MATERIAL CHARACTERIZATION AND FORMING OF LIGHT WEIGHT

ALLOYS AT ELEVATED TEMPERATURE

THESIS

Presented in Partial Fulfillment of the Requirements for

the Degree Masters in the Graduate

School of the Ohio State University

By

MANAN K. SHAH, B.S

Mechanical Engineering Graduate Program

The Ohio State University

2011

Thesis Committee:

Dr. Taylan Altan, Advisor

Dr. Jerald Brevick

Copyright by

Manan K. Shah

2011

ii

ABSTRACT

The increase in using light weight alloys such as aluminum and magnesium

sheet materials is accompanied by many challenges in forming these alloys due

to their unique mechanical properties and/or low formability. Alternative

forming operations, such as warm forming or sheet hydroforming, are potential

solutions for the low formability problem of aluminum alloys. Identifying

potential difficulties in forming these materials early in the product realization

process is important to avoid expensive late changes. Finite Element (FE)

simulation is a powerful tool for this purpose provided that the inputs to the FE

model, including the flow stress data, are reliable. However, obtaining the flow

stress under near production condition (state of stress, strain rate, temperature)

may be challenging especially if the flow stress is required at elevated

temperature for warm forming applications.

In this study, elevated temperature biaxial Viscous Pressure Bulge (VPB) tests

were conducted for Aluminum (AA 5182) and Magnesium (Mg AZ61 L) alloys

and the resulting flow stress curves were obtained. Using the Surface Response

Method that evaluates the error function gave the prediction of flow stress

coefficients K, n and m that fit the Power Law Equation. Results of this work

predict the flow stress data under a variable strain rate and thus cannot be

directly compared with other results which were conducted under a constant

strain rate. The fact that the state of stress in actual stamping processes is almost

always biaxial, suggest that the bulge test is a more suitable test for obtaining the

flow stress of light weight alloys to be used as an input to FE models.

iii

The sheet hydroforming with punch (SHF-P) process offers great potential for

low and medium volume production, especially for forming: (1) lightweight

sheet materials such as aluminum and magnesium alloys and (2) thin gage high

strength steels (HSS). Aluminum and Magnesium alloys are being increasingly

considered for automotive applications, primarily due to their lightweight and

high strength-to-weight ratios. However, there is limited experience-based

knowledge of process parameter selection and tool design for SHF-P of these

materials. Thus, there is a need for a fundamental understanding of the

influence of process parameters on part quality.

A Sheet Hydroforming with a Punch (SHF-P) process was successfully simulated

using the FE software Pamstamp 2G 2009. The objective was to develop a

fundamental understanding of the process to reduce the expensive experimental

trial and error. A systematic methodology to design the process was suggested

and applied using FE simulation.

iv

Dedicated to my family

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ACKNOWLEDGEMENT

I am sincerely grateful to my advisor, Dr. Taylan Altan for his supervision

during my Masters studies at the Center for Precision Forming. His intellectual

support, encouragement, and guidance are the main factors for making this

research work possible. I also thank my committee member Dr. Jerald Brevick for

his support.

Special thanks to the sponsors of this research: General Motors (G.M.), Dr. John

Carlsey, for supporting the Warm Bulge Test and Sheet hydroforming project.

Special thanks to Interlaken Technology Corporation (ITC), Dr. Patrick Cain, for

working with CPF and providing technical support for the elevated temperature

sheet bulge test project.

I thank my colleagues of the CPF, Dr. Partchapol Sartkulvanich, Eren Billur, Jose

Gonzalez-Mendez, Deepak Ravindran, Ambikapathy Naganathan, Nimet

Kardes, Yurdaer Demiralp, Adam Groseclose, and Soumya Subramonian for

their assistance and encouragement.

vi

VITA

July 2, 1987 Born, Mumbai, India

2005-2009 B.S, Mechanical Engineering

The Ohio State University

2009-2011 Graduate Research Associate

Center for Precision Forming (formerly ERC/NSM),

Columbus, OH-USA

PUBLICATIONS

Shah M., Billur E., Sartkulvanich P., Carsley J., Altan T., (2011), ―Cold and Warm

Hydroforming of AA5754-O Sheet: FE Simulations and Experiments‖,

Numisheet 2011 Conference, (In the progress of publication)

Shah M., Sartkulvanich P., (2011), ―Process Simulations in Sheet Metal Forming‖,

Chapter for ASM Sheet Metal Forming Handbook, Editor: Prof. Taylan Altan (In

Progress)

Serhat K., Shah M., (2011), ―Warm Forming‖, Chapter for ASM Sheet Metal

Forming Handbook, Editor: Prof. Taylan Altan (In Progress)

FIELD OF STUDY

Major Field: Mechanical Engineering (Design and Manufacturing)

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NOMENCLATURE

Latin Letters dc Diameter of die cavity (Bulge test) Engineering strain in axial direction (Tensile test) The objective Error function to be minimized

Clamping force (Bulge test) hd Dome height (Bulge test) The measured dome height at time t (Experimental)

The simulation dome height at time t (FE output) Strength Coefficient Strain rate sensitivity exponent Strain hardening exponent p Bulging pressure (Bulge test) Rc Die corner radius (Bulge test) Rd Radius of curvature at dome apex (Bulge test) Time point at which simulation and experiment were

compared to Initial sheet thickness (Bulge test) td Instantaneous thickness at dome apex (Bulge test)

Greek Letters

Effective strain True strain in thickness direction (Tensile test, Bulge test) Principle strains in the sheet surface (Bulge test) Principle strain in the sheet thickness direction (Bulge test) Effective stress Principal stresses in the sheet surface (Bulge test)

Principal stress in the sheet thickness direction (Bulge test)

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TABLE OF CONTENTS

ABSTRACT ii

ACKNOWLEDGEMENT v

VITA vi

LIST OF FIGURES xi

LIST OF TABLES xiv

CHAPTER 1 Introduction 1

1.1 Sheet Hydroforming 1

1.2 Forming technology at Elevated Temperature (ET) 4

1.3 Forming of Light Weight Sheet Materials 7

1.3.1 Aluminum (Al) alloys 7

1.3.2 Magnesium (Mg) alloys 9

CHAPTER 2 Objectives and Approach 11

2.1 Objectives 11

2.2 Approach 11

2.3 Organization of the thesis 13

CHAPTER 3 Background and Literature Review 14

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3.1 Principles of Sheet Hydroforming with a Punch (SHF-P) 14

3.1.1 Process Window in SHF-P Process 17

3.1.2 Challenges in Warm hydroforming 19

CHAPTER 4 Determination of the flow stress for Aluminum and Magnesium

sheet alloys at Elevated Temperature 21

4.1 Biaxial Viscous Pressure Bulge (VPB) Test 21

4.2 Previous work on determining the flow stress data of sheet material at elevated

temperature 24

4.2.1 Virginia Commonwealth University (VCU), USA [Koc 2007] 24

4.2.2 ERC/NSM (OSU), USA [Al-Nasser 2009] 26

4.3 Determination of the flow stress at elevated temperature using the FE Inverse

Analysis Technique 28

4.3.1 Description of the FE inverse analysis technique 28

4.3.2 Experimental Setup and Results (Machine and Tool Design) 31

4.3.3 Finite Element Method (FEM) Database used for Surface Response Method

36

4.3.4 Results from the FE inverse analysis technique 40

4.3.5 Conclusions 47

CHAPTER 5 Cold and Warm Hydroforming of AA 5754 Sheet: FE Simulations

and Experiments 49

5.1 Model Part and Tools Geometry 50

5.2 Experimental Results 53

5.3 Finite Element Method (FEM) Setup 57

5.4 Comparison of FE predictions with experimental results 60

5.5 Conclusions 66

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CHAPTER 6 Case studies in sheet metal forming at elevated temperature 68

6.1 Warm Forming of MgAZ31B sheet alloy 68

6.1.1 Summary of Inputs for PAMSTAMP v. 2009 Simulation 69

6.1.2 Results for FE Simulations and comparison with experiments 70

6.1.3 Conclusion 75

6.2 Hot Stamping/Forming of 22MnB5 Steel to form experimental part 76

6.2.1 Objective 76

6.2.2 FE Setup 76

6.2.3 FE Results and comparison with the experimental data 77

6.2.4 Future Work 79

CHAPTER 7 Discussion, Conclusion and Future Work 80

7.1 Discussion and Conclusions 80

7.1.1 Determination of the flow stress at elevated temperature 80

7.1.2 Design of Sheet hydroforming with Punch Process (SHF-P) 82

7.2 Future Work 83

7.2.1 Determination of flow stress at elevated temperature 83

7.2.2 Simulation of SHF-P Process 83

REFERENCES 85

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LIST OF FIGURES

Figure 1.1-(a) Conventional Deep Drawing, (b) Fluid Forming (Sheet Hydroforming with

Punch) [Maki and Walter 2007] ......................................................................................... 2

Figure 1.2-(a) Schematic of Sheet Hydroforming with Punch [Aust, 2001], (b) Sheet

Hydroforming with Die [Jager, 2005] ................................................................................ 3

Figure 1.3-Stylish body shape for the Pontiac Solstice [Maki and Walter 2007] ............... 4

Figure 1.4- True stress-strain curves of AA5182-O at several elevated temperatures for

the rolling direction [Abedrabbo 2007] .............................................................................. 8

Figure 1.5-Activation of additional sliding planes for magnesium at elevated

temperatures [Doege 2001] ............................................................................................... 10

Figure 1.6- Effect of temperature on the flow stress curve of MgAZ31B alloy

[Neugebauer 2006]............................................................................................................ 10

Figure 3.1- Schematic illustration of the SHF-P process [Aust 2001] ............................. 14

Figure 3.2-Schematic of the warm hydroforming process [Groche 2002] ....................... 15

Figure 3.3- Process window in the SHF-P Process [Palaniswany 2007] .......................... 18

Figure 4.1- Viscous Pressure Bulge (VPB) test tooling [Al-Nasser 2009]....................... 22

Figure 4.2- Geometrical features of the VPB test [Al-Nasser 2009] (nomenclature is

before chapter 1) ............................................................................................................... 22

Figure 4.3- Hydraulic Bulge test setup with Feedback control loop [Koc 2007] ............. 25

Figure 4.4- Schematic of the Fluid-based Elevated Temperature Biaxial Bulge Test

Apparatus [(AES), LLC] ................................................................................................... 26

Figure 4.5- Methodology to obtain K, n and m values by calculating the lowest error

function (E) ....................................................................................................................... 30

Figure 4.6- Bulge height profile at various time steps (tn) ................................................ 30

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Figure 4.7- Gas bulge tooling with 2 Cameras and data acquisition systems [provided by

Interlaken] ......................................................................................................................... 32

Figure 4.8- Experimental pressure vs. Bulge Height for AA 5182 sheet samples formed at

Pressure Rate = 0.5 MPa/sec at various temperatures (30, 200, 250, 300 and 350 degree

Celsius) ............................................................................................................................. 34

Figure 4.9- Experimental Strain vs Time data for AA5182 @ 200⁰C for PR=0.5 MPa/sec

........................................................................................................................................... 35

Figure 4.10- Calculated Strain Rate (s-1

) vs Time for AA5182 @ 200⁰C for PR=0.5

MPa/sec ............................................................................................................................. 36

Figure 4.11- FE Setup Sketch ........................................................................................... 38

Figure 4.12- FE Input for Pressure vs time (for 3 Pressure Rates) ................................... 39

Figure 4.13- FE outputs (Bulge Height vs time and Strain vs time) collected at apex for

every combination of k, n and m and stored in the FE Database ...................................... 40

Figure 4.14- Comparison of Bulge Height vs. Pressure curve at (a) Temperature =30⁰C

and (b) 200⁰C for a linear Pressure Rate= 0.5 MPa/sec ................................................... 41

Figure 4.15-Flow stress curves for AA5182 obtained using Surface Response Method for

PR=0.5 MPa/sec (at variable Strain Rate) ........................................................................ 43

Figure 4.16- Flow stress curves for MgAZ61L obtained using Surface Response Method

for PR=0.5 MPa/sec (at variable Strain Rate) ................................................................... 44

Figure 4.17- Flow stress data obtained using the calculated Bulge Test (B.T.) data

(Surface Response) and Tensile Test (T. T.) data from [Abedrabbo 2007] ..................... 45

Figure 4.18- True stress-True Strain data for AA5182-O obtained using tensile tests at

260 ⁰C for several strain rate values [Abedrabbo 2007] ................................................... 46

Figure 5.1- Schematic of the tooling for SHF-P experiments: (a) initial setup (b) after

deformation, where ri = initial blank radius, Dd = draw depth and h = bulge height. ...... 51

Figure 5.2- Pressure flow schematic to heat or cool the tooling ....................................... 52

Figure 5.3- Pressure flow schematic to form the part using the SHF-P process by

controlling pressure with the relief valve.......................................................................... 53

Figure 5.4- Position of thermocouples on the ITC hydroforming machine ...................... 57

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Figure 5.5- Experimental output Pot pressure vs time for part formed at elevated

temperature (150 ⁰C)- Sample # 33 .................................................................................. 60

Figure 5.6- Thickness profile along the curvilinear length measured by the mechanical

indicator and compared with FE results for Sample #5 at room temperature (Punch

Stroke= 1.35 in, BHF = 6.81 kip, pot pressure = 304.7 psi) ............................................. 61

Figure 5.7- FE setup for the initial clearance of 1 mm between the blank holder and sheet

........................................................................................................................................... 62

Figure 5.8- (a) experimental workpiece, (b) Pam-Stamp result of quarter model, (c)

comparison part profile from FEM and experiment, for the SHF-P of Sample #33 (punch

stroke = 1.50 in, average temperature = 150C, pot pressure = 1494 psi) ........................ 63

Figure 5.9- Thickness profile along the curvilinear length measured by the mechanical

indicator and compared with FE results for Sample #33 (punch stroke = 1.50 in, average

temperature = 150C, pot pressure = 1494 psi) ................................................................ 64

Figure 5.10- Comparison of flange perimeter measurement and prediction between initial

blank and final part after SHF-P at room (Sample#5) and elevated (Sample#33)

temperatures ...................................................................................................................... 66

Figure 6.1- Schematic of warm forming tooling [Kaya 2008] ......................................... 70

Figure 6.2- Temperature vs Punch stroke at Point (P1) using variable HTC [CASE 1m:

Draw Ratio= 3, Punch stroke=65 mm , Forming velcity= 5 mm/sec] .............................. 72

Figure 6.3- Comparison of the results from FE simulations and experiments of CASE 1m,

for thinning distribution and punch load vs. stroke .......................................................... 73

Figure 6.4- Comparison of the results from FE simulations and experiments of CASE 4m,

for thinning distribution and punch load vs. stroke .......................................................... 74

Figure 6.5- Steps in the Forming stage at a) Initial position and b) Final position .......... 78

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LIST OF TABLES

Table 1.1- Significant variables in the Warm Forming Process [Kaya 2008] .................... 6

Table 3.1- Summary of possible defects in the hydroforming process. Recreated based on

[Palaniswamy 2007 and Yadav 2008] .............................................................................. 18

Table 3.2- Data required as input to FEM for accurate process simulation of the warm

sheet hydroforming process [Yadav 2008] ....................................................................... 20

Table 4.1- Summary of the tests performed at elevated temperature [Al-Nasser 2009] .. 26

Table 4.2-Summary of the experimental tests performed at room and elevated

temperature at ITC ............................................................................................................ 33

Table 4.3 Simulation Geometry Parameters ..................................................................... 37

Table 4.4- Flow Stress Coefficients Material Input Set .................................................... 38

Table 4.5-Predicted flows stress coefficients K, n and m for AA5182 at PR =0.5 MPa/sec

........................................................................................................................................... 42

Table 4.6- Predicted flows stress coefficients K, n and m for MgAZ61L at PR =0.5

MPa/sec ............................................................................................................................. 44

Table 5.1- Input parameters for SHF-P tests at room temperature (punch velocity=0.075

in/sec) ................................................................................................................................ 54

Table 5.2- Input parameters used to conduct warm SHF-P test at elevated temperature of

about 150°C (cycle time = 20 sec) .................................................................................... 55

Table 5.3- Comparison of experimental input to the output readings and measurements at

room temperature (initial flange perimeter, fi= 53.41 in) ................................................. 55

Table 5.4- Comparison of experimental input and output readings and profile

measurements, for SHF-P experiments at elevated temperature (Initial flange perimeter,

Fi = 53.41 in) .................................................................................................................... 56

Table 5.5- Input parameters for FE simulations of SHF-P ............................................... 59

xv

Table 5.6- Percent thinning affected by the applied pot pressure while keeping the other

process parameters constant (BHF ≈ 2.2 kiPs, punch stroke = 0.56 in, cycle time = 20 sec,

average temperature = 150°C) .......................................................................................... 65

Table 6.1- Thermal and mechanical data used for warm forming simulations of Mg

AZ31-O [Braga 2008] ....................................................................................................... 69

Table 6.2- Test conditions from [Braga 2008] were selected for preliminary simulations

........................................................................................................................................... 71

Table 6.3- Material Properties for 22MnB5 Sheet............................................................ 77

Table 6.4- Process Parameters in Hot stamping- Forming operation only ....................... 77

1

CHAPTER 1 Introduction

Due to the need to significantly reduce the part weights in automotive

manufacturing, the use of lightweight materials becomes very important.

Unfortunately, these materials are often associated with limited room

temperature formability. Due to this fact, production of large, complex sheet

metal components using forming technology frequently requires increased

expenditures. In order to find a solution to counter the disadvantages mentioned

above, the use of elevated temperatures as a process parameter in forming

operations represents a potential solution approach.

1.1 Sheet Hydroforming

In Sheet hydroforming with a Punch (SHF-P), also known as hydromechanical

deep drawing (HMD), the female die used in conventional stamping is replaced

by a pressure pot as seen in Figure 1.1. The sheet is deep drawn to form over the

punch surface, as the counter pressure is exerted on the sheet by the pressurizing

fluid. During the SHF-P, the friction at the punch sheet interface prevents the

sheet from sliding over the punch surface, thus giving a more uniform wall

thickness and increased deep drawability. Some other considerable advantages

of this process are: (1) it eliminates the need for a female die, thus lowering tool

costs; (2) it may reduce the number of stamping operations to form complex

parts and (3) it eliminates sidewall wrinkles during forming due to fluid

pressure, thug giving a better surface quality.

2

Figure 1.1-(a) Conventional Deep Drawing, (b) Fluid Forming (Sheet Hydroforming with

Punch) [Maki and Walter 2007]

This innovative forming technology (hydroforming) offers an additional

potential for weight reduction in automobiles when used with lightweight

materials like aluminum and magnesium alloys. However, the high alloy

percentages in aluminum alloys and the hexagonal structure of magnesium, lead

to a relatively low formability of these sheet materials at room temperature.

Thus, a promising strategy for the enhancement of the formability is the

conduction of the forming processes at elevated temperatures below the

recrystallization temperature [Geiger 2001].

Forming at elevated temperature will lower forming forces and increase the

ductility of the work piece as additional slip planes become active, especially for

magnesium alloys. Furthermore, while forming aluminum alloys springback is

an issue and can be drastically reduced when formed at elevated temperatures.

3

Sheet Hydroforming is conducted as Sheet Hydroforming with Punch (SHF-P)

and Sheet Hydroforming with Die (SHF-D) as seen in Figure 1.2. In the SHF-P

process, the sheet metal is forced against the punch by the hydraulic pressure,

whereas in the SHF-D process, the sheet metal is forced against the die by the

hydraulic pressure.

Figure 1.2-(a) Schematic of Sheet Hydroforming with Punch [Aust, 2001], (b) Sheet

Hydroforming with Die [Jager, 2005]

Sheet hydroforming has fewer restrictions, when forming complicated parts,

which allows styling designers and manufacturing engineers more flexibility

during the design process. For example in Pontiac Solstice ®, GM chose sheet

hydroforming (SHF-P) to manufacture its hood, door, deck lid and body

assemblies as seen in Figure 1.3 [Maki and Walter 2007].

(a) (b)

4

Figure 1.3-Stylish body shape for the Pontiac Solstice [Maki and Walter 2007]

A counter pressure deep-draw approach with a reverse toggle draw orientation,

called fluid forming is used to form Solstice‘s panels. During this process, the

punch with the shape of the part draws the sheet metal into a pressure vessel and

the change in fluid volume naturally builds a counter pressure. A relief valve

controls fluid pressure throughout the stroke. The limitation of conventional

deep drawing is localized thinning at the punch shoulder radius as shown in

Figure 1.1 (a). However, in Figure 1.1 (b), the water pressure pushed the sheet

firmly to the walls of the punch during the forming process and an increase in

friction along the wall ensures uniform thinning along the length of the wall

instead of one local area.

1.2 Forming technology at Elevated Temperature (ET)

The use of temperature opens up the possibility of significantly increasing the

ductility of the material and the associated forming capability. On the other

5

hand, it also offers the possibility of significantly reducing the yield point and

hence the forming forces and pressures required. In order to be able to fully

exploit the potential of temperature-supported forming processes and guarantee

economic production of complex component geometries, the related challenges

must be faced. Some of these include [Neugebauer 2006]:

1) Identification of suitable temperatures or temperature distributions

2) Integration of the temperature-supported forming process within the

overall process chain

3) Regulation of the temperature or temperature distributions within a

satisfactory time limit

4) Qualification of the FE simulation for use as an effective design tool

5) Ensuring safety in the workplace

6) Guaranteeing economic viability

With the increasing importance of temperature in various sheet metal forming

operations, a distinction has been adopted in practice. The forming process can

be classified based on the forming characteristics of materials below and above

recrystallization temperature. 1) Warm forming can be defined as the forming

operation below recrystallization temperature in which the yield point and

forming strength of the work piece are distinctly reduced. 2) In the hot

forming/stamping operation, permanent strengthening of the work piece can be

achieved [Neugebauer 2006].

Compared to room temperature forming, elevated temperature forming brings

many complexities which require a systems approach. Similar to other well-

established processes, it is also important to consider this process as a system. A

fundamental understanding of the relationship between the input and output

6

variables of the system is essential for developing a robust, productive and

economical manufacturing process. Issues that affect the warm forming process

are summarized in Table 1.1.

Table 1.1- Significant variables in the Warm Forming Process [Kaya 2008]

Sheet material and blank

Flow stress as a function of strain, strain rate,

temperature and microstructure (constitutive

equation)

Formability as a function of strain, strain

rate, temperature and microstructure

(forming limit curves)

Surface texture

Thermal / physical properties (density,

melting point, specific heat, thermal

conductivity and expansions, resistance to

corrosion and oxidation)

Initial conditions (composition, temperature,

history / pre-strain)

Plastic anisotropy

Property variation within the coil (rolling

technique) from same production line

Property variation for the same material from

different suppliers

Blank size, location, and thickness

Equipment used

Mechanical/Hydraulic/Servo Press

Constant/variable speed / production rate

Force / energy capabilities

Rigidity and accuracy

Tooling

Geometry of tools

Heating/cooling techniques

Insulation (between heated tooling and press)

Binder forces and application method

(hydraulic/air or servo motor driven cushion

pins)

Surface conditions

Material / heat treatment / hardness

Condition at tool/material interface

Lubricant type and temperature

Insulation and cooling characteristics of the

interface layer

Lubricity and frictional shear stress

Ease of lubricant application and removal

Deformation Zone

Deformation mechanics and model used for

analysis

Metal flow, velocities, strain (kinematic),

strain rate

Stresses (variation during deformation)

Temperatures (heat generation and transfer)

Product

Geometry

Increased dimensional accuracy/tolerances

compared to room temperature forming

Surface finish

Microstructure, metallurgical and

mechanical properties

Environment

Available man power

Air, noise and wastewater pollution

Plant and production facilities and control

Safety

Appropriate metal fire extinguishing systems

(for possible Mg fire)

7

1.3 Forming of Light Weight Sheet Materials

Because of the close correlation between vehicle weight and fuel consumption,

there is huge potential for meeting this challenge by employing measures to

improve performance capability and increase the effectiveness of engines, but

above all by reducing the weight of components. The objective of lightweight

construction design concepts is to minimize the dead weight of a construction

without having an effect on its function, or safety. In addition to condition-

related and form-related or structure related lightweight construction, the use of

lightweight construction materials constitutes one of the most promising

strategies capable of contributing to the fulfillment of this task [Geiger 2001].

Examples of sheet metal materials that exhibit lightweight construction are

aluminum, magnesium or thin high-strength steel materials, and some titanium

alloys.

1.3.1 Aluminum (Al) alloys

Aluminum alloys offer the largest weight reduction after Magnesium alloys, but

their formability is also low at room temperature. Al sheet alloys with yield

strengths comparable to those of low carbon steels are less formable by current

processes used in the automotive industry. When attempting to form Al alloy

parts on dies normally used for steels, splits often develop in the regions

subjected to severe stretching or drawing. In today‘s practice, sections from Al

alloy tubes are only used for calibration (i.e. expanded with very limited amount

of strain; 4% to 6% versus 35% to 40% in steels) due to their low formability. The

reason for the lower formability of two-phase alloys, as opposed to single-phase

alloys or pure metals, is that the strengthening effect of the second-phase reduces

8

ductility. This is particularly apparent in Al alloys. Thus thoughts have turned to

forming at elevated temperatures [Shehata 1978].

[Abedrabbo 2007] conducted uniaxial tests for Aluminum alloys at several

elevated temperatures in the range of 25–260 ⁰C. To study the strain-rate

sensitivity of the material, uniaxial tests were performed under several strain

rates (0.001–0.08 s-1) at each temperature. The materials were assumed to follow

the Field and Backofen constitutive model ( ) and the parameters were

obtained by fitting the experimental data obtained in the uniaxial tensile test. As

temperature increases, flow stress of the material decreases with a corresponding

increase in the elongation to failure (see Figure 1.4). This is due to the increase in

the mobility of the solutes which eliminates the serrated flow behavior.

Figure 1.4- True stress-strain curves of AA5182-O at several elevated temperatures for

the rolling direction [Abedrabbo 2007]

9

[Li 2003] attributed the increase in the total elongation of AA5754+Mn and

AA5182 to the increase in post-uniform elongation. This is related to the higher

m-value at elevated temperature which results in more resistance of the material

to strain localization in the neck region (where strain rate is high) after

instability. Moreover, it was shown that one order of magnitude increase in the

strain rate, at elevated temperature, will dramatically reduce the total elongation

of these two alloys.

1.3.2 Magnesium (Mg) alloys

Mg and Al are 78% and 65% lighter per unit volume than Fe respectively.

Magnesium has the highest strength-to-weight ratio of all commercially available

structural materials. Another important factor is the ease of fabrication and

joining. Magnesium is quite easy to form; often, operations that require several

steps for steel can be done in only one step for Mg. But due to the hexagonal

closed packed (hcp) crystal lattice structure at room temperature, magnesium

provides only low ductility for cold forming operations. At temperatures above

225⁰ C, additional sliding planes are activated (see Figure 1.5) thus increasing

ductility and lowering the yield stress, besides the conventional temperature

effect on ductility and yield stress [Yadav 2008]. Figure 1.6 shows the effect of

temperature on the flow stress curve of MgAZ31B alloy (Thickness= 1.3 mm).

10

Figure 1.5-Activation of additional sliding planes for magnesium at elevated

temperatures [Doege 2001]

Figure 1.6- Effect of temperature on the flow stress curve of MgAZ31B alloy

[Neugebauer 2006]

Due to this raised ductility of Mg alloy and its growing importance in the

automotive industry, many investigations are underway to get a better

understanding of the material behavior. Thus, it is very important to have a

reliable test which could predict the flow stress of this material at elevated

temperatures.

11

CHAPTER 2 Objectives and Approach

2.1 Objectives

1) The overall objective of this study is to determine the flow stress of

Aluminum and Magnesium alloy sheet materials, of interest to the

automotive industry, at room and elevated temperatures, respectively.

2) In addition improve the sheet hydroforming process of aluminum alloys

using FE simulations and validated by experimentation. More

specifically, the goal was to establish an efficient method for estimating

the process parameters (Blank Holder Force (BHF), pot pressure) that are

used for room and elevated temperature SHF-P processes to produce

defect-free parts.

2.2 Approach

The following tasks were performed to achieve the objective (1) of the study: To

determine flow stress of Aluminum and Magnesium alloys at elevated

temperature.

1) To analyze formability of the following aluminum alloys: AA 5182, AA

5754 (at room and elevated temperature) by FEM simulations in the code

DEFORM 2D.

12

2) To create a FEM Database for several values of K, n and m, chosen based

on [Abedrabbo 2007]. This database would include the bulge height, strain

of the bulge at the apex point at several time steps during the Viscous

Pressure Bulge (VPB) test.

3) To establish a Surface Response (SR) methodology to approximate the

flow stress data for the VPB test of aluminum and magnesium alloys at

elevated temperature. The flow stress data should be defined by the

power law equation . This methodology takes the bulge height

vs pressure, and strain from the FE simulations at various time steps and

compares it to the experimental bulge height vs pressure, and strain.

4) To program the methodology in MATLAB. Thus the following steps are

conducted: reading experimental data, comparing experimental data vs

FE database, calculation of the error function (difference between the

experimental and the FE data for the bulge height and strain)

5) To determine the lowest error function for the several combinations of K,

n and m by plotting the surface response.

Approach for objective (2) - Establish a method to improve the warm

hydroforming of light weight alloys using FE simulations and experiments:

1) To analyze formability of the aluminum alloy AA5754-O by FE

simulations using the FE code PAMSTAMP.

2) Conduct experiments to find the process parameters (blank holder force,

pot pressure) that are suitable for SHF-P process.

13

3) Understand the working of the ITC Hydroforming machine located at the

G. M. Technical Center (Interlaken UniTEST software, Fluid Pressure

Control System and Temperature Control System-Mokon System).

4) Measure the experimental samples either by CMM or height gauge

measurement system to compare them with the FE results.

2.3 Organization of the thesis

The following tasks were performed to achieve the objectives of the study:

1) Conduct a literature review on the Sheet Hydroforming process at room

and elevated temperature (Chapter 3)

2) Review the previous work/literature on determining the flow stress data

at elevated temperature (Chapter 4)

3) Develop a method to determine the flow stress of light weight alloys at

elevated temperature using the FE inverse analysis technique (Chapter 4)

4) Conduct experimental tests of different Aluminum and Magnesium alloys

at elevated temperature using the bulge test at ITC and applying the

surface response methodology to obtain the flow stress data (Chapter 4).

5) Suggest a methodology for designing process parameters (Pot pressure,

blank holder force) in SHF-P of AA5754-O by using FE simulation and

experiments (Chapter 5).

6) Conduct case studies on non-isothermal forming using the FE code PAM-

STAMP: i) Warm forming of MgAZ31 alloy and ii) Hot

Forming/Stamping of 22MnB5 Steel (Chapter 6)

14

CHAPTER 3 Background and Literature Review

3.1 Principles of Sheet Hydroforming with a Punch (SHF-P)

For the sheet hydroforming with punch (SHF-P) forming method, a sheet blank

is deep drawn against a counter pressure from compressed fluid inside the pot,

as presented in Figure 3.1, rather than against a female die as in conventional

stamping operations. The medium in the pressure pot can be either ―passive‖

(pressure generated due to incompressibility of the medium during forward

stroke of the punch) or ―active‖ (pressure generated by an external pump) as

defined by [Aust 2001].

Figure 3.1- Schematic illustration of the SHF-P process [Aust 2001]

For the warm hydroforming method, the sheet and the flange portion of the die

and the blank holder are heated to the required temperature (see Figure 3.2). The

15

pressurizing fluid may be maintained at slightly higher than room temperature,

while the punch is cooled. During the process, the lower temperature of the

punch cools the portion of the sheet that is in contact with the punch and

increases its load carrying capacity. Thus, failure caused by excessive thinning is

postponed and the process yields a higher limiting draw ratio (LDR) than those

obtained from deep drawing at room temperature [Groche 2002].

Figure 3.2-Schematic of the warm hydroforming process [Groche 2002]

The most common defects encountered during the SHF-P process are wrinkling,

excessive thinning (leading to fracture) and leaking of the pressurized fluid

during forming. Conventionally, the process parameters are estimated by

performing trial and error experiments which requires considerable time and

effort. Therefore, the present research focuses on the use of finite element (FE)

simulations along with physical experiments to estimate the optimum blank

holder force (BHF) vs. punch stroke and optimum pressure vs. punch stroke that

is needed to form a part successfully. This preliminary study assumes

16

isothermal conditions in the analysis of SHF-P at elevated temperatures

(meaning all tooling components, blank and fluid were heated to approximately

the same temperature).

Following are the benefits of the SHF-P process compared to conventional

stamping [Al-Nasser 2009]:

1) SHF-P gives higher limiting draw ratio (LDR) than conventional

stamping, since the pot pressure separates the sheet from the die corner

radius, so no friction energy is consumed at this location. The process

helps to lower the punch force and increases the LDR.

2) SHF-P has lower tooling cost: As mentioned earlier in the CHAPTER 1,

the Solstice body is a complicated deep-drawn component, which

undergoes three fluid forming/hydroforming operations as compared to

five stamping operations. Also, elimination of the female die results in

lower tool cost and lower die development time.

3) Pot pressure reduces/eliminates side wall wrinkling.

4) Better surface quality can be achieved as the outer surface of the sheet is

in contact with fluid only, thereby reducing the chance of tool marks.

5) Also a higher dimensional accuracy can be achieved for simple

symmetric parts.

Disadvantages of the hydroforming process [Al-Nasser 2009]:

1) Higher cycle time/ lower production rate. Sheet hydroforming is

slower than conventional stamping, because it takes time to control fluid

17

pressure and refill the die with fluid. Because of this, sheet hydroforming

is more suitable for small-lot production—from 5,000 to 40,000 vehicles

per year.

2) As a result of pot pressure, both the required ram and blankholder force

are larger than in conventional stamping (larger presses required).

3) Dimensional tolerances, especially at corner radii, may not be attainable

without a solid die.

3.1.1 Process Window in SHF-P Process

A successfully formed part will be characterized by minimum thinning and no

wrinkles, and will be formed without leaking/ minor leakage. In the SHF- P

process, the two main process parameters, the pot pressure and blankholder

force (BHF), should be optimized to successfully create a part. The limits of the

two parameters in which the process operates successfully are called the

―Process Limits‖ and the region within the limit is called the ―Process Window‖

as shown in Figure 3.3.

18

Figure 3.3- Process window in the SHF-P Process [Palaniswany 2007]

Table 3.1- Summary of possible defects in the hydroforming process. Recreated based on

[Palaniswamy 2007 and Yadav 2008]

# Type of Defect Cause Avoided/Postponed

1 Flange wrinkling -BHF too small

2 Side wall wrinkling -Insufficient pressure

-Punch geometry

-Excessive flange wrinkling

3 Fracture -High BHF

-Insufficient Pot Pressure

-Increasing Pot Pressure

-Decreasing BHF

19

4 Leaking of the pressurized medium

-Low BHF -Increase BHF or Reduce Fluid Pressure

5 Bulging against drawing direction

-Excessive fluid pressure -Decreasing the pressure

Table 3.1 summarizes the possible defects in the SHF-P process, explaining the

reasons for occurrence and possible methods of avoiding or postponing the

defects.

[Meinhard 2005] stated that small BHF should be applied at the beginning of the

process and then increased toward the end of the process, because the sheet

thickens as it flows in the flange and parts of the flange loose contact with the

tools at the end of the stroke, thus wrinkling may occur. Moreover, higher BHF is

required to generate the same moment about the die corner (in order to prevent

lifting) at the end of the stroke where the flange width becomes smaller.

3.1.2 Challenges in Warm hydroforming

According to the previous research conducted at ERC/NSM, the results for the

warm forming using finite element simulations were compared with the

experimental results available in [Droder 1999] literature. DEFORM 2D and 3D

codes were used to simulate cylindrical cup and rectangular pan geometries

using magnesium alloys. The results from the simulations predicted a higher

punch force and thinning distribution as compared to the experimental results.

For accurate finite element simulation of the warm sheet hydroforming process,

the mechanical and thermal changes in the workpiece need to be modeled as

shown in Table 3.2. Material flow stress data and material anisotropy are needed

20

over the range of forming temperatures (25 to 300⁰ C), along with strain rate

sensitivity. Heat transfer coefficient and friction between the workpiece and the

tools are also needed.

Table 3.2- Data required as input to FEM for accurate process simulation of the warm

sheet hydroforming process [Yadav 2008]

Mechanical data (for sheet) Thermal data (for sheet,

forming medium and hard

tools)

Process data

-Young‘s Modulus

-True stress-strain data

(function of temperature

and strain rate)

-Yield surface (function of

temperature)

-Anisotropy coefficients

(function of temperature)

-Thermal expansion

-Thermal conductivity

-Heat capacity

-Heat transfer

-Heat dissipation

-Friction between sheet and

tools

-Temperature (sheet and

tools)

-Interface pressure

-Process parameters

(forming pot pressure,

applied blank holder force)

Currently, in most commercially available FE codes, the interface of heat transfer

coefficient is assumed to be constant. But the heat transfer between the sheet and

the tools is dependent on the interface contact pressure. Since contact pressure

varies with location, the heat transfer coefficient should be an input as a function

of pressure [Yadav 2008]. PAMSTAMP version 2011 is capable of conducting

non-isothermal simulations using the heat transfer coefficient as a function of

pressure and/or gap. Additionally, it gives a user the option to input the

Young‘s Modulus (E), Poisson‘s ratio (υ), thermal density, thermal conductivity,

and specific heat capacity as a constant or as a function of temperature.

21

CHAPTER 4 Determination of the flow stress for Aluminum

and Magnesium sheet alloys at Elevated Temperature

4.1 Biaxial Viscous Pressure Bulge (VPB) Test

For the determination of flow curves at elevated temperatures and constant

strain rates, a particularly suitable measure is the viscous pressure bulge (VPB)

test. In comparison with tensile testing, this allows higher true strains to be

obtained. The higher true strains that can be reached in hydraulic bulge testing

as compared with tensile testing considerably reduce the required extrapolation

of the flow curve values for the numerical simulation based on finite elements.

Figure 4.1 is a schematic of the tooling used in the VPB test at Ohio State

University (OSU). The upper die is connected to the slide and the cushion pins

support the lower die (the blank holder) to provide the required clamping force.

The punch in the lower die is fixed to the press table and therefore stationary.

At the beginning, the tooling is open and the viscous material is filled into the

area on the top of the punch. When the tooling closes, the sheet is totally

clamped [Figure 4.1] between the upper and lower dies using a lockbead to

prevent any material draw-in, in order to maintain the sheet in a pure stretching

condition throughout the test. The clamping force (the selected press cushion

force) depends on the material and thickness tested. The slide then moves down

22

together with the upper die and blank holder. Consequently, the viscous

medium is pressurized by the stationary punch and the sheet is bulged into the

upper die. Since the tools are axisymmetric, the sheet is bulged under balanced

biaxial stress. Figure 4.2 shows the details of the geometrical features of the VPB

test tooling.

Figure 4.1- Viscous Pressure Bulge (VPB) test tooling [Al-Nasser 2009]

Figure 4.2- Geometrical features of the VPB test [Al-Nasser 2009] (nomenclature is

before chapter 1)

(a) Before Forming (b) After Forming

Upper die

Lower die

Potentiometer

Test Sample

Viscous Medium

Stationary Punch

Pressure Transducer

23

The membrane theory is usually used to calculate the flow stress from the

experimental data [Gutscher 2000]. This theory assumes that the dome is

spherical in shape and neglects bending stresses in the sheet. The relationship

between membrane stresses and process parameters is:

Equation 1

Under balanced biaxial tension, which is the case in the bulge test, the formula

reduces to:

Equation 2

The average compressive stress in the thickness direction is -p/2. Using Von-

Mises yield criterion, the effective stress and effective strain can be calculated:

√

Equation 3

Equation 4

√

Equation 5

Equation 6

It can be noticed from Equations 4 and 6 that the pressure, radius of curvature

and thickness at the dome apex should be measured to be able to calculate the

effective stress and strain. To reduce the number of measured parameters,

different FE-based inverse analysis methodologies are used at the ERC/NSM

where only two relatively easy-to-measure parameters are required. These are

24

the bulging pressure, measured using a pressure transducer and the dome

height, measured using a potentiometer.

4.2 Previous work on determining the flow stress data of sheet material at

elevated temperature

4.2.1 Virginia Commonwealth University (VCU), USA [Koc 2007]

[Koc 2007] used a non-contact sensor (ARAMIS system) in calculating strains at

the dome apex. At elevated temperatures, the influence of strain rate in

deformation needs consideration. Thus the author suggests, in characterizing

material properties, it is essential to collect data at constant strain rate. Through

flow control, this study focused on obtaining a near constant strain rate at the

dome apex during the bulging process. Flow stress was calculated using the

membrane theory assumptions (spherical dome shape) discussed in Section 4.1.

25

Figure 4.3- Hydraulic Bulge test setup with Feedback control loop [Koc 2007]

In this study, magnesium alloy AZ31B-O blanks were bulged at four different

temperatures (room, 100, 200, and 300°C) and at two different strain rates (0.0013

and 0.013 s-1). The test results revealed the effects of temperature and strain rate

on the sheet formability as well as the failure mode. In general, better sheet

formability (i.e., more elongation, lower flow stress) could be obtained when

forming processes were carried out at elevated temperatures or at low forming

rates. The premature shear fracture (i.e., die corner rupture) could be prevented

when bulging above 200°C and at the lower strain rate.

26

4.2.2 ERC/NSM (OSU), USA [Al-Nasser 2009]

A fluid-based elevated temperature biaxial bulge system was designed and

developed by Applied Engineering Solutions, LLC (AES) wherein the tested

samples were submerged within a heated fluid. Die design was collaboratively

accomplished with the CPF. Figure 4.4 shows a schematic of the machine design.

Figure 4.4- Schematic of the Fluid-based Elevated Temperature Biaxial Bulge Test

Apparatus [(AES), LLC]

Table 4.1- Summary of the tests performed at elevated temperature [Al-Nasser 2009]

Material Thickness

(mm)

Temperature (oC) Pressurization rate (in3/sec)

# of samples/ condition 200 230 260

AA5754-O 1 √ √ √ 0.2 and 2 3

AA5182-O 1 √ √ √ 0.2 and 2 3

AA3003-O 1 √ √ √ 0.2 and 2 3

LVDT

Sensors

Heat Exchanger

Fluid

Preheater

Hydraulic

Power

Supply

Computer

Controller

Fluid Pressure

Intensifier

Hydraulic Ram

Hydraulic Ram

Bulge Test

Specimen

Fluid Tank

Die Seal Plate

Fluid

Heater

27

Optimization Technique:

Since the material at elevated temperature is strain rate sensitive, two samples,

one pressurized fast (2 in3/second), and the other pressurized slow (0.2

in3/second) were tested and the resulting dome height evolutions were

compared with FE simulations run with the corresponding pressure vs. time

curves. LS-OPT generates LS-DYNA FE simulations files for selected

combinations of the three parameters; K, n, and m. In Each LS-DYNA file, two

bulging processes (Fast and Slow) are simulated simultaneously and the dome

height in each can be extracted.

Conclusions:

The optimal K, n, and m values (and corresponding flow stress curves) obtained

by applying the new methodology to the ET bulge test did not match with the

flow stress data available in the literature [Abedrabbo 2006]. This discrepancy

may be due to different reasons:

1) Problems of leakage and pre-bulging were observed in the experiments

2) The data in the literature is a tensile data, while data in this study is a bulge

test data (biaxial)

3) The optimization methodology needs to be further improved.

28

4.3 Determination of the flow stress at elevated temperature using the FE

Inverse Analysis Technique

As opposed to the previous studies/methods to determine the flow stress

coefficients at elevated temperature, this FE Inverse Analysis technique does not

require the assumption that the bulge profile needs to be spherical at the apex

location.

Different methods of heating the sheet in hydraulic bulge testing exist. Most

common method is holding the sheet between heated tools and applying air or

gas for obtaining the deformation. Another approach in hydraulic bulging of

sheets is to conduct the test under a heated liquid bath. In our study, a gas

pressure elevated temperature biaxial bulge system was used, which is designed

and developed by Interlaken (ITC).

4.3.1 Description of the FE inverse analysis technique

At CPF, we developed a technique to approximate flow stress data of lightweight

alloys through Viscous Pressure Bulge (VPB) test at elevated temperatures. This

technique should be capable to use experimental data (bulge height and strain)

from a VPB test to meet our objective (1)- to calculate the flow stress in terms of

the power law equation , where is the stress, is the strain, is the

strain rate and K, n and m are coefficients that shape the flow stress of the

material.

1) In light of this objective (1), a methodology called Surface Response (SR)

Approach, which is based on Inverse Analysis, has been proposed. This

29

methodology takes advantage of the optical measuring fixture developed

by Interlaken (ITC) and the capabilities of Finite Element Modeling.

2) The Finite Element tool is used to conduct a wide number of simulations

of the VPB test of a lightweight alloy under a wide range of values for

coefficients K, n and m. The ranges of K, n and m are taken from the

tensile tests at elevated temperature conducted by [Abedrabbo 2007]. By

doing this we are mapping the different bulge forming behaviors that the

alloy can present under different temperature and pressure conditions.

The FE simulation output of interest are the bulge height, strain at the

apex of the bulge profile and the pressure rate.

3) This Surface Response approach can be described as taking the

experimental data from VPB test for a given material and comparing it

with the different simulations conducted in the FE code. The simulation

that resembles the most to the experimental behavior of the VPB test will

provide the best approximation for that material to the power law

equation.

4) Transferring this idea to a more systematical approach, an extensive Finite

Element Database is built. This database contains bulge height and strain

distribution along the apex of the bulge and at different pressure level. An

error function is defined in the methodology that compares every

experimental variable/output (i.e. bulge height, etc.) with its equivalent in

the FE database at the same bulge location and pressure level (see Figure

4.5 and Figure 4.6). An error function is calculated for every combination

of K, n and m that exists in the database. The minimum error function is

selected as the best approximation and its corresponding values of K, n

and m assumed as the resulting flow stress coefficients.

30

Figure 4.5- Methodology to obtain K, n and m values by calculating the lowest error

function (E)

Figure 4.6- Bulge height profile at various time steps (tn)

Bulge height, Hexp vs TimeOne experimental output is

compared with FE output for

every combination (Kj, nj

and mj)Strain, Sexp vs Time

FE Output

Comparison

Every comparison

results in an error

function (E1, E2,

…, Ej)

Bulge height, HFE vs Time

Strain, SFE vs Time

Experimental Output

31

Equation to calculate the Error function (Ej) calculated for every combination of

Kj, nj, mj:

√∑(

)

4-1

Where,

Hexp(t)= Bulge Height at time t- Experimental measurement, HFE(t)= Bulge Height at time

t from FE simulation j, j= number of simulations

4.3.2 Experimental Setup and Results (Machine and Tool Design)

Figure 4.7 shows a schematic of the machine design at ITC, which consists

essentially of the tools (the forming upper and lower die, 2 camera systems, light

source, and 2 data acquisition systems. One of data acquisition systems (on the

left) collects experimental data for bulge height, strain, thickness and curvature

of the formed sample. The other system (on the right) controls the gas pressure

either by setting either pressure or strain limits. Thus, forcing the gas pressure to

drop immediately as one of these limits has reached.

Experimental test procedure:

The steps to conduct a test are as follows:

1) Prepare a speckle pattern on sample for the correct use of cameras.

2) Gas tank and pump should be turned on. Set the controls for linear pressure ramp input and maximum pressure/strain limit.

3) Both dies should be at required temperature.

32

4) Position the sample and close the dies as much as possible without clamping, wait 3 to 5 minutes to allow heating of the sample.

5) Apply clamping force and open the controlled gas inlet, confirm that pressure control command and pressure reading match.

6) Initialize optical gauge and start recording.

7) Proceed with bulge. It will stop according to maximum pressure or maximum strain criteria.

8) Extract sample.

9) Enter to post-processor, and compute all pictures to obtain all necessary information such as bulge height, strain, thickness and curvature of the bulge profile.

Figure 4.7- Gas bulge tooling with 2 Cameras and data acquisition systems [provided by

Interlaken]

2 cameras

Upper die

Lower die

Light

source

Lock bead

Gas

pressure

inlet

Gas bulge tooling with camera

Bulge height (Hexp)

Strain (Sexp)

Test is controlled by

either strain/ pressure

limit, meaning that

pressure input stops

when reaching one of

these stopping criteria

33

The pressure input selected were linear ramps (see Figure 4.12) based on the

discussions and the preliminary experimental results from the sponsor. Three

pressure rates; 0.1 MPa/sec (14.5 psi/sec), 0.5 MPa/sec (72.5 psi/sec) and 2.5

MPa/sec (362.5 psi/sec) were selected that accounted for a wide range of strain

rates.

The tooling dies (upper and lower) are made of A2 tool steel and are heated by

the heat bands. The heating time was quite fast (e.g. dies reach 200C in 20 min).

The optical system consisted of two cameras mounted on a fixture on top of the

dies. The optical system needed sporadic calibration for accuracy of results.

Post-processing the data required importing all pictures taken by the cameras,

selecting an area to analyze, and compute the parameters of interest. Post-

processing data was obtained for each test including: bulge height, strain,

pressure, thickness and curvature of the bulge. The average time to conduct one

test from preparation to post processing was around 20 min.

Testing Matrix

Table 4.2-Summary of the experimental tests performed at room and elevated

temperature at ITC

Material Thickness

(mm)

Temperature (oC) Pressurization rate (MPa/sec)

# of samples/ condition

25 150 200 250 300 350

AA5182-O

1.1 √ - √ √ √ √ 0.1, 0.5, 2.5 2

Mg AZ61L

1.1 - √ √ √ √ - 0.1, 0.5 2

Figure 4.8 shows the plot for experimental Bulge Height, Hexp vs Pressure, Pexp

for AA 5182 formed at a linear pressure rate of 0.5 MPa/sec. This experimental

34

data will be used to compare with the FE output of Bulge Height vs Pressure.

The combination of k, n and m which calculates the minimum error value will be

used to obtain the flow stress data of the material.

Figure 4.8- Experimental pressure vs. Bulge Height for AA 5182 sheet samples formed at

Pressure Rate = 0.5 MPa/sec at various temperatures (30, 200, 250, 300 and 350 degree

Celsius)

Post-processing the experimental data gives the Strain vs time (see Figure 4.9) at

the apex location on the formed sample. This strain vs time data can be further

differentiated on small time intervals to calculate the Strain Rate vs Time as

shown in the equation below:

0

5

10

15

20

25

30

0 2 4 6 8 10

Bu

lge

Hei

ght,

Hex

p (

mm

)

Pressure, Pexp (MPa)

350 C

300 C

250 C

200 C

30 C

35

t= time step S

exp (t

2) = Experimental strain at time step (t

2)

Sexp

(t1) = Experimental strain at time step (t

1)

The purpose of obtaining the data for Strain (ε) vs time and calculating the Strain Rate

( ) vs time is to give the flow stress in terms of the Power Law Equation.

Figure 4.9- Experimental Strain vs Time data for AA5182 @ 200⁰C for PR=0.5 MPa/sec

0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Stra

in (

mm

/mm

)

Time (sec)

Experimental data: Strain vs Time

36

Figure 4.10- Calculated Strain Rate (s-1

) vs Time for AA5182 @ 200⁰C for PR=0.5

MPa/sec

4.3.3 Finite Element Method (FEM) Database used for Surface Response

Method

Several methods for building the flow stress data through FEM have been

implemented. The selected approach for this work defines a VPB test database

obtained from FE simulations. This FE database includes: time, pressure, bulge

height and strain at the apex of the formed sample. The database intends to cover

ranges of coefficients K, n and m that would describe the flow stress of aluminum

0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Stra

in R

ate

(sec

-1)

Time (sec)

Calculated data: Strain Rate vs Time

37

and magnesium alloys at different temperatures. The FE database is an essential

part of the determination of flow stress.

The Viscous Pressure Bulge (VPB) Test is simulated in the Finite Element code

DEFORM-2D with an axisymmetric model and the geometry parameters

mentioned in Table 4.3:

Table 4.3 Simulation Geometry Parameters

diameter of the cavity, dc 105.66 mm

Die Radius, Rc 6.35 mm

Initial Sheet Thickness, t0 1 mm

Based on the conducted literature review on aluminum alloys flow stress at

elevated temperatures, the material properties used for the project are provided

by the following work by [Abedrabbo 2006]. [Abedrabbo 2006] presents the

resulting K, n and m coefficients obtained from tensile tests for aluminum alloys

(AA3003-H111, AA5182-O and AA5754-O) at different material temperatures,

ranging from room temperature up to 260 °C.

The values for the flow stress coefficients K, n and m have the following ranges:

70-550 MPa, 0.08-0.32 and 0.01-0.1 respectively. With the purpose of building a

FE database that maps through the spectrum of values, the ranges are discretized

and combined. Thus, the VPB test is simulated for various ranges of K, n and m

at different temperatures. Table 4.4 lists the ranges of coefficients that are

simulated in DEFORM-2D, the number of simulations is defined by number of

possible combinations of these coefficients.

38

Table 4.4- Flow Stress Coefficients Material Input Set

K n m

70 0.08 0

130 0.14 0.01

190 0.2 0.035

250 0.26 0.05

310 0.32 0.065

430 0.085

550 0.1

Figure 4.11 shows the setup of the FE Simulation in DEFORM-2D with the

geometrical parameters indicated.

Figure 4.11- FE Setup Sketch

39

Since this is a strain rate sensible process due to temperature, it is important to

simulate the VPB test at different strain rates. Three inputs of pressure have been

selected, these being: 2.5 MPa/sec (362.5 psi/sec), 0.5 MPa/sec (72.5 psi/sec),

and 0.1 MPa/sec (14.5 psi/sec), all of them in linear increment. In result, for each

pressure rate (Pressure vs time) a set of simulations as mentioned in Table 4.4

should be conducted. The pressure rates are applied as boundary conditions

along the sheet inner sheet profile as shown in Figure 4.12.

Figure 4.12- FE Input for Pressure vs time (for 3 Pressure Rates)

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100

Pre

ssu

re (

MP

a)

Time (sec)

FE Input-Pressure vs Time

Pressure Rate=0.1 MPa/sec Pressure Rate=0.5 MPa/sec

Pressure Rate=2.5 MPa/sec

40

The simulations listed will assemble the FE database for a given pressure rate.

The other FE model parameters (geometry, symmetry, step size, etc.) should

remain the same. Once the FE simulations are finished, the following data will be

extracted from every simulation: time, pressure, instantaneous height at the apex

of the bulge (HFE) and instantaneous strain (SFE) at the apex of the bulge (see

Figure 4.13).

Figure 4.13- FE outputs (Bulge Height vs time and Strain vs time) collected at apex for

every combination of k, n and m and stored in the FE Database

4.3.4 Results from the FE inverse analysis technique

To simplify the process of matching one experimental data of Pressure vs Bulge

Height to several combinations of K, n and m from the FE output (Pressure vs

Bulge Height) we developed a code using MATLAB. This code would calculate

the error function (Ej) using the Equation shown below. Using this equation, the

K

n

n1 n2 n3 n4 … nj

K1

K2

K3

K4

…

Kj

m1

m2

…mj

m

0 10 20 30 40 50 60 700

5

10

15

20

25

30

35

40

Radial Coordinate (mm)

Bul

ge H

eigh

t (m

m)

tn

t2

t1

Bulg

e H

eig

ht (m

m)

Radial Coordinate (mm)

r0 r1 r2 r3 r4 r5

FE Database

For every combination of Kj, nj and mj,

Bulge Height (HFE) vs time, and Strain (SFE)

vs time output is collected at apex point

41

MATLAB code would compute the error function (Ej) [see Equation 4-1] for

every combination of K, n and m in the FE database. Finally, MATLAB would

give out the corresponding combination of K, n and m that matched the

experimental data of Bulge Height vs Pressure closest.

Figure 4.14 shows the comparison of the Bulge Height vs Pressure curve at a)

Room temperature (30 ⁰C) and b) at 200 ⁰C for linear Pressure Rate = 0.5

MPa/sec. The values of K and n tend to decrease with increase in temperature

and the m value increases with an increase in temperature.

Figure 4.14- Comparison of Bulge Height vs. Pressure curve at (a) Temperature =30⁰C

and (b) 200⁰C for a linear Pressure Rate= 0.5 MPa/sec

0 1 2 3 4 5 60

5

10

15

20

25

Pressure vs Height

Pressure (MPa)

Heig

ht

(mm

)

FE database approximation

experimental data

0 1 2 3 4 5 6 70

5

10

15

20

Pressure vs Height

Pressure (MPa)

Heig

ht

(mm

)

FE database approximation

experimental data

K=430 n=0.08 m=0.05K=550 n=0.20 m=0

Bulge Height vs Pressure Bulge Height vs Pressure

42

The same methodology has been applied to the experimental data obtained at

ITC for AA 5182 and MgAZ61L at several temperatures and the corresponding

flow stress coefficients (K, n and m) are listed in Table 4.5 and Table 4.6,

respectively. Please note that currently the MATLAB code is programmed to

approximate the experimental test to the existing K, n and m coefficients in the

current FE database (listed in Table 4.4). Using the strain and calculated strain

rate values we have plotted the flow stress for AA 5182 (see Figure 4.15) and

MgAZ61L (see Figure 4.16) alloys for various temperatures by curve fitting them

in the Power Law Equation.

Table 4.5-Predicted flows stress coefficients K, n and m for AA5182 at PR =0.5 MPa/sec

Temperature (⁰C)

K (MPa)

n m Strain Rate (s-1)

30 550 0.2 0 0.005-0.05

200 430 0.08 0.05 0.008-0.16

250 430 0.08 0.085 0.002-0.08

300 310 0.08 0.065 0.003-0.18

350 250 0.14 0.035 0.004-0.095

43

Figure 4.15-Flow stress curves for AA5182 obtained using Surface Response Method for

PR=0.5 MPa/sec (at variable Strain Rate)

0

50

100

150

200

250

300

350

400

450

0 0.05 0.1 0.15 0.2 0.25

Tru

e St

ress

(M

Pa)

True Strain

AA5182 at PR= 0.5 MPa/sec (Variable Strain Rate)

30 C 200 C 250 C 300 C 350 C

30 C

200 C

250 C

300 C

350 C

44

Table 4.6- Predicted flows stress coefficients K, n and m for MgAZ61L at PR =0.5

MPa/sec

Temperature (⁰C) K (MPa) n m Strain Rate (s-1)

150 430 0.08 0.01 0-0.023

200 430 0.08 0.05 0-0.020

250 250 0.08 0.035 0-0.052

300 250 0.08 0.085 0-0.055

Figure 4.16- Flow stress curves for MgAZ61L obtained using Surface Response Method

for PR=0.5 MPa/sec (at variable Strain Rate)

0

50

100

150

200

250

300

350

400

0 0.02 0.04 0.06 0.08 0.1

Tru

e S

tre

ss (

MP

a)

True Strain (mm/mm)

Mg AZ61L @ Pressure Rate= 0.5 MPa/sec

300 C 250 C 200 C 150 C

150 C

200 C

250 C 300 C

45

Using the tensile data available in the literature for AA 5182 alloy for a constant

Strain Rate of 0.0083 s-1, we have used this flow stress data to compare the

behaviour of the flow stress curve obtained from the bulge tests using the

Surface Response Method (see Figure 4.17). Our purpose here, is not to match the

flow stress data obtained using the 2 tests (tensile and bulge), but to see the trend

of the flow stress curves at various temperatures for AA 5182 material. When we

try to carefully look at the data obtained from the 2 tests (tensile vs bulge) at the

same temperature, we see that there seems to be a shift in the flow stress data

obtained for the bulge tests and this shift is consistent across all the three

temperatures (30, 200, 250 ⁰ C) as shown in this Figure 4.17.

Figure 4.17- Flow stress data obtained using the calculated Bulge Test (B.T.) data

(Surface Response) and Tensile Test (T. T.) data from [Abedrabbo 2007]

0

50

100

150

200

250

300

350

400

450

0 0.05 0.1 0.15 0.2 0.25

Tru

e S

tre

ss (

MP

a)

True Strain

30 C 200 C 250 C

Tensile Test_250 C Tensile Test_200 C Tensile Test_30 C

BT_30C

BT_200C

BT_250C

TT_30C

TT_200C

TT_250C

46

Please note that the Figure 4.10 plots the data for Strain Rate vs time for AA 5182

material, so we can clearly see that the bulge tests were not conducted at a

constant strain rate value, whereas the tensile tests obtained from [Abedrabbo

2007] were conducted at a constant strain rate value= 0.0083 s-1. Figure 4.18

shows the true stress-true strain curves for the AA5182-O material at 260 ⁰C in

the rolling direction at different strain rates (0.008, 0.01, 0.05, and 0.08 s-1) using

the uniaxial tests. As seen in the figure, the material became more strain rate

sensitive with increase in temperature and tends to shift upwards with the

increase in strain rate value.

Figure 4.18- True stress-True Strain data for AA5182-O obtained using tensile tests at

260 ⁰C for several strain rate values [Abedrabbo 2007]

47

4.3.5 Conclusions

Experimental tests at elevated temperature for AA 5182 and MgAZ61L alloys

were conducted at ITC using gas as pressure media. These tests were carried out

under a linear pressure rate. The test equipment was still in its development

phase at ITC and the ultimate goal of the testing device would be to conduct the

bulge tests under a constant strain rate even at elevated temperature by

implementing a feedback loop in the device that controls the pressure vs time.

Currently, the equipment is capable of post-processing the bulge profile, strain,

pressure, thickness even after the sample is burst during forming. This is possible

because the camera device takes a lot of images at very small time intervals to

capture the data till the step until the sample bursts.

Our objective at CPF was to use the given experimental data to predict the flow

stress behavior of the material at elevated temperature. Thus, a Surface Response

method to determine flow stress data at elevated temperature through VPB tests

has been developed. This methodology can be applicable only when we have the

means to correctly measure the bulge height, strain and strain rate, as in our case

with the device at ITC. Surface response method calculates a minimum of an

Error function (Ej) using an application code developed in MATLAB, by

comparing the experimental result (Pressure vs Bulge Height) with FE database.

Flow stress data currently predicted for AA 5182 and Mg AZ61L alloys using the

experimental data taken from ITC at a linear Pressure Rate of 0.5 MPa/sec.

Keeping the pressure rate constant does not mean that the strain rate remains

constant as seen from Figure 4.10. Thus, we cannot make a direct comparison of

the flow stress data obtained in this bulge test study with the tensile test data

available in the literature which were carried out under a constant strain rate.

48

The approximations of the flow stress coefficients given by the Surface Response

Method depend a lot on the density of the FE database.

49

CHAPTER 5 Cold and Warm Hydroforming of AA 5754 Sheet:

FE Simulations and Experiments

Warm hydroforming technique has the advantages of both hydroforming and

warm forming. These enable complex parts to be produced with materials those

have poor formability with less force/pressure compared to conventional

methods. In warm hydroforming process, the pressurized fluid medium is

usually hydraulic oil. Oil – when compared to gas – has higher thermal capacity

and higher pressures can be applied easily [Billur 2008].

When designing a warm hydroforming setup up to 300ºC (using oil as the fluid

medium), following concerns should be addressed [Novotny 2003]:

1. Key components, such as pumps, valves, sealing elements, etc. should be

suitable for both high pressure and temperature.

2. In order to have constant temperature during forming (isothermal

forming), heating is necessary for both the fluid medium and the dies.

3. For safety of operator, guards for splash should be properly designed. In

case of any burst in the work piece, hot oil should not contact the operator

or nearby people.

4. Vapor of lubricants and/or the pressurizing fluid should be removed

50

5.1 Model Part and Tools Geometry

The schematic of the tooling is presented in Figure 5.1. The lower die consisted of

three main components including the pressure pot, lower post (fixed in the

center) and blank holder. The upper die consisted of the punch and the spring

setup which allowed the punch to travel to a maximum stroke of 1.5 in (38 mm).

The purpose of the lower post was to create a reverse bulge at the center of the

deformed part when forming a part by conventional deep drawing without

using fluid pressure. However, necessary modifications of the deep drawing

tooling restricted the travel distance of the punch. In these SHF-P tests, the lower

post did not touch the sheet and the fluid pressure can be considered as the only

active force that forms the reverse bulge into the center recess of the punch.

51

Figure 5.1- Schematic of the tooling for SHF-P experiments: (a) initial setup (b) after

deformation, where ri = initial blank radius, Dd = draw depth and h = bulge height.

A Mokon heating system was used to control the forming fluid temperature.

With the fill and vent valves open, fluid will circulate through the tool (see Figure

5.2) to heat up the tooling along with the band heaters and cartridges. The

system includes a reservoir that maintains fluid at temperature and available for

filling and draining the tool cavity through the fill and vent valves. Dynalene

600, synthetic oil, was used as the fluid for building up forming pressure in the

pot cavity.

ir

dDh

Punch

Post

Die

Blankholder

Blank

(a)

Initial setup

(b)

After Deformation

52

Figure 5.2- Pressure flow schematic to heat or cool the tooling

While conducting our experiments for the SHF-P process, the part was formed

by conducting the following steps:

1) Close the bypass, vent and relief valve

2) Relief valve is programmed to a certain limit pressure

3) Tool cavity is sealed with the clamped sample

4) During the process, the punch moves down, displaces oil and builds

pressure, and at the same time, the relief valve helps to release pressure if

it exceeds the pressure limit value as shown in Figure 5.3.

The displaced oil from the tool follows the path of the 1) fill valve, 2) relief valve,

3) in from process and 4) Mokon system.

53

Figure 5.3- Pressure flow schematic to form the part using the SHF-P process by

controlling pressure with the relief valve

5.2 Experimental Results

Prior to forming tests at room and elevated temperatures, preliminary FE

simulations were conducted to establish initial test parameters (BHF, punch

velocity, and pot pressure) that could be used as experimental inputs. The sheet

material was AA 5754 with an initial diameter, di, and thickness, ti, of 17 in (432

mm) and 0.039 in (1.0 mm), respectively. Table 5.1 lists the input parameters for

the room temperature experiments.

In the preliminary FE experiments of the room temperature SHF-P process, the

pot pressure was maintained at approximately 300 psi (2.07 MPa) for BHF of 5.6

kips (25 kN). With the downward movement of the punch, the punch displaced

oil causing an increase in counter pressure. As this pressure approached the set

54

limit of 300 psi (2.07 MPa), the relief valve cycled to maintain a steady pot

pressure.

Table 5.1- Input parameters for SHF-P tests at room temperature (punch velocity=0.075

in/sec)

Sample # BHF (kip) Pot Pressure (psi) Punch stroke (inch)

5 5.6 300 1.35

6 5.6 300 1.13

In the case of experimental tests conducted at elevated, the maximum pot

pressure input for the relief valve was set to limiting pressure levels as listed in

Table 5.2. Initially, the same process parameters that were used for room

temperature forming were used (pot pressure of 300 psi (2.07 MPa) and BHF of

5.6 kip (25 kN)), but the part consistently failed around the punch corner region.

Therefore, new process conditions were used by applying a lower BHF, around 1

kip (4.45 kN), and increase in the pot pressure input.

A set of samples were formed at a constant BHF and draw depth of 0.56 in (14

mm), but with variable pressure limits of 500, 1000 and 2000 psi (3.4, 6.9 and 13.8

MPa), to study the effect of forming pressure on the part shape. For the pressure

limit of 2000 psi (13.8 MPa), the sample parts were further drawn to depths of

0.7, 1.0 and 1.5 in (17.8, 25.4 and 38.1 mm), to measure the amount draw-in.

55

Table 5.2- Input parameters used to conduct warm SHF-P test at elevated temperature of

about 150°C (cycle time = 20 sec)

Sample # Pot Pressure (psi) BHF (kip) Punch Stroke (inch)

21 500 1 0.56

27 1000 1 0.56

28 2000 1 0.56

29 2000 1 0.70

30 2000 1 1.00

33 2000 1 1.50

Table 5.3 compares input (entered at the control panel) and output values (BHF

and pot pressure measured from sensors inside the press machine) and the

measured draw depth, Dd, of the formed part at room temperature. Since the

output values of BHF fluctuated throughout the punch stroke, an average value

of BHF was calculated. Measured flange perimeter, Ff, draw depth, Dd, and the

bulge height, h, are presented in Table 5.3.

Table 5.3- Comparison of experimental input to the output readings and measurements at

room temperature (initial flange perimeter, fi= 53.41 in)

EXPERIMENTAL

INPUT EXPERIMENTAL OUTPUT

Sample

#

BHF

(kip)

Pot

Pressure

(psi)

Punch

stroke

(in)

BHF

(kip)

Pot

Pressure

(psi)

Flange

Perimeter,

Ff (in)

Draw

Depth,

Dd (in)

Bulge

Height,

h (in)

5 5.6 300 1.35 6.78 304.7 49.1 1.349 0.353

6 5.6 300 1.13 6.81 307.5 50.1 1.083 0.333

Table 5.4 compares the input and output values (BHF and forming pressure) and

the measured draw depths, Dd, of the samples formed at elevated temperature.

The steady BHF output obtained from the experimental results is higher than the

56

experimental input value. This may be because the BHF (clamp load) was very

small relative to the press capacity. Also, this load was measured using pressure

transducers, which are placed on either side of the actuator‘s piston and the cross

sectional areas of the piston areas are then considered to calculate the load.

Thus, it gave only approximation for measurement of a very small load. The

comparison of output values of pot pressure for samples 21, 27, and 28 indicates

that a maximum of 842.5 psi (5.8 MPa) was needed to draw this part to a depth of

0.56 in (14 mm). In order to draw the part to a depth of 1.5 in (38 mm), the

required pot pressure was increased to 1494 psi (10.3 MPa), keeping the BHF to

the same value of 2.2 kip (9.8 kN).

Table 5.4- Comparison of experimental input and output readings and profile

measurements, for SHF-P experiments at elevated temperature (Initial flange perimeter,

Fi = 53.41 in)

EXPERIMENTAL INPUT EXPERIMENTAL OUTPUT

Sample

#

BHF

(kips)

Pot

Pressure

(psi)

Punch

Stroke

(inch)

BHF

(kips)

Pot

Pressure

(psi)

Flange

Perimeter,

Ff (in)

Draw

Depth,

Dd (in)

21 1 500 0.56 2.19 595.3 52.3 0.578

27 1 1000 0.56 2.21 834.6 51.9 0.570

28 1 2000 0.56 2.21 842.5 52.1 0.573

29 1 2000 0.70 2.23 977.5 51.8 0.715

30 1 2000 1.00 2.19 1140.1 50.2 1.025

33 1 2000 1.50 2.22 1494.4 47.9 1.514

The temperature of the tooling (die, blank holder and punch) was controlled by

two dual channel Watlow F4 temperature controllers using resistance heaters.

The fourth Watlow channel was used to monitor the oil temperature with a

thermocouple positioned inside the lower die. Thermal data was collected for

57

each component of the tooling using thermocouples that were embedded in the

tooling as shown in Figure 5.4. Due to the constraints of the machine, it was very

difficult to obtain isothermal conditions within a 10C range. Results indicate

that the temperatures of the blank holder, die and oil ranged from 127 to 140C,

while the punch temperature was measured to be 157C.

Figure 5.4- Position of thermocouples on the ITC hydroforming machine

5.3 Finite Element Method (FEM) Setup

The part geometry was designed at General Motors as representative of a

challenging feature to form with aluminum by conventional stamping. The

58

AA5754 sheet blank was 0.039 in (1 mm) in thickness (ti) and 17 in (432 mm) in

diameter (di). The FE model was created using PAM-STAMP 2G, Ver. 2009,

which enabled input of the material model as a function of temperature and

strain rate simultaneously. Only one quarter of the geometry was modeled since

the tooling and part geometries were axisymmetric.

For all temperatures, the process was modeled using the Aquadraw Module in

PAM-STAMP 2G, which allows efficient control of pressure input in the tool

cavity, based on compressed fluid volume and maximum pressure limit to be

applied on the blank. To create a simplified model and replicate the elevated

temperature deformation, an ‗isothermal condition‘ was assumed. By

approximation, the FE model was set up at 150C (whereas temperature readings

of tools and fluid ranged from 127 to 157C).

The input parameters used during the simulation are summarized in Table 5.5.

The major difference between simulation of this process at room and elevated

temperature conditions is the input of material properties. As the material at

elevated temperature is strain rate sensitive, the deformation speed at different

regions of the blank in the simulation should take into account the influence of

strain rate.

[Abedrabbo 2007] conducted tensile tests and applied the Fields and Backofen‘s

material model (power law equation) to describe the stress-strain behavior of AA

5754. Flow stress data was input as a function of strain, strain rate and

temperature, in tabular format in PAM-STAMP 2G.

mnK

Where:

K = 503.7-0.592*T (for T = 25-93C) and 641.3-1.829*T (for T = 93-260C)

59

n = 0.3304 -0.000529*T (for T = 25-93C) and 0.4048-0.001192*T (for T = 93-260C)

m = 0.00118*exp (0.0161*T) (for T = 25-260C)

Table 5.5- Input parameters for FE simulations of SHF-P

Mechanical Properties

Blank material AA5754

Flow stress (obtained by tensile test) [Abedrabbo 2007]

Young‘s Modulus (E) 69 GPa

Poisson‘s ratio (ν) 0.3

R0, R45, R90 1 (material assumed isotropic)

Interface Condition

Friction coefficient µ (blank/ tools) 0.12

Mesh

Element type Shell (Belytschko-Tsay )

Object type

Blank Elastic, Plastic

Tools Rigid

Sheet Hydroforming with Punch (SHF-P)

Aquadraw Activate

Bulk Modulus, K 50 GPa

Pot Pressure Experimental output (see Figure 5.5)

Blank Holder stroke Experimental output

Punch stroke Room temp=1.35 in

Elevated temp= 1.50 in

Punch Velocity 0.074 in/sec

60

Figure 5.5- Experimental output Pot pressure vs time for part formed at elevated

temperature (150 ⁰C)- Sample # 33

5.4 Comparison of FE predictions with experimental results

The results from room temperature FE simulations have been summarized below

for Sample #5 (BHF = 6.8 kip, pot pressure = 304.7 psi and punch stroke = 1.35

in). For comparison of the thickness profile generated from the FE simulations,

the mechanical indicator (Mitutoyo) was used to measure thickness along the

curvilinear length of the formed sample. Figure 5.6 presents the thickness

distribution along the curvilinear length of the part. Note that the maximum

thinning location occurred near the punch corner region (location #4) for the part

formed at room temperature.

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25

Po

t P

ress

ure

(p

si)

Time (sec)

Pot pressure vs Time

61

Figure 5.6- Thickness profile along the curvilinear length measured by the mechanical

indicator and compared with FE results for Sample #5 at room temperature (Punch

Stroke= 1.35 in, BHF = 6.81 kip, pot pressure = 304.7 psi)

For FE analysis at elevated temperature, Sample #33 (BHF= 1 kip (4.45 kN), pot

pressure = 2000 psi (13.8 MPa) and punch stroke=1.5 in (38 mm)) was selected.

The results of SHF-P at the elevated temperature of 150C are presented in Table

5.4. The BHF prediction of the FE simulation for Sample #33 indicates some

fluctuation, but the average value remains close to the experimental output. The

FEA input of BHF force did not work in PAM-STAMP because forming pressure

is balanced by blank holder only, but in reality the punch force adds to BHF to

balance the forming pressure. So in simulation, the forming pressure caused the

0 25 50 75 100 125 150 175 200 2250.78

0.82

0.86

0.90

0.94

0.98

1.02

1.06

1.10

Curvilinear Length (mm)

Thic

kness (

mm

)

FE Output

Measured

0 25 50 75 100 125 150 175 200 2250.78

0.82

0.86

0.90

0.94

0.98

1.02

1.06

1.10

Curvilinear Length (mm)

Thic

kness (

mm

)

1

2

34

56

7

8

1 2

3

45

67

8

Maximum thinning location

62

blank holder to open up. Therefore, input blank holder stroke of 1 mm was used

in the FE simulations at elevated temperature (instead of BHF) that was close to

the recorded blank holder stroke in ITC data file, as indicated in Figure 5.7.

Figure 5.7- FE setup for the initial clearance of 1 mm between the blank holder and sheet

Figure 5.8 is a comparison of the part profile measurement using the CMM and

the FE results of SHF-P for sample #33. For the CMM measurement of the

experimental sample, a significant bend in the reverse bulge region of the part

was observed. This bend in the part may be due to springback and distortion

from thermal contraction after part was removed from the press and cooled to

room temperature.

63

Figure 5.8- (a) experimental workpiece, (b) Pam-Stamp result of quarter model, (c)

comparison part profile from FEM and experiment, for the SHF-P of Sample #33 (punch

stroke = 1.50 in, average temperature = 150C, pot pressure = 1494 psi)

(a)

(b)

0 25 50 75 100 125 150 175 200

0

5

10

15

20

25

30

35

40

Radial Distance (in)

Part

Depth

(in

)

0

--

--0.00

1

--

--0.20

2

--

--0.40

3

--

--0.60

4

--

--0.80

5

--

--1.00

6

--

--1.20

7

--

--1.40

--1.60FEA

CMM

0 25 50 75 100 125 150 175 200

0

5

10

15

20

25

30

35

40

Radial Distance (in)

Part

Depth

(in

)

0

--

--0.00

1

--

--0.20

2

--

--0.40

3

--

--0.60

4

--

--0.80

5

--

--1.00

6

--

--1.20

7

--

--1.40

--1.60

0 25 50 75 100 125 150 175 200

0

5

10

15

20

25

30

35

40

Radial Distance (mm)P

art

Depth

(m

m)

0

--

--0.00

1

--

--0.20

2

--

--0.40

3

--

--0.60

4

--

--0.80

5

--

--1.00

6

--

--1.20

7

--

--1.40

--1.60FEA

CMM

0 25 50 75 100 125 150 175 200

0

5

10

15

20

25

30

35

40

Radial Distance (mm)P

art

Depth

(m

m)

0

--

--0.00

1

--

--0.20

2

--

--0.40

3

--

--0.60

4

--

--0.80

5

--

--1.00

6

--

--1.20

7

--

--1.40

--1.60

0 25 50 75 100 125 150 175 200

0

5

10

15

20

25

30

35

40

Radial Distance (in)

Part

Depth

(in

)

0

--

--0.00

1

--

--0.20

2

--

--0.40

3

--

--0.60

4

--

--0.80

5

--

--1.00

6

--

--1.20

7

--

--1.40

--1.60FEA

CMM

0 25 50 75 100 125 150 175 200

0

5

10

15

20

25

30

35

40

Radial Distance (in)

Part

Depth

(in

)

0

--

--0.00

1

--

--0.20

2

--

--0.40

3

--

--0.60

4

--

--0.80

5

--

--1.00

6

--

--1.20

7

--

--1.40

--1.60

height Bulge h

Dd

= D

raw

Dep

th

(c)

64

Figure 5.9- Thickness profile along the curvilinear length measured by the mechanical

indicator and compared with FE results for Sample #33 (punch stroke = 1.50 in, average

temperature = 150C, pot pressure = 1494 psi)

Figure 5.9 presents the comparison of the thickness profile of Sample #33 formed

at elevated temperature. The thickness profile for the FE simulation matches

fairly well with the measurements. FE results predict that maximum thinning

occurred near the reverse bulge region (position 8) along the curvilinear length.

Another set of tests were simulated to determine the effect of pot pressure on the

formed part geometry. The formed samples are # 23, 27 and 28, for BHF ~2.2 kip

(9.8 kN), cycle time = 20 sec, 0.56 in (14 mm) punch stroke and variable pressure

limits of 500, 1000 and 2000 psi (3.4, 6.9 and 13.8 MPa). From Table 5.6, it can be

0 25 50 75 100 125 150 175 200 2250.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

Curvilinear Length (mm)

Thic

kness (

mm

)

1

2

3

4

5 6 7

8

9

FE Output

Measured

0 25 50 75 100 125 150 175 200 2250.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

Curvilinear Length (mm)

Thic

kness (

mm

)

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

0 50 100 150 200 250

Thic

kne

ss (

mm

)

Curvilinear Length (mm)

Thickness profile along the curvilinear length for Sample 33 (BHF= 2.22 kip, Pot Pressure limit= 2000 psi, Punch Stroke= 1.50 in)

Experimental measurements with Error bar FE profile

12

3

4

5 6 78

91

2

3

4

5 6 7

Maximum

Thinning Location

65

inferred that with an increase in the input pot pressure limit, the maximum

thinning along the part would increase. However, there is not a significant

experimental difference in percent thinning between 1000 and 2000 psi (6.9 and

13.8 MPa), because the physical output for the maximum pressure only attained

about 840 psi (5.8 MPa), regardless of the value input at the control panel. In

order to form a part at elevated temperature (ET) for a draw depth (Dd) of 0.56 in

(14 mm) and 2.2 kip (9.8 kN) BHF, a maximum of 592.5 psi (4.1 MPa) pot

pressure should be used to achieve the least thinning percentage ~ 6.5%.

Table 5.6- Percent thinning affected by the applied pot pressure while keeping the other

process parameters constant (BHF ≈ 2.2 kiPs, punch stroke = 0.56 in, cycle time = 20 sec,

average temperature = 150°C)

Sample

#

Set pot

pressure

(psi)

Max.

thinning

(%)

Max.

thinning

location

Max. output

pot pressure

(psi)

23 500 6.54 Reverse bulge

region 592.5

27 1000 8.51 Reverse bulge

region 834.6

28 2000 8.56 Reverse bulge

region 842.5

The results compared in Figure 5.10 indicate that the flange perimeter

measurements, Ff from the experimental and FE predictions match very well.

There was only a small difference (0.5%) in the values of the final flange

perimeter determined by FE simulation and experimental measurement.

66

Figure 5.10- Comparison of flange perimeter measurement and prediction between initial

blank and final part after SHF-P at room (Sample#5) and elevated (Sample#33)

temperatures

5.5 Conclusions

FE modeling of the SHF-P process at room and elevated temperatures with the

assumption of isothermal conditions was completed using PAM-STAMP 2G Ver.

2009. Simulation results compared favorably with experimental measurements.

The experimental values of the process parameters (i.e. fluid pressure) were

input into the FE model to emulate similar conditions. The final flange perimeter

(Ff) predictions for both room and elevated temperature were within ± 0.5% of

the experimental results. For the elevated temperature case, there was some

difference in the part profile in the reverse bulge region. This difference could be

caused by artifacts of springback and thermal distortion as the part cooled to

room temperature or by thermal gradients within the part during the forming

Initial Perimeter SHF-P at Room Temp SHF-P at Elevated Temp44

46

48

50

52

54

1118

1168

1219

1270

1321

1372

(Sample #5)

Fla

nge P

erim

ete

r (in)

(Sample #33)

Initial Perimeter SHF-P at Room Temp SHF-P at Elevated Temp44

46

48

50

52

54

1118

1168

1219

1270

1321

1372

(Sample #5)

Fla

nge P

erim

ete

r (in)

(Sample #33)

FE Output

Measured

Initial Perimeter SHF-P at Room Temp SHF-P at Elevated Temp44

46

48

50

52

54

1118

1168

1219

1270

1321

1372

(Sample #5)

Fla

nge P

erim

ete

r (m

m)

(Sample #33)

Initial Perimeter SHF-P at Room Temp SHF-P at Elevated Temp44

46

48

50

52

54

1118

1168

1219

1270

1321

1372

(Sample #5)

Fla

nge P

erim

ete

r (m

m)

(Sample #33)

Measured

FE Output

67

process. The maximum thinning for the room temperature drawn part was

predicted to occur near the punch corner region. For elevated temperature,

however, the maximum thinning location occurred within the reverse bulge

region of the part. Simulation of thickness strain or thinning distribution across a

curvilinear length of the part matched reasonably well with the experimental

measurements. This study also shows that the SHF-P at elevated temperature

can form a cup with larger cup height and better reverse bulge profile than SHF-

P at room temperature.

68

CHAPTER 6 Case studies in sheet metal forming at elevated

temperature

6.1 Warm Forming of MgAZ31B sheet alloy

In warm forming, the punch is cooled in order to selectively cool the sheet that

comes in contact with the punch, while the flange is kept at higher temperature

to promote easy material flow into the die. Having the right temperature

distribution in the part during forming, is a key factor in improving formability

with the warm forming process. The use of FE simulations will help in a

systematic development of elevated temperature forming processes minimizing

the number of the expensive and time-consuming experimental tryouts.

Non-isothermal stamping processes of these materials have been done at

ERC/NSM in the past using the commercial codes DEFORM 2D, DEFORM 3D

[Palaniswamy 2004, Kaya 2008], commercial code LS-DYNA 9.70 [Spampinato

2006] and PAM-STAMP 2G 2007 [Braga 2008]. There are still unsolved issues in

the non-isothermal FE simulations of elevated temperature sheet forming

processes, namely, (a) reliability of flow stress data, (b) yield function, (c)

interface heat transfer coefficient (d) friction coefficient between sheet and tools

[Braga 2008].

69

In this study the new version of commercial FE code PAM-STAMP 2G 2009 has

been used to simulate warm deep drawing of magnesium alloy AZ31B-O, since it

is now able to conduct heat transfer calculations and allows modeling the flow

stress as function of strain rate and temperature simultaneously. Flow stress data

is input in a tabular form and can be extrapolated linearly beyond the given

input strain values. Temperature distribution, punch load-stroke curves and

thinning distributions in the sheet obtained in experiments [Kaya 2008],

[Spampinato 2006] were compared with FE simulation results for various

forming conditions.

6.1.1 Summary of Inputs for PAMSTAMP v. 2009 Simulation

Values of thermal properties, contact definitions and other material property

inputs for PAM-STAMP are summarized in Table 6.1. Please note that the values

are similar to those used in [Braga, 2008].

Table 6.1- Thermal and mechanical data used for warm forming simulations of

Mg AZ31-O [Braga 2008]

Thermal conductivity 77 W m-1C-1

Specific heat capacity 1020 J kg-1 C-1

Heat Transfer Coefficient (HTC) sheet-punch

1 kW m-2 C-1 HTC sheet-die

HTC sheet-blank holder

Fraction of mechanical work converted to heat 95%

Friction coefficient sheet-punch

0.04 (PTFE film Vac-Pak HT-620) Friction coefficient sheet-die

Friction coefficient sheet-blank holder

Young‘s modulus E (room temperature) 45 GPa

Poisson‘s ratio 0.35

70

6.1.2 Results for FE Simulations and comparison with experiments

Figure 6.1 gives a schematic view of the warm forming tooling used in Kaya‘s

study [Kaya, 2008]. Blank is initially placed on the bottom die/blank holder. The

top ram moves down till it touches the blank and dwells. During this dwell time,

the blank is heated to the required temperature by the heated die and blank

holder. After the dwelling period, the top ram moves further down against the

stationary punch (which is cooled to room temperature) to form the sheet.

In this study, only forming operation was simulated, while analyses of heat

transfer during dwelling and change in tool temperatures were neglected. In FE

simulations, it assumed that a blank was heated to uniform temperatures of 250-

300 C, according to the measurement given in Kaya‘s study [Kaya, 2008].

Although the punch could be gradually heated up by the blank in reality,

simulation assumed tool temperature as constant and above room temperature,

about 60-70 C. Test conditions were simulated, as shown in Table 6.2.

Figure 6.1- Schematic of warm forming tooling [Kaya 2008]

71

Table 6.2- Test conditions from [Braga 2008] were selected for preliminary simulations

Case

no.

Draw

Ratio

(Sheet diam. /

punch diam.)

Die-blank

holder

Temperature

[⁰C]

Punch

Temperature

[⁰C]

Stroke

(cup

height)

[mm]

Forming

velocity

[mm/s]

Blank

holder

force [kN]

1m 3.0 300 70 65 5 Linearly

increasing

from 1.1 to

4

2m

3m 2.7 55 35

4m 2.8 12

5m 2.7 250 60 48 10

Figure 6.2 shows a comparison of the temperature on the bottom cup during the

process between the experimental results and 4 simulations with different HTC

values (HTC= 1 and 4 kW/m2/C) and PAM-STAMP versions (2007 and 2009).

Same value of HTC was considered for all contacts (i.e. sheet-punch, sheet-die,

sheet- blankholder). The values of HTC were chosen following our previous

work in [Kaya, 2008; Braga, 2008]. From Figure 6.2, simulation with HTC of 1

kW/m2/C predicted the sheet temperature close to the experiment and this HTC

value was applied for all warm forming simulations for Mg alloy. Also from

Figure 6.2, there is no difference in temperature predictions between 2 different

versions of PAM-STAMP.

72

Figure 6.2- Temperature vs Punch stroke at Point (P1) using variable HTC [CASE 1m:

Draw Ratio= 3, Punch stroke=65 mm , Forming velcity= 5 mm/sec]

73

Figure 6.3- Comparison of the results from FE simulations and experiments of CASE 1m,

for thinning distribution and punch load vs. stroke

Figure 6.3 shows the thinning distributions and load-stroke curves for Case 1m

(drawing ratio = 3, forming velocity = 5 mm/s, initial sheet temperature = 300

C, stroke = 65 mm). Comparison was made between the results from simulation

using PAM-STAMP ver. 2007 and PAM-STAMP ver. 2009, and the experimental

data. Both PAM-STAMP versions are able to predict thinning distribution very

close to the experiment. However, PAM-STAMP ver. 2009 predicts stamping

load closer to the experiment. PAM-STAMP ver. 2007 overestimates the

maximum load by 67%. This may be due to the assumptions of constant strain

rate throughout stamping process and uniform strain rate for the whole regions

of the sheet. This limitation has been resolved in PAM-STAMP ver. 2009.

74

Figure 6.4 shows similar comparison for another case, Case 4m (drawing ratio =

2.8, forming velocity = 12 mm/s, initial sheet temperature = 300 C, stroke = 55

mm). Again, PAM-STAMP ver. 2009 predicts load closer to the experiment than

PAM-STAMP ver. 2007.

Figure 6.4- Comparison of the results from FE simulations and experiments of CASE 4m,

for thinning distribution and punch load vs. stroke

75

6.1.3 Conclusion

By using the PAM-STAMP 2G ver. 2009, the accuracy of the predictions

improved significantly by introducing a material model to describe flow stress as

function of both temperature and strain rate simultaneously. In particular, the

punch load results match closely with experimental using PAM-STAMP ver.

2009, which were predicted 50% higher than the experimental results in the

previous version (ver. 2007) of PAM-STAMP, possibly due to the constant strain

rate assumption used in the material model at elevated temperature.

For magnesium alloy AZ31B-O, the best value of the interface heat transfer

coefficient (HTC= 1 kW/m2/C) was chosen by comparing the experimental cup

bottom temperature during the process with the simulations results.

76

6.2 Hot Stamping/Forming of 22MnB5 Steel to form experimental part

In this case study, we will see the non-isothermal hot forming of 22MnB5 sheet to

form an automotive part. Hot stamping/forming is the second category of

forming above recrystallization temperature as mentioned earlier. The actual

process cycle for hot stamping involves: 1) Heating of the blank to its

austenization temperature, 2) Transferring the blank from the furnace to the die,

3) Forming operation and 4) Quenching of the formed part by holding it within

the tools after the forming process is completed.

6.2.1 Objective

The objective of this study was to develop a method through finite element

simulations using PAM-STAMP to perform the Hot Stamping- Forming

operation only.

Specific objectives were to:

a) Predict the flow of material during deformation of the blank.

b) Estimate the thinning distributions along a section of the final part and

compare them with the experimental results.

6.2.2 FE Setup

The 3-D surface parts of the geometry were provided by the sponsor company.

These models were then input to Altair Hypermesh software to generate a

refined mesh in the curved regions of the part. The material properties listed in

Table 6.3 and the process parameters listed in Table 6.4 are obtained from the

literature [Numisheet 2008].

77

Table 6.3- Material Properties for 22MnB5 Sheet

Material property Symbol Value

Young‘s Modulus E 100 GPa (constant)

Poisson‘s ratio ν 0.3 (constant)

Flow stress data for 22MnB5

Function of Temperature and Strain rate

[Numisheet 2008]

Thermal conductivity k 32 W/mK (constant)

Specific heat capacity cp 650 J/KgK (constant)

Heat transfer coefficient-between sheet and tooling

HTC Function of pressure

[Numisheet 2008]

Table 6.4- Process Parameters in Hot stamping- Forming operation only

Process Condition Symbol Value

Upper die and blank holder velocity

V Assumed constant

Lower die

Constrained in all directions

Temperature of blank at the beginning of forming

process Tf

Above austenization temperature ~ 700-750 °C

Temperature of tooling-upper die and lower die

Tt 30 ⁰C (assumption)

Coefficient of friction µ 0.4 (constant)

6.2.3 FE Results and comparison with the experimental data

The FE prediction of the material flow under the given setup and process

condition is shown schematically in Figure 6.5. The lower die is held stationary;

78

whereas the upper die and blank holder move down to deform the work piece.

In this FE setup, the distance between the upper and the lower die minus the

initial thickness of the blank was used as the stopping criteria.

Figure 6.5- Steps in the Forming stage at a) Initial position and b) Final position

The thinning distribution obtained from simulation was compared with

experimental data along one section of the formed part. It was found that the

overall trend of the thinning distribution predicted by the simulation closely

follows the experimental thinning distribution. The maximum thinning

calculated by the FE model is approximately 10.1%, which is quite close to the

experimental values of maximum thinning (approximately 13%). Thus, overall

thinning predictions can be considered to be in fairly good agreement.

Upper die

Lower die

Blank Holder Blank

79

6.2.4 Future Work

Following are the activities that could be performed in the near future on this

topic/ case study:

1) Since PAM-STAMP 2G 2011 can now handle heat transfer within the tools,

quenching simulations can be done for this case study and the results will

be validated against experimental data.

2) Finally, the microstructure analysis on the quenched part can be carried

out. This feature is built-in with the material model in PAM-STAMP 2G

2011.

80

CHAPTER 7 Discussion, Conclusion and Future Work

7.1 Discussion and Conclusions

7.1.1 Determination of the flow stress at elevated temperature

Experiments:

Experimental tests at elevated temperature were conducted for AA5182 and

MgAZ61L alloys at ITC using gas as pressure medium.

Experimental data of Pressure vs Bulge Height could be obtained for

samples which burst during forming. This was possible using the

sophisticated camera device which took a lot of pictures during the forming

process. And then using these images the data for Pressure, Strain, Bulge

height and thickness could be found.

Experiments could be controlled at a linear Pressure Rate of 0.1, 0.5 and 2.5

MPa/sec and stopped either by specifying a pressure or a strain limit.

FE Inverse Analysis Technique:

Surface Response method to determine flow stress data at elevated

temperature through VPB tests has been developed

81

Surface response method calculates a minimum of an Error function (Ej)

by comparing the experimental result (Pressure vs Bulge Height) with FE

database

Flow stress data has been predicted for AA 5182 and Mg AZ61L alloys

using the experimental data taken from ITC at a linear Pressure Rate of

0.5 MPa/sec

The approximated K, n, and m values were limited to the flow stress

coefficients that were simulated using the FE code and stored in the FE

database. Because of this limitation, the MATLAB code predicted different

combinations of K, n and m values at the same temperature conditions.

Further, expanding the FE database to include more combinations of K, n

and m could result in a better prediction of the flow stress coefficients.

The corresponding flow stress curves obtained by applying the surface

response methodology to the elevated temperature bulge test predicted a

higher flow stress data when compared to the data available in the

literature [Abbedrabbo 2006 and Abbedrabbo 2007] obtained using tensile

tests at a constant strain rate. This discrepancy may be due to different

reasons. First, the sample pre-bulging observed in the experiments.

Second, data in the literature was tensile data conducted at a constant

strain rate = 0.0083 s-1.

82

7.1.2 Design of Sheet hydroforming with Punch Process (SHF-P)

Experiments:

Experiments were conducted using Sheet hydroforming with Punch at

room and elevated temperature at the G.M. Tech Center for AA 5754-O

alloy. The process parameters (blank holder and pot pressure) have been

recorded earlier that were used to form these samples.

Flange perimeter measurements, bulge height, part profile and thickness

measurements on the formed samples were taken in order to compare

them with the FE predictions.

FE Simulations:

FE simulations were conducted for SHF-P at room and elevated

temperature using the isothermal assumption using the code PAM-

STAMP. The FE predictions were then compared to the experimental

measurements to validate the results.

Results show that the FE predictions of final flange perimeter, location of

the maximum thinning and part profile seem to match fairly well to the

experimental measurements taken

83

7.2 Future Work

7.2.1 Determination of flow stress at elevated temperature

Apply the same Surface Response Methodology to predict the flow stress

coefficients at Pressure Rate of 0.1 and 2.5 MPa/sec

Compare the flow stress data obtained using the Surface Response

method with the data available in the literature

Extend the FE database to more combinations of K, n and m

To develop the capability on the experimental device to control the strain

at the dome apex by controlling the flow rate of the pressurizing medium.

7.2.2 Simulation of SHF-P Process

Since the tooling (blank holder, lower die, punch and fluid) temperatures

used to conduct the experiments during the actual forming process were

not isothermal, ranging from 127 to 157C, elevated temperature FE

simulation was attempted using a non-isothermal model that considered

heat transfer. In this non-isothermal model, the initial temperature

conditions and the heat transfer coefficients were the required inputs of

the FE model, but this exceeded the capability of the FE code. The current

software used for this study did not allow modeling of the hydroforming

process (using the Aquadraw module) and heat transfer simultaneously.

There was also difficulty to define the heat transfer condition between the

fluid and the blank under non-isothermal conditions. ESI Group (USA) is

improving the capability of the PAM-STAMP code in order to model the

warm SHF-P process.

84

Future research in the continuation of this study would include additional

experimentation and FE analysis at higher forming temperatures (250C)

and warm forming of other materials (e.g. Mg alloys) using solid dies.

Furthermore, non-isothermal conditions will be modeled to study the

benefit of using a punch that is cooler than the remaining tooling

environment to enhance warm forming of sheet metal.

85

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