Evaluation of Formability and Determination of Flow

Home , Biaxial tensile testing, Formability

EVALUATION OF FORMABILITY AND DETERMINATION OF FLOW

STRESS CURVE OF SHEET MATERIALS WITH DOME TEST

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Ji You Yoon

Graduate Program in Mechanical Engineering

The Ohio State University

2012

Master's Examination Committee:

Taylan Altan, Advisor

Jerald Brevick

Ji You Yoon

2012

Abstract

Determination of flow stress curve of sheet material is important for designing stamping process efficiently. Entering accurate flow stress curve to FE simulations is necessary to obtain reliable results from simulations. Furthermore, in most Advanced High Strength Steels (AHSS), material properties may vary from coil to coil and that can affect to product quality.

The dome test is a material test to evaluate formability and determine the flow stress curve of the sheet materials. The dome test is a biaxial test which consequently achieves greater maximum true strain without localized necking compared to that of uniaxial tensile test. As a result, the flow stress curve obtained from the dome test can be determined up to larger strains than in tensile test. This reduces possible errors from extrapolation of flow stress curve obtained from tensile test.

FE simulations are performed in order to understand the deformation process in the dome test and to develop database for computer program, PRODOME, (MATLAB). With PRODOME, flow stress curve is calculated (determining K and n values in Hollomon’s Law (σ=Kεn)) by inputting dome test outputs of punch force vs. stroke. It is calculated by using inverse analysis method.

From the dome test, JAC 590R (t = 1.6 mm), JAC 780 TRIP (thickness = 1.0 mm) and Al 6022 (t = 1.0 mm) are tested. Lubrication system is developed from the dome test. With lubrication system, samples are evaluated how much they deviate from the apex of the dome by having percentage error they have in the flow stress curve.

Dedication

This document is dedicated to my parent, my sister and friends

iii

Acknowledgements

Thanks God, I barely finish my study without Your help and Your strength that comes from You. To be able to accomplish this study, I have been supported and supervised by many people that God sent to me. To my family, I cannot express my gratitude enough. I am indebted to my family and my friends who helped me a lot during my school period. I believe that I would not be able to name everyone separately and to thank for everything that they did for me, however, I would like to express a few words of thanks from the bottom of my heart. I would like to express my deepest gratitude to:

Prof. Taylan Altan for his great support and his valuable suggestions which make me strong to step up beyond my deficiency. His intellectual support, advice and guidance make me possible to accomplish this research works. I thank my committee member Dr. Jerald Brevick for support.

I thank my colleagues of the CPF, Eren Billur, Dr. Hyun-Sung Son, Soumya Subramonian, Tingting Mao, Xi Yang, Adam Groseclose, Niranjan Rajagopal for their assistance. I also want to express great thanks to HRA, Jim Dykeman and Ben Flocken for their support.

Specially, I would like to thank my parents and my sister for their endless encouragement, inspiration, advice and support.

I would like to thank all those too numerous to mention here, who have assisted and encouraged to complete of my work.

Vita

February 2006 ...... Se-Hwa Girls’ High School

2010 ...... B.S. Mechanical Engineering,

Hanyang University

2011 to present ...... Graduate Research Associate,

Department of Mechanical

Engineering, The Ohio State

University

Fields of Study

Major Field: Mechanical Engineering

Table of Contents

Abstract ...... ii

Dedication ...... iii

Acknowledgements ...... iv

Vita ...... v

CHAPTER 1 INTRODUCTION ...... 1

CHAPTER 2 BACKGROUND ...... 3

2.1 Uniaxial Tensile Test ...... 4

2.2 Biaxial Tension Test ...... 16

2.2.1 Cupping tests ...... 16

2.2.2 Limiting Dome Height (LDH) Test ...... 17

2.2.3 Bulge Test ...... 20

2.2.4 Dome Test (extension of LDH test) ...... 24

CHAPTER 3 OBJECTIVES AND APPROACH ...... 25

3.1 Objectives ...... 25

3.2 Approach ...... 25

CHAPTER 4 INVERSE ANALYSIS METHODOLOGY ...... 30 vi

CHAPTER 5 EXPERIMENTAL WORK AND RESULTS ...... 33

5.1 Experiments and Tooling ...... 33

5.2 Test Procedure ...... 34

5.3 Output from the Dome Tests ...... 35

5.4 Test Parameters and Selection of Materials ...... 36

5.5 Test Results ...... 39

CHAPTER 6 FE SIMULATIONS ...... 41

6.1 Simulation Parameters ...... 41

6.2 Computer Program “PRODOME” Using MATLAB ...... 43

6.2.1 General concepts of computer program using MATLAB ..... 43

6.2.2 Running the PRODOME ...... 44

CHAPTER 7 RESULTS AND DISCUSSION ...... 47

7.1 Determination K and n Values of the Sheet Materials ...... 47

7.2 Anisotropy Correction ...... 48

7.3 Comparison of the Flow Stress Curves ...... 49

7.3.1 Tensile test vs. dome test ...... 49

7.3.2 VPB test vs. Dome test from DEFORM and PAMSTPMP ... 51

7.4 Zero Point Adjustment ...... 53

7.5 Lubrication System ...... 55

vii

7.5.1 Preliminary Evaluation Lubricant Test ...... 55

7.5.2 Measurement of angle of fractures ...... 56

CHAPTER 8 SUMMARY AND CONCLUSIONS ...... 64

REFERNECES ...... 68

APPENDIX A: Lubricants list ...... 72

APPENDIX B: Evaluation lubricant tests for high formability material (JSC

270F, t = 0.8 mm) ...... 73

viii

List of Tables

Table 1. Dome test experiment matrix [Dykeman 2011, POSCO 2012]...... 33

Table 2. Material properties evaluated by tensile test provided by Honda ...... 37

Table 3. Test parameters of the dome test ...... 38

Table 4. K & n values and of the materials with isotropic assumption ( =

1) ...... 47

Table 5. Normal anisotropy of the materials (provided by Honda) ...... 49

Table 6. Determined parameters from VPB test (w/o considering anisotropy),

DEFORM and PAMSTAMP ...... 52

List of Figures

Figure 1. Tensile test specimen, according to ASTM E8 [Altan 2012, ASTM

2011] ...... 4

Figure 2. Schematic of a fixture used in a tensile test [Altan 2012] ...... 5

Figure 3. The schematic of the force vs. elongation curve obtained from tensile test [Altan 2012] ...... 5

Figure 4. Engineering stress vs. engineering strain curve [Kalpakjian 2008] ...... 7

Figure 5. Comparison stress vs. strain curve between engineering state and true state [Hosford 2007] ...... 8

Figure 6. True stress and true strain curve of Al 1100-O, plotted on log-log scale

[Hosford 2007, Altan 2012] ...... 9

Figure 7. Some of the flow curve equations used in plastic deformation studies

[Marciniak 2002, Altan 2012]: (a) Hollomon’s Law, (b) Swift’s Law, (c) Linear strain hardening, and (d) Constant ...... 10

Figure 8. Predicted flow stress curves by different equations [Nasser 2010, Paul

2012] ...... 10

Figure 9. Schematic representation of stress-strain conditions for necking in simple tension [Altan 2012] ...... 13

Figure 10. Flow stress curve obtained from tensile test and bulge test [Billur

2011] ...... 13

Figure 11. Sheet orientations relative to normal and planar anisotropy [Totten

2003, Altan 2012] ...... 14

Figure 12. Definitions of width and thickness strains in a tensile specimen [Davis

2004] ...... 15

Figure 13. Schematic of Fukui conical cup test [Hosford 2007] ...... 16

Figure 14. Schematic of Erichsen cup test [Doege 2010, Altan 2012] ...... 17

Figure 15. Schematic of LDH tooling [Grote 2009] ...... 18

Figure 16. Location of maximum thinning when friction is (a) 0 and (b) 0.075

[Ngaile 2000] ...... 18

Figure 17. Influence of interface friction (a) on the location of maximum thinning,

(b) on punch force [Ngaile 2000]...... 19

Figure 18. Comparison of stretchability results of different steels from LDH test

[WSA 2009, Altan 2012] ...... 19

Figure 19. Schematic of Hydraulic Bulge Test [Gutscher 2004] ...... 21

Figure 20. Viscous Pressure Bulging (VPB) test set-up [Ngaile 2000] ...... 21

Figure 21. Geometry of bulge test [Billur 2011] ...... 22

Figure 22. Fracture location of (a) frictionless dome test with fracture at apex,

TRIP 780 (t = 1mm) with lubrication (Teflon and Clay) (b) with no lubrication 24

Figure 23. Punch force vs. stroke curve of 780 TRIP. Fracture occurred at the apex of the dome ...... 26

Figure 24. Normalized punch force vs. stroke curve of 780 TRIP (t = 1.0mm) with fracture at the apex of the dome ...... 31

Figure 25. Flow chart of inverse analysis methodology [Cho 2005] ...... 32

Figure 26. Schematic of the dome test [Grote 2009, Interlaken] ...... 34

Figure 27. Dome test tooling ...... 35

Figure 28. Punch force vs. stroke curve from experiment, 780 TRIP (t = 1.0 mm) with lubricants of Teflon and Clay ...... 36

Figure 29. Top and front view of burst sample from dome test ( JAC 590R, t =

1.6mm) ...... 38

Figure 30. Punch force vs. stroke curve of JAC 590R (t = 1.6mm) ...... 39

Figure 31. Punch force vs. stroke curve of 780 TRIP (t = 1.0mm) ...... 40

Figure 32. Punch force vs. stroke curve of Al 6022 (t = 1.0mm) ...... 40

Figure 33. Quarter model of simulation at stroke of 50 mm ...... 42

Figure 34. Process of the PRODOME ...... 43

Figure 35. PRODOME window to select experimental punch force vs. stroke data

...... 44

Figure 36. PRODOME window to input initial thickness and normal anisotropy of the sheet material ...... 45

Figure 37. PRODOME window shows punch force vs. stroke curve from experiment and buttons to renew data, initial thickness and/or normal anisotropy

...... 45

Figure 38. PRODOME window that shows calculated flow stress curve ...... 46

xii

Figure 39. PRODOME window that shows buttons which can save data ...... 46

Figure 40. Flow stress curves of materials of JAC 590R, TRIP 780 and Al 6022 with isotropic assumption ( = 1) ...... 48

Figure 41. Comparison flow stress curve obtained from the dome test (isotropic, anisotropic) and the tensile test for JAC 590R (t = 1.6 mm) ...... 50

Figure 42. Comparison flow stress curve obtained from the dome test (isotropic, anisotropic) and tensile test for JAC 780 TRIP (t = 1.6 mm) ...... 51

Figure 43. Digitized punch force vs. stroke curve obtained from experiment ..... 52

Figure 44. Comparison K and n values among VPB test, DEFORM and

PAMSTAMP...... 53

Figure 45. (a) Punch force vs. stroke curve with good zero point adjustment and shifted zero point adjustment (b) flow stress curve of good zero point adjustment and shifted zero point adjustment ...... 54

Figure 46. Reference sample of JSC 270F (t = 0.8 mm) for calibration, stroke up to 1.00 inch...... 54

Figure 47. Change in the location of maximum thinning with increased of coefficient of friction ...... 55

Figure 48. Dome test sample of JAC 780 TRIP (t = 1.6 mm) with lubricant of

Teflon and Clay of (a) sample 1, (b) sample 2 and (c) sample 3 ...... 56

Figure 49. Measuring the angle of fracture using AutoCAD software (780 TRIP with no lubrication, t = 1.0 mm) ...... 57

Figure 50. Flow stress curve with angle of fractures for JAC 590R (t = 1.6mm) 59

xiii

Figure 51. Flow stress curve with angle of fractures for 780 TRIP (t = 1.0mm) . 59

Figure 52. Flow stress curve with angle of fractures for Al 6022 (t = 1.0mm) .... 60

Figure 53. Percentage error, maximum strain and the dome height on each angle of fractures for JAC 590R (t = 1.6mm) ...... 60

Figure 54. Percentage error, maximum strain and the dome height on each angle of fractures for 780 TRIP (t = 1.0mm) ...... 61

Figure 55. Percentage error, maximum strain and the dome height on each angle of fractures for Al 6022 (t = 1.0mm) ...... 61

Figure 56. Angle of fracture with increasing friction (JAC 590R, t = 1.6 mm) ... 62

xiv

CHAPTER 1 INTRODUCTION

In sheet metal forming or stamping, mechanical properties of the sheet material (e.g., flow stress curve) significantly influence metal flow and product quality. This information is essential as an input to FEM (Finite Element Method). Sheet metal forming companies use FE simulations widely because it is a very beneficial and powerful tool to significantly reduce the time and cost of die try- outs and productions. To obtain reliable results from FE simulations, accurate material property must be entered into the analysis. Furthermore, in a stamping plant, the quality control of the incoming sheet material is necessary for establishing a robust production process. In most Advanced High Strength Steels (AHSS), material properties may vary from coil to coil and this affects part quality and scrap rate. Therefore, accurate and reliable method of determination of formability and flow stress curve of sheet material are important for designing a reproducible and robust stamping operation.

Uniaxial tensile test is a standard test which is commonly used by sheet material suppliers/steel mills to determine the formability of sheet materials. The flow stress curve obtained from the tensile test is under uniaxial state of stress which is not enough to emulate the stress state in actual stamping. Another effect of this is that true strain range obtained from the tensile test is limited because local necking starts at the Ultimate Tensile Strength (UTS). Extrapolation of flow stress data from the tensile test to obtain large strains is an approximation and not accurate compared to the data from a biaxial test. Therefore, it is necessary to conduct a biaxial test to obtain flow stress curve with a larger range of strain compared to that of a tensile test.

The dome test is used to evaluate formability and flow stress curve of sheet materials. The main reason of using the dome test instead of hydraulic bulge test is the ease in conducting the dome test. With these benefits, companies may prefer to conduct the dome test to obtain sheet material property. In this thesis, K and n values are determined in Hollomon’s law (σ=Kεn) from the output of the dome test (punch force vs. stroke curve). Finite element based inverse analysis technique [Cho 2005] is used to determine K and n values.

The overall study is broken up into Chapters;  Chapter 2: Background  Chapter 3: Objectives and Approaches  Chapter 4: Inverse Analysis Methodology  Chapter 5: Experimental Works and Results  Chapter 6: FE simulations  Chapter 7: Results and Discussion The information contained in this thesis will cover research which is performed at HONDA R&D and CPF.

CHAPTER 2 BACKGROUND

In a manufacturing process, a given material, usually shapeless or of a simple geometry, (in case of sheet metal forming a blank) is transformed into a useful part having a complex geometry with well-defined shape, size, accuracy and tolerances, appearance, and properties [Altan 1983]. Metal forming includes (a) bulk forming processes such as forging, extrusion, rolling and drawing and (b) sheet forming processes such as brake forming, deep drawing and stretch forming [Altan 2012]. The most important properties which are related to forming behavior are [Pöhlandt 1989]:  Stress vs. strain curve (also known as flow stress curve): yield strength (Y

or ), ultimate tensile strength (UTS or ), strain hardening exponent (n value)  Plastic anisotropy: normal anisotropy ( ̅), planar anisotropy (∆r)

 Forming limits: uniform elongation ( ), reduction of area ( ), upsettability, Erichsen cupping depth

 Surface properties: roughness ( , , , ), chemical and physical surface properties

When a material deforms, elastic deformation and plastic deformation occurs. During elastic deformation, when load is removed, the material recovers the form to what originally it was. However, when load is applied further, material will reach plastic phase. In this phase, the material deforms permanently. Because of factors such as strain hardening and area reduction, relationship between load and deformation becomes nonlinear. In uniaxial tensile test, those explanations are more understandable [Altan 2012].

2.1 Uniaxial Tensile Test The uniaxial tensile test is the standard test to determine mechanical properties of metals. As shown in Figure 1, standard size specimen is cut out from the sheet metal and stretched slowly until it fractures.

Overall Length = 203.2 mm (8 in)

Gage Length

l 0 = 50.8mm (2 in)

Width = 12.7mm Width = 19.1 mm (0.50 in) (0.75 in) Figure 1. Tensile test specimen, according to ASTM E8 [Altan 2012, ASTM 2011]

Wider ends of the specimen are gripped by the special fixtures not influencing deformation. The specimen is attached to fixed and moving crossheads as shown in Figure 2. During the test, fixed crosshead is fixed and moving crosshead is pulled down. Consequently, gripped specimen is pulled down and reaction forces are applied on both sides of the specimen. Extensometer measures the elongation of gage length in real time. Through the test, load vs. elongation curve is obtained as shown in Figure 3. It is normalized with respect to the geometry of specimen to calculate stress and strain. lU is uniform elongation and lF is total elongation at load vs. elongation curve.

F Column Fixed Crosshead

Specimen

Moving Crosshead v F Table

Base and Actuator

Figure 2. Schematic of a fixture used in a tensile test [Altan 2012]

Fracture

Load Uniform Force (F) Force Plastic Deformation Non-uniform Plastic l U Deformation

ElongationElongation (Δl)

Figure 3. The schematic of the force vs. elongation curve obtained from tensile test [Altan 2012]

Engineering stress ( ) is defined as the force (F) divided by the original cross- sectional area ( ) as shown in Eq. 1.

Eq. 1

Engineering strain (e) is defined as shown in Eq. 2.

Eq. 2

where is the original length of the gage and is the elongation. As illustrated in Figure 4, there is useful information in engineering stress vs. engineering strain curve. Yield strength (Y or ) is the stress value where elastic phase finishes. After yield strength, plastic phase starts. Yield strength can be determined by any three of these techniques: (a) offset method, (b) Extension under load method, (c) Autographic diagram method [ASTM 2011]. For elastic phase, linear slope indicates Young’s modulus (E). When engineering stress reaches maximum engineering stress, specimen starts localized necking ending uniform elongation

( ), and the stress value at this point is called ultimate tensile strength (UTS or

). Uniform elongation ( ) is considered to be an indicator of ductility or formability of the material because after necking, material starts to fail [Altan 2012]. Engineering stress and engineering strain are based on original cross- sectional area. However, true stress (or flow stress, ) is the ratio of applied load (F) and instantaneous cross-section area (A) as shown in Eq. 3 [Altan 2012].

Eq. 3

Figure 4. Engineering stress vs. engineering strain curve [Kalpakjian 2008]

Eq. 4 shows how true stress (flow stress) is derived from engineering stress and engineering strain [Marciniak 2002]. True strain is calculated by considering instantaneous gage length (l) divided by initial length of the gage ( ) as shown in Eq. 5.

Eq. 4

Eq. 5

According to the definition of true stress and true strain curve, flow stress curve can be drawn up to the strain of b’ which corresponds to the ultimate tensile strength (UTS) at the engineering stress and engineering strain curve as shown in Figure 5.

Relationship between stress and strain can be expressed with Hooke’s Law n ( ) in elastic region and Hollomon’s Law in plastic region (σ=Kε ). In elastic region, stress and strain have linear relationship. Young’s modulus (E) can be determined by the slope of the engineering stress ( ) and engineering strain (e) curve. In the plastic region, Hollomon’s Law is the most commonly used nonlinear relationship between true stress and true strain. K indicates the strength coefficient and n is the strain hardening exponent. Figure 6 shows the true stress and true strain curve of Al 1100-O [Hosford 2007, Altan 2012].

Figure 5. Comparison stress vs. strain curve between engineering state and true state [Hosford 2007]

10000

Value of elastic modulus, E = 10x103 ksi which is the value of , when  = 1.0 by extrapolation of the line denoting the elastic region.

1000

[ksi]  100

25 ExtrapolationK of= elastic 25 ksi region (value of True Stress,True  for  = 1.00) n 10 1 Slope = n = 0.25

I II III 1 0.0001 0.001 0.010 0.100 1.00 True Strain,  Figure 6. True stress and true strain curve of Al 1100-O, plotted on log-log scale [Hosford 2007, Altan 2012]

Flow stress curve is the curve after yield stress and before plastically necking. Flow stress is important in metal forming processes as it defines the behavior of material deformation. It is a function of strain ( ),̅ strain rate ( ̇),̅ temperature ( ) and microstructure (S) as shown in Eq. 6.

   f , , ,S Eq. 6

In most materials, flow stress increases with strain in room temperature because of strain hardening which is a result of interaction of dislocations or inclusions in the crystalline structure [Lange 1985]. Flow stress curve equations are developed in different ways as shown in Figure 7. Including Hollomon’s Law which is a good approximation of the flow stress curve [Pöhlandt 1989], there are several other equations which are shown in Figure 8.

Figure 7. Some of the flow curve equations used in plastic deformation studies [Marciniak 2002, Altan 2012]: (a) Hollomon’s Law, (b) Swift’s Law, (c) Linear strain hardening, and (d) Constant

Figure 8. Predicted flow stress curves by different equations [Nasser 2010, Paul 2012]

Flow stress curve from tensile test is generally preferred because of its simplicity and the conditions of tensile test have been well defined by standards [Pöhlandt 1989]:

 ASTM E 6-09b: Standard Definitions of Terms Relating to Methods of Mechanical Testing, 2009  ASTM E8/E8M-11: Standard Test Methods for Tension Testing of Metallic Materials 2011.  ASTM A 370: Standard Methods and Definitions for Mechanical Testing of Steel Products, 2012  ASTM B 557: Standard Methods of Tension Testing Wrought and Cast Aluminum and Magnesium Alloy Products, 2010  ASTM B 557M: Standard Methods of Tension Testing of Wrought and Cas Aluminum and Magnesium Products (Metric), 2010  ISO 6892: Metallic materials — Tensile testing — Part 1: Method of test at room temperature - First Edition, 2009  Euronorm 2-80: Tensile Testing on Steel (Revision), 1980  ASTM E83 REVa: Standard Practice for Verification and Classification of Extensometers, 2010  ASTM E 1012: Standard Practice for Verification of Testing Frame and Specimen Alignment Under Tensile and Compressive Axial Force Application, 2012

However, there is a demand for another test method to determine flow stress curve for metal forming purposes. In practice, strain hardening exponent (n) is considered as an indication of material formability since it corresponds to the value of uniform elongation in the engineering stress and engineering strain curve. The necking (instability in tensile test) starts when normal force (F) is at the condition of maximum and this can be formulated by Eq. 7.

dF  0 Eq. 7 d

Right before reaching maximum force, the normal force can be expressed as shown in Eq. 8.

A  A exp   F A exp  0   0   Eq. 8

Instantaneous area (A) is plugged into Eq. 7:

dF  d   0  A0 exp  exp  Eq. 9 d  d  d    d

Therefore, tensile instability condition is obtained by Eq. 10 when the flow stress is assumed to follow Hollomon’s Law.

d  nK n1    K n Eq. 10 d or:

Figure 9 illustrates true stress and true strain condition at necking in tensile test. For most of the metals, strain hardening exponent lies in the range of 0.1 to 0.5 [Pöhlandt 1989], tensile test can only determine flow stress curve for a small range of strain as shown in Figure 10.



  K n

d  Slope    d 1

  1 Figure 9. Schematic representation of stress-strain conditions for necking in simple tension [Altan 2012]

1000

800

Bulge Test

) [MPa] _  600

400

Tensile Test 200 Effective Stress ( DP 600, t = 1.0mm 0 0 0.1 0.2 0.3 0.4 0.5 Effective Strain (  )

Figure 10. Flow stress curve obtained from tensile test and bulge test [Billur 2011]

As a result, the widely used tensile test has deficiencies [Altan 2012]:

 It gives material properties for uniaxial conditions while in practical

stamping the deformation is biaxial.

 It is limited to relatively low strains, due to necking.

 It needs extrapolation in FE based process simulations that may lead to

errors.

On the other hand, tensile test can be useful to determine anisotropy properties. In real world, microstructures of the materials are not always uniform in all directions (isotropic) but are aligned in certain directions (anisotropic). It is important to get anisotropy coefficients of the sheet material. Anisotropy can be defined by two forms: (1) normal anisotropy, and (2) planar anisotropy. As shown in Figure 11, while normal anisotropy differs through the thickness of the material, planar anisotropy changes according to various directions within the plane of the sheet [Altan 2012].

Normal Anisotropy Planar r (r) 0 Anisotropy r45 r

r90

Rolling Direction

Figure 11. Sheet orientations relative to normal and planar anisotropy [Totten 2003, Altan 2012]

While sheet metal is processed, grains of the material’s microstructure are aligned in rolling direction and packed in thickness direction. This leads to significant differences in strength properties in “rolling” direction and “perpendicular” to

14 rolling direction. Ratio of the strains in the width to thickness directions determined by tensile test is referred to as r-value, also known as the plastic strain ratio. It is given by Eq. 11 where  w is the width strain and  t is the thickness strain, as illustrated in Figure 12.

 r  w Eq. 11  t

 w

 t

Figure 12. Definitions of width and thickness strains in a tensile specimen [Davis 2004]

With higher r values, sheet material tends to resist to thinning. The plastic strain ratio (r) is determined along parallel ( ), transverse ( ) and diagonal ( ) to rolling direction of the sheet material. Normal anisotropy ( ̅ ) and planar anisotropy ( ) are defined as shown in Eq. 12 and Eq. 13 [Pöhlandt 1989, Altan 2012].

̅ Eq. 12

r2 r r r 0 45 90 Eq. 13 2

2.2 Biaxial Tension Test

2.2.1 Cupping tests

There are several cupping tests to determine formability, such as Swift cup test, Fukui test, and Erichsen test. From Swift cup test, limiting drawing ratio for the flat bottom cups is determined. Fukui conical cup test as illustrated in Figure 13 determines both stretching and drawing over a spherical indenter [Hosford 2007].

Figure 13. Schematic of Fukui conical cup test [Hosford 2007]

In Erichsen test, as shown in Figure 14, circular punch with diameter of 20 mm (0.787”) stretches clamped sheet material under biaxial condition. The sheet material deforms to a hemispherical shape and finally fractures. The depth of the ball refers as Erichsen Index (IE), and the larger Erichsen Index means the better formability. Cupping tests have limitations and are losing favor because of irreproducibility. Hecker described the limitation of cupping tests as “insufficient size of the penetrator, inability to prevent inadvertent draw-in of the flange and inconsistent lubrication [Hecker 1974].” That is, cupping tests are limited to use in practice because the area of the sheet material is subjected to deformation is relatively small. And thickness of the sheet material influences significantly on formability. Also, friction between sheet material and tooling affects the test results [Hosford 2007, Altan 2012].

Figure 14. Schematic of Erichsen cup test [Doege 2010, Altan 2012]

2.2.2 Limiting Dome Height (LDH) Test

Hecker proposed Limiting Dome Height (LDH) Test to avoid the small area of deformation which was one of the limitations of the Erichsen cup test, and Ghosh modified Hecker test to simulate plane-strain condition where 80% of stamping failure occurs [Ayers 1979]. LDH test uses 101.6 mm (4”) diameter of the punch and sheet material is stretched in biaxial directions while clamped at the edges by lockbead to avoid draw-in (Figure 15). At ERC/NSM, the LDH test was used to evaluate lubricants. FE simulations for the LDH test showed that the test is very sensitive to friction and it affect the test measurements [Ngaile 1999]. FE simulations, shown in Figure 16, are conducted to study relationships of interface friction. As expected maximum thinning when friction is zero occurred at the apex of the dome. For friction of 0.075, location of maximum thinning shifted by 20 mm away from the apex [Ngaile 2000, Hosford 2007, Altan 2012].

Figure 15. Schematic of LDH tooling [Grote 2009]

Generally, location of maximum thinning moves away from the apex of the dome as interface friction increases, and punch force also increase as interface friction increases as shown in Figure 17.

Maximum thinning Maximum thinning

(a) (b) Figure 16. Location of maximum thinning when friction is (a) 0 and (b) 0.075 [Ngaile 2000]

Y 30 1.2 55

to 25 1

54 puch 20 0.8 53 Y 15 0.6 52

51 10 0.4

Hemispherical [tons] load Punch 50

Distance from center of center from Distance Distance from center of punch center to from Distance 5 punch 0.2 thinning [in] locationof maximum location of maximum thinning [mm] locationof maximum 49 0 0.02 0.04 0.06 0.08 0.1 0 0 0 0.02 0.04 0.06 0.08 0.1 X Coefficient of friction Coefficient of friction (a) (b)

Figure 17. Influence of interface friction (a) on the location of maximum thinning, (b) on punch force [Ngaile 2000]

Figure 18 shows limiting dome height of several materials which indicates each material’s stretchability.

Figure 18. Comparison of stretchability results of different steels from LDH test [WSA 2009, Altan 2012]

LDH test can simulate the most critical strain state in plane strain conditions, so it is usually used in industry. However, there are several limitations for using LDH test [Narasimham 1995]:  Large scatter of results from LDH test needed special detailed procedure recommended by North American Deep Drawing Research Group (NADDRG) [ASM/NADDRG 1987]. Despite the special procedure, it is nearly impossible to reproduce the results within a laboratory and between different laboratories [ASM/NADDRG 1990].  It is hard to obtain stable reproducible plane-strain condition over large region of the sheet material.  Result is dependent critically upon small variations in plastic anisotropy, friction and constraint of the drawbead [Ghosh 1975].  It is time consuming.  There is imprecise definition of failure because of nature of the crack [Narasimham 1995].

2.2.3 Bulge Test

In bulge test, sheet material is deformed under balanced biaxial deformation while it is clamped around its periphery (Figure 19). There are two types of bulge test: (a) hydraulic bulge test using pressurized fluid (such as oil) and (b) Viscous Pressure Bulge test using viscous medium as shown in Figure 20.

Figure 19. Schematic of Hydraulic Bulge Test [Gutscher 2004]

Figure 20. Viscous Pressure Bulging (VPB) test set-up [Ngaile 2000]

Viscous Pressure Bulge (VPB) Test as shown in Figure 20 is installed in hydraulic press with a die cushion or nitrogen cylinders. When ram moves down, punch pushes the viscous medium so that pressure is generated within the medium acting on the sheet material. Instantaneous variables during bulging to determine flow stress curve are dome height ( ), pressure (P), dome apex thickness (t) and bulge radius ( ). Figure 21 shows the geometry of bulge test where constant

21 parameters for die sets are initial sheet material thickness ( , clamping force ( ), upper die fillet radius ( ), die cavity radius ( ).

Figure 21. Geometry of bulge test [Billur 2011]

Biaxial strain can be calculated by reduction of sheet thickness as following Eq. 14 [Hill 1950, Billur 2008]:

Eq. 14

Eq. 15

̅ Eq. 16

To calculate effective strain ( ̅), measured parameters, which are pressure (P) and dome height ( ), need to be determined and there are several methods such as Hill [Hill 1950], Enikeev-Kruglov [Kruglov 2002, Slota 2008] and Chakrabarty- Alexander. In a recent study, Slota showed that the result from Enikeev-Kruglov approach is more accurate than that of Hill approach [Slota 2008].

Since bulge test is applied to a thin sheet material (i.e., ⁄ , where is die cavity diameter), membrane theory can be assumed in which bending effects are negligible [Hill 1950, Ranta 1979, Gutscher 2004, Billur 2008]. Based on von Mises yield criterion, the effective stress can be calculated by Eq. 17 [Gutscher 2004].

̅ Eq. 17

To calculate the effective stress ( ̅), bulge radius ( ) needs to be determined first. Hill method [Hill 1950] and Panknin method [Gutscher 2004, Kaya 2008] are the approaches of determination of bulge radius.

There are some limitations with using hydraulic bulge test as follows [Young 1981, Koç 2011, Altan 2012]:

 This test has not been standardized so that it is difficult to compare results from different tooling and laboratories.

 Spraying related issues exist in optical measurement system (reported by [Koç 2011]).

 3-D optical measurement system (ARAMIS) is highly reliable at room temperature condition. However, when temperature increases, smoke/vapor blocks the vision and big deflections occur in the prediction of bulge radius [Billur 2008].

 Tooling gets dirty after sheet bursts because of using oil or viscous medium.

 It is highly demanding time and labor to analyze the data from the test.

2.2.4 Dome Test (extension of LDH test)

Using same tooling of LDH test (Figure 15), dome test can be utilized to determine flow stress, formability and anisotropy for stamping under biaxial deformation condition. It should be noted that adequate lubrications (near zero friction) are needed to obtain flow stress accurately. Maximum thinning occurs at the apex of the dome when friction is zero as in the bulge test as shown in Figure 22(a). Friction at tool-workpiece interface has an effect on formability and thinning distribution. As friction increases, maximum thinning location moves toward die corner radius as shown in Figure 22 (b).

By using dome test, it may be possible to determine (a) flow stress under biaxial deformation, (b) formability under biaxial stretch and (c) a flow stress equation in Hollomon’s Law (σ=Kεn) that provide reliable input data on mechanical properties of sheet materials to generate FE simulations of metal flow in stamping.

(a) (b)

Figure 22. Fracture location of (a) frictionless dome test with fracture at apex, TRIP 780 (t = 1mm) with lubrication (Teflon and Clay) (b) with no lubrication

CHAPTER 3 OBJECTIVES AND APPROACH

3.1 Objectives Overall objective is to determine flow stress curves (determining K and n values in Hollomon’s law, σ=Kεn ) of sheet metal, by using the dome test which is easier to use in industry than the bulge test. There are two parts to satisfy overall objective:

1) Experiments:

a. Dome test: a proposed test to obtain flow stress (by recording, punch force vs. stroke) at large strains,

b. Tensile test: a well-established, standard test for determination of anisotropy and uniaxial formability.

2) Inverse Analysis:

a. FE simulations: To build the database for inverse analysis,

b. Computer program “PRODOME” using MATLAB: To inversely calculate K and n values, based on simulation database and experimental measurements (punch force vs. stroke).

3.2 Approach 1) Phase 1: Conduct preliminary experiments for evaluation of the lubricants for dome tests at Honda R&D.

a. Punch force and punch stroke are recorded during dome test.

b. Punch force vs. stroke curves are generated by using MS Excel.

c. Fracture occurred at the apex of 780 TRIP (Lubricants: Hydro- Aluminum’s suggestion [Hydro-Aluminum 2012], thickness =

1mm). Hydro-Aluminum’s suggestion is to achieve a nearly friction-less state making 7 layer system. This sample is our reference model for making FE simulations. Recorded punch force vs. stroke curve from experiment is shown in Figure 23.

200

Max. punch force =150 kN 150

100

Punch[kN] Force 50

780 TRIP (t = 1.0mm)

0 0 10 20 30 40 50 Stroke [mm] Final punch stroke from exp.= 37.5 mm Figure 23. Punch force vs. stroke curve of 780 TRIP. Fracture occurred at the apex of the dome

2) Phase 2: Run 3-D (PAMSTAMP) dome test simulations.

Simulations were conducted for constant K and several n values by using tool geometry provided by Interlaken and punch force will be calculated as a function of punch stroke as described below:

a. The material model is assumed to be following Hollomon law (Power law) σ=Kεn where K is strength coefficient and n is strain hardening exponent.

b. n affects the shape of the punch force vs. punch stroke curve.

c. However, K does not affect the shape of the punch force vs. punch stroke curve but affects the magnitude of the punch force vs. punch stroke curve. Thus, the FE simulations will be conducted for a preselected K value and various n values (K = 1000MPa, n = 0.06…0.6 with 0.01 increments).

d. Sheet thickness is assumed to be same as 780 TRIP (t=1mm) and final punch stroke is decided to be 50mm.

e. Experimental punch force vs. punch stroke curve will be normalized to eliminate the effect of K on the magnitude of the punch force and will be compared with normalized punch force vs. punch stroke curve from FE simulations.

3) Phase 3: Make computer program.

a. 55 polynomial equations which fit the normalized punch force vs. stroke curves from simulations (n=0.06…0.6) are obtained.

b. Experimental stroke is plugged into each equation to obtain FE normalized punch force as a function of n-value.

c. Difference ( ) between experimental normalized punch force and FE normalized punch force is calculated using Eq. 18 [Cho 2005, Demiralp 2011]:

∑ √ ̅ ̅ Eq. 18

Where:

Difference at a parameter of n (strain hardening exponent) in

FE simulation,

Applied strain hardening exponent to FE simulation n (n=0.06…0.6 with 0.01 increments)

j jth stroke (total punch stroke is divided into m intervals, j=1:m),

Normalized measured punch force during experiments for jth

̅ stroke, (“normalized” means that measured punch force is divided by the maximum punch force)

Normalized calculated punch force for jth stroke from FE ̅ simulation with n .

d. Determine n value and calculate K using Eq. 19 [Demiralp 2011]:

K = Eq. 19

Where,

(n) : Maximum punch force from FE simulation with determined n value (Eq. 18) at maximum experimental stroke

: Initial sheet thickness

4) Phase 4: Conduct tensile tests to determine: (a) uniaxial stress-strain

curves and (b) anisotropy coefficients (r0, r45 and r90) to apply anisotropy correction on the biaxial flow stress.

a. Flow stress curve is obtained, Hollomon law (Power law) σ=Kεn

b. Tensile test is conducted for anisotropy coefficient (r0, r45 and r90) by Honda.

c. Anisotropy correction factor is calculated using Eq. 20 and Eq. 21 [Hill 1948, Billur 2011].

̅ ̅ √ Eq. 20 ̅

̅ ̅ √ ̅ Eq. 21

Where, ̅ =

CHAPTER 4 INVERSE ANALYSIS METHODOLOGY

Inverse analysis methodology was used to determine the flow stress and the interface friction at elevated temperatures by [Cho 2003]. Following procedure is the inverse analysis methodology applied to this study:

1) The data points on experimental punch force vs. stroke curve were provided by Honda.

2) Material is assumed to follow Hollomon’s Law (σ=Kεn) where K is strength coefficient and n is strain hardening exponent. FE simulations were conducted for constant K (1000 MPa) and several n values (from 0.06 to 0.6) by using the same tool geometry used in the experiments provided by Honda and Interlaken (who built the test machine for the dome test). Punch forces were calculated as a function of punch stroke.

3) After obtaining punch force vs. stroke curves from experiments and FE simulations, each curve was normalized by dividing the force at various stroke positions by the punch force at the maximum experimental stroke (Figure 24). Normalization of the punch force vs. stroke curve on both experiment and FE simulation was done to eliminate the effect of K on the magnitude of the punch force vs. stroke curve. n value only affects the shape of the punch force vs. stroke curve.

4) n values were determined by Eq. 18 which brought the minimum

difference ( ) between normalized experimental punch force vs. stroke curve and normalized FE punch force vs. stroke curve [Cho 2005].

5) K does not affect shape of the punch force vs. punch stroke curve but affects the magnitude of the punch force vs. stroke curve. Since FE

simulations were done with K = 1000 MPa, K value can be calculated by Eq. 19. Since initial thickness of FE simulation model was 1 mm, maximum punch force from FE simulation should be multiplied by initial thickness. This is on approximation to be evaluated later.

Figure 25 shows inverse analysis methodology to determine n value of a tested material.

1.0

0.8

0.6

0.4

NormalizedPunch[kN] Force 0.2 780 TRIP (t = 1.0mm)

0.0 0 10 20 30 40 50 Stroke [mm] Final punch stroke from exp.= 37.5 mm Figure 24. Normalized punch force vs. stroke curve of 780 TRIP (t = 1.0mm) with fracture at the apex of the dome

Initial guess of K (1000 MPa) and n (0.06)

Run FE simulations with several n values (n = 0.06 to 0.6)

Extract FE simulation results

n = n + 0.01 Calculate Difference ( )

Store Difference ( )

No n = 0.6 ?

Yes Find minimum

Determine n value

Figure 25. Flow chart of inverse analysis methodology [Cho 2005]

CHAPTER 5 EXPERIMENTAL WORK AND RESULTS

5.1 Experiments and Tooling The dome tests were conducted at Honda by using INTERLAKEN 150T press (Figure 26). During the test, punch force and stroke data were recorded. There are four categories of tested sheet materials: (1) ASTM 1008 Low Carbon Steel, (2) TRIP Steel, (3) High Strength Low Alloy Steel and (4) Aluminum tempered as of T4 condition (solution heat treated and naturally aged).

Table 1. Dome test experiment matrix [Dykeman 2011, POSCO 2012]

Equipment INTERLAKEN 150T press  JSC 270F (t = 0.8 mm)  JAC 780TRIP (t=1.0 mm and t = 1.6 Sheet Material mm)  JAC 590R (t=1.6 mm)  Al 6022-T4 (t=1.0 mm) Sheet dimensions 165.1 mm × 165.1 mm (6.5 in × 6.5 in) (length × width)

Punch radius, Rp 50.8 mm (2 in)

Die corner radius, Rdie corner 6.35 mm (0.25 in)

Die diameter, Ddie 105.76 mm ( 4.16 in)

Lockbead diameter, Dlock 132.58 mm (5.22 in) Punch stroke Until the sample fractures Lubricants Teflon, Clay and others (given in Appendix A)

6.35 mm 0.25 in.

Figure 26. Schematic of the dome test [Grote 2009, Interlaken]

5.2 Test Procedure

The dome test experiments were done with the tooling described in the previous section. The press used for these experiments is a 150 ton press manufactured by Interlaken as shown in Figure 27.

At the beginning, the tooling is open and the sheet material is placed between die and blankholder. When the press runs, the sheet is clamped by lockbead. Then the solid hemispherical punch moves upward and deforms the sheet. As a result of high clamping force and lockbead, the sheet is prevented from drawing into die cavity. The sheet is deformed until it fractures.

With the computer controlled system, it is possible to record punch force, punch stroke, clamp force and clamp stroke with time. From this data acquisition, punch force vs. stroke curve can be made, and this curve is needed to determine flow stress curve of the material.

Camera system

Die

Solid punch (inside) Monitor

Blank holder UniTest control system

Figure 27. Dome test tooling

5.3 Output from the Dome Tests

In the dome test, punch force and punch stroke were recorded by the computer controlled system. Since the punch force vs. stroke curve is invalid after the sheet fractures, the data has to be deleted after fracture. Punch force vs. stroke curve is plotted shown as Figure 28. From punch force vs. stroke curve, dome height (AC) and maximum punch force also can be detected.

200 Max. punch force =150 kN Dome height (distance AC) Reference 150 B

100

Punch[kN] Force 50

780 TRIP (t = 1.0mm) A C 0 0 10 20 30 40 50 Stroke [mm] Final punch stroke from exp.= 37.5 mm

Figure 28. Punch force vs. stroke curve from experiment, 780 TRIP (t = 1.0 mm) with lubricants of Teflon and Clay

5.4 Test Parameters and Selection of Materials The material tested using the dome test are JSC 270F, JAC 590R, 780 TRIP and Al 6022. These materials are widely used in stamping. The material properties evaluated by uniaxial tensile tests are presented in Table 2.

Table 2. Material properties evaluated by tensile test provided by Honda

Al 6022- Parameter Unit JSC 270F JAC 590R 780 TRIP T4

mm 0.8 1.6 1.0 1.0 Initial sheet thickness inch 0.031 0.063 0.039 0.039

MPa 119 468 447 N/A Yield Strength psi 17,259 67,900 64,800 N/A

Ultimate MPa 283 638 811 N/A Tensile Strength psi 41,046 92,500 117,600 N/A

% elongation % 50.7 24.2 26.3 N/A

n-value 0.32 0.17 0.23 N/A

In Table 3, the parameters for the dome test are shown. The speed of the punch is set to 1.35 mm/s (0.06 in/sec). The clamping force of 445 kN (100,000 lbs) and lockbead ensured that the sheet is not drawn into the die cavity. The test specimen is square of 165.1 mm × 165.1 mm (6.5 in × 6.5 in). Figure 29 shows a burst sample of JAC 590R. The best location of the fracture is the apex of the dome to have frictionless condition. Lubricant system will be discussed in more detail in Section 7.5. The ring mark around the sample is formed by lockbead.

Table 3. Test parameters of the dome test

Parameter Metric British

Punch speed 1.35 mm/s 0.06 in/sec

Clamping force 445 kN 100,000 lbs

Diameter of the cavity of 105.76 mm 4.16 in the die

Radius of the fillet of the 6.35 mm 0.25 in cavity

Size of the test sample 165.1 mm × 165.1 mm 6.5 in × 6.5 in.

Figure 29. Top and front view of burst sample from dome test ( JAC 590R, t = 1.6mm)

5.5 Test Results

From experiments, punch force vs. stroke curve of three materials (JAC 590R, 780 TRIP, Al 6022) are obtained. Fracture occurred at the apex of the dome by eliminating or minimizing the friction (combination of Teflon and Clay as lubricants). Punch force vs. stroke curves are shown in Figure 30, 31 and 32. Since, fracture did not occur at the apex of the dome for JSC 270F (t = 0.8mm) and JAC 780 TRIP (t = 1.6 mm), the results are not included.

200

Max. punch force =188 kN 150

100

Punch[kN] Force 50

JAC 590R (t = 1.6mm)

0 0 10 20 30 40 50

Stroke [mm] Final punch stroke from exp.= 43.1 mm Figure 30. Punch force vs. stroke curve of JAC 590R (t = 1.6mm)

200

Max. punch force =150 kN 150

100

Punch[kN] Force 50

780 TRIP (t = 1.0mm)

0 0 10 20 30 40 50 Stroke [mm] Final punch stroke from exp.= 37.5 mm

Figure 31. Punch force vs. stroke curve of 780 TRIP (t = 1.0mm)

200

Al 620 (t = 1.0mm)

150

100

Punch[kN] Force 50 Max. punch force =40 kN

0 0 10 20 30 40 50

Stroke [mm] Final punch stroke from exp.= 35.7 mm

Figure 32. Punch force vs. stroke curve of Al 6022 (t = 1.0mm)

CHAPTER 6 FE SIMULATIONS

FE simulations were conducted to a establish database for the dome test. Simulations were conducted for constant K (1000 MPa) and several n values (from 0.06 to 0.6 with 0.1 increments). The database was built using MS Excel and has punch stroke, punch force and plastic maximum strain ( ) at the apex of the dome from simulations. With these results, the experiment can be analyzed to determine K & n values and maximum strain value ( ) of the sheet material. The simulations were conducted by PAMSTAMP, a dynamic explicit code for 3- D simulation with shell elements.

6.1 Simulation Parameters The geometrical model in simulation is shown in Figure 33. The diameter of die cavity (Ddie), die corner radius (Rdie corner) and punch radius (Rp) are same dimensions as in the experimental tooling. The sheet is modeled until the lockbead. Therefore, outer nodes of the sheet in simulation are fixed so that they cannot draw into the die cavity. This ensures that the sheet only stretches in biaxial direction. The geometry of the simulation is symmetric. Therefore, only one quarter of model is simulated to reduce simulation time (Figure 33). Material type for sheet is elastic-plastic and other tools (punch, blank holder and die) are rigid. The sheet is modeled with 1566 elements with element size of 1.5mm. Punch force vs. stroke curves were then used as the database of computer program using MATLAB to determine K and n values of the sheet.

Sheet Die

Blankholder

Punch

Figure 33. Quarter model of simulation at stroke of 50 mm

The flow stress of the sheet material can be described by the Hollomon’s Law:

̅ ̅ Eq. 22

Range of the n values were investigated in literatures to cover n values of overall steel and aluminum grades [POSCO 2012, Altan 2012]. Final punch stroke for FE simulation was up to 50 mm. Since radius of the punch is 50.8 mm, it is no more biaxial stretching after 50.8 mm. Like other usual dynamic explicit simulations, the speed of punch was set much faster than that of the experiment to reduce computing time. Punch velocity for these simulations was used as 5mm/ms, appropriate value from literature [Gutscher 2004].

6.2 Computer Program “PRODOME” Using MATLAB

6.2.1 General concepts of computer program using MATLAB

A Computer program, PRODOME, was developed using MATLAB R2012b. This PRODOME has two inputs, 1) punch force vs. stroke curve from the experiment and 2) punch force vs. stroke curve database from FE simulations. By running the PRODOME, punch force vs. stroke curves on both from the experiment and FE simulations were normalized. After normalization, differences of punch force were calculated according to n values. n value was determined by obtaining the minimum difference between experimental normalized punch force and normalized punch force obtained from FE simulations (Eq. 18). K was calculated by Eq. 19. Anisotropy correction was considered in the PRODOME. More detail about anisotropy correction will be in Section7.2. Process of the PRODOME is illustrated in Figure 34.

Computer program

Experimental . Normalize punch force vs. stroke punch force vs. curve Determine K & n . According to experimental stroke, stroke curve values and calculate difference between exp. (Excel File) normalized punch force and normalized FE punch force . Determine n value that brings minimum difference between exp. and simulation . Calculate K value . Consider initial thickness ( ) . Consider anisotropy correction

FE simulation database (PAMSTAMP)

Figure 34. Process of the PRODOME

6.2.2 Running the PRODOME

When the PRODOME is run, it asks to open an Excel file with the experimental punch force vs. stroke data as shown in Figure 35.

Figure 35. PRODOME window to select experimental punch force vs. stroke data

Once the punch force vs. stroke data is copied from the Excel file, the

PRODOME will ask for the initial thickness ( ) and normal anisotropy ( ̅) of the sheet material as shown in Figure 36. As shown in Figure 37, once all the parameters are entered, the punch force vs. stroke curve is plotted on the upper right side of the screen. Punch force vs. stroke data, initial thickness and normal anisotropy can be changed by clicking the relevant buttons. By clicking the yellow “Calculate Stress – Strain” button, the PRODOME inversely calculates K and n values, and the maximum strain. Flow stress is plotted on the lower right side as shown in Figure 38.

As shown in Figure 39, true stress and true strain data can be saved in Excel file by clicking the button below the true stress and true strain table. Plots can also be saved by clicking the buttons.

Figure 36. PRODOME window to input initial thickness and normal anisotropy of the sheet material

Figure 37. PRODOME window shows punch force vs. stroke curve from experiment and buttons to renew data, initial thickness and/or normal anisotropy

Figure 38. PRODOME window that shows calculated flow stress curve

Figure 39. PRODOME window that shows buttons which can save data

CHAPTER 7 RESULTS AND DISCUSSION

7.1 Determination of K and n Values of the Sheet Materials When the “PRODOME” is run with input of punch force vs. stroke curve obtained from experiment, difference ( ) of punch force vs. stroke curve was compared between the experimental result and FE database from n value of 0.06 to 0.6. Calculated K and n values are listed in Table 4 and flow stress curves are shown in Figure 40.

Table 4. K & n values and of the materials with isotropic assumption ( ̅ = 1)

( = plastic strain at maximum dome height (at fracture) in simulation)

Material K [MPa] n-value

JAC 590R 955 0.30 0.72 (t = 1.6mm)

TRIP 780 1335 0.28 0.54 (t = 1.0mm)

Al 6022 348 0.20 0.53 (t = 1.0mm)

1400 JAC 590R (t=1.6mm) TRIP 780 (t =1.0mm) 1200 Al 620 (t=1.0mm)

1000 K = 1335 MPa, n = 0.28

800

600

K = 955 MPa, n = 0.30 True stress [MPa] stress True 400

200 K = 348 MPa, n = 0.20

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 True strain

Figure 40. Flow stress curves of materials of JAC 590R, TRIP 780 and Al 6022 with isotropic assumption ( ̅ = 1)

7.2 Anisotropy Correction In practice, sheet material is almost never isotropic. Since FE simulation database was based on isotropic assumption ( ̅ ), it should be modified by obtaining appropriate plastic anisotropy coefficients (r0, r45 and r90) from uniaxial tensile test. Therefore, calculated flow stress curves in Section 7.1 should be corrected for anisotropy. [Hill 1990]’s anisotropic yield criteria is used. Eq. 20 and Eq. 21 shows how to calculate correction factor for anisotropy correction [Hill 1948,

Hill 1990, Nasser 2010, Billlur 2011]. Normal anisotropies are calculated for the materials as shown in Table 5.

Table 5. Normal anisotropy of the materials (provided by Honda)

JAC 780 TRIP JAC 590R (t=1.6mm) (t=1.0mm)

Normal anisotropy ( ̅) 0.573 0.955

Plastic ratio along parallel to rolling 0.45 0.86

direction ( )

Plastic ratio along diagonal to rolling 0.51 1.01

direction ( )

Plastic ratio along transverse to rolling 0.82 0.94

direction ( )

7.3 Comparison of the Flow Stress Curves

7.3.1 Tensile test vs. dome test

Flow stress curves obtained from the dome test and tensile test were compared as shown in Figures 41 and 42. Flow stress curves obtained from the dome test were anisotropy corrected as discussed in Section 7.2. Since tensile test result of Al

6022 (t = 1.0 mm) was not available, flow stress curve comparison could not be made for Al.

1400 Dome test w/o anisotropy 1200 Dome test w anisotropy Tensile test

1000 K = 1117 MPa, n = 0.30, = 0.64

800

600 K = 955 MPa, n = 0.30, = 0.72

True Stress [MPa] Stress True 400 K = 984 MPa, n = 0.18, = 0.15 200

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 True Strain

Figure 41. Comparison of flow stress curves obtained from the dome test (isotropic, anisotropic) and the tensile test for JAC 590R (t = 1.6 mm)

1400 Dome test w/o anisotropy Dome test w anisotropy 1200 Tensile test

1000 K = 1355 MPa, n = 0.28, = 0.53 800

K = 1335 MPa, n = 0.28, = 0.54 600

True Stress [MPa] Stress True 400 K = 1507 MPa, n = 0.26, = 0.15

200

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 True Strain

Figure 42. Comparisons flow stress curves obtained from the dome test (isotropic, anisotropic) and tensile test for JAC 780 TRIP (t = 1.6 mm)

7.3.2 VPB test vs. Dome test from DEFORM and PAMSTAMP

In a preliminary study on the dome test, JAC 270E (t = 0.69 mm) was used for sheet material[Demiralp 2011]. In the report, K and n values were determined by conducting FE simulation using DEFORM. K and n values from VPB test was also reported on this report. To calculate K and n values from the PRODOME (based on PAMSTAMP), 10 digitized points of punch force vs. stroke curve (Figure 43) (experimental dome test) were used as input to the PRODOME. Table 6 describes each K and n values from VPB test, DEFORM and PAMSTAMP.

Figure 43. Digitized punch force vs. stroke curve obtained from dome test experiment (JAC 270E)

Table 6. Determined parameters from VPB test (w/o considering anisotropy), DEFORM and PAMSTAMP

PAMSTAMP Parameters VPB test [MPa] DEFORM [MPa] [MPa]

K 691 711 680

n 0.265 0.25 0.25

800 VPB test 700 DEFORM K = 711 MPa, n = 0.25 PAMSTAMP 600

500 K = 680 MPa, n = 0.25

400

300 K = 691 MPa, n = 0.265 True Stress [MPa] Stress True 200

100

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 True Strain Figure 44. Comparison K and n values among VPB test, DEFORM and PAMSTAMP

7.4 Zero Point Adjustment When punch force vs. stroke curve from experiment is copied to the PRODOME, zero point adjustment is important. When the experiment is started, punch force has some fluctuations depending on the experimental conditions. These fluctuations should be deleted to adjust the zero point. The adjustment has significant effect on n values as shown in Figure 45. To avoid error due to zero point adjustment, it is good to find the point where punch force starts to increase continuously.

200 1200 good zero point adjustment (A) shifted zero point adjustment (B) 1000 A 150 K = 955 MPa, n = 0.30

800 B

100 600

K = 980 MPa, n = 0.52

400

Punch Force [kN] Punch Force True Stress [MPa] Stress True 50

200 good zero point adjustment (A) shifted zero point adjustment (B)

0 0 0 10 20 30 40 50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Stroke [mm] True Strain

(a) (b)

Figure 45. (a) Punch force vs. stroke curve with good zero point adjustment and shifted zero point adjustment (b) flow stress curve of good zero point adjustment and shifted zero point adjustment

To extablish a good method to make a zero point adjustment, one test was done by stopping the punch at 1 inch before fracture occurred at the sample of JSC 270F (t = 0.8 mm) as shown in Figure 46. Dome height (AC from Figure 28) was measured with height gage. The zero point on the experimental load vs. stroke curve was determined, i.e., measured AC on the sample and maximum stroke on the load vs. stroke curve were equal.

Figure 46. Reference sample of JSC 270F (t = 0.8 mm) for calibration, stroke up to 1.00 inch 54

7.5 Lubrication System To obtain the flow stress curve accurately, maximum thinning should occur at the apex of the dome as in the VPB test. However, fracture does not occur always at the apex of the dome in the dome test. When friction exists, maximum thinning occurs away from the apex of the dome as shown in Figure 47. Therefore, it is necessary to know how much angle of the fracture (θ in Figure 47) is acceptable to use the flow stress curve obtained from the dome test. In this Section, percentage error between reference sample (of which fracture occurred at the apex) and other samples are calculated.

Necking when friction = 0 Necking moves with increased friction

Figure 47. Change in the location of maximum thinning with increased of coefficient of friction

7.5.1 Preliminary Evaluation Lubricant Test

In these dome tests, various lubricants were used to eliminate the friction between the punch and the sheet. Lubricants applied to the experiments are described in APPENDIX A.

For JSC 270F (t = 0.8 mm), samples were tested with a number of combinations of lubricants listed in APPENDIX B. However, all samples showed fracture far from the apex. For a different way to obtain fracture at the apex, punch stroke was stopped after some distance and lubricants were renewed. This procedure also could not help to obtain fracture at the apex of the dome (APPENDIX B). Dome height and maximum punch force did not much change after renewing lubricants. Also, for JAC 780 TRIP (t = 1.6 mm), fracture did not occur at the apex of the dome with the same lubrication condition that caused fracture at the apex for other thickness (t = 1.0 mm) and other materials (JAC 590R and Al 6022). as shown in Figure 48 .

Fracture Fracture Fracture

(a) (b) (c)

Figure 48. Dome test sample of JAC 780 TRIP (t = 1.6 mm) with lubricant of Teflon and Clay of (a) sample 1, (b) sample 2 and (c) sample 3

7.5.2 Measurement of angle of fractures

To measure the angle of fracture from the apex, Figure 49, AutoCAD software was used. After the photo of a sample is taken from front side as in Figure 49, it

56 was exported to AutoCAD and the radius was measured. Ruler was set together beside of the sample to obtain absolute radius of the dome.

Fracture

Figure 49. Measuring the angle of fracture using AutoCAD software (780 TRIP with no lubrication, t = 1.0 mm)

The angle (θ) can be calculated by using Eq. 23:

Eq. 23

where l is curvature length from the apex of the dome to the fracture, and r is radius of the dome. r is measured by making 3 points circle fit of the sample in Auto CAD. Reference samples for each material are considered to be used as follows:

 JAC 590R (t = 1.6 mm) with lubricants of Teflon and Clay,

 JAC 780 TRIP (t = 1.0 mm) with lubricants of Hydro Aluminum’s suggestion (7 layer system conceiting of lanolin/Teflon foil/lanolin/Mipolam (2 mm thick)/lanolin/Teflon foil/lanolin),

 Al 6022 (t = 1.0 mm) with lubricants of Teflon and Clay.

Angle of the fractures of the reference samples were measured to be smaller than 2 degrees. Average percentage error of the flow stress curve is calculated by using Eq. 24:

∑ Eq. 24

where i corresponds to the strain with increment of 0.01 until maximum strain

( ) of either reference flow stress ( ) or objective flow stress ( ). Flow stress curve with different angles of fracture for each material are shown in Figures 50, 51 and 52. Lubrication system which contains percentage error at the angle where fracture occurred, maximum strain and dome height are shown in Figures 53, 54 and 55.

A 1400 BC D 1200

1000 D

800 A, B, C

600

True Stress [MPa] Stress True 400 A: fracture at 2 deg. B: fracture at 12 deg. 200 C: fracture at 16 deg. D: fracture at 46 deg. 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 True Strain

Figure 50. Flow stress curve with angle of fractures (θ) for JAC 590R (t = 1.6mm)

1400 D ABC 1200 A DE F B, C G 1000

800

600

True Stress [MPa] Stress True 400 A: fracture at 2 deg. B: fracture at 5 deg. 200 C: fracture at 7 deg. D: fracture at 12 deg. 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 True Strain

Figure 51. Flow stress curve with angle of fractures (θ) for 780 TRIP (t = 1.0mm)

400 A B C

300 A, B, C

200

True Stress [MPa] Stress True 100 A: fracture at 2 deg. B: fracture at 5 deg. C: fracture at 38 deg. 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 True Strain

Figure 52. Flow stress curve with angle of fractures (θ) for Al 6022 (t = 1.0mm)

0.8 50 Maximum Strain A Dome Height BC D 40 0.6

Dome Height [mm]Height Dome

0.4 Reference 0.6 % error 0.9 % error 25 % error

Strain Max.

0.2 10

0.0 0 A B C D (2 deg.) (12 deg.) (16 deg.) (46 deg.)

Figure 53. Percentage error, maximum strain and the dome height on each angle of fracture (θ) for JAC 590R (t = 1.6mm)

0.8 50

Maximum Strain Dome Height [mm] ABC D 40 E 0.6

F [mm]Height Dome G 30

0.4

20 Strain Max. Reference 6 % 7 % 10 % 8 % 22 % 21 % 0.2 error error error error error error 10

0.0 0 A B C D E F G (2 deg.) (5 deg.) (7 deg.) (15 deg.)(20 deg.)(47 deg.)(49 deg.)

Figure 54. Percentage error, maximum strain and the dome height on each angle of fracture (θ) for 780 TRIP (t = 1.0mm)

0.8 50

Maximum Strain A B Dome Height C 40 0.6

Dome Height [mm]Height Dome

0.4

20 Max. Strain Max.

0.2 Reference 0.6 % error 2 % error 10

0.0 0 A B C (2 deg.) (5 deg.) (38 deg.) Figure 55. Percentage error, maximum strain and the dome height on each angle

of fracture (θ) for Al 6022 (t = 1.0mm)

For JAC 590R (t = 1.6 mm), simulations were conducted with different coefficient of friction (0.05…0.35 with 0.05 increments). For K and n values for flow stress curve to input, 955 MPa and 0.30 are used as same as the reference 61 sample of JAC 590R has. Punch stroke was up to 35.6 mm to obtain coefficient of friction in dry condition (46 degree of angle of fracture shown in Figure 53). At maximum thinning distribution, the location of maximum thinning (possible fracture) could be predicted. Angle of fracture were calculated by using same methodology which were used for measurement of angle of fractures on experimental samples.

Minimum angle

Maximum angle

(a)

46.2 43.8 42.1 40 40.4 41.4 40.4 39.8 36.4 38.0 34.2 30 30.0

27.9

20 17.4

15.2 Angle of Fracture [deg.] AngleFracture of 10

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Coefficient of Friction

(b)

Figure 56. Angle of fracture from apex (θ) with increasing friction (JAC 590R, t = 1.6 mm) (simulations) 62

Because of element size, minimum angle of fracture and maximum angle of fracture were calculated as shown in Figure 56 (a). In Figure 56 (b), angle of fracture are described as a function of coefficient of friction. In this result, JAC 590R sample in dry condition (46 deg.) has coefficient of friction approximately of 0.35 (Figure 56 (b)).

CHAPTER 8 SUMMARY, CONCLUSIONS AND FUTURE WORK

Obtaining and using precise material property is important for designing stamping process. Only accurate inputs to FE simulations give reliable outputs. The dome test is a material test for sheet materials to evaluate formability and determine the flow stress curve. Since the stress state of the dome test is biaxial, the maximum achievable strain without localized necking is much larger than that of the tensile test.

In this study, inverse analysis methodology was used to obtain flow stress curves (assumed to be following Hollomon’s Law: ̅ ̅ ) from punch force vs. stroke curves of the tested sheet materials. (JAC 590R (t = 1.6 mm), JAC 780 TRIP (t = 1.0mm) and Al 6022 (t = 1.0 mm)). From experiments, punch force vs. stroke curves were recorded. PRODOME was developed using MATLAB with database obtained from FE simulations (K = 1000 MPa, n = 0.06 ~ 0.6 with 0.01 increments). By running the PRODOME, K & n and maximum plastic strain

( ) can be determined. Also, lubrication system was investigated when friction cannot be eliminated.

 Fracture did not occur at the apex of the dome of JSC 270F (t = 0.8mm). For future work, it is desirable to try with combination of lubricants of beef tallow which is oil that performs high viscosity, and urethane. It is reported that lubricant causes fracture to occur at the apex of the dome for both mild steel and high strength steel. Garbage bag can also be considered to try to be used as lubricant.

 With the same lubricants which successfully worked for JAC 780 TRIP (t = 1.0mm), the thicker material (JAC 780T, t=1.6mm) did not give the

fracture at the apex because friction stress which is dependent on interface pressure is higher for thicker material. (Coulomb’s law, Friction stress ( ) = Coefficient of friction (μ)*Pressure (p)).

 K & n and are determined for following materials:

o JAC 590R (t = 1.6 mm): K = 1117 MPa, n = 0.30 and = 0.64 (with normal anisotropy of 0.573)

o JAC 780 TRIP (t = 1.0 mm): K = 1355 MPa, n = 0.28, = 0.53 (with normal anisotropy of 0.955)

o Al 6022 (t = 1.0 mm): K = 348 MPa, n = 0.20, = 0.53 (with isotropic assumption)

 In comparison of the flow stress curve between the tensile test and the dome test, flow stress curve for JAC 590R gets closer to the flow stress curve from the tensile test. For JAC 780 TRIP, flow stress curve did not change much after anisotropy correction.

 In a sample of 1.6mm thick JAC 590R, the flow stress curve determined by the dome test with anisotropy correction was up to a true strain of 0.64, whereas by the tensile test, it was up to 0.15. For sample of 1.0mm thick JAC 780 TRIP, the flow stress curve determined by the dome test with anisotropy correction was up to a true strain of 0.53, whereas by the tensile test, it was up to 0.15.

 The flow stress curve obtained from the VPB test, was compared with the dome test analysis using DEFORM and using PAMSTAMP. The flow stress curve from PAMSTAMP follows well the result from VPB test (average 1% error). Between the VPB test and the dome test using the DEFORM, average error is approximately 5%.

 The “Dome Test” allows, under biaxial deformation, the determination of: (a) the flow stress curve up to larger strains compared to the tensile test and (b) formability under biaxial stretch.

 It is important to be aware of zero point adjustment. By cutting fluctuations at the beginning of the punch force vs. stroke curves recorded from experiments, continuous punch force vs. stroke curve should be obtained. For one sample of JSC 270F (t = 0.8 mm), experiment was conducted and stopped at 1 inch of the dome height not having fracture. As a result, measured dome height was used to calibrate zero point adjustment. For future idea, it is better to conduct two experiments for each material, one for (a) the formability of the material by obtaining fracture at the apex and the other for (b) purpose of calibration by stopping punch before fracture occurs. And the dome height of the sample can be measure by either Coordinate-Measuring Machine (CMM) or height gage.

 Lubricants of Teflon + Clay reduce friction well for JAC 780T (t=1.0mm), JAC 590R (t=1.6mm) and Al 6022 (1.0 mm) and they are easy to use compared to “Hydro Aluminum’s suggestion”.

 In lubrication system, percentage errors of the flow stress curve between reference sample and objective samples were investigated:

o JAC 590R (t = 1.6 mm): up until 16 degrees of angle of fracture, the percentage errors were less than 1 %.

o JAC 780TRIP (t = 1.0 mm): until approximately 20 degrees, the percentage errors were less than 10 %.

o Al 6022 (t = 1.0 mm): there were small percentage errors (under 2 %) in overall range of angle of fractures (2 deg., 5 deg. and 38 deg.)

 This study attempted to investigate the errors introduced when the fracture occurred away from the apex. However, more work is needed with other sheet materials to establish guidelines for the proper used of the dome test.

REFERENCES

Altan, T., Oh, S., and Gegel, H. L., “Metal Forming: Fundamentals and Applications”, American Society for Metals, (1983).

Altan, T., "Metal Forming Processes in Manufacturing", Ch. 4 in Handbook of Sheet Metal Forming, (2012).

ASM/NADDRG: Recommended referee practice for the LDH test, (1987).

ASM/NADDRG: Final report of the LDH committee, (1990).

ASTM E 6-09b: Standard Definitions of Terms Relating to Methods of Mechanical Testing, (2009).

ASTM B 557: Standard Methods of Tension Testing Wrought and Cast Aluminum and Magnesium Alloy Products, (2010).

ASTM B 557M: Standard Methods of Tension Testing of Wrought and Cas Aluminum and Magnesium Products (Metric), (2010).

ASTM E 83 Rev a: Standard Practice for Verification and Classification of Extensometers, (2010).

ASTM E8/E8M-11: Standard Test Methods for Tension Testing of Metallic Materials, (2011).

ASTM A 370: Standard Methods and Definitions for Mechanical Testing of Steel Products, (2012).

ASTM E 1012: Standard Practice for Verification of Testing Frame and Specimen Alignment Under Tensile and Compressive Axial Force Application, (2012).

Ayers, R. A., Brazier, W.G. and Sajewski, V. F., J. Appl. Metal working, 1,(1979).

Billur, E. and Koç, M., " a Comparative Study on Hydraulic Bulge Testing and Analysis Methods ", Proceedings of the 2008 International Manufacturing Science and Engineering Conference, (2008).

Billur, E., et al., “Factor Affecting the Accuracy of Flow Stress Determined by the Bulge Test”, Steel Research Journal, (2011).

Cho, H., “Determination of flow stress and interface friction at elevated temperatures by inverse analysis technique”, Journal of Materials Processing Technology 170, (2005).

Cho, H., Ngaile, G. and Altan, T.,2003, “Simultaneous determination of flow stress and interface friction by finite element based inverse analysis technique”, Annals of the CIRP Vol. 52/1/2003, pp. 221-224, (2003).

Davis, J.R., Tensile Testing, 2nd Edition, ASM International. ISBN 0-87170-806- X, (2004).

Demiralp, Y., et al., “Determination of Flow Stress by using Dome Test and Finite Element Based Inverse Analysis – Preliminary Study”, CPF report- 2.1/11/01, (2011).

Doege, E., Behrens, B.A., ed. Handbuch Umformtechnik (Metalforming Handbook, in German), Springer-Verlag, Berlin, (2010).

Dykeman, J., “Strain Limit Analysis for JAC 270E_3”, (2011).

Euronorm 2-80: Tensile Testing on Steel (Revision), (1980).

Ghosh, A.K., Metals Eng. Quarter 15(53), (1975).

Gronostajski, Z., The constitutive equations for FEM analysis, Journal of Materials Processing Technology 106, 40-44 ,(2000).

Grote, K.H. and Antonsson, E.K., ed. Springer Handbook of Mechanical Engineering, Springer, Würzburg, (2009).

Grote, K.H. and Antonsson, E.K., Eds., Springer Handbook of Mechanical Engineering, Springer, (2009).

Gutscher, G., Wu, H., Ngaile, G., and Altan, T., “Determination of flow stress for sheet metal forming using the viscous pressure bulge (VPB) test”, Journal of Materials Processing Technology Vol.146, pp.1-7, (2004).

Hecker, S. S., Met. Engr Q. v. 14, (1974).

Hill, R., “A Theory of the yielding and plastic flow of anisotropic metals”, Proceedings of the Royal Society of London, 193A, p.281-297, (1948).

Hill, R.: A Theory of Plastic Bulging of a Metal Diaphragm by Lateral Pressure, Philosophical Magazine Series 7 (41), 1133-1142, (1950).

Hill, R., "Constitutive modeling of orthotropic plasticity in sheet metals", Journal of Mechanical Physics of Solids 38, 405–417., (1990).

Hosford, W.F. and Caddell, R.M.. Metal Forming: Mechanics and Metallurgy, 3rd Edition, Cambridge University Press . ISBN 978-0-521-88121-0., (2007).

ISO 6892: Metallic materials — Tensile testing — Part 1: Method of test at room temperature - First Edition, (2009).

Kalpakjian, S. and Schmid, S., Manufacturing Processes for Engineering Materials, 5th ed., Pearson Education, (2008).

Kaya, S., T. Altan, T., Groche, P., Klöpsch, C.,: Determination of the flow stress of magnesium AZ31-O sheet at elevated temperatures using the hydraulicbulge test, International Journal of Machine Tools & Manufacture 48 550-557., (2008).

Kruglov, A. A., Enikeev, F. U., Lutfullin, R. Ya.: Superplastic forming of a spherical shell out a welded envelope, Materials Science and Engineering A323 416-426., (2002).

Lange, K., ed. Handbook of Metal Forming, McGraw-Hill, New York , (1985).

Marciniak, Z., J.L. Duncan and S.J. Hu. Mechanics of Sheet Metal Forming, Butterworth Heinemann ISBN 0-7506-5300-0, (2002).

Narasimhan, K., Miles, M.P., Wagoner, R.H., A Better sheet-formability test, Journal of Materials Processing Technology Vol 50, pp. 385-394, (1995).

Nasser, A., Yadav, A., Pathak, P., Altan, T., Journal of Materials Processing Technology 210 429–436., (2010).

Ngaile, G., Altan, T. Model Test to Evaluate Lubricants and Die coatings in Tube Hydroforming, Report No. THF/ERC/NSM-99-R-4, (1999).

Ngaile, G., Gutscher, G. and Altan, T. “Evaluation of Friction and Formability in Stamping: Practical Methods for Production,” presented at the Sheet Forming Conference, April 12/13, Detroit, MI, Stamping Journal, Sept/Oct,p.26. , (2000).

Paul, S.K., "Predicting the flow behavior of metals under different strain rate and temperature through phenomenological modeling", Computer Materials Science 65 , p. 91-99, (2012).

Pohlandt, K., "Determining of Flow Curves of Sheet Metal", Ch. 3 in Handbook of Materials Testing for the Metal Forming Industry, (1989).

POSCO, Automotive Steel Data Book, (2012).

Ranta-Eskola, A. J.: Use Of The Hydraulic Bulge Test In Biaxial Tensile Testing, Int. J. of Mech. Sciences 21 p.457-465., (1979).

Slota, J., Spišák, E.: Determination of Flow Stress by the Hydraulic Bulge Test, Metalurgija 47, (2008).

Totten, G.E. and MacKenzie, D.S., ed. Handbook of Aluminum, Volume 1: Physical Metallurgy and Process, Marcel Dekker, Inc., New York, NY, (2003).

APPENDIX A: Lubricants list

 Lanolin (sheep wool fat/wax spray type) from TriState Distributors, Inc (Product info: http://tsdnetwork.com/Fluid-Film.php)

 Mipolam Elegance 290/ 0131 Opal (2mm thick) from Gerflor North America (Product info: http://www.gerflor.com/int/floors-for- professionals/product-page/mipolam-elegance-290,8.html)

 Teflon foil: Honda uses Teflon sheets (thickness=0.1mm) and this lubricant is offered by Honda (product of Grainger).

 Clay offered by Honda

 Hydro-Aluminum’s Suggestion: To achieve a nearly friction-less state, 7 layer system.

 557 Silicon: Dow Corning Silicone Dry Film 557 (Product info: http://www.firstpowergroupllc.com/DCC_Product_Sheets/Molykote_557. pdf)

 Gr spray: CRC Industrial Dry Graphite Lubricant Spray

 Rubbers are offered by Honda

o Rubber 1: Rubber Burna-N (a type of Nitrile rubber)1/16 in thick (Grainger Item# 2UNR1: http://www.grainger.com/Grainger/wwg/search.shtml?searchQuery =2UNR1&op=search&Ntt=2UNR1&N=0&GlobalSearch=true&ss t=subset )

o Rubber 2: Thin and stretchy more than that of Rubber 1.

APPENDIX B: Evaluation lubricant tests for high formability material (JSC 270F, t = 0.8 mm)

 Various combination of lubricants

Max. Max. sam Lube Punch Punch ple pic note condition force Stroke # [lbs] [inch]

Fracture 1 557Si+Gr 15899 1.432

557Si+Teflo n+557Si+Ru 2 bber2+557Si 16455 1.64 Fracture +Teflon+557 Si

Fracture 3 557Si 15972 1.441

Fracture 4 557Si 16212 1.471

2 layered 5 16215 1.622 Fracture Teflon

Necking 6 Dry 15449 1.399

7 Dry 15385 1.392

8 Dry 15257 1.376 Necking

Fracture 9 Lanolin 15900 1.443

ME290 - Fracture 10 2.05mm 16323 1.335 thick

Punch is covered Punch 11 15077 1.402 Teflon Fracture with Teflon.

Fracture Rubber1+Cl 12 16827 1.673 ay

Rubber1+Te Necking 13 17886 1.616 flon+Clay

Rubber1+Te 14 16951 1.651 Fracture flon+clay

Rubber1+Ru 15 bber2+Teflo 17288 1.619 Fracture n+Clay

Fracture 16 Teflon 16862 1.652

17 Teflon+Clay 16405 1.692 Fracture

18 Teflon+Clay 16808 1.723 Fracture

Teflon-Clay- 19 16654 1.648 557Si Fracture

 Different punch stroke

Max. sam Max. Lube Punch ple Punch pic note condition Stroke # force [lbs] [inch] Out of Teflon + 1 center of Clay punch reference sample for Teflon + calibration 2 N/A N/A Clay of 2 stage up to 1.00"

2stage: Teflon + 1.0'' 3 16077 1.759 Fracture Clay stop/failur e

Teflon + 4 16468 1.761 Fracture non stop Clay

Teflon + Fracture 5 15414 1.472 non stop Clay

2stage: Teflon + 1.2'' 6 15899 1.779 Fracture Clay stop/failur e

3stage: Teflon + 12 15758 1.723 Fracture 1.00''/1.4''/ Clay failure