum Alloys, Kluwer Academic Publishers (1999).

[7] W. Assaad, H.J.M. Geijselaers, J.Huétink: 3-D numerical simulation of direct aluminum extrusion and die deformation (Extrusion Technology, Orlando 2008).

[8] J.Lof: Developments in finite element simulations of aluminum extrusion (2000), p. 86

[9] H. Mooi: Finite element simulations of aluminum extrusion (1996), p. 127

[10] W. Assaad, H.J.M. Geijselaers, J.Huétink: Boundary conditions applied on bearing corner in direct aluminum extrusion (Esaform, Enschede 2009).


Creep-fatigue interaction in the AISI H11 tool steel

B. Reggiani 1,a, M. D’Ascenzo 2,b, L. Donati 1,c J. Zhou 2,d and L. Tomesani 1,e

1University of Bologna, DIEM Department, Viale Risorgimento 2, 40136 Bologna, Italy 2Delft University of Technology, Department of Materials Science and Engineering,

Mekelweg 2, 2628 CD Delft, The Netherlands

a [email protected], b [email protected], c [email protected], [email protected], e [email protected]

Keywords: Creep-fatigue interaction; AISI H11 tool steel; Extrusion die; Tool lifetime Abstract. The effect of process parameters on the creep-fatigue behavior of a hot-work tool steel for aluminum extrusion die was investigated through a technological test in which the specimen geometry resembled the mandrel of a hollow extrusion die. Tests were performed on a Gleeble thermomechanical simulator by heating the specimen using joule’s effect and by applying cyclic loading up to 6.30 h or till specimen failure. Displacements during the tests at 380, 490, 540 and 580°C and under the average stresses of 400, 600 and 800 MPa were determined. A dwell time of 3 min was introduced during each of the tests to understand the creep behavior. The results showed that the test could indeed physically simulate the cyclic loading on the hollow die during extrusion and reveal all the mechanisms of creep-fatigue interaction.

Introduction

During aluminum extrusion, a severe and complex state of stress acts on the tool system, especially on the die. The load is produced by the ram forcing aluminum to flow through the die at a temperature in a range of 400°C – 580°C. Loading and unloading cycles correspond to repetitive ram strokes at a frequency of 1 to 5 billets every 10 min [1]. Depending on the batch size and die lifetime, up to hundred billets may be consecutively extruded, thus placing the die in the typical low-cycle fatigue regime. The amplitude of the mechanical load on the die is large, varying from zero to a peak value at the beginning of each ram stroke. When a thermal balance of the press is attained after a small number of ram strokes, the die temperature remains fairly stable [2]. Thus, for simplification purpose, the thermal oscillations of the die may be neglected. In addition, the total loading/unloading time for the whole batch and the temperature that the die is exposed to are high enough to consider the creep behavior of the die, particularly for hollow dies. In a hollow die, thin bridges supporting the mandrel, i.e. the part of the die defining the internal shape of the profile, are the most stressed and vulnerable in the die assembly, as these are exposed to the highest process temperature and stress. Hence, the combination of dynamic, heavy loading and high temperature sets a hostile working condition for the mandrel. Premature failure may occur after a certain number of loading/unloading cycles as a result of creep-fatigue interaction. Many investigations have been carried out to analyze the initiation and propagation of microcracks under creep-fatigue conditions [3-4]. In parallel to experimental investigations, numerical simulations through finite element (FE) calculations have been performed to predict the levels of stress and strain as well as the lifetime of the tools during the extrusion process. It has been acknowledged that the accuracy of the predicted results depends on the ability of the constitutive model to describe the complex thermomechanical behavior of the material. Therefore, the material model is of critical importance. A model suitable for the extrusion die should be capable of dealing with the material damage under creep-fatigue conditions.

Creep-fatigue interaction in the AISI H11 tool steel

B. Reggiani 1,a, M. D’Ascenzo 2,b, L. Donati 1,c J. Zhou 2,d and L. Tomesani 1,e

1University of Bologna, DIEM Department, Viale Risorgimento 2, 40136 Bologna, Italy 2Delft University of Technology, Department of Materials Science and Engineering,

Mekelweg 2, 2628 CD Delft, The Netherlands

a [email protected], b [email protected], c [email protected], [email protected], e [email protected]

Keywords: Creep-fatigue interaction; AISI H11 tool steel; Extrusion die; Tool lifetime Abstract. The effect of process parameters on the creep-fatigue behavior of a hot-work tool steel for aluminum extrusion die was investigated through a technological test in which the specimen geometry resembled the mandrel of a hollow extrusion die. Tests were performed on a Gleeble thermomechanical simulator by heating the specimen using joule’s effect and by applying cyclic loading up to 6.30 h or till specimen failure. Displacements during the tests at 380, 490, 540 and 580°C and under the average stresses of 400, 600 and 800 MPa were determined. A dwell time of 3 min was introduced during each of the tests to understand the creep behavior. The results showed that the test could indeed physically simulate the cyclic loading on the hollow die during extrusion and reveal all the mechanisms of creep-fatigue interaction.

Introduction

During aluminum extrusion, a severe and complex state of stress acts on the tool system, especially on the die. The load is produced by the ram forcing aluminum to flow through the die at a temperature in a range of 400°C – 580°C. Loading and unloading cycles correspond to repetitive ram strokes at a frequency of 1 to 5 billets every 10 min [1]. Depending on the batch size and die lifetime, up to hundred billets may be consecutively extruded, thus placing the die in the typical low-cycle fatigue regime. The amplitude of the mechanical load on the die is large, varying from zero to a peak value at the beginning of each ram stroke. When a thermal balance of the press is attained after a small number of ram strokes, the die temperature remains fairly stable [2]. Thus, for simplification purpose, the thermal oscillations of the die may be neglected. In addition, the total loading/unloading time for the whole batch and the temperature that the die is exposed to are high enough to consider the creep behavior of the die, particularly for hollow dies. In a hollow die, thin bridges supporting the mandrel, i.e. the part of the die defining the internal shape of the profile, are the most stressed and vulnerable in the die assembly, as these are exposed to the highest process temperature and stress. Hence, the combination of dynamic, heavy loading and high temperature sets a hostile working condition for the mandrel. Premature failure may occur after a certain number of loading/unloading cycles as a result of creep-fatigue interaction. Many investigations have been carried out to analyze the initiation and propagation of microcracks under creep-fatigue conditions [3-4]. In parallel to experimental investigations, numerical simulations through finite element (FE) calculations have been performed to predict the levels of stress and strain as well as the lifetime of the tools during the extrusion process. It has been acknowledged that the accuracy of the predicted results depends on the ability of the constitutive model to describe the complex thermomechanical behavior of the material. Therefore, the material model is of critical importance. A model suitable for the extrusion die should be capable of dealing with the material damage under creep-fatigue conditions.


The models available in the literature describing creep-fatigue interaction are formulated in terms of strain, energy or stress. The Manson-Coffin law [5] and the damage parameters proposed by Ostergren and Skelton [6-7] are the most common formulations based on strain and energy, respectively. However, the former has a range of applications limited to small variations of strain and to low temperatures where the creep damage is almost negligible [8]. Moreover, both approaches consider a linear damage accumulation and so does the Wöhler-Miner law formulated in terms of stress and assuming the damage evolution to be a linear function of the number of cycles. Such a condition is however poorly verifiable in experiments. A more comprehensive model based on the internal state variable has been developed by Chaboche et al. [8-9]. It belongs to the unified elasto-viscoplastic models which describe viscoplasticity without separation in time-dependent (creep) and time-independent effects. Despite its ability to describe most of the experimentally observed effects under monotonic or cyclic loadings correctly, the Chaboche model has enjoyed limited popularity, probably due to the perceived complexity of calibrating the material parameters. It is only partially available within the main commercial FE codes. The development of new technologies for aluminum extrusion aims at a minimum interference between the tool system and the material flow and thus at the optimization of the mechanical performance of the tool that is related both to tool design and tool material. It requires methods capable of fast analysis in order to verify the possible solutions found. The bridges of the mandrel represent the most critical region of the hollow extrusion die and these bridges are indispensible in the extrusion of hollow profiles. A technological test, which allows the analysis to be focused in this region, can help in finding solutions to the problems related to the hollow die and process optimization (e.g. the selection of tool material, the definition of an optimum fillet radius, the assessment of the time-displacement diagram of the mandrel, etc.). The test is desired to cover all the damage mechanisms that the bridges may encounter during aluminum extrusion. On the basis of the above considerations, a novel testing method for the evaluation of die material and process-related issues were developed. Purposely designed specimens with a shape close to that of the die bridges were tested using a thermomechanical simulator (Gleeble). An experimental campaign at different temperatures and under different loading conditions was undertaken, which allowed the analysis of the correlation of die deformation and lifetime with process parameters in the creep-fatigue regime. In the follow-up research, analytical models available in the literature to describe the material behavior in the creep-fatigue regime will be experimentally validated by using this testing method.

Material and Testing Method

The material of the specimens investigated in the present study was the hot-work tool steel AISI H11 (or DIN 1.2343, X37CrMoV5-1) with a tempered martensitic structure. Its chemical composition is presented in Table 1. The material was subjected to a four-step heat treatment, typical of that applied to aluminum extrusion dies. It consisted of austenitizing at 1000°C, quenching in a nitrogen atmosphere and double tempering, which led to a Rockwell hardness value of 46 HRC. The details of the heat treatment are given in Table 2. Table 1 Chemical composition of the AISI H11 steel used in the present study (in wt. %)

C Si Mn P S Al Cr Mo Ni Cu V

0.380 1.060 0.450 0.016 0.002 0.005 4.960 1.210 0.220 0.070 0.310

Table 2 Heat treatment applied to the AISI H11 steel

Austenitizing Quenching First tempering Second tempering

Time 30 min (nitrogen) 5 h 4.5 h

Temperature 1000° C 550° C 585° C

The models available in the literature describing creep-fatigue interaction are formulated in terms of strain, energy or stress. The Manson-Coffin law [5] and the damage parameters proposed by Ostergren and Skelton [6-7] are the most common formulations based on strain and energy, respectively. However, the former has a range of applications limited to small variations of strain and to low temperatures where the creep damage is almost negligible [8]. Moreover, both approaches consider a linear damage accumulation and so does the Wöhler-Miner law formulated in terms of stress and assuming the damage evolution to be a linear function of the number of cycles. Such a condition is however poorly verifiable in experiments. A more comprehensive model based on the internal state variable has been developed by Chaboche et al. [8-9]. It belongs to the unified elasto-viscoplastic models which describe viscoplasticity without separation in time-dependent (creep) and time-independent effects. Despite its ability to describe most of the experimentally observed effects under monotonic or cyclic loadings correctly, the Chaboche model has enjoyed limited popularity, probably due to the perceived complexity of calibrating the material parameters. It is only partially available within the main commercial FE codes. The development of new technologies for aluminum extrusion aims at a minimum interference between the tool system and the material flow and thus at the optimization of the mechanical performance of the tool that is related both to tool design and tool material. It requires methods capable of fast analysis in order to verify the possible solutions found. The bridges of the mandrel represent the most critical region of the hollow extrusion die and these bridges are indispensible in the extrusion of hollow profiles. A technological test, which allows the analysis to be focused in this region, can help in finding solutions to the problems related to the hollow die and process optimization (e.g. the selection of tool material, the definition of an optimum fillet radius, the assessment of the time-displacement diagram of the mandrel, etc.). The test is desired to cover all the damage mechanisms that the bridges may encounter during aluminum extrusion. On the basis of the above considerations, a novel testing method for the evaluation of die material and process-related issues were developed. Purposely designed specimens with a shape close to that of the die bridges were tested using a thermomechanical simulator (Gleeble). An experimental campaign at different temperatures and under different loading conditions was undertaken, which allowed the analysis of the correlation of die deformation and lifetime with process parameters in the creep-fatigue regime. In the follow-up research, analytical models available in the literature to describe the material behavior in the creep-fatigue regime will be experimentally validated by using this testing method.

Material and Testing Method

The material of the specimens investigated in the present study was the hot-work tool steel AISI H11 (or DIN 1.2343, X37CrMoV5-1) with a tempered martensitic structure. Its chemical composition is presented in Table 1. The material was subjected to a four-step heat treatment, typical of that applied to aluminum extrusion dies. It consisted of austenitizing at 1000°C, quenching in a nitrogen atmosphere and double tempering, which led to a Rockwell hardness value of 46 HRC. The details of the heat treatment are given in Table 2. Table 1 Chemical composition of the AISI H11 steel used in the present study (in wt. %)

C Si Mn P S Al Cr Mo Ni Cu V

0.380 1.060 0.450 0.016 0.002 0.005 4.960 1.210 0.220 0.070 0.310

Table 2 Heat treatment applied to the AISI H11 steel

Austenitizing Quenching First tempering Second tempering

Time 30 min (nitrogen) 5 h 4.5 h

Temperature 1000° C 550° C 585° C


Designed to replicate the geometry of the die mandrel on a smaller scale, the specimens contained a core support and two bridges (Fig. 1). This geometry included all the characteristic elements of a hollow die, including fillet radius, the height and width of the bridges.

Fig. 1: Geometry and dimensions of the specimen.

FE analysis of the tool-specimen contact and specimen deformation was performed to optimize the specimen geometry and dimensions and to select the load intensities in order to achieve specific average values of stress on the specimen legs (400, 600 and 800 MPa). Fig. 2 shows an average stress of 400 MPa at the specimen legs reached under a particular loading condition.

Fig. 2 (left) FE model of the tool-specimen contact and (right) Von Mises stress distribution in the specimen (400 MPa being the average value of the stress in the bridge of the specimen).

During the test, a fully compressive cyclic load was applied to the specimen mandrel and transferred to the bridges, resulting in mostly shear stresses. In order to replicate the loading conditions that occur to the die during the extrusion process, a dwell time (DT) of 3 min was included in the stress-controlled fatigue loops. The time-history of mechanical waveforms and thermal load is schematically shown in Fig. 3.

9 sec

3 min

(unload)

10 sec

2 KN

T°

Time

Load

600 sec 600 sec

Fig. 3: Mechanical waveforms and thermal load as a function of time.

Designed to replicate the geometry of the die mandrel on a smaller scale, the specimens contained a core support and two bridges (Fig. 1). This geometry included all the characteristic elements of a hollow die, including fillet radius, the height and width of the bridges.

Fig. 1: Geometry and dimensions of the specimen.

FE analysis of the tool-specimen contact and specimen deformation was performed to optimize the specimen geometry and dimensions and to select the load intensities in order to achieve specific average values of stress on the specimen legs (400, 600 and 800 MPa). Fig. 2 shows an average stress of 400 MPa at the specimen legs reached under a particular loading condition.

Fig. 2 (left) FE model of the tool-specimen contact and (right) Von Mises stress distribution in the specimen (400 MPa being the average value of the stress in the bridge of the specimen).

During the test, a fully compressive cyclic load was applied to the specimen mandrel and transferred to the bridges, resulting in mostly shear stresses. In order to replicate the loading conditions that occur to the die during the extrusion process, a dwell time (DT) of 3 min was included in the stress-controlled fatigue loops. The time-history of mechanical waveforms and thermal load is schematically shown in Fig. 3.

9 sec

3 min

(unload)

10 sec

2 KN

T°

Time

Load

600 sec 600 sec

Fig. 3: Mechanical waveforms and thermal load as a function of time.


The first 600 s were given to allow the specimen to reach the temperature set, while thermal expansion of the specimen occurred. A minimum compressive load of 2 kN was maintained during the test in order to keep the specimen on hold between the tools. The tools were made of the same steel as the specimen and had a hardness value of 55 HRC. Four temperatures (380, 490, 540 and 580 °C) and three levels of stress (400, 600 and 800 MPa which were the average values of the Von Mises stress at the bridge area of the specimen) were applied to cover the thermomechanical conditions that the mandrel of a hollow die may encounter in extrusion practice. A servo-hydraulic thermomechanical simulator, Gleeble-1500D, was used for the tests (Fig. 4). The specimen was heated using Joule’s effect, with a close-loop feedback signal enabling precise control of the heat input throughout the test. Two thermocouples were spot-welded on the surface of the specimen, one for regulating heating in order to maintain the preset temperature during the test and another for additional monitoring. The displacements of the anvils were registered throughout the test. All the tests were terminated after 6.30 h, corresponding to 106 loading cycles, unless the specimen broke prematurely. After unloading and cooling down to room temperature, the final height of the specimen was measured to obtain the data of its final permanent deformation.

Fig. 4: Specimen placed in the Gleeble 1500D thermomechanical simulator.

To ascertain the thermal stability of the specimen during the test and determine the temperature distribution, two additional tests were performed during which the temperatures at 15 points distributed all over the specimen surfaces were monitored. The thermophysical properties of the AISI H11 tool steel as a function of temperature are reported in [10]. Accurate determination of displacement during the test was considered very important. As the displacement transducer is located at the end of the loading system of the Gleeble machine, the measurement is the sum of various contributions including those from the specimen, the hydraulic loading system, anvils, etc. In order to quantify the yielding of the Gleeble system, a block of material, assumed to be rigid, was placed between the tools. The displacement under the static compressive loads corresponding to 400, 600 and 800 MPa in the bridges of the specimen was taken as that of the Gleeble system.


The insertion of one or two copper plates between the tool and specimen was found to be a workable solution to the stabilization of the specimen temperature during the test. Fig. 5c shows the temperature distribution at the 15 measurement points on the specimen (Fig. 5a). The evolutions of these temperatures over a period of time are presented in Fig. 5b which clearly shows the stability of the temperatures after 600 s. The differences in temperature between the two sides of the specimen at the mirror points (2-12, 1-11 and 3-13) were noticed. The maximum difference was 33°C between points 2 and 12. This was attributed mainly to the imperfect contact at the specimen-copper plates-tool interfaces. The temperature non-uniformity was thought to be acceptable, considering the accuracy of the thermocouple measurements (± 6°C).

specimen

tools

The first 600 s were given to allow the specimen to reach the temperature set, while thermal expansion of the specimen occurred. A minimum compressive load of 2 kN was maintained during the test in order to keep the specimen on hold between the tools. The tools were made of the same steel as the specimen and had a hardness value of 55 HRC. Four temperatures (380, 490, 540 and 580 °C) and three levels of stress (400, 600 and 800 MPa which were the average values of the Von Mises stress at the bridge area of the specimen) were applied to cover the thermomechanical conditions that the mandrel of a hollow die may encounter in extrusion practice. A servo-hydraulic thermomechanical simulator, Gleeble-1500D, was used for the tests (Fig. 4). The specimen was heated using Joule’s effect, with a close-loop feedback signal enabling precise control of the heat input throughout the test. Two thermocouples were spot-welded on the surface of the specimen, one for regulating heating in order to maintain the preset temperature during the test and another for additional monitoring. The displacements of the anvils were registered throughout the test. All the tests were terminated after 6.30 h, corresponding to 106 loading cycles, unless the specimen broke prematurely. After unloading and cooling down to room temperature, the final height of the specimen was measured to obtain the data of its final permanent deformation.

Fig. 4: Specimen placed in the Gleeble 1500D thermomechanical simulator.

To ascertain the thermal stability of the specimen during the test and determine the temperature distribution, two additional tests were performed during which the temperatures at 15 points distributed all over the specimen surfaces were monitored. The thermophysical properties of the AISI H11 tool steel as a function of temperature are reported in [10]. Accurate determination of displacement during the test was considered very important. As the displacement transducer is located at the end of the loading system of the Gleeble machine, the measurement is the sum of various contributions including those from the specimen, the hydraulic loading system, anvils, etc. In order to quantify the yielding of the Gleeble system, a block of material, assumed to be rigid, was placed between the tools. The displacement under the static compressive loads corresponding to 400, 600 and 800 MPa in the bridges of the specimen was taken as that of the Gleeble system.


The insertion of one or two copper plates between the tool and specimen was found to be a workable solution to the stabilization of the specimen temperature during the test. Fig. 5c shows the temperature distribution at the 15 measurement points on the specimen (Fig. 5a). The evolutions of these temperatures over a period of time are presented in Fig. 5b which clearly shows the stability of the temperatures after 600 s. The differences in temperature between the two sides of the specimen at the mirror points (2-12, 1-11 and 3-13) were noticed. The maximum difference was 33°C between points 2 and 12. This was attributed mainly to the imperfect contact at the specimen-copper plates-tool interfaces. The temperature non-uniformity was thought to be acceptable, considering the accuracy of the thermocouple measurements (± 6°C).

specimen

tools


(a)

(b)

(c)

Fig. 5 (a) Positions of the 15 measurement points on the specimen to check the temperature distribution, (b) evolution of the temperatures over time and (c) temperature distribution on the specimen at a set temperature of 380°C. Table 3 Experimental results obtained from the creep-fatigue tests at each of the temperatures and stresses (σAVM) in the form of the time (sec-x axis)-stroke (mm–y axis) diagram. In The diagrams have the same scale except those of the tests at (i) 490°C and 800 MPa, (ii) 540°C and 800 MPa, (iii) 580°C and 600 MPa and (iv) 580°C and 800 MPa.

T = 380°C T = 490°C T = 540°C T = 580°C

σAVM = 400

MPa

σAVM = 600

MPa

σAVM = 800

MPa

Stroke (mm)

Time (sec)

(a)

(b)

(c)

Fig. 5 (a) Positions of the 15 measurement points on the specimen to check the temperature distribution, (b) evolution of the temperatures over time and (c) temperature distribution on the specimen at a set temperature of 380°C. Table 3 Experimental results obtained from the creep-fatigue tests at each of the temperatures and stresses (σAVM) in the form of the time (sec-x axis)-stroke (mm–y axis) diagram. In The diagrams have the same scale except those of the tests at (i) 490°C and 800 MPa, (ii) 540°C and 800 MPa, (iii) 580°C and 600 MPa and (iv) 580°C and 800 MPa.

T = 380°C T = 490°C T = 540°C T = 580°C

σAVM = 400

MPa

σAVM = 600

MPa

σAVM = 800

MPa

Stroke (mm)

Time (sec)


In Table 3, the results of the creep-fatigue tests performed are shown in the form of the time-displacement diagram. The tests at 800 MPa and 540°C and those at 580°C were ended after 1.8 h and 0.5 h, respectively, due to the failure of the specimens. In Table 4, the values of the final permanent deformation of the specimens after 106 loading cycles and cooling, measured by means of a caliper, are reported. These measurements had an uncertainty of ±0.05 mm. Table 4 Final permanent deformation of the specimens after unloading and at room temperature

T= 380°C T= 490°C T= 540°C T= 580°C

400 MPa 0.01 0.01 0.06 0.13

600 MPa 0.04 0.02 0.11 fracture (83rd cycle)

800 MPa 0.06 0.34 Fracture (25th cycle) fracture(1st cycle) The yielding of the Gleeble system under the static compressive loads of 400, 600 and 800 MPa in the bridges of the specimen is reported in Table 5. It is indeed reasonable to assume a constant yielding of the system over the test duration, even when the deformation of the copper plates is taken into consideration. (Note the small thickness of the copper plates (0.5 mm) relative to the whole system.)

Table 5 Displacements due to the Gleeble system yielding (mm) 400 MPa 600 MPa 800 MPa

1 copper plate -0.370 -0.560 -0.705

2 copper plate -0.380 -0.570 -0.720

The displacements of the specimens at the first, tenth, sixtieth and hundredth cycle, after the effect of the Gleeble machine yielding has been accounted for, are reported in Table 6. The displacements during the dwell time (in the middle and at the end of the dwell time, i.e. 1.5DT and 3.0DT, respectively) are also reported in Table 6 to show the creep behaviour (Fig. 6). The displacement in the last row of Table 6 was registered at the last cycle (the 106th) with the load applied and at the corresponding temperature. Table 6 Displacement of the specimen due to deformation during the creep-fatigue tests 380°C 490°C 540°C 580°C cycle 400 600 800 400 600 800 400 600 800 400 600 800 1st (u1) -0.080 -0.125 -0.166 -0.063 -0.188 -0.283 -0.095 -0.136 -0.300 -0.105 -0.168 -0.407

1.5DT -0.082 -0.129 -0.180 -0.070 -0.205 -0.362 -0.109 -0.169 -0.483 -0.140 -0.263 -1.593

3.0DT -0.080 -0.125 -0.174 -0.067 -0.202 -0.374 -0.108 -0.170 -0.538 -0.146 -0.290 -2.894

10st -0.113 -0.156 -0.224 -0.094 -0.246 -0.480 -0.137 -0.211 -0.986 -0.205 -0.497

1.5DT -0.121 -0.170 -0.239 -0.104 -0.267 -0.508 -0.153 -0.232 -1.045 -0.223 -0.536

3.0DT -0.121 -0.170 -0.235 -0.103 -0.268 -0.507 -0.155 -0.232 -1.072 -0.226 -0.547

60st -0.256 -0.308 -0.407 -0.257 -0.437 -0.763 -0.301 -0.434 -0.434 -1.880

1.5DT -0.257 -0.310 -0.408 -0.258 -0.438 -0.767 -0.302 -0.437 -0.437 -1.899

3.0DT -0.259 -0.310 -0.409 -0.259 -0.439 -0.765 -0.302 -0.436 -0.435 -1.906

100st -0.292 -0.347 -0.459 -0.298 -0.483 -0.843 -0.338 -0.489 -0.482

1.5DT -0.291 -0.349 -0.461 -0.299 -0.486 -0.855 -0.343 -0.493 -0.492

3.0DT -0.288 -0.347 -0.458 -0.296 -0.482 -0.852 -0.339 -0.487 -0.489

Displacement* -0.291 -0.346 -0.459 -0.299 -0.480 -0.843 -0.336 -0.489 -0.483

% e** 0.702 0.737 0.977 0.786 0.973 1.868 0.805 1.179 2.575 1.260 5.793 8.290

* measured with the load applied and at the corresponding temperature ** deformation in percentage calculated as the ratio of (uf-u1) to the specimen height (30 mm)

In Table 3, the results of the creep-fatigue tests performed are shown in the form of the time-displacement diagram. The tests at 800 MPa and 540°C and those at 580°C were ended after 1.8 h and 0.5 h, respectively, due to the failure of the specimens. In Table 4, the values of the final permanent deformation of the specimens after 106 loading cycles and cooling, measured by means of a caliper, are reported. These measurements had an uncertainty of ±0.05 mm. Table 4 Final permanent deformation of the specimens after unloading and at room temperature

T= 380°C T= 490°C T= 540°C T= 580°C

400 MPa 0.01 0.01 0.06 0.13

600 MPa 0.04 0.02 0.11 fracture (83rd cycle)

800 MPa 0.06 0.34 Fracture (25th cycle) fracture(1st cycle) The yielding of the Gleeble system under the static compressive loads of 400, 600 and 800 MPa in the bridges of the specimen is reported in Table 5. It is indeed reasonable to assume a constant yielding of the system over the test duration, even when the deformation of the copper plates is taken into consideration. (Note the small thickness of the copper plates (0.5 mm) relative to the whole system.)

Table 5 Displacements due to the Gleeble system yielding (mm) 400 MPa 600 MPa 800 MPa

1 copper plate -0.370 -0.560 -0.705

2 copper plate -0.380 -0.570 -0.720

The displacements of the specimens at the first, tenth, sixtieth and hundredth cycle, after the effect of the Gleeble machine yielding has been accounted for, are reported in Table 6. The displacements during the dwell time (in the middle and at the end of the dwell time, i.e. 1.5DT and 3.0DT, respectively) are also reported in Table 6 to show the creep behaviour (Fig. 6). The displacement in the last row of Table 6 was registered at the last cycle (the 106th) with the load applied and at the corresponding temperature. Table 6 Displacement of the specimen due to deformation during the creep-fatigue tests 380°C 490°C 540°C 580°C cycle 400 600 800 400 600 800 400 600 800 400 600 800 1st (u1) -0.080 -0.125 -0.166 -0.063 -0.188 -0.283 -0.095 -0.136 -0.300 -0.105 -0.168 -0.407

1.5DT -0.082 -0.129 -0.180 -0.070 -0.205 -0.362 -0.109 -0.169 -0.483 -0.140 -0.263 -1.593

3.0DT -0.080 -0.125 -0.174 -0.067 -0.202 -0.374 -0.108 -0.170 -0.538 -0.146 -0.290 -2.894

10st -0.113 -0.156 -0.224 -0.094 -0.246 -0.480 -0.137 -0.211 -0.986 -0.205 -0.497

1.5DT -0.121 -0.170 -0.239 -0.104 -0.267 -0.508 -0.153 -0.232 -1.045 -0.223 -0.536

3.0DT -0.121 -0.170 -0.235 -0.103 -0.268 -0.507 -0.155 -0.232 -1.072 -0.226 -0.547

60st -0.256 -0.308 -0.407 -0.257 -0.437 -0.763 -0.301 -0.434 -0.434 -1.880

1.5DT -0.257 -0.310 -0.408 -0.258 -0.438 -0.767 -0.302 -0.437 -0.437 -1.899

3.0DT -0.259 -0.310 -0.409 -0.259 -0.439 -0.765 -0.302 -0.436 -0.435 -1.906

100st -0.292 -0.347 -0.459 -0.298 -0.483 -0.843 -0.338 -0.489 -0.482

1.5DT -0.291 -0.349 -0.461 -0.299 -0.486 -0.855 -0.343 -0.493 -0.492

3.0DT -0.288 -0.347 -0.458 -0.296 -0.482 -0.852 -0.339 -0.487 -0.489

Displacement* -0.291 -0.346 -0.459 -0.299 -0.480 -0.843 -0.336 -0.489 -0.483

% e** 0.702 0.737 0.977 0.786 0.973 1.868 0.805 1.179 2.575 1.260 5.793 8.290

* measured with the load applied and at the corresponding temperature ** deformation in percentage calculated as the ratio of (uf-u1) to the specimen height (30 mm)


1st cycle - 400MPa

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

1.0 1.5 2.0 2.5 3.0

dwell-time (minutes)

"creep

displac

emen

t" (mm)

380

490

540

580

10th cycle - 400MPa

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

1.0 1.5 2.0 2.5 3.0


"creep

displac

emen

t" (mm)

380

490

540

580

60th cycle - 400MPa

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

1.0 1.5 2.0 2.5 3.0


"creep

displac

emen

t" (mm)

380

490

540

580

100th cycle - 400MPa

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

1.0 1.5 2.0 2.5 3.0


"creep

displac

emen

t" (mm)

380

490

540

580

Fig. 6 Displacements occurring during the dwell-time with a stress of 400 MPa released, at the four temperatures and at (a) first, (b) tenth, (c) sixtieth and (d) hundredth cycle.

From Tables 3 and 6, a progressive increment of the displacement rate from the first to the last cycle was observed. The increment became greater as the level of stress increased (e.g. from 0.702 mm to 0.977 mm at 380°) and as the temperature rose (e.g. from 0.702 mm to 1.260 mm at 400 MPa). Velay, Bernhart et al. investigated the cyclic behavior of tempered martensitic hot-work tool steels with particular reference to the AISI H11 tool steel [10-12]. Cyclic softening of the material was observed, which could be divided into three stages: an initial strong softening followed by a slow steady softening that took the major part of the material life, and finally a drastic softening driven by crack propagation. In the present research, the first two stages of the cyclic softening were captured during almost all of the tests performed (Table 3) in which a change in the slope of the time-displacement history occurred. This behavior became more remarked at a higher level of stress and/or at a higher temperature (i.e., 800 MPa and 490°C, or 400 MPa and 580°C). Indeed, the rate of stress softening increased as the test temperature and stress intensity increased. The second and third stages of the cyclic softening were detected at the most critical test conditions of both parameters (600MPa/580°C, 800MPa/540°C, 800MPa/580°C) that lead to a premature failure of the specimens.

As can be seen in Fig. 6, the presence of a dwell-time of 3 min introduced a time-dependent effect on the specimen deformation. Such a time-dependent effect (material viscosity) produced an increased displacement, which could be explained by the additional inelastic strain, as described in [8]. Indeed, the viscoplastic strain had the time to develop, resulting in an enlarging hysteresis loop. The path of the displacement over the dwell time suggested that a primary as well as a secondary creep phase took place during this time. Moreover, the stabilization of the creep displacement during the dwell time from the first to the sixtieth cycle, as shown in Fig. 6, confirmed the presence of slow steady stage of the softening (Fig. 6c).

Summary

Previous research has shown that creep plays a fundamental role in resulting in deformation even during short cycles. Thus, hot-work steels used for extrusion tools should be evaluated with respect not only to their hot strength but also to their time-dependant creep strength. The latter is also of

1st cycle - 400MPa

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

1.0 1.5 2.0 2.5 3.0


"creep

displac

emen

t" (mm)

380

490

540

580

10th cycle - 400MPa

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

1.0 1.5 2.0 2.5 3.0


"creep

displac

emen

t" (mm)

380

490

540

580

60th cycle - 400MPa

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

1.0 1.5 2.0 2.5 3.0


"creep

displac

emen

t" (mm)

380

490

540

580

100th cycle - 400MPa

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

1.0 1.5 2.0 2.5 3.0


"creep

displac

emen

t" (mm)

380

490

540

580

Fig. 6 Displacements occurring during the dwell-time with a stress of 400 MPa released, at the four temperatures and at (a) first, (b) tenth, (c) sixtieth and (d) hundredth cycle.

From Tables 3 and 6, a progressive increment of the displacement rate from the first to the last cycle was observed. The increment became greater as the level of stress increased (e.g. from 0.702 mm to 0.977 mm at 380°) and as the temperature rose (e.g. from 0.702 mm to 1.260 mm at 400 MPa). Velay, Bernhart et al. investigated the cyclic behavior of tempered martensitic hot-work tool steels with particular reference to the AISI H11 tool steel [10-12]. Cyclic softening of the material was observed, which could be divided into three stages: an initial strong softening followed by a slow steady softening that took the major part of the material life, and finally a drastic softening driven by crack propagation. In the present research, the first two stages of the cyclic softening were captured during almost all of the tests performed (Table 3) in which a change in the slope of the time-displacement history occurred. This behavior became more remarked at a higher level of stress and/or at a higher temperature (i.e., 800 MPa and 490°C, or 400 MPa and 580°C). Indeed, the rate of stress softening increased as the test temperature and stress intensity increased. The second and third stages of the cyclic softening were detected at the most critical test conditions of both parameters (600MPa/580°C, 800MPa/540°C, 800MPa/580°C) that lead to a premature failure of the specimens.

As can be seen in Fig. 6, the presence of a dwell-time of 3 min introduced a time-dependent effect on the specimen deformation. Such a time-dependent effect (material viscosity) produced an increased displacement, which could be explained by the additional inelastic strain, as described in [8]. Indeed, the viscoplastic strain had the time to develop, resulting in an enlarging hysteresis loop. The path of the displacement over the dwell time suggested that a primary as well as a secondary creep phase took place during this time. Moreover, the stabilization of the creep displacement during the dwell time from the first to the sixtieth cycle, as shown in Fig. 6, confirmed the presence of slow steady stage of the softening (Fig. 6c).

Summary

Previous research has shown that creep plays a fundamental role in resulting in deformation even during short cycles. Thus, hot-work steels used for extrusion tools should be evaluated with respect not only to their hot strength but also to their time-dependant creep strength. The latter is also of


importance in the creep-fatigue interaction regime. With this in mind, the present research was performed to investigate the performance of a hot-work tool steel H11 under the normal working conditions as applied to hollow extrusion dies in industrial practice. The purposely designed specimens were tested under creep-fatigue loading, e.g. low-cycle fatigue with a dwell-time at different levels of stress and at different temperatures. The resulting evolution of the displacements indicated a mixed time- and cycle-dependant damage mechanism; at a high temperature, the cycling loading led to the softening of the material which was accelerated by the superimposed creep.

The results of the present research confirmed the capabilities of the testing method to evaluate the effects of both the design (stress) and process (temperature) parameters in extrusion on the deformation and lifetime of the mandrel in the hollow die. The geometry of the specimen designed on the basis of FE analysis allowed the dedicated analysis of the regions affected by creep and fatigue. This made the test a powerful tool for the die designer.

Acknowledgments

The authors would like to thank COMPES S.p.A. for providing the tool material and specimens and Mr. A.R. Eivani and Mr. J.M. Hofman for their assistance during the tests.

References

[1] L. Donati and L. Tomesani: J. Mat. Process. Technol., Vol. 164-165 (2005), p.1025.

[2] A. Assaad, H.J.M. Geijselaers and J. Huétink, in: Proc. of Int. Deep Drawing Research Group Conference (IDDRG 2008), Olofstrom, Sweden (2008).

[3] J. Granacher, T.S. Mao, K. Maile and R. Fisher: Mater. High. Temp. Vol. 15 (1998), p. 289.

[4] D.J. Michel and A.W. Thomson: Fatigue Vol. 87 (1987), 1057.

[5] L. Coffin, in: Fracture, Vol. 1, ICF4, Waterloo, Ontario, Canada (1977), p. 263.

[6] W. Ostergren: J. Test. Eval. Vol. 4 (1976), p. 327.

[7] R. Skelton: Mater. Sci. Technol. Vol. 7 (1981), p. 427.

[8] J. Lemaitre and J.L. Chaboche: Mechanics of Solid Materials (Cambridge University Press, Cambridge, U.K. 1990).

[9] J.L. Chaboche: Int. J. Plast. Vol. 5 (1989), p. 247.

[10] Z. Ahmer, V. Velay, G. Bernhart and F. Rezai-Aria: Int. J. Microstruct. Mater. Prop. Vol. 3 (2008), p. 326.

[11] Z. Zhang, D. Delagne and G. Bernhart: Int. J. Fatigue Vol. 24 (2002), p. 635.

[12] V. Velay, G. Bernhart, D. Delagnes and L. Penazzi: Fatigue Fract. Eng. Mater. Struct. Vol. 28 (2005), p. 1023.

importance in the creep-fatigue interaction regime. With this in mind, the present research was performed to investigate the performance of a hot-work tool steel H11 under the normal working conditions as applied to hollow extrusion dies in industrial practice. The purposely designed specimens were tested under creep-fatigue loading, e.g. low-cycle fatigue with a dwell-time at different levels of stress and at different temperatures. The resulting evolution of the displacements indicated a mixed time- and cycle-dependant damage mechanism; at a high temperature, the cycling loading led to the softening of the material which was accelerated by the superimposed creep.

The results of the present research confirmed the capabilities of the testing method to evaluate the effects of both the design (stress) and process (temperature) parameters in extrusion on the deformation and lifetime of the mandrel in the hollow die. The geometry of the specimen designed on the basis of FE analysis allowed the dedicated analysis of the regions affected by creep and fatigue. This made the test a powerful tool for the die designer.

Acknowledgments

The authors would like to thank COMPES S.p.A. for providing the tool material and specimens and Mr. A.R. Eivani and Mr. J.M. Hofman for their assistance during the tests.

References

[1] L. Donati and L. Tomesani: J. Mat. Process. Technol., Vol. 164-165 (2005), p.1025.

[2] A. Assaad, H.J.M. Geijselaers and J. Huétink, in: Proc. of Int. Deep Drawing Research Group Conference (IDDRG 2008), Olofstrom, Sweden (2008).

[3] J. Granacher, T.S. Mao, K. Maile and R. Fisher: Mater. High. Temp. Vol. 15 (1998), p. 289.

[4] D.J. Michel and A.W. Thomson: Fatigue Vol. 87 (1987), 1057.

[5] L. Coffin, in: Fracture, Vol. 1, ICF4, Waterloo, Ontario, Canada (1977), p. 263.

[6] W. Ostergren: J. Test. Eval. Vol. 4 (1976), p. 327.

[7] R. Skelton: Mater. Sci. Technol. Vol. 7 (1981), p. 427.

[8] J. Lemaitre and J.L. Chaboche: Mechanics of Solid Materials (Cambridge University Press, Cambridge, U.K. 1990).

[9] J.L. Chaboche: Int. J. Plast. Vol. 5 (1989), p. 247.

[10] Z. Ahmer, V. Velay, G. Bernhart and F. Rezai-Aria: Int. J. Microstruct. Mater. Prop. Vol. 3 (2008), p. 326.

[11] Z. Zhang, D. Delagne and G. Bernhart: Int. J. Fatigue Vol. 24 (2002), p. 635.

[12] V. Velay, G. Bernhart, D. Delagnes and L. Penazzi: Fatigue Fract. Eng. Mater. Struct. Vol. 28 (2005), p. 1023.


FEM-assisted design of a multi-hole pocket die to extrude U-shaped aluminum profiles with different wall thicknesses

G. Fang1, a, J. Zhou2, b, J. Duszczyk2, c 1 Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

2 Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands


Keywords: Aluminium; Extrusion; Die; FEM Abstract. Wide, thin-wall profiles exiting simultaneously from a multi-hole die during aluminum extrusion tend to have different velocities and deflect from the straight line. The pockets in front of the die orifices are often used to balance the metal flow and equalize the velocities. In practice, the effect of a pocket die design on metal flow becomes known, only after the die is manufactured and a trial extrusion run is completed. The present research was intended to demonstrate the feasibility of using FEM simulation to predict metal flow, thereby reducing or hopefully eliminating trial extrusion runs. The extrusion of U-shaped profiles with different wall thicknesses through a multi-hole pocket was taken as an example to show the scope of adjusting the die pocket to regulate metal flow. The effect of pocket shape on metal flow was evaluated. It is clear that 3D FEM simulation can indeed be effectively used to optimize die design, before the die design is finalized.

Introduction

Simple and complex U-shaped aluminum profiles are frequently used in the building and construction, automotive and aircraft industries. Compared to flat profiles, they are far more difficult to extrude, especially when the wall thicknesses are not the same. During the extrusion of a U-shaped aluminum profile, the metal far away from the die center and in the thinner walls tends to flow more slowly than the rest of the profile, possibly resulting in dimensions out of tolerances and geometrical irregularities such as waviness, twist, bending and even cracks. The main cause for the non-uniform metal flow is the friction at the billet/container and billet/die interfaces. Extrudate shape, extrudate dimensions (including wall thickness and circumscribing circle diameter relative to the container diameter), the number and position of die orifices, die layout, bearing length, bearing angle, bearing surface roughness, and extrusion parameters such as die temperature and billet temperature may all have influences on the flow uniformity.

A U-shaped aluminum profile may be extruded through a flat die. With such a die, the die bearing length and angle (choke or relief) can be used to balance the metal flow so that the profile emerging from the die can be made straight. In principle, the die designer can specify different bearing lengths along the radius and according to the section thickness. And modern numerically controlled machining facilities can realize the desired variations of bearing lengths and angles during die manufacturing. However, after trial extrusion runs, the correction of such a complexly shaped die is quite difficult. The high sensitivity of the die bearing to metal flow may make the correction efforts unsuccessful. To avoid this, a careful, iterative approach is taken, which requires a number of trial-correction cycles and leads to losses in material and production time.

In recent years, pocket dies have become popular to replace flat dies, mostly for the extrusion of complex solid profiles [1]. The main advantage of a pocket die, in comparison with a flat die with the same die orifice, is that it allows extrusion to run in a semi-continuous manner. In addition, the pocket may be used to spread the metal flow to allow the production of a wide profile using an extrusion press having a relatively small container. A further advantage is that the metal can pre-deform in the pocket and, through appropriate adjustment of pocket geometrical parameters, metal flow velocity at

FEM-assisted design of a multi-hole pocket die to extrude U-shaped aluminum profiles with different wall thicknesses

G. Fang1, a, J. Zhou2, b, J. Duszczyk2, c 1 Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

2 Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands


Keywords: Aluminium; Extrusion; Die; FEM Abstract. Wide, thin-wall profiles exiting simultaneously from a multi-hole die during aluminum extrusion tend to have different velocities and deflect from the straight line. The pockets in front of the die orifices are often used to balance the metal flow and equalize the velocities. In practice, the effect of a pocket die design on metal flow becomes known, only after the die is manufactured and a trial extrusion run is completed. The present research was intended to demonstrate the feasibility of using FEM simulation to predict metal flow, thereby reducing or hopefully eliminating trial extrusion runs. The extrusion of U-shaped profiles with different wall thicknesses through a multi-hole pocket was taken as an example to show the scope of adjusting the die pocket to regulate metal flow. The effect of pocket shape on metal flow was evaluated. It is clear that 3D FEM simulation can indeed be effectively used to optimize die design, before the die design is finalized.

Introduction

Simple and complex U-shaped aluminum profiles are frequently used in the building and construction, automotive and aircraft industries. Compared to flat profiles, they are far more difficult to extrude, especially when the wall thicknesses are not the same. During the extrusion of a U-shaped aluminum profile, the metal far away from the die center and in the thinner walls tends to flow more slowly than the rest of the profile, possibly resulting in dimensions out of tolerances and geometrical irregularities such as waviness, twist, bending and even cracks. The main cause for the non-uniform metal flow is the friction at the billet/container and billet/die interfaces. Extrudate shape, extrudate dimensions (including wall thickness and circumscribing circle diameter relative to the container diameter), the number and position of die orifices, die layout, bearing length, bearing angle, bearing surface roughness, and extrusion parameters such as die temperature and billet temperature may all have influences on the flow uniformity.

A U-shaped aluminum profile may be extruded through a flat die. With such a die, the die bearing length and angle (choke or relief) can be used to balance the metal flow so that the profile emerging from the die can be made straight. In principle, the die designer can specify different bearing lengths along the radius and according to the section thickness. And modern numerically controlled machining facilities can realize the desired variations of bearing lengths and angles during die manufacturing. However, after trial extrusion runs, the correction of such a complexly shaped die is quite difficult. The high sensitivity of the die bearing to metal flow may make the correction efforts unsuccessful. To avoid this, a careful, iterative approach is taken, which requires a number of trial-correction cycles and leads to losses in material and production time.

In recent years, pocket dies have become popular to replace flat dies, mostly for the extrusion of complex solid profiles [1]. The main advantage of a pocket die, in comparison with a flat die with the same die orifice, is that it allows extrusion to run in a semi-continuous manner. In addition, the pocket may be used to spread the metal flow to allow the production of a wide profile using an extrusion press having a relatively small container. A further advantage is that the metal can pre-deform in the pocket and, through appropriate adjustment of pocket geometrical parameters, metal flow velocity at


the die exit can be unified. In designing a pocket die, the designer first attempts to control the metal flow within the pocket and uses only a single, minimum bearing for the shaping of the extruded profile. He may adjust a number of geometric parameters, such as pocket width, depth, distance to the die centre and feed. The same as in the case of designing a flat die, the designer determines these geometric parameters for a new pocket die with a degree of uncertainty, because he has no capabilities of predicting metal flow through the pocket die of draft design. In the case of designing a die for a U-shaped profile, the stress acting on the tongue of the die may be so high that the die deflects or even factures. As a consequence, a scheduled production order will have to be terminated. Therefore, developing prediction capabilities are of great importance for the extrusion die designer to know the metal flow and the pressure acting on the die in advance before the die design is finalized.

There is a highly limited amount of information on the pocket design rules in the open literature. Rodriguez, et al. [2-4] introduced a pocket design procedure and a feed angle concept. Mason [5] proposed another method to determine the pocket shape and dimensions; the pocket was contoured in direct proportion to the bearing length. Ingraldi, et al. [6] compared the styles of pocket die design between the European and American designers; in the US, the die orifice was mostly centered in the pocket, while in Europe other solutions were sought, such as offsetting the position relative to the die orifice, thereby making the profile more squared and controlling the flatness of a long-sided profile more easily.

There have been few articles published on metal flow through commercial dies [7]. Clearly, to meet today’s demands of the aluminum extrusion industry for zero die trial, thin walls, tight tolerances, fast extrusion speed, reduced extrusion pressure and high productivity, a good understanding of the geometrical factors that control metal flow through a pocket die is necessary. Duplancic et al. [8] shared their knowledge and practical experience in designing pocket dies for wide thin-walled profiles, thick-walled profiles, profiles with different wall thicknesses and U-shaped profiles with equal wall thickness and showed the sensitivity of pocket geometrical parameters to the shapes and dimensions of these profiles. Li, et al. [9-10] made use of 2D computer simulation based on the finite element method (FEM) to indicate the effects of pocket angle and size on metal flow through two-hole dies to extrude bars under the isothermal conditions. It was found that pocket angle plays an important role in influencing metal flow velocity while pocket volume has much less effect on velocity. In the industrial practice, however, the vast majority of aluminum profiles have cross-section shapes far more complex than round bars. Moreover, the temperatures of the billet and extrusion tooling (die, container and stem) play a critical role in determining the product quality in terms of shape, dimensions, microstructure and mechanical properties. It is therefore be of great interest to apply the FEM simulation technology to extrusion under the conditions close to the industrial reality, i.e. with the temperature evolution of the workpiece and extrusion tooling incorporated into the FEM simulation of the extrusion process to produce complex profiles that the extrusion industry encounters on the daily basis.

The present study concerned the FEM simulation to extrude a typical aluminum alloy for extrusion (AA6063) through two-hole pocket dies to manufacture U-shaped thin-walled profiles with different wall thicknesses. It was a typical industrial case with a high degree of difficulty for the extrusion die designer. A flat die was designed for comparison purposes to show the flow non-uniformity. Then, three pocket dies were designed to evaluate the effect of pocket geometrical parameters on the velocity uniformity which determined the shape and dimensions of the extruded profiles.

Die designs and FEM simulation procedures

Fig. 1 shows the cross-section shape of the U-shaped profile used in the present research. The main wall (i.e. the long side) has a thickness of 1.5 mm, while the two side walls (the shorter sides) have a thickness of only 1 mm. As the side walls are farther away from the die center and thinner, the metal flow there will be retarded, if no measures are taken to regulate the metal flow.

the die exit can be unified. In designing a pocket die, the designer first attempts to control the metal flow within the pocket and uses only a single, minimum bearing for the shaping of the extruded profile. He may adjust a number of geometric parameters, such as pocket width, depth, distance to the die centre and feed. The same as in the case of designing a flat die, the designer determines these geometric parameters for a new pocket die with a degree of uncertainty, because he has no capabilities of predicting metal flow through the pocket die of draft design. In the case of designing a die for a U-shaped profile, the stress acting on the tongue of the die may be so high that the die deflects or even factures. As a consequence, a scheduled production order will have to be terminated. Therefore, developing prediction capabilities are of great importance for the extrusion die designer to know the metal flow and the pressure acting on the die in advance before the die design is finalized.

There is a highly limited amount of information on the pocket design rules in the open literature. Rodriguez, et al. [2-4] introduced a pocket design procedure and a feed angle concept. Mason [5] proposed another method to determine the pocket shape and dimensions; the pocket was contoured in direct proportion to the bearing length. Ingraldi, et al. [6] compared the styles of pocket die design between the European and American designers; in the US, the die orifice was mostly centered in the pocket, while in Europe other solutions were sought, such as offsetting the position relative to the die orifice, thereby making the profile more squared and controlling the flatness of a long-sided profile more easily.

There have been few articles published on metal flow through commercial dies [7]. Clearly, to meet today’s demands of the aluminum extrusion industry for zero die trial, thin walls, tight tolerances, fast extrusion speed, reduced extrusion pressure and high productivity, a good understanding of the geometrical factors that control metal flow through a pocket die is necessary. Duplancic et al. [8] shared their knowledge and practical experience in designing pocket dies for wide thin-walled profiles, thick-walled profiles, profiles with different wall thicknesses and U-shaped profiles with equal wall thickness and showed the sensitivity of pocket geometrical parameters to the shapes and dimensions of these profiles. Li, et al. [9-10] made use of 2D computer simulation based on the finite element method (FEM) to indicate the effects of pocket angle and size on metal flow through two-hole dies to extrude bars under the isothermal conditions. It was found that pocket angle plays an important role in influencing metal flow velocity while pocket volume has much less effect on velocity. In the industrial practice, however, the vast majority of aluminum profiles have cross-section shapes far more complex than round bars. Moreover, the temperatures of the billet and extrusion tooling (die, container and stem) play a critical role in determining the product quality in terms of shape, dimensions, microstructure and mechanical properties. It is therefore be of great interest to apply the FEM simulation technology to extrusion under the conditions close to the industrial reality, i.e. with the temperature evolution of the workpiece and extrusion tooling incorporated into the FEM simulation of the extrusion process to produce complex profiles that the extrusion industry encounters on the daily basis.

The present study concerned the FEM simulation to extrude a typical aluminum alloy for extrusion (AA6063) through two-hole pocket dies to manufacture U-shaped thin-walled profiles with different wall thicknesses. It was a typical industrial case with a high degree of difficulty for the extrusion die designer. A flat die was designed for comparison purposes to show the flow non-uniformity. Then, three pocket dies were designed to evaluate the effect of pocket geometrical parameters on the velocity uniformity which determined the shape and dimensions of the extruded profiles.

Die designs and FEM simulation procedures

Fig. 1 shows the cross-section shape of the U-shaped profile used in the present research. The main wall (i.e. the long side) has a thickness of 1.5 mm, while the two side walls (the shorter sides) have a thickness of only 1 mm. As the side walls are farther away from the die center and thinner, the metal flow there will be retarded, if no measures are taken to regulate the metal flow.


(a) (b)

Fig. 1 (a) Shape and dimensions of the U-shaped profile and (b) two-hole flat die layout. To increase the extrusion throughput, two die openings were placed in one die so that two

U-shaped profiles would flow out of the die simultaneously. Fig. 1 also shows the die layout; the two die holes are symmetrically placed around the die center. In the case of the two-hole die, the side walls are farther away from the die center in comparison with a single-hole dies with the die opening exactly in the die center. The ratio of the circumscribing circle diameter to the container diameter (50 mm, or the dash line in Fig. 1) is about 59.5%, which is below the commonly acknowledged limit of 80% [7]. It was expected that, because the side walls were quite close to the container liner and the two side walls were thinner than the main wall, the side walls would tend to flow more slowly. To demonstrate the natural flow non-uniformity, a flat die with a uniform bearing length was designed first. The flat die had a bearing length of 3 mm, the outlet behind the die bearing was 2 mm wider than the orifice, and the back taper angle was 30.

Fig. 2 shows the dimensions and shapes of three pocket dies. They were determined on the basis of the velocity distributions of the profiles exiting from the flat die. A larger pocket angle [11] was given to the part of the U-shaped profile that tended to flow more slowly than the rest of the profile, in order to speed up the metal flow there. Every pocket in front of the main wall of the die orifice had a 1 mm oversize on each side. The pockets in front of the side walls of the die orifice had different shapes and dimensions, as shown on Fig. 3. These designs of pockets were meant to accelerate the metal flow at the side walls.

(a) pocket die 1 (b) pocket die 2 (c) pocket die 3

Fig. 2: Pocket die shapes and dimensions (pocket depth 10 mm). (The thick lines represent the pocket outlines, while the thin lines represent the profile outlines.)

FEM simulations were performed using DEFORM 3D version 6.1 with a self-adapting remeshing

mechanism built-in to allow the simulation of extrusion involving intensive local deformation in front of the die. Considering the symmetry of the die layout (Fig. 1), one half of the billet model was built and the symmetrical boundary conditions were applied. The models of billet, die, container and stem were discretized into four-node tetrahedron elements for FEM calculation. Thermal effects of the

(a) (b)

Fig. 1 (a) Shape and dimensions of the U-shaped profile and (b) two-hole flat die layout. To increase the extrusion throughput, two die openings were placed in one die so that two

U-shaped profiles would flow out of the die simultaneously. Fig. 1 also shows the die layout; the two die holes are symmetrically placed around the die center. In the case of the two-hole die, the side walls are farther away from the die center in comparison with a single-hole dies with the die opening exactly in the die center. The ratio of the circumscribing circle diameter to the container diameter (50 mm, or the dash line in Fig. 1) is about 59.5%, which is below the commonly acknowledged limit of 80% [7]. It was expected that, because the side walls were quite close to the container liner and the two side walls were thinner than the main wall, the side walls would tend to flow more slowly. To demonstrate the natural flow non-uniformity, a flat die with a uniform bearing length was designed first. The flat die had a bearing length of 3 mm, the outlet behind the die bearing was 2 mm wider than the orifice, and the back taper angle was 30.

Fig. 2 shows the dimensions and shapes of three pocket dies. They were determined on the basis of the velocity distributions of the profiles exiting from the flat die. A larger pocket angle [11] was given to the part of the U-shaped profile that tended to flow more slowly than the rest of the profile, in order to speed up the metal flow there. Every pocket in front of the main wall of the die orifice had a 1 mm oversize on each side. The pockets in front of the side walls of the die orifice had different shapes and dimensions, as shown on Fig. 3. These designs of pockets were meant to accelerate the metal flow at the side walls.

(a) pocket die 1 (b) pocket die 2 (c) pocket die 3

Fig. 2: Pocket die shapes and dimensions (pocket depth 10 mm). (The thick lines represent the pocket outlines, while the thin lines represent the profile outlines.)

FEM simulations were performed using DEFORM 3D version 6.1 with a self-adapting remeshing

mechanism built-in to allow the simulation of extrusion involving intensive local deformation in front of the die. Considering the symmetry of the die layout (Fig. 1), one half of the billet model was built and the symmetrical boundary conditions were applied. The models of billet, die, container and stem were discretized into four-node tetrahedron elements for FEM calculation. Thermal effects of the


workpiece and its interactions with the extrusion tooling were incorporated into the simulation. The process parameters and friction factors used in the FEM simulations are given in Table 1.

Table 1 Materials, process parameters and friction factors used in FEM simulation

Billet material 6063 aluminium alloy Workpiece material model Rigid-visco-plastic

Billet diameter 50 mm Reduction ratio 33.1

Container diameter 50 mm Initial billet temperature 480 °C

Initial tooling temperature 400 °C Tooling material H13 tool steel

Tooling material model Rigid Ram speed 5 mm/s

Shear friction factor 0.9 between the workpiece and container/stem 0.4 between the workpiece and die

Results and discussions

Metal flow through the flat die. Fig. 3 shows the front end of the U-shaped profile exiting from the flat die. It can be seen that the front is uneven; the main wall must have flown faster than the sidewalls. To illustrate the velocity differences at the extrudate front end, the velocities in the extrusion direction Vz are plotted against the location in the profile (Fig. 4). The sampling was made at 0.5 mm behind the die bearing exit. The velocities were taken at the time when the metal was just exiting the flat die. (d1 denotes the main wall from the die center outwards and d2 the sidewall from the main wall.) It can be seen that, along one half of the main wall, the velocities are in the range from 163.5 to 161.7 mm/s with a maximum difference of 1.8 mm/s, while along the sidewall the maximum velocity difference was as much as 21.5 mm/s (from 161.7 to 140.2 mm). As expected, the closer to the die center, the faster the metal flow. Close to the junction between the main wall and the side wall, the metal is dragged by the fast-flowing metal in the mainwall. Moreover, because the die opening is not at the die centerline in the case of the two-hole die layout, the tip is farther away from the die center, leading to the minimum velocity at the tip (Fig. 4). On the cross section of the U-shaped profile, the overall velocity difference is 23.3 mm/s.

Fig. 3: Front end of the U-shaped profile through the flat die.

In addition, the U-shaped profile was bent towards to the die centre due to velocity differences on the cross section. Fig. 5 shows the distribution of the velocities in the x direction. The slower flow of the thinner side wall restricts the metal flow of the inner main wall. The transverse flow velocity Vx is severe, which is the cause for the bending of the profile.

The significant differences in flow velocity may lead to the distortion and bending of the U-shaped profile. Although the puller may be able to counteract the bending to some extent, severe bending may

workpiece and its interactions with the extrusion tooling were incorporated into the simulation. The process parameters and friction factors used in the FEM simulations are given in Table 1.

Table 1 Materials, process parameters and friction factors used in FEM simulation

Billet material 6063 aluminium alloy Workpiece material model Rigid-visco-plastic

Billet diameter 50 mm Reduction ratio 33.1

Container diameter 50 mm Initial billet temperature 480 °C

Initial tooling temperature 400 °C Tooling material H13 tool steel

Tooling material model Rigid Ram speed 5 mm/s

Shear friction factor 0.9 between the workpiece and container/stem 0.4 between the workpiece and die

Results and discussions

Metal flow through the flat die. Fig. 3 shows the front end of the U-shaped profile exiting from the flat die. It can be seen that the front is uneven; the main wall must have flown faster than the sidewalls. To illustrate the velocity differences at the extrudate front end, the velocities in the extrusion direction Vz are plotted against the location in the profile (Fig. 4). The sampling was made at 0.5 mm behind the die bearing exit. The velocities were taken at the time when the metal was just exiting the flat die. (d1 denotes the main wall from the die center outwards and d2 the sidewall from the main wall.) It can be seen that, along one half of the main wall, the velocities are in the range from 163.5 to 161.7 mm/s with a maximum difference of 1.8 mm/s, while along the sidewall the maximum velocity difference was as much as 21.5 mm/s (from 161.7 to 140.2 mm). As expected, the closer to the die center, the faster the metal flow. Close to the junction between the main wall and the side wall, the metal is dragged by the fast-flowing metal in the mainwall. Moreover, because the die opening is not at the die centerline in the case of the two-hole die layout, the tip is farther away from the die center, leading to the minimum velocity at the tip (Fig. 4). On the cross section of the U-shaped profile, the overall velocity difference is 23.3 mm/s.

Fig. 3: Front end of the U-shaped profile through the flat die.

In addition, the U-shaped profile was bent towards to the die centre due to velocity differences on the cross section. Fig. 5 shows the distribution of the velocities in the x direction. The slower flow of the thinner side wall restricts the metal flow of the inner main wall. The transverse flow velocity Vx is severe, which is the cause for the bending of the profile.

The significant differences in flow velocity may lead to the distortion and bending of the U-shaped profile. Although the puller may be able to counteract the bending to some extent, severe bending may


result in the profile being out of the geometrical and dimensional specifications and even cracking on the part under severe tensile stresses. Fig. 6 shows the distribution of the maximum principal stress in the extrudate. On the surface of the extrudate, the tensile stresses are present, with a maximum value of 35 MPa at the profile tip, which falls in the range of the flow stresses of the AA6063 alloy (11 – 72 MPa at 500 0C over a strain rate range of 0.01 to 180 s-1) and may not cause fracture.

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1.0 2.0 3.0 4.0 5.0100

110

120

130

140

150

160

170

(0)d2(mm)

Extrusion Velocity (mm/s)

d1(mm)

Points on main wall Points on side wall

Fig. 4: Velocity distribution of the extrudate through the flat die.

Fig. 5: Differential velocities Vx of the extruded profile through the flat die, resulting in bending inwards.

Fig. 6: Distribution of the maximum principal stresses in the extrudate through the flat die.

Metal flow through the pocket dies. The pocket dies designed were intended to improve the balance of the metal flow. Fig. 7 shows the velocities at the selected positions (d1 along the main wall and d2 along the side wall of the profile) through the pocket dies under the same conditions as those in the case of the flat die. It is evident that the velocity differences are decreased.

result in the profile being out of the geometrical and dimensional specifications and even cracking on the part under severe tensile stresses. Fig. 6 shows the distribution of the maximum principal stress in the extrudate. On the surface of the extrudate, the tensile stresses are present, with a maximum value of 35 MPa at the profile tip, which falls in the range of the flow stresses of the AA6063 alloy (11 – 72 MPa at 500 0C over a strain rate range of 0.01 to 180 s-1) and may not cause fracture.

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1.0 2.0 3.0 4.0 5.0100

110

120

130

140

150

160

170

(0)d2(mm)


d1(mm)


Fig. 4: Velocity distribution of the extrudate through the flat die.

Fig. 5: Differential velocities Vx of the extruded profile through the flat die, resulting in bending inwards.

Fig. 6: Distribution of the maximum principal stresses in the extrudate through the flat die.

Metal flow through the pocket dies. The pocket dies designed were intended to improve the balance of the metal flow. Fig. 7 shows the velocities at the selected positions (d1 along the main wall and d2 along the side wall of the profile) through the pocket dies under the same conditions as those in the case of the flat die. It is evident that the velocity differences are decreased.


0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1.0 2.0 3.0 4.0 5.0100

110

120

130

140

150

160

170

(0)d2(mm)


d1(mm)


(a) through pocket die 1

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1.0 2.0 3.0 4.0 5.0100

110

120

130

140

150

160

170

(0) d2(mm)


d1(mm)


(b) through pocket die 2

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1.0 2.0 3.0 4.0 5.0100

110

120

130

140

150

160

170

180

(0) d2(mm)


d1(mm)


(c) through pocket die 3

Fig. 7: Velocity distributions of the extrudate through the pocket dies. Compared to the flat die, the pocket dies can balance the metal flow more effectively. Through the

pocket die 3, the maximum velocity difference on the side wall (from 162.32 to 165.95 mm/s) is decreased to 3.33 mm/s. The maximum velocity occurs at the tip of the profile, which is in contrast with the flat die that has the lowest velocity at the tip. The extrudate has a nearly uniform velocity at 0.5 mm behind the die bearing exit. Obviously, the pocket die 3 has the best outline to regulate the metal flow than the other two pocket dies.

The deflection of the U-shaped profiles is another concern. The velocity distributions of the extruded profiles Vx are shown in Fig. 8. It is can be seen that the deflection occurs at the sidewall (when Vx is positive) when the profile flow through these three pocket dies. Through the pocket die 3,

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1.0 2.0 3.0 4.0 5.0100

110

120

130

140

150

160

170

(0)d2(mm)


d1(mm)



0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1.0 2.0 3.0 4.0 5.0100

110

120

130

140

150

160

170

(0) d2(mm)


d1(mm)



0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1.0 2.0 3.0 4.0 5.0100

110

120

130

140

150

160

170

180

(0) d2(mm)


d1(mm)



Fig. 7: Velocity distributions of the extrudate through the pocket dies. Compared to the flat die, the pocket dies can balance the metal flow more effectively. Through the

pocket die 3, the maximum velocity difference on the side wall (from 162.32 to 165.95 mm/s) is decreased to 3.33 mm/s. The maximum velocity occurs at the tip of the profile, which is in contrast with the flat die that has the lowest velocity at the tip. The extrudate has a nearly uniform velocity at 0.5 mm behind the die bearing exit. Obviously, the pocket die 3 has the best outline to regulate the metal flow than the other two pocket dies.

The deflection of the U-shaped profiles is another concern. The velocity distributions of the extruded profiles Vx are shown in Fig. 8. It is can be seen that the deflection occurs at the sidewall (when Vx is positive) when the profile flow through these three pocket dies. Through the pocket die 3,


the velocity differences are the smallest, as compared to the other two pocket dies, and nearly straight profiles can be expected.

It is important to note that these three pocket dies have different shapes only at the sidewall tip of the pocket. Clearly, the shape of the pocket at the profile tip affects the metal flow significantly. The pocket 3 has the widest tip and, as a result, the metal flow velocity there is increased and the velocity differences are decreased. The results of the present FEM simulation show that the pocket width is an important factor in regulating metal flow through the pocket die.




Fig. 8: Velocities distributions Vx of the extrudate through the pocket dies.

the velocity differences are the smallest, as compared to the other two pocket dies, and nearly straight profiles can be expected.

It is important to note that these three pocket dies have different shapes only at the sidewall tip of the pocket. Clearly, the shape of the pocket at the profile tip affects the metal flow significantly. The pocket 3 has the widest tip and, as a result, the metal flow velocity there is increased and the velocity differences are decreased. The results of the present FEM simulation show that the pocket width is an important factor in regulating metal flow through the pocket die.




Fig. 8: Velocities distributions Vx of the extrudate through the pocket dies.


Summary

In recent years, single-bearing pocket dies have been increasingly used across the aluminum extrusion industry. However, the methodology of pocket design in terms of regulating metal flow is not well documented. The present communication shows that in the case of extruding two U-shaped profiles with different wall thicknesses through a pocket die, the width of pocket has strong influence on the metal flow. On the basis of the FEM simulation of extrusion through a number of pocket dies, velocity non-uniformity, as occurring to the flat die, can be decreased and the deflection of the extruded profile minimized. The FEM-assisted design of extrusion dies can reduce the number of die trial-correction cycles.

Acknowledgements

The authors gratefully acknowledge the support of Natural Science Foundation of China (No. 50775123).

References

[1] K. Müller, Fundamentals of Extrusion Technology (Giesel Verlag GmbH, Isernhagen, 2004), p. 189.

[2] A. Rodriguez and P. Rodriguez, in: Proceedings of the 5th International Aluminum Extrusion Technology Seminar, Vol. I, Aluminum Association and Aluminum Extruder’s Council, Wauconda, Illinois (1992), p. 283.

[3] A. Rodriguez and P. Rodriguez, in: Proceedings of the 5th International Aluminum Extrusion Technology Seminar, Vol. I, Aluminium Association and Aluminium Extruder’s Council, Wauconda, Illinois (1996), p. 155.

[4] EP 0 569 315 B1, Method of Constructing Dies for Extruding Solid Aluminum Shapes, European Patent Specification.

[5] W.J. Mason, in: Proceedings of the 4th International Aluminium Extrusion Technology Seminar, Vol. II, Aluminum Association and Aluminum Extruder’s Council, Wauconda, Illinois (1988), p. 21.

[6] L. Ingraldi, V. Giacomello and M. Pedersoli, in: Proceedings of the 5th International Aluminum Extrusion Technology Seminar, Vol. II, Aluminum Association and Aluminum Extruder’s Council, Wauconda, Illinois (1992) p. 369.

[7] T. Sheppard, Extrusion of Aluminium Alloys (Kluwer Academic Publishers, Dordrecht, 1999) p. 358.

[8] I. Duplancic, M. Mico and Z. Bracic, in: Proceedings of the 7th International Extrusion Technology Seminar, Vol. II, Aluminum Association and Aluminum Extruder’s Council, Wauconda, Illinois (2000), p. 177.

[9] Q. Li, C. J. Smith, C. Harris and M. R. Jolly, J. Mater. Process. Technol. Vol. 135 (2003), p. 189.


[11] G. Fang, J. Zhou and J. Duszczyk, J. Mater. Process. Technol. Vol. 209 (2009), p. 1891.

Summary

In recent years, single-bearing pocket dies have been increasingly used across the aluminum extrusion industry. However, the methodology of pocket design in terms of regulating metal flow is not well documented. The present communication shows that in the case of extruding two U-shaped profiles with different wall thicknesses through a pocket die, the width of pocket has strong influence on the metal flow. On the basis of the FEM simulation of extrusion through a number of pocket dies, velocity non-uniformity, as occurring to the flat die, can be decreased and the deflection of the extruded profile minimized. The FEM-assisted design of extrusion dies can reduce the number of die trial-correction cycles.

Acknowledgements

The authors gratefully acknowledge the support of Natural Science Foundation of China (No. 50775123).

References

[1] K. Müller, Fundamentals of Extrusion Technology (Giesel Verlag GmbH, Isernhagen, 2004), p. 189.

[2] A. Rodriguez and P. Rodriguez, in: Proceedings of the 5th International Aluminum Extrusion Technology Seminar, Vol. I, Aluminum Association and Aluminum Extruder’s Council, Wauconda, Illinois (1992), p. 283.

[3] A. Rodriguez and P. Rodriguez, in: Proceedings of the 5th International Aluminum Extrusion Technology Seminar, Vol. I, Aluminium Association and Aluminium Extruder’s Council, Wauconda, Illinois (1996), p. 155.

[4] EP 0 569 315 B1, Method of Constructing Dies for Extruding Solid Aluminum Shapes, European Patent Specification.

[5] W.J. Mason, in: Proceedings of the 4th International Aluminium Extrusion Technology Seminar, Vol. II, Aluminum Association and Aluminum Extruder’s Council, Wauconda, Illinois (1988), p. 21.

[6] L. Ingraldi, V. Giacomello and M. Pedersoli, in: Proceedings of the 5th International Aluminum Extrusion Technology Seminar, Vol. II, Aluminum Association and Aluminum Extruder’s Council, Wauconda, Illinois (1992) p. 369.

[7] T. Sheppard, Extrusion of Aluminium Alloys (Kluwer Academic Publishers, Dordrecht, 1999) p. 358.

[8] I. Duplancic, M. Mico and Z. Bracic, in: Proceedings of the 7th International Extrusion Technology Seminar, Vol. II, Aluminum Association and Aluminum Extruder’s Council, Wauconda, Illinois (2000), p. 177.



[11] G. Fang, J. Zhou and J. Duszczyk, J. Mater. Process. Technol. Vol. 209 (2009), p. 1891.


Localization of the Shear Zone in Extrusion Processes

by means of Finite Element Analysis

Matthias Kammler1, a 1Leibniz Universität Hannover, Institute of Metal Forming and Metal-Forming Machines, Germany

[email protected]

Keywords: Extrusion, Shear Zone, Interaction, FEA, Shear Criteria Abstract. A characteristic feature of extrusion processes is the formation of a shear zone, which separates the deformation zone and the dead metal zone [1, 2]. The deformations occurring in the shear zone cause inner separation and welding effects, which are of great importance for the material flow and the microstructure development of the extruded profiles.

The material in the dead metal zone is not participating directly in the forming process but the shape of this zone influences eminently the forming zone and thus the forming of the extruded profile. Furthermore the extreme shear deformation causes according to the Hall-Petch relationship a significant grain refinement in these regions of extruded profiles [3, 4]. So the knowledge on the effects in the shear zone during extrusion processes is fundamental for subsequent numerical investigations on the microstructure development for example regarding quenching techniques.

The aim of this study is to localize the formation of the shear zone during extrusion processes by means of the finite element analysis. On the basis of the assumption that separation and welding effects take place in the shear zone, numerical investigations were carried out to indicate these microscopic effects on the macroscopic scale. The considered process was the extrusion of a solid round profile of the alloy EN AW 6082 at 450°C with a punch velocity of 10.5 mm/s. For the localization of the shear zone mechanical parameters were chosen for a shear criterion, which are taken from numerical simulations. A user subroutine was implemented into the FE-models in order to evaluate the shear criterion for the localization of the shear zone. According to [5, 6] the friction model used for the numerical simulations has a strong influence on the formation of the shear zone. In this study a combined friction model according to [7] was used.

Introduction

Aluminum profiles are widely used in automotive and aeronautical industries. The material and its alloys have good plastic deformation characteristics for conventional metallurgical processes as extrusion processes. Especially in these processes the mechanical properties and in particular the strength and deformability of the extrudates are of great interest. These properties are mostly related to the microstructure development of the alloy during the whole production cycle from billet casting to profile aging [8]. The microstructure evolution and thus the properties of extruded aluminum products are significantly influenced by the way the metal flows during extrusion. This is affected by many parameters like the type of extrusion (direct or indirect), size and shape of container, frictional effects on die and container walls, design of die, length of billet and alloy type as well as the general thermal conditions, the extrusion ratio and the ram speed [9]. For example Flitta and Sheppard used the Zenner-Hollomon parameter for the prediction of the static recrystallization in extrusion processes [10, 11]. This parameter depends mainly on the equivalent strain rate and the current temperature. But even for the numerical simulation of dynamic recrystallization according to the Johnson-Mehl-Avrami-Kologorov-Model (JMAK) the equivalent strain rate is of importance [12]. It is remarkable that the simulation results presented in [9, 10] show in general a good

Localization of the Shear Zone in Extrusion Processes

by means of Finite Element Analysis

Matthias Kammler1, a 1Leibniz Universität Hannover, Institute of Metal Forming and Metal-Forming Machines, Germany

[email protected]

Keywords: Extrusion, Shear Zone, Interaction, FEA, Shear Criteria Abstract. A characteristic feature of extrusion processes is the formation of a shear zone, which separates the deformation zone and the dead metal zone [1, 2]. The deformations occurring in the shear zone cause inner separation and welding effects, which are of great importance for the material flow and the microstructure development of the extruded profiles.

The material in the dead metal zone is not participating directly in the forming process but the shape of this zone influences eminently the forming zone and thus the forming of the extruded profile. Furthermore the extreme shear deformation causes according to the Hall-Petch relationship a significant grain refinement in these regions of extruded profiles [3, 4]. So the knowledge on the effects in the shear zone during extrusion processes is fundamental for subsequent numerical investigations on the microstructure development for example regarding quenching techniques.

The aim of this study is to localize the formation of the shear zone during extrusion processes by means of the finite element analysis. On the basis of the assumption that separation and welding effects take place in the shear zone, numerical investigations were carried out to indicate these microscopic effects on the macroscopic scale. The considered process was the extrusion of a solid round profile of the alloy EN AW 6082 at 450°C with a punch velocity of 10.5 mm/s. For the localization of the shear zone mechanical parameters were chosen for a shear criterion, which are taken from numerical simulations. A user subroutine was implemented into the FE-models in order to evaluate the shear criterion for the localization of the shear zone. According to [5, 6] the friction model used for the numerical simulations has a strong influence on the formation of the shear zone. In this study a combined friction model according to [7] was used.

Introduction

Aluminum profiles are widely used in automotive and aeronautical industries. The material and its alloys have good plastic deformation characteristics for conventional metallurgical processes as extrusion processes. Especially in these processes the mechanical properties and in particular the strength and deformability of the extrudates are of great interest. These properties are mostly related to the microstructure development of the alloy during the whole production cycle from billet casting to profile aging [8]. The microstructure evolution and thus the properties of extruded aluminum products are significantly influenced by the way the metal flows during extrusion. This is affected by many parameters like the type of extrusion (direct or indirect), size and shape of container, frictional effects on die and container walls, design of die, length of billet and alloy type as well as the general thermal conditions, the extrusion ratio and the ram speed [9]. For example Flitta and Sheppard used the Zenner-Hollomon parameter for the prediction of the static recrystallization in extrusion processes [10, 11]. This parameter depends mainly on the equivalent strain rate and the current temperature. But even for the numerical simulation of dynamic recrystallization according to the Johnson-Mehl-Avrami-Kologorov-Model (JMAK) the equivalent strain rate is of importance [12]. It is remarkable that the simulation results presented in [9, 10] show in general a good


agreement with the results from experimental investigations. However the computed subgrain sizes in the areas of the shear zone and the dead metal zone show significant deviations up to 15%. Many investigations were carried out for the numerical simulation of extrusion processes in order to predict the microstructure evolution and the related mechanical properties of the extrudates. Apart from the microstructure prediction, the focus of other investigations was the formulation of the frictional behavior between the billet and the tools, the temperature evolution during the process and the formation of seam welds. Usually for the characterization of the constitutive behavior of the material a hyperbolic sine function is used and for the description of the frictional properties often the Tresca friction law is applied. But for the numerical description of the material flow behavior the chosen yield criterion is also of importance.

Fig. 1: Velocity profile using von Mises yield criterion

During extrusion severe shear deformations occur compared to the metal flow of other metal forming processes [9]. In the process of direct extrusion the center of the billet extrudes first and at higher speed than the peripheral part of billet which retains at the die wall. The retained material causes dead metal zones between the die outlet and the container which are separated by a shear zone from the deformation zone (Fig. 1). The material in the forming zone moves over the dead metal zone which appears in the investigated process as a conical die surface. Due to the high hydrostatic pressure which is typical for extrusion processes the use of damage models known from other applications is not suitable, as one amongst other preconditions for these models is that a tensile stress triaxiality must prevail. In order to determine the shear zone during extrusion processes on the basis of a yield criterion in this study investigations on the beginning of an extrusion process using Tresca’s in comparison to von Mises yield criterion were carried out to localize the shear zone. These investigations were done based on the assumption that the deformations occurring in the shear zone, cause inner separation and welding effects.

Comparison of von Mises’ and Tresca’s yield criterion

The von Mises yield criterion FvM (Eq. 1), for a better comparison here shown with the principle stresses, which is commonly used for the numerical simulation of forming processes, suggests that

agreement with the results from experimental investigations. However the computed subgrain sizes in the areas of the shear zone and the dead metal zone show significant deviations up to 15%. Many investigations were carried out for the numerical simulation of extrusion processes in order to predict the microstructure evolution and the related mechanical properties of the extrudates. Apart from the microstructure prediction, the focus of other investigations was the formulation of the frictional behavior between the billet and the tools, the temperature evolution during the process and the formation of seam welds. Usually for the characterization of the constitutive behavior of the material a hyperbolic sine function is used and for the description of the frictional properties often the Tresca friction law is applied. But for the numerical description of the material flow behavior the chosen yield criterion is also of importance.

Fig. 1: Velocity profile using von Mises yield criterion

During extrusion severe shear deformations occur compared to the metal flow of other metal forming processes [9]. In the process of direct extrusion the center of the billet extrudes first and at higher speed than the peripheral part of billet which retains at the die wall. The retained material causes dead metal zones between the die outlet and the container which are separated by a shear zone from the deformation zone (Fig. 1). The material in the forming zone moves over the dead metal zone which appears in the investigated process as a conical die surface. Due to the high hydrostatic pressure which is typical for extrusion processes the use of damage models known from other applications is not suitable, as one amongst other preconditions for these models is that a tensile stress triaxiality must prevail. In order to determine the shear zone during extrusion processes on the basis of a yield criterion in this study investigations on the beginning of an extrusion process using Tresca’s in comparison to von Mises yield criterion were carried out to localize the shear zone. These investigations were done based on the assumption that the deformations occurring in the shear zone, cause inner separation and welding effects.

Comparison of von Mises’ and Tresca’s yield criterion

The von Mises yield criterion FvM (Eq. 1), for a better comparison here shown with the principle stresses, which is commonly used for the numerical simulation of forming processes, suggests that


the yielding of the material begins when the second deviatoric stress invariant J2 reaches the shear yield strength k. This yield criterion applies well to ductile materials, such as aluminum. Prior to yield, material response is assumed to be elastic.

( ) ( ) ( )[ ] 021

f2

IIII2

IIIII2

IIIvM =−−+−+−= kF σσσσσσ (1)

In material science and engineering the von Mises yield criterion can also be formulated in terms of the von Mises stress or equivalent tensile stress σvM, a scalar stress value that can be computed from the stress tensor. In this case, a material starts yielding when its von Mises stress reaches a critical value known as the yield strength, kf. The von Mises stress is used to predict yielding of materials under any loading condition from results of simple uniaxial tensile tests. The von Mises stress satisfies the property that two stress states with equivalent distortion energy have equal von Mises stress. Because the von Mises yield criterion is independent of the first stress invariant I1, it is applicable for the analysis of plastic deformation of metals, as the onset of yield for these materials does not depend on the hydrostatic component of the stress tensor.

( ) 0|||,||,|max fIIIIIIIIIIIIT =−−−−= kF σσσσσσ (2)

Similar to the von Mises criterion the Tresca or maximum shear stress yield criterion (Eq. 2) represents a yield surface in the three-dimensional space of principal stresses. It is a hexagonal prism having infinite length. This means that the material remains elastic when all three principal stresses are roughly equivalent, no matter how much it is compressed or stretched. However, when one of principal stresses becomes smaller or larger than the others the material is subjected to shearing. In such situations, the material enters the plastic domain if the shear stress reaches the yield limit. In Fig. 2 both yield criteria are shown. Observe that Tresca's yield surface is circumscribed by von Mises. Therefore, it predicts yielding already for stress states that are still elastic according to the von Mises criterion. Especially under plain shear conditions as they appear in the shear zone of extrusion processes the maximum deviations may amount up to 15 %. For the numerical simulation of these processes using Tresca’s yield criterion the consequence is, that the formation of the shear zone begins earlier and the shape of the dead metal zone deviates significantly from the shape computed with the von Mises yield criterion. A further consequence is that the flow behavior of the material is also influenced. Due to the circumstance that the results of the microstructure development depends on the strain rate it is obvious that with the change of the used yield criterion subsequent numerical investigations on the microstructure leads to differing results.

Fig. 2: Comparison of von Mises and Tresca’s yield surfaces

the yielding of the material begins when the second deviatoric stress invariant J2 reaches the shear yield strength k. This yield criterion applies well to ductile materials, such as aluminum. Prior to yield, material response is assumed to be elastic.

( ) ( ) ( )[ ] 021

f2

IIII2

IIIII2

IIIvM =−−+−+−= kF σσσσσσ (1)

In material science and engineering the von Mises yield criterion can also be formulated in terms of the von Mises stress or equivalent tensile stress σvM, a scalar stress value that can be computed from the stress tensor. In this case, a material starts yielding when its von Mises stress reaches a critical value known as the yield strength, kf. The von Mises stress is used to predict yielding of materials under any loading condition from results of simple uniaxial tensile tests. The von Mises stress satisfies the property that two stress states with equivalent distortion energy have equal von Mises stress. Because the von Mises yield criterion is independent of the first stress invariant I1, it is applicable for the analysis of plastic deformation of metals, as the onset of yield for these materials does not depend on the hydrostatic component of the stress tensor.

( ) 0|||,||,|max fIIIIIIIIIIIIT =−−−−= kF σσσσσσ (2)

Similar to the von Mises criterion the Tresca or maximum shear stress yield criterion (Eq. 2) represents a yield surface in the three-dimensional space of principal stresses. It is a hexagonal prism having infinite length. This means that the material remains elastic when all three principal stresses are roughly equivalent, no matter how much it is compressed or stretched. However, when one of principal stresses becomes smaller or larger than the others the material is subjected to shearing. In such situations, the material enters the plastic domain if the shear stress reaches the yield limit. In Fig. 2 both yield criteria are shown. Observe that Tresca's yield surface is circumscribed by von Mises. Therefore, it predicts yielding already for stress states that are still elastic according to the von Mises criterion. Especially under plain shear conditions as they appear in the shear zone of extrusion processes the maximum deviations may amount up to 15 %. For the numerical simulation of these processes using Tresca’s yield criterion the consequence is, that the formation of the shear zone begins earlier and the shape of the dead metal zone deviates significantly from the shape computed with the von Mises yield criterion. A further consequence is that the flow behavior of the material is also influenced. Due to the circumstance that the results of the microstructure development depends on the strain rate it is obvious that with the change of the used yield criterion subsequent numerical investigations on the microstructure leads to differing results.

Fig. 2: Comparison of von Mises and Tresca’s yield surfaces


Finite Element Model

The numerical investigations were carried out using the FEM package simufact.forming®. Due to the symmetry of the process only a rotational-symmetric model was built up. All dies were modeled as rigid components whereas the plastic behavior of the billet was defined using a piecewise linear approach with basis data taken from the materials database of the FE package Forge3®. The initial billet temperature was set to 470°C while all dies were set to 450°C. For the description of the frictional behavior between the billet and the tools a combined approach, described in [7] was used. A friction factor m = 0.5 was chosen. For the localization of the shear zone using Tresca’ yield criterion a user subroutine written in Fortran was implemented into the FE-models. With the help of this subroutine occurring main stresses can be determined and thus the formulation of Tresca’s yield criterion for the metal flow analysis.


In Fig. 3 and Fig. 4 a comparison of the computed main shear stress and the equivalent plastic strain rate using the von Mises and Tresca yield criterion are shown. Even if the maximal deviation of both criteria in case of plain shear conditions is about 15 % the results differ significantly. As can be seen in Fig. 3 the formation of the shear zone as expected begins earlier. The distribution of the main shear stress deviates clearly from the results obtained with the von Mises yield criterion. As a consequence the resulting strain rates differ significantly. The distributions of the equivalent plastic strain rate, shown in Fig. 4 displays that the maximum values using Tresca’s yield criterion are much higher in comparison to the usage of von Mises criterion. Using von Mises criterion a maximum value of plε& = 3.5 is found. In contrast to this result the usage of Tresca’s criterion leads

to a maximum value of plε& = 9.5. The factor of about 2.7 between these values for the equivalent

plastic strain rate shows the strong influence of the chosen yield criterion on the flow behavior of the extruded material. Hence the influence of the chosen yield criterion on the computation of the microstructure development during extrusion processes has also to be taken into account. Furthermore it can be assumed, that the formation of the dead metal zone at the beginning of the extrusion process influences the subsequent material flow significantly. Especially the quasistatic state of the process is influenced by the shear zone due to separation and welding effects. Therefore further investigations on the formation of the shear zone and the occurring effects are necessary.

Fig. 3: Comparison of the main shear stress τmax computed with von Mises (left) and Tresca’s (right) yield criterion

Finite Element Model

The numerical investigations were carried out using the FEM package simufact.forming®. Due to the symmetry of the process only a rotational-symmetric model was built up. All dies were modeled as rigid components whereas the plastic behavior of the billet was defined using a piecewise linear approach with basis data taken from the materials database of the FE package Forge3®. The initial billet temperature was set to 470°C while all dies were set to 450°C. For the description of the frictional behavior between the billet and the tools a combined approach, described in [7] was used. A friction factor m = 0.5 was chosen. For the localization of the shear zone using Tresca’ yield criterion a user subroutine written in Fortran was implemented into the FE-models. With the help of this subroutine occurring main stresses can be determined and thus the formulation of Tresca’s yield criterion for the metal flow analysis.


In Fig. 3 and Fig. 4 a comparison of the computed main shear stress and the equivalent plastic strain rate using the von Mises and Tresca yield criterion are shown. Even if the maximal deviation of both criteria in case of plain shear conditions is about 15 % the results differ significantly. As can be seen in Fig. 3 the formation of the shear zone as expected begins earlier. The distribution of the main shear stress deviates clearly from the results obtained with the von Mises yield criterion. As a consequence the resulting strain rates differ significantly. The distributions of the equivalent plastic strain rate, shown in Fig. 4 displays that the maximum values using Tresca’s yield criterion are much higher in comparison to the usage of von Mises criterion. Using von Mises criterion a maximum value of plε& = 3.5 is found. In contrast to this result the usage of Tresca’s criterion leads

to a maximum value of plε& = 9.5. The factor of about 2.7 between these values for the equivalent

plastic strain rate shows the strong influence of the chosen yield criterion on the flow behavior of the extruded material. Hence the influence of the chosen yield criterion on the computation of the microstructure development during extrusion processes has also to be taken into account. Furthermore it can be assumed, that the formation of the dead metal zone at the beginning of the extrusion process influences the subsequent material flow significantly. Especially the quasistatic state of the process is influenced by the shear zone due to separation and welding effects. Therefore further investigations on the formation of the shear zone and the occurring effects are necessary.

Fig. 3: Comparison of the main shear stress τmax computed with von Mises (left) and Tresca’s (right) yield criterion


Fig. 4: Comparison of the equivalent plastic strain rate plε& computed

with von Mises (left) and Tresca’s (right) yield criterion Conclusions

The used yield criterion is of importance for the localization of the shear zone and the dead metal zone in extrusion processes and further investigations of the microstructure development. Therefore Tresca’s or the maximum shear stress yield criterion was chosen to determine the influence of the yield criterion on the material flow and thus on the formation of the shear zone by means of FEA. The results reveal that the usage of Tresca’s criterion causes an earlier formation of the shear zone and hence a significantly differing equivalent plastic strain rate. Since the microstructure development depends on the strain rate, the chosen yield criterion has to be taken into account for the evaluation of such investigations. Within the framework of this project further investigations on the microstructure development and on separation effects in the shear zone will be carried out in order to determine the influences on the material flow during extrusion processes.

Acknowledgement

The financial support of the German Research Foundation within the framework of the research unit 922 is gratefully acknowledged.

References

[1] H. Valberg, “Experimental techniques to characterize large plastic deformations in unlubricated hot aluminum extrusion”, Extrusion Workshop 2007 and 2nd Extrusion Benchmark, 20-21 September 2007 - Bologna, Italy

[2] M. Bauser., G. Sauer., K. Siegert, Strangpressen. Aluminium Verlag GmbH, Düsseldorf, 2001, ISBN 3-87017-249-5

[3] M. Lewandowska, K. J. Kurzydlowski, “Recent development in grain refinement by hydrostatic extrusion”, J. Mater. Sci. (2008) 43: 7299–7306

[4] Evolution of Surface Recrystallization during indirect Extrusion of 6xxx Aluminum Alloys, W.H. van Geertuyden, H.M. Browne, W.Z. Misiolek, Metallurgical and Materials Transactions, Volume 36A, April 2005, 1049 - 1056

Fig. 4: Comparison of the equivalent plastic strain rate plε& computed

with von Mises (left) and Tresca’s (right) yield criterion Conclusions

The used yield criterion is of importance for the localization of the shear zone and the dead metal zone in extrusion processes and further investigations of the microstructure development. Therefore Tresca’s or the maximum shear stress yield criterion was chosen to determine the influence of the yield criterion on the material flow and thus on the formation of the shear zone by means of FEA. The results reveal that the usage of Tresca’s criterion causes an earlier formation of the shear zone and hence a significantly differing equivalent plastic strain rate. Since the microstructure development depends on the strain rate, the chosen yield criterion has to be taken into account for the evaluation of such investigations. Within the framework of this project further investigations on the microstructure development and on separation effects in the shear zone will be carried out in order to determine the influences on the material flow during extrusion processes.

Acknowledgement

The financial support of the German Research Foundation within the framework of the research unit 922 is gratefully acknowledged.

References

[1] H. Valberg, “Experimental techniques to characterize large plastic deformations in unlubricated hot aluminum extrusion”, Extrusion Workshop 2007 and 2nd Extrusion Benchmark, 20-21 September 2007 - Bologna, Italy

[2] M. Bauser., G. Sauer., K. Siegert, Strangpressen. Aluminium Verlag GmbH, Düsseldorf, 2001, ISBN 3-87017-249-5

[3] M. Lewandowska, K. J. Kurzydlowski, “Recent development in grain refinement by hydrostatic extrusion”, J. Mater. Sci. (2008) 43: 7299–7306

[4] Evolution of Surface Recrystallization during indirect Extrusion of 6xxx Aluminum Alloys, W.H. van Geertuyden, H.M. Browne, W.Z. Misiolek, Metallurgical and Materials Transactions, Volume 36A, April 2005, 1049 - 1056


[5] P. Hora, C. Karadogan, L. Tong, “Neue Entwicklungen im Bereich der virtuellen Abbildung von Strangpressprozessen“, Symposium Strangpressen des Fachauschusses Strangpressen der DGM, Weimar, 2007

[6] D. Ringhand, „Einsatz der Prozesssimulation beim Strangpressen von Schwermetallen“, Symposium Strangpressen des Fachauschusses Strangpressen der DGM, Weimar, 2007

[7] T. Neumaier, “Optimierung der Verfahrensauswahl von Kalt-, Halbwarm- und Warmmassivumformverfahren“, Dissertation, Universität Hannover, 2003

[8] M. Schikorra, L. Donati, L. Tomesani, A.E. Tekkaya, Microstructure analysis of aluminum extrusion: Prediction of microstructure on AA6060 alloy, Journal of Materials Processing Technology 201, 2008, 156-152

[9] H. Valberg, Y.A. Kahn, P.T. Moe, The mechanics of two-dimensional aluminum extrusion welding investigated by FEM-analysis with experiment, ITCP 2008, Gyeongju, Korea

[10] Z. Peng, T. Sheppard, Prediction of static recrystallization during shaped Extrusion, Aluminum Extrusion Technology, 2004

[11] I. Flitta, T. Sheppard, Prediction of Substructure Influencing static Recrystallization using FEM Analysis, Esaform 2009, Enschede, The Netherlands

[12] T. Sheppard, Extrusion of 2024 Alloy, Materials Science and Technology 9, 1993, 430-440

[12] Y.A. Kahn, H. Valberg, I.Irgens, Joining of Metal Streams in Extrusion Welding, Esaform 2009, Enschede, The Netherlands

[5] P. Hora, C. Karadogan, L. Tong, “Neue Entwicklungen im Bereich der virtuellen Abbildung von Strangpressprozessen“, Symposium Strangpressen des Fachauschusses Strangpressen der DGM, Weimar, 2007

[6] D. Ringhand, „Einsatz der Prozesssimulation beim Strangpressen von Schwermetallen“, Symposium Strangpressen des Fachauschusses Strangpressen der DGM, Weimar, 2007

[7] T. Neumaier, “Optimierung der Verfahrensauswahl von Kalt-, Halbwarm- und Warmmassivumformverfahren“, Dissertation, Universität Hannover, 2003

[8] M. Schikorra, L. Donati, L. Tomesani, A.E. Tekkaya, Microstructure analysis of aluminum extrusion: Prediction of microstructure on AA6060 alloy, Journal of Materials Processing Technology 201, 2008, 156-152

[9] H. Valberg, Y.A. Kahn, P.T. Moe, The mechanics of two-dimensional aluminum extrusion welding investigated by FEM-analysis with experiment, ITCP 2008, Gyeongju, Korea

[10] Z. Peng, T. Sheppard, Prediction of static recrystallization during shaped Extrusion, Aluminum Extrusion Technology, 2004

[11] I. Flitta, T. Sheppard, Prediction of Substructure Influencing static Recrystallization using FEM Analysis, Esaform 2009, Enschede, The Netherlands

[12] T. Sheppard, Extrusion of 2024 Alloy, Materials Science and Technology 9, 1993, 430-440

[12] Y.A. Kahn, H. Valberg, I.Irgens, Joining of Metal Streams in Extrusion Welding, Esaform 2009, Enschede, The Netherlands


A case study to solve the problem of wall thickness attenuation during extrusion to produce a complex hollow magnesium profile

L. Li1,2,a, J. Zhou1,2,b, X. He1,2,c, J. Zhou3,d and J. Duszczyk3,e 1State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Changsha, China

2College of Materials Science and Engineering, Hunan University, Changsha, China 3Department of Materials Science and Engineering, Delft University of Technology, The Netherlands [email protected], [email protected], [email protected], [email protected],

[email protected]

Keywords: Magnesium; Extrusion; Hollow profile; Porthole die; FEM simulation Abstract. The present case study addressed a practical problem of wall thickness attenuation during extrusion to produce a complex thin-walled hollow magnesium profile. A HyperWorks FEM software package was employed to aid in identifying the causes for the wall thickness attenuation. Recommendations were made to adjust the interspacing between the mandrels and the height of the welding chamber. The modified dies yielded much improved results in terms of velocity and hydrostatic pressure uniformity. The wall thickness of the extrudate predicted using FEM simulation was very close to experimental measurements. The case study demonstrated the feasibility of using FEM simulation as a useful tool to solve industrial problems encountered in the production of complex profiles.

Introduction

The low density, high specific strength and high specific stiffness of magnesium alloys make them attractive for a wide range of engineering applications, in particular, for transport applications [1-2]. However, the low workability of wrought magnesium alloys remains to be one of the barriers to making inroads in these applications. It is therefore necessary to define the formability of magnesium alloys and characterize their response to deformation under different conditions in individual forming processes. While there is a wealth of information on the response of aluminum alloys to extrusion deformation, especially on metal flow through solid and hollow dies, in-depth studies on the characteristic behavior of magnesium alloys in extrusion are comparatively scarce. The profiles with hollow section are mostly produced by using direct extrusion through porthole dies. During the process, the metal is divided into individual streams and flows through the feeder ports, then gathered and welded in the welding chamber, before flowing through the die bearing. Metal flow is affected by a number of parameters including die geometry, billet temperature, die temperature and extrusion speed. Among those parameters, die geometry is of critical importance, which largely determines the metal flow balance and welding pressure. To meet the specifications of extrudates in shape and dimensions, uniform metal flow on the cross section at the die exit is a must. There are a number of well-established measures that can be taken to lessen or eliminate non-uniform metal flow, in case it occurs. For instance, the shape, size and location of the feeder ports and welding chamber may be modified and local bearing length adjusted [3]. The effect of any change will be known after a new die or a corrected die is tested. Metal flow through porthole dies is invisible. In this case, FEM simulation is of use in revealing the characteristic flow behavior. Li et al., for example, conducted a numerical and experimental study on the thermomechanical behavior of the AZ31B magnesium alloy during extrusion to produce a square tube and proposed a criterion to ensure the longitudinal weld seam quality [4]. Liu et al. showed the thermomechanical characteristics of metal flow while magnesium was flowing through a porthole die, and indicated the beneficial effect of increasing extrusion speed on the longitudinal weld seam quality

A case study to solve the problem of wall thickness attenuation during extrusion to produce a complex hollow magnesium profile

L. Li1,2,a, J. Zhou1,2,b, X. He1,2,c, J. Zhou3,d and J. Duszczyk3,e 1State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Changsha, China

2College of Materials Science and Engineering, Hunan University, Changsha, China 3Department of Materials Science and Engineering, Delft University of Technology, The Netherlands [email protected], [email protected], [email protected], [email protected],

[email protected]

Keywords: Magnesium; Extrusion; Hollow profile; Porthole die; FEM simulation Abstract. The present case study addressed a practical problem of wall thickness attenuation during extrusion to produce a complex thin-walled hollow magnesium profile. A HyperWorks FEM software package was employed to aid in identifying the causes for the wall thickness attenuation. Recommendations were made to adjust the interspacing between the mandrels and the height of the welding chamber. The modified dies yielded much improved results in terms of velocity and hydrostatic pressure uniformity. The wall thickness of the extrudate predicted using FEM simulation was very close to experimental measurements. The case study demonstrated the feasibility of using FEM simulation as a useful tool to solve industrial problems encountered in the production of complex profiles.

Introduction

The low density, high specific strength and high specific stiffness of magnesium alloys make them attractive for a wide range of engineering applications, in particular, for transport applications [1-2]. However, the low workability of wrought magnesium alloys remains to be one of the barriers to making inroads in these applications. It is therefore necessary to define the formability of magnesium alloys and characterize their response to deformation under different conditions in individual forming processes. While there is a wealth of information on the response of aluminum alloys to extrusion deformation, especially on metal flow through solid and hollow dies, in-depth studies on the characteristic behavior of magnesium alloys in extrusion are comparatively scarce. The profiles with hollow section are mostly produced by using direct extrusion through porthole dies. During the process, the metal is divided into individual streams and flows through the feeder ports, then gathered and welded in the welding chamber, before flowing through the die bearing. Metal flow is affected by a number of parameters including die geometry, billet temperature, die temperature and extrusion speed. Among those parameters, die geometry is of critical importance, which largely determines the metal flow balance and welding pressure. To meet the specifications of extrudates in shape and dimensions, uniform metal flow on the cross section at the die exit is a must. There are a number of well-established measures that can be taken to lessen or eliminate non-uniform metal flow, in case it occurs. For instance, the shape, size and location of the feeder ports and welding chamber may be modified and local bearing length adjusted [3]. The effect of any change will be known after a new die or a corrected die is tested. Metal flow through porthole dies is invisible. In this case, FEM simulation is of use in revealing the characteristic flow behavior. Li et al., for example, conducted a numerical and experimental study on the thermomechanical behavior of the AZ31B magnesium alloy during extrusion to produce a square tube and proposed a criterion to ensure the longitudinal weld seam quality [4]. Liu et al. showed the thermomechanical characteristics of metal flow while magnesium was flowing through a porthole die, and indicated the beneficial effect of increasing extrusion speed on the longitudinal weld seam quality


[5]. Mooi et al. [6] analyzed the extrusion process to produce circular tubes and calculated the deformation of the die. Kim et al. developed a modified porthole die for tube extrusion in order to obtain enhanced welding pressure relative to that of the original porthole die [7]. These preceding studies using FEM simulation have provided fundamentally important insights into the metal flow in porthole dies to produce tubular profiles. However, in industrial extrusion practice, the cross-section shapes encountered are much more complex than square and round hollow shapes and, in turn, the metal flow through industrial hollow dies are far more complex. In these cases, the design and correction of complex hollow dies still rely on the experience of the die designer/corrector. When flow non-uniformity occurs, a number of die correction and testing cycles are needed until the shape and dimensions of the extruded profile meet the specifications of the product. The present study attempted to address an industrial problem encountered in the production of a complex thin-walled hollow magnesium profile by means of FEM simulation. It was hoped that the recommendations made, based on the FEM analysis, could effectively reduce the number of die redesign-testing-correction cycles, thereby shortening the non-productive time of the extrusion press and the lead-time of the product.

Problem statement and FEM simulation details

Fig. 1 shows the cross-section of a multi-core hollow profile with a wall thickness of 1.5 mm. The problem encountered was that the wall thicknesses at some locations such as Zones I and II in Fig. 2 were smaller than the wall thickness in the customer specification, resulting in scrap. Moreover, the extent of wall-thickness attenuation varied. The wall thickness attenuation in Zone I was severer than in Zone II; the wall thickness attenuation in Zone I was 0.4 mm, while in Zone II it was 0.2 mm. It was required to identify the causes for the wall thickness attenuations and provide guidelines for modifying the die design so that a modified die could be put into use for defect-free profile manufacturing. FEM simulations of the extrusion process to produce this complex hollow profile were performed using a HyperWorks FEM software package. The models of one quarter of the billet and extrusion tooling were established and the symmetrical boundary conditions applied. A magnesium alloy (AZ61) billet with a diameter of 113 mm was preheated to 400 and extruded at a ram speed of 1 mm/s. To validate the predictions from numerical simulation, the predicted wall thickness attenuation of the profile was compared with the measurements taken from extrusion experiments under the conditions identical to those applied in three-dimensional numerical simulation.

Fig. 1: Cross-section of the multi-core hollow profile. Fig. 2 Profile with wall-thickness attenuations.

[5]. Mooi et al. [6] analyzed the extrusion process to produce circular tubes and calculated the deformation of the die. Kim et al. developed a modified porthole die for tube extrusion in order to obtain enhanced welding pressure relative to that of the original porthole die [7]. These preceding studies using FEM simulation have provided fundamentally important insights into the metal flow in porthole dies to produce tubular profiles. However, in industrial extrusion practice, the cross-section shapes encountered are much more complex than square and round hollow shapes and, in turn, the metal flow through industrial hollow dies are far more complex. In these cases, the design and correction of complex hollow dies still rely on the experience of the die designer/corrector. When flow non-uniformity occurs, a number of die correction and testing cycles are needed until the shape and dimensions of the extruded profile meet the specifications of the product. The present study attempted to address an industrial problem encountered in the production of a complex thin-walled hollow magnesium profile by means of FEM simulation. It was hoped that the recommendations made, based on the FEM analysis, could effectively reduce the number of die redesign-testing-correction cycles, thereby shortening the non-productive time of the extrusion press and the lead-time of the product.

Problem statement and FEM simulation details

Fig. 1 shows the cross-section of a multi-core hollow profile with a wall thickness of 1.5 mm. The problem encountered was that the wall thicknesses at some locations such as Zones I and II in Fig. 2 were smaller than the wall thickness in the customer specification, resulting in scrap. Moreover, the extent of wall-thickness attenuation varied. The wall thickness attenuation in Zone I was severer than in Zone II; the wall thickness attenuation in Zone I was 0.4 mm, while in Zone II it was 0.2 mm. It was required to identify the causes for the wall thickness attenuations and provide guidelines for modifying the die design so that a modified die could be put into use for defect-free profile manufacturing. FEM simulations of the extrusion process to produce this complex hollow profile were performed using a HyperWorks FEM software package. The models of one quarter of the billet and extrusion tooling were established and the symmetrical boundary conditions applied. A magnesium alloy (AZ61) billet with a diameter of 113 mm was preheated to 400 and extruded at a ram speed of 1 mm/s. To validate the predictions from numerical simulation, the predicted wall thickness attenuation of the profile was compared with the measurements taken from extrusion experiments under the conditions identical to those applied in three-dimensional numerical simulation.

Fig. 1: Cross-section of the multi-core hollow profile. Fig. 2 Profile with wall-thickness attenuations.


Analysis of metal flow and solutions to the problem

Fig. 3 shows the velocity distribution of metal flow through the complex hollow die in the extrusion direction. Velocity differences between various areas can be noticed. The metal in Area 1 flows faster than that in Area 2; the maximum velocity difference between Area 1 and 2 is more than 20 mm/s. Obviously, the non-uniformity of metal flow must be one of the causes for the wall thickness attenuations.

Fig. 3: Velocity distribution in the extrusion direction.

Fig. 4 shows the hydrostatic pressure distribution in the billet flowing through the hollow die, which seems to be quite uniform. However, a closer examination of the hydrostatic pressure shows marked differences in the area between the die cap and mandrels (Fig. 4) and inside the welding chamber (Fig. 5). Areas 1 and 2 have hydrostatic pressures lower than the other areas inside the welding chamber and, moreover, the hydrostatic pressure in Area 1 is 200 MPa higher than in the Area 2 (see Figs. 4 and 5). Fig. 6 presents the lateral displacements of Mandrels A and B due to bulging during extrusion. The data of lateral displacement were captured along the arrowed red lines A and B in Fig. 6a. The abscissa in Fig. 6b represents the height of the mandrels, starting from their bottom plane that is perpendicular to the red lines. As can be seen in Fig. 6b, Mandrels A and B are deformed only to very limited extents. The maximum lateral displacement of Mandrel A is 0.0055 mm, which is unlikely to be responsible for the wall thickness attenuation of the extrudate. Therefore, the combination of varied velocities and lower hydrostatic pressures in Areas 1 and 2 was thought to be the causes for the wall thickness attenuation.

Fig. 4: Hydrostatic pressure distribution in the billet.

Analysis of metal flow and solutions to the problem

Fig. 3 shows the velocity distribution of metal flow through the complex hollow die in the extrusion direction. Velocity differences between various areas can be noticed. The metal in Area 1 flows faster than that in Area 2; the maximum velocity difference between Area 1 and 2 is more than 20 mm/s. Obviously, the non-uniformity of metal flow must be one of the causes for the wall thickness attenuations.

Fig. 3: Velocity distribution in the extrusion direction.

Fig. 4 shows the hydrostatic pressure distribution in the billet flowing through the hollow die, which seems to be quite uniform. However, a closer examination of the hydrostatic pressure shows marked differences in the area between the die cap and mandrels (Fig. 4) and inside the welding chamber (Fig. 5). Areas 1 and 2 have hydrostatic pressures lower than the other areas inside the welding chamber and, moreover, the hydrostatic pressure in Area 1 is 200 MPa higher than in the Area 2 (see Figs. 4 and 5). Fig. 6 presents the lateral displacements of Mandrels A and B due to bulging during extrusion. The data of lateral displacement were captured along the arrowed red lines A and B in Fig. 6a. The abscissa in Fig. 6b represents the height of the mandrels, starting from their bottom plane that is perpendicular to the red lines. As can be seen in Fig. 6b, Mandrels A and B are deformed only to very limited extents. The maximum lateral displacement of Mandrel A is 0.0055 mm, which is unlikely to be responsible for the wall thickness attenuation of the extrudate. Therefore, the combination of varied velocities and lower hydrostatic pressures in Areas 1 and 2 was thought to be the causes for the wall thickness attenuation.

Fig. 4: Hydrostatic pressure distribution in the billet.


Fig. 5: Hydrostatic pressure distributions on different sections in the welding chamber.

5 10 15 20 25 300.000

0.001

0.002

0.003

0.004

0.005

0.006

Displacement (mm)

Height (mm)

Mandrel A Mandrel B

(a) (b)

Fig. 6: (a) One quarter of the porthole die and (b) lateral displacements of Mandrels A and B.

There are a number of known measures that may be take to lessen or eliminate non-uniform material flow during the extrusion process, including the modification of the shape, size and location of feeder ports and welding chamber and the adjustment of local bearing lengths. In the present research, two adjustments were made, namely (i) increasing the interspacing between the mandrels in order to balance the metal flow and hydrostatic pressure and (ii) increasing the height of the welding chamber so as to increase the hydrostatic pressure inside the welding chamber. Increasing the interspacing between Mandrels A and B was taken as the first measure to counteract the wall-thickness attenuation. As shown in Fig. 7, the interspacing between Mandrels A and B was adjusted from D1 to D2 with an increment of 2 mm. Fig. 8 shows the velocity distribution of metal flow through the modified porthole die in the extrusion direction. The maximum velocity difference between Areas 1 and 2 becomes less than 8 mm/s. Clearly, the decrease in velocity difference is beneficial to the balance of metal flowing. As shown in Fig. 9, the hydrostatic pressures in the interspacing between mandrels become more uniformly distributed, when compared with Fig. 4. The maximum difference in hydrostatic pressure in the area between the die cap and mandrel and inside

Section-1 Section-2

Section-9

....

Section-2

Section-7 Section-8 Section-9

2

1

A B

Fig. 5: Hydrostatic pressure distributions on different sections in the welding chamber.

5 10 15 20 25 300.000

0.001

0.002

0.003

0.004

0.005

0.006

Displacement (mm)

Height (mm)

Mandrel A Mandrel B

(a) (b)

Fig. 6: (a) One quarter of the porthole die and (b) lateral displacements of Mandrels A and B.

There are a number of known measures that may be take to lessen or eliminate non-uniform material flow during the extrusion process, including the modification of the shape, size and location of feeder ports and welding chamber and the adjustment of local bearing lengths. In the present research, two adjustments were made, namely (i) increasing the interspacing between the mandrels in order to balance the metal flow and hydrostatic pressure and (ii) increasing the height of the welding chamber so as to increase the hydrostatic pressure inside the welding chamber. Increasing the interspacing between Mandrels A and B was taken as the first measure to counteract the wall-thickness attenuation. As shown in Fig. 7, the interspacing between Mandrels A and B was adjusted from D1 to D2 with an increment of 2 mm. Fig. 8 shows the velocity distribution of metal flow through the modified porthole die in the extrusion direction. The maximum velocity difference between Areas 1 and 2 becomes less than 8 mm/s. Clearly, the decrease in velocity difference is beneficial to the balance of metal flowing. As shown in Fig. 9, the hydrostatic pressures in the interspacing between mandrels become more uniformly distributed, when compared with Fig. 4. The maximum difference in hydrostatic pressure in the area between the die cap and mandrel and inside

Section-1 Section-2

Section-9

....

Section-2

Section-7 Section-8 Section-9

2

1

A B


the welding chamber becomes less than 100 MPa, which is much lower than in the original die at the same location. Obviously, the smaller differences in hydrostatic pressure inside the welding chamber are favorable to balanced metal flow. Considering the improved uniformity of metal flow and hydrostatic pressure in the welding chamber, the extrudate with less wall-thickness attenuation can be expected.

Fig. 7: Modification of the interspacing between Mandrels A and B from D1 to D2

Fig. 8: Velocity distribution of the billet through the modified die with an increased interspacing

between Mandrels A and B (in the extrusion direction).

Fig. 9: Hydrostatic pressure distribution in the billet through the modified die with an increased

interspacing between Mandrels A and B.

1 2

the welding chamber becomes less than 100 MPa, which is much lower than in the original die at the same location. Obviously, the smaller differences in hydrostatic pressure inside the welding chamber are favorable to balanced metal flow. Considering the improved uniformity of metal flow and hydrostatic pressure in the welding chamber, the extrudate with less wall-thickness attenuation can be expected.

Fig. 7: Modification of the interspacing between Mandrels A and B from D1 to D2

Fig. 8: Velocity distribution of the billet through the modified die with an increased interspacing

between Mandrels A and B (in the extrusion direction).

Fig. 9: Hydrostatic pressure distribution in the billet through the modified die with an increased

interspacing between Mandrels A and B.

1 2


However, the increase of the interspacing between Mandrels A and B leads to a decrease in their thickness, which will in turn decrease the rigidity of the whole die. As shown in Fig. 10, with the interspacing between Mandrels A and B increased, the maximum lateral displacement of Mandrels A and B becomes approximately 0.015 mm, which is nearly 3 times as much as that of the original die. Therefore, this modification may negatively affect the rigidity of the die and its service life, even though the improved dimensional uniformity of the extruded product can be expected.

0 5 10 15 20 25 30

0.000

0.002

0.004

0.006

0.008

0.010

0.012Displacement (mm)

Height (mm)

Mandrel A Mandrel B

Fig. 10: Lateral displacements of Mandrels A and B in the modified die with an increased interspacing between Mandrels A and B. Increasing the height of the welding chamber was taken as the second measure to improve the flow uniformity. The height of the welding chamber was adjusted from H1 to H2 with an increment of 10 mm (see Fig. 11). The velocity distribution of metal flow in the extrusion direction is shown in Fig. 12. When the velocities in Areas 1 and 2 (Fig. 3) at the die exit are compared, far less differences can be noted, which means that metal flows more uniformly through the die exit. The maximum velocity difference is less than 10 mm/s. In addition, with the height of the welding chamber modified, the hydrostatic pressures inside the welding chamber as well as in the interspacing between Mandrels A and B become more uniform and higher than in the original die, as shown in Fig. 13. The hydrostatic pressure difference in the space between the die cap and the mandrels and inside the welding chamber is less than 80 MPa. As a result, the metal flow becomes better balanced under more uniform pressures in the welding chamber, as shown in Fig. 12.

(a) (b)

Fig. 11: Adjustment of the height of the welding chamber: (a) original die and (b) modified die.

H1 H2

However, the increase of the interspacing between Mandrels A and B leads to a decrease in their thickness, which will in turn decrease the rigidity of the whole die. As shown in Fig. 10, with the interspacing between Mandrels A and B increased, the maximum lateral displacement of Mandrels A and B becomes approximately 0.015 mm, which is nearly 3 times as much as that of the original die. Therefore, this modification may negatively affect the rigidity of the die and its service life, even though the improved dimensional uniformity of the extruded product can be expected.

0 5 10 15 20 25 30

0.000

0.002

0.004

0.006

0.008

0.010

0.012Displacement (mm)

Height (mm)

Mandrel A Mandrel B

Fig. 10: Lateral displacements of Mandrels A and B in the modified die with an increased interspacing between Mandrels A and B. Increasing the height of the welding chamber was taken as the second measure to improve the flow uniformity. The height of the welding chamber was adjusted from H1 to H2 with an increment of 10 mm (see Fig. 11). The velocity distribution of metal flow in the extrusion direction is shown in Fig. 12. When the velocities in Areas 1 and 2 (Fig. 3) at the die exit are compared, far less differences can be noted, which means that metal flows more uniformly through the die exit. The maximum velocity difference is less than 10 mm/s. In addition, with the height of the welding chamber modified, the hydrostatic pressures inside the welding chamber as well as in the interspacing between Mandrels A and B become more uniform and higher than in the original die, as shown in Fig. 13. The hydrostatic pressure difference in the space between the die cap and the mandrels and inside the welding chamber is less than 80 MPa. As a result, the metal flow becomes better balanced under more uniform pressures in the welding chamber, as shown in Fig. 12.

(a) (b)

Fig. 11: Adjustment of the height of the welding chamber: (a) original die and (b) modified die.

H1 H2


Fig. 12: Velocity distribution through the modified Fig. 13 Hydrostatic pressure distribution in the die with the welding chamber height increased. billet with the welding chamber height increased. Due to the increase in the height of the welding chamber, the contact area between the billet and die increased and thus the friction would rise, which would lead to an increase in extrusion pressure. Indeed, the peak extrusion load was found to increase by 500 KN, as shown in Fig. 14. It is believed that such a small increment of extrusion load will have little influence on the feasibility of extruding the alloy with the existing extrusion press and die assembly. Therefore, increasing the height of the welding chamber appears to be a viable solution to the problem of wall thickness attenuation during extrusion to produce a complex hollow magnesium profile.

0 10 20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

Load (KN)

Stroke (mm)

Original die Modified die

Fig. 14: Comparison of the loads during extrusion through the modified die and the original die.

Validation of simulation results

Fig. 15 shows the velocity distribution of metal flow in the extrusion direction at the die orifice. The average velocities in Areas 1 and 2 were calculated to be 9.04 mm/s and 12.89 mm/s, respectively. These velocity values are considerably lower than the velocity in the other area of the profile (23.46 mm/s). According to the principle of volume constancy, the wall thickness at the die exit S1 can be derived by using the following equation:

S0×v0 = S1×v1

where S0 is the wall thickness of the profile at the die orifice, which is 1.5 mm in the present study, and v0 and v1 are the average metal flow velocities in the extrusion direction at the die orifice and die exit , respectively. The predicted metal flow velocities and wall thicknesses and the measured wall thicknesses at Areas 1, 2 and 3 are presented in Table 1. The differences between the predicted and measured wall thicknesses in Areas 1 and 2 are no more than 7% and the agreement is considered quite good.

1 2

Fig. 12: Velocity distribution through the modified Fig. 13 Hydrostatic pressure distribution in the die with the welding chamber height increased. billet with the welding chamber height increased. Due to the increase in the height of the welding chamber, the contact area between the billet and die increased and thus the friction would rise, which would lead to an increase in extrusion pressure. Indeed, the peak extrusion load was found to increase by 500 KN, as shown in Fig. 14. It is believed that such a small increment of extrusion load will have little influence on the feasibility of extruding the alloy with the existing extrusion press and die assembly. Therefore, increasing the height of the welding chamber appears to be a viable solution to the problem of wall thickness attenuation during extrusion to produce a complex hollow magnesium profile.

0 10 20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

Load (KN)

Stroke (mm)

Original die Modified die

Fig. 14: Comparison of the loads during extrusion through the modified die and the original die.

Validation of simulation results

Fig. 15 shows the velocity distribution of metal flow in the extrusion direction at the die orifice. The average velocities in Areas 1 and 2 were calculated to be 9.04 mm/s and 12.89 mm/s, respectively. These velocity values are considerably lower than the velocity in the other area of the profile (23.46 mm/s). According to the principle of volume constancy, the wall thickness at the die exit S1 can be derived by using the following equation:

S0×v0 = S1×v1

where S0 is the wall thickness of the profile at the die orifice, which is 1.5 mm in the present study, and v0 and v1 are the average metal flow velocities in the extrusion direction at the die orifice and die exit , respectively. The predicted metal flow velocities and wall thicknesses and the measured wall thicknesses at Areas 1, 2 and 3 are presented in Table 1. The differences between the predicted and measured wall thicknesses in Areas 1 and 2 are no more than 7% and the agreement is considered quite good.

1 2


Fig. 15: Velocity distribution in the extrusion direction at the die orifice.

Table 1 The predicted metal flow velocity and wall thickness and measured wall thickness

Position Velocity/wall thickness Area 1 Area 2 Area 3

Average metal flow velocity at the die orifice [mm/s] 10 15.7 24 Average metal flow velocity at the die exit [mm/s] 14.6 18.4 24

Average predicted wall thickness [mm] 1.02 1.27 1.5 Average measured wall thickness [mm) 1.1 1.3 1.5

Summary

On the basis of FEM analysis, recommendations to adjust the interspacing between the mandrels and the height of the welding chamber were made. Both modifications yielded improved uniformity in metal flow and hydrostatic pressure distribution. However, increasing the interspacing between the mandrels may lead to a decreased die rigidity and service life. Increasing the height of the welding chamber appears to be a viable solution to the problem. FEM predicted profile wall thicknesses agreed with experimental measurements very well. The present case study demonstrates the feasibility of using FEM simulation as a useful tool to solve the practical problem encountered in the production of complex hollow profiles.

References

[1] R.S. Busk, Magnesium Products Design (Marcell Dekker, New York 1987) p.12.

[2] J.C. Tan and M.J. Tan, in: Proceedings of the Symposium on Materials and Science in Sports, edited by F.H. (Sam) Froes and S.J. Haake, TMS, Warrendale, PA (2001) p. 95.

[3] X.H. Wu, G.Q. Zhao, Y.G. Luan and X.W. Ma, Mater. Sci. Eng. A, Vol. 435–436 (2006) p.266.

[4] L. Li, et al., Mater. Des. Vol. 29 (2008) p. 1190.

[5] G. Liu, J. Zhou and J. Duszczyk, J. Mater. Process. Technol. Vol. 200 (2008) p. 185.

[6] H.G. Mooi, P.T.G. Koenis and J. Huetink, J. Mater. Process. Technol. Vol. 88 (1999) p.67.

[7] K.J. Kim, C.H. Lee and D.Y. Yang, J. Mater. Process. Technol. Vol. 130–131 (2002) p. 426.

1

2

3

Fig. 15: Velocity distribution in the extrusion direction at the die orifice.

Table 1 The predicted metal flow velocity and wall thickness and measured wall thickness

Position Velocity/wall thickness Area 1 Area 2 Area 3

Average metal flow velocity at the die orifice [mm/s] 10 15.7 24 Average metal flow velocity at the die exit [mm/s] 14.6 18.4 24

Average predicted wall thickness [mm] 1.02 1.27 1.5 Average measured wall thickness [mm) 1.1 1.3 1.5

Summary

On the basis of FEM analysis, recommendations to adjust the interspacing between the mandrels and the height of the welding chamber were made. Both modifications yielded improved uniformity in metal flow and hydrostatic pressure distribution. However, increasing the interspacing between the mandrels may lead to a decreased die rigidity and service life. Increasing the height of the welding chamber appears to be a viable solution to the problem. FEM predicted profile wall thicknesses agreed with experimental measurements very well. The present case study demonstrates the feasibility of using FEM simulation as a useful tool to solve the practical problem encountered in the production of complex hollow profiles.

References

[1] R.S. Busk, Magnesium Products Design (Marcell Dekker, New York 1987) p.12.

[2] J.C. Tan and M.J. Tan, in: Proceedings of the Symposium on Materials and Science in Sports, edited by F.H. (Sam) Froes and S.J. Haake, TMS, Warrendale, PA (2001) p. 95.

[3] X.H. Wu, G.Q. Zhao, Y.G. Luan and X.W. Ma, Mater. Sci. Eng. A, Vol. 435–436 (2006) p.266.

[4] L. Li, et al., Mater. Des. Vol. 29 (2008) p. 1190.

[5] G. Liu, J. Zhou and J. Duszczyk, J. Mater. Process. Technol. Vol. 200 (2008) p. 185.

[6] H.G. Mooi, P.T.G. Koenis and J. Huetink, J. Mater. Process. Technol. Vol. 88 (1999) p.67.

[7] K.J. Kim, C.H. Lee and D.Y. Yang, J. Mater. Process. Technol. Vol. 130–131 (2002) p. 426.

1

2

3


Manufacturing of Carbon/Resin Separator by Die Sliding Extrusion

M. Hoshino1,a and K. Suzuki2,b 1 Nihon University, College of Science and Technology, Department of Mechanical Engineering,

1-8-14, Surugadai, Kanda Chiyoda-ku, Tokyo, 101-8308 JAPAN 2 Graduate Student of Nihon University, ibid

[email protected], b [email protected]

Keywords: Die sliding extrusion, Fuel cell separator, Orthogonal channels. Abstract. A fuel cell will play a part of a module of power generator instead of an internal- combustion engine. It is required to improve the productivity and miniaturizing of the fuel cell. The separator in the fuel cell is an important part. The manufacturing process of carbon/resin separators usually is injection molding or compression forming. On the other hand, the authors have developed die sliding extrusion based on the friction extrusion [1] and side flow extrusion [2]. The die sliding extrusion is a kind of valuable shape extrusion [3,4]. It is applied to manufacturing fuel cell separators which have linear channels on its upper and lower surfaces in the orthogonal direction.

Introduction

The separator of the fuel cell is shaped something like a sheet which has usually different pattern surfaces in both sides. Because hydrogen gas is supplied in one side and oxygen gas is supplied in the other side. A model of the separator is shown in Figure 1. It has linear channels on its upper and lower surfaces, but the channels on the upper side are orthogonal to those on the underside. The configuration of the cross section in Fig. 2-(a) is different from that in Fig. 2-(b), illustrating that a separator with this geometry cannot be produced by conventional extrusion. In the case of manufacturing the carbon/resin separators as this figure by compression forming, there is sometimes incomplete filling in a watershed of the material flow. The authors therefore developed a new process for extrusion of a fuel cell separator with orthogonal channels.

Fig. 1: Model of separator

(a) With lower channel

(b) With lower protuberance

Fig. 2: Shape of cross section

(a) With lower channel (b) With lower protuberance

Manufacturing of Carbon/Resin Separator by Die Sliding Extrusion

M. Hoshino1,a and K. Suzuki2,b 1 Nihon University, College of Science and Technology, Department of Mechanical Engineering,

1-8-14, Surugadai, Kanda Chiyoda-ku, Tokyo, 101-8308 JAPAN 2 Graduate Student of Nihon University, ibid

[email protected], b [email protected]

Keywords: Die sliding extrusion, Fuel cell separator, Orthogonal channels. Abstract. A fuel cell will play a part of a module of power generator instead of an internal- combustion engine. It is required to improve the productivity and miniaturizing of the fuel cell. The separator in the fuel cell is an important part. The manufacturing process of carbon/resin separators usually is injection molding or compression forming. On the other hand, the authors have developed die sliding extrusion based on the friction extrusion [1] and side flow extrusion [2]. The die sliding extrusion is a kind of valuable shape extrusion [3,4]. It is applied to manufacturing fuel cell separators which have linear channels on its upper and lower surfaces in the orthogonal direction.

Introduction

The separator of the fuel cell is shaped something like a sheet which has usually different pattern surfaces in both sides. Because hydrogen gas is supplied in one side and oxygen gas is supplied in the other side. A model of the separator is shown in Figure 1. It has linear channels on its upper and lower surfaces, but the channels on the upper side are orthogonal to those on the underside. The configuration of the cross section in Fig. 2-(a) is different from that in Fig. 2-(b), illustrating that a separator with this geometry cannot be produced by conventional extrusion. In the case of manufacturing the carbon/resin separators as this figure by compression forming, there is sometimes incomplete filling in a watershed of the material flow. The authors therefore developed a new process for extrusion of a fuel cell separator with orthogonal channels.

Fig. 1: Model of separator

(a) With lower channel

(b) With lower protuberance

Fig. 2: Shape of cross section

(a) With lower channel (b) With lower protuberance


ew extrusion method

The new manufacturing process is illustrated in Figure 3. －The material is extruded from the inflow entrance in the upper part of the chamber towards the lower die (direction of the arrow) by the punch. The material to be processed is injected into the lower die and fills the chamber (Fig. 3-(a)). －After the material fills the chamber, it is injected into the channel part of the lower die and molded to its shape (Fig. 3-(b)). －Once the lower channel is filled, the channel is moved to the left as shown in the Figure. As a result, both upper and lower channels are molded (Fig. 3-(c)). The extrusion tool for manufacturing separators is shown in Figure 4. The separator is molded using three important tools: the container, upper die, and lower die. A brief description of the experimental device is provided in Figure 5. The experimental apparatus used for the actual experiment is a structure in which the extrusion tool for the separator is installed directly in the extrusion device. The extrusion device and the lower die are driven by a stepping motor.

An extrusion tool that provided two versions of the separator was then configured. An attachment was interpolated between the die and the container. As a result, the device with the attachment has a different configuration from that of the device without an attachment. The experimental device without the attachment is termed Version 1 (Fig. 6-(a)), and the device with the attachment is termed Version 2 (Fig. 6-(b)). The length of this attachment must be optimized because the distance L from the entrance of chamber to the exit of upper die is synchronized with the pitch of lower channel. It is

Fig. 3: New extrusion method

(a) Filling in channel

(b) Filling into lower slots (c) Extrusion from die with upper slots

Fig. 4: Extrusion tool for separator

Fig. 5: Experimental device

ew extrusion method

The new manufacturing process is illustrated in Figure 3. －The material is extruded from the inflow entrance in the upper part of the chamber towards the lower die (direction of the arrow) by the punch. The material to be processed is injected into the lower die and fills the chamber (Fig. 3-(a)). －After the material fills the chamber, it is injected into the channel part of the lower die and molded to its shape (Fig. 3-(b)). －Once the lower channel is filled, the channel is moved to the left as shown in the Figure. As a result, both upper and lower channels are molded (Fig. 3-(c)). The extrusion tool for manufacturing separators is shown in Figure 4. The separator is molded using three important tools: the container, upper die, and lower die. A brief description of the experimental device is provided in Figure 5. The experimental apparatus used for the actual experiment is a structure in which the extrusion tool for the separator is installed directly in the extrusion device. The extrusion device and the lower die are driven by a stepping motor.

An extrusion tool that provided two versions of the separator was then configured. An attachment was interpolated between the die and the container. As a result, the device with the attachment has a different configuration from that of the device without an attachment. The experimental device without the attachment is termed Version 1 (Fig. 6-(a)), and the device with the attachment is termed Version 2 (Fig. 6-(b)). The length of this attachment must be optimized because the distance L from the entrance of chamber to the exit of upper die is synchronized with the pitch of lower channel. It is

Fig. 3: New extrusion method

(a) Filling in channel

(b) Filling into lower slots (c) Extrusion from die with upper slots

Fig. 4: Extrusion tool for separator

Fig. 5: Experimental device


suitable in the case that the fluctuation volume of chamber in processing of the extrusion is minimized [5]. The following is the result of experiment by using Version 2.

Experiment for forming shapes by using coloured clay

In experiments, coloured clay is used as a billet. This is similar to the actual material, which is carbon powder combined with phenolic resin. In extrusions carried out to observe the external shape of a product, the billet is white (Fig. 7). Figure 8 shows the size of employed product. In this experiment, the punch speed is constant. The lower die speed is the variable parameter. The internal flow of product was then observed. The experimental conditions are shown below in Table 1. The velocity ratio is

1

2

VV

R v =

Relation between state of extruded product and Rv Successful, waving, and incomplete filling results are shown in Fig. 9. For these conditions in Version 2, successful examples are shown in Table 2.

Lower die Exit of upper die Entrance of chamber

Upper die Spacer Container

Fig. 6: Two configurations of the experimental device

(b) Version 2 (a) Version 1

Fig. 8 Size of employed product Fig. 7 Billet of experimental material

(a) Front view

(1)

Lower protuberance

(b) Side view

Base

0.7

W ith lower protuberance 8.0

W ithout lower protuberance 13.3

6.5～10.5

Punch Speed V1 [m m /s]Extrusion Ratio

Ratio of velocity Rv [-]Table1 Conditions of experiment

.

suitable in the case that the fluctuation volume of chamber in processing of the extrusion is minimized [5]. The following is the result of experiment by using Version 2.

Experiment for forming shapes by using coloured clay

In experiments, coloured clay is used as a billet. This is similar to the actual material, which is carbon powder combined with phenolic resin. In extrusions carried out to observe the external shape of a product, the billet is white (Fig. 7). Figure 8 shows the size of employed product. In this experiment, the punch speed is constant. The lower die speed is the variable parameter. The internal flow of product was then observed. The experimental conditions are shown below in Table 1. The velocity ratio is

1

2

VV

R v =

Relation between state of extruded product and Rv Successful, waving, and incomplete filling results are shown in Fig. 9. For these conditions in Version 2, successful examples are shown in Table 2.

Lower die Exit of upper die Entrance of chamber

Upper die Spacer Container

Fig. 6: Two configurations of the experimental device

(b) Version 2 (a) Version 1

Fig. 8 Size of employed product Fig. 7 Billet of experimental material

(a) Front view

(1)

Lower protuberance

(b) Side view

Base

0.7

W ith lower protuberance 8.0

W ithout lower protuberance 13.3

6.5～10.5

Punch Speed V1 [m m /s]Extrusion Ratio

Ratio of velocity Rv [-]Table1 Conditions of experiment

.


In Fig. 9-(a), the lower protuberance is cut off from the base of separator and the thickness of the base is more than the width of die exit. Ratio of velocity Rv 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 Shape of product overfilling Good unfilling

Experiment of carbon/resin separators

In experiments, the volume ratio of carbon powder (average diameter 5 micro meters) is 62% and the remnant is resin. At the first, the length of die is 20mm and extrusion temperature is room temperature. Figure 10 shows the upper protuberance of extruded products. The product in Fig. 10-(a) looks like good but the width of its upper protuberance is less than 1.0mm. Figure 11 shows the cross section of extruded product.

Table 2: Experimental results as formed shapes

(a) Overfilling (b) Unfilling

Fig. 9 Result of forming shape

(c) Good condition

Fig. 10: Aspect of extruded product

(a) Rv = 9.0 (b) Rv = 10.0

Fig. 11: Cross section of product

(a) Rv=10.0 (b) Rv=9.0

(c) Rv=8.0 (d) Rv=7.0

In Fig. 9-(a), the lower protuberance is cut off from the base of separator and the thickness of the base is more than the width of die exit. Ratio of velocity Rv 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 Shape of product overfilling Good unfilling

Experiment of carbon/resin separators

In experiments, the volume ratio of carbon powder (average diameter 5 micro meters) is 62% and the remnant is resin. At the first, the length of die is 20mm and extrusion temperature is room temperature. Figure 10 shows the upper protuberance of extruded products. The product in Fig. 10-(a) looks like good but the width of its upper protuberance is less than 1.0mm. Figure 11 shows the cross section of extruded product.

Table 2: Experimental results as formed shapes

(a) Overfilling (b) Unfilling

Fig. 9 Result of forming shape

(c) Good condition

Fig. 10: Aspect of extruded product

(a) Rv = 9.0 (b) Rv = 10.0

Fig. 11: Cross section of product

(a) Rv=10.0 (b) Rv=9.0

(c) Rv=8.0 (d) Rv=7.0


0.00.51.01.52.02.56.0 7.0 8.0 9.0 10.0Ratio of Velocity Rv [-]Ratio of Velocity Rv [-]Ratio of Velocity Rv [-]Ratio of Velocity Rv [-]Size of produ

ct [mm]Size of product [mm]Size of product [mm]Size of product [mm] Thickness of baseWidth of upper protuberanceHeight of upper protuberance

In Fig. 11-(a), ratio of velocity Rv is too high not to form the upper protuberances. On the other hand, the width of upper protuberance and the thickness of base are more than target value in Fig. 11-(d). Figure 12 shows the size of the protuberances and the base. The ratio of velocity Rv is the higher, the thickness of the base and the size of the protuberance are decreasing. In case that Rv is too low, the velocity of extruded product is faster than the velocity of lower die and excess of material in the chamber is extruded into the base of separator. In this case, the length of the upper die is too long and the material stays at the surface of the upper die. The upper die is changed for the die with short length in order to decrease the friction between the material and the die. Figure 13 shows the result by using the die whose length is 2mm. The width and height of the upper protuberance are slightly decreasing in consequence of higher ratio of velocity. But the thickness of base approaches the target value in case that Rv is equal to 9.0. Supposing that the material is incompressible fluid without the phase transition and the material dose not leak out from a gap except for die exit, the ideal ratio of velocity is 10.65. In this experimental equipment, there are some gaps between tools. Therefore, the suitable ratio of velocity becomes nearly 9.0.

Fig. 12: Relation between Rv and sizes of each part (length of the upper die=20mm)

0.00.51.01.52.0

6.0 7.0 8.0 9.0 10.0 11.0Ratio of velocity ＲRatio of velocity ＲRatio of velocity ＲRatio of velocity Ｒｖｖｖｖ [-] [-] [-] [-]Size of product [mm]Size of product [mm]Size of product [mm]Size of product [mm]

Thickness of baseWidth of upperprotuberanceHeight of upperprotuberanceTarget value


0.00.51.01.52.02.56.0 7.0 8.0 9.0 10.0Ratio of Velocity Rv [-]Ratio of Velocity Rv [-]Ratio of Velocity Rv [-]Ratio of Velocity Rv [-]Size of produ

ct [mm]Size of product [mm]Size of product [mm]Size of product [mm] Thickness of baseWidth of upper protuberanceHeight of upper protuberance

In Fig. 11-(a), ratio of velocity Rv is too high not to form the upper protuberances. On the other hand, the width of upper protuberance and the thickness of base are more than target value in Fig. 11-(d). Figure 12 shows the size of the protuberances and the base. The ratio of velocity Rv is the higher, the thickness of the base and the size of the protuberance are decreasing. In case that Rv is too low, the velocity of extruded product is faster than the velocity of lower die and excess of material in the chamber is extruded into the base of separator. In this case, the length of the upper die is too long and the material stays at the surface of the upper die. The upper die is changed for the die with short length in order to decrease the friction between the material and the die. Figure 13 shows the result by using the die whose length is 2mm. The width and height of the upper protuberance are slightly decreasing in consequence of higher ratio of velocity. But the thickness of base approaches the target value in case that Rv is equal to 9.0. Supposing that the material is incompressible fluid without the phase transition and the material dose not leak out from a gap except for die exit, the ideal ratio of velocity is 10.65. In this experimental equipment, there are some gaps between tools. Therefore, the suitable ratio of velocity becomes nearly 9.0.


0.00.51.01.52.0

6.0 7.0 8.0 9.0 10.0 11.0Ratio of velocity ＲRatio of velocity ＲRatio of velocity ＲRatio of velocity Ｒｖｖｖｖ [-] [-] [-] [-]Size of product [mm]Size of product [mm]Size of product [mm]Size of product [mm]

Thickness of baseWidth of upperprotuberanceHeight of upperprotuberanceTarget value



Fig. 14: Volume Resistibility

Ratio of velocity RV [-]

Vol

ume

resi

stib

ility

ρv

[Ω・

]

2030405060708090

6.0 7.0 8.0 9.0 10.0

The requirement for the separator is mechanical strength and low electrical resistibility. Figure 14 shows relation between volume resistibility and ratio of velocity. The volume resistibility is increasing in consequence of higher ratio of velocity. The ratio of velocity is the lower, the hydrostatic pressure in the chamber is the higher. In case that the hydrostatic pressure is high, the resin is squeezed from the material which is the composite of carbon/resin. The volume ratio of carbon in the extruded product may be more than one of the material (62 vol%).

Summary

It is success that the carbon/resin separator for fuel cell is made by the die sliding extrusion. The basic characteristic of this process is investigated. The important factors of the die sliding extrusion are the ratio of velocity and the length of the upper die. The volume electric resistibility has relation to the ratio of velocity because the hydrostatic pressure in the chamber is increasing in inverse proportion as the ratio of velocity is increasing.

Acknowledgements

The experiments in this report are achieved with the support of T. Kojima and A. Yamamoto, who are a graduate student and a bachelor student.

References

[1] T. Nakamura, M. Hiraiwa, H. Imaizumi, “Development of Friction-Assisted Extrusion Process for Producing Thin Metal Strips”, JSME Int. Journal. Ser. C. Mech. Systems, Mach. Elem. Manuf., vol.38 no.1(1995) pp. 143-148;

[2] K. Shinozaki, “Further investigation of cold lateral extrusion to form staggered branches from a cylindrical billet”, CIRP Ann., vol.38 No.1 (1989) pp.253-256.

[3] M.Kato, “The Technical Introduction Regarding One Method of Variable Section Extrusion”, Aluminum(in Japanese), vol.5 No.25(1998), pp.164-168.

[4] K.Hasegawa, M.Murata, “Extrusion with Changing Cross Section Shape of Tube”, Advanced Technology of Plasticity 1999, vol.3(1999), pp.677-680.

[5] Y.Suzuki, M.Hoshino, Y. Uchida, “A new extrusion technique for manufacturing fuel cell separators with orthogonal channels”, 9th International Conference on Technology of Plasticity, vol.1(2008), pp.153-154.

Fig. 14: Volume Resistibility

Ratio of velocity RV [-]

Vol

ume

resi

stib

ility

ρv

[Ω・

]

2030405060708090

6.0 7.0 8.0 9.0 10.0

The requirement for the separator is mechanical strength and low electrical resistibility. Figure 14 shows relation between volume resistibility and ratio of velocity. The volume resistibility is increasing in consequence of higher ratio of velocity. The ratio of velocity is the lower, the hydrostatic pressure in the chamber is the higher. In case that the hydrostatic pressure is high, the resin is squeezed from the material which is the composite of carbon/resin. The volume ratio of carbon in the extruded product may be more than one of the material (62 vol%).

Summary

It is success that the carbon/resin separator for fuel cell is made by the die sliding extrusion. The basic characteristic of this process is investigated. The important factors of the die sliding extrusion are the ratio of velocity and the length of the upper die. The volume electric resistibility has relation to the ratio of velocity because the hydrostatic pressure in the chamber is increasing in inverse proportion as the ratio of velocity is increasing.

Acknowledgements

The experiments in this report are achieved with the support of T. Kojima and A. Yamamoto, who are a graduate student and a bachelor student.

References

[1] T. Nakamura, M. Hiraiwa, H. Imaizumi, “Development of Friction-Assisted Extrusion Process for Producing Thin Metal Strips”, JSME Int. Journal. Ser. C. Mech. Systems, Mach. Elem. Manuf., vol.38 no.1(1995) pp. 143-148;

[2] K. Shinozaki, “Further investigation of cold lateral extrusion to form staggered branches from a cylindrical billet”, CIRP Ann., vol.38 No.1 (1989) pp.253-256.

[3] M.Kato, “The Technical Introduction Regarding One Method of Variable Section Extrusion”, Aluminum(in Japanese), vol.5 No.25(1998), pp.164-168.

[4] K.Hasegawa, M.Murata, “Extrusion with Changing Cross Section Shape of Tube”, Advanced Technology of Plasticity 1999, vol.3(1999), pp.677-680.

[5] Y.Suzuki, M.Hoshino, Y. Uchida, “A new extrusion technique for manufacturing fuel cell separators with orthogonal channels”, 9th International Conference on Technology of Plasticity, vol.1(2008), pp.153-154.


Prediction of the extrusion load and exit temperature using

artificial neural networks based on FEM simulation

J. Zhou1,2,a, L. Li1,2,b, J. Mo1,2,c, J. Zhou3,d and J. Duszczyk3,e

1State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Changsha, China

2College of Materials Science and Engineering, Hunan University, Changsha, China

3Department of Materials Science and Engineering, Delft University of Technology, The Netherlands


Keywords: FEM simulation; Artificial neural network; Extrusion; Magnesium

Abstract. In the present study, the extrusion process for the AZ31B magnesium alloy was simulated

using a DEFORM-3D software package to establish a database in order to provide input data for

artificial neural networks (ANN). The network model was trained by taking extrusion ratio, ram

speed, shape complexity and ram displacement as the input variables and the extrusion load and exit

temperature as the output parameters. The data from FEM simulations were submitted for ANN as a

training file and then ANN built were used to predict the target parameters. The ANN predicted

results were found to be in agreement with the FEM simulated and experimental measured ones.

Introduction

Fast and accurate prediction of the extrusion load and exit temperature is of practical importance

in choosing extrusion press, designing extrusion die and selecting extrusion process parameters.

There are a number of well-established methods that can be used to estimate the extrusion load and

exit temperature, for example, through theoretical analysis, empirical equations and nomography.

However, these conventional methods offer limited efficiency and accuracy in dealing with the

extrusion process involving multiple, interacting parameters.

The artificial neural networks (ANN) learn from past experience and make predictions on the basis

of experiences. By adjusting the network weight of each layer in the backward manner, ideally, the

output value should be quite close to the target value. This method has, to a very limited extent, been

used to predict the process parameters that are dependent on the input parameters in the case of metal

extrusion involving multiple, interacting parameters. Hsiang and Kuo [1-2], for example,

successfully built ANN to learn from the results of extrusion experiments to forecast the timing of

adjusting the initial extrusion speed and to correlate the billet temperature with the tensile strength of

an extruded magnesium alloy. The approach of using experimental results as training data to

implementing ANN is, however, rather costly and time-consuming.

The present study aimed at developing an alternative approach to predicting the extrusion load and

exit temperature of the extrusion process by using ANN based on FEM simulation results. The main

focus was placed on the effect of the shape complexity of the extruded profile on the extrusion load

and exit temperature.

Across the metal extrusion industry, there are almost uncountable shapes of extruded profiles. A

universally understood and accepted definition of shape complexity applicable to a wide range of

extruded profiles does not exist. As a result, the extrusion load predicted is valid only for one

particular extruded profile shape and any extension of the prediction to another shape needs careful

adjustment; otherwise, the prediction will entail a certain degree of uncertainty [3-6]. Qamar [7]

introduced a new definition of shape complexity of extruded profiles:

Prediction of the extrusion load and exit temperature using

artificial neural networks based on FEM simulation

J. Zhou1,2,a, L. Li1,2,b, J. Mo1,2,c, J. Zhou3,d and J. Duszczyk3,e

1State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Changsha, China

2College of Materials Science and Engineering, Hunan University, Changsha, China

3Department of Materials Science and Engineering, Delft University of Technology, The Netherlands


Keywords: FEM simulation; Artificial neural network; Extrusion; Magnesium

Abstract. In the present study, the extrusion process for the AZ31B magnesium alloy was simulated

using a DEFORM-3D software package to establish a database in order to provide input data for

artificial neural networks (ANN). The network model was trained by taking extrusion ratio, ram

speed, shape complexity and ram displacement as the input variables and the extrusion load and exit

temperature as the output parameters. The data from FEM simulations were submitted for ANN as a

training file and then ANN built were used to predict the target parameters. The ANN predicted

results were found to be in agreement with the FEM simulated and experimental measured ones.

Introduction

Fast and accurate prediction of the extrusion load and exit temperature is of practical importance

in choosing extrusion press, designing extrusion die and selecting extrusion process parameters.

There are a number of well-established methods that can be used to estimate the extrusion load and

exit temperature, for example, through theoretical analysis, empirical equations and nomography.

However, these conventional methods offer limited efficiency and accuracy in dealing with the

extrusion process involving multiple, interacting parameters.

The artificial neural networks (ANN) learn from past experience and make predictions on the basis

of experiences. By adjusting the network weight of each layer in the backward manner, ideally, the

output value should be quite close to the target value. This method has, to a very limited extent, been

used to predict the process parameters that are dependent on the input parameters in the case of metal

extrusion involving multiple, interacting parameters. Hsiang and Kuo [1-2], for example,

successfully built ANN to learn from the results of extrusion experiments to forecast the timing of

adjusting the initial extrusion speed and to correlate the billet temperature with the tensile strength of

an extruded magnesium alloy. The approach of using experimental results as training data to

implementing ANN is, however, rather costly and time-consuming.

The present study aimed at developing an alternative approach to predicting the extrusion load and

exit temperature of the extrusion process by using ANN based on FEM simulation results. The main

focus was placed on the effect of the shape complexity of the extruded profile on the extrusion load

and exit temperature.

Across the metal extrusion industry, there are almost uncountable shapes of extruded profiles. A

universally understood and accepted definition of shape complexity applicable to a wide range of

extruded profiles does not exist. As a result, the extrusion load predicted is valid only for one

particular extruded profile shape and any extension of the prediction to another shape needs careful

adjustment; otherwise, the prediction will entail a certain degree of uncertainty [3-6]. Qamar [7]

introduced a new definition of shape complexity of extruded profiles:


1.5

0

0.95 0.05 SPC

P

（1）

where C is the complexity index, PS is the perimeter of an extruded section and P0 is the perimeter of

a round shape with the same cross-sectional area as the extruded section. This definition of shape

complexity of extruded profiles was applied in the present study.

In the present study, the extrusion process for a magnesium alloy was simulated using a

DEFORM-3D software package to establish a database and to provide input data for ANN. The

database established included the material type, extrusion ratio, extruded profile type (solid, hollow

and semi-hollow), shape complexity, die half angle, billet temperature, extrusion speed, tooling

temperature, etc. The main variable selected in the study was the shape complexity of the extruded

profile. A back-propagation (BP) Artificial Neural Network (ANN) was developed based on the

MATLAB platform.

Simulation details

The material of the billet used in FEM simulation was a wrought magnesium alloy, AZ31B, which

was considered thermo-viscoplastic. The flow stresses of the AZ31B alloy were obtained from hot

compression tests over wide ranges of temperatures and strain rates [8]. The flow stresses were

corrected for temperature rise during compression tests at high strain rates.

Fig. 1 presents the cross sections of the representative profiles studied, namely, a round bar, an H

shape, two U shapes, a strip and a cross shape. For a given billet diameter, these profiles

corresponded to different extrusion ratios, wall thicknesses and shape complexities. The extrusion

tooling, comprised of container, die and stem whose sizes are given in Table 1, was made of the H13

hot-work tool steel and considered thermo-rigid in FEM simulation.

a b c

d e f

Fig. 1: Cross sections of the profiles studied: (a) a round bar, (b) an H shape, (c) a complex H shape,

(d) a U shape, (e) a strip and (f) a cross shape.

Table 1 Dimensions of the billet, die and other extrusion tooling

Billet [mm] Dia. 120 × 280

Container [mm] Internal dia. 125 × 300

Stem [mm] Dia. 125 × 10

Die [mm] Dia. 135 × 30

The friction between the billet and extrusion tooling was assumed to be of shear type. The friction

coefficient at the billet/tooling interfaces was assumed to be a constant value of 1. The extrusion

parameters used in FEM simulation are given in Table 2.

1.5

0

0.95 0.05 SPC

P

（1）

where C is the complexity index, PS is the perimeter of an extruded section and P0 is the perimeter of

a round shape with the same cross-sectional area as the extruded section. This definition of shape

complexity of extruded profiles was applied in the present study.

In the present study, the extrusion process for a magnesium alloy was simulated using a

DEFORM-3D software package to establish a database and to provide input data for ANN. The

database established included the material type, extrusion ratio, extruded profile type (solid, hollow

and semi-hollow), shape complexity, die half angle, billet temperature, extrusion speed, tooling

temperature, etc. The main variable selected in the study was the shape complexity of the extruded

profile. A back-propagation (BP) Artificial Neural Network (ANN) was developed based on the

MATLAB platform.

Simulation details

The material of the billet used in FEM simulation was a wrought magnesium alloy, AZ31B, which

was considered thermo-viscoplastic. The flow stresses of the AZ31B alloy were obtained from hot

compression tests over wide ranges of temperatures and strain rates [8]. The flow stresses were

corrected for temperature rise during compression tests at high strain rates.

Fig. 1 presents the cross sections of the representative profiles studied, namely, a round bar, an H

shape, two U shapes, a strip and a cross shape. For a given billet diameter, these profiles

corresponded to different extrusion ratios, wall thicknesses and shape complexities. The extrusion

tooling, comprised of container, die and stem whose sizes are given in Table 1, was made of the H13

hot-work tool steel and considered thermo-rigid in FEM simulation.

a b c

d e f

Fig. 1: Cross sections of the profiles studied: (a) a round bar, (b) an H shape, (c) a complex H shape,

(d) a U shape, (e) a strip and (f) a cross shape.

Table 1 Dimensions of the billet, die and other extrusion tooling

Billet [mm] Dia. 120 × 280

Container [mm] Internal dia. 125 × 300

Stem [mm] Dia. 125 × 10

Die [mm] Dia. 135 × 30

The friction between the billet and extrusion tooling was assumed to be of shear type. The friction

coefficient at the billet/tooling interfaces was assumed to be a constant value of 1. The extrusion

parameters used in FEM simulation are given in Table 2.


Table 2 Extrusion process parameters

Billet temperature [0C] 350

Stem temperature [0C] 350

Die and container temperature [0C] 320

Ram speed [mm/s] 1, 2, 4

Parameter setting for ANN

During the hot extrusion process, the major variables that affect the extrusion load and exit

temperature are extrusion ratio, ram speed, shape complexity and initial billet temperature. In the

present study, extrusion ratio, ram speed and shape complexity were chosen as the input data for

ANN, and the output data included the extrusion load and exit temperature. The results obtained from

FEM simulations of extrusion under different conditions were complied as training examples for

ANN to learn from. In the present paper, two cases are presented. In Case I, extrusion ratio and ram

speed remained unchanged, being 26.4 and 2 mm/s, respectively (Table 3), while the shape

complexity index varied from 1 to 1.45. Twelve runs of extrusion were simulated, covering the cross

sections of the profiles studied (Fig. 1). The major objective of this case study was to determine the

effect of the profile shape complexity on the extrusion load and exit temperature.

Table 3 Case 1 to determine the effect of the profile shape complexity on the extrusion load and exit

temperature

Profile No. Cross section Shape complexity

1 Round bar 1.00

2 H shape-1 1.04

3 H shape-2 1.31

4 H shape-3 1.36

5 H shape-4 1.45

6 Complex H shape 1.38

7 U shape-1 1.16

8 Cross shape-1 1.03



11 Strip 1 1.12

12 Strip 2 1.23

In Case II, combinations of extrusion ratio, shape complexity and ram speed were considered as

variables. As shown in Table 4, each set of extrusion runs had three variable values. For instance,

extrusion ratio had three values, namely, 8.1, 17.4 and 26.4. Twenty-seven extrusion runs were

simulated. In this case study, the focus was placed on determining the effects of extrusion ratio, ram

speed and shape complexity on the extrusion load and exit temperature.

Artificial neural networks learn from past experience and reach new findings. The ANN structure

is a three-layer feed forward network consisting of an input layer, a hidden layer and an output layer.

In the network, the data are fed forward into the network without feedback, all links between neurons

are unidirectional and there are no neuron-to-neuron connections in the same layer. Unlike the

neurons of the input layer, the neurons of the hidden layer and output layer possess computational

property. The back-propagation (BP) learning algorithm is based on searching an error surface using

gradient descent for a point with minimum error. Adjusting the network weight of each layer in the

backward manner, the output value should be close to the target value. In the present study, as shown

in Fig. 2, the network model for the prediction of the extrusion load and exit temperature contained



Stem temperature [0C] 350

Die and container temperature [0C] 320

Ram speed [mm/s] 1, 2, 4

Parameter setting for ANN

During the hot extrusion process, the major variables that affect the extrusion load and exit

temperature are extrusion ratio, ram speed, shape complexity and initial billet temperature. In the

present study, extrusion ratio, ram speed and shape complexity were chosen as the input data for

ANN, and the output data included the extrusion load and exit temperature. The results obtained from

FEM simulations of extrusion under different conditions were complied as training examples for

ANN to learn from. In the present paper, two cases are presented. In Case I, extrusion ratio and ram

speed remained unchanged, being 26.4 and 2 mm/s, respectively (Table 3), while the shape

complexity index varied from 1 to 1.45. Twelve runs of extrusion were simulated, covering the cross

sections of the profiles studied (Fig. 1). The major objective of this case study was to determine the

effect of the profile shape complexity on the extrusion load and exit temperature.

Table 3 Case 1 to determine the effect of the profile shape complexity on the extrusion load and exit

temperature

Profile No. Cross section Shape complexity

1 Round bar 1.00

2 H shape-1 1.04

3 H shape-2 1.31

4 H shape-3 1.36

5 H shape-4 1.45

6 Complex H shape 1.38

7 U shape-1 1.16




11 Strip 1 1.12

12 Strip 2 1.23

In Case II, combinations of extrusion ratio, shape complexity and ram speed were considered as

variables. As shown in Table 4, each set of extrusion runs had three variable values. For instance,

extrusion ratio had three values, namely, 8.1, 17.4 and 26.4. Twenty-seven extrusion runs were

simulated. In this case study, the focus was placed on determining the effects of extrusion ratio, ram

speed and shape complexity on the extrusion load and exit temperature.

Artificial neural networks learn from past experience and reach new findings. The ANN structure

is a three-layer feed forward network consisting of an input layer, a hidden layer and an output layer.

In the network, the data are fed forward into the network without feedback, all links between neurons

are unidirectional and there are no neuron-to-neuron connections in the same layer. Unlike the

neurons of the input layer, the neurons of the hidden layer and output layer possess computational

property. The back-propagation (BP) learning algorithm is based on searching an error surface using

gradient descent for a point with minimum error. Adjusting the network weight of each layer in the

backward manner, the output value should be close to the target value. In the present study, as shown

in Fig. 2, the network model for the prediction of the extrusion load and exit temperature contained


four neurons in the input layer, nine neurons in the hidden layer and two neurons in the output layer.

The network model was trained by taking extrusion ratio, ram speed, shape complexity and ram

displacement (stroke) as the input variables. The extrusion load and exit temperature were yielded as

the output parameters.

Table 4 Case II to determine the effects of extrusion ratio, ram speed and shape complexity on the

extrusion load and exit temperature

Extrusion ratio Cross sectional area [mm2] Cross section of profile Shape complexity index

8.1 1520 Round bar-1 1.00

Cross shape-1 1.22

H shape-1 1.36

17.4 706.9 Round bar-2 1.00

Cross shape-2 1.22

H shape-2 1.36

26.4 464 Round bar-3 1.00

Cross shape-3 1.22

H shape-3 1.36

Fig. 2: ANN for the prediction of the extrusion load and exit temperature.


Effect of profile shape complexity on the extrusion load and exit temperature. The whole cycle

of the extrusion run was simulated by using a DEFORM-3D software package. Fig. 3 shows the

results of the simulation of the extrusion processes at an extrusion ratio of 8.1, a ram speed of 1 mm/s

and various profile shape complexity index values (Eq. 1). It can be seen that the extrusion load

increases with increasing shape complexity at the transient extrusion stage as well as at the

steady-state extrusion stage. Fig. 3b shows the evolutions of the exit temperature at various C values.

It can be seen that the exit temperature increases rapidly when ram displacement reaches 25 mm, due

to the establishment of an intensive deformation zone in front of the die opening, leading to

deformational heating. In addition, the extent of the exit temperature increase increases with

increasing shape complexity. In other words, when the shape complexity is greater, more

deformational heat is generated, which cannot dissipate within a short period of time, leading to the

increase of the exit temperature.

four neurons in the input layer, nine neurons in the hidden layer and two neurons in the output layer.

The network model was trained by taking extrusion ratio, ram speed, shape complexity and ram

displacement (stroke) as the input variables. The extrusion load and exit temperature were yielded as

the output parameters.

Table 4 Case II to determine the effects of extrusion ratio, ram speed and shape complexity on the

extrusion load and exit temperature

Extrusion ratio Cross sectional area [mm2] Cross section of profile Shape complexity index

8.1 1520 Round bar-1 1.00

Cross shape-1 1.22

H shape-1 1.36

17.4 706.9 Round bar-2 1.00

Cross shape-2 1.22

H shape-2 1.36

26.4 464 Round bar-3 1.00

Cross shape-3 1.22

H shape-3 1.36

Fig. 2: ANN for the prediction of the extrusion load and exit temperature.


Effect of profile shape complexity on the extrusion load and exit temperature. The whole cycle

of the extrusion run was simulated by using a DEFORM-3D software package. Fig. 3 shows the

results of the simulation of the extrusion processes at an extrusion ratio of 8.1, a ram speed of 1 mm/s

and various profile shape complexity index values (Eq. 1). It can be seen that the extrusion load

increases with increasing shape complexity at the transient extrusion stage as well as at the

steady-state extrusion stage. Fig. 3b shows the evolutions of the exit temperature at various C values.

It can be seen that the exit temperature increases rapidly when ram displacement reaches 25 mm, due

to the establishment of an intensive deformation zone in front of the die opening, leading to

deformational heating. In addition, the extent of the exit temperature increase increases with

increasing shape complexity. In other words, when the shape complexity is greater, more

deformational heat is generated, which cannot dissipate within a short period of time, leading to the

increase of the exit temperature.


0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000L

oad

(K

N)

Stroke (mm)

C =1.00

C =1.22

C =1.36

0 50 100 150 200 250340

350

360

370

380

390

400

410

420

430

440

Exit

Tem

per

ature

(

)

Stroke (mm)

C =1.00

C =1.22

C =1.36

(a) (b)

Fig. 3: Extrusion at an extrusion ratio of 8.1, a ram speed of 1 mm/s and various shape complexity

index values: (a) the extrusion load and (b) the exit temperature.

Comparison between FEM simulation and ANN. The data obtained from the FEM simulations

were submitted for ANN learning. In Case I, extrusion ratio and ram speed were 26.4 and 2 mm/s,

respectively. The input data of ANN were composed of extrusion ratio, ram speed, shape complexity

and ram displacement. The extrusion load and exit temperature were reached as the output data of

ANN. The shape complexity index values as the input data of ANN ranged from 1 to 1.45. Among the

results obtained from the simulations of the twelve extrusion runs with different shape complexity

index values, eleven were input as the training file to build ANN. With the networks built, the

extrusion load and exit temperature of the extrusion run at a shape complexity index of 1.03, which

was not included in the training file, were predicted. As can be seen in Fig. 4, the ANN predicted

results are in agreement with the FEM simulated ones.

0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000

8000

Lo

ad

(K

N)

Stroke (mm)

Simulation

Prediction

0 50 100 150 200 250300

320

340

360

380

400

420

440

460

480

Simulation

Prediction

Ex

it T

emp

erat

ure

(

)

Stroke (mm)

(a) (b)

Fig. 4: Comparison between the ANN predicted and FEM simulated results of the extrusion run at an

extrusion ratio of 26.4, a ram speed of 2 mm/s and a shape complexity index of 1.03: (a) the extrusion

load and (b) the exit temperature.

In Case II, there were four variables as the input data for ANN and two parameters as the output

data. Extrusion ratios were 8.1, 17.4 and 26.4, the shape complexity index values 1, 1.22 and 1.36,

and ram speeds 1, 2 and 4 mm/s. The extrusion load and exit temperature were yielded as the output

data. The networks were trained by the results of the simulations of 32 extrusion runs. The extrusion

load and exit temperature of an extrusion run that was not included in the training file were predicted

with the ANN built. As can be seen in Fig. 5 the ANN predicted results also agree very well with the

FEM simulation ones. Fig. 6 shows the error curve of the ANN prediction.

0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000L

oad

(K

N)

Stroke (mm)

C =1.00

C =1.22

C =1.36

0 50 100 150 200 250340

350

360

370

380

390

400

410

420

430

440

Exit

Tem

per

ature

(

)

Stroke (mm)

C =1.00

C =1.22

C =1.36

(a) (b)

Fig. 3: Extrusion at an extrusion ratio of 8.1, a ram speed of 1 mm/s and various shape complexity

index values: (a) the extrusion load and (b) the exit temperature.

Comparison between FEM simulation and ANN. The data obtained from the FEM simulations

were submitted for ANN learning. In Case I, extrusion ratio and ram speed were 26.4 and 2 mm/s,

respectively. The input data of ANN were composed of extrusion ratio, ram speed, shape complexity

and ram displacement. The extrusion load and exit temperature were reached as the output data of

ANN. The shape complexity index values as the input data of ANN ranged from 1 to 1.45. Among the

results obtained from the simulations of the twelve extrusion runs with different shape complexity

index values, eleven were input as the training file to build ANN. With the networks built, the

extrusion load and exit temperature of the extrusion run at a shape complexity index of 1.03, which

was not included in the training file, were predicted. As can be seen in Fig. 4, the ANN predicted

results are in agreement with the FEM simulated ones.

0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000

8000

Lo

ad

(K

N)

Stroke (mm)

Simulation

Prediction

0 50 100 150 200 250300

320

340

360

380

400

420

440

460

480

Simulation

Prediction

Ex

it T

emp

erat

ure

(

)

Stroke (mm)

(a) (b)

Fig. 4: Comparison between the ANN predicted and FEM simulated results of the extrusion run at an



In Case II, there were four variables as the input data for ANN and two parameters as the output

data. Extrusion ratios were 8.1, 17.4 and 26.4, the shape complexity index values 1, 1.22 and 1.36,

and ram speeds 1, 2 and 4 mm/s. The extrusion load and exit temperature were yielded as the output

data. The networks were trained by the results of the simulations of 32 extrusion runs. The extrusion

load and exit temperature of an extrusion run that was not included in the training file were predicted

with the ANN built. As can be seen in Fig. 5 the ANN predicted results also agree very well with the

FEM simulation ones. Fig. 6 shows the error curve of the ANN prediction.


0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000

8000L

oad

(K

N)

Stroke (mm)

Simulation

Prediction

0 50 100 150 200 250340

360

380

400

420

440

460

480

Simulation

Prediction

Exit

Tem

per

ature

(

)

Stroke (mm)

(a) (b)

Fig. 5: Comparison between the ANN predicted and FEM simulation results of the extrusion run at an



Fig. 6: Error curve of the ANN prediction.

Isothermal extrusion is an advanced mode of the extrusion process and can be effectively used to

increase the productivity and enhance the extrudate quality consistency. Adjusting ram speed during

the process is one of the ways to realize isothermal extrusion. In the present study, a ram speed curve

for the isothermal extrusion of the AZ31 magnesium alloy was predicted by using the ANN built. As

shown in Fig. 7, the evolutions of the exit temperature at various ram speeds, a constant shape

complexity index and a constant extrusion ratio were predicted by utilizing the ANN built. The target

temperature for isothermal extrusion was set at 420 0C. In Fig. 7a, each point of the intersection

represents the ram speed at a particular ram displacement where the target temperature can be reached

and should be maintained. A series of the points form the basis of a ram speed profile for isothermal

extrusion, see Fig. 7b.

0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000

8000L

oad

(K

N)

Stroke (mm)

Simulation

Prediction

0 50 100 150 200 250340

360

380

400

420

440

460

480

Simulation

Prediction

Exit

Tem

per

ature

(

)

Stroke (mm)

(a) (b)

Fig. 5: Comparison between the ANN predicted and FEM simulation results of the extrusion run at an



Fig. 6: Error curve of the ANN prediction.

Isothermal extrusion is an advanced mode of the extrusion process and can be effectively used to

increase the productivity and enhance the extrudate quality consistency. Adjusting ram speed during

the process is one of the ways to realize isothermal extrusion. In the present study, a ram speed curve

for the isothermal extrusion of the AZ31 magnesium alloy was predicted by using the ANN built. As

shown in Fig. 7, the evolutions of the exit temperature at various ram speeds, a constant shape

complexity index and a constant extrusion ratio were predicted by utilizing the ANN built. The target

temperature for isothermal extrusion was set at 420 0C. In Fig. 7a, each point of the intersection

represents the ram speed at a particular ram displacement where the target temperature can be reached

and should be maintained. A series of the points form the basis of a ram speed profile for isothermal

extrusion, see Fig. 7b.


0 50 100 150 200 250340

360

380

400

420

440

460E

xit

Tem

pera

ture

(

)

Stroke (mm)

1.00 mm/s

2.00 mm/s

2.50 mm/s

3.00 mm/s

3.50 mm/s

4.00 mm/s

0 50 100 150 200 2500

1

2

3

4

5

6

7

8

9

Ram

sp

eed

(m

m/s

)

Stroke (mm) (a) (b)

Fig. 7: Prediction of a ram speed curve for isothermal extrusion: (a) evolutions of the exit temperature

during extrusion runs at different ram speeds, a constant shape complexity of 1.12 and an extrusion

ratio of 8.1 and (b) ram speed curve for isothermal extrusion.

Experimental verification. To validate the results predicted from the ANN built, an extrusion

experiment was performed with a flat-faced die to produce a solid cross-shaped profile. As shown in

Fig. 8, the shape complexity of this particular extrudate was 1.03 and extrusion ratio 8.84. The

extrusion parameters used in extrusion test are given in Table 5.



Container temperature [0C] 350

Ram speed [mm/s] 3

Fig. 8: Solid profile with cross shape.

It can be seen in Fig. 9 that the results predicted from the ANN agree well with the FEM simulated

and measured ones. The average error between the ANN predicted and experimentally measured

extrusion pressures throughout the ram stroke is 6.3%. In Fig. 9, the peak extrusion pressure is of

most interest. The error between the ANN predicted and experimentally measured peak extrusion

pressure is as small as 1.5%.

0 50 100 150 200 250340

360

380

400

420

440

460E

xit

Tem

pera

ture

(

)

Stroke (mm)

1.00 mm/s

2.00 mm/s

2.50 mm/s

3.00 mm/s

3.50 mm/s

4.00 mm/s

0 50 100 150 200 2500

1

2

3

4

5

6

7

8

9

Ram

sp

eed

(m

m/s

)

Stroke (mm) (a) (b)

Fig. 7: Prediction of a ram speed curve for isothermal extrusion: (a) evolutions of the exit temperature

during extrusion runs at different ram speeds, a constant shape complexity of 1.12 and an extrusion

ratio of 8.1 and (b) ram speed curve for isothermal extrusion.

Experimental verification. To validate the results predicted from the ANN built, an extrusion

experiment was performed with a flat-faced die to produce a solid cross-shaped profile. As shown in

Fig. 8, the shape complexity of this particular extrudate was 1.03 and extrusion ratio 8.84. The

extrusion parameters used in extrusion test are given in Table 5.



Container temperature [0C] 350

Ram speed [mm/s] 3

Fig. 8: Solid profile with cross shape.

It can be seen in Fig. 9 that the results predicted from the ANN agree well with the FEM simulated

and measured ones. The average error between the ANN predicted and experimentally measured

extrusion pressures throughout the ram stroke is 6.3%. In Fig. 9, the peak extrusion pressure is of

most interest. The error between the ANN predicted and experimentally measured peak extrusion

pressure is as small as 1.5%.


0 50 100 150 200 2500

100

200

300

400

500

600

Ex

tru

sio

n p

ress

ure

(M

Pa)

Stroke (mm)

Prediction

Experiment

Simulation

Fig. 9: Comparison in extrusion pressure between ANN prediction, FEM simulation and

experimental measurement.

Summary

The effect of the shape complexity of the extruded profiles on the extrusion load and exit temperature

was investigated using artificial neural networks based on the data obtained from FEM simulations.

Extrusion ratio, ram speed, shape complexity and ram displacement were taken as the input data for

ANN, and the extrusion load and exit temperature were yielded as the output data. The data from

FEM simulations were submitted for ANN as a training file and then ANN built were used to predict

the target parameters. The ANN predicted extrusion pressures were in agreement with the FEM

simulated and experimentally measured ones. The results obtained in the present study demonstrate

the feasibility of using ANN as a useful tool for the extrusion process design.

References

[1] Su-Hai Hsiang and Jer-Liang Kuo, Int. J. Adv. Manuf. Technol. Vol. 25 (2005) p. 292.

[2] Su-Hai Hsiang, Jer-Liang Kuo and Fu-Yuan Yang, J. Intell. Manuf. Vol. 17 (2006) p. 191.

[3] J.A. Schey, Introduction to Manufacturing Processes, The 3rd

Ed., McGraw-Hill, New York,

2000.

[4] K. Laue and H. Stenger, Extrusion: Processes, Machinery, Tooling, American Society for

Metals, Metals Park, Ohio, 1981.

[5] E.M. Mielnik, Metalworking Science and Engineering, McGraw-Hill, New York, 1991.

[6] T. Altan, S.-I. Oh and H.L. Gegel, Metal Forming: Fundamentals and Applications, American

Society for Metals, Metals Park, Ohio, 1983.

[7] S.Z. Qamar, A.F.M. Arif and A.K. Sheikh, J. Mater. Process. Technol. Vol. 155-156 (2004) p.

1734.

[8] L. Li, J. Zhou and J. Duszczyk, J. Mater. Process. Technol. Vol. 172 (2006) p. 372.

0 50 100 150 200 2500

100

200

300

400

500

600

Ex

tru

sio

n p

ress

ure

(M

Pa)

Stroke (mm)

Prediction

Experiment

Simulation

Fig. 9: Comparison in extrusion pressure between ANN prediction, FEM simulation and

experimental measurement.

Summary

The effect of the shape complexity of the extruded profiles on the extrusion load and exit temperature

was investigated using artificial neural networks based on the data obtained from FEM simulations.

Extrusion ratio, ram speed, shape complexity and ram displacement were taken as the input data for

ANN, and the extrusion load and exit temperature were yielded as the output data. The data from

FEM simulations were submitted for ANN as a training file and then ANN built were used to predict

the target parameters. The ANN predicted extrusion pressures were in agreement with the FEM

simulated and experimentally measured ones. The results obtained in the present study demonstrate

the feasibility of using ANN as a useful tool for the extrusion process design.

References

[1] Su-Hai Hsiang and Jer-Liang Kuo, Int. J. Adv. Manuf. Technol. Vol. 25 (2005) p. 292.

[2] Su-Hai Hsiang, Jer-Liang Kuo and Fu-Yuan Yang, J. Intell. Manuf. Vol. 17 (2006) p. 191.

[3] J.A. Schey, Introduction to Manufacturing Processes, The 3rd

Ed., McGraw-Hill, New York,

2000.

[4] K. Laue and H. Stenger, Extrusion: Processes, Machinery, Tooling, American Society for

Metals, Metals Park, Ohio, 1981.

[5] E.M. Mielnik, Metalworking Science and Engineering, McGraw-Hill, New York, 1991.

[6] T. Altan, S.-I. Oh and H.L. Gegel, Metal Forming: Fundamentals and Applications, American

Society for Metals, Metals Park, Ohio, 1983.

[7] S.Z. Qamar, A.F.M. Arif and A.K. Sheikh, J. Mater. Process. Technol. Vol. 155-156 (2004) p.

1734.

[8] L. Li, J. Zhou and J. Duszczyk, J. Mater. Process. Technol. Vol. 172 (2006) p. 372.


Contrasting models to determine the approximate extrusion process conditions for the first billet

M. Sabater1,a*, M. L. Garcia-Romeu1,b 1 University of Girona, Dept of Mechanical Engineering and Industrial Construction, Campus

Montilivi PII, Girona 17071,Spain [email protected], [email protected]

Keywords: First billet, ram speed, billet temperature, process parameters, neural network tool Abstract. This paper is focused on determining extrusion process conditions for the first billet and, particularly, on selecting an adequate billet temperature and extrusion speed. It is important to predict these values before adjusting the die to avoid lengthy and unproductive preparation times, and to make die adjustment easier during the tests. With that in mind, this study employs two models to determine the first billet temperature (TFB) and the extrusion speed (SE) parameters: one that applies regression techniques and another that uses neural networks. The aim of this paper is to present the results obtained by comparing the performance of the two models to determine which one offers the best results. We also analyze whether changing the number of patterns for construction of the models will improve results. The models are based on extrusion process parameters taken from real industry contexts. The results indicate that the variables chosen as predictor variables for the extrusion speed output must be refined.

Introduction and framework approach

In an extrusion plant there are two basic criteria for obtaining good performance: productivity of the press and the quality of the cross-section profile it produces. For the first criterion, press productivity depends on extrusion time and dead time between consecutive billets. Extrusion time depends on the maximum speed allowed by the piston rod, which, in turn, depends not only on chemical composition, profile geometry, and product quality requirements, but also on the extrusion force which can be supplied by the hydraulic can be sustained by the die [1]. The second criterion, product quality, includes different characteristics to be controlled, such as roughness, metal homogeneity and mechanical properties like strength. Due to the great variety of extruded products, the different functions they can be applied to, and the wide range of working methods employed by machine operators, it is difficult to identify only one criterion for quality assurance.

Experience and knowledge of metallurgy reveal that for a geometrical cross-section of a fixed material, mechanical properties and the final surface of the profiles depend on burn-out temperature, profile speed and billet temperature, although these three characteristics are not related to one another.

This complication, among other difficulties, has meant that extrusion has made quick progress in the field of automation over the last two decades. This has been encouraged by increased labor costs, increased productivity, and the demand for higher quality profiles. The main objective of this kind of automation has focused on three areas: process control, the billet logistics and extrusion profiles [1].

Data acquisition, evaluation and storage have assumed great importance in the automation process, as there is a need to determine the optimal process parameters for a constant and highest possible exit temperature, a minimum billet temperature, a maximum extrusion speed and the hydraulics can supply the required extrusion force and the die can withstand the force. Hence the need to provide the system with an empirical process control model which is continuously updated using previous extrusions [1].

Contrasting models to determine the approximate extrusion process conditions for the first billet

M. Sabater1,a*, M. L. Garcia-Romeu1,b 1 University of Girona, Dept of Mechanical Engineering and Industrial Construction, Campus

Montilivi PII, Girona 17071,Spain [email protected], [email protected]

Keywords: First billet, ram speed, billet temperature, process parameters, neural network tool Abstract. This paper is focused on determining extrusion process conditions for the first billet and, particularly, on selecting an adequate billet temperature and extrusion speed. It is important to predict these values before adjusting the die to avoid lengthy and unproductive preparation times, and to make die adjustment easier during the tests. With that in mind, this study employs two models to determine the first billet temperature (TFB) and the extrusion speed (SE) parameters: one that applies regression techniques and another that uses neural networks. The aim of this paper is to present the results obtained by comparing the performance of the two models to determine which one offers the best results. We also analyze whether changing the number of patterns for construction of the models will improve results. The models are based on extrusion process parameters taken from real industry contexts. The results indicate that the variables chosen as predictor variables for the extrusion speed output must be refined.

Introduction and framework approach

In an extrusion plant there are two basic criteria for obtaining good performance: productivity of the press and the quality of the cross-section profile it produces. For the first criterion, press productivity depends on extrusion time and dead time between consecutive billets. Extrusion time depends on the maximum speed allowed by the piston rod, which, in turn, depends not only on chemical composition, profile geometry, and product quality requirements, but also on the extrusion force which can be supplied by the hydraulic can be sustained by the die [1]. The second criterion, product quality, includes different characteristics to be controlled, such as roughness, metal homogeneity and mechanical properties like strength. Due to the great variety of extruded products, the different functions they can be applied to, and the wide range of working methods employed by machine operators, it is difficult to identify only one criterion for quality assurance.

Experience and knowledge of metallurgy reveal that for a geometrical cross-section of a fixed material, mechanical properties and the final surface of the profiles depend on burn-out temperature, profile speed and billet temperature, although these three characteristics are not related to one another.

This complication, among other difficulties, has meant that extrusion has made quick progress in the field of automation over the last two decades. This has been encouraged by increased labor costs, increased productivity, and the demand for higher quality profiles. The main objective of this kind of automation has focused on three areas: process control, the billet logistics and extrusion profiles [1].

Data acquisition, evaluation and storage have assumed great importance in the automation process, as there is a need to determine the optimal process parameters for a constant and highest possible exit temperature, a minimum billet temperature, a maximum extrusion speed and the hydraulics can supply the required extrusion force and the die can withstand the force. Hence the need to provide the system with an empirical process control model which is continuously updated using previous extrusions [1].


The aim of the controls inside the extrusion plants, and of any control in general, is to apply different inputs (alloy, die parameters, final cross-section parameters, etc.) to make it possible to extract different process parameters as controlled outputs. Different control methods are applied to the extrusion field: open loop, closed loop, etc. When applied to extrusion plants, most control systems are capable of dynamically feed forwarding billet to billet, and they can even recommend a press speed and a billet warm-up. Despite these controls, however, extrusion still requires an engineer to estimate the first process conditions for the first billet [2].

Nowadays, the first process parameter values are determined for the first billet from enterprise tables [3] and engineers’ and operators’ knowledge and experience. This is an iterative process [4] carried out during die testing inside the press. This traditional method is based on a trial and error procedure; consequently it is usually a slow and at times costly process [5].

This study is focused on determining two parameters, billet temperature and extrusion speed, these being two parameters whose prediction values it is important to know before the die adjustment phase. Moreover, there is no linear or empirical relationship between the temperature of the first billet and the extrusion speed; they depend on several other parameters, such as, for example, the extrusion ratio, the extrusion speed, the aluminum alloy type, etc.

Due to the impossibility of predicting extrusion speed using easy input parameters, it is difficult to make a cost evaluation of a fixed profile without a testing phase, and without experience with this extrusion. This is because the extrusion speed sets the busy time of the press, how much time is consumed by the process, and the cost of the profile per linear meter. Consequently, designers ignore this cost because they do not have any tools to determine it, and they therefore cannot obtain the most economical profile to fulfil design requirements.

Lozina et al. [6] analyze the influence of different parameters in optimizing the extrusion of a thin wall tube profile and a 7XXX alloy. Their study compares the results obtained by linear regression with those obtained by an artificial network, and proves the latter method to be more efficient, as the errors obtained were lower using neural networks. In [7], the same author uses neural networks and a genetic algorithm as suggested in the previous study to optimize the aluminum extrusion and die design. In [8], Karavel and Ozkan model and simulate the direct extrusion process and use neuronal networks and finite element methods to optimize die design, highlighting the advantage that neuronal networks have with regard to response time (5 min) in comparison with the finite element (60 min). In [9], Camargo and Lesley use neural networks to model an industrial extrusion system for determining die output temperature.

In this study, it has been applied two techniques to develop a tool for predicting the first billet temperature and extrusion speed; they have then been compared in order to choose the best technique, i.e. where error is minimized.

Methodology

The methodology employed in this study was as follows: • First, the data were obtained from a factory press with a capacity of 22 MN and billet of

8" in diameter. Data were compiled for 31 products. • Then, the variables influencing the extrusion process were studied, especially those

concerning the temperature of the first billet and the extrusion speed. The most important parameters to be considered had been identified in a previous study [10].

• The third step was to develop and validate a multiple regression analysis (MRA) model [10].

• In the fourth step, an artificial neural network (ANN) tool was developed and validated. • As errors were not improving, we decided to include a fifth step in which more data were

compiled in the factory, until we had a total of 60 products. • The MRA and ANN tools were developed and validations for these 60 products.

The aim of the controls inside the extrusion plants, and of any control in general, is to apply different inputs (alloy, die parameters, final cross-section parameters, etc.) to make it possible to extract different process parameters as controlled outputs. Different control methods are applied to the extrusion field: open loop, closed loop, etc. When applied to extrusion plants, most control systems are capable of dynamically feed forwarding billet to billet, and they can even recommend a press speed and a billet warm-up. Despite these controls, however, extrusion still requires an engineer to estimate the first process conditions for the first billet [2].

Nowadays, the first process parameter values are determined for the first billet from enterprise tables [3] and engineers’ and operators’ knowledge and experience. This is an iterative process [4] carried out during die testing inside the press. This traditional method is based on a trial and error procedure; consequently it is usually a slow and at times costly process [5].

This study is focused on determining two parameters, billet temperature and extrusion speed, these being two parameters whose prediction values it is important to know before the die adjustment phase. Moreover, there is no linear or empirical relationship between the temperature of the first billet and the extrusion speed; they depend on several other parameters, such as, for example, the extrusion ratio, the extrusion speed, the aluminum alloy type, etc.

Due to the impossibility of predicting extrusion speed using easy input parameters, it is difficult to make a cost evaluation of a fixed profile without a testing phase, and without experience with this extrusion. This is because the extrusion speed sets the busy time of the press, how much time is consumed by the process, and the cost of the profile per linear meter. Consequently, designers ignore this cost because they do not have any tools to determine it, and they therefore cannot obtain the most economical profile to fulfil design requirements.

Lozina et al. [6] analyze the influence of different parameters in optimizing the extrusion of a thin wall tube profile and a 7XXX alloy. Their study compares the results obtained by linear regression with those obtained by an artificial network, and proves the latter method to be more efficient, as the errors obtained were lower using neural networks. In [7], the same author uses neural networks and a genetic algorithm as suggested in the previous study to optimize the aluminum extrusion and die design. In [8], Karavel and Ozkan model and simulate the direct extrusion process and use neuronal networks and finite element methods to optimize die design, highlighting the advantage that neuronal networks have with regard to response time (5 min) in comparison with the finite element (60 min). In [9], Camargo and Lesley use neural networks to model an industrial extrusion system for determining die output temperature.

In this study, it has been applied two techniques to develop a tool for predicting the first billet temperature and extrusion speed; they have then been compared in order to choose the best technique, i.e. where error is minimized.

Methodology

The methodology employed in this study was as follows: • First, the data were obtained from a factory press with a capacity of 22 MN and billet of

8" in diameter. Data were compiled for 31 products. • Then, the variables influencing the extrusion process were studied, especially those

concerning the temperature of the first billet and the extrusion speed. The most important parameters to be considered had been identified in a previous study [10].

• The third step was to develop and validate a multiple regression analysis (MRA) model [10].

• In the fourth step, an artificial neural network (ANN) tool was developed and validated. • As errors were not improving, we decided to include a fifth step in which more data were

compiled in the factory, until we had a total of 60 products. • The MRA and ANN tools were developed and validations for these 60 products.


• Finally, the developed models were compared with regard to the two techniques and the different amounts of data used.

The first three steps were presented in Extrusion Workshop 2007 and 2nd Extrusion Benchmark and provided the starting point for developing the points presented in this methodology.

Influential variables and MRA results

As mentioned in the previous section, the data were obtained from a working extrusion plant with a 22 MN press and an 8-inch billet diameter. Data were initially obtained for 31 different products, and then for 29 more. Some of the data are summarized in article [10].

Of the first 31 products, 4 were retained for validation and the remaining 27 were used for statistical analysis. The statistical analyses to find the most influential variables in determining the temperature of the first billet and the extrusion speed were explained widely in article [10]. The selected variables were the extrusion ratio (ER), the circumscribing circle diameter the cross-section of the shape (CCD), the form factor (FF), the billet length (L), the elongation (A) and extrusion temperature (TE).

Following this analysis, which helped to obtain information regarding the attributes and the dependent variables, two models of prediction were constructed. The first one is for the first billet temperature (TFB), Eq. 1, and the second for the extrusion speed (SE), Eq. 2. Initially, these did not differ from flat and tubular cross-sections, but due to their error, two more models were later developed for each variable. All these models and their corresponding coefficients (bx) are summarized in Tables 1 and 2, which include the results of the second MRA analysis using 52 data points.

Table 1. Parameters to predict the first billet temperature TFB = b0 + b1 ER + b2 CCD.+ b3 FF + b4 L + b5 A +b6 TE. (1)

b0 b1 b2 b3 b4 b5 b6 r R2 Error

Flat and tubes (27 data) 443.795 -0.100 0.053 -0.131 0.017 -2.224 0.101 0.541 0.293 13.68

Flat (11 data) 1002.936 0.009 -0.099 0.637 -0.043 -7.038 -0.812 0.692 0.478 16.190

Tube (16 data) 247.484 -0.045 0.057 -0.202 0.011 -1.554 0.460 0.717 0.513 9.694

Flat and tubes (52 data) 487.747 -0.015 0.006 -0.014 0.018 -2.130 0 0.285 0.081 16.999

Flat (23 data) 479.057 0.229 -0.033 0.091 0.013 -3.150 0 0.541 0.293 12.587

Tube (29 data) 461.863 0.051 0.020 0.040 0.028 -1.152 0 0.326 0.106 15.573

Table 2. Parameters to predict the first billet extrusion speed SE = b0 + b1 ER + b2 CCD.+ b3 FF + b4 L + b5 A +b6 TE. (2)


Flat and tubes (27 data) -102.414 0.192 0.037 -0.002 0.025 1.285 0.124 0.819 0.672 4.134

Flat (11 data) 211.864 0.125 -0.001 0.149 -0.008 -1.008 -0.341 0.868 0.755 3.753

Tube (16 data) -67.600 0.167 0.060 -0.050 0.008 1.065 0.088 0.763 0.582 3.79

Flat and tubes (52 data) -11.649 0.154 -0.008 0.007 0.010 0.923 0 0.749 0.561 3.769

Flat (23 data) -10.300 0.136 -0.010 0 0.016 0.878 0 0.782 0.612 3.373

Tube (29 data) -6.959 0.118 -0.004 0.004 0.005 0.854 0 0.754 0.568 3.327

• Finally, the developed models were compared with regard to the two techniques and the different amounts of data used.

The first three steps were presented in Extrusion Workshop 2007 and 2nd Extrusion Benchmark and provided the starting point for developing the points presented in this methodology.

Influential variables and MRA results

As mentioned in the previous section, the data were obtained from a working extrusion plant with a 22 MN press and an 8-inch billet diameter. Data were initially obtained for 31 different products, and then for 29 more. Some of the data are summarized in article [10].

Of the first 31 products, 4 were retained for validation and the remaining 27 were used for statistical analysis. The statistical analyses to find the most influential variables in determining the temperature of the first billet and the extrusion speed were explained widely in article [10]. The selected variables were the extrusion ratio (ER), the circumscribing circle diameter the cross-section of the shape (CCD), the form factor (FF), the billet length (L), the elongation (A) and extrusion temperature (TE).

Following this analysis, which helped to obtain information regarding the attributes and the dependent variables, two models of prediction were constructed. The first one is for the first billet temperature (TFB), Eq. 1, and the second for the extrusion speed (SE), Eq. 2. Initially, these did not differ from flat and tubular cross-sections, but due to their error, two more models were later developed for each variable. All these models and their corresponding coefficients (bx) are summarized in Tables 1 and 2, which include the results of the second MRA analysis using 52 data points.

Table 1. Parameters to predict the first billet temperature TFB = b0 + b1 ER + b2 CCD.+ b3 FF + b4 L + b5 A +b6 TE. (1)


Flat and tubes (27 data) 443.795 -0.100 0.053 -0.131 0.017 -2.224 0.101 0.541 0.293 13.68

Flat (11 data) 1002.936 0.009 -0.099 0.637 -0.043 -7.038 -0.812 0.692 0.478 16.190

Tube (16 data) 247.484 -0.045 0.057 -0.202 0.011 -1.554 0.460 0.717 0.513 9.694

Flat and tubes (52 data) 487.747 -0.015 0.006 -0.014 0.018 -2.130 0 0.285 0.081 16.999

Flat (23 data) 479.057 0.229 -0.033 0.091 0.013 -3.150 0 0.541 0.293 12.587

Tube (29 data) 461.863 0.051 0.020 0.040 0.028 -1.152 0 0.326 0.106 15.573

Table 2. Parameters to predict the first billet extrusion speed SE = b0 + b1 ER + b2 CCD.+ b3 FF + b4 L + b5 A +b6 TE. (2)


Flat and tubes (27 data) -102.414 0.192 0.037 -0.002 0.025 1.285 0.124 0.819 0.672 4.134

Flat (11 data) 211.864 0.125 -0.001 0.149 -0.008 -1.008 -0.341 0.868 0.755 3.753

Tube (16 data) -67.600 0.167 0.060 -0.050 0.008 1.065 0.088 0.763 0.582 3.79

Flat and tubes (52 data) -11.649 0.154 -0.008 0.007 0.010 0.923 0 0.749 0.561 3.769

Flat (23 data) -10.300 0.136 -0.010 0 0.016 0.878 0 0.782 0.612 3.373

Tube (29 data) -6.959 0.118 -0.004 0.004 0.005 0.854 0 0.754 0.568 3.327


A(( design An artificial neural network is a mathematical model composed of several neurons distributed in different layers, and joined across several variables called weights. The weights are calculated using an iterative method known as training, in which the network is fed pairs of data (input - output) that represent the pattern the network must try to model. In addition, artificial neural networks are non-linear analysis tools and, as already mentioned, the temperature and the extrusion speed of the first billet do fulfil this characteristic since they have multiple interactions with different parameters.

A neural network of two layers is generally capable of precisely modelling any type of continuous performance if it is provided with a sufficient amount of secret nodes. This universal property can be applied to function approximation, which fits with the aim of the variables we wanted to predict in this study. Therefore, in this case, a two-layer perceptron is chosen, with a back propagation algorithm that is widely used in general engineering applications.

The neural network model will have two outputs (temperature and extrusion speed for the first billet) across the same six predictor variables used by MRA models: the extrusion ratio (ER), the circumscribing circle diameter of the cross-section of the shape (CCD), the form factor (FF), the billet length (L), the elongation (A) and extrusion temperature (TE). All of this defines a neural network architecture of 6-X-2 (Fig. 1), X being the number of hidden nodes in the hidden layer. There are no well-established procedures to determine the suitable number of hidden neurons; most researchers use trial and error procedures. This is the approach we applied in this study, taking into account that the more hidden neurons there are, the more weights will have to be adjusted. This is also related to the number of patterns of training needed for a network to carry out a good generalization (with good precision).

Fig. 1. Architecture 6-X-2

Training A supervised learning strategy is used, which means that for all patterns - inputs knows its corresponding values of outputs. The Levenberg-Marquardt algorithm is used. Construction of the training data set is very important, especially to avoid overfitting cases (Fig. 2). For this reason, in this study we have used the early stopping technique, which forces the training data to be divided into three groups: training, validation and test. Table 3 presents the training percentages for each group.

ER

CCD

FF

L

TE

A

Tfb

SE

.

.

.

A(( design An artificial neural network is a mathematical model composed of several neurons distributed in different layers, and joined across several variables called weights. The weights are calculated using an iterative method known as training, in which the network is fed pairs of data (input - output) that represent the pattern the network must try to model. In addition, artificial neural networks are non-linear analysis tools and, as already mentioned, the temperature and the extrusion speed of the first billet do fulfil this characteristic since they have multiple interactions with different parameters.

A neural network of two layers is generally capable of precisely modelling any type of continuous performance if it is provided with a sufficient amount of secret nodes. This universal property can be applied to function approximation, which fits with the aim of the variables we wanted to predict in this study. Therefore, in this case, a two-layer perceptron is chosen, with a back propagation algorithm that is widely used in general engineering applications.

The neural network model will have two outputs (temperature and extrusion speed for the first billet) across the same six predictor variables used by MRA models: the extrusion ratio (ER), the circumscribing circle diameter of the cross-section of the shape (CCD), the form factor (FF), the billet length (L), the elongation (A) and extrusion temperature (TE). All of this defines a neural network architecture of 6-X-2 (Fig. 1), X being the number of hidden nodes in the hidden layer. There are no well-established procedures to determine the suitable number of hidden neurons; most researchers use trial and error procedures. This is the approach we applied in this study, taking into account that the more hidden neurons there are, the more weights will have to be adjusted. This is also related to the number of patterns of training needed for a network to carry out a good generalization (with good precision).

Fig. 1. Architecture 6-X-2

Training A supervised learning strategy is used, which means that for all patterns - inputs knows its corresponding values of outputs. The Levenberg-Marquardt algorithm is used. Construction of the training data set is very important, especially to avoid overfitting cases (Fig. 2). For this reason, in this study we have used the early stopping technique, which forces the training data to be divided into three groups: training, validation and test. Table 3 presents the training percentages for each group.

ER

CCD

FF

L

TE

A

Tfb

SE

.

.

.


Fig. 2. Evolution of training data. Example of overfitting 6-2-1architecture, speed (right).

Example of correct training 6-1-2 architecture, speed and temperature (left).

The training set has the function of training and carrying out the weight adjustments. Validation refines the network by means of the early stopping technique. And finally, the test set (data not seen during the training) is used to determine the performance of the network by means of a calculation of error. Table 3 summarizes the conditions used in each of the architectures tested during the training.

Table 3. Training strategies

Architectures 6-5-2 6-4-2 6-3-2 6-2-2 6-1-2

Arch. for every variable 6-5-1 6-4-1 6-3-1 6-2-1 6-1-1

Patterns of training 271 (11 flat2 y 16 tube2)

521 (23 flat2 y 29 tube2)

Train /Val. /Test. [%] 80 /10 /101 70 /15 /151 60 /20 /201,2 50/25/252

Aim of execution 0.1

As can be deduced from the table, different network architectures were trained with two outputs.

Next, different networks were trained, separating each variable, so different architectures were trained for the first billet temperature and for the extrusion speed. In addition to trained networks supporting the input parameters, the training was repeated dividing the input data into two subgroups, that is, among tubular and flat profiles. And finally the analysis was also repeated with more input data, from 27 (11 flat and 16 tubular ones) to 52 input-output patterns (23 flat and 29 tubular ones).

One of the ways to analyze the response of the trained network in more detail is to carry out a regression analysis between the output networks and their corresponding objective value. This analysis returns three parameters: the slope and the intersection on the Y axis, the best linear regression that relates the objective pattern with the exits of the network, and the correlation value between the outputs (A) and the targets (T). All of these networks were trained by designing an algorithm that uses functions and routines from the Neural Network MATLAB Toolbox. Fig. 3 shows an example of the regression analysis obtained for an architecture 6-3-2 with the test information group, with a data division of 80/10/10.

Fig. 2. Evolution of training data. Example of overfitting 6-2-1architecture, speed (right).

Example of correct training 6-1-2 architecture, speed and temperature (left).

The training set has the function of training and carrying out the weight adjustments. Validation refines the network by means of the early stopping technique. And finally, the test set (data not seen during the training) is used to determine the performance of the network by means of a calculation of error. Table 3 summarizes the conditions used in each of the architectures tested during the training.

Table 3. Training strategies

Architectures 6-5-2 6-4-2 6-3-2 6-2-2 6-1-2

Arch. for every variable 6-5-1 6-4-1 6-3-1 6-2-1 6-1-1

Patterns of training 271 (11 flat2 y 16 tube2)

521 (23 flat2 y 29 tube2)

Train /Val. /Test. [%] 80 /10 /101 70 /15 /151 60 /20 /201,2 50/25/252

Aim of execution 0.1

As can be deduced from the table, different network architectures were trained with two outputs.

Next, different networks were trained, separating each variable, so different architectures were trained for the first billet temperature and for the extrusion speed. In addition to trained networks supporting the input parameters, the training was repeated dividing the input data into two subgroups, that is, among tubular and flat profiles. And finally the analysis was also repeated with more input data, from 27 (11 flat and 16 tubular ones) to 52 input-output patterns (23 flat and 29 tubular ones).

One of the ways to analyze the response of the trained network in more detail is to carry out a regression analysis between the output networks and their corresponding objective value. This analysis returns three parameters: the slope and the intersection on the Y axis, the best linear regression that relates the objective pattern with the exits of the network, and the correlation value between the outputs (A) and the targets (T). All of these networks were trained by designing an algorithm that uses functions and routines from the Neural Network MATLAB Toolbox. Fig. 3 shows an example of the regression analysis obtained for an architecture 6-3-2 with the test information group, with a data division of 80/10/10.


Fig. 3. Regression analysis from test set. Architecture 6-3-2, division 80/10/10.

Discussion of results

Then, all the trained networks were validated. For validation, the set-aside data (which have not seen by the networks during the training) was fed to them. Each network gave a prediction which it was compared with the real value corresponding to the conditions. The set-aside data were built in this way: 4 data saved for the network trained with 27 flat and tubular data, 1 data for the network trained with 11 flat data, 3 data for the network trained with 16 tubular data, 8 data the network trained with saved for 52 flat and tubular data, 4 data for the network trained with 23 flat data and finally, 4 data for the network trained with 29 tubular data. A summary of the comparative results for the validation data is given in Tables 4, 5 and 6. The MRA and ANN prediction models show better prediction values for the first billet temperature than for the extrusion speed. This means that the choice of these six predictor variables represents the behavior of first billet temperature better than the extrusion speed. Consequently, a new study should be conducted to predict variables for the extrusion speed parameter, which could include new process/section parameters and/or the removal of some others.

As far as a comparison of the two techniques is concerned, the neural network models display a low percentage of error when compared to the MRA technique.The neural network method would therefore be chosen, despite the fact that for the first billet temperature and extrusion speed the prediction error presented by the MRA technique does not differ much from the values obtained using the ANN technique.

Tables 4, 5 and 6 present the results of the relative error for first billet temperature and extrusion speed predicted for MRA technologies, the best trained ANN with two outputs (6-X-2), the best trained ANN with an output for first billet temperature (6-X-1) and the best trained ANN with an output for extrusion speed (6-X-1). The technologies were compared using 27 data points and 52 data points. In addition, the tables show that in the ANN the combination of hidden nodes and proportions of training / validation / test minimizes the relative error. Table 4 does not distinguish between flat and tube cross-section data. The results of this table show that the relative errors of the first billet temperature are similar, while the ANN results improve with respect to MRA in extrusion speed for training with 27 data points. There is no difference in the relative error in extrusion speed with 52 data points, because with more data the MRA improves but the ANN does not.

Table 5 shows the results with only the flat cross-section data. This table, which only includes 11 data points, presents a few very unlikely errors, denoting that they are fairly reliable for a small quantity of data (0.4 % ~ 5.8 % first billet temperature and 0.6 % ~ 63.1 % extrusion speed). With

Fig. 3. Regression analysis from test set. Architecture 6-3-2, division 80/10/10.

Discussion of results

Then, all the trained networks were validated. For validation, the set-aside data (which have not seen by the networks during the training) was fed to them. Each network gave a prediction which it was compared with the real value corresponding to the conditions. The set-aside data were built in this way: 4 data saved for the network trained with 27 flat and tubular data, 1 data for the network trained with 11 flat data, 3 data for the network trained with 16 tubular data, 8 data the network trained with saved for 52 flat and tubular data, 4 data for the network trained with 23 flat data and finally, 4 data for the network trained with 29 tubular data. A summary of the comparative results for the validation data is given in Tables 4, 5 and 6. The MRA and ANN prediction models show better prediction values for the first billet temperature than for the extrusion speed. This means that the choice of these six predictor variables represents the behavior of first billet temperature better than the extrusion speed. Consequently, a new study should be conducted to predict variables for the extrusion speed parameter, which could include new process/section parameters and/or the removal of some others.

As far as a comparison of the two techniques is concerned, the neural network models display a low percentage of error when compared to the MRA technique.The neural network method would therefore be chosen, despite the fact that for the first billet temperature and extrusion speed the prediction error presented by the MRA technique does not differ much from the values obtained using the ANN technique.

Tables 4, 5 and 6 present the results of the relative error for first billet temperature and extrusion speed predicted for MRA technologies, the best trained ANN with two outputs (6-X-2), the best trained ANN with an output for first billet temperature (6-X-1) and the best trained ANN with an output for extrusion speed (6-X-1). The technologies were compared using 27 data points and 52 data points. In addition, the tables show that in the ANN the combination of hidden nodes and proportions of training / validation / test minimizes the relative error. Table 4 does not distinguish between flat and tube cross-section data. The results of this table show that the relative errors of the first billet temperature are similar, while the ANN results improve with respect to MRA in extrusion speed for training with 27 data points. There is no difference in the relative error in extrusion speed with 52 data points, because with more data the MRA improves but the ANN does not.

Table 5 shows the results with only the flat cross-section data. This table, which only includes 11 data points, presents a few very unlikely errors, denoting that they are fairly reliable for a small quantity of data (0.4 % ~ 5.8 % first billet temperature and 0.6 % ~ 63.1 % extrusion speed). With


23 data points the errors have become stable, remaining very similar for all of the technologies. More data would be required to distinguish which is technically better.

Table 4. Result validation with flat and tube dies

27 data TFB

Relative Error [%]

SE

Relative Error [%]

52 data

TFB Relative Error [%]

SE

Relative Error [%]

Flat & Tube MRA 2.4 29.1 Flat & Tube MRA 2.4 23

Flat & Tube A(( 6-1-2 60/20/20

2.8 14.2 Flat & Tube A((

6-3-2 60/20/20 2.1 24.5

Flat & Tube A(( 6-5-1 60/20/20 Variable TFB

1.8 Flat & Tube A((

6-4-1 80/10/10 Variable TFB

2

Flat & Tube A(( 6-4-1 80/10/10

Variable SE 19

Flat & Tube A(( 6-3-1 60/20/20

Variable SE 26.4

Table 5. Result validation with flat dies.

11 data TFB

Relative Error [%]

SE

Relative Error [%]

23 data


SE

Relative Error [%]

Flat MRA 1.9 30.7 Flat MRA 5 13

Flat A(( 6-1-2 50/25/25

5.8 63.1 Flat A((

6-4-2 60/20/20 5.7 23.6

Flat A(( 6-3-1 50/25/25 Variable TFB

0.4 Flat A((


3.2

Flat A(( 6-2-1 50/25/25

Variable SE 0.6

Flat A(( 6-5-1 60/20/20

Variable SE 17.3

Table 6 shows the results with only the tube cross-section data. In this table with 16 data points the results improve in the technical ANN in comparison to MRA, especially with regard to extrusion speed. With 29 data points, in an ANN 6-X-1, the relative error drops considerably; this demonstrates that distinguishing between flat and tube and a single output with sufficient data minimizes the relative error.

Table 6. Result validation with tube dies

16 data TFB

Relative Error [%]

SE

Relative Error [%]

29 data


SE

Relative Error [%]

Tube MRA 3.8 20.7 Tube MRA 4 16

Tube A(( 6-1-2 50/25/25

3.7 8.9 Tube A((

6-2-2 60/20/20 3.2 16.6

Tube A(( 6-1-1 50/25/25 Variable TFB

2.9 Tube A((


1.2

Tube A(( 6-2-1 50/25/25

Variable SE 15

Tube A(( 6-2-1 60/20/20

Variable SE 6.9

23 data points the errors have become stable, remaining very similar for all of the technologies. More data would be required to distinguish which is technically better.

Table 4. Result validation with flat and tube dies

27 data TFB

Relative Error [%]

SE

Relative Error [%]

52 data


SE

Relative Error [%]

Flat & Tube MRA 2.4 29.1 Flat & Tube MRA 2.4 23

Flat & Tube A(( 6-1-2 60/20/20

2.8 14.2 Flat & Tube A((

6-3-2 60/20/20 2.1 24.5

Flat & Tube A(( 6-5-1 60/20/20 Variable TFB

1.8 Flat & Tube A((


2

Flat & Tube A(( 6-4-1 80/10/10

Variable SE 19

Flat & Tube A(( 6-3-1 60/20/20

Variable SE 26.4

Table 5. Result validation with flat dies.

11 data TFB

Relative Error [%]

SE

Relative Error [%]

23 data


SE

Relative Error [%]

Flat MRA 1.9 30.7 Flat MRA 5 13

Flat A(( 6-1-2 50/25/25

5.8 63.1 Flat A((

6-4-2 60/20/20 5.7 23.6

Flat A(( 6-3-1 50/25/25 Variable TFB

0.4 Flat A((


3.2

Flat A(( 6-2-1 50/25/25

Variable SE 0.6

Flat A(( 6-5-1 60/20/20

Variable SE 17.3

Table 6 shows the results with only the tube cross-section data. In this table with 16 data points the results improve in the technical ANN in comparison to MRA, especially with regard to extrusion speed. With 29 data points, in an ANN 6-X-1, the relative error drops considerably; this demonstrates that distinguishing between flat and tube and a single output with sufficient data minimizes the relative error.

Table 6. Result validation with tube dies

16 data TFB

Relative Error [%]

SE

Relative Error [%]

29 data


SE

Relative Error [%]

Tube MRA 3.8 20.7 Tube MRA 4 16

Tube A(( 6-1-2 50/25/25

3.7 8.9 Tube A((

6-2-2 60/20/20 3.2 16.6

Tube A(( 6-1-1 50/25/25 Variable TFB

2.9 Tube A((


1.2

Tube A(( 6-2-1 50/25/25

Variable SE 15

Tube A(( 6-2-1 60/20/20

Variable SE 6.9


Besides betting on the neural networks, the availability of a larger number of training patterns would theoretically improve the accuracy of the prediction. In this study, however, it has been observed that when the number of training patterns is over 20, accuracy stabilizes around 2-2.5% for first billet temperature, and around 20% for extrusion speed.

Summary and conclusions

The validation carried out for both technologies shows that the predictor variables chosen for both outputs should be refined or new variables should be sought for the case of extrusion speed. Although we expected to obtain better results from the neural network prediction technique, the validation has demonstrated that although good results are obtained by both techniques, the neural networks present better error results than multiple regression.

Therefore, applying the prediction models proposed by the neural networks will help the user (engineer or die manufacturer) to determine which values are closer to the first conditions of the extrusion process for the first billet. Although it is not possible to directly calculate the time and cost savings that the use of this tool would represent for an inexperienced operator, companies are not aware of the exact amounts of time they dedicate to this adjustment. This approximate value will always mean a reduction in the number of trial and error cycles that must be conducted during die adjustment.

References

[1] K. Muller, A. Ames, O. Diegritz, et al.: Fundamentals of extrusion technology, edited by Giesel Verlag. Isernhagen. (2004)

[2] M.P. Reddy, H.E. Bertolini, and B.W. Biel,: HyperXtrude/Process - extrusion process optimization software, edited by Proceedings of the Eighth International Aluminum Extrusion Technology Seminar. Vol. I. 231-235 (2004)

[3] Fichas técnicas A-GS, edited by Aluminium Pechiney (1987) [4] P.K. Saha: Aluminum extrusion technology, edited by ASM International. United States of

America (2000) [5] M.L. Garcia-Romeu and J. Ciurana: Springback and geometry prediction - neural networks

applied to the air bending process, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4113 LNCS - I 470-475. (2006)

[6] Z. Lozina, I. Duplancic and J. Prgin: Evolution- and biology-based approach to the optimization of the extrusion process, edited by Proceedings of the Seventh International Aluminum Extrusion Technology Seminar. (2000)

[7] Z. Lozina, I. Duplancic, B. Lela, et al.: Optimisation of aluminum extrusion and die design using neural networks and genetic algorithms, edited by Aluminium Two Thousand 5th World Congress. Rome. (2003)

[8] D. Karayel and S.S. Ozkan: Simulation of direct extrusion process and optimal design of technological parameters using FEM and artificial neural network, edited by Key Engineering Materials. Vol. 367. (2008)

[9] R. Camargo and R. Lesley: Use of adaptive neural networks (A**) in aluminum extrusion process control. Proceedings of the Ninth International Aluminum Extrusion Technology Seminar. Orlando. (2008)

[10] M. Sabater, M.L. Garcia-Romeu and J. Ciurana: Input parameters determination for predicting ram speed and billet temperature for the first billet, edited by Key Engineering Materials. Vol. 367. 161-168. (2008)

Besides betting on the neural networks, the availability of a larger number of training patterns would theoretically improve the accuracy of the prediction. In this study, however, it has been observed that when the number of training patterns is over 20, accuracy stabilizes around 2-2.5% for first billet temperature, and around 20% for extrusion speed.

Summary and conclusions

The validation carried out for both technologies shows that the predictor variables chosen for both outputs should be refined or new variables should be sought for the case of extrusion speed. Although we expected to obtain better results from the neural network prediction technique, the validation has demonstrated that although good results are obtained by both techniques, the neural networks present better error results than multiple regression.

Therefore, applying the prediction models proposed by the neural networks will help the user (engineer or die manufacturer) to determine which values are closer to the first conditions of the extrusion process for the first billet. Although it is not possible to directly calculate the time and cost savings that the use of this tool would represent for an inexperienced operator, companies are not aware of the exact amounts of time they dedicate to this adjustment. This approximate value will always mean a reduction in the number of trial and error cycles that must be conducted during die adjustment.

References

[1] K. Muller, A. Ames, O. Diegritz, et al.: Fundamentals of extrusion technology, edited by Giesel Verlag. Isernhagen. (2004)

[2] M.P. Reddy, H.E. Bertolini, and B.W. Biel,: HyperXtrude/Process - extrusion process optimization software, edited by Proceedings of the Eighth International Aluminum Extrusion Technology Seminar. Vol. I. 231-235 (2004)

[3] Fichas técnicas A-GS, edited by Aluminium Pechiney (1987) [4] P.K. Saha: Aluminum extrusion technology, edited by ASM International. United States of

America (2000) [5] M.L. Garcia-Romeu and J. Ciurana: Springback and geometry prediction - neural networks

applied to the air bending process, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4113 LNCS - I 470-475. (2006)

[6] Z. Lozina, I. Duplancic and J. Prgin: Evolution- and biology-based approach to the optimization of the extrusion process, edited by Proceedings of the Seventh International Aluminum Extrusion Technology Seminar. (2000)

[7] Z. Lozina, I. Duplancic, B. Lela, et al.: Optimisation of aluminum extrusion and die design using neural networks and genetic algorithms, edited by Aluminium Two Thousand 5th World Congress. Rome. (2003)

[8] D. Karayel and S.S. Ozkan: Simulation of direct extrusion process and optimal design of technological parameters using FEM and artificial neural network, edited by Key Engineering Materials. Vol. 367. (2008)

[9] R. Camargo and R. Lesley: Use of adaptive neural networks (A**) in aluminum extrusion process control. Proceedings of the Ninth International Aluminum Extrusion Technology Seminar. Orlando. (2008)

[10] M. Sabater, M.L. Garcia-Romeu and J. Ciurana: Input parameters determination for predicting ram speed and billet temperature for the first billet, edited by Key Engineering Materials. Vol. 367. 161-168. (2008)


Study of flow balance and temperature evolution over multiple aluminum extrusion press cycles with HyperXtrude 9.0

Amin Farjad Bastani1,2,a, Trond Aukrust1,b , Inge Skauvik3,c 1SINTEF Materials and Chemistry, PB-124 Blindern, N-0314 Oslo, Norway

2Department of Informatics, University of Oslo, PB-1060 Blindern, N-0316 Oslo, Norway 3Hydro Aluminium a.s R&D Materials Technology, Håvik, N-4265 Karmøy, Norway


Keywords: Aluminum extrusion, flow balance, temperature evolution, FEM, HyperXtrude. Abstract. In this research, transient finite element simulations of the aluminum extrusion process have been performed in order to study how process parameters influence flow balance and exit temperature. This has been achieved by investigating the influence of billet taper, front billet temperature and ram speed on the run-out velocity and temperature of two separate outlets. Analysis of variance (ANOVA) has been employed to study the effect of each parameter on the velocity and temperature variation of the extruded section. Results show that increasing each of these three parameters results in an undesired increase in exit velocity and temperature. The front billet temperature is found to be the most significant factor affecting the variation. The finite elements software used was Altair HyperXtrude 9.0.

Introduction

The mechanical and geometrical properties of extruded aluminum sections depend on a number of parameters in the extrusion process, including flow and temperature evolution in the container and die. Simulation models, which achieve sufficiently accurate quantification of the flow conditions in the container and die, can be very useful tools when understanding how to control problematic effects on shape and mechanical properties. For this reason, the use of Finite Element Method (FEM) has become more and more immanent in the field of aluminum extrusion. It enables interpretation of three dimensional problems and complex material behavior and allows a full overview of the flow, stress, and temperature fields. Much research has been conducted on FEM simulation of the aluminum extrusion processes in the last few decades [1]. The applications involve nearly all aspects of the extrusion process, i.e. predicting load [2], temperature [3], material flow [4], surface formation [5], surface cracks [6], microstructure [7, 8], isothermal extrusion control [9] and steady state analysis of extrusion [10, 11, 12]. However, due to large deformations, high temperature and high strain rates, FEM simulations of the extrusion process continues to be very challenging.

In a transient study of the extrusion process, with thermal coupling between the tools and aluminum, the commercial FE software Altair HyperXtrude 9.0 [13], which is a recognized solution for 3D extrusion problems [14] has been used. To study how the flow balance and the exit temperature vary over a press cycle, a generic axisymmetric case has been designed (Fig. 1). The model has two outlets with the same bearing lengths and wall thickness at two different radial distances from the centre of the die. This corresponds to extruding two concentric tubes, one inside the other, which can only be realized with a hollow die. However, in order to study the variation of the velocity and temperature of the two outlets, it was decided to model this as a generic case with a flat axisymmetric die. To capture the heat exchange between the aluminum and the surrounding extrusion press, a container, die, ram and bolster have been included in the model.

Study of flow balance and temperature evolution over multiple aluminum extrusion press cycles with HyperXtrude 9.0

Amin Farjad Bastani1,2,a, Trond Aukrust1,b , Inge Skauvik3,c 1SINTEF Materials and Chemistry, PB-124 Blindern, N-0314 Oslo, Norway

2Department of Informatics, University of Oslo, PB-1060 Blindern, N-0316 Oslo, Norway 3Hydro Aluminium a.s R&D Materials Technology, Håvik, N-4265 Karmøy, Norway


Keywords: Aluminum extrusion, flow balance, temperature evolution, FEM, HyperXtrude. Abstract. In this research, transient finite element simulations of the aluminum extrusion process have been performed in order to study how process parameters influence flow balance and exit temperature. This has been achieved by investigating the influence of billet taper, front billet temperature and ram speed on the run-out velocity and temperature of two separate outlets. Analysis of variance (ANOVA) has been employed to study the effect of each parameter on the velocity and temperature variation of the extruded section. Results show that increasing each of these three parameters results in an undesired increase in exit velocity and temperature. The front billet temperature is found to be the most significant factor affecting the variation. The finite elements software used was Altair HyperXtrude 9.0.

Introduction

The mechanical and geometrical properties of extruded aluminum sections depend on a number of parameters in the extrusion process, including flow and temperature evolution in the container and die. Simulation models, which achieve sufficiently accurate quantification of the flow conditions in the container and die, can be very useful tools when understanding how to control problematic effects on shape and mechanical properties. For this reason, the use of Finite Element Method (FEM) has become more and more immanent in the field of aluminum extrusion. It enables interpretation of three dimensional problems and complex material behavior and allows a full overview of the flow, stress, and temperature fields. Much research has been conducted on FEM simulation of the aluminum extrusion processes in the last few decades [1]. The applications involve nearly all aspects of the extrusion process, i.e. predicting load [2], temperature [3], material flow [4], surface formation [5], surface cracks [6], microstructure [7, 8], isothermal extrusion control [9] and steady state analysis of extrusion [10, 11, 12]. However, due to large deformations, high temperature and high strain rates, FEM simulations of the extrusion process continues to be very challenging.

In a transient study of the extrusion process, with thermal coupling between the tools and aluminum, the commercial FE software Altair HyperXtrude 9.0 [13], which is a recognized solution for 3D extrusion problems [14] has been used. To study how the flow balance and the exit temperature vary over a press cycle, a generic axisymmetric case has been designed (Fig. 1). The model has two outlets with the same bearing lengths and wall thickness at two different radial distances from the centre of the die. This corresponds to extruding two concentric tubes, one inside the other, which can only be realized with a hollow die. However, in order to study the variation of the velocity and temperature of the two outlets, it was decided to model this as a generic case with a flat axisymmetric die. To capture the heat exchange between the aluminum and the surrounding extrusion press, a container, die, ram and bolster have been included in the model.


Fig. 1: Axi-symmetric model including the ram, billet, container, bearing, a part of profile, a part of die and bolster. The profiles are two concentric tubes with the radius of 25 and 75 mm.

FEM Simulation

Geometry. The billet has a radius of 105 mm and length of 1100 mm. The two sections are located at 25 mm and 75 mm from the centerline of the billet. The thickness of both sections is 2 mm. A bearing length of 2 mm is used on all bearing surfaces. The extrusion ratio is almost 27.5.

This problem can be modeled with 2D axisymmetric elements. However, due to higher versatility and better convergence of 3D elements compared to 2D elements in the HyperXtrude solver, the model has been meshed with 3D brick elements as a thin slice of a full cylinder, as shown in Fig. 2. Approximately 2600 fluid elements (aluminum) and 1900 solid elements (steel) are used in the model. Heat conduction is applied wherever aluminum meets the tools, i.e. at the billet-container, billet-ram, billet-die and bearing-die interfaces. Air cooling is applied around the container, die, ram and the bolster.

Fig. 2: 3D slice modeled with 2nd order 20 nodes brick elements. Symmetry conditions have been applied on the both left and right sides of the slice to simulate the geometry of the generic model with two concentric tubes.

RAM BILLET

CONTAINER

Outer profile Inner profile

Axis of symmetry

DIE BOLSTER

Fig. 1: Axi-symmetric model including the ram, billet, container, bearing, a part of profile, a part of die and bolster. The profiles are two concentric tubes with the radius of 25 and 75 mm.

FEM Simulation

Geometry. The billet has a radius of 105 mm and length of 1100 mm. The two sections are located at 25 mm and 75 mm from the centerline of the billet. The thickness of both sections is 2 mm. A bearing length of 2 mm is used on all bearing surfaces. The extrusion ratio is almost 27.5.

This problem can be modeled with 2D axisymmetric elements. However, due to higher versatility and better convergence of 3D elements compared to 2D elements in the HyperXtrude solver, the model has been meshed with 3D brick elements as a thin slice of a full cylinder, as shown in Fig. 2. Approximately 2600 fluid elements (aluminum) and 1900 solid elements (steel) are used in the model. Heat conduction is applied wherever aluminum meets the tools, i.e. at the billet-container, billet-ram, billet-die and bearing-die interfaces. Air cooling is applied around the container, die, ram and the bolster.

Fig. 2: 3D slice modeled with 2nd order 20 nodes brick elements. Symmetry conditions have been applied on the both left and right sides of the slice to simulate the geometry of the generic model with two concentric tubes.

RAM BILLET

CONTAINER

Outer profile Inner profile

Axis of symmetry

DIE BOLSTER


In the problems with moving boundaries, HyperXtrude uses Arbitrary Lagrangian-Eulerian description. The mesh in the tools, bearing, profile and a thin 10mm region in the billet closed to the die face is fixed, but in the billet region the elements scale down linearly in the extrusion direction in each time step.

For each case studied, the model runs for 4 consecutive press cycles, each comprising 100 sequential steps.

Full sticking is used in the bearing channel. Since the main focus of this paper is the effect of process parameters on the flow and temperature variations of the two outlets, the full sticking assumption between all aluminum–steel contact surfaces will shift the exit velocity or the exit temperature distribution slightly but it will not influence the variation of them. Material model. The container, die and bolster were modeled as a “stationary rigid body” made of the H13 tool steel and only used in the thermal analysis. The ram was made of the same material and modeled as a “moving rigid body”. The material model used for aluminum was the Sellars-Tegart model [15]:

n

AZ

Sinh1

11

= −

ασ (1)

where σ is the flow stress, α, n and A are temperature independent constants and Z is the Zener-Hollomon parameter, defined by:

=RTQ

Z expε& (2)

where ε& is the effective strain rate, Q is the activation energy, R is the universal gas constant and T is the absolute temperature. Values used for the 6063 alloy are as follows [16]: α= m28104 −× ,

n= 5.385, A= 191091052.5 −× s , Q= molkJ5104155.1 × and R= ( )KmolJ314.8 . Extrusion process parameters. A designed set of experiments was conducted to study the effect of process parameters on the flow balance and the temperature variation in the extrusion of aluminum. There are many different types of DOE (Design of Experiments) methods, each one suitable for a particular case. Factorial design is one of the most frequently used methods when the results from all the combination of parameters are available. The case described here has three parameters, which permits either 32 or 33 designs, resulting in 8 or 27 experiments. Due to the fact that the experiments are done on a computer instead of in a real extrusion plant, it was possible to run the more time-consuming but exhaustive 33 design. Three level factorial design with three factors, front billet temperature (ºC), billet taper (ºC/billet length), and ram speed (mm/sec) was implemented. Table 1 shows the process parameters and their levels. The selection of parameters was based on recommendations and empirical data from process engineers. Table 1: Process parameters and levels

Parameter Level

Low Intermediate High Billet temperature [ºC] 450 480 510 Billet taper [ºC/billet length] 10 40 70 Ram speed [mm/sec] 6 12 18

In the problems with moving boundaries, HyperXtrude uses Arbitrary Lagrangian-Eulerian description. The mesh in the tools, bearing, profile and a thin 10mm region in the billet closed to the die face is fixed, but in the billet region the elements scale down linearly in the extrusion direction in each time step.

For each case studied, the model runs for 4 consecutive press cycles, each comprising 100 sequential steps.

Full sticking is used in the bearing channel. Since the main focus of this paper is the effect of process parameters on the flow and temperature variations of the two outlets, the full sticking assumption between all aluminum–steel contact surfaces will shift the exit velocity or the exit temperature distribution slightly but it will not influence the variation of them. Material model. The container, die and bolster were modeled as a “stationary rigid body” made of the H13 tool steel and only used in the thermal analysis. The ram was made of the same material and modeled as a “moving rigid body”. The material model used for aluminum was the Sellars-Tegart model [15]:

n

AZ

Sinh1

11

= −

ασ (1)

where σ is the flow stress, α, n and A are temperature independent constants and Z is the Zener-Hollomon parameter, defined by:

=RTQ

Z expε& (2)

where ε& is the effective strain rate, Q is the activation energy, R is the universal gas constant and T is the absolute temperature. Values used for the 6063 alloy are as follows [16]: α= m28104 −× ,

n= 5.385, A= 191091052.5 −× s , Q= molkJ5104155.1 × and R= ( )KmolJ314.8 . Extrusion process parameters. A designed set of experiments was conducted to study the effect of process parameters on the flow balance and the temperature variation in the extrusion of aluminum. There are many different types of DOE (Design of Experiments) methods, each one suitable for a particular case. Factorial design is one of the most frequently used methods when the results from all the combination of parameters are available. The case described here has three parameters, which permits either 32 or 33 designs, resulting in 8 or 27 experiments. Due to the fact that the experiments are done on a computer instead of in a real extrusion plant, it was possible to run the more time-consuming but exhaustive 33 design. Three level factorial design with three factors, front billet temperature (ºC), billet taper (ºC/billet length), and ram speed (mm/sec) was implemented. Table 1 shows the process parameters and their levels. The selection of parameters was based on recommendations and empirical data from process engineers. Table 1: Process parameters and levels

Parameter Level

Low Intermediate High Billet temperature [ºC] 450 480 510 Billet taper [ºC/billet length] 10 40 70 Ram speed [mm/sec] 6 12 18


Simulation Results

Each of the 27 combinations has been solved with a transient nonlinear model over 4 sequential press cycles. Each model took almost 6 hours of CPU time on a Linux machine with 3.8 GB of RAM and a 3.4 GHz Intel Xeon processor.

The temperature of the extruded section is an important variable to control as it influences the product quality and is indicative of increasing extrusion speed [17]. There is also a direct relationship between the temperature and the material properties of the extruded section. Maintaining a homogenous temperature distribution throughout the section helps to obtain homogenous material properties. Since the flow stress is a function of temperature, (Eq. 1), the temperature distribution also influences the velocity field.

On the other hand, metal flow has a strong influence on the geometrical tolerance of the profile. By studying the difference between the outlets’ velocities for the two exits, one gets a clear indication of the flow balance of the die.

A sample velocity and temperature distribution at the middle of the 4th cycle for the middle case, i.e., a front billet temperature of 480°C, a ram speed of 12 mm/s and a taper of 40°C/billet length is shown in Fig. 3. Fig. 4 shows the exit velocity and exit temperature for the two outlets over four press cycles.

Fig. 3: Velocity and temperature distribution at t= 344 sec, in the middle of the 4th cycle. Front billet temperature = 480°C, ram speed = 12 mm/s and taper = 40°C/billet length.

(a) (b)

Fig. 4: (a) Exit temperature and (b) exit velocity for the inner and outer outlets over four press cycles for the same case as Fig. 3. Responses. In order to quantify the flow and temperature variations, the normalized difference between the temperature and the velocity has been measured at each outlet and during the 4th press cycles. Only the central 80% of the time span of the last cycle after the acceleration time has been used due to some start and end effects (see Fig. 5a and b). For each process parameter, a unique response of the exit speed and temperature has been calculated:

Simulation Results

Each of the 27 combinations has been solved with a transient nonlinear model over 4 sequential press cycles. Each model took almost 6 hours of CPU time on a Linux machine with 3.8 GB of RAM and a 3.4 GHz Intel Xeon processor.

The temperature of the extruded section is an important variable to control as it influences the product quality and is indicative of increasing extrusion speed [17]. There is also a direct relationship between the temperature and the material properties of the extruded section. Maintaining a homogenous temperature distribution throughout the section helps to obtain homogenous material properties. Since the flow stress is a function of temperature, (Eq. 1), the temperature distribution also influences the velocity field.

On the other hand, metal flow has a strong influence on the geometrical tolerance of the profile. By studying the difference between the outlets’ velocities for the two exits, one gets a clear indication of the flow balance of the die.

A sample velocity and temperature distribution at the middle of the 4th cycle for the middle case, i.e., a front billet temperature of 480°C, a ram speed of 12 mm/s and a taper of 40°C/billet length is shown in Fig. 3. Fig. 4 shows the exit velocity and exit temperature for the two outlets over four press cycles.

Fig. 3: Velocity and temperature distribution at t= 344 sec, in the middle of the 4th cycle. Front billet temperature = 480°C, ram speed = 12 mm/s and taper = 40°C/billet length.

(a) (b)

Fig. 4: (a) Exit temperature and (b) exit velocity for the inner and outer outlets over four press cycles for the same case as Fig. 3. Responses. In order to quantify the flow and temperature variations, the normalized difference between the temperature and the velocity has been measured at each outlet and during the 4th press cycles. Only the central 80% of the time span of the last cycle after the acceleration time has been used due to some start and end effects (see Fig. 5a and b). For each process parameter, a unique response of the exit speed and temperature has been calculated:


[ ])min()max(1

inoutinoutaverage

T TTTTT

i −−−= (3)

[ ])min()max(1

inoutinoutaverage

V VVVVV

i −−−= (4)

(a) (b)

(c) (d)

Fig. 5: (a) Exit temperature and (b) exit velocity of inner and outer outlets during the last press cycle. (c) Normalized temperature variation curve and (d) Normalized velocity variation curve showing the maximum and minimum values for the same case as Fig. 3. Following this definition of the response parameters, a relative shift of one or both of the exit values will not influence the result significantly. For instance, a change in the bearing lengths will shift the exit speeds and the exit temperature for all the cases. However, since this will influence all iV (or iT) equally, it will not alter the results of this analysis iV and iT. It should be pointed out that in some cases, the response parameters iV and iT are sensitive to the internal time span chosen, as the min(Tout

- Tin) or min(Vout - Vin) are in general found to be at the upper or lower border for the time span used (as in Fig. 5c and d), and therefore can change with the time span used.

The selection of the cycle has some influence on the variation indexes. Fig. 4 shows that the variation of difference between the two outlets will change significantly from the 1st to the 2nd press cycle. However between the 3rd and the 4th cycle this change is very small. Due to this fact it is a reasonable choice to study the variation indexes in the 4th cycle. The results for iV and iT for all the simulations are listed in Table 2 and illustrated in Fig 6:

Max Max

Min Min

[ ])min()max(1

inoutinoutaverage

T TTTTT

i −−−= (3)

[ ])min()max(1

inoutinoutaverage

V VVVVV

i −−−= (4)

(a) (b)

(c) (d)

Fig. 5: (a) Exit temperature and (b) exit velocity of inner and outer outlets during the last press cycle. (c) Normalized temperature variation curve and (d) Normalized velocity variation curve showing the maximum and minimum values for the same case as Fig. 3. Following this definition of the response parameters, a relative shift of one or both of the exit values will not influence the result significantly. For instance, a change in the bearing lengths will shift the exit speeds and the exit temperature for all the cases. However, since this will influence all iV (or iT) equally, it will not alter the results of this analysis iV and iT. It should be pointed out that in some cases, the response parameters iV and iT are sensitive to the internal time span chosen, as the min(Tout

- Tin) or min(Vout - Vin) are in general found to be at the upper or lower border for the time span used (as in Fig. 5c and d), and therefore can change with the time span used.

The selection of the cycle has some influence on the variation indexes. Fig. 4 shows that the variation of difference between the two outlets will change significantly from the 1st to the 2nd press cycle. However between the 3rd and the 4th cycle this change is very small. Due to this fact it is a reasonable choice to study the variation indexes in the 4th cycle. The results for iV and iT for all the simulations are listed in Table 2 and illustrated in Fig 6:

Max Max

Min Min


Table 2 and Fig. 6: Simulation results for the variation responses defined by Eq. 3:

Analysis of Variance. Using the Analysis of Variance (ANOVA) method, the effect of billet taper, front billet temperature and ram speed on the variations of the exit velocity and the exit temperature has been studied. The analysis of variance is summarized in Table 3a and 3b, where DF is the degrees of freedom, SeqSS is the sequential sum of squares, F is the F-test value and P is the P-test value:

Table 3: ANOVA table for Ti (a) and Vi (b).

Source DF SeqSS F P Source DF SeqSS F P Ram Speed 2 0.0000420 7.29 0.004 Ram Speed 2 0.0009019 3.76 0.041 Temperature 2 0.0002353 40.80 0.000 Temperature 2 0.0146479 61.09 0.000 Taper 2 0.0000828 14.36 0.000 Taper 2 0.0028904 12.05 0.000 Error 20 0.0000577 Error 20 0.0023978 Total 26 0.0004178 Total 26 0.0208380

(a) (b) The F-test value is found by dividing the mean square of each parameter by the mean square of the error term. This value can be used to test the “significance” of the parameters considered. Depending on the degree of freedom for the parameter and the error, the F-value will have a certain distribution. In our case, all the parameters have a degree of freedom of 3 – 1 = 2 and the error has a degree of freedom of 26 – 2 – 2 – 2 = 20. If one uses a significance level of 0.05, this results in F0.05,2,20 = 3.49. The implication of this is that if the F-value is larger than 3.49, one can say with confidence that the parameter considered has a significant effect on the response [18]. For instance, for the response iV in Table 3b, the F-value for the temperature parameter is F= 0.0146479/0.0023978= 61.09. Since F = 61.09 is much larger than 3.49, this implies that the temperature parameter significantly affects iV. The same conclusion can be drawn for the effect of ram speed and taper, showing that all the parameters are significantly affecting both iV and iT (see Table 3a and b).

One of the easiest ways to investigate the effect of parameters on the response is the Main Effects Plot. It is the effect of each parameter alone when averaged over the other parameters. For example for a taper of 10 ºC/billet length the average of the other responses in Table 2 gives 0.0067 for iT and 0.05 for iV , and for a front billet temperature of 450 ºC the average gives 0.0056 for iT and 0.037 for iV (See Fig. 7).

Taper Temp Speed Ti Vi

10

450 06 0.23% 1.74% 12 0.42% 3.02% 18 0.53% 3.54%

480 06 0.64% 5.03% 12 0.40% 3.10% 18 0.56% 3.83%

510 06 1.28% 9.88% 12 1.00% 7.58% 18 1.00% 7.42%

40

450 06 0.29% 2.18% 12 0.51% 3.44% 18 0.81% 5.05%

480 06 0.72% 5.46% 12 0.67% 4.88% 18 0.99% 6.61%

510 06 1.33% 10.11% 12 1.13% 8.45% 18 1.28% 8.96%

70

450 06 0.38% 2.80% 12 0.64% 4.24% 18 1.23% 7.35%

480 06 0.86% 6.32% 12 0.95% 6.53% 18 1.42% 9.12%

510 06 1.39% 10.39% 12 1.36% 9.78% 18 1.66% 1.36%

Ti

Vi

Table 2 and Fig. 6: Simulation results for the variation responses defined by Eq. 3:

Analysis of Variance. Using the Analysis of Variance (ANOVA) method, the effect of billet taper, front billet temperature and ram speed on the variations of the exit velocity and the exit temperature has been studied. The analysis of variance is summarized in Table 3a and 3b, where DF is the degrees of freedom, SeqSS is the sequential sum of squares, F is the F-test value and P is the P-test value:

Table 3: ANOVA table for Ti (a) and Vi (b).

Source DF SeqSS F P Source DF SeqSS F P Ram Speed 2 0.0000420 7.29 0.004 Ram Speed 2 0.0009019 3.76 0.041 Temperature 2 0.0002353 40.80 0.000 Temperature 2 0.0146479 61.09 0.000 Taper 2 0.0000828 14.36 0.000 Taper 2 0.0028904 12.05 0.000 Error 20 0.0000577 Error 20 0.0023978 Total 26 0.0004178 Total 26 0.0208380

(a) (b) The F-test value is found by dividing the mean square of each parameter by the mean square of the error term. This value can be used to test the “significance” of the parameters considered. Depending on the degree of freedom for the parameter and the error, the F-value will have a certain distribution. In our case, all the parameters have a degree of freedom of 3 – 1 = 2 and the error has a degree of freedom of 26 – 2 – 2 – 2 = 20. If one uses a significance level of 0.05, this results in F0.05,2,20 = 3.49. The implication of this is that if the F-value is larger than 3.49, one can say with confidence that the parameter considered has a significant effect on the response [18]. For instance, for the response iV in Table 3b, the F-value for the temperature parameter is F= 0.0146479/0.0023978= 61.09. Since F = 61.09 is much larger than 3.49, this implies that the temperature parameter significantly affects iV. The same conclusion can be drawn for the effect of ram speed and taper, showing that all the parameters are significantly affecting both iV and iT (see Table 3a and b).

One of the easiest ways to investigate the effect of parameters on the response is the Main Effects Plot. It is the effect of each parameter alone when averaged over the other parameters. For example for a taper of 10 ºC/billet length the average of the other responses in Table 2 gives 0.0067 for iT and 0.05 for iV , and for a front billet temperature of 450 ºC the average gives 0.0056 for iT and 0.037 for iV (See Fig. 7).

Taper Temp Speed Ti Vi

10

450 06 0.23% 1.74% 12 0.42% 3.02% 18 0.53% 3.54%

480 06 0.64% 5.03% 12 0.40% 3.10% 18 0.56% 3.83%

510 06 1.28% 9.88% 12 1.00% 7.58% 18 1.00% 7.42%

40

450 06 0.29% 2.18% 12 0.51% 3.44% 18 0.81% 5.05%

480 06 0.72% 5.46% 12 0.67% 4.88% 18 0.99% 6.61%

510 06 1.33% 10.11% 12 1.13% 8.45% 18 1.28% 8.96%

70

450 06 0.38% 2.80% 12 0.64% 4.24% 18 1.23% 7.35%

480 06 0.86% 6.32% 12 0.95% 6.53% 18 1.42% 9.12%

510 06 1.39% 10.39% 12 1.36% 9.78% 18 1.66% 1.36%

Ti

Vi


As shown in Fig. 7, one can easily see that by increasing the front billet temperature and the taper the variation increases almost linearly. For the ram speed the effect is non-linear, with the highest values for the highest ram speed.

(a) (b)

Fig. 7: Main effect plots for and iT (a) and iV (b).

Discussion and concluding remarks

In this work, transient finite element simulation of the aluminum extrusion process has been performed in order to study how process parameters influence extrusion flow balance and exit temperature. This has been done by investigating the effect of billet taper, front billet temperature and rams speed on the run-out velocity and temperature of two separate outlets. Analysis of variance has been used to study the effect of each parameter on the exit velocity and temperature variations across the section.

It has been shown that all three parameters have a significant influence on the variations of the exit velocity and temperature. The results show that an increase in taper and front billet temperature will result in an undesired increase in the variation of the exit temperature and velocity. When it comes to the effect of the ram speed, it has a non-linear variation with a local minimum (at around 12 mm/s in this case) and with the highest variation at the highest ram speed.

Acknowledgment

This work has been supported by Norsk Hydro ASA and the Research Council of Norway (NFR) through the project ProExtru. The authors would like to thank Sverre Brandal for helpful discussions and comments.

References

[1] X. Duan, X. Velay, T. Sheppard: Application of finite element method in the hot extrusion of aluminium alloys, Materials Science and Engineering A, Volume 369, Issues 1-2, 25 March 2004, pp. 66-75

[2] X. Velay, X. Duan and T. Sheppard., Mater. Sci. Forum 426–432 (2003), p. 3807

[3] J. Zhou, L. Li and J. Duszczyk., J. Mater. Process. Tech. 134 (2003), p. 383

[4] Q. Li, C.J. Smith, C. Harris and M.R. Jolly. J. Mater. Process. Tech. 135 (2003), p. 189

[5] T. Sheppard, X. Duan, in: Z. Jin (Ed.), Hot Deformation of Aluminum Alloys III, Times of Acadiana Pr, Inc., 2003, p. 289

[6] J. Lof and Y. Blokhuis. J. Mater. Process. Tech. 122 (2002), p. 344

As shown in Fig. 7, one can easily see that by increasing the front billet temperature and the taper the variation increases almost linearly. For the ram speed the effect is non-linear, with the highest values for the highest ram speed.

(a) (b)

Fig. 7: Main effect plots for and iT (a) and iV (b).

Discussion and concluding remarks

In this work, transient finite element simulation of the aluminum extrusion process has been performed in order to study how process parameters influence extrusion flow balance and exit temperature. This has been done by investigating the effect of billet taper, front billet temperature and rams speed on the run-out velocity and temperature of two separate outlets. Analysis of variance has been used to study the effect of each parameter on the exit velocity and temperature variations across the section.

It has been shown that all three parameters have a significant influence on the variations of the exit velocity and temperature. The results show that an increase in taper and front billet temperature will result in an undesired increase in the variation of the exit temperature and velocity. When it comes to the effect of the ram speed, it has a non-linear variation with a local minimum (at around 12 mm/s in this case) and with the highest variation at the highest ram speed.

Acknowledgment

This work has been supported by Norsk Hydro ASA and the Research Council of Norway (NFR) through the project ProExtru. The authors would like to thank Sverre Brandal for helpful discussions and comments.

References

[1] X. Duan, X. Velay, T. Sheppard: Application of finite element method in the hot extrusion of aluminium alloys, Materials Science and Engineering A, Volume 369, Issues 1-2, 25 March 2004, pp. 66-75

[2] X. Velay, X. Duan and T. Sheppard., Mater. Sci. Forum 426–432 (2003), p. 3807

[3] J. Zhou, L. Li and J. Duszczyk., J. Mater. Process. Tech. 134 (2003), p. 383

[4] Q. Li, C.J. Smith, C. Harris and M.R. Jolly. J. Mater. Process. Tech. 135 (2003), p. 189

[5] T. Sheppard, X. Duan, in: Z. Jin (Ed.), Hot Deformation of Aluminum Alloys III, Times of Acadiana Pr, Inc., 2003, p. 289

[6] J. Lof and Y. Blokhuis. J. Mater. Process. Tech. 122 (2002), p. 344


[7] K. Marthinsen, B. Holmedal, S. Abtahi, S. Chen and E. Nes. Mater. Sci. Forum 426–432 (2003), p. 3777

[8] R.J. Dashwood, H.B. McShane, A. Jackson, in: Proceedings of the 6th International Seminar on Aluminum Extrusion Technology, vol. I, Chicago, IL, USA, May 1996, Aluminum Extruders Council, 1996, pp. 331–339.

[9] L. Li, J. Zhou and J. Duszczyk. Modell. Simul. Mater. Sci. Eng. 11 (2003), p. 401

[10] B.P.P.A. Gouveia, J.M.C. Rodrigues, N. Bay, P.A.F. Martins, Finite-element modelling of cold forward extrusion, Journal of Materials Processing Technology, Volume 94, Issues 2-3, 29 September 1999, Pages 85-93

[11] B.P.P.A. Gouveia, J.M.C. Rodrigues, N. Bay, P.A.F. Martins, Deformation analysis of the round-to-square extrusion: a numerical and experimental investigation, Finite Elements in Analysis and Design, Volume 35, Issue 3, 1 June 2000, Pages 269-282

[12] B.P.P.A. Gouveia, J.M.C. Rodrigues, N. Bay, P.A.F. Martins, Physical modelling and numerical simulation of the round-to-square forward extrusion, Journal of Materials Processing Technology, Volume 112, Issues 2-3, 25 May 2001, Pages 244-251

[13] HyperXtrude 9.0, Altair Engineering, Inc., Troy, MI 48083-2031

[14] http://diemtech.ing.unibo.it/extrusion07

[15] C.M. Sellars, and W.J. Tegart, 1972. Hot workability. Int. Met. Rev. 17, 1-24.

[16] M. P. Clode, 1992. Material flow and microstructure development during extrusion of AA6063. In: Proceedings of the Fifth International Aluminium Extrusion Technology Seminar, Aluminium Association and Aluminium Extruder’s Council, Wauconda, Illinois, pp. 79–99.

[17] G. Fang, et al., FEM simulation of aluminium extrusion through two-hole multi-step pocket dies, J. Mater. Process. Tech. (2008), doi:10.1016/j.jmatprotec.2008.04.036

[18] D. C. Montgomery, Design and Analysis of Experiments, 7th Ed., 2009, ISBN: 978-0-470-39882-1

[7] K. Marthinsen, B. Holmedal, S. Abtahi, S. Chen and E. Nes. Mater. Sci. Forum 426–432 (2003), p. 3777

[8] R.J. Dashwood, H.B. McShane, A. Jackson, in: Proceedings of the 6th International Seminar on Aluminum Extrusion Technology, vol. I, Chicago, IL, USA, May 1996, Aluminum Extruders Council, 1996, pp. 331–339.

[9] L. Li, J. Zhou and J. Duszczyk. Modell. Simul. Mater. Sci. Eng. 11 (2003), p. 401

[10] B.P.P.A. Gouveia, J.M.C. Rodrigues, N. Bay, P.A.F. Martins, Finite-element modelling of cold forward extrusion, Journal of Materials Processing Technology, Volume 94, Issues 2-3, 29 September 1999, Pages 85-93

[11] B.P.P.A. Gouveia, J.M.C. Rodrigues, N. Bay, P.A.F. Martins, Deformation analysis of the round-to-square extrusion: a numerical and experimental investigation, Finite Elements in Analysis and Design, Volume 35, Issue 3, 1 June 2000, Pages 269-282

[12] B.P.P.A. Gouveia, J.M.C. Rodrigues, N. Bay, P.A.F. Martins, Physical modelling and numerical simulation of the round-to-square forward extrusion, Journal of Materials Processing Technology, Volume 112, Issues 2-3, 25 May 2001, Pages 244-251

[13] HyperXtrude 9.0, Altair Engineering, Inc., Troy, MI 48083-2031

[14] http://diemtech.ing.unibo.it/extrusion07

[15] C.M. Sellars, and W.J. Tegart, 1972. Hot workability. Int. Met. Rev. 17, 1-24.

[16] M. P. Clode, 1992. Material flow and microstructure development during extrusion of AA6063. In: Proceedings of the Fifth International Aluminium Extrusion Technology Seminar, Aluminium Association and Aluminium Extruder’s Council, Wauconda, Illinois, pp. 79–99.

[17] G. Fang, et al., FEM simulation of aluminium extrusion through two-hole multi-step pocket dies, J. Mater. Process. Tech. (2008), doi:10.1016/j.jmatprotec.2008.04.036

[18] D. C. Montgomery, Design and Analysis of Experiments, 7th Ed., 2009, ISBN: 978-0-470-39882-1


Numerical design of extrusion process using finite thermo-elastoviscoplasticity with damage. Prediction of chevron shaped cracks

C. Labergère1, a, K. Saanouni1,b and P. Lestriez2,c 1UTT, ICD/LASMIS, FRE CNRS 2848, 12 rue Marie Curie BP2060, 10010 Troyes, France

2URCA, GRESPI/LMNGMMS EA 2617, Moulin de la Housse BP1039, 51687 Reims, France [email protected], [email protected], [email protected]

Keywords: chevron cracks, extrusion, thermo-elastoviscoplasticity, ductile damage, numerical design, FEM. Abstract. The influence of the initial temperature and its evolution with large plastic deformation on the formation of the fully coupled chevron shaped cracks in extrusion is numerically investigated. Fully coupled thermo-elasto-viscoplastic constitutive equations accounting for thermal effects, mixed and nonlinear isotropic and kinematic hardening, isotropic ductile damage with micro-cracks closure effects are used. These constitutive equations have been implemented in Abaqus/Explicit code thanks to the user subroutine vumat and used to perform various numerical simulations needed to investigate the problem. It has been shown that the proposed methodology is efficient to predict the chevron shaped cracks in extrusion function of the main process parameters including the temperature effect.

Introduction

Extrusion is the process by which a round block of metal is reduced in cross section by forcing it through a die orifice under high pressure. Concerning the axisymmetric forward extrusion, the main process parameters that influence the product quality are: the area reduction factor (Ar), the die cone angle (α d), the frictional conditions at the die material interface, the material parameters (hardening, ductility, …) and the working temperature. According to the large plastic deformation experienced by the extruded metal together with effect of the above discussed parameters, products obtained by extrusion are sometimes defective. One common defect, under concern in this paper, is the central bursts or chevron shaped cracks. These internal defects appear along the central axis of the billet as chevron shaped cracks that point in the direction of the metal flow. Although this type of defect occurs with a small frequency, it is highly insidious because it is usually not visible from the outside and needs special non destructive technique control to be detected. This problem has been addressed in many works using various kinds of local fracture criteria in order to predict the discontinuous chevron shaped cracks formation ([1-5], [6-7] and [9-10]) dealing with cold extrusion, the material behaviour has been taken as elastoplastic and isothermal in all these works. In this paper, thermoelasto-viscoplastic constitutive equations with both non linear isotropic and kinematic hardenings strongly coupled with isotropic ductile damage and thermal effects are used. In order to better describe the micro-cracks closure under compressive stress state and its effect in both the material properties (elastic modulus, hardening modulus, …) and the damage growth, a modified damage criterion differentiating between the tensile and the compressive stress states is used following the idea originally proposed by [5] and recently used in [10] for cold extrusion problem. This fully coupled model is implemented into ABAQUS/Expl and the material parameters are identified for 100Cr6 steel for different temperature [11]. A special care is given to the development of a numerical design methodology in order to study the influence of some extrusion parameters on the ‘discontinuous’ formation of central bursts; as the effects of the friction coefficient, the initial temperature of the billet and the velocity of the punch. A 3D process which transform the initial cylindrical section of a 3D billet to a final triangular section is also studied.

Numerical design of extrusion process using finite thermo-elastoviscoplasticity with damage. Prediction of chevron shaped cracks

C. Labergère1, a, K. Saanouni1,b and P. Lestriez2,c 1UTT, ICD/LASMIS, FRE CNRS 2848, 12 rue Marie Curie BP2060, 10010 Troyes, France

2URCA, GRESPI/LMNGMMS EA 2617, Moulin de la Housse BP1039, 51687 Reims, France [email protected], [email protected], [email protected]

Keywords: chevron cracks, extrusion, thermo-elastoviscoplasticity, ductile damage, numerical design, FEM. Abstract. The influence of the initial temperature and its evolution with large plastic deformation on the formation of the fully coupled chevron shaped cracks in extrusion is numerically investigated. Fully coupled thermo-elasto-viscoplastic constitutive equations accounting for thermal effects, mixed and nonlinear isotropic and kinematic hardening, isotropic ductile damage with micro-cracks closure effects are used. These constitutive equations have been implemented in Abaqus/Explicit code thanks to the user subroutine vumat and used to perform various numerical simulations needed to investigate the problem. It has been shown that the proposed methodology is efficient to predict the chevron shaped cracks in extrusion function of the main process parameters including the temperature effect.

Introduction

Extrusion is the process by which a round block of metal is reduced in cross section by forcing it through a die orifice under high pressure. Concerning the axisymmetric forward extrusion, the main process parameters that influence the product quality are: the area reduction factor (Ar), the die cone angle (α d), the frictional conditions at the die material interface, the material parameters (hardening, ductility, …) and the working temperature. According to the large plastic deformation experienced by the extruded metal together with effect of the above discussed parameters, products obtained by extrusion are sometimes defective. One common defect, under concern in this paper, is the central bursts or chevron shaped cracks. These internal defects appear along the central axis of the billet as chevron shaped cracks that point in the direction of the metal flow. Although this type of defect occurs with a small frequency, it is highly insidious because it is usually not visible from the outside and needs special non destructive technique control to be detected. This problem has been addressed in many works using various kinds of local fracture criteria in order to predict the discontinuous chevron shaped cracks formation ([1-5], [6-7] and [9-10]) dealing with cold extrusion, the material behaviour has been taken as elastoplastic and isothermal in all these works. In this paper, thermoelasto-viscoplastic constitutive equations with both non linear isotropic and kinematic hardenings strongly coupled with isotropic ductile damage and thermal effects are used. In order to better describe the micro-cracks closure under compressive stress state and its effect in both the material properties (elastic modulus, hardening modulus, …) and the damage growth, a modified damage criterion differentiating between the tensile and the compressive stress states is used following the idea originally proposed by [5] and recently used in [10] for cold extrusion problem. This fully coupled model is implemented into ABAQUS/Expl and the material parameters are identified for 100Cr6 steel for different temperature [11]. A special care is given to the development of a numerical design methodology in order to study the influence of some extrusion parameters on the ‘discontinuous’ formation of central bursts; as the effects of the friction coefficient, the initial temperature of the billet and the velocity of the punch. A 3D process which transform the initial cylindrical section of a 3D billet to a final triangular section is also studied.


Thermo-elasto-viscoplastic model with isotropic ductile damage

The fully coupled thermo-elasto-visco-plastic behaviour is modelled in the framework of the thermodynamics of irreversible processes with state variables ([5], [8]) assuming the small elastic strain and large plastic strain hypothesis. According to the first gradient formulation, two ‘external’ state variables are introduced: (ε, σ) for total strain tensor and the Cauchy stress tensor; (T, s) for absolute temperature and specific entropy. The ‘internal’ state variables and their conjugate forces

are : (εe , σ) for small elastic strain tensor and the Cauchy stress tensor; ( =q ,g grad(T )T

) for

thermal flux vector and its conjugate force; (α, X) for back-strain and back-stress deviator tensors that describe the kinematic hardening (i.e. translation of the yield surface center); (r, R) equivalent plastic driving strain and stress representing the isotropic hardening (i.e. variation of the yielding surface size) and (D, Y) for isotropic damage and its conjugate force, which is also known as a damage strain energy release rate [8]. The dual variables ( ),R, X ,Y ,sσ are derived from the state potential, classically taken as the

Helmholtz free energy ( )e

,r , ,D,TΨ ε α additively decomposed and written in the present isotropic case as:

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

2ve e eT 0 0

0

2

E T C1 11 D : T : 1 D T T :1 T T2 1 2 2 T1 11 D C T : 1 D Q T r3 2

ω

ρψ = − ε Λ ε −η − − ε − ρ −− ν

+ − α α+ −

(1)

Where ρ is the material density, Cv is the specific heat coefficient, C and Q are the kinematic and isotropic hardening modulus respectively. Tη is the thermal expansion parameter of the material,

( ) ( )( ) ( )E ET 1 1 2 1

1 1 2 2 1ν

Λ = ⊗ ++ ν − ν + ν

is the fourth order symmetric elastic properties tensor for the

isotropic material where E is the Young modulus and ν is the Poisson coefficient To take into account the thermal coupling, all the material parameter should be decreasing functions of the absolute temperature T. By introducing the above state potential into the Clausius-Duhem basic inequality [8] the following state relations are obtained:

( ) ( ) ( ) ( )e T 0 H

3E Tσ 1 D T :ε 1 D T T 1

1 2= − Λ − − η − ε

− ν (2)

( )( )

0T H v

0

3E T (T T )s 1 D C1 2 T

−= − η ε +ρ − ν

(3)

( ) ( )2X 1-D C T α3

= (4)

( ) ( )R 1 D Q T rω= − (5)

e ther ineY Y Y YD

ρ∂ψ= − = + +

∂ with

( ) ( )

( ) ( )

e ee

Tther 0 H

1 2ine

1Y : (T) :2

3E TY T T

1 22 1 D2 1Y C T : D Q T r3 2

ω−

⎧ = ε Λ ε⎪⎪

η⎪ = − − ε⎨ − ν−⎪⎪

= α α+ ω⎪⎩

(6)

Thermo-elasto-viscoplastic model with isotropic ductile damage

The fully coupled thermo-elasto-visco-plastic behaviour is modelled in the framework of the thermodynamics of irreversible processes with state variables ([5], [8]) assuming the small elastic strain and large plastic strain hypothesis. According to the first gradient formulation, two ‘external’ state variables are introduced: (ε, σ) for total strain tensor and the Cauchy stress tensor; (T, s) for absolute temperature and specific entropy. The ‘internal’ state variables and their conjugate forces

are : (εe , σ) for small elastic strain tensor and the Cauchy stress tensor; ( =q ,g grad(T )T

) for

thermal flux vector and its conjugate force; (α, X) for back-strain and back-stress deviator tensors that describe the kinematic hardening (i.e. translation of the yield surface center); (r, R) equivalent plastic driving strain and stress representing the isotropic hardening (i.e. variation of the yielding surface size) and (D, Y) for isotropic damage and its conjugate force, which is also known as a damage strain energy release rate [8]. The dual variables ( ),R, X ,Y ,sσ are derived from the state potential, classically taken as the

Helmholtz free energy ( )e

,r , ,D,TΨ ε α additively decomposed and written in the present isotropic case as:

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

2ve e eT 0 0

0

2

E T C1 11 D : T : 1 D T T :1 T T2 1 2 2 T1 11 D C T : 1 D Q T r3 2

ω

ρψ = − ε Λ ε −η − − ε − ρ −− ν

+ − α α+ −

(1)

Where ρ is the material density, Cv is the specific heat coefficient, C and Q are the kinematic and isotropic hardening modulus respectively. Tη is the thermal expansion parameter of the material,

( ) ( )( ) ( )E ET 1 1 2 1

1 1 2 2 1ν

Λ = ⊗ ++ ν − ν + ν

is the fourth order symmetric elastic properties tensor for the

isotropic material where E is the Young modulus and ν is the Poisson coefficient To take into account the thermal coupling, all the material parameter should be decreasing functions of the absolute temperature T. By introducing the above state potential into the Clausius-Duhem basic inequality [8] the following state relations are obtained:

( ) ( ) ( ) ( )e T 0 H

3E Tσ 1 D T :ε 1 D T T 1

1 2= − Λ − − η − ε

− ν (2)

( )( )

0T H v

0

3E T (T T )s 1 D C1 2 T

−= − η ε +ρ − ν

(3)

( ) ( )2X 1-D C T α3

= (4)

( ) ( )R 1 D Q T rω= − (5)

e ther ineY Y Y YD

ρ∂ψ= − = + +

∂ with

( ) ( )

( ) ( )

e ee

Tther 0 H

1 2ine

1Y : (T) :2

3E TY T T

1 22 1 D2 1Y C T : D Q T r3 2

ω−

⎧ = ε Λ ε⎪⎪

η⎪ = − − ε⎨ − ν−⎪⎪

= α α+ ω⎪⎩

(6)


Following the idea by Lemaitre [5], the simplest way to describe the micro-cracks closure and its loss of effects on the material stiffness as well as on the damage growth under compressive loading state, is to decompose the stress tensor in positive and negative parts. In the principal stress space:

I I I

II II II

III III III

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

+ −

+ −

+ −

+ −

σ σ

⎡ ⎤ ⎡ ⎤σ σ σ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥σ = σ + σ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥σ σ σ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

(7)

( )H H H1 trace3 + −

σ = σ = σ + σ (8)

Where ( )H1 trace3

σ = σ is the hydrostatic stress and σI, σII and σIII are the three principal stresses with

the notation ( )x x x / 2+= + and ( )x x x / 2

−= − . Accordingly, the effective stress tensor can be

written under the following form:

clo1 D 1 h D

+ −σ σσ = +

− − (9)

where hclo∈[0-1] is the micro-crack closure parameter. It is clear that if hclo=1 the damage effect is similar for tensile and compressive stress states. On the other hand, if hclo=0 the damage has no effect on the mechanical properties when the stress state is compressive. In this case, the new form of Ye is given in the stress space by:

( ) ( ) ( )( ) ( ) ( ) ( )

2 2 2 2 2 2 2 2I II III clo I II III H clo H

e

1 h 9 hY

2 1 D E T 2 1 D E T+ + + − − − + −

⎡ ⎤ ⎡ ⎤+ ν σ + σ + σ + σ + σ + σ ν σ + σ⎢ ⎥⎣ ⎦ ⎣ ⎦= −− −

(10)

A classical von Mises yield function is used to determine the plastic limit and a plastic potential is build to obtain the different evolution of the state variables:

( )y

X Rf T1 D 1 Dω

σ −= − −σ

− − (11)

Application of the generalized normality rule leads to the definition of the required complementary relations or constitutive equations as following:

pvp nε = δ with

D3 1 Xn2 X1 D

σ −=

σ−− (12)

( )vp n aα = δ − α (13)

vp1r br

1 Dω

⎛ ⎞= δ −⎜ ⎟

−⎝ ⎠ (14)

svp 0Y Y

D(1 D) Sβ

δ ⎛ ⎞−= ⎜ ⎟− ⎝ ⎠

(15)

where Dσ is the deviatoric part of the Cauchy stress; a and b characterize the non linearity of the kinematic and isotropic hardening respectively; S, s , β and Y0 characterize the ductile damage evolution and D DX (1.5)( X) : ( X)σ− = σ − σ − is the Von Mises equivalent stress: The scalar vpδ is the ‘visco-plastic multiplier’ given by the Norton Hoff viscoplastic potential:

( )( )

vn

vpv

f ,X,R,D;TK T

σδ = (16)

where Kv(T) and nv are the viscosity material parameters.

Following the idea by Lemaitre [5], the simplest way to describe the micro-cracks closure and its loss of effects on the material stiffness as well as on the damage growth under compressive loading state, is to decompose the stress tensor in positive and negative parts. In the principal stress space:

I I I

II II II

III III III

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

+ −

+ −

+ −

+ −

σ σ

⎡ ⎤ ⎡ ⎤σ σ σ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥σ = σ + σ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥σ σ σ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

(7)

( )H H H1 trace3 + −

σ = σ = σ + σ (8)

Where ( )H1 trace3

σ = σ is the hydrostatic stress and σI, σII and σIII are the three principal stresses with

the notation ( )x x x / 2+= + and ( )x x x / 2

−= − . Accordingly, the effective stress tensor can be

written under the following form:

clo1 D 1 h D

+ −σ σσ = +

− − (9)

where hclo∈[0-1] is the micro-crack closure parameter. It is clear that if hclo=1 the damage effect is similar for tensile and compressive stress states. On the other hand, if hclo=0 the damage has no effect on the mechanical properties when the stress state is compressive. In this case, the new form of Ye is given in the stress space by:

( ) ( ) ( )( ) ( ) ( ) ( )

2 2 2 2 2 2 2 2I II III clo I II III H clo H

e

1 h 9 hY

2 1 D E T 2 1 D E T+ + + − − − + −

⎡ ⎤ ⎡ ⎤+ ν σ + σ + σ + σ + σ + σ ν σ + σ⎢ ⎥⎣ ⎦ ⎣ ⎦= −− −

(10)

A classical von Mises yield function is used to determine the plastic limit and a plastic potential is build to obtain the different evolution of the state variables:

( )y

X Rf T1 D 1 Dω

σ −= − −σ

− − (11)

Application of the generalized normality rule leads to the definition of the required complementary relations or constitutive equations as following:

pvp nε = δ with

D3 1 Xn2 X1 D

σ −=

σ−− (12)

( )vp n aα = δ − α (13)

vp1r br

1 Dω

⎛ ⎞= δ −⎜ ⎟

−⎝ ⎠ (14)

svp 0Y Y

D(1 D) Sβ

δ ⎛ ⎞−= ⎜ ⎟− ⎝ ⎠

(15)

where Dσ is the deviatoric part of the Cauchy stress; a and b characterize the non linearity of the kinematic and isotropic hardening respectively; S, s , β and Y0 characterize the ductile damage evolution and D DX (1.5)( X) : ( X)σ− = σ − σ − is the Von Mises equivalent stress: The scalar vpδ is the ‘visco-plastic multiplier’ given by the Norton Hoff viscoplastic potential:

( )( )

vn

vpv

f ,X,R,D;TK T

σδ = (16)

where Kv(T) and nv are the viscosity material parameters.


Extension of the present constitutive equation to the large elasto-viscoplastic scheme can be easily performed using the so called rotated frame formulation [8].

The Thermal dissipation analysis

The evolution of the temperature is obtained by the generalised heat equation including the mechanical dissipation [8]:

( ) emv

X R Ydiv kgradT C T T : : : r : D 0T T T T∂σ ∂ ∂ ∂⎡ ⎤+ φ −ρ + ε + α + − =⎢ ⎥∂ ∂ ∂ ∂⎣ ⎦

(17)

where k is the heat conduction coefficient. And φm is the intrinsic dissipation defined by: pm : X : Rr YD 0φ = σ ε − α − + ≥ (18)

In this work, some material parameter P(T) ( vP E,C,Q, K ,S∈ ) are taken function of temperature under the following form :

( )m

00

F 0

T TP T P 1T T

⎛ ⎞⎛ ⎞−⎜ ⎟= − ⎜ ⎟⎜ ⎟−⎝ ⎠⎝ ⎠ (19)

With Tf is the melting temperature, T0 is the reference (room) temperature, P0 is the value of the mechanical parameter for T=T0 and m is a material parameter measuring its sensitivity to the temperature

Numerical aspect

The fully coupled thermomechanical constitutive equations presented above have been implemented into Abaqus/Explicit FE code using the Vumat user subroutine. The dynamic explicit resolution procedure has been used in order to solve the thermomechanical problem based on both weak forms relative to the equilibrium and thermal equations. The local integration of the fully coupled constitutive equations is performed using an iterative implicit scheme based on the well known elastic prediction – plastic correction with a radial return procedure applied a reduced number of equations (see [8] for more details).

2D axisymmetric cold/hot extrusion

The proposed numerical methodology is now applied to the chevron shaped cracks prediction in an axisymmetric extrusion of a round bar schematized in Fig. 1. Re is the initial radius of the billet, Rs is the final radius of the billet after extrusion; L the initial length of the billet, α is the cone semi-angle of the die and Ar=(Re-Rs)/Re) is the radius reduction factor.

The sample is taken from [10] using the same process parameters and the same material 100Cr6 steel. The geometrical parameters are: initial radius of the billet Re=9.55mm, the final radius Rs=7.5mm, the die angle α=45°.

The billet is regularly discretized using quadrangular (bilinear) elements with reduced integration (CAX4R from the ABAQUS element library) having a constant size of 0.2mm [10]

Fig. 1: Schematic representation of the extrusion process.

Re

Rs α Billet

Die

Moving punch Central line

Outer line

L

Extension of the present constitutive equation to the large elasto-viscoplastic scheme can be easily performed using the so called rotated frame formulation [8].

The Thermal dissipation analysis

The evolution of the temperature is obtained by the generalised heat equation including the mechanical dissipation [8]:

( ) emv

X R Ydiv kgradT C T T : : : r : D 0T T T T∂σ ∂ ∂ ∂⎡ ⎤+ φ −ρ + ε + α + − =⎢ ⎥∂ ∂ ∂ ∂⎣ ⎦

(17)

where k is the heat conduction coefficient. And φm is the intrinsic dissipation defined by: pm : X : Rr YD 0φ = σ ε − α − + ≥ (18)

In this work, some material parameter P(T) ( vP E,C,Q, K ,S∈ ) are taken function of temperature under the following form :

( )m

00

F 0

T TP T P 1T T

⎛ ⎞⎛ ⎞−⎜ ⎟= − ⎜ ⎟⎜ ⎟−⎝ ⎠⎝ ⎠ (19)

With Tf is the melting temperature, T0 is the reference (room) temperature, P0 is the value of the mechanical parameter for T=T0 and m is a material parameter measuring its sensitivity to the temperature

Numerical aspect

The fully coupled thermomechanical constitutive equations presented above have been implemented into Abaqus/Explicit FE code using the Vumat user subroutine. The dynamic explicit resolution procedure has been used in order to solve the thermomechanical problem based on both weak forms relative to the equilibrium and thermal equations. The local integration of the fully coupled constitutive equations is performed using an iterative implicit scheme based on the well known elastic prediction – plastic correction with a radial return procedure applied a reduced number of equations (see [8] for more details).

2D axisymmetric cold/hot extrusion

The proposed numerical methodology is now applied to the chevron shaped cracks prediction in an axisymmetric extrusion of a round bar schematized in Fig. 1. Re is the initial radius of the billet, Rs is the final radius of the billet after extrusion; L the initial length of the billet, α is the cone semi-angle of the die and Ar=(Re-Rs)/Re) is the radius reduction factor.

The sample is taken from [10] using the same process parameters and the same material 100Cr6 steel. The geometrical parameters are: initial radius of the billet Re=9.55mm, the final radius Rs=7.5mm, the die angle α=45°.

The billet is regularly discretized using quadrangular (bilinear) elements with reduced integration (CAX4R from the ABAQUS element library) having a constant size of 0.2mm [10]

Fig. 1: Schematic representation of the extrusion process.

Re

Rs α Billet

Die

Moving punch Central line

Outer line

L


The identification of the material parameters is based on the experimental results taken from [10] and [11]. The different materials and thermal parameters are given in the Table 1 and 2 Table 1: Thermo elastic material properties

E (GPa) ν Cv (J.kg-1.C-1) K (W.m-1.C-

1) ηT (C-1) T0

(°C) Tf (°C)

205 0.28 475 32 12.5 25 1520

Table 2: Viscoplastic, hadening and ductile damage properties σy

MPa Q

MPa b C

MPa a Kv

MPa nV S

MPa s β Y0

MPa ω hclo

650 720 3 2000 30 100 10 3.8 1.2 1 0 6 0.01

The Coulomb friction model is used with μ=0.04 corresponding to coated contact condition.. The tools are considered as rigid bodies. The initial temperature of the billet is Tb=25°C. The velocity of the punch is Vp=5mm/s. Fig 2 shows the von Mises stress distribution at the end of extrusion process. The maximum value 980 Mpa is localized in the contact zone between the die and the billet.

Fig. 2: von Mises stress (N/m2) distribution

The temperature distribution for the same configuration is shown in Fig 3 with 230°C as maximum value starting form the room temperature. The increase of the temperature is generated by inelastic work and the friction at the contact interface.

Fig. 3: Temperature distribution at the end of the extrusion process

Fig 4. shows the comparison between the numerical chevron cracks with the experimental one [10]. Five chevrons cracks are clearly predicted according with experimental results.

Fig. 4: Comparison of the experimental [10] and predicted chevron cracks after 40 mm punch

displacement

The identification of the material parameters is based on the experimental results taken from [10] and [11]. The different materials and thermal parameters are given in the Table 1 and 2 Table 1: Thermo elastic material properties

E (GPa) ν Cv (J.kg-1.C-1) K (W.m-1.C-

1) ηT (C-1) T0

(°C) Tf (°C)

205 0.28 475 32 12.5 25 1520

Table 2: Viscoplastic, hadening and ductile damage properties σy

MPa Q

MPa b C

MPa a Kv

MPa nV S

MPa s β Y0

MPa ω hclo

650 720 3 2000 30 100 10 3.8 1.2 1 0 6 0.01

The Coulomb friction model is used with μ=0.04 corresponding to coated contact condition.. The tools are considered as rigid bodies. The initial temperature of the billet is Tb=25°C. The velocity of the punch is Vp=5mm/s. Fig 2 shows the von Mises stress distribution at the end of extrusion process. The maximum value 980 Mpa is localized in the contact zone between the die and the billet.

Fig. 2: von Mises stress (N/m2) distribution

The temperature distribution for the same configuration is shown in Fig 3 with 230°C as maximum value starting form the room temperature. The increase of the temperature is generated by inelastic work and the friction at the contact interface.

Fig. 3: Temperature distribution at the end of the extrusion process

Fig 4. shows the comparison between the numerical chevron cracks with the experimental one [10]. Five chevrons cracks are clearly predicted according with experimental results.

Fig. 4: Comparison of the experimental [10] and predicted chevron cracks after 40 mm punch

displacement


The punch force (see Fig. 5) increases then oscillates around 250 kN. It is noted that the number of peaks corresponds to the number of chevron cracks. Then these oscillations indicate the presence of the discontinuous chevrons shaped cracks.

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

course (mm)

Punc

h fo

rce

(kN

)

Fig. 5: Punch force versus Punch course

(a) [Vp=5mm/s, Tb=20°C, μ=0.04]

(b) [Vp=5mm/s, Tb=300°C, μ=0.04]

(c) [Vp=5mm/s, Tb=600°C, μ=0.04] (d) [Vp=1000mm/s, Tb=20°C, μ=0.04],

(e) [Vp=1000mm/s, Tb=600°C, μ=0.04],

(f) [Vp=5mm/s, Tb=20°C, μ=0.1],

Fig. 6: Accumulated plastic strain distribution for a punch displacement of 25mm

Fig 6 shows the effect of the main process parameters on the chevron cracks formation. When increasing the temperature to 300°C or 600°C (Fig 6a to Fig 6c), there are the same number of chevron crack and only the form of central bursts is slightly modified. Now if the punch velocity is increased to 1000 mm/s (Fig 6a and Fig 6d), no significant change is observed, just the accumulated plastic strain along the outside surface seems affected. By increasing the friction coefficient the number and the amplitude of chevron cracks are significantly reduced along the billet axis and the damage is increased on the outer surface of the billet (Fig 6a and 6f).

3D extrusion of a cylindrical bar with a triangular die

The last 3D sample process consists to reduce a cylindrical bar by forcing it through a triangular die orifice under high pressure. The initial radius of the bar is 10 mm and the geometry of the outside die is given in Fig 7a. Two configurations of the die are investigated by changing the value of the die angle α as α=15° or α=60°

The punch force (see Fig. 5) increases then oscillates around 250 kN. It is noted that the number of peaks corresponds to the number of chevron cracks. Then these oscillations indicate the presence of the discontinuous chevrons shaped cracks.

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

course (mm)

Punc

h fo

rce

(kN

)

Fig. 5: Punch force versus Punch course

(a) [Vp=5mm/s, Tb=20°C, μ=0.04]

(b) [Vp=5mm/s, Tb=300°C, μ=0.04]

(c) [Vp=5mm/s, Tb=600°C, μ=0.04] (d) [Vp=1000mm/s, Tb=20°C, μ=0.04],

(e) [Vp=1000mm/s, Tb=600°C, μ=0.04],

(f) [Vp=5mm/s, Tb=20°C, μ=0.1],

Fig. 6: Accumulated plastic strain distribution for a punch displacement of 25mm

Fig 6 shows the effect of the main process parameters on the chevron cracks formation. When increasing the temperature to 300°C or 600°C (Fig 6a to Fig 6c), there are the same number of chevron crack and only the form of central bursts is slightly modified. Now if the punch velocity is increased to 1000 mm/s (Fig 6a and Fig 6d), no significant change is observed, just the accumulated plastic strain along the outside surface seems affected. By increasing the friction coefficient the number and the amplitude of chevron cracks are significantly reduced along the billet axis and the damage is increased on the outer surface of the billet (Fig 6a and 6f).

3D extrusion of a cylindrical bar with a triangular die

The last 3D sample process consists to reduce a cylindrical bar by forcing it through a triangular die orifice under high pressure. The initial radius of the bar is 10 mm and the geometry of the outside die is given in Fig 7a. Two configurations of the die are investigated by changing the value of the die angle α as α=15° or α=60°


(a) (b) Fig. 7: Geometrie of the die

The bar is regularly discretized using hexahedral elements with reduced integration (C3D8R from the ABAQUS element library) having a constant size of 0.5mm. The 100CR6 material is used with the same parameters given in table 1 and 2. The initial temperature of the bar is 25°C and the velocity of the punch is equal to 5 mm/s. The coefficient of friction is equal to μ=0.04. Fig 9 show the von Mises stress distribution inside the bar at the end of the processwith a die angle α=15°. Clearly, the bar section is changed from cylindrical to triangular one. With α=15° no defects are observed inside the bar (Fig. 8a). However with α=60° (see Fig 8b) many little cracks are observed along the central axis of the bar as well as along the outer surface (snake skins).

α=15° (a)

α=60° (b) Fig. 8: Damage distribution at the end of extrusion

Fig. 9: von Mises stress distribution at he end of extrusion with die angle α=15°

α

(a) (b) Fig. 7: Geometrie of the die

The bar is regularly discretized using hexahedral elements with reduced integration (C3D8R from the ABAQUS element library) having a constant size of 0.5mm. The 100CR6 material is used with the same parameters given in table 1 and 2. The initial temperature of the bar is 25°C and the velocity of the punch is equal to 5 mm/s. The coefficient of friction is equal to μ=0.04. Fig 9 show the von Mises stress distribution inside the bar at the end of the processwith a die angle α=15°. Clearly, the bar section is changed from cylindrical to triangular one. With α=15° no defects are observed inside the bar (Fig. 8a). However with α=60° (see Fig 8b) many little cracks are observed along the central axis of the bar as well as along the outer surface (snake skins).

α=15° (a)

α=60° (b) Fig. 8: Damage distribution at the end of extrusion

Fig. 9: von Mises stress distribution at he end of extrusion with die angle α=15°

α


Conclusion

Thermo-elasto-viscoplastic constitutive equations fully coupled with ductile damage with micro cracks closure effect have been used to investigate the effect of temperature in the formation of the chevron shaped cracks in extrusion. Numerical results given by the proposed model seems accurate when compared to some available experimental data.

References

[1] N. Aravas, The analysis of void growth that leads to central bursts during extrusion, J. Mech. Phys. Solids, Vol. 34, (1986) pp :55-79

[2] B. Kim, D-C Ko, The prediction of central burst defects in extrusion and wire drawing, Journal of Materials Processing Technology, Vol. 102, (1998) pp. 19-24

[3] K. Komori, Proposal ans use of a void model for the simulation of inner fracture defect in drawing Acta Materials, vol. 54, (2006), pp. 4351-4364.

[4] C. Labergere, P. Lestriez, K. Saanouni, A. Rassineux, Adaptive FEA Simulation of burst defects in cold extrusion with fully coupled elastoplastic constitutive equations, 12 international Conference Metalforming, Krakow, CD, (2008)

[5] J. Lemaitre , A course on Damage Machanics, Springer Verlag, Berlin, (1992).

[6] Mcallen P., Phelan P., Ductile fracture by central bursts in drawn 2011 aluminium wire, International Journal of Fracture, Springer edition, vol. 135, (2005) pp. 19-33.

[7] C. Mc Veigh, W.K. Liu,Prediction of central bursting during axisymmetric cold extrusion of a metal alloy containing particles, International Journal of Solid ans Structures, vol. 43, (2006), pp. 3087-3105

[8] K. Saanouni, J.L. Chaboche, Computational Damage Mechanics. Application to Metal Forming, Chapter 7 of the Volume 3: ‘Numerical and Computational methods’, (2003)

[9] K. Saanouni, J.F. Mariage, A. Cherouat, P. Lestriez, Numerical prediction of discontinuous central bursting in axisymmetric forward extrusion by continuum damage mechanics, Computers and Structures, vol. 82, (2004) pp. 2309-2332.

[10] Soyarslan C., E. Tekkaya, U. Akyuz, Application of Continuum Damage Mechanics in discontinuous crak formation: Forward extrusion chevron prediction, Z. Angew. Math. Mech. 88, No 6, (2008), pp 436-453

[11]D. Umbrello, J. Hua, R. Shivpuri, Hardness-based flow stress and fracture models for numerical simulation of hard machining AISI52100 bearing, Materials Science and Engineering, vol 374, (2004), pp90-100

Conclusion

Thermo-elasto-viscoplastic constitutive equations fully coupled with ductile damage with micro cracks closure effect have been used to investigate the effect of temperature in the formation of the chevron shaped cracks in extrusion. Numerical results given by the proposed model seems accurate when compared to some available experimental data.

References

[1] N. Aravas, The analysis of void growth that leads to central bursts during extrusion, J. Mech. Phys. Solids, Vol. 34, (1986) pp :55-79

[2] B. Kim, D-C Ko, The prediction of central burst defects in extrusion and wire drawing, Journal of Materials Processing Technology, Vol. 102, (1998) pp. 19-24

[3] K. Komori, Proposal ans use of a void model for the simulation of inner fracture defect in drawing Acta Materials, vol. 54, (2006), pp. 4351-4364.

[4] C. Labergere, P. Lestriez, K. Saanouni, A. Rassineux, Adaptive FEA Simulation of burst defects in cold extrusion with fully coupled elastoplastic constitutive equations, 12 international Conference Metalforming, Krakow, CD, (2008)

[5] J. Lemaitre , A course on Damage Machanics, Springer Verlag, Berlin, (1992).

[6] Mcallen P., Phelan P., Ductile fracture by central bursts in drawn 2011 aluminium wire, International Journal of Fracture, Springer edition, vol. 135, (2005) pp. 19-33.

[7] C. Mc Veigh, W.K. Liu,Prediction of central bursting during axisymmetric cold extrusion of a metal alloy containing particles, International Journal of Solid ans Structures, vol. 43, (2006), pp. 3087-3105

[8] K. Saanouni, J.L. Chaboche, Computational Damage Mechanics. Application to Metal Forming, Chapter 7 of the Volume 3: ‘Numerical and Computational methods’, (2003)

[9] K. Saanouni, J.F. Mariage, A. Cherouat, P. Lestriez, Numerical prediction of discontinuous central bursting in axisymmetric forward extrusion by continuum damage mechanics, Computers and Structures, vol. 82, (2004) pp. 2309-2332.

[10] Soyarslan C., E. Tekkaya, U. Akyuz, Application of Continuum Damage Mechanics in discontinuous crak formation: Forward extrusion chevron prediction, Z. Angew. Math. Mech. 88, No 6, (2008), pp 436-453

[11]D. Umbrello, J. Hua, R. Shivpuri, Hardness-based flow stress and fracture models for numerical simulation of hard machining AISI52100 bearing, Materials Science and Engineering, vol 374, (2004), pp90-100


Integrated Extruder Plant Automation with Learning Control

Madhukar Pandit1, a 1Fachbereich Elektrotechnik u.Informationstechnik, Technische Universität Kaiserslautern,

67653 Kaiserslauternm, Germany

[email protected]

Keywords: Extrusion automation, modelling, control, lumped parameter, identification

Introduction

Integrated automation in a manufacturing plant demands control of manufacturing and material and

product flow processes. Efficient data archiving and retrieval, quality control and process

automation facilities are essential components which should be deployed to form one coherent

system. As managers of extruder plants running look for ways and means for meeting market

requirements, the demand for such integrated automation systems is rising. Integrated Process

automation involves:

- Overall production and process control

- Data acquisition, archiving evaluation with feed-back to production planning and process

control

- Decentral control in local control loops for achieving isothermal extrusion

- On-line visualisation of process variables for tighter man-machine interaction

Providing the facility for prescribing the ranges of relevant process variables viz. billet temperature,

die temperature, profile temperature at die exit, rate of cooling of the profile and extrusion speed is

part of the integrated automation system.

Fig. 1: Hierarchy in an automation system

At the heart of the system are processes for mastering the core task of management of the thermal

processes in the extruder by employing sensors and control techniques. Goal is to minimise the time

to extrude a billet and simultaneously keep the process variables within prescribed limits.

Automation in extrusion plants is made possible by progress in sensor technology and enhanced

possibilities of data processing and organisation, advanced control methods which require simple

models and facilities of integration of hardware and software employing state-of-the-art networking

and protocols. Crucial is the non-contact temperature measurement of the billet and the profile at

die exit. Since about two decades there has been a continuous progress in temperature measurement

technology based on multi-spectral radiation pyrometers. They perform well for a large number of

Integrated Extruder Plant Automation with Learning Control

Madhukar Pandit1, a 1Fachbereich Elektrotechnik u.Informationstechnik, Technische Universität Kaiserslautern,

67653 Kaiserslauternm, Germany

[email protected]

Keywords: Extrusion automation, modelling, control, lumped parameter, identification

Introduction

Integrated automation in a manufacturing plant demands control of manufacturing and material and

product flow processes. Efficient data archiving and retrieval, quality control and process

automation facilities are essential components which should be deployed to form one coherent

system. As managers of extruder plants running look for ways and means for meeting market

requirements, the demand for such integrated automation systems is rising. Integrated Process

automation involves:

- Overall production and process control

- Data acquisition, archiving evaluation with feed-back to production planning and process

control

- Decentral control in local control loops for achieving isothermal extrusion

- On-line visualisation of process variables for tighter man-machine interaction

Providing the facility for prescribing the ranges of relevant process variables viz. billet temperature,

die temperature, profile temperature at die exit, rate of cooling of the profile and extrusion speed is

part of the integrated automation system.

Fig. 1: Hierarchy in an automation system

At the heart of the system are processes for mastering the core task of management of the thermal

processes in the extruder by employing sensors and control techniques. Goal is to minimise the time

to extrude a billet and simultaneously keep the process variables within prescribed limits.

Automation in extrusion plants is made possible by progress in sensor technology and enhanced

possibilities of data processing and organisation, advanced control methods which require simple

models and facilities of integration of hardware and software employing state-of-the-art networking

and protocols. Crucial is the non-contact temperature measurement of the billet and the profile at

die exit. Since about two decades there has been a continuous progress in temperature measurement

technology based on multi-spectral radiation pyrometers. They perform well for a large number of


alloys and surface finishes and are reliable for industrial use. Disturbances can be suppressed using

adequate signal processing.

Description of the extrusion process

The majority of extrusion plants for manufacturing aluminium bars are of the direct type

schematically shown in Fig.2. A billet Bi of the metal is heated to a temperature of about 500°C in

an electric furnace Fu and loaded into the container Re in the extruder. A hydraulic ram Ra

squeezes the metal through an orifice, and forms the bars Ba. Subsequently, the next billet (heated

in the meantime in the furnace) is loaded into the extruder and the process repeated successively.

The heat generated by friction and deformation causes a rise of the temperature of the aluminium in

the die and also heats up the die and the container.

Fig. 2 Schematic layout of an extruder

Metallurgical and extruder technology experience indicates that the quality of the product is best

and the productivity high if the exit temperature of the aluminium bar (sometimes also referred to as

profile) as it leaves the die is maintained at a constant value (which lies in the range of 540°C -

570°C), as described by Akeret and Strehmel, 1986 [1].

The goal of iso-thermal extrusion is to operate the extruder in such a way that the profile

temperature at die exit is constant [2]. This exit temperature can be influenced by varying either the

temperature to which the billets are preheated and/or the velocity with which the ram squeezes the

metal out of the die. Now it is of great interest to process engineers to control the exit temperature

and the extrusion speed by choosing the right set of parameters and runs of the process variables.

For doing, this they have to have as precise a knowledge as possible of the relationship between

these functions. Determining the relationships between input and output process variables and

presenting them in a usable form is the task of modelling [3].

Modelling of the extrusion process for control design

The objective of modelling is generally to gain insight into the process and/or - more pragmatically

- to create a basis for the design of a process, of components of the process (hardware or software)

or for process control. Models of the process of metal extrusion investigated hitherto have been

primarily those sought for studying process behaviour in order to design dies and to prescribe the

limits of process parameters and mostly employ partial differential equations. A different aspect of

alloys and surface finishes and are reliable for industrial use. Disturbances can be suppressed using

adequate signal processing.

Description of the extrusion process

The majority of extrusion plants for manufacturing aluminium bars are of the direct type

schematically shown in Fig.2. A billet Bi of the metal is heated to a temperature of about 500°C in

an electric furnace Fu and loaded into the container Re in the extruder. A hydraulic ram Ra

squeezes the metal through an orifice, and forms the bars Ba. Subsequently, the next billet (heated

in the meantime in the furnace) is loaded into the extruder and the process repeated successively.

The heat generated by friction and deformation causes a rise of the temperature of the aluminium in

the die and also heats up the die and the container.

Fig. 2 Schematic layout of an extruder

Metallurgical and extruder technology experience indicates that the quality of the product is best

and the productivity high if the exit temperature of the aluminium bar (sometimes also referred to as

profile) as it leaves the die is maintained at a constant value (which lies in the range of 540°C -

570°C), as described by Akeret and Strehmel, 1986 [1].

The goal of iso-thermal extrusion is to operate the extruder in such a way that the profile

temperature at die exit is constant [2]. This exit temperature can be influenced by varying either the

temperature to which the billets are preheated and/or the velocity with which the ram squeezes the

metal out of the die. Now it is of great interest to process engineers to control the exit temperature

and the extrusion speed by choosing the right set of parameters and runs of the process variables.

For doing, this they have to have as precise a knowledge as possible of the relationship between

these functions. Determining the relationships between input and output process variables and

presenting them in a usable form is the task of modelling [3].

Modelling of the extrusion process for control design

The objective of modelling is generally to gain insight into the process and/or - more pragmatically

- to create a basis for the design of a process, of components of the process (hardware or software)

or for process control. Models of the process of metal extrusion investigated hitherto have been

primarily those sought for studying process behaviour in order to design dies and to prescribe the

limits of process parameters and mostly employ partial differential equations. A different aspect of


modelling is gaining importance due to the increasing use of automation and control of extruders

because:

a. models are required which can be employed on-site in extruder in control systems

b. it is possible to acquire data under production conditions with the new measurement and control

systems for setting up the required models.

The task here is to determine the optimal structure of a suitable model and the algorithms for

determining the model parameters from measured process runs during extruder operation.

In commercially available extrusion, control systems one can identify two types of models for

process control:

a) Systems in which one trial extrusion is performed after every die change and the process

runs measured during the trial extrusion. The measured data is used to adjust the parameters

of the model which are fixed for the following extrusions until the next die change.

b) Systems in which the model is adjusted continuously over the cycles. Here gradual drifts of

process variables such as heating up of the die and container are automatically taken into

account.

The objective of modelling is to set up a set of equations to be used to simulate the process and

predict the behaviour of dependent variables (outputs) which results when the independent

variables (inputs) are made to follow prescribed functions. In the case of a model for process

control, the variables which can be considered to be independent - and can be changed at will - are

a. the input to the hydraulic aggregate, generally the reference input to the control loop controlling

the rate of oil flow to the cylinder or the reference input to the ram (or profile) speed control loop

and

b. the billet temperature.

The variables considered as outputs could be the actual ram speed and the profile temperature at die

exit. A common feature of all models is that ultimately they contain relationships between two time

functions or sets of time functions. Such relations are known in mathematics as operators or

mappings and their genera treatment is possible in most cases only formally, which is of little avail

for dealing with concrete problems.

For determining these relationships for practical applications involving control, there are some

possibilities:

a. Set up the equations using laws of physics, in our case laws of thermodynamics, mechanics

etc. (physical model).

b. Set up a black-box model.

- Collect data from various tests and fit the data to a mathematical model with an assumed

structure and initially free constants by choosing the constants appropriately, so that the

model behaviour is as close as possible to the original system behaviour (black box

model).

- If such data is available, neural networks offer the possibility for determining a black box

model. Here the data is first used to 'train' the network which in principle consists of

adjusting parameters of the network iteratively such that the network outputs are

sufficiently close to the measured outputs.

- One more method of arriving at a black-box model setting out from measured data

involves using fuzzy sets to describe a nonlinear function.

Whereas model a. suffers from the disadvantage that it is eventually not feasible because of the

complexity of the process, model b. has the disadvantage that an enormous amount of data is

necessary to cover all eventualities. Consequently, generally a via media path is followed, i.e. a

combination of both is used. Then the following procedure is followed:

modelling is gaining importance due to the increasing use of automation and control of extruders

because:

a. models are required which can be employed on-site in extruder in control systems

b. it is possible to acquire data under production conditions with the new measurement and control

systems for setting up the required models.

The task here is to determine the optimal structure of a suitable model and the algorithms for

determining the model parameters from measured process runs during extruder operation.

In commercially available extrusion, control systems one can identify two types of models for

process control:

a) Systems in which one trial extrusion is performed after every die change and the process

runs measured during the trial extrusion. The measured data is used to adjust the parameters

of the model which are fixed for the following extrusions until the next die change.

b) Systems in which the model is adjusted continuously over the cycles. Here gradual drifts of

process variables such as heating up of the die and container are automatically taken into

account.

The objective of modelling is to set up a set of equations to be used to simulate the process and

predict the behaviour of dependent variables (outputs) which results when the independent

variables (inputs) are made to follow prescribed functions. In the case of a model for process

control, the variables which can be considered to be independent - and can be changed at will - are

a. the input to the hydraulic aggregate, generally the reference input to the control loop controlling

the rate of oil flow to the cylinder or the reference input to the ram (or profile) speed control loop

and

b. the billet temperature.

The variables considered as outputs could be the actual ram speed and the profile temperature at die

exit. A common feature of all models is that ultimately they contain relationships between two time

functions or sets of time functions. Such relations are known in mathematics as operators or

mappings and their genera treatment is possible in most cases only formally, which is of little avail

for dealing with concrete problems.

For determining these relationships for practical applications involving control, there are some

possibilities:

a. Set up the equations using laws of physics, in our case laws of thermodynamics, mechanics

etc. (physical model).

b. Set up a black-box model.

- Collect data from various tests and fit the data to a mathematical model with an assumed

structure and initially free constants by choosing the constants appropriately, so that the

model behaviour is as close as possible to the original system behaviour (black box

model).

- If such data is available, neural networks offer the possibility for determining a black box

model. Here the data is first used to 'train' the network which in principle consists of

adjusting parameters of the network iteratively such that the network outputs are

sufficiently close to the measured outputs.

- One more method of arriving at a black-box model setting out from measured data

involves using fuzzy sets to describe a nonlinear function.

Whereas model a. suffers from the disadvantage that it is eventually not feasible because of the

complexity of the process, model b. has the disadvantage that an enormous amount of data is

necessary to cover all eventualities. Consequently, generally a via media path is followed, i.e. a

combination of both is used. Then the following procedure is followed:


c. Data is collected from various tests. The data is studied and a mathematical model with a

structure which is derived from the physical laws - say a linear differential equation with

constant coefficients as an approximation - and initially free parameters is chosen. The

parameters of the model are adjusted appropriately, so that the model behaviour is as close

as possible to the original system behaviour. (grey box model).

Model of the extrusion process based on an exact thermo-dynamical analysis

Following notation is used in the sequel:

x : position of ram with respect to its starting point , simultaneously the front end of the billet

t : time elapsed since the beginning of extrusion

v(x,t ): velocity of the ram when it is at position x

B(x,t): billet temperature

P(x,t) , P(x) : profile temperature

F(x,t) : extrusion force

R(t) : temperature of the container

die(t) : temperature of the die.

When the ram traverses the path x to x+dx, one has the following heat inflows and outflows:

a. Heat inflow due to friction between billet and container

b. Heat conduction into the container

c. Heat conduction into the exiting profile

d. Heat inflow due to deformation

Using these terms, the Fourier heat equation can be set up for the element, which is a partial

differential equations involving time and space coordinates. This equation depicts the starting point

for calculation of the heat development using finite element model (FEM) techniques. The

computing effort required is generally large, the application of the techniques is generally restricted

to problems dealing with die design and material flow.

An exact mathematical description of extrusion involves apparently a nonlinear, time variant,

distributed parameter model with dead-time for the plant. Simplified mathematical models

employing lumped parameters which lead to ordinary nonlinear differential equations, depict a first

step towards developing models for process control.

The Buchheit Model

The model proposed by Buchheit [4] is one such and is based on the work of Lange [5]. The exit

temperature of the profile P(t) depends on the initial temperature in the deformation zone I(t) and

the temperature rise D(t), the temporal temperature change is given by

dP(t)/dt = -(1/T2). P(t) + (K2/T2).(I(t)+D(t), (1)

where K2 depends on the temperature of the die die(t) and the velocity of ram v(t ) which in turn

depends on the hydraulic pressure p(t) or the force exerted by the ram F(t). The temperature of the

die die(t) is not measurable in most extrusion plants and must be estimated. The initial temperature

I(t) is calculated from the billet temperature B(t) the container temperature R(t) which is

assumed to be constant within a cycle, and the velocity of the ram v (t )

I(t) =B(t) + c1 t

0

Ra d)(v + c2(B(t) -R ). t (2)

The temperature change D(t) in the deformation zone is determined by a nonlinear equation in

which the velocity of the ram v (t ) and the initial temperature I(t) appear as follows:

dD(t)/dt = -(1/T1). D(t) + (K1/T1)(c3.v (t).exp(c4 .I(t) ). (3)

c. Data is collected from various tests. The data is studied and a mathematical model with a

structure which is derived from the physical laws - say a linear differential equation with

constant coefficients as an approximation - and initially free parameters is chosen. The

parameters of the model are adjusted appropriately, so that the model behaviour is as close

as possible to the original system behaviour. (grey box model).

Model of the extrusion process based on an exact thermo-dynamical analysis

Following notation is used in the sequel:

x : position of ram with respect to its starting point , simultaneously the front end of the billet

t : time elapsed since the beginning of extrusion

v(x,t ): velocity of the ram when it is at position x

B(x,t): billet temperature

P(x,t) , P(x) : profile temperature

F(x,t) : extrusion force

R(t) : temperature of the container

die(t) : temperature of the die.

When the ram traverses the path x to x+dx, one has the following heat inflows and outflows:

a. Heat inflow due to friction between billet and container

b. Heat conduction into the container

c. Heat conduction into the exiting profile

d. Heat inflow due to deformation

Using these terms, the Fourier heat equation can be set up for the element, which is a partial

differential equations involving time and space coordinates. This equation depicts the starting point

for calculation of the heat development using finite element model (FEM) techniques. The

computing effort required is generally large, the application of the techniques is generally restricted

to problems dealing with die design and material flow.

An exact mathematical description of extrusion involves apparently a nonlinear, time variant,

distributed parameter model with dead-time for the plant. Simplified mathematical models

employing lumped parameters which lead to ordinary nonlinear differential equations, depict a first

step towards developing models for process control.

The Buchheit Model

The model proposed by Buchheit [4] is one such and is based on the work of Lange [5]. The exit

temperature of the profile P(t) depends on the initial temperature in the deformation zone I(t) and

the temperature rise D(t), the temporal temperature change is given by

dP(t)/dt = -(1/T2). P(t) + (K2/T2).(I(t)+D(t), (1)

where K2 depends on the temperature of the die die(t) and the velocity of ram v(t ) which in turn

depends on the hydraulic pressure p(t) or the force exerted by the ram F(t). The temperature of the

die die(t) is not measurable in most extrusion plants and must be estimated. The initial temperature

I(t) is calculated from the billet temperature B(t) the container temperature R(t) which is

assumed to be constant within a cycle, and the velocity of the ram v (t )

I(t) =B(t) + c1 t

0

Ra d)(v + c2(B(t) -R ). t (2)

The temperature change D(t) in the deformation zone is determined by a nonlinear equation in

which the velocity of the ram v (t ) and the initial temperature I(t) appear as follows:

dD(t)/dt = -(1/T1). D(t) + (K1/T1)(c3.v (t).exp(c4 .I(t) ). (3)


Fig. 3 Lumped parameter model

The model of Buchheit contains several constants denoted by kw, k1, T1 and k2 and T2.in Fig. 3

which are related to physical parameters and are difficult to estimate. Also, the container

temperature R requires to be estimated. Consequently, a simpler model is targeted.

Nonlinear model with Hammerstein structure

The principle difficulty of representing a non-linear operator or mapping in a general form can be

overcome by resolving the operator into a structure consisting of 2 parts: a part which is described

by a linear differential equation with constant coefficients and which can thus be represented by its

transfer function and a part which is described by a nonlinear function of the type y = f(x). One

such structure due to Hammerstein has proved to be of merit and is derived setting out from the

Buchheit Model under the following assumptions and approximations:

a. The temperature change in the deformation zone is constant.

b. The recipient temperature R is nearly equal to the billet temperature B.

c. The temperature of the profile P follows changes of heat input instantaneously without lag.

d. A term is introduced to weight the influence of a ram speed change v(t) depending on the billet

temperature B and ram position such that a change of the ram speed has less impact on the profile

temperature P when most material was already extruded. Furthermore, an improvement is obtained

with the following model - employing what is known in the control system literature as

‘Hammerstein model’ as described by Ljung [6]- is obtained by employing a nonlinear function and

a dynamic part. For an application one uses the equations in discrete form with the various variables

represented in the form Ta.kt)t()k( with Ta = sample time.

P(k) =w(k) + B*(k) (4)

w(k) = w(k-) + F(k).(xx (5)

B*(k) =

0

g1().f(B (k-)) (6)

f(.) is a non-linear function which is approximated to a fairly good degree by

f(B (k))=

3

1n

1,n.Bn(k) (7)

Thus the model for the temperature P(k) takes on the form in Fig. 4.

Fig. 3 Lumped parameter model

The model of Buchheit contains several constants denoted by kw, k1, T1 and k2 and T2.in Fig. 3

which are related to physical parameters and are difficult to estimate. Also, the container

temperature R requires to be estimated. Consequently, a simpler model is targeted.

Nonlinear model with Hammerstein structure

The principle difficulty of representing a non-linear operator or mapping in a general form can be

overcome by resolving the operator into a structure consisting of 2 parts: a part which is described

by a linear differential equation with constant coefficients and which can thus be represented by its

transfer function and a part which is described by a nonlinear function of the type y = f(x). One

such structure due to Hammerstein has proved to be of merit and is derived setting out from the

Buchheit Model under the following assumptions and approximations:

a. The temperature change in the deformation zone is constant.

b. The recipient temperature R is nearly equal to the billet temperature B.

c. The temperature of the profile P follows changes of heat input instantaneously without lag.

d. A term is introduced to weight the influence of a ram speed change v(t) depending on the billet

temperature B and ram position such that a change of the ram speed has less impact on the profile

temperature P when most material was already extruded. Furthermore, an improvement is obtained

with the following model - employing what is known in the control system literature as

‘Hammerstein model’ as described by Ljung [6]- is obtained by employing a nonlinear function and

a dynamic part. For an application one uses the equations in discrete form with the various variables

represented in the form Ta.kt)t()k( with Ta = sample time.

P(k) =w(k) + B*(k) (4)

w(k) = w(k-) + F(k).(xx (5)

B*(k) =

0

g1().f(B (k-)) (6)

f(.) is a non-linear function which is approximated to a fairly good degree by

f(B (k))=

3

1n

1,n.Bn(k) (7)

Thus the model for the temperature P(k) takes on the form in Fig. 4.


Fig. 4 Nonlinear model with Hammerstein structure

FReaction takes into account the shear force, frictional force and the deformation. The force F(k) is

estimated as a function of the ram speed v (k) under the assumption FReaction is constant.

If an estimate of the temperature P(k) is required during an extrusion, one can directly determine

F(k) by multiplying the measured pressure p(k) by a constant. This model can be used for

implementing simulated isothermal extrusion system which does away with on-line profile

temperature measurement but which is rather crude in comparison to systems with the facility.

In an application, one can set up the model to calculate the profile temperature P(k) for given runs

of B(k), F(k) and v(k) [3, 6].

The following Fig. 5 shows typical results obtained with the Hammerstein model.

Fig. 5 Results with the Hammerstein model

Iso-thermal extrusion - profile temperature control at die exit

Due to large time delays between the inputs and outputs, conventional on-loop control is not

feasible. Simulated control using complete process models have been tried with some success in

individual applications. Iterative Learning Control has been employed with success, as this control

method comes to terms with the large delays inherent to the extrusion process, variations of die and

container temperatures and disturbances of the pyrometer signal. For the hierarchical control

scheme employed, the basic functionality to be realised is the determination of the appropriate run

of the ram velocity vk+1(l), which corresponds to the desired exit temperature d and the actual

measured billet temperature as a function of the ram position and the driving of the velocity control

Fig. 4 Nonlinear model with Hammerstein structure

FReaction takes into account the shear force, frictional force and the deformation. The force F(k) is

estimated as a function of the ram speed v (k) under the assumption FReaction is constant.

If an estimate of the temperature P(k) is required during an extrusion, one can directly determine

F(k) by multiplying the measured pressure p(k) by a constant. This model can be used for

implementing simulated isothermal extrusion system which does away with on-line profile

temperature measurement but which is rather crude in comparison to systems with the facility.

In an application, one can set up the model to calculate the profile temperature P(k) for given runs

of B(k), F(k) and v(k) [3, 6].

The following Fig. 5 shows typical results obtained with the Hammerstein model.

Fig. 5 Results with the Hammerstein model

Iso-thermal extrusion - profile temperature control at die exit

Due to large time delays between the inputs and outputs, conventional on-loop control is not

feasible. Simulated control using complete process models have been tried with some success in

individual applications. Iterative Learning Control has been employed with success, as this control

method comes to terms with the large delays inherent to the extrusion process, variations of die and

container temperatures and disturbances of the pyrometer signal. For the hierarchical control

scheme employed, the basic functionality to be realised is the determination of the appropriate run

of the ram velocity vk+1(l), which corresponds to the desired exit temperature d and the actual

measured billet temperature as a function of the ram position and the driving of the velocity control


loop with this as reference input. For this, the measured runs of the billet temperature and the exit

temperature and the other process variables including the limits on the cooling capacity are

considered. Signal processing is necessary to eliminate disturbances in the measured signals. In the

case of multi- strand extrusion, appropriate signal processing means have to be adopted for the

determination of the temperature of the sections exiting the die as described in [2].

A robust and accurate control is achieved using iterative learning control in combination with a

predictive component. The principle algorithms for iterative learning control are

vk+1(l) = vk(l) + vk+1(l) ,

vk+1(l) = F[d, k(l), k+1(l), B k(l), B k+1(l), pk+1(l), vk(l),vk+1(l), Ck (l)]

with:

l : Ram position

vk(l) : Ram velocity in previous cycle k

vk+1(l) : Ram velocity in current cycle k+1

vk+1(l) : Increment of input calculated for cycle k+1

d : Desired run of exit temperature (constant over l)

k(l) : Run of exit temperature in previous cycle k

k+1(l) : Run of exit temperature in current cycle k+1

Ck (l) : Cooling in cycle k

B k(l) : Billet temperature in previous cycle k

B k+1(l) : Billet temperature in current cycle k+1

pk+1(l) : Extrusion force in current cycle

F [...] : Control operator.

Models for application in iterative learning control

Calculating the inputs for the cycle k+1is greatly eased if an appropriate model for determining the

effects of the inputs on the outputs for the cycle k+1is available. The alleviating fact is that for

gaining such a model the knowledge of the runs of the process variables collected in the previous

cycles can be exploited. In order to reduce the effects of inevitable disturbances present in the

measured runs, it is expedient to continuously update the model as the process progresses. This is

the rationale for looking for a model which suffices to describe the relation between the deviations

of the runs of the variables between two successive cycles.

Implementation of automation systems for extruders

Two aspects which are of interest, viz. integration of an automation system in an existing plant and

experience in installed systems, will be briefly described.

Integration in existing process control environment

Existing extruders are generally run using a PLC and some basic electronics. The operator sets a

profile speed which is maintained at the pre-set value by a local closed-loop control implemented

with the PLC. Now an overall control has to be installed with minimal interruption of production

and should be compatible with existing practices. With modern networking and communication

hardware and protocols, it is indeed feasible to introduce an automation system with no interruption

of production. Communication between the PLC and the supervising computer is effected using

OPC, in conjunction with ETHERNET. Often this requires some fine tuning.

By employing a suitable hierarchical architecture, process optimisation is continuously effected

from the background without demanding any special training or attention from the operator.

loop with this as reference input. For this, the measured runs of the billet temperature and the exit

temperature and the other process variables including the limits on the cooling capacity are

considered. Signal processing is necessary to eliminate disturbances in the measured signals. In the

case of multi- strand extrusion, appropriate signal processing means have to be adopted for the

determination of the temperature of the sections exiting the die as described in [2].

A robust and accurate control is achieved using iterative learning control in combination with a

predictive component. The principle algorithms for iterative learning control are

vk+1(l) = vk(l) + vk+1(l) ,

vk+1(l) = F[d, k(l), k+1(l), B k(l), B k+1(l), pk+1(l), vk(l),vk+1(l), Ck (l)]

with:

l : Ram position

vk(l) : Ram velocity in previous cycle k

vk+1(l) : Ram velocity in current cycle k+1

vk+1(l) : Increment of input calculated for cycle k+1

d : Desired run of exit temperature (constant over l)

k(l) : Run of exit temperature in previous cycle k

k+1(l) : Run of exit temperature in current cycle k+1

Ck (l) : Cooling in cycle k

B k(l) : Billet temperature in previous cycle k

B k+1(l) : Billet temperature in current cycle k+1

pk+1(l) : Extrusion force in current cycle

F [...] : Control operator.

Models for application in iterative learning control

Calculating the inputs for the cycle k+1is greatly eased if an appropriate model for determining the

effects of the inputs on the outputs for the cycle k+1is available. The alleviating fact is that for

gaining such a model the knowledge of the runs of the process variables collected in the previous

cycles can be exploited. In order to reduce the effects of inevitable disturbances present in the

measured runs, it is expedient to continuously update the model as the process progresses. This is

the rationale for looking for a model which suffices to describe the relation between the deviations

of the runs of the variables between two successive cycles.

Implementation of automation systems for extruders

Two aspects which are of interest, viz. integration of an automation system in an existing plant and

experience in installed systems, will be briefly described.

Integration in existing process control environment

Existing extruders are generally run using a PLC and some basic electronics. The operator sets a

profile speed which is maintained at the pre-set value by a local closed-loop control implemented

with the PLC. Now an overall control has to be installed with minimal interruption of production

and should be compatible with existing practices. With modern networking and communication

hardware and protocols, it is indeed feasible to introduce an automation system with no interruption

of production. Communication between the PLC and the supervising computer is effected using

OPC, in conjunction with ETHERNET. Often this requires some fine tuning.

By employing a suitable hierarchical architecture, process optimisation is continuously effected

from the background without demanding any special training or attention from the operator.


Installed automation systems

An automation system for integrated automation which employs Iterative Learning Control and

offers functions such as process control, data base and production handling named MoMAS®

('Modular Measurement and Automation System') was introduced about a decade back. Continuous

interaction with extruder operators and maintenance crews in extruder plants have contributed to

make MoMAS®

especially a user-friendly tool for process control, visualisation and management.

Salient features and results of experiences of using automation systems are:

a. Measurement and visualization

b. Hierarchical process control

- Feed-back control of individual variables

- Process control and optimisation

c. Quality control and fault diagnosis

d. Data archival and recipe management

Conclusions and Outlook

Automation systems for extruders employing modern instrumentation and iterative learning control

have attained maturity and can be employed with success in industrial plants. Long term tests in

industrial extruders have proved that automation yields increased productivity and more uniform

product quality. Iso-thermal extrusion at constant extrusion rate has been implemented employing

control and signal processing techniques with pyrometers, tapered heating / cooling leading to

better quality and productivity.

Modelling the extrusion process is an important pre-requisite for effectively designing control. A

review of the status of modelling for has been given and some models for simulation of the profile

temperature have been developed. There is scope to develop the models further and also look for

new models especially for predicting the maximum force. Basis for further work is the collection

and organisation of vast base of measurement data under production conditions. In particular non-

linear state space models which offer a standard formalism for representing dynamical systems have

to be investigated. Methods based on neural networks could also lead to useful black-box models,

especially if facility for collecting and processing large amounts of data which is available is put to

use.

A consequence of the progress of extruder automation is that expertise for specifying the proper

conditions of extrusion tends to be the bottle-neck rather than realising the conditions in production.

Here, the data archiving and retrieval capabilities of automation systems could be of good use.

References

[1] Akeret, R., Strehmel, W.: Heat balance and exit temperature control in the extrusion of alumi-

nium alloys Aluminium Technology, 19861]

[2] M. Pandit, H. Hengen, T. Heger : Trends and perspectives of automation of aluminium

extruders, Aluminium H.5 2008

[3] Heger, T., Pandit, M., Pieschel, M: Models of the Aluminium Extrusion Process for Design of

Extruder Automation and Control, 3rd Australasian-Pacific Aluminium Extrusion Conference,

July 2005

[4] Buchheit, K., Pandit, M.: Isothermes Strangpressen von Aluminium, Teil I, Aluminium, Heft 4

, 1995, S. 483-487; Teil II, Aluminium, Heft 5, 1995, S. 614-619

[5] Lange, G., Stüwe, H.P.: Der Wärmehaushalt beim Strangpressen Zeitschrift für Metallkunde 62

(1971), Nr. 8

[6] Ljung, L.: System Identification:Theory for the User. 2nd edition. Prentice Hall PTR, 1999

Installed automation systems

An automation system for integrated automation which employs Iterative Learning Control and

offers functions such as process control, data base and production handling named MoMAS®

('Modular Measurement and Automation System') was introduced about a decade back. Continuous

interaction with extruder operators and maintenance crews in extruder plants have contributed to

make MoMAS®

especially a user-friendly tool for process control, visualisation and management.

Salient features and results of experiences of using automation systems are:

a. Measurement and visualization

b. Hierarchical process control

- Feed-back control of individual variables

- Process control and optimisation

c. Quality control and fault diagnosis

d. Data archival and recipe management

Conclusions and Outlook

Automation systems for extruders employing modern instrumentation and iterative learning control

have attained maturity and can be employed with success in industrial plants. Long term tests in

industrial extruders have proved that automation yields increased productivity and more uniform

product quality. Iso-thermal extrusion at constant extrusion rate has been implemented employing

control and signal processing techniques with pyrometers, tapered heating / cooling leading to

better quality and productivity.

Modelling the extrusion process is an important pre-requisite for effectively designing control. A

review of the status of modelling for has been given and some models for simulation of the profile

temperature have been developed. There is scope to develop the models further and also look for

new models especially for predicting the maximum force. Basis for further work is the collection

and organisation of vast base of measurement data under production conditions. In particular non-

linear state space models which offer a standard formalism for representing dynamical systems have

to be investigated. Methods based on neural networks could also lead to useful black-box models,

especially if facility for collecting and processing large amounts of data which is available is put to

use.

A consequence of the progress of extruder automation is that expertise for specifying the proper

conditions of extrusion tends to be the bottle-neck rather than realising the conditions in production.

Here, the data archiving and retrieval capabilities of automation systems could be of good use.

References

[1] Akeret, R., Strehmel, W.: Heat balance and exit temperature control in the extrusion of alumi-

nium alloys Aluminium Technology, 19861]

[2] M. Pandit, H. Hengen, T. Heger : Trends and perspectives of automation of aluminium

extruders, Aluminium H.5 2008

[3] Heger, T., Pandit, M., Pieschel, M: Models of the Aluminium Extrusion Process for Design of

Extruder Automation and Control, 3rd Australasian-Pacific Aluminium Extrusion Conference,

July 2005

[4] Buchheit, K., Pandit, M.: Isothermes Strangpressen von Aluminium, Teil I, Aluminium, Heft 4

, 1995, S. 483-487; Teil II, Aluminium, Heft 5, 1995, S. 614-619

[5] Lange, G., Stüwe, H.P.: Der Wärmehaushalt beim Strangpressen Zeitschrift für Metallkunde 62

(1971), Nr. 8

[6] Ljung, L.: System Identification:Theory for the User. 2nd edition. Prentice Hall PTR, 1999


Keywords Index A

AA6082 27, 137

AISI H11 Tool Steel 205

Aluminium Extrusion 161, 257

Aluminium-MagnesiumCompound

129

Aluminum 35, 51, 113,153, 213

Aluminum Alloy 1, 9, 43, 57,105, 173

Artificial Neural Network (ANN) 241

B

Benchmark 19

Billet Temperature 249

Bonding Strength 129

Boundary Condition 65

C

CDRX 1

Chevron Cracks 265

Coextrusion 113, 129

Contact Condition 145

Control 273

Cooling 65

Cosine Die 181

Creep-Fatigue Interaction 205

D

Decoupled 197

Deflection Measurement 19

Deformation 197

Die 189, 197, 213

Die Channel 145

Die Deformation 19

Die Sliding Extrusion 235

Dislocation Density Evolution 27

Dual Stream Function 181

Ductile Damage 265

E

Equal Channel Angular Extrusion(ECAE)

71

Experiment 71

Extruded Profile 137

Extrusion 1, 19, 35, 43,65, 79, 87, 97,105, 153, 167,173, 181, 189,197, 213, 221,227, 241, 265

Extrusion Automation 273

Extrusion Die 205

Extrusion Seam 113

F

Filling Material 137

Finite Element (FE) Simulation 153, 227, 241

Finite Element Analysis (FEA) 35, 51, 71,221

Finite Element Model (FEM) 27, 65, 79, 87,97, 121, 129,213, 257, 265

First Billet 249

Flow Balance 257

Four-Hole Die 173

Friction 153

Friction Modeling 161

Friction Stir Welding (FSW) 137

Fuel Cell Separator 235

Fully Thermo-MechanicalCoupled Analysis

167

Functionally Graded Material(FGM)

43

G

Gas Quenching 57

GDRX 1

Guide Position 121

H

Hollow Profile 227

Hot Extrusion 27

HyperXtrude 257

I

Identification 273

Interaction 221


J

Joining 121

Jominy End-Quench Test 51

L

Lumped Parameter 273

M

Magnesium 113, 227, 241

Magnesium Alloy 167

Material Flow 113

Meshless Method 97

Metal Flow 9, 145, 173

Microstructure 35, 43

Microstructure Modeling 27

Modeling 9, 273

N

Neural Network Tool 249

New Extrusion Method (NEM) 97, 121

Nucleation 27

Numerical Calculation 105, 173

Numerical Design 265

O

Octagon 189

Orthogonal Channel 235

P

PCG 1

Plug Flow 145

Polypropylene (PP) 71

Porthole Die 105, 227

Process Parameter 249

Q

Quenching Simulation 57

R

Ram Speed 249

Rate-Dependent-J3 Plasticity 167

Recrystallization 1

Round 189

S

Seam Weld 87

SERR 189

Shear Criteria 221

Shear Layer 145

Shear Zone 221

Simulation 43

Spray Quenching 57

Square Section 181

Structure Evolution 9

T

Temperature Evolution 257

Thermo-Elastoviscoplasticity 265

Tool Lifetime 205

Torsion 1

Tube Wall Thickness 121

U

Upper Bound 181

W

Weld Seam 9

Welding Chamber 105

Welding Line 79, 87

Authors Index A

Alfaro, I. 97

Andersson, B. 65

Aour, B. 71

Assaad, W. 197

Aukrust, T. 257

Awiszus, B. 129

B

Ben Khalifa, N. 19, 35, 51, 87

Bikass, S. 65

Bohlen, J. 167

Brocks, W. 167

Brosius, A. 35

C

Ceretti, E. 79

Chinesta, F. 97

Cueto, E. 97

D

D’Ascenzo, M. 205

den Bakker, A.J. 9

Donati, L. 19, 137, 205

Duczczyk, J. 153, 213, 227,241

E

Ertürk, S. 167

F

Fang, G. 213

Farjad Bastani, A. 257

Filice, L. 79, 97

Foydl, A. 35

Fratini, L. 79

G

Gagliardi, F. 79, 97

Gall, S. 113

García-Romeu, M.L. 249

Geijselaers, H.J.M. 197

Giardini, C. 79

Gloaguen, J.M. 71

Grueebler, R. 161

Grydin, O. 57

Güzel, A. 51

H

He, X. 227

Hora, P. 161

Hoshino, M. 235

J

Jäger, A. 51

K

Kammler, M. 221

Karadogan, C. 161

Katgerman, L. 9

Kayser, T. 43

Kessler, O. 57

Kittner, K. 129

Kloppenborg, T. 87

Krumphals, F. 27

Kuboki, T. 121

L

La Spisa, D. 79

Labergère, C. 265

Lefebvre, J.M. 71

Leśniak, D. 105, 173

Lestriez, P. 265

Letzig, D. 167

Li, L.X. 227, 241

Libura, W. 105, 173

M

Ma, X. 65

Maity, K.P. 181, 189

Majhi, K. 181

Misiolek, W.Z. 1

Mitsche, S. 27

Mo, J. 241

Moroi, T. 121

Muehlhause, J. 113


Mueller, S. 113

Murata, M. 121

N

Naït-Abdelaziz, M. 71

Nilsen, K.E. 197

Nowak, M. 57

Nürnberger, F. 57

P

Pandit, M. 273

Parvizian, F. 43

Pietzka, D. 19

R

Randjelovic, S. 27

Reggiani, B. 205

Reich, M. 57

Rękas, A. 105, 173

Richert, J. 105

Rout, A.K. 181, 189

S

Saanouni, K. 265

Sabater, M. 249

Schaper, M. 57

Schöne, S. 57

Sherstnev, P. 27

Sillekens, W.H. 9

Skauvik, I. 257

Sommitsch, C. 27

Steglich, D. 167

Suzuki, K. 235

Svendsen, B. 43

T

Tekkaya, A.E. 19, 35, 51, 87

Tomesani, L. 19, 137, 205

V

Valberg, H.S. 145

Van Geertruyden, W.R. 1

W

Wang, L.L. 153

Werkhoven, R.J. 9

Z

Zaïri, F. 71

Zasadziński, J. 105

Zhou, J. 153, 205, 213,227, 227, 241,

241

Advances on hot extrusion and simulation of light alloys : selected, peer reviewed papers from the International Conference on Extrusion and Benchmark (ICEB), Dortmund 2009, Germany,

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