FSW Simulation Friction Simulation

Simulation of Friction Stir Spot Welding (FSSW) Process: Study of Friction Phenomena

Mokhtar Awang

Dissertation

Submitted to the College of Engineering and Mineral Resources at West Virginia University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in

Mechanical Engineering

Victor H. Mucino, Ph.D. (Chairman) Bruce Kang, Ph.D. Jacky Prucz, Ph.D. Ken Means, Ph.D.

Powsiri Klinkhachorn Ph.D.

Department of Mechanical and Aerospace Engineering

Morgantown, West Virginia 2007

Keywords: Friction Stir Spot Welding (FSSW), Adaptive Mesh, Friction Coefficient, Contact Friction, Internal Friction, Heat Generation

Copyright © 2007 Mokhtar Awang

UMI Number: 3300890

33008902008

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ABSTRACT

Simulation of Friction Stir Spot Welding (FSSW) Process: Study of Friction Phenomenon

Mokhtar Awang

Recently, friction stir spot welding (FSSW), a variant of “linear” friction stir welding (FSW) has

received considerable attention from automobile industries to replace electric resistance spot

welding with aluminum frames. Thus far, the FSSW process has been successfully developed

and applied in various cases, but the physics behind the process is not yet fully understood.

Effective and reliable computational models of the FSSW process would greatly enhance the

study of friction phenomena during the process as well as energy dissipation. Approaches for

the computational modeling of the FSSW process, however, are still under development and

much work is still needed, particularly the application of explicit finite element codes for a

verifiable simulation. The main objective of this dissertation research is aimed at describing the

friction phenomena and heat generation during FSSW process. To achieve this objective, a

three-dimensional fully coupled thermal-stress finite element (FE) model has been developed in

Abaqus/Explicit code. The simulation model utilizes the advantages offered by the arbitrary

Lagrangian Eulerian (ALE) formulation in simulating severe element distortion using an

adaptive mesh scheme. Rate dependent Johnson-Cook material model is used for elastic plastic

work deformations. Since friction in FSSW cannot be effectively treated by a simple “friction

coefficient”, a friction coefficient, which is dependant on pressure, temperature and slip rate is

used with sliding Coulomb friction at the interface between the workpiece and the welding tool.

The simulation results include temperature, stress and strain distributions as well as frictional

dissipation energy, which are presented at the end of this dissertation. The peak temperature at

the tip of the pin and frictional dissipation energy are in close agreement with the experimental

work done by Gerlich et al. [1], which is about 5.1% different.

iii

TABLE OF CONTENTS

ABSTRACT...................................................................................................................................ii

TABLE OF CONTENTS ............................................................................................................ iii

LIST OF FIGURES .................................................................................................................... vii

LIST OF TABLES ........................................................................................................................ x

ACKNOWLEDGEMENTS ....................................................................................................... xii

CHAPTER 1:INTRODUCTION................................................................................................. 1

1.1 Background of the Friction Stir Welding (FSW) ......................................................... 1

1.2 Friction Stir Spot Welding (FSSW) Process ................................................................. 5

1.2.1 Basic Mechanism of FSSW Process ......................................................................... 6

1.2.2 FSSW Equipment....................................................................................................... 7

1.2.3 FSSW Metallurgy....................................................................................................... 8

1.2.4 Advantages of FSSW ............................................................................................... 11

1.3 Problem Statement ........................................................................................................ 11

1.4 Objectives ....................................................................................................................... 12

1.5 Scope of Dissertation ..................................................................................................... 12

1.6 Structure of the Dissertation ........................................................................................ 13

CHAPTER 2:LITERATURE REVIEW .................................................................................. 16

2.1 Research in FSW ........................................................................................................... 16

2.1.1 Experimental Studies of FSW ................................................................................. 16

2.1.2 Numerical study of FSW ......................................................................................... 17

2.1.3 Analytical Study of FSW ......................................................................................... 19

iv

2.2 Friction Coefficient Used in the Numerical Study of FSW........................................ 20

2.3 Research in FSSW ......................................................................................................... 21

CHAPTER 3:FRICTION FUNDAMENTALS........................................................................ 23

3.1 Basic Definitions of Friction Quantities ...................................................................... 23

3.2 Sliding Friction Phenomena ......................................................................................... 24

3.3 Anisotropy of Friction................................................................................................... 28

3.4 Factors Affecting the Friction Coefficient................................................................... 31

3.4.1 Effects of Surface Temperature .............................................................................. 32

3.4.2 Effects of Sliding Velocity ....................................................................................... 34

3.4.3 Effects of Contact Pressure ..................................................................................... 35

CHAPTER 4:FINITE ELEMENT AND ARBITRARY LAGRANGIAN EULERIAN

(ALE) FORMULATIONS.......................................................................................................... 36

4.1 Introduction ................................................................................................................... 36

4.2 Fundamental of Differential Approximation.............................................................. 37

4.3 Fully Coupled Thermal-Stress Analysis ...................................................................... 38

4.3.1 Mechanical Analysis ................................................................................................ 39

4.3.2 Thermal Analysis ..................................................................................................... 41

4.4 Arbitrary Lagrangian Eulerian (ALE) Formulations ............................................... 42

4.4.1 Remeshing and Remapping Schemes in Abaqus/Explicit...................................... 44

4.4.2 Governing equations ................................................................................................ 46

CHAPTER 5:FINITE ELEMENT SIMULATION OF FSSW PROCESS........................... 48

5.1 Introduction ................................................................................................................... 48

5.2 Mesh and Geometry ...................................................................................................... 49

v

5.3 Welding Parameters ...................................................................................................... 51

5.4 Assumptions ................................................................................................................... 51

5.5 Boundary Conditions .................................................................................................... 53

5.6 Contact Friction............................................................................................................. 54

5.7 Material Model and Properties .................................................................................... 57

5.8 Adaptive Mesh ............................................................................................................... 59

CHAPTER 6:DISCUSSION OF RESULTS ............................................................................ 61

6.1 Overview of Frictional Dissipation Energy during FSSW Process........................... 61

6.2 Energy Dissipation during FSSW Process .................................................................. 63

6.2.1 Heat Generation due to Friction Work at the Tool and Workpiece Interface ...... 64

6.2.2 Heat Generation due to Friction Work at the Top and Bottom Workpieces

Interface................................................................................................................................. 66

6.2.3 Heat Generation due to Internal Friction/Plastic Work ........................................ 68

6.3 Study of Friction Coefficient Dependence................................................................... 69

6.4 Effect of Welding Tool Plunge Rate............................................................................. 72

6.5 Effect of Welding Tool’s Rotational Speed ................................................................. 74

6.6 Thermal Response ......................................................................................................... 76

6.7 Plastic Strain .................................................................................................................. 83

6.8 Material Flow................................................................................................................. 84

CHAPTER 7:DISCUSSION OF FRICTION PHENOMENA AND HEAT GENERATION

DURING FSSW PROCESS....................................................................................................... 86

7.1 Introduction ................................................................................................................... 86

7.2 Friction at Welding the Tool and Workpiece Interface............................................. 86

vi

7.3 Friction at Top Workpiece and Bottom Workpiece Interface .................................. 89

7.4 Internal Friction ............................................................................................................ 89

7.5 Friction Coefficient between the Tool and the Workpiece ........................................ 91

7.6 Heat Generation in FSSW ............................................................................................ 91

CHAPTER 8:CONCLUSIONS AND FUTURE WORK ........................................................ 96

8.1 Conclusions .................................................................................................................... 96

8.2 Contributions of the Dissertation to the FSSW Technology ..................................... 97

8.3 Future Work .................................................................................................................. 98

NOMENCLATURES ............................................................................................................... 100

ABBREVIATIONS................................................................................................................... 105

REFERENCES.......................................................................................................................... 106

APPENDIX A ............................................................................................................................ 113

A-1 Chemical Composition of Al 6061. ......................................................................... 113

APPENDIX B ............................................................................................................................ 114

B-1 Abaqus’s Input File.................................................................................................. 114

vii

LIST OF FIGURES

Fig. 1. 1: Schematic representation of the friction stir welding (FSW) [4]. ................................. 2

Fig. 1. 2: Plates being welded by "linear" FSW [4]...................................................................... 2

Fig. 1. 3: Typical FSW tool [4]..................................................................................................... 3

Fig. 1. 4: Friction stir welding (FSW) micrograph [14]. .............................................................. 5

Fig. 1. 5: Schematic representation of FSSW............................................................................... 6

Fig. 1. 6: Friction stir spot welding (FSSW) process [16]. ........................................................... 7

Fig. 1. 7: Top surface of the stir spot welded specimen [14]........................................................ 7

Fig. 1. 8: Examples of (a) FSSW equipment [17] and (b) welding tool [18]. .............................. 8

Fig. 1. 9: Cross section view of a typical friction stir spot welded [19]. ...................................... 9

Fig. 1. 10: SEM images show interface between two workpieces [19]...................................... 10

Fig. 1. 11: Bonding location of a welded aluminum alloy specimen (Courtesy of ORNL). ....... 10

Fig. 3. 1: Schematic diagram of friction concept........................................................................ 23

Fig. 3. 2: Schematic representation of asperity bonding (k is spring stiffness).......................... 25

Fig. 3. 3: Schematic representation of friction phenomena. ....................................................... 27

Fig. 3. 4: Hysteresis loop. ........................................................................................................... 28

Fig. 3. 5: Schematic representation of anisotropic friction in composites [49]. ......................... 30

Fig. 3. 6: Theoretical dependent of the rail steel friction coefficient on absolute temperature

[51]. ............................................................................................................................................... 33

Fig. 3. 7: Plot of friction coefficient versus temperature (oC) for a cast Inconel alloy pin sliding

on an M-10 tool steel disk [40]. .................................................................................................... 33

Fig. 3. 8: Friction coefficient versus velocity for various metals [40]........................................ 34

viii

Fig. 3. 9: Plot of friction coefficient versus normal force for 440C stainless steel and Ni3Al

alloy [40]. ...................................................................................................................................... 35

Fig. 4. 1: Comparison between explicit and implicit methods [53]............................................ 37

Fig. 4. 2: Finite difference scheme. ............................................................................................ 40

Fig. 4. 3: 1-D example of Lagrangian, Eulerian, and ALE Mesh with material point motion

[54]. ............................................................................................................................................... 43

Fig. 4. 4: Node relocation during mesh sweeping process. ........................................................ 45

Fig. 5. 1: Mesh representation of two layers of work piece with a pin and an anvil. ................. 50

Fig. 5. 2: Mesh scheme for workpieces. ..................................................................................... 50

Fig. 5. 3: Tool geometry. ............................................................................................................ 51

Fig. 5. 4: Schematic diagram of boundary conditions. ............................................................... 54

Fig. 5. 5: Plot of friction coefficient versus slip rate (mm/sec.). ................................................ 55

Fig. 5. 6: Plot of friction coefficient versus contact pressure (MPa). ......................................... 56

Fig. 5. 7: Plot of friction coefficient versus surface temperature (0C)........................................ 57

Fig. 5. 8: Plot of stress strain curve for Johnson-Cook work hardening..................................... 59

Fig. 6. 1: Three stages of friction between the tool and the workpiece. Left: Temperature

profile, Right: Friction dissipation energy history....................................................................... 63

Fig. 6. 2: Frictional dissipation energy history at the tool and workpiece interface................... 65

Fig. 6. 3: Slip rate distribution on upper surface of the top workpiece. ..................................... 65

Fig. 6. 4: Frictional dissipation energy at the top and bottom workpiece interface. .................. 67

Fig. 6. 5: Slip rate distribution on lower surface of the top workpiece. ..................................... 67

Fig. 6. 6: Slip rate distribution on upper surface of the bottom workpiece. ............................... 68

ix

Fig. 6. 7: Plastic dissipation energy history. ............................................................................... 69

Fig. 6. 8: Frictional (dotted line) and plastic (solid line) dissipation energies history for various

friction coefficient dependences. .................................................................................................. 71

Fig. 6. 9: Energy dissipation for different tool rotational speed. ................................................ 73

Fig. 6. 10: Frictional dissipation energy for various rotational speeds....................................... 75

Fig. 6. 11: Temperature contours at various times. .................................................................... 80

Fig. 6. 12: Plot of temperatures versus distance away from the center of the tool. .................... 81

Fig. 6. 13: Experimental versus FE simulation results of temperature history at the tip of

welding tool. ................................................................................................................................. 82

Fig. 6. 14: Plot of equivalent plastic strains versus distance away from the center of the tool. . 83

Fig. 6. 15: Locations of particle tracking.................................................................................... 84

Fig. 6. 16: Plots of particle displacements history...................................................................... 85

Fig. 7. 1: Schematic representation of friction between the tool and the workpiece.................. 87

Fig. 7. 2: Schematic representation relative velocity of the material and the tool (FN is the

normal force, Vmat is the material velocity, Vtool is the tool velocity). .......................................... 88

Fig. 7. 3: Schematic showing dislocation of the grains. ............................................................. 90

Fig. 7. 4: Schematic representation of tool interfaces that generate heat. .................................. 95

Fig. A - 1: Chemical composition of Aluminum Alloy 6061-T6. ........................................... 113

x

LIST OF TABLES

Table 5. 1: Temperature dependent material properties for Aluminum alloy 6061-T6 [31]...... 58

Table 5. 2: Constants for Johnson-Cook material model [57]. ................................................... 58

Table 6. 1: Summary of energy dissipation during FSSW process.............................................64

Table 6. 2: Summary of friction and plastic dissipation energies for different tool’s plunge rate.

....................................................................................................................................................... 74

Table 6. 3: Summary of frictional dissipation energy for different tool’s rotational speeds...... 76

xi

Dedication To

My Family

xii

ACKNOWLEDGEMENTS

I would like to express my deep and sincere gratitude to my research advisor, Prof.

Victor H. Mucino for his support, encouragement, and most importantly patience. His guidance

is a large part in making this dissertation possible.

I am deeply grateful for having an exceptional doctoral committee and wish to thank

Professors Jacky Prucz, Bruce Kang, Ken means, and Powsiri Klinkhachorn for their support and

encouragement.

I also would like to thanks Dr. Stan David and Dr. Zhili Feng of Oak Ridge National

Laboratory for their supervision and help during my SURA/ORNL summer internship program.

The initial part of this research was done under their supervision.

I owe my loving thanks to my wife Ku Zilati Ku Shaari, my son Faris, and my daughters

Hureen and Hanna for their endless love and patience especially during our difficult times.

Without their encouragement and understanding, it would have been impossible for me to finish

this work. My special thanks are due to my mother, and my parents in-law for their unfailing

supports and prayers.

1

CHAPTER 1: INTRODUCTION

1.1 Background of the Friction Stir Welding (FSW)

In 1991, a variation of the more common friction welding method called friction stir

welding (FSW) was invented and later patented by The Welding Institute (TWI) of United

Kingdom [2]. This relatively new welding method involves a solid state joining process that

uses a non-consumable tool to generate frictional heating and produce a plasticized region at a

welding zone, resulting in complex mixing of the material along a seam line. In FSW, the plates

to be joined are placed on a backing anvil and securely clamped to prevent relative motion

between parts. A specially shaped cylindrical tool rotates and slowly plunges into the joint line

between two pieces of the plate until a shoulder of the tool touches the plate surface.

When the shoulder contacts the work piece, it produces frictional heat around the point of

the weld, which drags the material around it and lowers its mechanical strength in a plastic

range. As the tool translates along the joint line, the friction from the rotating tool heats up the

material to the extent that it plastically deforms and flows from the front of the tool to the back,

where it subsequently cools and produces a weld. Simple FSW equipment can be constructed

using a conventional milling machine with a specially designed tool, made of a harder material

as compared to the workpiece [3]. Fig. 1. 1 and Fig. 1. 2 illustrate a schematic diagram of the

FSW and a real friction stir welding process, respectively, as applied to a butt joint of two plates.

2

Fig. 1. 1: Schematic representation of the friction stir welding (FSW) [4].

Fig. 1. 2: Plates being welded by "linear" FSW [4].

Normally, the tool is designed with a stepped shoulder and a threaded pin. The threads of

the pin assist in ensuring that the plastically deformed material flows around the pin. The length

of the pin is slightly shorter than the thickness of the plates to be welded. Fig. 1. 3 depicts a

3

typical FSW tool. Basically, different joint configurations use different tool geometries; for

instance, cone shaped probes are used for butt joints, and flared probes are used for lap joints, as

reported by Thomas and Dolby [5].

Fig. 1. 3: Typical FSW tool [4].

FSW was developed mainly for aluminum and its alloys [6]. In the recent years, this

method has been studied to join various other metals such as mild steel [7,8], aluminum alloy to

steel [3], magnesium alloy to aluminum alloy [9], and aluminum alloy to silver [10].

FSW has several advantages as compared to conventional fusion welding processes.

First, since the process occurs at a temperature below the melting point of the work piece

material, the problem with solidification cracking, liquation cracking, and porosity are

eliminated [11]. Second, due to the solid state nature of the process, FSW also has the potential

to avoid significant changes in microstructure and mechanical properties around the joint.

Consequently, FSW often exhibit improved mechanical properties relative to those of fusion

welds on the same material [12]. Third, because of a low temperature level compared to fusion

4

welding method, the residual stresses and the distortion in friction stir welds are typically lower

than those of fusion welds [13].

Another benefit of the FSW is that it has relatively fewer process parameters to control as

compared to fusion welding. In fusion welding, for instance, many process parameters such as

voltage and amperage, electrode feed, travel speed, shield gas, arc gap need to be controlled in

order to get a good quality weld. In FSW, however, there are only three process variables; i.e.,

rotational speed, transverse speed and pressure that need to be controlled. Therefore, due to the

excellence performance in welding technology as compared to fusion methods, FSW has been

successfully used in many applications such as aerospace, shipbuilding, aircraft, and automobile

industries.

FSW morphology can be described by four regions as shown in Fig. 1. 4. Region I is a

base metal, an area where the material was far enough removed from the weld to be unaffected

by the process. Region II is a heat affected zone (HAZ), an area where material has experienced

a thermal cycle without undergoing plastic deformation. Region III is a thermo-mechanically

affected zone (TMAZ), an area where material has been plastically deformed by the friction stir

welding tool. Region IV is a weld nugget, a region of a heavily deformed material that roughly

corresponds to the location of the pin during welding.

5

Fig. 1. 4: Friction stir welding (FSW) micrograph [14].

1.2 Friction Stir Spot Welding (FSSW) Process

Recently, a variant of the “linear” FSW called friction stir spot welding (FSSW) has been

developed and implemented in automotive industry as a replacement of resistance spot welding

for aluminum. Mazda Motor Co., for instance, uses the FSSW technique for production of new

RX-8 sports car [15]. This welding technology involves a process similar to FSW, except that,

instead of moving the tool along the weld seam, the tool only indents the parts, which are placed

on top of each other as illustrated in Fig. 1. 5. The welding operation can be done remarkably

quickly since cycle times are within a few seconds, for example, cycle time for friction spot weld

of 1 mm thickness 6061-T6 aluminum alloy is about 2 seconds.

During FSSW process, the pin experiences direct contact with the workpiece for longer

period as compared to the shoulder. As a result, the friction force between the pin and the

workpiece generates most of the heat energy. This characteristic make the FSSW process

different from FSW process.

6

Fig. 1. 5: Schematic representation of FSSW.

1.2.1 Basic Mechanism of FSSW Process

The FSSW process consists of three phases; plunging, stirring, and retraction as shown in

Fig. 1. 6. The process starts with spinning the tool with high rotational speed and plunging it

into a weld spot until the shoulder contacts the top surface of the workpiece. Then, the stirring

phase enables the materials of the two workpieces mix together with a present of a strong

compressive forging pressure. At this stage, the bonding occurs due to the pressure and

temperature that cause inter-diffusion of material across the interface at atomic level. Lastly,

once a predetermined penetration is reached, the process stops and the tool retracts from the

7

workpiece. Fig. 1. 7 shows a dent made by plunging and stirring processes during FSSW on a

lap joint configuration specimen.

Fig. 1. 6: Friction stir spot welding (FSSW) process [16].

Fig. 1. 7: Top surface of the stir spot welded specimen [14].

1.2.2 FSSW Equipment

FSSW equipment comprises four major components; a tool, a spindle, servomotor and an

anvil. The servomotor provides axial loads. Fig. 1. 8(a) illustrates a FSSW equipment

manufactured by Friction Stir Link, Inc. [17]. The tool can be fabricated using H13 tool steel

8

with heat treatment process. The tool can be with or without a shoulder. Fig. 1. 8(b) shows a

typical welding tool geometry with a shoulder.

a) b)

Fig. 1. 8: Examples of (a) FSSW equipment [17] and (b) welding tool [18].

1.2.3 FSSW Metallurgy

It has been suggested by Mitlin et al. [19] that two microstructural zones are created

around the pin, namely, thermo-mechanically affected zone (TMAZ) and heat affected zone

(HAZ). The microstructural details of both zones, however, are yet to be fully elucidated in

literature. A rough approximation of the microstructural regions of a cross-section of a friction

9

stir spot welded specimen is shown in Fig. 1. 9. Region I and region II represent TMAZ and

HAZ, respectively.

Fig. 1. 9: Cross section view of a typical friction stir spot welded [19].

In the same paper, Mitlin et al. [19] also noticed that joint interface of a welded 6111-T4

aluminum alloy can be categorized into four areas. Looking towards the pin hole, the four

regions are defined as an area of no contact, a region of only mechanical bonding (“kissing

bond”), an interface of partially metallurgically bonded, and a zone with a full metallurgical

bond. Fig. 1. 10 illustrates the transition from no contact to “kissing bond” interface (A), the

transition from the “kissing bond” to partially metallurgically joined region (B), and nearly

perfect metallurgical bond (C). Bonding location of the FSSW specimen can be visualized in

Fig. 1. 11. The two specimens are bonded together in a circular shape around the hole left by the

tool.

10

Fig. 1. 10: SEM images show interface between two workpieces [19].

Fig. 1. 11: Bonding location of a welded aluminum alloy specimen (Courtesy of ORNL).

11

1.2.4 Advantages of FSSW

FSSW has several advantages over the electric resistance welding process in terms of

weld quality and process efficiency as reported by Hancock [15]. In car manufacturing, this new

process eliminates the need for the large electric current, coolant and compressed air as required

for conventional resistance welding. Furthermore, the FSSW has simplified the overall joining

systems, which in turn eliminates the need for specialized joining equipments and large-scale

electricity supply facility and is environmentally friendly as there are no fumes. Other benefits

of FSSW over traditional welding methods are similar to linear FSW as discussed in the previous

section (Sec. 1.1).

1.3 Problem Statement

Friction phenomena is a very important aspect in FSSW since the process itself relies on

the heat generated from the frictional force between tool and workpiece to soften and join the

workpieces. Although this welding technique has been successfully developed and applied in

various cases in industries, the friction phenomena during the process is not yet fully understood.

Therefore, this dissertation addresses the friction phenomena between the tool and the workpiece

interface, between the plates interface as well as the internal friction in the material.

One of the unresolved issues in numerical study of FSW is the use of a “friction

coefficient”. Most of the FE element models of FSW oversimplified friction with the use of a

“friction coefficient”, which is typically considered a constant in value. Theoretically, a friction

coefficient does not exist, but empirically it can be assumed to be a function of several variables.

12

In Abaqus/Eplicit code, the friction coefficient can be modeled as a function of slip rate, contact

pressure, and surface temperature. Based on the literature survey in Chapter 2, none of the

research works had used friction coefficient dependence of slip rate, contact pressure, and

surface temperature. Therefore, the FE models in this dissertation are directed at determining the

dependency of friction to these process parameters in the context of a FSSW application.

1.4 Objectives

Two objectives have been set forth in this work. The first objective aims to study the

friction phenomena at the tool and workpiece interface, between workpieces interface, as well as

inside the material of the workpieces. In addition, the intention is also to study the significance

and contribution to energy dissipation for each of them. The second goal is to determine the

friction coefficient as a function of slip rate, contact pressure, and surface temperature in order to

conduct simulations that are more realistic. To achieve these objectives, a fully coupled

thermomechanical 3-dimensional FE model has been developed and verified experimentally,

based on temperature and frictional dissipation energy histories.

1.5 Scope of Dissertation

The scope of the dissertation is focused on the FE simulation of friction stir spot welding

(FSSW) for thin aluminum alloy Al 6061-T6 while some limited access to original data is

available. The FE model uses Lagrangian adaptive mesh domain for the workpieces, thus, actual

13

material bonding between two workpieces is not addressed in this work. Since the tool and the

backing anvil are modeled using rigid body surfaces, mechanical responses for the tool and the

backing anvil are not available in this study. The two rigid body surfaces, however, have an

isothermal temperature response, which is in itself an approximation.

The friction model in the FE simulation uses Coulomb’s friction law for sliding friction

at the interfaces but the friction coefficient used is dependent on surface temperature, contact

pressure, and slip rate. In addition, the frictions at the interfaces are assumed to be isotropic

Coulomb frictions.

This work also tracks particles motion, but they are only the particles on the surface. Due

to the computer hard drive space limitations, the simulation time for modeling material flow is

only 0.08 seconds (full simulation takes 1.75 seconds), which consumes 2.5 gigabytes of space.

1.6 Structure of the Dissertation

This dissertation is presented in the following sequence. Chapter 1 presents an

introduction to friction stir welding (FSW) as well as friction stir spot welding (FSSW). In

addition, this chapter also derives the problem statement, and defines the objective and scope of

dissertation.

Previous works of FSW and FSSW are reviewed in Chapter 2. Research in FSW can be

categorized into experimental, numerical and analytical works. Several numerical approaches to

solve FSW problems are briefly presented. The implementation of friction coefficient in

14

numerical works is also discussed. Lastly, research in FSSW is presented at the end of the

chapter.

Chapter 3 presents a discussion about friction. In the beginning of the chapter, basic

friction quantities are defined using classical Coulomb’s friction. The concepts of anisotropic

contact friction, with linear mathematical model of anisotropic friction are also discussed briefly.

Finally, the factors that affecting the friction behavior are listed at the end of the chapter.

Finite element formulations and the arbitrary Lagrangian Eulerian (ALE) concept used in

the finite element simulation are discussed in Chapter 4. In the early section of this chapter,

forward and central difference approximations are derived from Taylor series. Then, the chapter

presents how the mechanical and thermal analyses are formulated in the FE model. The

discussion in this chapter also includes adaptive mesh methodology used in Abaqus/Explicit.

The main subject of this dissertation, which is finite element simulation of FSSW

process, is discussed in Chapter 5. The discussions include model geometry and meshing

scheme, welding parameters, modeling assumptions, boundary conditions, mechanical and

thermal contacts, and material model. The friction coefficient data used for the FE model are

also listed in this chapter.

Chapter 6 presents the simulation results. This chapter begins with a discussion of FE

model verification. The discussions in this chapter include energy dissipation, study of friction

coefficients, parametric study of plunge rate and rotational velocity, thermal and strain rate

responses, and material flow.

15

The friction phenomena and heat generation during FSSW process is presented in

Chapter 7. In this chapter, the discussion of friction phenomena during FSSW process includes

many aspects such as friction mechanism, friction coefficient and friction heating.

Conclusions from the FE simulation results are presented in the last chapter, which is

Chapter 8. Contribution of the dissertation to the FSSW technology and future work are

discussed in this chapter.

16

CHAPTER 2: LITERATURE REVIEW

2.1 Research in FSW

Since its invention in 1991, FSW has been an active research area. The following

paragraphs discuss the research area in FSW, which can be grouped into experimental, numerical

and analytical studies.

2.1.1 Experimental Studies of FSW

Experimentally, it is rather challenging to measure thermomechanical responses on the

welding zone, so most studies measure responses near the welding zone. Experimental study on

the temperature distribution and the heat generation during FSW process has been reported by

many researchers. Tang et al., [20] was among the first to measure temperature history and

thermal profile in FSW butt-joined geometry. They observed that temperature distribution was

symmetric about the weld centerline and the peak temperature at the weld center of Al 6061-T6

specimen was about 4500C. They also concluded that the maximum temperature was about 80 %

less than the melting point for Al 6061-T6, which was about 5820C. Dickerson, et al. [21]

conducted a thermal experiment to measure heat profile specifically at the weld tool. They

found that using solid tools, the steady state heat loss into the tool was about 10 % of the total

heat generated. Chao et al. [22] have also conducted experimental studies on heat transfer in

FSW. They concluded that about 95 % of heat generated from the friction was transferred into

17

the workpiece and only 5 % flowed into the tool. Moreover, they also drew a conclusion that

about 80 % of the plastic work was dissipated as heat.

2.1.2 Numerical study of FSW

Considerable numerical works of FSW have been reported in published literatures, which

are focused on heat transfer and material flow aspects. Several approaches have been used to

simulate the FSW process. To describe the heat transfer and the mixing action during FSW

process, a computational fluid dynamics (CFD) based simulations have been used. Colegrove

and Shercliff [23], for instance, developed a 2-D model of material flow around a welding tool

using CFD code, Fluent®. Hyoe et al. [24] also used Fluent® code in their models to the predict

hardness profile across a weld as well as thermal histories as a function of position in the weld

cross-section. The thermal history in their works was simulated by applying a uniform heat flux

over the contact surfaces and a prescribed power input, which is obtained from an experiment.

Another material flow study was done by Zhao [25] using LS-DYNA code. In the study, ALE

formulations have been used with a “moving mesh” in order to simulate the material flow around

the tool. The same methodology could be used to study the material flow in FSSW process.

To capture severe deformation during FSW process and particle movement, an arbitrary

Lagrangian Eulerian (ALE) formulation adopted in Abaqus/Explict has been utilized by Schmidt

and Hattel [26]. The model in their works includes heat generation from friction between the

tool and the workpiece interface as well as plastic straining. This dissertation uses the same

18

commercial FE code to simulate FSSW process, but with some variations in the treatment of

friction.

FSW process can also be modeled using some other approaches. Askari et al. [27] used a

3-D CTH code (a finite difference hydrodynamics code) to capture the coupling between tool

geometry, heat generation, and plastic flow during FSW process. The CTH models are

sequentially coupled thermal and mechanical models, which are based on the finite volume and

Eulerian formulations. The CTH code has the advantage of treating the material as a solid rather

than a liquid as several other models do. Smoothed particle hydrodynamics (SPH) approach has

also been used to model heat generation and material flow as done by Tartakovsky et al. [28].

SPH code is a Lagrangian particle method that can simulate the dynamics of interfaces, large

material deformations, void formations, and the material’s strain and temperature history of FSW

process, but no provisions are made to include energy release when particles slip and break away

from the adjacent grains.

Some of the previous efforts to model the thermal profiles in FSW are considered non

Newtonian flow for the mass. Ulysse [29] introduced a 3-D visco-plastic FE model for solving

the a coupled thermomechanical state during FSW. In his model, slip velocity is assumed at the

contact interface. The heat is mainly generated from the rotation of the shoulder and that of the

pin, which is modeled by prescribing a constant tangential velocity. The A visco-plastic

approach has also been done by Nandan et al. [30] to model 3-D heat transfer and plastic flow

during FSW. The slip between the shoulder and the workpiece was adjusted to achieve good

agreement between the calculated and the measured temperature. This approach makes it

difficult to predict the response without experimental results available.

19

In many FE models in the past, heat flux is an input in the model to describe thermal

behavior during FSW. Chao and Qi [31] have developed one of the earliest three-dimensional (3-

D) heat transfer model of FSW using a trial and error procedure in order to adjust the heat input

until all calculated temperatures matches with the measured values. They assumed a constant

heat flux input from a tool shoulder-workpiece interface. Frigaard et al. [32] assumed the heat

input from the tool shoulder to be a frictional heat in their two-dimensional (2-D) model of FSW.

Song and Kovacevic [33] introduced a moving coordinate system to ease modeling the moving

tool in their paper. They also included the heat input from the tool shoulder and the tool pin in

their 3-D heat transfer model.

2.1.3 Analytical Study of FSW

Analytical study of FSW has also been receiving a great deal of attention by some

researchers. Gould and Feng [34] developed a heat flow model based on the classical Rosenthal,

which describes a quasi-steady state temperature field due to a moving heat source of a constant

velocity. They assumed that two sources of heat generation during FSW process; friction at the

interface of the tool shoulder and the work piece, and the plastic deformation of the weld metal

around the pin. More recently, Schmidt et al. [35] established an analytical model for heat

generation based on different assumptions of the contact condition between the tool and the

workpiece. The assumptions that they used for contact condition between the tool and the

workpiece interface were sticking, sliding, and partial sticking/sliding conditions. In this

dissertation, sliding friction was assumed at the tool and the workpiece interface.

20

2.2 Friction Coefficient Used in the Numerical Study of FSW

The friction coefficient between tool and workpiece is an input parameter in FE model

and used in heat generation formulations. A variety of friction coefficient values have been

found in literatures with the majority of them being a constant value. Song and Kovacevic [36]

and Xu et al. [37] used friction coefficient of 0.4 and 0.3, respectively for friction between

aluminum alloy 6061-T6 and tool steel. Chen and Kovacevic [38], also used a constant value of

the friction coefficient for friction between aluminum alloy 6061-T6 and tool steel, but they did

not report the value they used to verify the temperature history. Schmidt and Hattel [26]

assumed the friction coefficient equals to 0.3 in their thermomechanical model of welded

aluminum alloy 2024-T3. Song et al. [39], however, adopted a linear temperature dependent

coefficient in the model. In their model, the friction coefficient for aluminum is 0.5 at 300K and

linearly decreases to 0.3 at the melting point. Frigaard et al. [32] reported that they adjusted the

friction coefficient in their heat transfer model’s calculation to keep the thermal solution from

exceeding the material melting point.

In reality, if a friction coefficient is assumed, it should be dependent on surface finish,

contact pressure, temperature, sliding velocity, type of sliding motion, surface films, system

stiffness, and vibrational interactions [40]. In addition, there is an “internal friction” inherent in

the material, which in reality more a tensor than it is a scalar. In this dissertation, a nonlinear

distributed friction coefficient will be used between welding tool and workpiece. The physical

data of friction coefficients dependence of slip rate, contact pressure, and surface temperature for

Al 6061-T6 and tool steel, however are available in the literature.

21

2.3 Research in FSSW

As a relatively new manufacturing process, there is limited published research work on

FSSW process as compared to FSW. Several works, however, have been discussed in symposia

and conferences. Lin et al. [41] investigated microstructures and failure mechanisms of FSSW

in aluminum 6111-T4 based on experimental observations. Feng et al. [42] reported about their

feasibility study of FSSW in advanced high-strength steels such as AHSS. Mitlin et al. [19]

conducted experiments to investigate structure-properties relations in spot friction welded 6111

T4 Aluminum. More recent works on FSSW include Pan et al. [16] on sheet aluminum joining

and Sakano et al. [43] on development of FSSW robot system for automobile industry.

Recently, some researchers studied the thermal and heat generation aspects of FSSW

process. Gerlich et al. [1] measured peak temperature in aluminum and magnesium alloys

friction stir spot welds. Two thermocouples were embedded in a welding tool assembly in the

experiment. They found out that the peak temperatures during FSSW of Al 5754 and Mg alloy

AZ91D were 565 oC and 462 oC, respectively. Energy utilization during FSSW process has been

studied by Su et al. [44]. The group reported that less than 4.03 % of the energy generated

during the FSSW was required for stir zone formation in Al 6111 welds. The study of Gerlich is

used in this dissertation as a reference in relation to the numerical results obtained in this work.

FE modeling has been developed to study the temperature and stress/strain distribution as

presented by Awang et al. [45]. In their work, Coulomb’s friction with temperature dependent

friction coefficient has been modeled at contact interface. A FE modeling of FSSW, which is

developed by Kakarla et al. [46] also, used Abaqus/Explicit to model the stress and the strain

22

responses of FSSW process. In their model, a constant friction coefficient of 0.64 was used and

the simulation time only for the initial part of plunge phase (0.75 seconds).

23

CHAPTER 3: FRICTION FUNDAMENTALS

3.1 Basic Definitions of Friction Quantities

Fig. 3. 1: Schematic diagram of friction concept.

Friction can be defined as a force that opposes the relative motion between two

contacting bodies parallel to a surface that separates them. The friction concept can be

visualized by sliding a block on a plate as shown in Fig. 3. 1. Block 1 will not move relative to

block 2 if applied force, F is less than the friction force Ff. On the other hand, if the applied

force, F is greater than the friction force, Ff, block 1 will slide on block 2. The figure also

illustrates that the friction coefficient can be a function of normal force, FN, temperature, T and

slip rate, v.

The classical approximation of the friction force known as Coulomb’s friction law

(named after Charles-Augustin de Coulomb) is expressed as

24

Nf FF µ≤ 3.1

where µ is the coefficient of friction (sometimes it is called friction coefficient), FN is the force

normal to the contact surface, and Ff is the force exerted by friction. The classical laws of

friction that were published by French scientist, Guillaume Amontos and later verified by

Coulomb, states that the friction is directly proportional to the normal force and independent of

contact area.

In general, there are three types of friction, i.e., static friction, kinetic friction, and rolling

friction. Static friction is the force that opposes a stationary object from moving relative to the

contacting surface. When the two contacting surfaces move relative to each other, the force that

opposes the motion is referred as a kinetic friction. Rolling friction is the frictional force

associated with the rotational movement of a circular object along a surface. Generally, the

kinetic friction is smaller than the static friction, but larger than the rolling friction.

By the definition, friction coefficient is a dimensionless quantity, which describes the

ratio of the force of friction between two bodies and the normal force. Friction coefficient can

be categorized based on the type of friction, i.e., static friction coefficient, sµ kinetic friction

coefficient, kµ and rolling friction coefficient.

3.2 Sliding Friction Phenomena

In reality, friction originates when asperities of two surfaces are in contact. As the

normal force increases, the contact area increases and the asperity junctions grow. The growth

25

of the junctions stops when the reaction force distributed over an expanding contact area exactly

balances the applied normal pressure. Adhesive bonds form at the contact points. When the

contacting surfaces move relative to each other, a tangential force breaks the bonds and the force

needed to overcome the shear strength of the bonds produces the friction force. The bonding

between contacting asperities can be modeled as a small stiff spring as shown in Fig. 3. 2.

Microscopic sliding starts when the bonding breaks.

Fig. 3. 2: Schematic representation of asperity bonding (k is spring stiffness).

Sliding friction can be considered as elastic and plastic deformation forces of

microscopical asperities in contact. Fig. 3. 3 shows friction at microscopic level. The asperities

each carry a part fi of the normal load FN. If we assume plastic deformation of the asperities

until the contact area of each junction has grown large enough to carry its part of the normal

load, the contact area of each asperity junction is

Hf

a ii = 3.2

26

where, H is the hardness of the weakest bulk material of the bodies in contact. The total contact

area can thus, be written as

HF

A NT = 3.3

For each asperity contact, the tangential deformation is elastic until the applied shear pressure

exceeds the shear strength, τy of the surface materials, when it becomes plastic. In sliding, the

friction force thus is

Tyf AF τ= 3.4

Based of the definition, the friction coefficient can be expressed as

N

f

FF

=µ 3.5

Substitute equations 3.3 and 3.4 into 3.5 yields

HHA

A y

T

Ty ττµ == 3.6

Therefore, the friction coefficient can be computed from the shear strength of asperity junctions

and the material hardness of two materials in contact.

27

a) Asperities without load b) Asperities with load

Fig. 3. 3: Schematic representation of friction phenomena.

As discussed previously, the material at the contact interface experiences elastic and

plastic deformation. This elasto-plastic characteristic of sliding friction can be described by

elastic hysteresis theory. Assumed that a material is subjected to a completely reversed stress

cycle as shown in stress – strain curve of Fig. 3. 4. The area underneath the “a-b” curve

represents the work done on the workpiece per unit volume, by straining forces. The area

underneath the “b-c” curve represents the work per unit volume done by the elastic restoring

force. The different between the work done by the straining forces and work done by the elastic

restoring force, which is represented by the area of “a-b-c”, is the dissipation energy. This

energy is in the form of heat. Therefore, the area of the loop “b-c-d-e” represents the energy loss

for the complete cycle.

28

Fig. 3. 4: Hysteresis loop.

3.3 Anisotropy of Friction

Friction is more commonly treated as an isotropic term in engineering formulations. In

reality, however friction can be considered as anisotropic, in which its magnitude is directionally

dependent, acquiring a tensorial nature. The anisotropic friction is the friction whose properties

vary with the direction of sliding. Fig. 3. 5 depicts the concept of friction anisotropy in

composites.

Microscopically, a flat surface contains asperities, which is originated from machining or

wearing processes. The characteristic of the asperities determines an anisotropic surface

roughness, which is defined as a structure in which highs and hollows in the surface are clearly

29

oriented. Therefore, the friction of two contacting surfaces that depends on the sliding direction

due to the anisotropic surface roughness is called anisotropic friction.

A linear model of anisotropic friction has been derived from the work of Zmitrowicz

[47]. According to the thermodynamical theory of constitutive equations of friction presented by

Zmitrowicz [48], the friction force vector Ff can be a function of the slip velocity unit vector v

and the normal pressure FN. The equation can be expressed as

)(fFN vFf −= 3.7

Let us assume ik (i=1,2) is an orthogonal unit vector basis in 2-D vector space 21S .

Vector Ff can be expressed as linear combination of tensors ik in index notation as

iifF kFf = 3.8

Then, let us assume ej (j=1,2) is an arbitrary unit vector basis in 22S . Similarly, vector v can be

written as linear combination of vectors ej in index notation as

jjv ev = 3.9

Now, let us consider a linear case of equation 3.7, which is written as

vMF 1f NF−= 3.10

M1 in equation 3.10 is a second order tensor, which belongs to vector space 2P . Vector space

2P in this case is the tensor product of the vector spaces 21S and 2

2S , which yields four tensor

basis elements ji ek ⊗ .

30

The tensor M1 can be expressed as a linear combination of tensor ji ek ⊗ as

ji1 ekM ⊗= ijM 3.11

Substituting equation 3.9 and equation 3.11 into equation 3.10, yields

( )( )jjij

N vMF eekF jif ⊗−= 3.12

Simplifying equation 3.12 yields

if kF jijN vMF−= where i,j=1,2 3.13

Mij are four friction coefficients for dry friction model formulated by Amontons and Coulomb.

Therefore, the friction can be treated as a second order tensor, similar to other physical

properties such as stress, heat conduction, diffusion, etc.

Fig. 3. 5: Schematic representation of anisotropic friction in composites [49].

31

Anisotropy of friction phenomenon not only occurs in contact friction, but also in internal

friction. The reason for anisotropy of internal friction is due to mechanical properties of single

crystals that depend on crystallographic direction. When material undergoes plastic

deformation, slip occurs because of dislocations between grains. The force that resists the

motion of slip in crystal structure is called internal friction. Therefore, the internal friction also

depends on crystallographic orientation.

Abaqus/Standard, which is another Abaqus solver for solving implicit finite element

analyses, is capable to model an anisotropic friction. The FE code allows for different friction

coefficients in two orthogonal directions on a contact surface. In Abaqus/Explicit, however, the

friction models available are based on isotropic friction, which assumes that the friction

coefficient is the same in all directions.

3.4 Factors Affecting the Friction Coefficient

The friction coefficient is believed to vary during the FSSW process. The detail of the

variation, however, is still not clear so far. Friction coefficient in Abaqus/Explicit can be defined

as a function of surface temperature, slip rate (relative velocity), and contact pressure. The

physical data that describe variable dependent friction coefficient for aluminum alloy 6061-T6

and the tool steel are not available. The friction coefficient data in this dissertation, therefore, is

assumed based on what is available in the literature.

32

3.4.1 Effects of Surface Temperature

Heat energy generated due to friction in a sliding interface affects the properties of the

materials in the vicinity of that interface. As the temperature of the material under a sliding

object elevates, the strength of the material decreases. Therefore, the resistance to sliding

offered by those materials will be changed if the properties of the materials change by the

heating.

Temperature dependent friction coefficient data for the friction between aluminum alloy

6061-T6 and tool steel are assumed based on previous works documented in the literature. Back

in 1965, Male and Cockcoft [50] published a friction coefficient and temperature relationship

using a ring compression test. They observed that the friction coefficient of most metals

appeared to be independent of temperature at temperatures below 120-140 0C. Above this

temperature range, friction coefficient may increase or decrease with increasing temperature, or

it may remain constant over relatively wide temperature ranges.

The trend of friction coefficient versus temperature for some metals has been found in a

published paper of Popov et al. [51]. They proposed that the coefficient of friction between the

rail and the wheel is constant at temperature below 650 0C and gradually decreases as the

temperature increases above that level. Fig. 3. 6 shows friction coefficient temperature

dependent plot of the rail steel. A plot of friction coefficient versus temperature cited by Blau

[40] also shows similar trend as illustrated in Fig. 3. 7.

Physically, this trend can be explained since higher friction coefficient directly relate to

the capacity of transforming motion energy into heat energy (braking). The higher the

33

temperature, the less capacity of transforming motion energy into heat, and thus, the less

capacity for braking. This is a well-known fact in brake design.

Fig. 3. 6: Theoretical dependent of the rail steel friction coefficient on absolute temperature [51].

Fig. 3. 7: Plot of friction coefficient versus temperature (oC) for a cast Inconel alloy pin sliding on an M-10 tool steel disk [40].

34

3.4.2 Effects of Sliding Velocity

The friction force acting over a distance in a period of time generates energy per unit

time or power, which can be expressed as

vFP f= 3.14

where P is the power, Ff is the friction force, and v is the velocity.

Most of the energy produced by the frictional contact is converted into heat. This heat

reduces the strength of the material. Consequently, the resistance of the material movement

decreases as the velocity increases. Fig. 3. 8 shows how the friction coefficient of various metals

decrease as velocity increases. This trend is the basis of the assumption made for coefficient

friction velocity dependent.

Fig. 3. 8: Friction coefficient versus velocity for various metals [40].

35

3.4.3 Effects of Contact Pressure

A friction experiment conducted by Blau [40] showed that the friction coefficient

decreases with increasing normal load as shown in Fig. 3. 9. This trend behavior can be

explained by considering two surfaces that are placed together under a normal load. Due to the

pressure distribution, the asperities of the two contacting surfaces will deform to support the

load. When sliding occurs, the shear force parallel to the surface causes asperity contacts to

stretch out and break up into small contact regions. As a result, the shear strength of solids may

be changed by increasing pressure and sliding motion. Therefore, the deformation of materials

during sliding may alter their near-surface crystallographic orientation to produce easier shear,

which means less friction.

Fig. 3. 9: Plot of friction coefficient versus normal force for 440C stainless steel and Ni3Al alloy [40].

36

CHAPTER 4: FINITE ELEMENT AND ARBITRARY LAGRANGIAN

EULERIAN (ALE) FORMULATIONS

4.1 Introduction

In this research work, a finite element analysis has been conducted using Abaqus/Explicit

codes. The main reason why the explicit formulation is chosen as opposed to implicit is that the

modeling of FSSW process required the solutions in a short simulation time efficiently. The

Abaqus/Explicit formulations are well-suited to solving high-speed dynamic events that require

many small increments to obtain a high-resolution solution [52]. Moreover, contact conditions

and other extremely discontinuous events are readily formulated in the explicit method and can

be enforced on a node-by-node basis without iteration.

The term “explicit” in the FE method refers to the fact that the state at the end of the

increment is based exclusively on the displacements, velocities, and accelerations at the

beginning of the increment. Generally, the time increments in explicit formulation are quite

small in order to produce accurate results. Therefore, it requires a lot of increments so that the

accelerations during an increment are nearly constant. Even though it requires a lot of

increments in the analysis, each increment in explicit formulation is inexpensive since there are

no simultaneous equations need to be solved. Fig. 4. 1 depicts comparison between explicit and

implicit formulations.

37

Fig. 4. 1: Comparison between explicit and implicit methods [53].

4.2 Fundamental of Differential Approximation

The explicit forward difference and the explicit central difference integration rules can be

derived differential approximation technique.

Derivatives of any function can be approximated using Taylor series,

nn

)n(

Rh!n

)x(f...!2

)x("f)x('hf)x(f)hx(f +++++=+ 4.1

Simplifying equation 4.1 yields,

h

)x(f)hx(f)x('f −+≅ 4.2

38

This is called forward difference approximation since it finds the derivative in the positive

(forward) direction of the profile from the point x. Similarly, if the Taylor series of f(x-h) is

expended, a so-called backward difference approximation can be obtained as shown below.

h

)hx(f)x(f)x('f −−≅ 4.3

A more accurate representation of the first derivative can be computed from the difference

between Taylor series of f(x+h) and f(x-h) and is called central difference approximation.

h2

)hx(f)hx(f)x('f −−+≅ 4.4

In Abaqus/Explicit method, the heat transfer equations are formulated using an explicit

forward difference time integration rule, and the mechanical solution response is obtained using

an explicit central difference integration rule. Section 4.3.1 and section 4.3.2 discuss how the

two analyses are derived.

4.3 Fully Coupled Thermal-Stress Analysis

In this dissertation, a fully coupled thermal-stress analysis was used to simulate both

thermal and mechanical responses of FSSW process. The FSSW process involves significant

heating due to contact friction and inelastic deformation of the material, which in turn, changes

the material properties. Therefore, in this analysis, the thermal and mechanical solutions must be

obtained simultaneously rather than sequentially. In fully coupled thermal-stress formulation,

39

the stress analysis is dependent on the temperature distribution and the temperature distribution

depends on the stress solution.

4.3.1 Mechanical Analysis

In this analysis, the mechanical response is governed by the differential equation of

motion such as

Fukucu =++ &&&ρ 4.5

where ρ is the mass, c is the damping coefficient, k is the stiffness coefficient, F is the body

force, and u&& , u& , and u are the nodal acceleration, nodal velocity and nodal displacement,

respectively. Equation 4.5 can be rewritten in matrix form as

FKuuCuM =++ &&& 4.6

where, M is the discrete mass matrix, C is the viscous damping matrix, K is the stiffness matrix,

F is vector of external discrete forces, and u&& , u& , and u are the nodal acceleration, velocity and

displacement vectors, respectively.

Equation 4.6 can then be rewritten to obtain nodal acceleration in the beginning of time

increment as

)KuuC(FMu ii1

i −−= − &&& 4.7

where i is the time step.

40

An explicit central difference scheme is used in the discretization of the control

equations. Fig. 4. 2 illustrates the finite difference scheme applied in the discrete equations.

Therefore, the acceleration equation can be written as

( ) 2/tt i1i

2/1i2/1ii ∆∆ +

−=

+

−+ uuu

&&&& 4.8

Solving equation 4.8 for the velocity at the middle of current increment yields

2/1iii1i

2/1i 2tt

−+

+ +

+

= uuu &&&&∆∆

4.9

Replacing the nodal acceleration term in the above equation from the previous nodal acceleration

vector equation yields the velocity expression.

2/1i1i1i

2/1i )(2

tt−

−++ +−−

+

= uKuuCFMu ii &&&∆∆

4.10

Fig. 4. 2: Finite difference scheme.

41

4.3.2 Thermal Analysis

The governing equation describing transient heat transfer process during FSSW can be

written as,

QzTk

zyTk

yxTk

xtTc zyxp +

∂∂

∂∂

+

∂∂

∂∂

+

∂∂

∂∂

=∂∂ρ 4.11

where, ρ is the material density, cp is the material specific heat, k is heat conductivity (i.e., kx, ky,

and kz are the heat conductivity in x, y, and z directions), T is the temperature, t is the time and Q

is the heat generation. In finite element formulation, equation 5.11 can be discretized into

)t()t()t( QTKTC =+& 4.12

where, C(t) is the time dependent capacitance matrix, T is the nodal temperature vector, K(t) is

the time dependent conductivity matrix, T& is the derivative of the temperature with respect to

time (i.e., dT/dt), T is the nodal temperature vector and Q(t) is the time dependent heat vector.

Solving the nodal temperature rate from the above equation yields,

)( i1 KTFCTi −= −& 4.13

Applying a forward difference integration for the nodal temperature rate gives,

1it +

+ −=

∆i1i

iTT

T& 4.14

The above expression can be rewritten as

ii1i1i )t( TTT += ++&∆ 4.15

42

Thus, the final explicit expression for the nodal temperature rate can be written as,

ii1

1i1i )()t( TKTFCT +−= −++ ∆ 4.16

4.4 Arbitrary Lagrangian Eulerian (ALE) Formulations

Numerical problems in continuum mechanics are normally solved using two classical

descriptions of motion; Lagrangian description, and Eulerian description. Lagrangian

description, which is mainly used in structural analysis allows the mesh and the material to move

together, making it easy to track surfaces and apply boundary conditions. Its weakness is

difficulty in convergence when the elements are subjected to severe distortion. Eulerian, in the

other hand allows the material move through the mesh and it is suitable for solving problem in

fluid dynamics. The disadvantage of this scheme is that the surfaces and boundary conditions

are difficult to track. The mesh distortion however, is not a problem because the mesh never

changes. Therefore, the Arbitrary Lagrangian-Eulerian (ALE) formulation was developed to

combine the advantages of Lagrangian and Eulerian algorithms, while minimizing their

respective drawbacks as far as possible. Fig. 4. 3 depicts three different types of material

description; grid lines represent mesh and shaded area represents the material.

43

a) Lagrangian material description

Eulerian material description

c) ALE material description

Fig. 4. 3: 1-D example of Lagrangian, Eulerian, and ALE Mesh with material point motion [54].

44

4.4.1 Remeshing and Remapping Schemes in Abaqus/Explicit

FE simulation of FSSW process is very difficult to do without the use of adaptive feature

in Abaqus/Explicit. Adaptive mesh scheme enables a finite element model to maintain a high

quality mesh automatically even the model is subjected to severe deformations, by allowing the

mesh to move independently of the material. In Abaqus/Explicit, the feature uses a technique

called Arbitrary Lagrangian Euleraian (ALE), which combines pure Lagrangian and pure

Eulerian material descriptions. ALE formulations in Abaqus/Explicit consist of two processes,

i.e., remeshing and remapping (also known as an advection) processes.

In the remeshing process, a new mesh is created by sweeping iteratively over the

adaptive mesh domain and moving nodes to smooth the mesh at a specified frequency. During

each mesh sweep, nodes in the adaptive mesh domain are relocated based on the current

positions of neighboring nodes and elements. That means the boundary nodes remain on the

boundary while the interior nodes are moved in order to reduce element distortion.

According to Abaqus/Explicit [52], calculation of the new mesh is based on three basic

smoothing methods: volume smoothing, Laplacian smoothing, and equipotential smoothing as

illustrated in Fig. 4. 4.

a) Volume smoothing method relocates the node C by calculating a volume weighted

average of the element centers (C1, C2, C3, and C4) of the four surrounding elements.

Thus, it reduces element distortion by moving the node C away from element center C1,

toward element center C3.

45

b) Laplacian smoothing method relocates the node C by computing the average distance of

nodes M1, M2, M3, and M4 from node C. Thus, the positions of nodes M2 and M3 pull

the node C up and to the right.

c) Equipotential smoothing technique relocates a node by computing a higher order,

weighted average of the positions of the node’s eight nearest neighbor nodes in 2-D

problem (18 nearest neighbor nodes in 3-D case). In this case, the new position on node

C is based on the position of nodes A1, A2, A3, A4, M1, M2, M3, and M4.

Fig. 4. 4: Node relocation during mesh sweeping process.

After the distorted mesh is smoothed, solution variables are remapped from the old mesh

to the new mesh through a process called an advection process. By the definition, the advection

process is the process that allows to use a Lagrangian small step to take place at the end of which

the strain field is mapped back to the original mesh prior to taking the next step. In

46

Abaqus/Explicit code, the formulations used for advecting solution variables to the new mesh are

consistent, monotonic and accurate to the second order. Moreover, the methods also conserve

mass, momentum, and energy.

The ALE formulations in Abaqus/Explicit introduces advective terms into the momentum

balance and mass conservation equations to account for independent mesh and material motion.

These modified equations can be solved using two ways, i.e., fully coupled method, and operator

split method. In direct method, the nonsymmetrical system of equations are solved directly,

whereas the operator split method decouples the Lagrangian material motion from the additional

mesh motion. The operator split method is used in Abaqus/Explicit because of its computational

efficiency. Moreover, this method is suitable in an explicit setting because small time

increments limit the amount of motion within a single increment.

4.4.2 Governing equations

The advection method in Abaqus/Explicit must satisfy three conservation laws. The first

conservation law is conservation of mass, which states that the mass of any material body is

constant since there is no material flows through the boundaries of a material body. The

conservation equation can be written as

j

j

xt ∂

ν∂ρ−=

∂ρ∂ 4.17

where, ρ is the mass density, t is the time and ν is the material velocity.

47

The second conservation law is conservation of momentum, which states that the material time

derivative of the momentum is equal to the net force acting upon the object. The conservation

equation can be expressed as

ij

iji bxt

ρ+∂

σ∂=

∂ν∂

ρ 4.18

where ρ is the mass density, σji is the Cauchy stress, bi is the body force per unit volume.

The third conservation law is conservation of energy, which states that the rate of change

of the total energy in the body is equal to the work done by the external forces and rate of work

provided by heat flux and heat sources. The equation can be presented as

sxqD

tw

i

ijiji

int

ρ+∂∂

−σ=∂

∂ρ 4.19

where, wint is the internal energy per unit volume, Dji is the rate of deformation, qi is the heat flux

per unit area and ρs is the heat source per unit volume.

48

CHAPTER 5: FINITE ELEMENT SIMULATION OF FSSW PROCESS

5.1 Introduction

Understanding the real physics of the FSSW process depends to a great extent on the

success of the modeling efforts through numerical simulations. In this research, a commercial

finite element software code, Abaqus/Explicit version 6.5 is used to solve the thermo-mechanical

problem in FSSW process. One of the main reasons to use the Abaqus/Explicit software is that it

enables an explicit solution of the dynamic, coupled thermo-mechanical analysis. Moreover,

solving contact algorithm in the explicit formulation is less computationally expensive as

compared to solving an equivalent implicit problem. Not only less computational time, the

adaptive mesh feature enables the explicit solver to compute severe element deformation without

terminating the program.

In this work, two thin aluminum alloy 6061-T6 plates are modeled as two separate

workpieces. The bonding of the workpieces and retracting phase, however, have not been

modeled. The FE analysis has been conducted by prescribing plunge rate and angular velocity of

the pin tool, and by imposing appropriate boundary conditions.

The coupled thermomechanical analysis performed in Abaqus/Explicit uses 376.6 MB of

memory for solving the 517902 unknowns. The CPU time is 14 days and 12 hours on a 3.60

GHz Intel Pentium 4 processor for the simulation time of 1.505 seconds. The sample of input

file is attached in Appendix B-2.

49

5.2 Mesh and Geometry

The FE model is comprised of three main parts, i.e., workpiece, tool and backing anvil as

depicted in Fig. 5. 1. It only includes a limited part of the workpieces to optimize the resolution

close to the tool and minimize the computational expenses.

In the FE model, two workpieces are stacked on top of each other with a dimension of 25

mm by 25 mm by 1 mm. The mesh is dense at the center of the workpiece to reduce

hourglassing1 effect as depicted in Fig. 5. 2. The element size is approximately 0.1 mm in the

region surrounding the tool. A total of 132162 elements and 142816 nodes have been generated

in the model. The workpieces have been modeled using thermal coupled element C3D8RT.

This element type has 8-node tri-linear displacement and temperature degree of freedom and

reduced integration with hourglass control.

Since this work is not intended to study the mechanical responses of the tool and backing

anvil, they are modeled as analytical rigid surfaces with prescribed motion at a reference node.

The rigid body surfaces, however carry thermal response, which are assumed isothermal. The

tool has a shoulder and an unthreaded pin as shown in Fig. 5. 3. The diameters of the shoulder

and the pin are 10 mm and 3 mm, respectively. The backing anvil has a diameter of 15 mm. The

reference node is defined for each rigid body that has translation, rotation, and thermal degree of

freedoms.

1 Hourglassing is an element deformation that does not cause any strains at integration points.

50

Fig. 5. 1: Mesh representation of two layers of work piece with a pin and an anvil.

Fig. 5. 2: Mesh scheme for workpieces.

51

Fig. 5. 3: Tool geometry.

5.3 Welding Parameters

In FE simulation of FSSW process, there are two parameters that can be controlled,

which are rotational speed and plunge rate. The rotational speed and the plunge rate are

simulated by prescribing constants angular velocity and downward velocity, respectively at the

reference point.

5.4 Assumptions

To model the actual physics phenomena of the FSSW process is rather complicated.

Therefore, several simplifying assumptions have been made to the FE model.

52

a) Workpieces are assumed to be made of a deformable material (Al 6061-T6) that has

displacement and temperature degree of freedoms.

b) The workpieces are assumed to behave as elastic-plastic Johnson-Cook material model,

which is temperature, and strain rate dependent.

c) The workpieces and pin are assumed to experience frictional sliding contact described by

Coulomb’s friction law.

d) The tool and the backing anvil are considered rigid body that has translation, rotation and

thermal degree of freedoms.

e) The tool and the backing anvil are assumed isothermal.

f) The friction coefficient, µ is assumed to be a function of slip rate, contact pressure, and

surface temperature.

g) Initial temperatures for both workpieces, pin and anvil are assumed at 22 0C.

h) It is assumed that 100% of the dissipated energy caused by friction is transformed into

heat and 90 % of the heat goes to the workpiece.

i) The heat is distributed evenly at top and bottom workpieces interface.

j) 90 % of the energy due to plastic deformation process converted into heat.

53

5.5 Boundary Conditions

Boundary conditions that are imposed on the current FE model are described in the

following paragraphs. Fig. 5. 4 depicts a schematic diagram of the boundary conditions. The

edges of the top and the bottom workpieces are restrained in X direction. The tool can only have

translation and rotation in Y-direction. The backing anvil is fixed in all degree of freedoms to

avoid rigid body motion.

Heat convection coefficients, h on the top surface of the upper workpiece and the bottom

surface of lower workpiece are 30 W/m2-0C as used in Chao and Qi’s paper [31], with the

ambient temperature of 22 0C. In this research, a contact thermal gap conductance of 100,000

W/m2-0C [55] is introduced at the top and bottom workpieces interface to simulate the heat loss

through conduction between the two workpieces. It is noted that there is no data or theory to

predict precisely the heat loss through the bottom surface of the upper workpiece and the top

surface of the bottom workpiece.

54

Fig. 5. 4: Schematic diagram of boundary conditions.

5.6 Contact Friction

A friction model is one of the key input boundary conditions in finite element simulations

of FSSW process and it plays an important role in controlling the accuracy of necessary output

results predicted. Among the various friction models, the definition of which one is of higher

accuracy is still unknown and controversial. In the current FE model, friction behavior is

modeled using a default model in Abaqus/Explicit, which is Coulomb friction model, but the

Coulomb’s friction is defined as a function of slip rate, contact pressure, and surface

temperature.

In this model, the curve of friction coefficients varies with slip rate, contact pressure, and

surface temperature have been assumed based on experimental values of some metal presented in

[50], [51], and [40]. The friction coefficients dependence on slip rate, contact pressure, and

surface temperature used in this work are shown in Fig. 5. 5, Fig. 5. 6, and Fig. 5. 7, respectively.

55

Slip Rate (mm/sec.) versus Friction Coefficient

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 100 200 300 400 500 600

Slip Rate (mm/sec.)

Fric

tion

Coe

ffici

ent

Fig. 5. 5: Plot of friction coefficient versus slip rate (mm/sec.).

56

Friction Coefficient versus Pressure (Mpa)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 200 400 600 800 1000 1200 1400 1600

Pressure (MPa)

Fric

tion

Coe

ffici

ent

Fig. 5. 6: Plot of friction coefficient versus contact pressure (MPa).

57

Friction Coefficient versus Temperature

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 100 200 300 400 500 600 700

Temperature (deg. C)

Fric

tion

Coe

ffici

ent

Fig. 5. 7: Plot of friction coefficient versus surface temperature (0C).

5.7 Material Model and Properties

Aluminum alloy 6061-T6 was chosen as a material for workpieces. The main chemical

composition of Al 6061-T6 is shown in Appendix A-1. The temperature dependent material

properties for Al 6061-T6, taken from Chao and Qi [31] are listed in Table 5. 1. The thermal

conductivity property, however, was found incorrect in the paper. To simulate the workpieces

material behavior in the analysis, a temperature and strain rate dependent material law was used

using the elastic-plastic Johnson-Cook material model [56], which is given by

58

−

−−

εε

+ε+=σm

refmelt

ref

0

plnpl

y TTTT1lnC1])(BA[

&

& 5.1

where yσ is the yield stress, plε is the effective plastic strain, plε& is the effective plastic strain

rate, 0ε& is the normalizing strain rate (typically, 1.0 /s). A, B, C, n, Tmelt, and m are material

constants, which are listed in Table 5. 2. Tref is the ambient temperature, which is 22 0C in this

case. This material model is a type of Mises plasticity model with analytical forms of the

hardening law and rate dependence. Moreover, it is suitable for high-strain-rate deformation of

many materials. Fig. 5. 8 shows stress strain curves for Johnson-Cook hardening at various

temperatures.

Table 5. 1: Temperature dependent material properties for Aluminum alloy 6061-T6 [31].

Temperature 0C 37.8 93.3 148.9 204.4 260 315.6 371.1 426.7

Thermal Cond. W/m0C 162 177 184 192 201 207 217 223

Heat Capacity J/Kg0C 945 978 1004 1028 1052 1078 1104 1133

Density Kg/m3 2685 2685 2667 2657 2657 2630 2630 2602

Young’s Modulus GPa 68.54 66.19 63.09 59.16 53.99 47.48 40.34 31.72

Yield Strength MPa 274.4 264.6 248.2 218.6 159.7 66.2 34.5 17.9

Thermal Exp. 10-6/0C 23.45 24.61 25.67 26.60 27.56 28.53 29.57 30.71

Table 5. 2: Constants for Johnson-Cook material model [57].

Material Tmelt(oC) A (MPa) B (MPa) C n m

Al 6061-T6 582 293.4 121.26 0.002 0.23 1.34

59

Stress Strain Curves for Johnson-Cook Work Hardening

0

50

100

150

200

250

300

350

400

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Strain

Stre

ss (M

Pa) T=100 C

T=200 CT=300 CT=400 CT=500 C

Fig. 5. 8: Plot of stress strain curve for Johnson-Cook work hardening.

5.8 Adaptive Mesh

The simulation of FSSW process uses the advantage of adaptive meshing offered in

Abaqus/Explicit. Adaptive meshing is performed in Lagrangian domains, which is defined by

element sets. In this case, the whole workpieces mesh is considered the domain of the adaptive

mesh. The adaptive mesh domain has sliding boundary regions at the top and the bottom of both

workpieces. In sliding boundary regions, the mesh is constrained to move with the material in

60

the direction normal to the boundary region, but it is fully unconstrained in the directions

tangential to the boundary region.

For the model presented in this work, the remeshing is made after 10 increments and each

remeshing algorithm includes 3 mesh sweeps for optimizing the node positions. The calculation

of the new mesh is based on volume smoothing method.

61

CHAPTER 6: DISCUSSION OF RESULTS

FE simulation results discussed in this chapter consists of frictional dissipation history,

plastic dissipation history, thermal response, plastic strain and material flow. The geometry and

the mesh used in the FE models were kept the same throughout this work.

6.1 Overview of Frictional Dissipation Energy during FSSW Process

Friction between the tool and the workpiece occurs at three tool surfaces, i.e., tip of the

pin, vertical side of the pin and tool shoulder. Fig. 6. 1 (a-c) shows three phases of friction

between the tool and the workpiece. The figure on the left illustrates the temperature profile, and

the plot on the right shows the frictional dissipation energy history.

At the initial stage, when the tool slightly comes in contact with the upper plate while

spinning, it is seen that the high temperature concentrates around the tip of the tool and heat

generation starts to develop (Fig. 6. 1 (a)). The temperature profile is also distributed uniformly

due to the heat conduction from the first plate to the second plate.

While spinning, the tool also moves downward and the pressure exerted from the tool

causes the first plate to deform slightly, as shown in Fig. 6. 1(b). This leads to less heat

conduction from the top plate to the bottom plate, which results in higher temperature profile in

the top plate. At this stage, the heat generation increases as the welding process advances.

62

As the tool keeps pressing downward, its shoulder contacts the deformed top plate and

more heat is generated through the friction between the shoulder and the workpiece (Fig. 6.

1(c)). At this phase, more heat conduction occurs between the plates since the two plates come

in contact again and more uniform temperature profile can be seen. Since the tool is defined as

an isothermal surface, the temperature profile on the tool is constant through out the analysis.

a) Phase 1, t=0.245 s.

b) Phase 2, t=0.945 s.

63

c) Phase 3, t=1.365 s.

Fig. 6. 1: Three stages of friction between the tool and the workpiece. Left: Temperature profile, Right: Friction dissipation energy history.

6.2 Energy Dissipation during FSSW Process

The FSSW technique relies on the heat generated during the process to join the

workpieces together. There are three possible heat sources generated during FSSW process, i.e.,

friction work at the tool and top workpiece interface, friction work at the interface of top and

bottom workpiece, and plastic deformation of the workpiece material. In this work, the friction

and plastic works have been investigated using frictional energy dissipation and plastic energy

dissipation histories, respectively. The angular velocity and plunge rate were 3000 rpm and 1

mm/s, respectively. Table 6. 1 shows the summary of energy dissipation during FSSW process.

Su et al. [44] have conducted an experiment on energy generation of 6.3 mm Al 6061-T6.

In the experiment, rotational speed and plunge rate were set at 3000 rpm and 2.5 mm/s,

respectively. The average energy generated by 10 mm diameter tool with shoulder at five

different plunge depths was 1.964 kJ. Based on the FE results shown in Table 6. 1, the total

64

energy dissipation at plunge depth of 1.505 mm is 1.519 kJ. The discrepancy between the two

results is due to the different thickness of the workpiece and plunge rate.

Table 6. 1: Summary of energy dissipation during FSSW process.

Energy Dissipation (kJ)

Percentage (%)

Friction at tool and workpiece interface 1.471 96.84 %

Frictional at top and bottom workpieces interface

0.000375 0.02 %

Plastic deformation 0.0478 3.14 %

Total Energy Dissipation 1.519 100 %

6.2.1 Heat Generation due to Friction Work at the Tool and Workpiece Interface

The simulation results show that the friction work at the tool and top workpiece interface

contributes the most heat to the welding process. The frictional energy contributes 96.84 % of

the total energy as shown in Fig. 6. 2. This high percentage of energy generation is expected

due to the presence of high differential velocities (slip rate) on the workpiece surface that caused

by high rotational speed and pressure from the tool have created. The peak slip rate as shown in

Fig. 6. 3 is 2284 mm/s.

Fig. 6. 2 also shows that the frictional dissipation energy increases drastically after the

time reaches 0.9450 seconds. The increase of frictional energy is due to the additional friction

from the interface of the shoulder of the tool and the surface of the top workpiece.

65

Fig. 6. 2: Frictional dissipation energy history at the tool and workpiece interface.

Fig. 6. 3: Slip rate distribution on upper surface of the top workpiece.

66

6.2.2 Heat Generation due to Friction Work at the Top and Bottom Workpieces Interface

Based on the results in Table 6. 1, about 0.02 % of the total energy is due to frictional

force at the interface between the top and bottom workpieces. Even though the amount of

energy generated at this interface is almost negligible, the interface is important in FSSW

because the actual welding occurs here. Consequently, it is relevant to trace how much energy is

used at the interface and how this is affected by the process parameters.

Fig. 6. 4 shows frictional dissipation energy history at the top and bottom workpieces

interface is about 0.000375 kJ (375 mJ) at 1.505 seconds. The friction work at the interface

between the top and bottom workpieces gives the least contribution to the total heat generation

because the interface has very small relative motion due to friction as shown in Fig. 6. 5 and Fig.

6. 6. The maximum slip rates are 3.375 mm/s and 0.3985 mm/s on lower surface of the top

workpiece (Fig. 6. 5) and upper surface of the bottom workpiece (Fig. 6. 6), respectively.

67

Fig. 6. 4: Frictional dissipation energy at the top and bottom workpiece interface.

Fig. 6. 5: Slip rate distribution on lower surface of the top workpiece.

68

Fig. 6. 6: Slip rate distribution on upper surface of the bottom workpiece.

6.2.3 Heat Generation due to Internal Friction/Plastic Work

As shown in Fig. 6. 7, plastic dissipation energy in the material is 47.8 kJoule, which is

about 3.14 % of the total energy dissipated. This energy is due to the presence of internal

friction forces, which tends to resist the motion of the material. As can be seen from the figure,

the plastic dissipation energy increases drastically after 1.3 seconds. This is because, in addition

to the plastic straining process due to the pin penetration, a large plastic deformation occurs

when the shoulder of the tool touches the surface of the workpiece at the end of the cycle time.

69

Fig. 6. 7: Plastic dissipation energy history.

6.3 Study of Friction Coefficient Dependence

The dependence of friction coefficient on surface temperature, slip rate, and contact

pressure are investigated. In this work, the same FE models were run with three different

friction coefficient dependencies by trial and error until the peak temperatures were obtained.

Rotational speed and plunge rate of the welding tool are set to be 3000 rpm and 1 mm/second,

respectively.

The frictional and plastic dissipation energy history curves are compared after 1.435

second as shown in Fig. 6. 8. The maximum frictional dissipation energy are about 1.27 kJ, 1.20

kJ, and 1.15 kJ for friction coefficient dependence of contact pressure, slip rate and temperature,

70

respectively, which are within 8.4 % difference. Appendix B-2 shows the temperature profiles

for different friction coefficient dependencies at various times.

71

a) Contact pressure dependence b) Slip rate dependence c) Surface temperature dependence

Fig. 6. 8: Frictional (dotted line) and plastic (solid line) dissipation energies history for various friction coefficient dependences.

72

6.4 Effect of Welding Tool Plunge Rate

Parametric studies have been conducted to determine the effect of tool penetrating speed

on frictional and plastic dissipation energies. Three different tool speeds; 1 mm/s, 5 mm/s, and

10 mm/s, are modeled with contact pressure friction coefficient dependent. The welding tool

rotational speed was set at 3000 rpm. The targeted welding tool displacement was 1.505 mm.

Fig. 6. 9 shows frictional and plastic dissipation energy history for three different

welding speeds. Based on the curves, frictional and plastic dissipation energy increases as the

tool velocity decreases. The frictional dissipation energy of 5 mm/s plunge rate reduces to about

29 % of the 1 mm/second frictional dissipation energy. The same decreasing trend is observed

with 10 mm/s plunge rate (14 % decrement). This is because the slower the tool velocity, the

more time it spends to spin on the workpiece thus more energy is produced. The plastic

dissipation energy also follows the same trend of frictional dissipation energy curves. In short,

the slower the penetrate speed, the higher the plastic dissipation energy. Table 6. 2 summarizes

the frictional and plastic dissipation energy for different tool plunge rates.

73

Fig. 6. 9: Energy dissipation for different tool rotational speed.

Tool Velocity (mm/s)

Frictional Dissipation Energy

Plastic Dissipation Energy

1.0

5.0

10.0

74

Table 6. 2: Summary of friction and plastic dissipation energies for different tool’s plunge rate.

Plunge Rate

(mm/sec.)

Frictional Dissipation

Energy (kJ)

Percentage

Reduction (%)

Plastic Dissipation

Energy (kJ)

Percentage

Reduction (%)

1.0 1.471 100 0.0478 100

5.0 0.425 28.9 0.0237 49.6

10.0 0.207 14.1 0.0193 40.4

6.5 Effect of Welding Tool’s Rotational Speed

A parametric study has also been conducted for various rotational speeds. Three

different welding tool rotational speeds, which are 3000 rpm, 2500 rpm, and 2000 rpm, have

been run on the FE models in order to study the effect of welding tool’s rotational speed on heat

generation. Plunge rate was set to be 1 mm/s. The model used friction coefficient dependence

of contact pressure in this case.

Fig. 6. 10(a-c) show frictional dissipation energy histories for 3000 rpm, 2500 rpm, and

2000 rpm welding tool rotational speed, respectively. Based on the results, the higher the

rotational speed is, the higher the dissipation energy. The frictional dissipation energy is

reduced by about 8.4 % when the rotational speed is reduced from 3000 rpm to 2500 rpm and

reduced by about 19.2 % when it is reduced from 3000 rpm to 2000 rpm. This is because higher

rotational speed will result in higher relative velocity of the material, consequently higher energy

will be produced. Table 6. 3 summarizes frictional dissipation energy for different tool’s

rotational speeds.

75

a) 3000 rpm b) 2500 rpm c) 2000 rpm

Fig. 6. 10: Frictional dissipation energy for various rotational speeds.

76

Table 6. 3: Summary of frictional dissipation energy for different tool’s rotational speeds.

Tool’s Rotational Speed

(rpm)

Frictional Dissipation Energy

(kJ)

Percentage Reduction

%

3000 1.471 100

2500 1.347 91.6

2000 1.188 80.8

6.6 Thermal Response

Thermal response was studied using friction coefficient contact pressure dependent. Fig.

6. 11(a-g) shows the temperature fields at various times. Based on the results, the maximum

nodal temperature is 546.40C after 1.505 seconds when the welding tool penetrates 1.505 mm

into the workpieces. The peak temperature is consistent with the theory reported in Su, et al

[44], which suggested that the peak temperature is between 0.93Ts and 0.97Ts (Ts is the solidus

temperature of Al 6061-T6).

77

a) Time = 0.0 sec., nodal temperature = 22.000C.

b) Time = 0.175 sec., nodal temperature = 55.520C.

c) Time = 0.350 sec., nodal temperature = 99.540C.

78

d) Time = 0.525 sec., nodal temperature = 139.90C.

e) Time = 0.700 sec., nodal temperature = 183.10C.

f) Time = 0.875 sec., nodal temperature = 195.00C.

79

g) Time = 1.050 sec., nodal temperature = 264.90C.

h) Time = 1.225 sec., nodal temperature = 323.10C.

i) Time = 1.400 sec., nodal temperature = 512.80C

80

j) Time = 1.505 sec., nodal temperature = 546.40C

Fig. 6. 11: Temperature contours at various times.

Fig. 6. 12 shows the temperature distribution at the surfaces of both workpieces,

measured perpendicular from the center of the workpiece to the edge. At the tip of the tool, the

temperatures of both plates are the same, which is about 485 0C. The peak temperature of the

top surface of the upper plate is almost constant at the interface of tool’s shoulder and

workpiece, which is within the radius between 1.5 mm and 5 mm away from the center of the

workpiece. Then, the temperature starts to decease to about 150 0C at the edge of the workpiece.

At the top surface of the bottom plate, lower peak temperature is observed due to

conduction heat transfer from the upper plate. Beginning from 6 mm away from the center of

the workpiece towards to the edge, the temperature of the top surface of the upper plate and the

temperature of the top surface of the bottom plate become uniform.

81

Fig. 6. 12: Plot of temperatures versus distance away from the center of the tool.

Fig. 6. 13 shows the comparison of temperature history between the FE simulation results and

the experimental results, which reported by Su et al. [44]. Both analyses were performed on Al

6061-T6 material using 3000 rpm and 2.5 mm/s of rotational speed and plunge rate, respectively.

The tool geometry and the thickness of the workpiece, however, were different. Based on the

results, the FE simulation shows the maximum tool temperature is 514.3 0C and the experimental

shows peak temperature at the tip of the tool is about 542 0C and. From this, it can be concluded

that both results are fairly in agreement with each other, which is about 5.1 % different.

82

a) FE simulation result b) Experimental result [44]

Fig. 6. 13: Experimental versus FE simulation results of temperature history at the tip of welding tool.

83

6.7 Plastic Strain

Fig. 6. 14 shows an equivalent plastic strain as a function of distance from the center of

the tool. The equivalent plastic strain at the top surface of the upper plate shows an increasing

trend within 1.5 mm distance. This peak equivalent plastic strain region is the area under the

pin, where high pressure and torque generate tremendous heat and plasticize the materials.

Between the distance of 1.5 mm and 5 mm from the center of the workpiece, the equivalent

plastic strain drops drastically. This region is the area under the tool’s shoulder. The equivalent

plastic strain becomes zero at the distance of 5 mm from the center of the workpiece towards the

edge. The equivalent plastic strain at the top surface of the bottom plate is relatively small in the

region under the pin and becomes zero towards the edge.

Equivalent Plastic Strain versus Distance from the Tool (mm)

-25

0

25

50

75

100

125

150

175

200

225

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Distance from the Tool (mm)

Equ

ival

ent P

last

ic S

trai

n PEEQ-TOPPEEQ-BOTT

Fig. 6. 14: Plot of equivalent plastic strains versus distance away from the center of the tool.

84

6.8 Material Flow

Material flow during FSSW process has been investigated. Due to disk space constraint

that requires a lot of spaces to store large output database (.odb) file, the simulation time has

been cut short to 0.8 seconds. The rotational speed and plunge rate for this study are 3000 rpm

and 1 mm/second, respectively.

Three tracer particles, which are set of nodes in the adaptive mesh domain, are defined in

the FE model as shown in Fig. 6. 15. Tracer particle “A” is set to be underneath the pin, tracer

particle “B” is located right below the shoulder and tracer particle “C" is located slightly away

from the welding tool.

Based on Fig. 6. 16, particle “A” moves in all directions. Particles “B” and “C”,

however, move quite significantly in Z direction, and very small displacement in X and Y

direction. Since a sliding boundary region has been defined on the top surface of the workpiece,

the material is constrained to move with the mesh in the direction normal to the boundary region.

The material, however, is completely unconstrained in the directions tangential to the boundary

region.

Fig. 6. 15: Locations of particle tracking.

85

a) Tracer particle “A” b) Tracer particle “B” c) Tracer particle “C”

Fig. 6. 16: Plots of particle displacements history.

86

CHAPTER 7: DISCUSSION OF FRICTION PHENOMENA AND HEAT

GENERATION DURING FSSW PROCESS

A description of friction phenomena in FSSW is addressed in this chapter, which

includes several aspects such as the friction mechanism, friction coefficient and friction heating.

7.1 Introduction

In general, two types of friction occur during FSSW process, namely contact friction and

internal friction. The former is considered more dominant in terms of energy consumption, since

the interface experiences large pressures of contact and sliding velocity from the tool motion.

Internal friction is less dominant in terms of energy consumption as shown in the simulation

results. Contact friction in FSSW takes place at the tool and the workpiece interface and the

interface of between the two plates.

7.2 Friction at Welding the Tool and Workpiece Interface

The friction between the welding tool and the workpiece is very important during FSSW

process as it contributes most of the heat during the process. In FSSW, the friction between

rotating tool and deformable workpiece can be divided into three stages as depicted in Fig. 7. 1,

i.e., first stage, when the tip of the pin and workpiece come in contact; second phase, when the

87

pin penetrates into the workpiece; third phase, when the shoulder touches and spins on the

workpiece.

a) Phase 1 b) Phase 2 c) Phase 3

Fig. 7. 1: Schematic representation of friction between the tool and the workpiece.

Friction in FSSW process begins when the tool with high rotational speed plunges into

the workpiece. The load from the tool produces heat and contact pressure at the interface of the

tool and the workpiece, which in turn produces adhesive bonding between the contacting

surfaces. These adhesive bonds drag the surface of the workpiece, but relative sliding occurs at

the interface due to velocity differential. Fig. 7. 2 shows the direction of the friction force (Ff),

which is opposite to the direction of relative velocity (∆V).

88

Fig. 7. 2: Schematic representation relative velocity of the material and the tool (FN is the normal force, Vmat is the material velocity, Vtool is the tool velocity).

As the tool moves further down, the contact friction between the vertical pin surface and

the workpiece takes place. At this stage, the material around the pin becomes soft and the

bonding between material grains becomes loose due to heat. Consequently, the material moves

in a circular direction around the tool. As the material underneath the pin presses down, the

material around the pin moves up to the surface. This phase generates most of the energy

because the contact and the internal friction occur during the full cycle time.

Sliding friction takes place when the tool’s shoulder contacts the workpiece. Similar to

the friction between the tool tip and the workpiece, asperities at this interface deform because of

the pressure distribution from the shoulder. Although the shoulder has greatest radius, and thus

greatest velocity, the tendency to generate more heat is constrained by the short period of sliding

time. Therefore, the heat generated due to friction is relatively small since the shoulder only

comes in contact with the workpiece at the end of the welding cycle.

89

The temperature that develops due to friction works softens the material in proximity and

reduces the strength of the material. Consequently, the friction force between the tool and the

workpiece decreases over the time.

7.3 Friction at Top Workpiece and Bottom Workpiece Interface

The friction at the interface of the top and the bottom workpieces is insignificant in terms

of heat generation, as compared to the friction at the tool and workpiece interface. This was

shown by the FE simulation results. Since both workpieces are clamped together, the presence

of tangential reaction force at this interface is relatively small. Sliding friction may occur at this

interface due to relative motion between the top and bottom surfaces of the joint. The interface,

however, is very important since the bonding of the materials occurs at this interface. When the

tool shoulder contacts the workpiece and penetrates slightly into the workpiece, a strong

compressive forging pressure is generated. As a result, a solid state bond is formed at the

interface between the two workpieces.

7.4 Internal Friction

Physically, when a solid material is strained, energy, associated with the work done by

the straining process is produced. This energy, in the form of heat is due to the presence of

internal friction forces, which tend to resist the motion of the material.

90

When the tool rotates under pressure on the workpiece, the bonding between the

workpiece material breaks and deforms plastically. Microscopically, this plastic deformation is a

consequence of dislocations. According to the dislocation theory, atoms in a grain boundary slip

when there is crystallographic defect that produces weak points in the bonds between atoms

within crystal structure. The forces that oppose the grains to slip are called internal friction.

Therefore, the work done by the internal friction dissipates energy in the form of heat. In

general, the heat generation due to plastic deformation in FSSW is relatively small as compared

to heat generation from the friction work between the tool and the workpiece. Fig. 7. 3 depicts

the concept of dislocation.

Fig. 7. 3: Schematic showing dislocation of the grains.

The internal friction in a solid can be measured using two methods, i.e., strain-stress

curve and decay of vibration wave. A quantity, known as damping capacity, which is a ratio of

91

the energy lost per cycle due to friction to the total strain energy of the material can be computed

from the strain-stress curve. In the second method, the energy loss can be measured by

computing a logarithmic decrement, δ of vibration decay curve.

7.5 Friction Coefficient between the Tool and the Workpiece

Because of its simplicity, the Coulomb’s friction model is used to described sliding

friction between asperities surfaces. As shown in the FE simulation analysis, friction during

FSSW varies with contact pressure, slip rate and surface temperature. Contact pressure can

influence the near surface crystallographic orientation, which affects the mechanical properties

(like shear strength). This in turn promotes easier shear. When the material of the workpiece is

softened by the heat, the relative velocity (slip rate) increases and consequently, alters the shear

strength of the material. The shear strength of the workpiece depends on the temperature.

Therefore, the friction coefficient is expected to decrease as a function of contact pressure, slip

rate, and surface temperature.

7.6 Heat Generation in FSSW

Heat generation and rising surface temperatures are generally associated with friction that

converts kinetic energy into thermal energy. The energy generated is the result of the tangential

reaction force acting over a distance. In general, the energy from friction work is expressed as

92

∫=L

0Nk dx)x(FE µ 7.1

where, E is the energy, µk is the kinetic friction, FN is the friction force, and x is the distance of

an object moved. According to Blau [40], about 90-95% of the energy due to friction is

transformed into heat and about 5-10 % of the remaining energy is used to deform the material

and some is stored as defects in the contacting material.

In FSSW process, the mechanical interaction, which is due to velocity difference between

the rotating tool and the stationary workpiece, produces heat by friction work. Friction work at

the tool and the workpiece interface can be grouped into three categories based on tool geometry

as shown in Fig. 7. 4. Each contact surface experiences sliding friction during FSSW process.

The total heat produced due to friction work at the tool and the workpiece interface is the

summation of the heat generated at the contact interface of the shoulder, the tip of the pin as well

as the side of the pin. For simplicity in the formulations, the shoulder and the tip of the pin are

assumed flat.

First, let us consider heat generation at the shoulder. The heat generation can be

computed from torque formula. The total torque at the shoulder interface can be expressed as

∫=∫=oR

iRcontact

oR

iRs dr)r2)(r(dMM πτ

7.2

where, Ms is the torque at the shoulder interface, contactτ is the contact shear stress, r is the

distance from the tool axis, and Ro and Ri is the radii of the shoulder and the pin, respectively.

Solving equation 7.2, yields,

93

)RR(32M 3

i3ocontacts −= πτ 7.3

The power exerted to the workpiece is,

ωMP = 7.4

where, n2π=ω , n is the angular velocity of the tool (radians per second).

Substituting equation 7.3 and n2π=ω into equation 7.4, the heat rate at the shoulder, 1P can be

written as

)RR(n34P 3

i3ocontact

2s −= τπ 7.5

The heat generated by the friction work at the tip of the pin and the workpiece interface, pP can

be obtained by similar approach.

3icontact

2p nR

34P τπ= 7.6

The total torque at the vertical pin surface, Mv can be expressed as

∫=L

0iicontactv dy)R2)(R(M πτ

7.7

where L is the height of the pin. Solving equation 7.7, yields

2icontactv LR2M πτ=

7.8

94

Substituting equation 7.8 into equation 7.4 and n2π=ω , the heat rate at vertical pin surface, vP

is obtained as

2icontact

2v nLR4P τπ= 7.9

Therefore, total heat generation from the tool is vpsT PPPP ++= .

2icontact

23icontact

23i

3ocontact

2 nLR4nR34)RR(n

34P τπτπτπ ++−= 7.10

Simplifying equation 7.10, we obtain

)LR3R(n34P 2

i3ocontact

2 += τπ 7.11

Since, µστ =contact , equation 7.11 can be expressed as,

)LR3R(n34P 2

i3o

2 += µσπ 7.12

where, σ is the contact pressure and µ is the friction coefficient.

In FSSW process, the heat rate equation due to plastic deformation can be expresses as

plplP ετ &= 7.13

where, plP is the heat rate due to plastic deformation, τ is the shear stress, and plε& is the plastic

straining rate.

95

Fig. 7. 4: Schematic representation of tool interfaces that generate heat.

96

CHAPTER 8: CONCLUSIONS AND FUTURE WORK

8.1 Conclusions

A fully coupled thermomechanical 3-D FE modeling of FSSW process has been

developed using an Abaqus/Explicit code. The following conclusions can be drawn from this

work.

a) The trend of friction coefficients as a function of contact pressure, slip rate, and surface

temperature has been predicted. The simulation results show that the frictional

dissipation energies for the three friction coefficient dependencies are very close, which

falls within 8.4 % different from each other.

b) The peak temperature obtained from the simulation, which is equivalent to 0.95Ts (Ts is

solidous temperature of Al 6061-T6) is consistent with the theory as reported by Su, et al.

[1].

c) The affect of plunge rate on frictional dissipation energy is also noted. The results

indicate that the lower the plunge rate, the higher the energy. The frictional dissipation

energy for a plunge rate of 5 mm/s reduces to about 29 % of the 1 mm/s frictional

dissipation energy. The same decreasing trend is observed with 10 mm/s plunge rate (14

% decrement).

d) The simulation results also show a significant affect of welding tool’s rotational speed on

frictional dissipation energy. In general, lower rotational speed yields lower frictional

97

dissipation energy. The frictional dissipation energy is reduced by about 8.4 % when the

rotational speed is reduced from 3000 rpm to 2500 rpm and reduced by about 19.2 %

when it is reduced from 3000 rpm to 2000 rpm.

e) Friction work at the interface of the tool and the workpiece generates the most energy,

which is about 96.84 %, for the FSSW process. The rest of the energies come from the

friction work between the plates (0.02 %) and the plastic deformation (3.14 %).

f) The temperature underneath the tool is almost constant at 514.3 0C and gradually

decreases toward the edge of the workpiece.

g) The plastic strain is at the highest point underneath the tool surface and zero at the

interface with no contact with the tool.

h) The material particles can be traced in the adaptive mesh domain. In general, the particle

underneath the pin move more vigorously as compared the particle at the interface with

no contact with the tool.

8.2 Contributions of the Dissertation to the FSSW Technology

A description of friction phenomena have been addressed in this dissertation. The

friction in FSSW can be divided into two categories, i.e., contact pressure and material internal

friction. The contact friction occurs at two interfaces, which are the interface of the tool and the

workpiece and the top and the bottom workpieces interface. The former experiences the most

friction, which is indicated by the most heat generation during the welding process.

98

According to the FE simulation results, the heat generation due to frictional energy is

about 96.84 % of the total energy produced. Based on the parametric studies on rotational

speeds and plunge rates, the results also show that higher rotational speed and slower plunge rate

yield higher generated heat. Therefore, by choosing the right rotational speed and plunge rate,

we can obtain a better weld quality.

A literature survey has been conducted on friction coefficient used to assess friction

between the tool and the workpiece. The friction coefficients, which depend on contact pressure,

temperature and slip rate have been assumed and applied to the same FE model. The FE results

show that the temperature history for friction coefficient temperature dependent is about 5.1 %

different compared to the experimental study done by Gerlich et al. [1]. The dissipation energy

history curves for different friction coefficient (slip rate, contact pressure and temperature

dependant) produce almost the same results. Therefore, the assumed friction coefficient curves

can be used in the FE simulation of FSSW.

8.3 Future Work

Although the contact friction between the workpieces interface is insignificant in terms of

heat generation, the interface is very important because the physical bonding between the two

workpieces occurs at this interface. It is believed that there is an inter-diffusion of material

across the interface at atomic level, which is due to heat and pressure distributions. Therefore,

the research area in FE simulation of FSSW can be extended in a subject of material flow at the

bonding interface.

99

A FE code, namely LS DYNA is capable of simulating the material flow. The

methodology, which uses LS-DYNA has been developed by Zhao [25] in her Ph.D dissertation.

In her work, a “moving mesh” scheme has been deployed with ALE formulations in order to

simulate material flow during FSW process.

100

NOMENCLATURES

TA Total contact area

A, B, C, n Johnson Cook material constants

jiD Rate of deformation

E Energy

F Applied force

fF Friction force

NF Normal force

H Material hardness

L Height of the pin

M Moment

sM Moment at the tool’s shoulder

vM Moment at the vertical surface of the pin

pM Moment at the pin

P Power

101

pP Power generated at the pin

plP Heat generation (power) due to plastic work

sP Power generated at the shoulder

vP Power generated at the vertical surface of the pin

Q Heat generation

oR Radius of the shoulder

iR Radius of the pin

T Temperature

meltT Material melting temperature

refT Reference temperature

Vmat Velocity of material

Vtool Velocity of tool

ia Asperity contact area

ib body force per unit volume

c damping coefficient

102

cp Material specific heat

if Normal force exerted on asperity

h Convection heat transfer

k stiffness coefficient

kx, ky, kz heat conductivity in x, y, and z directions

n Angular velocity, rad./s

r Distance from the tool axis

iq Heat flux per unit volume

u&& Nodal acceleration

u& Nodal velocity

u displacement

v Velocity

intw Internal energy per unit volume

C Viscous damping matrix

C(t) Time dependent capacitance matrix

F External force vector

103

fF Friction force vector

K Stiffness matrix

K(t) Time dependent conductivity matrix

M Mass matrix

M1 Second order friction coefficient tensor

Q(t) Time dependent heat vector

T& Derivative of temperature

T Nodal temperature vector

ej Arbitrary unit vector basis

ki Orthogonal unit vector basis

u&& Nodal acceleration vector

u& Nodal velocity vector

u displacement vector

v Slip velocity unit vector

σ Contact pressure

ijσ Cauchy stress

104

yσ Yield stress

plε Effective plastic strain

plε& Plastic strain rate

0ε& Normalizing strain rate

µ Friction coefficient

sµ Static friction coefficient

kµ Kinetic friction coefficient

ρ Mass density

τ Shear stress

yτ Shear strength

contactτ Contact shear stress

ω Angular velocity, rpm

∆t Time increment

∆V Relative velocity

105

ABBREVIATIONS

ALE Arbitrary Lagrangian Eulerian

CFD Computational Fluid Dynamics

DOF Degree of freedom

FE Finite element

FSW Friction stir welding

FSSW Friction stir spot welding

HAZ Heat affected zone

ORNL Oak Ridge National Laboratory

SPH Smoothed Particle Hydrodynamics

TMAZ Thermo-mechanically affected zone

2-D Two dimensional

3-D Three dimensional

106

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113

APPENDIX A

A-1 Chemical Composition of Al 6061.

Aluminum Alloy 6061

Weight % Al Si Fe Cu Mn Mg Cr Zn Ti Others

each

Other

s total

6061 Bal 0.40-

0.80

0.70

max

0.15-

0.40

0.15 0.80-

1.20

0.04-

0.35

0.25

max

0.15

max

0.05 0.15

max

Fig. A - 1: Chemical composition of Aluminum Alloy 6061-T6.

114

APPENDIX B

B-1 Abaqus’s Input File

This appendix lists the Abaqus/Explicit input file used throughout this dissertation. Some lines

such as list of nodes and elements have been taken out due to space constraint.

*Heading

*Part, name=anvil

*End Part

*Part, name=pin

*End Part

*Part, name=workpiece-bot

*End Part

*Part, name=workpiece-top

*End Part

**

115

** ASSEMBLY

**

*Assembly, name=Assembly

**

*Instance, name=workpiece-top-1, part=workpiece-top

0., 0., -12.5

*Node

1, 0., 0., 20.

.

.

.

64736, -6.593723, 0.8333333, 18.38018

*Element, type=C3D8RT

1, 19737, 19739, 20142, 20077, 517, 519, 922, 857

.

.

116

.

55098, 64610, 17902, 17901, 64736, 18990, 144, 145, 19116

*Nset, nset=wp-top, generate

1, 64736, 1

*Elset, elset=wp-top, generate

1, 55098, 1

** Region: (wp1:Picked), (Controls:EC-1)

*Elset, elset=_I1, internal, generate

1, 55098, 1

** Section: wp1

*Solid Section, elset=_I1, controls=EC-1, material=Material-wp

1.,

*End Instance

**

*Instance, name=workpiece-bot-1, part=workpiece-bot

0., -1., -12.5

117

*Node

1, 0., 0., 20.

.

.

.

64736, -6.593723, 0.8333333, 18.38018

*Element, type=C3D8RT

1, 19737, 19739, 20142, 20077, 517, 519, 922, 857

.

.

.

55098, 64610, 17902, 17901, 64736, 18990, 144, 145, 19116

*Nset, nset=wp-bot, generate

1, 64736, 1

*Elset, elset=wp-bot, generate

1, 55098, 1

118

** Region: (wp2:Picked), (Controls:EC-1)

*Elset, elset=_I1, internal, generate

1, 55098, 1

** Section: wp2

*Solid Section, elset=_I1, controls=EC-1, material=Material-wp

1.,

*End Instance

**

*Instance, name=pin-1, part=pin

0., 1., 0.

** Region: (capacitance:Picked)

*Element, type=HEATCAP, elset=_I1_HEATCAP_

1, 1

*Heat Cap, elset=_I1_HEATCAP_

1000.,

*Node

119

1, 0., 0., 0.

*Nset, nset=pin-1-RefPt_, internal

1,

*Surface, type=REVOLUTION, name=sur-pin

START, 1.5, 0.42

CIRCL, 0., 0.00165564502766502, 0., 2.9

LINE, 0., 5.

LINE, 5., 5.

LINE, 5., 2.

CIRCL, 4.5, 1.5, 4.5, 2.

LINE, 2.1, 1.5

CIRCL, 1.5, 0.9, 2.1, 0.9

LINE, 1.5, 0.42

*Rigid Body, ref node=pin-1-RefPt_, analytical surface=sur-pin, isothermal=YES

*End Instance

**

120

*Instance, name=anvil-1, part=anvil

0., -1., 0.

** Region: (capacitance:Picked)

*Element, type=HEATCAP, elset=_I1_HEATCAP_

1, 1

*Heat Cap, elset=_I1_HEATCAP_

1000.,

*Node

1, 0., 0., 0.

*Nset, nset=anvil-1-RefPt_, internal

1,

*Surface, type=REVOLUTION, name=sur-anvil

START, 0., 0.

LINE, 6.75, 0.

CIRCL, 7.5, -0.75, 6.75, -0.75

LINE, 7.5, -1.

121

*Rigid Body, ref node=anvil-1-RefPt_, analytical surface=sur-anvil, isothermal=YES

*End Instance

*Nset, nset=anvil-ref, instance=anvil-1

1,

*Nset, nset=massscaling, instance=workpiece-top-1, generate

1, 64736, 1

*Nset, nset=massscaling, instance=workpiece-bot-1, generate

1, 64736, 1

*Elset, elset=massscaling, instance=workpiece-top-1, generate

1, 55098, 1

*Elset, elset=massscaling, instance=workpiece-bot-1, generate

1, 55098, 1

*Nset, nset=pin-ref, instance=pin-1

1,

*Nset, nset=edge-bot, instance=workpiece-bot-1

3, 4, 5, 6, 7, 8, 9, 10, 249, 250, 251, 252, 253, 254, 255, 256

122

.

.

.

19724, 19725, 19726, 19727, 19728, 19729, 19730, 19731, 19732, 19733, 19734, 19735, 19736

*Elset, elset=edge-bot, instance=workpiece-bot-1

50838, 50839, 50840, 50841, 50842, 50843, 50844, 50845, 50846, 50847, 50848, 50849, 50850

.

.

.

55011, 55012, 55013, 55014, 55015, 55016, 55017, 55018, 55019, 55020, 55021, 55022, 55023

*Nset, nset=edge-top, instance=workpiece-top-1

3, 4, 5, 6, 7, 8, 9, 10, 249, 250, 251, 252, 253, 254, 255, 256

.

.

.

19724, 19725, 19726, 19727, 19728, 19729, 19730, 19731, 19732, 19733, 19734, 19735, 19736

123

*Elset, elset=edge-top, instance=workpiece-top-1

50838, 50839, 50840, 50841, 50842, 50843, 50844, 50845, 50846, 50847, 50848, 50849, 50850

.

.

.

55011, 55012, 55013, 55014, 55015, 55016, 55017, 55018, 55019, 55020, 55021, 55022, 55023

*Elset, elset=_wpwp-bottom_S1, internal, instance=workpiece-bot-1, generate

42296, 50754, 1

*Elset, elset=_wpwp-bottom_S2, internal, instance=workpiece-bot-1, generate

54375, 55098, 1

*Surface, type=ELEMENT, name=wpwp-bottom

_wpwp-bottom_S1, S1

_wpwp-bottom_S2, S2

*Elset, elset=_wpconv-bot_S2, internal, instance=workpiece-bot-1, generate

1, 8459, 1

*Elset, elset=_wpconv-bot_S1, internal, instance=workpiece-bot-1, generate

124

50755, 51478, 1

*Surface, type=ELEMENT, name=wpconv-bot

_wpconv-bot_S2, S2

_wpconv-bot_S1, S1

*Elset, elset=_wpconv-top_S1, internal, instance=workpiece-top-1, generate

42296, 50754, 1

*Elset, elset=_wpconv-top_S2, internal, instance=workpiece-top-1, generate

54375, 55098, 1

*Surface, type=ELEMENT, name=wpconv-top

_wpconv-top_S1, S1

_wpconv-top_S2, S2

*Elset, elset=_bot-edge_S5, internal, instance=workpiece-bot-1

50854, 50855, 50856, 50857, 50858, 50859, 50860, 50861, 50862, 50863, 50864, 50865, 50866

.

.

.

125

55012, 55013, 55014, 55015, 55016, 55017, 55018, 55019, 55020, 55021, 55022, 55023

*Elset, elset=_bot-edge_S4, internal, instance=workpiece-bot-1

50838, 50839, 50840, 50841, 50842, 50843, 50844, 50845, 50846, 50847, 50848, 50849, 50850

.

.

.

54996, 54997, 54998, 54999, 55000, 55001, 55002, 55003, 55004, 55005, 55006, 55007, 55008

*Surface, type=ELEMENT, name=bot-edge

_bot-edge_S5, S5

_bot-edge_S4, S4

*Elset, elset=_top-edge_S5, internal, instance=workpiece-top-1

50854, 50855, 50856, 50857, 50858, 50859, 50860, 50861, 50862, 50863, 50864, 50865, 50866

.

.

.

55012, 55013, 55014, 55015, 55016, 55017, 55018, 55019, 55020, 55021, 55022, 55023

126

*Elset, elset=_top-edge_S4, internal, instance=workpiece-top-1

50838, 50839, 50840, 50841, 50842, 50843, 50844, 50845, 50846, 50847, 50848, 50849, 50850

.

.

.

54996, 54997, 54998, 54999, 55000, 55001, 55002, 55003, 55004, 55005, 55006, 55007, 55008

*Surface, type=ELEMENT, name=top-edge

_top-edge_S5, S5

_top-edge_S4, S4

*Elset, elset=_wpwp-top_S2, internal, instance=workpiece-top-1, generate

1, 8459, 1

*Elset, elset=_wpwp-top_S1, internal, instance=workpiece-top-1, generate

50755, 51478, 1

*Surface, type=ELEMENT, name=wpwp-top

_wpwp-top_S2, S2

_wpwp-top_S1, S1

127

*End Assembly

*Section Controls, name=EC-1, hourglass=relax STIFFNESS, SECOND ORDER

ACCURACY=yes ,KINEMATIC SPLIT=AVERAGE STRAIN

1, 1, 1

*Amplitude, name=constant, definition=SMOOTH STEP

0., 1, 1.425, 1.

*Amplitude, name=u2, definition=SMOOTH STEP

0., 0.,0.15,-0.01, 1.425, -1.544

*Amplitude, name=vr2, definition=SMOOTH STEP

0., 0., 0.15, 314, 1.425, 314

*Material, name=Material-wp

*Conductivity

162, -17.8

.

.

.

223, 426.7

128

*Density

2.713e-09, -17.8

.

.

.

2.602e-09, 426.7

*Elastic

70200., 0.33, -17.8

.

.

.

31720., 0.33, 426.7

*Expansion, zero=22

2.194e-05, -17.8

.

.

129

.

3.071e-05, 426.7

*Inelastic Heat Fraction

0.9,

*Plastic,Hardening=Johnson Cook

293.4, 121.26, 0.23, 1.34, 582, 22

*Rate dependent,Type=Johnson Cook

0.002 , 1

*Specific Heat

9.04e+08, -17.8

.

.

.

1.133e+09, 426.7

**

*Boundary

130

anvil-ref, ENCASTRE

** Name: fixed-pin Type: Displacement/Rotation

*Boundary

pin-ref, 1, 1

pin-ref, 2, 2

pin-ref, 3, 3

pin-ref, 4, 4

pin-ref, 5, 5

pin-ref, 6, 6

edge-top,1,1

edge-bot,1,1

*Initial Conditions, type=TEMPERATURE

workpiece-bot-1.wp-bot, 22.

workpiece-top-1.wp-top, 22.

pin-ref,22

anvil-ref,22

131

*Step, name=Step-1

*Dynamic Temperature-displacement, Explicit, element by element

, 1.425

*Bulk Viscosity

0.06, 1.2

**fixed mass scaling, elset= massscaling, dt=1e-4, type=below min

*Variable Mass Scaling,elset= massscaling, dt=1e-5, type=below min, frequency=10

*Boundary, op=NEW

anvil-ref, ENCASTRE

*Boundary, op=NEW, amplitude=constant

pin-ref, 1, 1

pin-ref, 3, 3

pin-ref, 4, 4

pin-ref, 6, 6

edge-top,1,1

edge-bot,1,1

132

**boundary,op=new,amplitude=constant

**pin-ref,11,11,22

**anvil-ref,11,11,22

*Boundary, op=NEW, amplitude=u2

pin-ref, 2, 2, 1.

*Boundary, op=NEW, amplitude=vr2, type=VELOCITY

pin-ref, 5, 5, 1.

*Adaptive Mesh Controls, name=Ada-1, mesh constraint angle=45., meshing

predictor=PREVIOUS

1,0, 0.

*Adaptive Mesh,elset= massscaling, frequency=18, mesh sweeps=3,controls=Ada-1,op=NEW

** INTERACTION PROPERTIES

**

*Surface Interaction, name=contact

*Friction

0.3 , 0 , 800 , 120

.

133

.

.

0.1 , 500 , 800 , 520

*Gap Conductance

1000, 0

0,0.3

*Gap Heat Generation

1.,0.9

*Surface Interaction, name=contact-wpwp

*Gap Conductance

1000, 0

0,0.3

*friction

0.42

*Gap Heat Generation

1., 0.9

134

*Contact Pair,interaction=contact-wpwp,mechanical constraint=kinematic

wpwp-top, wpwp-bottom

*Contact Pair, interaction=contact, mechanical constraint=KINEMATIC

anvil-1.sur-anvil, wpconv-bot

*Contact Pair, interaction=contact, mechanical constraint=kinematic

pin-1.sur-pin, wpconv-top

*Sfilm, amplitude=constant,op=new

wpconv-top, f, 22,0.03

wpconv-bot, f, 22,0.03

top-edge,f,22,0.03

bot-edge,f,22,0.03

*cfilm, amplitude=constant,op=new

pin-ref,1,22,0.03

anvil-ref,1,22,0.03

**

** OUTPUT REQUESTS

135

**

*Restart, write, number interval=1, time marks=NO

*Monitor, dof=2, node=pin-ref

*Output, field, number intervals=30, time marks=YES

*Node Output

U, V, A, RF, NT, RFL,coord

*Element Output,elset= massscaling

S, PE, PEEQ, LE, TEMP, HFL,elen,ener

*Contact Output

CSTRESS, cforce,fslip,fslipr

*Output, history, variable=PRESELECT

*Output, history

*Node Output, nset=pin-ref

U2, VR2, RF2, RM1,NT

RM2, RM3

*End Step