Finite Element Simulation of Hot Stamping - OhioLINK ETD

Finite Element Simulation of Hot Stamping

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in

the Graduate School of The Ohio State University

By

Deepak Ravindran

Graduate Program in Mechanical Engineering

The Ohio State University

2011

Master's Examination Committee:

Dr. Taylan Altan, Adviser

Dr. Jerald Brevick

Copyright by

Deepak Ravindran

2011

ii

Abstract

Hot stamping is a relatively new and upcoming technology in the automotive

industry used for the manufacturing of lightweight crash resistant parts with ultra high

strength. The Finite Element (FE) simulation of hot stamping has to consider the

combined effects of thermal, mechanical and microstructural fields. As a result,

simulation of hot stamping is a complex process and requires detailed information on

various factors such as material properties, process parameters and the right choice of

software code. This report presents a complete list of all the important material properties

and process parameters required for FE simulation of hot stamping. A sample part

geometry was obtained from an industrial partner of the Center for Precision Forming at

The Ohio State University and FE simulations of the part were carried out using the FE

code DEFORM. The modeling and results of these simulations are presented in this

report. Based on the results, a new methodology has been proposed that makes use of two

different FE codes namely, DEFORM and PAM-STAMP in order to combine the

advantages of the two in simulating hot stamping processes.

iii

Dedicated to my family and friends

iv

Acknowledgments

I am extremely grateful to my advisor, Dr. Taylan Altan, for providing me an

opportunity to be a part of the Center for Precision Forming (CPF) and for his constant

and valuable guidance throughout this research work. I am also grateful to our industrial

partners, IMRA America, Inc. and POSCO for sponsoring this research work and

providing valuable information during the course of the project. I am thankful to my

fellow colleagues at CPF, Dr. Changhyok Choi, Jose Gonzalez-Mendez, Dr. Jay

Sartkulvanich, Manan Shah and Allison Duarte da Silva for their involvement and

cooperation in this project. Finally, I would like to thank my mom, Subathira, my dad,

Ravindran, my sister, Kiruthika, and my friends, Abhijat, Arvind, Erhan, Karthik,

Nishanth, Pravin, Raghunath, Rakesh, Rohit, Shivam and Sumanth for their constant

support and motivation during tough times.

v

Vita

2009................................................................B.E. Manufacturing Engineering, Anna

University, India

2009 to present ..............................................Graduate Research Associate, Integrated

Systems Engineering, The Ohio State

University

Publications

Naganathan, A., Ravindran, D. & Altan, A. (2011). Hot-stamping Boron-alloyed Steels

for Automotive Parts. Stamping Journal, March/April 2011, 12-13.

Fields of Study

Major Field: Mechanical Engineering

vi

Table of Contents

Abstract ............................................................................................................................... ii

Acknowledgments.............................................................................................................. iv

Vita ...................................................................................................................................... v

Publications ......................................................................................................................... v

Fields of Study .................................................................................................................... v

Table of Contents ............................................................................................................... vi

List of Tables ................................................................................................................... viii

List of Figures .................................................................................................................... ix

Chapter 1: Introduction ...................................................................................................... 1

1.1 Direct Hot Stamping.................................................................................................. 2

1.2 Indirect Hot Stamping ............................................................................................... 3

1.3 Finite Element Simulation of Hot Stamping ............................................................. 4

1.4 Objective ................................................................................................................... 5

Chapter 2: Material Properties and Process Parameters for FE Simulations ...................... 6

2.2 Challenges in FE simulation of hot stamping ........................................................... 6

2.2 Material Properties of 22MnB5................................................................................. 8

vii

2.2.1 Flow Stress ......................................................................................................... 8

2.3 Process Parameters .................................................................................................... 9

2.3.1 Time taken for transferring the blank from furnace to die ............................... 10

2.3.2 Heat transfer coefficient between sheet and die ............................................... 10

2.3.3 Coefficient of friction ....................................................................................... 10

2.3.4 Quenching Time ............................................................................................... 10

Chapter 3: Finite Element Simulation of Hot Stamping ................................................... 12

3.1 Simulation of a sample part geometry..................................................................... 13

3.2 Material Model ........................................................................................................ 14

3.3 Simulation of 2D section using DEFORM-2D ....................................................... 20

3.4 Simulation of 3D part using DEFORM-3D ............................................................ 24

Chapter 4: New methodology for FE simulation of Hot Stamping .................................. 26

4.1 Coupled hot stamping simulations using DEFORM and PAM-STAMP 2G .......... 27

Chapter 5: Conclusion....................................................................................................... 34

REFERENCES ................................................................................................................. 35

viii

List of Tables

Table 1 Chemical composition of USIBOR 1500 in weight % .......................................... 6

Table 2 Young’s modulus in function of temperature used in the material model

[TURE08] ......................................................................................................................... 19

Table 3 Poisson’s ratio, thermal conductivity and heat capacity values used in the

material model [NUMI08] ................................................................................................ 19

ix

List of Figures

Figure 1 Direct hot stamping method [ENGE06] ............................................................... 3

Figure 2 Indirect method of hot stamping [ENGE06] ........................................................ 4

Figure 3 Interactions between the effects of deformation, heat transfer and

microstructural evolution [ERIK02] ................................................................................... 7

Figure 4 Flow stress curves for 22MnB5 at different temperatures and constant strain rate

of 0.1 /s [ERIK02]............................................................................................................. 15

Figure 5 Flow stress curves for 22MnB5 at 700 °C and different strain rates [ERIK02] . 16

Figure 6 Thermal dilatation in function of temperature [ERIK02] ................................... 17

Figure 7 Coefficient of thermal expansion in function of temperature used in the material

model................................................................................................................................. 18

Figure 8 2D section of the part geometry used for simulation with DEFORM-2D ......... 20

Figure 9 Temperature distribution on the blank at the end of the blank transfer simulation

........................................................................................................................................... 21

Figure 10 Heat transfer coefficient between blank and tool in function of pressure

[NUMI08] ......................................................................................................................... 22

Figure 11 Comparison of thinning distribution from DEFORM-2D with experimental

data .................................................................................................................................... 23

Figure 12 Flowchart for proposed FE modeling procedure with simultaneous use of

DEFORM and PAM-STAMP ........................................................................................... 27

x

Figure 13 Nodal positions plotted with respect to X and Y co-ordinates ......................... 29

Figure 14 Illustration of the method used for finding normal vector and applying

thickness to the shell blank ............................................................................................... 30

Figure 15 Final part generated through MATLAB using blank information from PAM-

STAMP. ............................................................................................................................ 31

1

Chapter 1: Introduction

The increased competition and more stringent safety requirements in today’s

automotive market has led to the need for improved crashworthiness and reduced weight

of automotive structural parts. As a result, the use of ultra high strength steels (UHSS) for

structural and safety components of automobiles has steadily increased over the past few

years. Traditionally, cold stamping i.e. stamping at room temperature is the preferred

method for manufacturing of automotive parts. However, ultra high strength steels cannot

be effectively cold stamped due to their low formability and high springback at room

temperature. These difficulties can be overcome by manufacturing the parts through a

process known as Hot Stamping.

Hot stamping or Press Hardening is a forming process for the manufacturing of

light weight body parts from Ultra High Strength Steels (UHSS). This process takes

advantage of the low flow stress and reduced springback of Manganese Boron Steel

(22MnB5) in austenitic phase at elevated temperatures, followed by quenching which

transforms the austenite into martensite providing the hot stamped part its ultra high

strength. The as-received 22MnB5 steel has a ferritic-pearlitic microstructure. The

process involves the heating of 22MnB5 blanks to its austenitization temperature of about

900 °C, forming in a die and then quenching under pressure within dies at a minimum

cooling rate of 27 °C/s. The formation of martensite, which gives the part its high

strength, will only occur if the part is cooled at this minimum cooling rate. In general, a

2

hot stamping process involves four major steps or stages. They are (a) Heating of the

blank to austenitization temperature, (b) Transferring of blank from furnace to die, (c)

forming of the blank within the dies, (d) Quenching within the dies and (e) air cooling of

the part. Since the desired strength levels are achieved without the need for additional

material, unlike in the case of low or high strength steels, the parts are also comparatively

lighter with reduced thicknesses. The parts produced by hot stamping have tensile

strengths up to 1600 MPa which is much higher than those produced by cold stamping.

B-pillars, A-pillars, C-pillars, roof rails and bumpers are some of the parts that are

currently manufactured through hot stamping. There are two different methods of hot

stamping namely, direct and indirect.

1.1 Direct Hot Stamping

This is a one stage process in that the forming of the blank occurs in a single die

pass. The blank is heated to its austenitization temperature of 900 to 950 °C in a furnace

for approximately 5 minutes. The heated blanks are then transferred to a die. The transfer

process usually takes 3 to 6 seconds. The blanks are formed within the dies and then

subsequently quenched under pressure for a particular amount of time depending on the

thickness of the part. The dies have integrated cooling channels through which they are

cooled continuously throughout the cycle with the help of circulating water. Usually, the

deformation process is very short while quenching takes anywhere between 10 to 25 s.

Since the blank material has very low formability at the elevated temperatures at which it

is formed, complex shapes can easily be achieved. The quenching of the part within the

internally cooled dies ensures the minimum cooling rate of 27 °C/s required for

3

martensitic transformation. Figure 1 shows a schematic of the direct hot stamping

method. This is the most common method of hot stamping followed in the industry.

Figure 1 Direct hot stamping method [ENGE06]

1.2 Indirect Hot Stamping

In indirect hot stamping (Figure 2) the part to be drawn is first stamped cold to

about 90-95 % of its final shape in a conventional die. This preform is then heated in a

furnace and subsequently quenched within a hot stamping die making it a two stage

process. The purpose behind the indirect method is the production of highly complex

shapes by extending the forming limits of the blank material. However, this method is

more cost-intensive and so less common in the industry.

4

Figure 2 Indirect method of hot stamping [ENGE06]

1.3 Finite Element Simulation of Hot Stamping

Finite Element (FE) simulation of hot stamping offers several advantages for the

automotive industry. They can be used to predict the final part properties such as the

thickness distribution, temperature distribution and hardness distribution etc. Since the

primary purpose behind using hot stamping is to increase the strength of manufactured

parts and reduce weight, obtaining the hardness distribution and thickness distribution

through simulations can be very useful for the manufacturer. Finite element simulations

help in determining the effect of the various parameters involved in the hot stamping

process. For example, the effect of variation in coefficient of friction and heat transfer

coefficients can be accurately predicted using simulations. This helps the manufacturer in

understanding the process better and thus can be used to optimize the process if

necessary. Also, simulations are used for designing tools for hot stamping. Hot stamping

5

tools typically have cooling channels integrated in them for quenching the part. In order

to manufacture quality parts with required characteristics and to do so economically it is

necessary to optimize the design of the tools. The primary concerns in designing the tools

are the location and size of the cooling channels. The location and size of the cooling

channels influence the cooling rate of the part which in turn influences the final part

characteristics. Thus, the use of finite element simulations in designing the tools for hot

stamping is crucial.

1.4 Objective

The objective of this research work was to develop an effective strategy for

accurate finite element simulation of hot stamping processes and carry out simulations for

a sample part geometry and compare the results with corresponding experimental data.

6

Chapter 2: Material Properties and Process Parameters for FE Simulations

2.1 Chemical composition of 22MnB5

The chemical composition of USIBOR® 1500, a 22MnB5 material produced by

ArcelorMittal, is shown in Table 1. Adding boron to the steel reduces the critical cooling

rate for martensitic transformation thereby increasing the chances of martensitic

formation. Manganese and chrome increase the tensile strength of the material.

Table 1 Chemical composition of USIBOR 1500 in weight %

2.2 Challenges in FE simulation of hot stamping

The simulation of hot stamping is different from other room temperature and

warm forming processes. For room temperature forming, since heat transfer is negligible

and there are no microstructural variations, the numerical simulations can be carried out

under isothermal conditions and without accounting for changes in microstructure

thereby simplifying the simulation process. However, in hot stamping, the blank is heated

to temperatures around 900 °C and then rapidly cooled down to roughly around 150 °C.

Therefore the simulations have to be non-isothermal in nature. Also, during quenching,

the microstructure of the part changes from one that is predominantly austenite to

7

martensite. This affects the properties of the part such as hardness and volume etc. Thus,

the evolution of microstructure should also be considered for accurate simulation of the

hot stamping process. Figure 3 shows the inter-relationships between the effects of

deformation, heat transfer and microstructural evolution. Therefore, an accurate FE

model of the process should consider interactions between the mechanical, thermal, and

microstructural effects. Owing to the complexity involved in numerical simulation of hot

stamping, researchers around the world have experimented using several different

commercial codes such as LS-Dyna, PAMSTAMP, AUTOFORM and Abaqus FEA etc.

Many have used a combination of two or more codes to capture the different interactions

involved in hot stamping.

Figure 3 Interactions between the effects of deformation, heat transfer and

microstructural evolution [ERIK02]

8

As a result of the various factors involved, numerical simulation of hot stamping

requires several blank material properties and process parameters. These are presented in

the following sections.

2.2 Material Properties of 22MnB5

The properties of the blank material (22MnB5) vary significantly with temperature. In

hot stamping, the temperature of the blank material varies from room temperature to

around 900 °C throughout the cycle. Thus, to build an accurate FE model of the process,

it is necessary to input the material properties in function of temperature. The material

properties in function of temperature that are required for FE simulations are

a) Flow stress in function of strain and strain rate

b) Young’s modulus

c) Poisson’s ratio

d) Emissivity

e) Thermal conductivity

f) Specific heat capacity

g) Coefficient of thermal expansion

2.2.1 Flow Stress

Several methods have been employed to determine the flow stress of the material.

Some of these include high temperature compression tests conducted by [ERIK02],

inverse analysis method used by [AKER05] and tensile tests using Gleeble 1500 and

Gleeble 3800 as done by [MERK06] and [TURE06] respectively. The wider the range of

temperatures and strain rates for which the flow stress data is given the better.

9

Extrapolation errors which occur as a result of extrapolation of flow stress data by FE

analysis codes due to lack of data for a particular temperature range or strain rate, can be

avoided if the data is provided beforehand.

2.3 Process Parameters

The process parameters that have to be defined for accurate FE modeling of hot

stamping are

a) Austenitization temperature of the blank

b) Time taken for transferring the blank from furnace to die

c) Temperature of the blank at the beginning of forming

d) Die stroke versus time

e) Contact heat transfer coefficient between blank and tool in function of pressure

f) Coefficient of friction between sheet and dies

g) Initial die temperature for non-isothermal simulation or average die temperature

for isothermal simulation

h) Temperature of the cooling medium used to cool the dies

i) Closing pressure at which the deformed blank is held between the tools during

quenching

j) Quenching times (dwell time of the press at bottom dead center)

k) Time required for air cooling.

l) Temperature of the environment

m) Heat transfer coefficient between the blank and environment (air)

10

2.3.1 Time taken for transferring the blank from furnace to die

The time taken to transfer the blank from the furnace to die is an important factor.

The blank loses heat to the environment during this process thereby resulting in a drop in

temperature. Since the flow stress of the material increases with decreasing temperature,

the ease of forming the material is directly linked to the temperature at which the blank

enters the die.

2.3.2 Heat transfer coefficient between sheet and die

Martensitic transformation, which gives the final part its high strength,

necessitates a minimum cooling rate of 27 °C/s. Thus heat transfer plays an important

role during the process. During the deformation and quenching stages, conduction is the

most dominant form of heat transfer and thus heat transfer coefficient for conduction

becomes paramount. This contact heat transfer coefficient is given as a function of

contact pressure (P), between the tools and the blank.

2.3.3 Coefficient of friction

The coefficient of friction is another important factor in the simulation of hot

stamping. Theoretically, the coefficient of friction, μ, varies with temperature and contact

pressure. But for most practical purposes, μ can be assumed to be constant since the

variation is negligible. The coefficient of friction can be found using a tribosimulator

[YANA09], modified cup drawing test [GEIG08] or pin on disc test [HARD08].

2.3.4 Quenching Time

The quenching time i.e. the dwell time of the press in its final closed position at the

end of the forming stroke is another important criterion. Knowing the exact quenching time is

11

essential since it determines the extent of martensitic transformation. If the final part is not

quenched long enough, it may result in localized “soft” regions.

The process parameters differ from one hot stamping process to another owing to

several factors such as differing presses, temperature conditions, level of automation etc.

12

Chapter 3: Finite Element Simulation of Hot Stamping

Apart from the advantages of predicting the final part properties, process

optimization and tool design, FE simulation of hot stamping also offers the advantage of

manufacturing parts with tailored properties. For instance, it is possible to manufacture

B-pillars with a softer lower end thereby allowing controlled buckling around the lower

end in order to avoid severe buckling at the top end. This could prevent possible

penetration into the passenger compartment [AKER06].

An ideal procedure for finite element simulation of hot stamping should be

divided into the following stages and each stage should be able to consider the various

effects as shown, in order to accurately emulate the physical conditions.

1) Blank heating and blank transfer simulation:

- Convective heat transfer with environment

- Radiation heat transfer

- Thermal expansion and contraction due to temperature rise and fall respectively.

2) Forming simulation:

- Blank should be modeled as an elasto-plastic object to account for both plastic material

flow and thermal contraction.

- Tools should be modeled as elastic objects since in the physical process there may be

elastic deflection of the tools.

13

- The heat transfer between the tool and die should be expressed in function of contact

pressure.

3) Quenching simulation:

- the location of cooling channels is critical and should be either known from existing

designs or if required cooling channels may be designed using separate quenching

simulations to determine optimum design.

- The flow rate of the cooling medium should be provided as an input for simulation as

this is directly related to the cooling efficiency of the tools.

- The FE model should be able to predict the microstructural evolution during quenching.

However, some the phenomenon or effects mentioned above can be neglected as

they may not be very significant or due to increased complexity of the FE model without

a significant increase in accuracy. For instance, elastic deflection of dies increases the

simulation time many-fold even though its significance is generally low.

3.1 Simulation of a sample part geometry

As part of a collaborative effort on hot stamping, a sample part and its

corresponding die geometries (both in 3D) were obtained from an industrial partner of

CPF and FE simulations were carried out for the entire hot stamping process. The FE

code DEFORM was used for running the simulations. Two different simulations were

carried out

1) A 2D section of the actual part, for which experimental results were available,

was chosen and simulations were run using DEFORM-2D.

14

2) Simulations were carried out with the 3D part using DEFORM-3D.

In both cases, the thinning distributions obtained from simulation were compared

with corresponding experimental data. The data obtained from the company includes the

blank and die geometries and relevant process parameters such as die velocity (V) and

quenching time (tq) etc. Owing to a confidentiality agreement signed with the company,

only non-proprietary and generic information and results have been presented in this

report.

3.2 Material Model

A material model was compiled for the blank material (22MnB5) based on data

available from various literature sources. The flow stress data was obtained from

[ERIK02]. [ERIK02] carried out experimental compression tests using Gleeble-1500

thermo-mechanical simulator and reported flow stress data for 22MnB5 in function of

strain, temperature and strain rate. [ERIK02] captured the effect of temperature by

calculating the flow stress data at temperatures between 300 °C to 900 °C (in steps of 50

°C) at a strain rate of 0.1 /s. The effect of strain rate was captured by calculating the flow

stress at strain rates ranging from 0.01 to 10 /s for different temperatures of 300, 350,

400, 450, 500 and 700 °C. Using this, the flow stress data for different strain rates at

other temperatures was interpolated in order to standardize it. Figure 4 shows the flow

stress curves for various temperatures at a constant strain rate of 0.1 /s and Figure 5

shows the flow stress curves for different strain rates at a constant temperature of 700 °C.

15

Figure 4 Flow stress curves for 22MnB5 at different temperatures and constant strain rate

of 0.1 /s [ERIK02]

16

Figure 5 Flow stress curves for 22MnB5 at 700 °C and different strain rates [ERIK02]

[ERIK02] also carried out experiments to determine the thermal volume change

(dilatation) of the material in function of temperature. This is shown in Figure 6.

17

Figure 6 Thermal dilatation in function of temperature [ERIK02]

The coefficient of thermal expansion in function of temperature was found using

the thermal dilatation and the following equation and is shown in Figure 7.

where,

α = coefficient of thermal expansion in /K

dεv = change in volumetric strain

dT = change in temperature in K

18

Figure 7 Coefficient of thermal expansion in function of temperature used in the material

model

[TURE08] calculated the Young’s modulus of 22MnB5 material in function of

temperature through experimental tensile tests. These values were directly used in this

material model and are shown in Table 1.

0.00E+00

5.00E-08

1.00E-07

1.50E-07

2.00E-07

2.50E-07

3.00E-07

3.50E-07

0 100 200 300 400 500 600 700 800 900 1000

Co

effi

cie

nt

of

the

rmal

exp

ansi

on

( /

C)

Temperature ( C)

19

Table 2 Young’s modulus in function of temperature used in the material model

[TURE08]

Temperature (°C) Young’s modulus (GPa)

20

212

100 205

200 200

300 164

400 158

500 140

600 95

700 62

800 55

900 45

The poisson’s ratio, thermal conductivity and heat capacity were chosen from

Benchmark Problem-03 of Numisheet Conference, 2008 [NUMI08]. These are presented

in Table 2.

Table 3 Poisson’s ratio, thermal conductivity and heat capacity values used in the

material model [NUMI08]

Poisson’s ratio 0.3

Thermal conductivity 32 W/mK

Heat capacity 650 J/kgK

20

3.3 Simulation of 2D section using DEFORM-2D

A 2D section of the 3D part and die geometries, for which experimental thinning

distribution was available from the industrial partner, was chosen. This 2D section

(Figure 8) was then simulated using DEFORM-2D. All four stages of the hot stamping

process namely, heating of the blank to austenitization temperature, blank transfer from

furnace to die, forming within the dies and quenching were simulated. The blank was

modeled as a plastic object and the tools as rigid objects. AISI H-13 was chosen as the

tool material for which the material data is available in DEFORM’s material library.

Since the profile of the actual 3D part has a nearly uniform cross section throughout its

width, plane strain condition was assumed. The number of elements in the mesh along the

thickness direction of the blank was four.

Figure 8 2D section of the part geometry used for simulation with DEFORM-2D

The data given by the company included the austenitization temperature of the

blank i.e. the temperature to which the sheet metal is heated in the furnace, the time taken

to transfer the blank from the furnace to the press, and the temperature of the blank at the

beginning of the forming operation. Using this information, the heat transfer coefficient

21

of the blank with air (He) was calculated by inverse analysis. The temperature distribution

on the blank at the end of the blank transfer stage is shown in Figure 9.

Figure 9 Temperature distribution on the blank at the end of the blank transfer simulation

Following the blank transfer simulation, the simulation of the forming process

was carried out. The heat transfer coefficient between the blank and tools (Ht) was given

in function of contact pressure (P) and was chosen from the reference [NUMI08]. Figure

10 shows the heat transfer coefficient vs. pressure curve. Based on review of various

literature sources such as [GEIG08], [KARB09], [NUMI08], [TURE08] and [YANA09],

it was concluded that a friction coefficient (µ) of 0.4 is appropriate for use in hot

stamping.

22

Figure 10 Heat transfer coefficient between blank and tool in function of pressure

[NUMI08]

During the forming simulation, initially, the die moves down until the gap

between the die and blank holder is equal to the thickness of the blank. Then, from here

on, both the die and blank holder move together, at the same velocity, till the end of the

forming process. The end of the forming process is defined by the maximum die force.

The thinning distribution calculated by DEFORM-2D at the end of the forming

simulation is shown in Figure 11. Due to proprietary reasons, the thinning distribution

measured by the company is not provided here. It was observed that although the

thinning distribution trends are similar, the actual values predicted by the FE simulations

are not in agreement with experimental data. For instance, the maximum thinning

23

calculated by DEFORM-2D was approximately 8.1 % which is much lower than the

corresponding experimental value of 10.53 % at this point. One of the possible reasons

for the mismatch could be the negligence of three dimensional material flow. In order to

verify this and to improve the accuracy of the FE results, simulations were run using

DEFORM-3D with 3D blank and tool geometries. Since the simulation of the stamping

process with DEFORM-2D, did not yield satisfactory results, the results of the

subsequent quenching simulations have been ignored and are not presented here.

Figure 11 Comparison of thinning distribution from DEFORM-2D with experimental

data

0

1

2

3

4

5

6

7

8

9

-100 -80 -60 -40 -20 0 20 40 60 80 100

Th

inn

ing

Dis

trib

uti

on

(%

)

Curvilinear length along the blank (mm)

24

3.4 Simulation of 3D part using DEFORM-3D

Since the geometries of the part and die were nearly symmetrical, only one half of

the geometries were modeled and simulated in order to reduce simulation time. As in the

previous case with the 2D section, the blank was modeled as a plastic object and the tools

as rigid objects and all four stages of the hot stamping process were simulated. During the

forming simulation, only the die force value used to specify the end of the forming

simulation was modified from the 2D simulation case study in order to account for the

3D part instead of the 2D part. All other process parameters such as heat transfer

coefficient between the blank and die, friction coefficient, die velocity etc. were left

unchanged from the 2D case study.

Similar to the 2D case study, the forming process simulation is divided into two

steps. The thinning distribution along a certain section of the formed part obtained from

the 3D simulation is compared with the corresponding experimental data. It was observed

that the thinning distribution obtained from the FE simulation is in fairly good agreement

with the experimental values. The maximum thinning percentage obtained from FE

simulation is approximately 9.9 %, which is close to the corresponding experimental

value of 10.5 %. Also the location of this maximum thinning point on the part is nearly

the same for both the experimental and numerically calculated cases. Small differences

were observed between the numerically calculated and experimental values around the

plane of symmetry and around the side walls of the part. The former is attributed to the

use of the symmetrical boundary condition which stretches the blank along the plane of

25

symmetry thereby resulting in increased thinning in this region. The latter could be due to

the difference in effects of friction between the experimental and numerically simulated

cases.

Simulations were also carried out for the quenching stage of the process. A

constant temperature of 20 °C was used for the cooling channels in order to simulate their

effect. This is under the assumption that in practice, the flow rate of the cooling medium

is such that it maintains the cooling channels at room temperature constantly. The cooling

channel geometries were provided by the company. The temperature distribution on the

part at the end of the quenching stage was obtained from simulation. The maximum and

minimum temperatures obtained from the simulation are 233 °C and 36 °C respectively.

The temperature at which Martensite begins to form is approximately 420 °C [ERIK02]

and the temperature at which it ceases to form is 280 °C [ERIK02]. It is useful to know

the temperature distribution of the part since it determines whether the criteria for

martensitic formation were achieved or not. The minimum cooling rate observed was 25

°C /s (at the maximum temperature point at the end of quenching). This is slightly lower

than the required minimum cooling rate of 27 °C/s for martensitic transformation. This is

due to reduced contact between the tools and the blank around this region (sidewalls).

26

Chapter 4: New methodology for FE simulation of Hot Stamping

The simulations presented in this report were run using the FE code DEFORM

(2D and 3D). DEFORM is an FE code developed primarily for the bulk forming industry.

As a result, it has a built-in heat transfer module that can accurately model heat transfer

related processes. Also, since the thickness of workpiece in bulk forming are significantly

large, it makes use of brick elements for meshing objects and hence can provide through-

thickness information such as through-thickness temperature gradients. This provides an

obvious advantage for its use in hot stamping since, unlike most other sheet forming

processes, heat transfer plays a very significant role in hot stamping. However, as a result

of the use of brick elements, the simulation time is considerably high. In particular, the

simulation time for the stamping stage is very high. Also, complex 3D geometries cannot

be easily simulated using DEFORM. In general, sheet forming processes are usually

simulated with codes like AUTOFORM, PAM-STAMP, LS-Dyna etc. These codes use

shell elements and therefore the simulation time is significantly reduced. They are also

capable of simulating very complex 3D geometries. However, the lack of through-

thickness information and the lack of an accurate heat transfer module mean that they

cannot be used as a standalone code for simulating hot stamping processes. Based on the

above conclusions a new methodology was proposed which could combine the

advantages of both bulk forming and sheet forming codes for FE simulation of hot

stamping.

27

4.1 Coupled hot stamping simulations using DEFORM and PAM-STAMP 2G

The proposed methodology makes use of the FE codes, DEFORM and PAM-

STAMP for simulation of the hot stamping process. Figure 12 shows the flowchart for

the procedure of the proposed methodology. Under this new methodology, the stamping

simulation will be carried out using PAM-STAMP 2G and the blank heating, blank

transfer and quenching simulations will be carried out using DEFORM-2D. This

combines the advantages of both the FE codes.

Figure 12 Flowchart for proposed FE modeling procedure with simultaneous use of

DEFORM and PAM-STAMP

Under the proposed methodology, simulation process starts with DEFORM for

heat transfer analysis of the blank, considering thermal expansion during blank heating

and shrinkage during blank transfer. The blank object is then transferred to PAM-

STAMP for simulation of stamping at elevated temperature. Blank information from

PAM-STAMP (blank profile, thinning distribution and pressure distribution) is

transferred back to DEFORM for thermal analysis of quenching of the blank. Due to

28

major differences in both FE packages such as shell vs. solid elements, it is necessary to

develop a practical interfacing software module in order to convert blank and process

information that provides seamless transfer between DEFORM and PAM-STAMP. A

preliminary procedure has been developed to convert blank and process information at

the end of the stamping simulation from PAM-STAMP into input data for DEFORM-2D

to run the quenching simulation. In this preliminary procedure, only the stamping and

quenching operations were modeled and simulated. This procedure is explained in the

following steps.

Step 1:

Stamping simulation is carried out with 3-D geometry using PAM-

STAMP.

Step 2:

The data required for running quenching simulations in DEFORM-2D is extracted

from PAM-STAMP. This data is taken along a single section of the 3D geometries.

- Coordinates (X and Y) of the nodes from the mesh of the blank in PAM-STAMP.

- Thickness distribution of the formed blank in function of the X-coordinate.

- Pressure values for each element on the part mesh.

- Profile of the die along the section where the blank information is being recorded.

- Area of each element on the formed blank mesh.

29

Step 3:

(a) The part geometry to be input into DEFORM is generated through MATLAB

using the following data obtained in the previous step.

- Nodal co-ordinates (X and Y).

- Thickness distribution in function of nodal X co-ordinate.

(b) PAM-STAMP uses the mid-plane of the actual blank as the input workpiece

geometry. This means that the nodes of the PAM-STAMP mesh are along the mid-plane

of the actual blank. Figure 13 shows the coordinates of the mesh from PAM-STAMP for

the 2D section geometry presented in chapter 3.

Figure 13 Nodal positions plotted with respect to X and Y co-ordinates

(c) Thus, when the blank with thickness is generated using MATLAB, half of the

thickness is applied along the normal vector in the direction of the top surface of the

blank. The same procedure is applied to the bottom surface. This is illustrated through

Figure 14. The normal vector for a node is calculated using the coordinates of that node

30

along with the co-ordinates of its adjacent nodes. Figure 15 shows the final part generated

through MATLAB.

Figure 14 Illustration of the method used for finding normal vector and applying

thickness to the shell blank

31

Figure 15 Final part generated through MATLAB using blank information from PAM-

STAMP.

Step 4:

(a) The next step in the procedure is setting up the simulation for quenching in

DEFORM. This in turn consists of two steps. They are

- Importing of the part geometry obtained from the previous step.

- Applying the force at which the blank is held at between the tools during quenching.

(b) Heat transfer during the quenching stage occurs primarily through conduction

from the blank to the dies and this is expressed through the heat transfer coefficient

between the blank and tool (Ht). The heat transfer coefficient is defined in function of

pressure and hence it is necessary to know the pressure values for each element (this

pressure remains constant throughout the quenching simulation). This is achieved by the

application of a constant holding force during quenching. This constant force is simply

the force value at the end of the forming process.

(c) PAM-STAMP can output the force at the end of the forming process on the entire

part. However, since quenching here involves a 2D section, it is necessary to calculate the

force acting along that section in order to make the FE model as accurate as possible.

PAM-STAMP cannot directly output the force along a particular section and hence an

32

indirect method is followed to obtain this. To find the force, the following formula is

used.

where, F = Force acting along the desired section

Pi = Pressure on element i, MPa

Ai = Area of element i, in mm2

n = total no. of elements in the section

Step 5:

The final step is to run the quenching simulation using DEFORM.

The procedure mentioned above was implemented for the sample geometry

presented in chapter 3 of this report. The geometry generated using this procedure is

shown in Figure 15. The 2D section was imported into DEFORM-2D and simulations

were run for the quenching stage of the hot stamping process. The temperature

distribution at the end of the quenching simulation was obtained. The temperature at the

maximum temperature point after 10 cycles is approximately 197 °C. This means that the

cooling rate at this point is around 27 °C/s (the initial temperature and quenching time are

not provided here due to proprietary reasons). This is just equal to the minimum required

cooling rate of 27 °C/s for martensitic transformation. The simulation thus suggests that

the formed part is likely to have a uniform martensitic microstructure (since the cooling

rate at all other points will be higher than that at the maximum temperature point and

hence have a higher chance of martensitic transformation). The experimental hardness

33

distribution provided by the company also indicates that the final part is almost 100%

martensitic in microstructure. This suggests that the results obtained using the proposed

methodology could be expected to be accurate.

34

Chapter 5: Conclusion

In this report, a complete study of the material properties and process parameters

required for FE simulation of hot stamping was presented. A sample part geometry was

obtained from an industrial partner of the Center for Precision Forming and 2D and 3D

simulations were run using the FE code, DEFORM. The thickness distribution of the

sample part obtained experimentally was used as for validation of the simulations results.

It was observed that 2D simulations with DEFORM-2D were not accurate in simulating

the hot stamping process. DEFORM-3D, on the other hand, was able to model and

simulate hot stamping process fairly accurately. However, since the simulation time

involved with DEFORM-3D was considerably long and so a new methodology was

proposed where in the stamping process is carried out using the FE code PAM-STAMP

2G, in order to reduce simulation time, and the quenching is done with DEFORM-2D.

The temperature distribution on the part at the end of the quenching simulation using this

methodology was observed and the cooling rate on the maximum temperature point was

used as the parameter to validate the methodology. The result suggests that with a few

additions, it is feasible to use this procedure for FE modeling of hot stamping.

35

REFERENCES

[AKER05] Akerstrom,P.,Wikman,B.,Oldenburg,M.,”Material parameter estimation

for boron steel from simultaneous cooling and compression

experiments”, Modelling and simulation in material science and

engineering 13, 2005, pp 1291-1308

[AKER06] Akerstrom, P., “Modeling and simulation of hot stamping”, Doctoral

thesis, Department of applied physics and mechanical engineering, Lulea

university of Technology, Sweden, 2006

[ENGE06] Engels, H., Schalmin, O., Müller-Bollenhagen, C., “Controlling and

monitoring of the hot-stamping process of boron-alloyed heat-treated

steels”, The International Conference “New Development in Sheet Metal

Forming Technology”, Stuttgart / Germany, 2006, pp. 135~150

[ERIK02] Eriksson, M., Oldenburg, M., Somani, M.C., Karjalainen, L.P., “Testing

and evaluation of material data for analysis of forming and hardening of

boron steel components”, Modeling and simulation in material science

and engineering, 2002, pp 277-194

[GEIG08] Geiger, M., Merklein, M., Lechler, J., “Determination of tribological

conditions within hot stamping”, German Academic Society for

Production Engineering, 2008

36

[HARD08] Hardell, J., Kassfeldt, E., Prakash, B., “Friction and wear behavior of

high strength boron steel at elevated temperature up to 800 °C”, Wear

264, 2008, pp 788-799

[KARB09] Karbasian, H., Brosius, A. and Tekkaya, A.E, “Influence of process

control on geometrical and mechanical properties of hot stamped parts”,

Proceedings of 2nd international conference on hot sheet metal forming

of high performance steel, June, 2009, pp 157-164

[MERK06] Merklein, M., Lechler, M., Geiger, M., “Characterization of the Flow

Properties of the Quenchable Ultra High Strength Steel 22MnB5”,

Institute of Mechanical Engineering, University of Erlangen-Nuremberg,

Annals of CIRP Vol.55/1/2006

[NUMI08] Numisheet 2008, The Numisheet Benchmark study, Benchmark problem

BM03, Interlaken, Switzerland, September, 2008

[TURE06] Turetta, A, Bruschi, S., Ghiotti, A., “Investigation of 22MnB5

formability in hot stamping operations”, Journal of Materials Processing

Technology 177, 2006, pp 396-400

[TURE08] Turetta, A., Fanini, S., Ghiotti, A., Bruschi, S., “Calibration of numerical

simulation for hot stamping”, Numisheet2008, Interlaken, Switzerland,

2008

37

[YANA09] Yanagida, A., Azushima, A., ”Evaluation of coefficients of friction for

hot stamping by newly developed tribosimulator”, International deep

drawing research group, IDDRG 2009 International Conference, USA,

2009