Prediction and Reduction of Defects in Sheet Metal Forming Dissertation

Home , Formability, Stamping (metalworking)

PREDICTION AND REDUCTION OF DEFECTS IN SHEET METAL FORMING

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Ali Fallahiarezoodar

M. S.

Graduate Program in Industrial and Systems Engineering

The Ohio State University

2018

Dissertation Committee: Taylan Altan, Advisor Farhang Pourboghrat Jerald Brevick

Ali Fallahiarezoodar

2018

ABSTRACT

Sheet metal forming as process of forming a metal blank into a useful part is a major metal forming process. The overall objective of the sheet metal forming process is to form the part within the required tolerances without any defects. Defects in sheet metal forming appeared as tearing, necking, wrinkling, and springback. In the last decade, the advanced high strength steels (AHSS) and high strength aluminum alloys are increasingly used in automotive industry to satisfy the demands for improved safety, fuel efficiency and low-emission of greenhouse gas. However, in general, in high strength materials, low formability and high springback are observed. Therefore, forming of these materials is more challenging than normal mild steels. Several parameters affect the quality of the final part. Blank and tool material, friction and lubrication, and process parameters such as forming speed and temperature can significantly affect the result.

Determination of material properties and formability is necessary for tooling and process design. The common methods for determination of material properties required for designing and simulating the sheet metal forming process are reviewed. Also, forming limit diagram as an indication of material formability is studied. The limitations of the forming limit diagram are presented and a practical method for developing the forming limit diagram is presented.

Friction and lubrication play an important role in providing high quality parts from a deep drawing process. Friction conditions depend on sheet and tool material, surface qualities, the type of the lubricant and process conditions such as contact pressure, sliding velocity, and temperature. Laboratory tests for evaluating deep drawing lubricants should be designed to emulate the conditions of actual forming processes. The cup drawing test and twist compression test are compared for evaluating metal stamping

iii lubricants. Effects of contact pressure and sliding velocities on lubricant performance are evaluated. Also, numerical simulations are developed to predict the temperature increase in the part during each test.

Results showed that the testing condition in the cup drawing test is closer to actual deep drawing operations and this test is more proper for evaluating metal stamping lubricants compared to the twist compression test.

Springback affects the dimensional accuracy and final shape of stamped parts. Accurate prediction of springback is necessary to design dies that produce the desired part geometry and tolerances. Springback occurs after stamping and ejection of the part because the state of the stresses and strains in the deformed material has changed. To accurately predict springback through finite element analysis, the material model should be well defined for accurate simulation and prediction of stresses and strains after unloading. Despite the development of several advanced material models that comprehensively describe the Bauschinger effect, transient behavior, permanent softening of the blank material, and unloading elastic modulus degradation, the prediction of springback is still not satisfactory for production parts.

Dies are often recut several times, after the first tryouts, to compensate for springback and achieve the required part geometry.

Material properties which affect the springback are studied and effect of each property is investigated.

Results showed that the E-modulus is the most important material property defining the elastic recovery of the material and springback. A methodology for determination of an average E-modulus that can provide accurate springback prediction is presented. The method is expanded to determine the variation of

E-modulus with plastic strain to simulate the springback in real industrial part and obtain reasonably accurate springback prediction before manufacturing a real die. Finally, effect of post-stretching method on reduction of springback is investigated both experimentally and numerically.

DEDICATION

To my beloved family

ACKNOWLEDGMENTS

First and foremost, I would like to thank God Almighty for giving me the strength, knowledge, ability and opportunity to undertake this research study and to persevere and complete it satisfactorily. Without his blessings, this achievement would not have been possible.

I would like to thank my advisor, Dr. Taylan Altan, for providing me the value of science with continuous assistance and support. He was the Key to my success.

I am also grateful to Dr. Brevick and Dr. Pourboghrat for the constant support to improve my dissertation.

I wish to thank the sponsors of the following research: Honda America, Shiloh, Posco, Nucor, Aida America, GM, and the other CPF member companies, as well as all of the personnel of those companies which assisted me.

I also thank my fellow coworkers and friends of the Center for Precision Forming (CPF). Adam Groseclose, Suraj Appachu Palecanda Krishna, Tingting Mao, Ruzgar Peker, David Diazinfante Hernandez, Pedro Stemler, Fabian Bader, Advaith Narayanan, Berk Aykas, Tanmay Gupta, Aanandita Katre, Pratik Mehta, Josh Hassenzahl, and Linda Anastasi, as well as many others, all helped me more than they can possibly imagine.

Lastly, I would like to thank my parents, whose love and guidance are with me in whatever I pursue. They are the foundation to which my education is built on and will continue to push me to bigger and better things. Most importantly I wish to thank my loving and supportive wife, Mina who provides unending inspiration.

VITA

Master of Science (Mechanical Engineering) ...... September 2010

Bachelor of Engineering (Mechanics of Agricultural Machines) ...... June 2008

PUBLICATIONS

1. A. Fallahiarezoodar, R. Peker, T. Altan, Temperature Increase in Forming of Advanced High- Strength Steels – Effect of Ram Speed Using a Servodrive Press, Journal of Manufacturing Science and Engineering, Vol 138, pp 094503-1-94503-7, 2016.

2. A. Fallahiarezoodar, A. Katre, T. Altan, Predicting springback when bending AHSS and aluminum alloys, Part I, Stamping journal, pp 12-13, November/December 2016.

3. A. Fallahiarezoodar, Z. Yin, T. Altan, Controlling material flow in drawing operations CNC hydraulic cushions help improve drawability, Stamping journal, pp 16-17, May/June 2016.

4. A. Fallahiarezoodar, K, Drotleff, M. Liewald, T. Altan, Lightweighting in automotive industry using sheet metal forming-advances and challenges, 5th international conference on accuracy in forming technology, Chemnitz, 2015.

5. A. Fallahiarezoodar, L. Ju, T. Altan, Use of FE simulation and servo press capabilities in forming of AHSS and aluminum alloys, Key engineering materials, Vol 639, pp 13-20, 2015.

6. A. Fallahiarezoodar, T. Altan, Determining flow stress data by combining uniaxial tensile and biaxial bulge test, Stamping journal, pp 16-17, September/October 2015.

7. A. Fallahiarezoodar, R, Peker, T. Altan, Heat generation in forming of AHSS, Stamping journal, pp 12-13, March/April 2015.

8. A. Fallahiarezoodar, J. Dykeman, T. Altan, Using the frictionless dome test to determine flow stress data, Stamping journal, pp 14-15, November/December 2014.

9. A. Fallahiarezoodar, M.R. Abdul Kadir, M. Alizadeh, Sangeetha Naveen, T. Kamarul, Geometric variable designs of cam/post mechanisms influence the kinematics of knee implants, Knee Surgery, Sports Traumatology, Arthroscopy Volume 22, Issue 12, pp 3019-3027, 2014. 10. M. Heydari, M. R. Abdulkadir, J. Kashani, A. Fallahiarezoodar, M. Alizadeh, Influences of rheumatoid arthritis on elbow: A finite element analysis, Journal of Advanced Science Letters, Volume 19, Number 11, pp. 3219-3222(4), November 2013.

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11. M Ailzaadeh, M.R. Abdul Kadir, M. Mohd Fadhil, A. Fallahiarezoodar, B. Azmi, M. R. Murali, T. Kamarul, The use of X shaped cross-link in posterior spinal constructs improves stability in thoracolumbar burst fracture: A finite element analysis, Journal of Orthopaedic Research, 31(9):1447-54, 2013 Sep.

12. M. Heydari, M. R. Abdulkadir, A. Fallahiarezoodar, Muhamad Noor Harun, Mina Alizadeh, and Jamal kashani., Biomechanical assessment of unconstrained elbow prosthesis after total elbow replacement: A finite element analysis. Journal of Applied Mechanics and Materials, Vol. 234, pp 7-10, 2012.

FIELDS OF STUDY

Major Field: Industrial and Systems Engineering

Specialization: Manufacturing

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TABLE OF CONTENTS

Abstract ...... iii

Dedication ...... v

Acknowledgements ...... vi

Vita ...... vii

List of Figures ...... xiii

List of Tables ...... xvii

CHAPTER 1: INTRODUCTION ...... 1

1. Background ...... 1 2. Material properties and forming limit of material ...... 1 3. Friction and lubrication ...... 3 4. Springback ...... 6 5. Objectives and approach ...... 7

CHAPTER 2: DETERMINATION OF MATERIAL PROPERTIES AND FORMABILITY ...... 9

1. Introduction ...... 9 2. Tensile test ...... 10 3. Biaxial bulge test ...... 12 4. Combined tensile and bulge test method for obtaining accurate flow stress data ...... 14 5. Evaluation of formability and prediction of failure ...... 15 5.1. Formability and drawability ...... 15 5.2. 3-point FLD ...... 19

CHAPTER 3: COMPARISON OF CUP DRAWING TEST VERSUS TWIST COMPRESSION TEST FOR EVALUATION OF STAMPING LUBRICANTS ...... 22

1. Introduction ...... 22 2. Cup Drawing Test (CDT) ...... 25 2.1. Experiment – Cup drawing test ...... 27 2.2. Numerical simulation – cup drawing test ...... 28 2.3. Results of CDT ...... 31 3. Twist Compression Test (TCT) ...... 35 3.1. Experiment – twist compression test ...... 37

3.2. Numerical simulation – twist compression test ...... 38 3.3. Results of the TCT ...... 40 4. Discussions – Comparison of the CDT and the TCT ...... 44 4.1. Contact pressure ...... 44 4.2. Sliding velocity...... 44 4.3. Temperature...... 44 5. Conclusions ...... 45

CHAPTER 4: TEMPERATURE INCREASE IN FORMING OF ADVANCED HIGH STRENGTH STEELS (AHSS) – EFFECT OF RAM SPEED USING A SERVO DRIVE PRESS ...... 46

1. Introduction ...... 46 2. Material model and element type ...... 49 3. U-channel drawing ...... 52 3.1. Simulation setup and validation of thermo-mechanical FE model ...... 52 3.2. Results of U-channel drawing and validation of thermo-mechanical FE model ...... 53 4. Dee drawing of non-symmetrical industrial size panel ...... 55 4.1. Experimental procedure ...... 55 4.2. FE model of deep drawing process and prediction of thinning ...... 57 4.3. Results of deep drawing process using nonsymmetrical die geometry and comparison with experimental results ...... 58 4.3.1. Prediction of thinning distribution and validation of the FE model ...... 59 4.3.2. Effect of the COF on temperature rise at die / sheet interface ...... 62 4.3.3. Effect of the material properties on temperature generation ...... 64 5. Multi-stroke forming operations ...... 66 5.1. Simulation setup ...... 66 5.2. Results and discussion ...... 68 6. Summary and conclusions ...... 71

CHAPTER 5: SPRINGBACK IN SHEET METAL FORMING – BACKGROUND AND FUNDAMENTALS ...... 73

1. Introduction ...... 73 2. Fundamentals of bending and springback ...... 74 3. Mechanical properties affecting springback ...... 77 3.1. Effect of stress-strain data and constitutive model on springback prediction ...... 77 3.1.1. Isotropic Hardening (IH) ...... 79 3.1.2. Kinematic Hardening (KH) ...... 81 3.1.3. Combined isotropic and kinematic hardening (IH+KH) ...... 82 3.1.4. Distortion yield function ...... 86 3.2. Effect of E-modulus ...... 90

CHAPTER 6: EFFECT OF E-MODULUS VARIATION ON SPRINGBACK AND A PRACTICAL SOLUTION...... 92

1. Introduction ...... 92 2. Effect of E-modulus on springback prediction ...... 93 2.1. Nonlinear elastic unloading behavior ...... 95 2.2. Variation of unloading elastic modulus with plastic strain ...... 95 2.3. Strain path dependency of unloading elastic modulus ...... 96 3. Inverse analysis method for determination of an apparent E-modulus ...... 97 4. Wipe bending ...... 100 4.1. Experiment and FE simulation ...... 100 4.2. Results and discussion for wipe bending ...... 101 5. Draw bending (U-drawing or Hat-shape bending) ...... 102 5.1. Experiment and FE simulation ...... 102 5.2. Results and discussion for U-drawing ...... 104 6. Crash forming (real production part) ...... 107 6.1. Experimental setup and FE simulation ...... 107 6.2. Results and discussion ...... 108 7. Conclusions ...... 109

CHAPTER 7: DETERMINATION OF VARIABLE E-MODULUS THROUGH WIPE BENDING TEST AND APPLICATION TO SPRINGBACK PREDICTION ...... 112

1. Introduction ...... 112 2. Experiments ...... 113 3. FE simulation of springback and inverse analysis ...... 115 3.1. Simulation setup ...... 115 3.2. Inverse analysis method ...... 116 3.3. Calculation of the E-modulus variation through the inverse analysis method ...... 116 4. Results and discussion ...... 117 4.1. Elastic modulus degradation with plastic strain ...... 117 4.2. Improvement in springback prediction using the variable E-modulus ...... 118 5. Conclusions ...... 119

CHAPTER 8: SPRINGBACK REDUCTION IN U-CHANNEL DRAWING OF AL 5182-O BY USING A SERVO PRESS AND A SERVO HYDRAULIC CUSHION ...... 121

1. Introduction ...... 121 2. Reduction of springback by post stretching – Use of servo hydraulic cushion ...... 123 2.1. Servo hydraulic cushion ...... 123 2.2. Experiments ...... 123

2.3. FE simulation ...... 124 2.4. Results and discussions ...... 125 3. Effect of coefficient of friction on springback prediction ...... 126 4. Elastic deflection of the tools ...... 127 5. Conclusions ...... 127

REFERENCES ...... 129

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LIST OF FIGURES

Figure 1.2: Example of Stribeck curve illustrating four lubricant regimes as a function of η, lubricant viscosity; V, sliding velocity; P, normal pressure ...... 4

Figure 2.1: Schematic of the dog-bone shape specimen for tensile test and the typical engineering stress-strain curve (Fallahiarezoodar and Altan, 2015) ...... 12

Figure 2.2: Schematic of the tooling and process of the viscous pressure bulge test ...... 13

Figure 2.3: Flow stress data obtained from the tensile test and the bulge test ...... 14

Figure 2.4: The flow stress data obtained from the combined method (combination of the tensile test and the bulge test)...... 15

Figure 2.5: Comparison of formability of material in uniaxial and biaxial strain state...... 16

Figure 2.6: (a) Example of specimen geometries required for developing the FLD, (b) schematic of a FLD...... 18

Figure 2.7: Comparison of FLCs developed by 3-point FLC method and conventional Nakajima test...... 21

Figure 3.1: 2-D schematic of the cup drawing tooling...... 26

Figure 3.2: (a) 2-D schematic of the formed cup and the flange area; (b) An example of the formed cup. The dashed line shows the perimeter of the flange...... 26

Figure 3.3: Schematic of ram velocity against time for a mechanical press with 300 mm total stroke and 25 SPM...... 30

Figure 3.4: Effect of ram speed (deformation speed) on temperature at tool / sheet interface during the CDT. Temperature calculations are for location around the die corner radius...... 32

Figure 3.5: Prediction the effect of the friction work on heat generated during the CDT. 60 mm/sec forming speed is considered...... 33

Figure 3.6: Effect of ram speed on sliding velocities between the sheet material and the die surface at location around the die corner radius (predicted results from FE simulation). (For variable ram motion please see Figure 3.3)...... 34

Figure 3.7: Prediction of contact pressure around the die corner radius in the CDT...... 35

Figure 3.8: Schematic of the twist compression test set-up...... 36

Figure 3.9: Example of the calculated coefficient of friction versus time in a TCT. 푡푏, 푡푒, 퐶푂퐹푏, and 퐶푂퐹푒 are used to calculate the TCT factor (Eq. 3-3)...... 37

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Figure 3.10: FE model of the TCT process...... 39

Figure 3.11: Coefficient of friction versus time data obtained from the TCT for the two test conditions that provided the highest and the lowest TCT factor. Please note that due to the large difference in test durations for the cases A and B, two horizontal time scales are considered at the top and the bottom of the graph. The time scale at the bottom is for the case A and the one at the top is for the case B...... 40

Figure 3.12: Effect of the contact pressure, the rotational speed and the lubricant weight on TCT factor and lubricant performance...... 41

Figure 3.13: Prediction of temperature increase in TCTs. Please note that due to the large difference in test durations for the cases A and B, two horizontal time scales are considered at the top and the bottom of the graph...... 43

Figure 4.1: Servo drive press provide flexible slide motion control (Miyoshi, 2004) ...... 47

Figure 4.2: Schematic cross section of the simulation setup and the geometrical parameters used for simulation of U-channel forming (Pereira and Rolfe 2014)...... 53

Figure 4.3: Max. Temperature predicted by FE simulation and measured experimentally at die / sheet interface during the U-channel drawing of 2 mm DP780. The experimental results are from Pereira and Rolfe (2014) ...... 55

Figure 4.4: Schematic of the non-symmetric industrial scale die used in this study for deep drawing process (die set built by Shiloh Industries) ...... 56

Figure 4.5. Measurement of the thinning distribution along a curvilinear length of 1.4 mm CP800 panel formed up to 48mm. Thickness of the six locations along the cutting line are measured in experimental samples and the thinning values are compared with simulation results for approximately the same locations A) simulation prediction B) the formed panel and the locations of measurements...... 60

Figure 4.6: Thinning percentage vs. curvilinear length at the corner of the formed panel, shown in Figure 4, material CP800, initial thickness 1.4 mm, Drawing depth 48 mm, and blankholder force 250 kN. Thickness of the six locations along the cutting line are measured in experimental sample and the thinning values are compared with simulation results...... 61

Figure 4.7: Thinning percentage vs. curvilinear length at the corner of the formed panel, material DP590, initial thickness 1.4 mm, Drawing depth 70 mm, and blankholder force 200 kN. Thickness of the six locations along the cutting line are measured in experimental sample and the thinning values are compared with simulation results ...... 62

Figure 4.8: Max. Temperature rise at die / sheet interface for two values of COF, during the deep drawing of 1.4 CP800 with 250 kN blankholder force and 75 mm/sec ram speed. (Die geometry is shown in Figure 3)...... 64

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Figure 4.9. Flow stress data for 1.4 mm CP800 and DP590 obtained from the viscous pressure bulge test ...... 64

Figure 4.10: Temperature predicted in panels formed up to 48 mm depth with 250 kN blankholder force and 75 mm/sec ram speed; top) 1.4 mm CP800, bottom) 1.4 mm DP590...... 66

Figure 4.11: Ram speed versus stroke curve used in 48 mm deep drawing of CP800 with Aida 300-ton servo drive press and 25-ton servo cushion, (Crank diameter=400 mm), Stroke=0 is the top dead center and stroke=400 is when the ram is at bottom dead center ...... 68

Figure 4.12: Calculated temperature rise at die / sheet interface in U-channel drawing with: A) 5 SPM and B) 30 SPM forming speed, F: forming stage; T: transfer stage...... 70

Figure 4.13: Temperature rise at die / sheet interface at deep drawing of 1.4 mm CP800 in consecutive multiple forming, F: forming stage; T: transfer stage ...... 71

Figure 5.1: Schematic of typical engineering stress-strain graph for three materials describing the effect of E-modulus and strength of the material on elastic recovery (springback) ...... 74

Figure 5.2: stress distribution in bending theory ...... 76

Figure 5.3: Schematic of stress-strain response of a sheet metal under tension-compression loading...... 78

Figure 5.4: Schematic of yield surface expansion in isotropic hardening model...... 80

Figure 5.5: Schematic of yield surface translation in kinematic hardening model ...... 82

Figure 5.6: Yoshida-Uemori two surface model. 훼 is the center of the yield surface, 훽 is the center of the bounding surface, and 훼∗ is the relative motion of the yield surface with respect to the bounding surface...... 83

Figure 5.7: Distortion of yield surface predicted by HAH model (A) initial von Mises yield criterion, (B) after uniaxial tensile loading in 휎1 direction, (c) after subsequent reverse compression loading in −휎1direction...... 89

Figure 6.1: [a] Example of a loading-unloading tensile test result for determining E-modulus variation with plastic strain. [b] Expanded view of the last unloaded cycle indicating the nonlinear elastic unloading behavior of the material. 퐸25 % and 퐸50 % are the calculated E- modulus using the line which connects the point of maximum stress before unloading and the point of 25% and 50 % of that maximum stress value. [c] E-modulus variation with plastic strain; Test results from (Xue et al., 2016)...... 94

Figure 6.2: Flowchart describing the inverse analysis method for the determination of an apparent E-modulus which can be used to obtain springback values, comparable to experimental measurement ...... 97

Figure 6.3: A schematic view of tools and dimensions used in the wipe bending tests ...... 101

Figure 6.4: Comparison of springback predictions with experimental measurement in wipe bending operation ...... 102

Figure 6.5: A schematic view of tools and dimensions for the U-draw bending (Lee et al., 2012b) ...... 103

Figure 6.6: Comparison of simulation and experimental results in U-drawing. (a) Effect of E- modulus and work hardening on springback prediction; (b) Expanded view of the wall area to compare the prediction of curl for different cases; Experimental results from (Lee et al., 2012b)...... 106

Figure 6.7: (left) 2-D section of the schematic of the tool set-up, (right) schematic of the final part geometry...... 108

Figure 6.8: Comparison of normal distance between the simulation results and 3-D scan of the part after springback...... 109

Figure 6.9: [a] conventional die manufacturing method; [b] New proposed procedure for reducing the number of die re-cut by improving the springback prediction...... 111

Figure 7.1: A schematic view of tools and dimensions used in the wipe bending tests...... 114

Figure 7.2: Bending angle under load for seven different punch strokes considered in this study...... 114

Figure 7.3: Inverse analysis method used to determine the apparent E-modulus for each punch stroke / bending angle under load...... 116

Figure 7.4: Selected apparent E-modulus through the inverse analysis at each punch stroke ...... 117

Figure 7.5: Comparison of the E-modulus versus plastic strain calculated from the inverse analysis method and the LUL method ...... 118

Figure 7.6: comparison of springback prediction results obtained from simulation models with different E-modulus and experimental measurement ...... 119

Figure 8.1: A schematic of tools and dimensions for the U-draw bending...... 124

Figure 8.2: Three different BHFs used in the tests. (a) constant 100 kN, (b) constant 400 kN, (c) variable 100 to 700 kN. The solid lines show the target force and the dashed lines indicate the actual force applied by the cushion...... 124

Figure 8.3: Experimental results and simulation predictions of springback for 3 different BHF values...... 125

Figure 8.4: Stress distribution along the sheet thickness at wall area for two different BHF values ...... 126

Figure 8.5: Effect of COF on springback prediction...... 126

Figure 8.6: Die displacement versus time for three different tested BHFs...... 127

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LIST OF TABLES

Table 3.1. Mechanical properties of DP590 ...... 28

Table 3.2. Thermal properties of the tools and specimen (Pereire and Rolfe 2014) ...... 29

Table 3.3 Parameters used in the TCT ...... 38

Table 4.1. Mechanical properties of sheet materials used in this study. Data for DP780 is from reference (Pereira and Rolfe 2014) ...... 50

Table 4.2. Thermal properties used in the thermo-mechanical FE simulation. Thermal properties for sheet are for low carbon steel and are from previous publication by Pereira, et al., (2014) ...... 51

Table 6.1. Three bending operations investigated in the present study. The data for DP 780 is provided in the benchmark report (Chung et.al. 2011). For DP980 and MP980 the mechanical properties are obtained from the tensile test and the E-modulus variation parameters are obtained from AutoForm default value...... 99

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CHAPTER 1: INTRODUCTION

1. Background

In sheet metal forming usually a metal blank is plastically deformed into a useful part with a complex geometry. Bending, flanging, deep drawing, and stretch forming are examples of sheet metal forming processes. The overall objective is to form the part without any defects and within the required tolerances. Sheet metal forming process is a system and several parameters affect the final result. These parameters can be categorized into two main groups:

1) Parameters related to the sheet material

2) Parameters related to the forming process

Design, analysis, and optimization of the forming processes require (a) theoretical knowledge regarding material elastic and plastic behavior, metal flow, contact conditions at tool/material interface, and heat transfer as well as (b) technological information related to lubrication, heating and cooling techniques, material handling, die design and manufacture, and forming equipment.

2. Material Properties and forming limit of material

In the last decade, the advanced high strength steels (AHSS) and high strength aluminum alloys are increasingly used in automotive industry to satisfy the demands for improved safety, fuel efficiency and low-emission of greenhouse gas. AHSS can help reducing the weight by using thinner sheets while increasing the crashworthiness. In general, the formability of high strength

1 steels and aluminum alloys is lower than milder grade steel. In addition, springback and die wear is more sever in forming high strength materials since the forming stresses and contact pressure is higher (Billur 2010).

Accurate determination of material properties (i.e., the flow stress data, E-modulus, and uniform elongation) is essential for designing the sheet forming process. These properties are conventionally determined using a standard tensile test. Despite the tensile test is simple and inexpensive to conduct, it has limitations as it only provides material properties in uniaxial strain state. In contrast, in actual stamping operation, the strain state at the part can be nonlinear and multi axial. In this condition, the true strain at the part may reach to the magnitude that cannot be determined through the tensile test. Therefore, biaxial bulge test is introduced where the sheet material is under balance biaxial strain state during the deformation. The membrane theory is commonly used along with the hydraulic bulge test for determining the flow stress of the material (Amaral at al., 2017; Chen et al., 2018).

In addition to mechanical properties, forming limit of the sheet material is the other parameter influencing the design of the forming process. Forming limit is the maximum strain that can be attained in sheet material before onset of necking (Kumar et al., 1994). Uniform elongation obtained from the tensile test is the simplest indicator of material formability. However, the uniform elongation provides the formability data in uniaxial loading state.

Forming Limit Diagram (FLD), a plot of major and minor limit strains in the principal strain space, is the other indicator of material formability (Werber et al., 2013). It measures the material resistance to localized necking at different strain states ranging from uniaxial tension to balance biaxial tension. In practice, FLD is a standard tool to determine the feasibility of the forming process. However, experimentally measurement of an FLD requires several tests with

2 different specimen geometries which is expensive and time consuming. Also, the scatter in experimental data is sometimes so large.

To save time and cost, theoretical and numerical approaches have been introduced for developing FLD. Most of the numerical approaches are based on the so-called M-K model developed by Marciniak and Kuczynski (1967) that assumes the existence of a material imperfection. Wu et al., (2003) investigated the effect of the yield function on predicted FLD.

Knockaert et al., (2002) combined the M-K model with the rate-independent polycrystalline plasticity model to predict the forming limits for Al 6116-T4.

FLD tests provide the forming limit for proportional loading paths while in many stamping operations, especially with complex die geometry or multi-step forming, the nonlinear strain path is inevitable. Therefore, forming limit curves fail to predict the failure where the deformation is not along linear strain path (Kuroda and Tvergaard, 2000; Tong et al., 2002). Several researchers proposed transferring the forming limit strain to forming limit stress which is assumed to be path independent (Wu et al., 2005; Werber et al., 2013). Arrieux et al. (1982) introduced stress based forming limit by plotting the calculated principal stresses at necking. Several researchers used the phenomenological plasticity (Arrieux, 1995; Haddad et al., 2000) and crystal plasticity (Wu et al., 2000) models to develop stress based forming limit.

3. Friction and lubrication

Friction and lubrication conditions in the actual production process significantly affect the sheet metal formed part. Friction conditions depend on sheet and tool material, coating and surface qualities, lubrication, and process conditions such as contact pressure, sliding velocity, and temperature. Despite the importance of the friction and lubrication, it is not considered in detail in Finite Element simulation of metal stamping (Sigvant et al., 2016).

As shown in Figure 1.2, four lubrication regimes may be present in metal forming (Altan and

Tekkaya 2012b). The most common encountered lubrication condition in sheet metal forming is the boundary condition where the solid surfaces are so close and surface interaction between single or multimolecular films of lubricants and the solid asperities dominate the contact

(Bhushan 2002).

Figure 1.2: Example of Stribeck curve illustrating four lubricant regimes as a function of η, lubricant viscosity; V, sliding velocity; P, normal pressure

It is important to measure the friction under conditions of actual forming processes. In order to provide a reliable lubrication evaluation test, it is necessary to completely understand the lubrication conditions in the real operation and simulating them in the screening test (Koistinen,

1978).

Two friction models, Coulomb’s friction model and shear friction model, are commonly used to describe the friction condition in simulation on metal forming. In most simulations a constant coefficient of friction is assumed for a given lubrication. Researchers have shown that for a given

4 lubrication, the friction coefficient depends on the contact pressure, sliding velocity, temperature, and the tools and material surface roughness.

Recently, software called TriboForm is introduced that provides friction coefficients as a function of contact pressure, surface roughness of the sheet material and tooling, and the type of lubricant. The friction model developed by TriboForm can be directly used in AutoForm or

PAM-STAMP to apply variable coefficient of friction at different location of the part during the deformation. Sigvant et al., (2016) used the friction model developed by the TriboForm to simulate the forming of rare door inner of Volvo XC90. They showed that the draw-in prediction is more close to experiments when the TriboForm model is used compared to the case of using a constant coefficient of friction.

In addition to reducing the friction force and the loads imposed on tooling and workpieces, lubrication can eliminate the thermal problems during the deformation. Proper lubrication not only reduces the heat generated by friction work but also provide and insulating film between the workpiece and the tooling (Koistinen, 1978).

In order to select the appropriate lubricant for stamping operation, in addition to lubrication performance, some other factor also should be considered such as (Altan and Tekkaya 2012b):

 In order to prevent the oxidation and corrosion, lubricants often have to provide a thin

surface film on the stamped parts

 For high quality painting and electro-cathodic coating the lubricant need to be removed

from the stamped part

 Lubricants affect the post metal forming operations such as welding and adhesive

bonding.

4. Springback

Springback which is generally defined as the elastic recovery of material after unloading and tools removal is stress driven and therefore becomes more critical in forming high strength materials. High strength materials experience higher springback than traditional steels under the same forming conditions (AS/P, 2009). Thus, it is very important to improve the accuracy of springback prediction to reduce the die development time and cost for springback compensation.

Nowadays, numerical simulation of springback prediction through finite element methods is helping the die makers to reduce the extensive trial-and-error method for final die modification.

Several parameters affect the prediction of springback. In general, accuracy of springback calculation depends on the accuracy of stress distribution prediction in the part (Gau and Kinzel,

2001; Geng, 2002; Yoshida and Uemori, 2003). Thus, all the parameters that influence the calculation of stress in finite element method affect the springback prediction.

Among the parameters affecting the springback, flow stress data and E-modulus are two most important material properties influencing the prediction results. Flow stress data provides the effective stress distribution at the part during the deformation and E-modulus controls the material unloading behavior after unloading. Also, yield function which determines the yield limits at different stress state affect the simulation of material behavior and springback. Recent research indicated that the isotropic hardening model is not enough to accurately simulate the material hardening behavior especially in the case of reverse loading (Gau and Kinzel, 2001;

Taherizadeh et al., 2009). Also, it is shown by several researchers that the assumption of constant, linear E-modulus was not accurate (Morestin and Boivin, 1996; Cleveland and Ghosh,

2002).

5. Objectives and approach

The overall objective of the current study is to analyze the important parameters that affect the quality of a part formed from stamping operation. The specific objectives are:

1) To determine material properties and failure criteria affecting the process design and

simulation of the forming process

2) To investigate the tribological conditions in stamping operation

3) To analyze springback as one of the major defects in forming new high strength materials

and investigate the challenges in reduction and prediction of springback.

In order to achieve these objectives, the following approach is followed:

Phase I: Determination of material properties and formability

1.1: Evaluation of different testing methods for determination of mechanical properties and flow

stress data

1.2: Determination of the flow stress data for the selected materials using tensile test and viscous

pressure bulge test

1.3: Determination of formability and evaluation of the formability of materials using different

test methods

Phase II: Evaluation of lubrication and temperature in sheet metal forming

2.1: Review of the available methods for evaluation of stamping lubricants

2.2: Investigating the parameters affecting the lubricant performance in sheet metal forming

2.3: Comparison of the cup drawing test with twist compression test for evaluation of stamping

lubricants

2.4. Prediction of temperature increase in forming of AHSS materials

Phase III: Springback, challenges and solutions

3.1: Investigation the parameters affecting the springback and developing a methodology for

increasing the accuracy of springback prediction

3.2: Investigation the possibility of reduction of springback using the post-stretching method and

servo hydraulic cushion

CHAPTER 2: DETERMINATION OF MATERIAL PROPERTIES AND FORMABILITY

1. Introduction

New metals continue to evolve and grow in application. In automotive industry, to meet the challenges of safety regulations and emission reduction, the application of Advanced High-

Strength Steels (AHSS) and high strength aluminum alloys, as lightweight and engineered materials, is accelerating.

AHSS are materials with complex chemical compositions and multiphase microstructures resulting from precisely controlled heating and cooling processes. The 1st and 2nd generations of

AHSS grades include Dual Phase (DP), Complex-Phase (CP), Ferritic-Bainitic (FB), Martensitic

(MS or MART), Transformation-Induced Plasticity (TRIP), Hot-Formed (HF), and Twinning-

Induced Plasticity (TWIP) (Billur and Altan, 2013). The 3rd generation grades of AHSS with improved strength-ductility combinations are recently becoming available for wide use in industrial applications.

The unique strength and environmental advantages of aluminum alloys cause the steadily growing interest of this material in automotive industry. Automakers usually use two types of aluminum alloys for body parts as nonheat-treatable and heat treatable alloys. Al-Mn of series

3000 and 5000, are the nonheat-treatable alloys and Al-Cu, Al-Cu-Mg, A-Mg-Si, and Al-Mg-Si-

Cu are some of the heat treatable alloys of 2000 and 6000 series used in automotive industry.

One of the most popular alloy is 5182-O that have a fine-grained structure and good formability

(Fridlyander et al, 2002).

Metal manufacturers evaluate properties, using certain standards. In AHSS the batch to batch variation of material properties can be significant and it can cause challenges in process development. To overcome this problem, the die makers have to consider a large safety factor and reduce the complexity of the tooling to avoid the failure of the stamped part.

Large variation in material properties and some specific material behavior such as Bauschinger effect show an essential need for more accurate tooling and process design. Therefore, it is essential to improve the material characterization methods to have a more advanced material model.

2. Tensile test

The uniaxial tensile test, an industry standard (ASTM E8), is the most common and cost effective test method for determination of mechanical properties of a sheet material. A dog bone shaped specimen, Figure 2.1, is used where the ends are gripped and the specimen is pulled at a constant rate until fracture. During the test, the load and elongation is measured and several mechanical properties as listed below can be obtained:

1) Engineering stress-strain,

2) Young’s modulus

3) Total and uniform elongation

4) Yield and ultimate tensile strength

5) Plastic strain ratio (R-values)

The true stress-true strain data that is used to describe the flow stress data of the material can be calculated as:

퐿 푑푙 퐿 휀푡푟푢푒 = ∫ = ln ( ) = ln⁡(휀푒푛푔 + 1) (2-1) 퐿0 푙 퐿0

휎푡푟푢푒 = 휎푒푛푔(휀푒푛푔 + 1) (2-2)

Figure 2.1 shows typical stress-strain curve obtained from the tensile test and the mechanical properties for the selected sheet materials. The tensile test is simple and relatively inexpensive.

However, in this test, the specimen is under in-plane uniaxial strain state. Therefore, the formability of the material is limited and the material data can only be obtained up to a small strain value compared to the strains observed in industrial stamping operations. In addition, in industrial stamping, the strain state may not be linear uniaxial and can cover different linear or non-linear strain path from pure shear to balanced biaxial. For numerical simulation of a sheet metal forming process extrapolation of the flow stress curve obtained from the tensile test is required to simulate the material behavior in strain values higher than what is obtained from the tensile test. Since the extrapolation is based on mathematical formula, it may not describe the actual hardening behavior of material in high strain values.

Figure 2.1: Schematic of the dog-bone shape specimen for tensile test and the typical engineering stress-strain curve (Fallahiarezoodar and Altan, 2015).

3. Biaxial Bulge test

Hydraulic Bulge (HB) test and Viscous Pressure Bulge (VPB) test are other test methods for

determination of flow stress data. In these tests, a sheet is clamped around its edge and stretched

against a circular die using hydraulic fluid or a viscous material as a pressure medium, Figure

2.2. The sheet material is deformed under balanced biaxial tension until it bursts. Compared to

uniaxial tensile test, higher range of strain can be obtained under biaxial tensile condition

(Gutscher et al., 2004; Sigvant et al., 2009). Gutscher et.al, measured the flow curve of an

aluminum killed drawing quality (AKDQ) steel up to 0.8 accumulated strain with viscous

pressure bulge (VPB) test while this material showed only 0.35 strain in uniaxial tensile test

(Gutscher et al., 2004). The higher strain range obtained from the biaxial test eliminates the need

for extrapolating the flow stress data to predict the material behavior in simulation of industrial

stamping operation.

To be able to consider the anisotropy behavior of material in simulations, yield functions such as

Hill 48, Yld2000-2d, or BBC2003 need to be used. For some of these yield functions, to determine the required coefficients, in addition to the uniaxial tensile test, results from the biaxial test is also required (Banabic 2010; Barlat et al., 2003).

The VPB test is developed to make the tooling design and equipment setup simple and easy to use compared to the HB test. In the VPB a semi solid punch made from viscous material such as polyurethane or silicone is used as pressure medium. Friction between the viscous material and blank is negligible. The dome height and the pressure of the viscous material are measured during the test. The pressure versus stroke curve obtained from the experiment is compared with a data base developed from Finite Element (FE) simulation, and the flow stress curve is calculated accordingly. A full description of the viscous pressure bulge test is published by

Gutscher et al. (2004).

Figure 2.2: Schematic of the tooling and process of the viscous pressure bulge test

In the VPB test, determination of the yield stress and also the flow stress data at strains close to

the yield point are challenging, Figure 2.3. Therefore, in this study a new approach is proposed to

combine the tensile test and bulge test result for determination a more reliable flow stress data.

DP980, t=1.2mm 1400 cannot determine data for strain values less than this point 1300

1200 Bulge test

1100 cannot determine data for strain 1000 values higher than this point

900 True stress (MPa) stress True 800 Tensile test 700

600 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 True strain Figure 2.3: Flow stress data obtained from the tensile test and the bulge test.

4. Combined – tensile and bulge test - method for obtaining accurate flow stress data

For more accurate determination of flow stress data a combined method is introduced. In this

method both the tensile test and the bulge test results are used to define the hardening behavior

of the material. The yield strain-stress of a selected material is determined through the tensile

test. Then, a power low equation (σ = Kεn) is fitted to the strain-stress data obtained from the

bulge test and the curve is extrapolated from left side until the yield stress is achieved, Figure

2.4. With this methodology, a reasonably reliable flow stress data can be determined from the

yield point up to the maximum strain values obtained from the VPB test.

Al5182-O, 1.2 mm 400

350

300

250 data obtained from the Bulge test 200

Extrapolation of bulge test True stress (MPa)stress True 150 result using power law

100 Yield stress from the 50 Tensile test 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 True strain

Figure 2.4: The flow stress data obtained from the combined method (combination of the tensile test and the bulge test).

5. Evaluation of formability and prediction of failure

5.1. Formability and drawability

In sheet metal forming, sometimes mistakenly the terms of formability is used to evaluate the

drawability of a sheet material in a selected forming process. The word formability refers to the

ability of material to plastically deform before necking and failure happens. Formability is a

material property independent of the process parameter. Drawability, on the other hand, is the

ability of the sheet material to deform into a specific part without failure. Not only the material

properties, but also the process parameters such as lubrication, tooling geometry, forming speed,

and blank size and geometry can affect the drawability of a material.

In sheet metal forming, for a successful tool and process design, information about both the

formability and the drawability of the selected material is crucial. There are several test methods

15 to evaluate the formability of a material. The tensile test is the most inexpensive and common method for determination the formability of a material. In the tensile test, the uniform elongation

(elongation at the onset of necking) is the indication of the formability of the material.

Formability of material can be different depend on the strain state. For example as shown in

Figure 2.5, in uniaxial strain state Al 6014 is more formable than Al 6205, while in biaxial strain state the trend is opposite.

27 35

25 34

33 23 32 21 31

19 Bulgeheight (mm)

Uniformelongation (%) 30

17 29 Bulge height

15 28 Uniform Al 6014, 1.2mm Al 5182-O 1.2 mm Al 6205, 1 mm elongation

Figure 2.5: Comparison of formability of material in uniaxial and biaxial strain state.

The tensile test provides the formability of material in uniaxial strain state. The bulge test and

Limiting Dome Height (LDH) test are two other test methods that can determine the formability of material in biaxial loading state. In these two tests, the maximum dome height before fracture is used to determine the formability of the material. Material with higher formability will have higher dome height before failure happen.

Forming Limit Diagram (FLD) is another method to evaluate the formability of material. It is a graphical description of surface strain limits of a material and depicts the major strains and minor

16 strains at the onset of localized necking. To develop a Forming Limit Curve (FLC), sheet metal specimens with different geometry, Figure 2.6, are formed using a hemispherical punch

(Nakazima) or a cup test (Marciniak). According to ASTM standard (ASTM E2218 – 15) a hemispherical punch is used to stretch the sheet material. The local major and minor strains close to the location of failure is measured using circle grid or digital image correlation (DIC) technique.

Sample preparation and experimental method for determination of FLC requires intensive effort and time. Some parameters such as the sheet thickness, specimen edge quality, and the friction and lubrication between the sheet and tool interfaces can significantly affect the test result.

Therefore, the FLC of a material is not only dependent to the material and the test condition also influences the result.

Figure 2.6: (a) Example of specimen geometries required for developing the FLD, (b) schematic of a FLD.

In order to predict failure in Finite Element (FE) stamping simulation a failure criterion is required. Even though the strain states in the sheet metal forming process is complex, the FLD is an important tool in practical press shop to predict the failure risk. Recently, due to the batch to batch variation of material properties in new developed steels (Advanced High Strength steels) the scatter in the resulting FLDs for each batch is large. In addition to the large scatter, the intensive efforts required to create the FLC for a batch of sheet material, reduces the applicability of using this method for prediction of failure.

Several studies have been conducted to simplify the calculation of the FLC by using empirical methods and tensile test data. Keeler and Brazier (1977) proposed a FLC with a standard shaped curve that the minimum of the curve is at the plane strain axis. In their model the major strain of the minimum point increases by increases the work hardening exponent or the sheet thickness.

Raghavan et al. (1992) proposed a curve that its minimum point changes in the vertical axis by the total elongation or the sheet thickness. It is reported by Shi and Gelisse (2006) that in automotive industry in North America still use the Keeler equation to calculate the FLC.

However, Cayssials (1998) reported that the Keller model is only reliable for low carbon steels.

Cayssials and Lemoine (2005) developed a model to calculate the FLC from ultimate tensile strength, R-values, uniform elongation, and the thickness of the sheet material.

Gerlach et al. (2010) proposed a FLC calculation by a linear function for the uniaxial strain state and an exponential function for the biaxial strain state area. They calculated the coefficients of the functions using a large set of FLCs conducted by Nakazima tests. Abspoel et al. (2013) introduce a method to develop the FLC using four nodes. They tested several sheet materials and found the relationship between the FLC points and the mechanical properties of the material obtained from the tensile test.

5.2. 3-point FLD

For practical description and reduction of the effort for developing a FLC a method is introduced to create the FLC for a batch of sheet material by using three points. The three points determine the major and minor strains at onset of necking for the uniaxial, plane strain, and balance biaxial strain state. The FLC-uniaxial tensile point is determined from mechanical properties obtained from the tensile test by using the formula proposed by Abspoel et al. (2013) as:

0.567 (0.0626 퐴 +(푡−1)(0.12−0.0024∗퐴 ) 휀 = 1 + 0.797푟0.701 80 80 (2-3) 1 √(1+(0.979푟0.701)2

0.567 (0.0626 퐴 +(푡−1)(0.12−0.0024∗퐴 )0.797푟0.701 휀 = − 80 80 (2-4) 2 √(1+(0.979푟0.701)2

where 퐴80 is the total elongation, 푟 is the Lankford coefficient, and 푡 is the initial sheet thickness.

The FLC biaxial point is determined through the VPB test and a DIC is used to measure the local necking strain. FLC-plane strain point is determined from a hemispherical punch as described by

Nakazima et al. (1968).

Figure 2.7 shows the FLCs developed for 0.96 mm DP600 steel material using both 3-point FLC method and the conventional Nakazima test. Results show that the 3-point FLC can provide a reasonably accurate data for prediction of failure. However, results showed that the formula developed by Abspoel et al. (2013) to calculate the local necking strain for FLC-uniaxial is not accurate for the tested material.

0.96 mm DP600 0.5 1

0.4

3 0.3

0.2 Major strain Major 3 Point FLC 2 0.1 FLC from Nakajima-Test 0.0 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

Minor strain Figure 2.7: Comparison of FLCs developed by 3-point FLC method and conventional Nakajima test.

CHAPTER 3: COMPARISON OF CUP DRAWING TEST VERSUS TWIST COMPRESSION TEST FOR EVALUATION OF STAMPING LUBRICANTS

Note: This chapter is prepared for submission to the Journal of Tribology International.

1. Introduction

Deep drawing is a major sheet metal forming process. In this process, a mechanically applied force forms a flat sheet of material to a desired shape. One of the most important parameters affecting the quality of the final part is friction and lubrication conditions between the sheet and tool surfaces. By controlling the lubrication condition defects such as wrinkling, tearing, and tool wear can be reduced (Yang 2008; Wang et al., 2017). Friction conditions also depend on sheet and tool materials (coatings and surface topography), lubrication, and process parameters such as contact pressure, sliding velocity, and temperature. Over the past decade, it has become convention to describe friction conditions with the Coulomb friction model using a constant friction coefficient:

푓푓푟푖푐푡푖표푛 = 휇퐹 (3-1) where 휇 is the coefficient of friction and 퐹 is the normal force. The friction force determines the restricting force which the material has to overcome to flow into the die cavity. The friction force varies proportionally with interfacial contact pressure and friction coefficient. Researchers have shown that the friction coefficient for a selected lubricant is not constant and depends on

22 contact pressure, sliding velocity, and temperature at tool / sheet interface (Gil et al., 2016; Wang et al., 2016; Sanchez 1999; Dohda et al., 2015; Grueebler and Hora 2009).

This is relevant when forming Advanced High Strength Steels (AHSS) and high strength aluminum alloys. Owing to the higher surface hardness and yield strength of AHSS, more force and energy is required to achieve the necessary plastic deformation. Therefore, the interfacial contact pressure and temperature between tool and workpiece is higher in forming high strength materials. As the contact pressure is increased, flattening of the asperities of the contact surfaces results a change of the friction coefficient (Ma et al., 2010). In addition to higher contact pressure in forming high strength materials, forming speed is also increased as a result of servo press use (Osakada et al., 2011). Faster sliding motion in addition to higher contact pressure and temperature provide different lubrication condition in forming high strength materials. Thus, conventional tribotest methods for evaluating the lubrication performance should be modified to provide proper testing conditions similar to actual deep drawing operation. Several laboratory test methods are used to evaluate stamping lubricants i.e. strip drawing test, drawbead test, Twist

Compression Test (TCT), and Cup Drawing Test (CDT).

In strip drawing test the sheet specimen is pulled between two clamping dies without plastic deformation. This represents the condition where sheet material is sliding under the blank holder during the deep drawing process. Kirkhorn et al., (2012) used parallel strip drawing to investigate the effect of the speed and normal load on lubrication performance and showed that the friction coefficient is lower when contact pressure is increased. Verneulen at al., (2001) investigated the effect of electron beam texturing on tribological behavior in the steel sheet and die contact using a strip drawing test. Effect of contact pressure on friction coefficient was

23 investigated by Gil et al., (2016). Trzepiecinski et al., (2017) evaluated the effect of sheet deformation and surface roughness on friction and lubrication using strip drawing test.

When forming large parts, like automobile body panels, material draw-in is controlled by drawbeads. Drawbead simulation test introduced by Nine (1978) was used to determine the frictional forces that arise during the bending, unbending, and sliding of the sheet material against a drawbead (Figueiredo et al., 2011). Sanchez and Weinmann (1996) used the drawbead test to evaluate the pulling and shear forces required to form the sheet metal. Schey (1996) used the drawbead simulation test and showed a decrease in friction coefficient by increasing the speed.

Gong et al., (2004) investigated the friction and lubrication conditions in the blank holder area using a rectangular drawing process and probe test method. Allen and Mahdavian (2008) used axisymmetrical cup drawing tools to investigate the effect of die expansion on hydrodynamic lubrication film thickness during the deep drawing process. Kim et al., (2009) used the cup drawing test to evaluate stamping lubricants in forming AHSS. They also investigated the lubrication performance in severe contact pressure between the tool and the workpiece using the ironing process. Ju et al., (2015a) evaluated the effect of lubricant and blank surface texturing on deep drawing of 5182-O aluminum alloy using the drawing of round cups.

Kim et al., (2008) used the TCT to investigate the effect of galling in forming of AHSS and found that the contact pressure at tool-sheet interface plays the major role in initiation of galling.

To correlate the laboratory test results to production forming operations, the test should be carefully designed to represent the actual forming conditions. In the current study, the process conditions (contact pressure, sliding velocity, and temperature) in the CDT are compared to the

TCT using both experimental and finite element simulation results. A lubricant developed for deep drawing of AHSS is used. In section 2 the experimental procedure and FE results for the

CDT are presented. The test procedure and FE model of the TCT is described in section 3.

Section 4 presents the discussion and comparison of the TCT and CDT results.

2. Cup Drawing Test (CDT)

2-D schematic of the tool set up for the CDT is shown in Figure 3.1. There are three components i.e. a die, a punch, and a blank holder. During the test, a circular sheet is drawn into the die cavity by the stationary punch while the drawing of the material is controlled by blank holder force. During the test, sufficient blank holder force is required to form the part successfully and avoid wrinkling.

Figure 3.2 shows an example of a cup formed by the CDT. In order to evaluate the stamping lubricant and determine the friction coefficient by using the CDT, the blank material is lubricated and formed up to a pre-selected depth. This depth is selected based on the tool geometry and blank size so that at the end of the forming process the cup has remaining flange. The perimeter of the flange can be used as an indicator of lubrication performance. Smaller perimeter is a result of more draw-in and less stretching of the material which consequently means better lubrication performance and lower friction coefficient. Since the friction force is directly related to the blank holder force, for a reliable CDT result, it is necessary to select proper blank holder force for a given material and thickness. Blank holder force should be high enough to avoid wrinkling while the material can be formed without tearing. Also, the performance of lubricants shows larger variations under higher blank holder forces. Therefore, for a selected sheet material and

25 thickness, the proper blank holder force, known as the critical blank holder force, is the highest blank holder force in which the part can be formed successfully without tearing.

Figure 3.1: 2-D schematic of the cup drawing tooling.

Figure 3.2: (a) 2-D schematic of the formed cup and the flange area; (b) An example of the formed cup. The dashed line shows the perimeter of the flange.

In order to determine the Coefficient of Friction (COF) through the CDT, Finite Element (FE) simulations of the CDT process were developed with different values of the COF. The flange perimeter predicted from each simulation was compared with experimental measurement. The

COF of the simulation model which predicts similar flange perimeter to the experimental measurement was considered as the average COF for the system.

During the CDT, the contact pressure, the temperature, and the sliding velocity at tool / sheet interfaces are different at each location of the part. Therefore, the actual COF is different at each location. However, it is very difficult to determine the value of the COF at each location, so an average value of the COF is assumed for the entire system.

2.1. Experiment - Cup Drawing Test

The CDT test was conducted using a 160 metric-ton hydraulic press. Schematic of the tool geometry and dimensions are shown in Figure 3.1. DP590 steel sheet with 1.4 mm thickness was used for this experiment. The basic mechanical properties were determined through the tensile test, Table 3.1. Viscous pressure bulge test was conducted to determine the stress-strain behavior of the material in large strain values. A full description of the viscous pressure bulge test is

푛 available in literature (Gutscher et al., 2004). The Swift law (휎̅ = 퐾(휀0 + 휀푝̅ ) ) was used to approximately describe the hardening behavior of the material according to the stress-strain data obtained from the tensile and the bulge test. Coefficients for the Swift law are presented in Table

3.1. The as-received DP590 sheet was cut to a 305 mm diameter circular shape by water jet. The surface roughness of the sheet was measured using a stylus profiler with 2 micron tip diameter.

The Ra value of the sheet was found to be 1.35±0.4.

The blank holder force was applied by a hydraulic cushion. The required blank holder force was initially predicted by FE simulation. Preliminary tests were conducted to determine the critical blank holder force. The tests were started with the value of the blank holder force obtained from the simulation. After each test, if the cup was formed successfully, the blank holder force was

increased for the subsequent test. Results indicated that a blank holder force of 650 kN is the

critical blank holder force for this material and tool geometry. The part was formed with forming

speed of 30 mm/sec. The drawing depth (forming stroke) was set to 83 mm. Prior to each test,

both blank and tools were cleaned with acetone. The specimens were lubricated to 1.0 g⁄m2

coating weight in each side using polymer synthetic lubricant developed for metal stamping of

AHSS (Fallahiarezoodar, 2014). The amount of the lubricant on the sheet surface was suggested

by the industrial partner. Three tests were repeated to confirm that the test results were

reproducible and the average flange perimeter of the three tests was used for calculation of the

friction coefficient.

Table 3.1. Mechanical properties of DP590

Young’s Yield Tensile Hardening Hardening 휀0 Lankford coeff. modulus E strength 휎 strength Exponent coefficient 푦 푅0 푅45 푅90 (GPa) (MPa) 휎푈푇푆 (MPa) n K (MPa) 210 357 620 0.27 1315 0.008 0.77 0.83 0.92

2.2. Numerical simulation – Cup Drawing Test

A thermomechanical Finite Element model of the CDT was developed using DEFORM V11.1.

In order to reduce the computational cost, the forming operation was simplified to a 2D

axisymmetric simulation. The tools were modeled using rigid analytical bodies. However, to

analyze the heat transfer through the tools, the tool geometries were meshed. The blank was

modeled using 4-node solid elements with five elements in the thickness direction of the sheet.

The effect of material anisotropy is neglected and von Mises yield criterion was used. The

Coulomb friction law was used with different values of friction coefficients from 0.05 to 0.15.

The coefficient of friction that predicted a flange perimeter similar to the experimental measurement was considered as the friction coefficient for the system.

The important parameters relating to the thermal properties of the sheet material and the tools were obtained from literature (Pereire and Rolfe 2014), Table 3.2. The thermal properties of low carbon steel were considered for the sheet material and tool steel for the tools. It is assumed that

90% of the friction work is converted to the heat and this heat is equally distributed between the sheet and the tools. A constant heat transfer coefficient of 20 J/s m2 °C was considered for the boundary between the tool material and the sheet. Convective heat loss was modeled using a constant coefficient of convection. Initial temperature of the tools and the sheet were considered as 20 °C.

Table 3.2. Thermal properties of the tools and specimen (Pereire and Rolfe 2014) Parameters tools Sheet Heat conductivity (J/s m °C) 22 52 Heat convection with air (W/m2 °C) 50 - Specific heat capacity (J/kg °C) 460 480 Surface heat transfer coefficient (J/s m2 °C) 20 20 Expansion coefficient (1/°C) 12×10-6 12×10-6 Friction energy heat dissipation factor (훼) 0.9 - Friction heat distribution factor (훽) 0.5 - In elastic heat fraction - 0.9 Initial temperature (°C) 20 20

Currently, majority of metal stamping operations are conducted with a mechanical press that has a forming speed faster than the speed used in the CDT (30 mm/sec). Also, in forming with a mechanical press, unlike a hydraulic press, the forming speed is not constant. Instead, it follows

29 a sine curve. In order to investigate the effect of forming speed on temperature increase during the CDT, additional simulations with 60 mm/sec constant speed and a variable speed which represents the use of a mechanical press was also conducted.

Figure 3.3 shows a schematic of the ram speed versus time in a mechanical press with total stroke of 300 mm when the press is running with 25 Stroke Per Minutes (SPM). As shown in this figure, the die velocity when it touches the material is about 300 mm/sec. In this case, it takes about 0.43 sec to form the cup to 83 mm height. For 30 mm/sec and 60 mm/sec constant forming speeds, the total deformation time was 2.77 sec and 1.38 sec.

Figure 3.3: Schematic of ram velocity against time for a mechanical press with 300 mm total stroke and 25 SPM.

2.3. Results of the CDT

The flange perimeter of the cups formed in the experiments was measured and results show the average flange perimeter of three cups was about 772.5 mm. Simulation results with different friction coefficients indicated that, in this specific test, a friction coefficient of 0.07 predicts a flange perimeter similar to experimental measurements.

Temperature increase in the tools and the specimen during the CDT is predicted using the FE simulation. In the CDT, plastic deformation of the sheet material and the friction work are the sources for the generated heat. Using lubricant between the sheet and the tool surface not only reduces the friction work but also it can act as coolant and reduce the temperature at the tool / sheet interface during the deformation. However, the cooling effect of the lubricant is not considered in this study.

In the CDT, the sheet material is bent and slides around the die corner radius. Therefore, from a tribological point of view, the die corner radius is the most critical area. Figure 3.4 shows the predicted temperature at the tool / sheet interface at the die corner radius. At all three forming speeds, the temperature continuously increases during the deformation. When forming at a high velocity, the heat generated in the material does not have enough time to be transferred to the tools. Therefore, the maximum temperature in the part is higher when the part is formed at a high stroke rate. A maximum predicted temperature of about 100 °C was observed in the case of using mechanical press stroke profile (seen in Figure 3.3).

120

100

C) 60

° ( Constant 30 mm/sec 40 Constant 60 mm/sec 20 Variable (Mechanical Press)

Temperature Temperature toolatsheet / interface 0 0 10 20 30 40 50 60 70 80 90 Deformation Stroke (mm)

Figure 3.4: Effect of ram speed (deformation speed) on temperature at tool / sheet interface during the CDT. Temperature calculations are for location around the die corner radius.

Results showed that the temperature increase in forming AHSS is significant and effect of this temperature increase in lubricant performance cannot be neglected. Figure 3.5 shows the effect of plastic deformation and the frictional work in temperature increase at the part during the CDT.

The simulation result with zero friction coefficient indicates the temperature increase only due to the plastic deformation and the simulation result with 0.07 friction coefficient shows the temperature increase due to both the plastic deformation and the friction work. This result shows that about 90% of the heat generated at the part is due to the plastic deformation.

100 90 80 70

C) ° ( 50 COF=0 40 COF=0.07 30 20

Temperature Temperature sheet / toolatinterface 10 0 0 20 40 60 80 100 Deformation Stroke (mm)

Figure 3.5: Prediction the effect of the friction work on heat generated during the CDT. 60 mm/sec forming speed is considered.

Figure 3.6 represents the predicted metal sliding velocity around the die corner radius for different forming speeds. In case of the variable forming speed (ram motion in mechanical press) the sliding speed reaches to about 225 mm/ sec at about 35 mm deformation stroke. This sliding speed is much higher than the maximum sliding speeds observed with deformation speed of constant 30 mm/sec and 60 mm/sec. Considering the sliding velocity as one of the effective parameters on lubricant performance, when the CDT is conducted to test a lubricant for stamping purpose, it is necessary to run the test with forming speed close to the forming speed in the production line where that lubricant will be used.

250

Constant, Hydraulic 200 press 30 mm/sec Constant, Hydraulic 150 press 60 mm/sec Variable, Mechanical 100 press (25 SPM)

Sliding Sliding speed (mm/sec) 50

0 0 20 40 60 80 Deformation Stroke (mm)

Figure 3.7 shows the predicted contact pressure around the die corner radius at 83 mm forming stroke. Results show that the contact pressure between the sheet and the die surface changes from

160 MPa to 500 MPa at different locations around the die corner radius. This contact pressure is very high and considering the sliding velocity around the die corner radius there is a high possibility of metal to metal contact in this location of the die. Sheet material and thickness, initial blank size, tool geometry, and the blank holder force are the parameters that influence the contact pressure.

Figure 3.7: Prediction of contact pressure around the die corner radius in the CDT.

3. Twist Compression Test (TCT)

In the TCT, an annular tool is compressed and rotates on a stationary workpiece, Figure 3.8.

During the test contact pressure between the tool insert and workpiece is measured. Also, reaction torque resulted from the friction force at contact interface is measured continuously. The contact pressure, rotational velocity of the tool insert, and the amount of lubricant on the sheet surface are the control variables in this test. The contact pressure should not overpass the yield strength of the tool and workpiece materials. Thus, no plastic deformation is involved in the

TCT. In addition to the yield strength, the coating and the surface quality of the specimen and the tool insert are the material parameters influencing the tribological condition.

The coefficient of friction as a function of time can be calculated using the measured torque and contact pressure as:

푇(푡) 퐶푂퐹 = (3-2) 푟푃퐴

35 where, T(t) is the torque as a function of time t, P is the applied pressure, and 푟 and 퐴 are the geometrical parameter of the tool inserts shown in Figure 3.8.

Figure 3.8: Schematic of the twist compression test set-up.

An example of the coefficient of friction versus time curve obtained from the TCT is shown in

Figure 3.9. In The beginning of the test, the contact pressure starts to rise up until reaches to the target value. The time 푡푏 in Figure 3.9 indicates the moment when the contact pressure reaches to the target value. The calculated coefficient of friction increases slightly and then drops and reaches to a steady state value. When the breakage in lubricant film happens, the coefficient of friction starts to rise up again. The time when the lubricant breakage happens is indicated by 푡푒.

퐶푂퐹푏 and 퐶푂퐹푒 are the calculated coefficient of friction at time 푡푏 and 푡푒, respectively. To evaluate the effect of contact pressure, sliding velocity, and amount of the lubricant on lubrication performance, a parameter called TCT factor (used by industry) was introduced as:

|t −t | TCT⁡factor = ⁡ e b (3-3) 0.2⁡COFb+0.8⁡COFe

Higher TCT factor indicates lower coefficient of friction and longer process before lubricant breakage.

Figure 3.9: Example of the calculated coefficient of friction versus time in a TCT. 푡푏, 푡푒, 퐶푂퐹푏, and 퐶푂퐹푒 are used to calculate the TCT factor (Eq. 3-3).

3.1. Experiment - Twist Compression Test

The TCTs were conducted to evaluate the effect of contact pressure, rotational velocity and lubricant coating weight on lubrication performance for a selected lubricant. Same lubricant as in the CDTs was used. The tests were conducted at Quaker®. DP590 steel sheet with 1.4 mm thickness was used as the specimen. Three values of contact pressure, three rotational speeds, and three different lubricant coating weights were considered which provide 27 testing conditions, Table 3.3. The unit for the rotational speed is revolutions per minute (RPM). The inner and outer diameters of the tool insert were 19.05 and 25.4 mm, respectively. Thus, the

RPM can be converted to linear velocity by:

푣 = 푟 × 푅푃푀 × 0.10472

푣 is the linear velocity, and r is the mean radius of the tool insert. The calculated sliding velocity for 10 RPM, 20 RPM and 30 RPM rotational speeds are 11.5 mm/sec, 23 mm/sec, and 34.5 mm/sec, respectively.

Table 3.3 Parameters used in the TCT Material Rotational Speed Pressure (MPa) Application of lubricant (RPM / mm/sec) DP590 10 / 11.5 70 1 g/m2 ( +/- 0.3g/m2) (t=1.4mm) 20 / 23 140 2 g/m2 ( +/- 0.3g/m2) 30 / 34.5 200 “fully flood”

Four tests were repeated for each testing condition. The amount of lubricant coating weight was determined by measuring the weight of the specimen before and after applying the lubricant. In the fully flooded case, the specimen was flooded into the lube during the test. After each test, the tool insert and the test specimen were renewed to eliminate the effect of the tool wear from the test results.

3.2. Numerical simulation – Twist Compression Test

To predict the temperature increase resulted from the friction work thermomechanical FE simulation model of the twist compression test was developed using DEFORM V11.1. Figure

3.10 shows the simulation model with three components i.e. the specimen, the tool insert, and a stationary base that the specimen was fixed on it. Simulations were conducted for two cases with the maximum and the minimum value of the TCT factor. The specimen was created using 4-node solid element with 16 elements through the thickness direction. The tool and the base were modeled as a rigid body but were meshed to allow the heat transfer calculation through the tools.

Thermal properties used for the tools and the sheet material are summarized in Table 3.2. The initial temperature of the tools and the specimen was assumed as 20 °C. The Coulomb friction law was assumed and coefficient of friction versus time data obtained from each TCT was used as the simulation input, Figure 3.11. Simulations are conducted for two test conditions which provide the highest and the lowest TCT factor. Due to the large difference in the test duration for case A and case B, two time axes are used in Figure 3.11. It was assumed that 90% of the friction work is converted to the heat and this heat is equally distributed between the specimen and the tools.

Figure 3.10: FE model of the TCT process.

3.3. Results of the TCT

The TCT factor calculated from the experimental result of each testing condition is presented in

Figure 3.12. Results show that all three variables i.e. the contact pressure, the sliding velocity, and the lubricant coating weight, significantly affect the TCT factor. For the case of 200 MPa contact pressure and 34.5 mm/sec sliding velocity (the highest contact pressure and the fastest sliding velocity used in the tests), with 1 g/m2 and 2 g/m2 lubricant coating weights, the breakage in lubricant film happened before the contact pressure reaches to the target value. Therefore, these two cases are eliminated from further analysis.

1 g/m2 lubricant weight 100

80 60 11.5 mm/sec 40 TCT Factor TCT 23 mm/sec 20 34.5 mm/sec 0 70 MPa 140 MPa 200 Mpa Contact pressure

2 g/m2 lubricant weight

150

100 11.5 mm/sec

TCT Factor TCT 50 23 mm/sec 34.5 mm/sec 0 70 MPa 140 MPa 200 Mpa Contact pressure

Fully flooded 800

600

400 11.5 mm/sec

TCT Factor TCT 23 mm/sec 200 34.5 mm/sec 0 70 MPa 140 MPa 200 Mpa Contact pressure

Figure 3.12: Effect of the contact pressure, the rotational speed and the lubricant weight on TCT factor and lubricant performance.

Result of the TCTs can be summarized as:

1) Increasing the sliding velocity from 11.5 mm/sec to 34.5 mm/sec reduces the TCT factor

in all tested lubricant coating weights and contact pressures

2) In the case of fully flooded lubricant coating and high contact pressure i.e. 140 MPa and

200 MPa, the effect of the sliding velocity on TCT factor is less significant compared to

the case of 1 g/m2 or 2 g/m2 lubricant coating weight.

3) For 1 g/m2 and fully flooded lubricant coating, increasing the contact pressure results

reduction of the TCT factor in all tested sliding velocities.

4) For 2 g/m2 lubricant coating weight increasing the contact pressure does not significantly

affect the TCT factor.

5) Increasing the lubricant coating weight increases the TCT factor.

6) The longest test duration before lubricant breakage, about 50 sec, was obtained for 70

MPa contact pressure, 11.5 mm/sec sliding velocity, and fully flooded lubricant coating.

The maximum TCT factor of 689 was calculated for this case.

7) The minimum TCT factor of 21.93 is obtained for 140 MPa contact pressure, 34.5

mm/sec sliding velocities and 1 g/m2 lubricant coating weight.

In conclusion, results showed that the lubrication performance was better in slower sliding velocity and lower contact pressure. Also, increasing the amount of the lubricant coating weight improved the lubrication performance.

Temperature increase at the TCT was calculated using a FE simulation. Simulations were conducted for two test conditions (A and B) which provide the highest (A) and the lowest (B)

TCT factor (lowest TCT factor was obtained for 200 MPa contact pressure, 23 mm/sec sliding

42 velocities, and 1 g/m2 lubricant coating weight and the highest TCT factor was obtained for 70

MPa contact pressure, 11.5 mm/sec sliding velocities, and fully flooded lubricant coating condition). The simulations were conducted up to the lubricant breakage time, 49 sec for the case

A and 5.4 sec for the case B.

Temperature increase during the TCT for the case A and the case B is shown in Figure 3.13.

Maximum temperature obtained in case A is about 25 °C. The temperature increase in this case is not significant and the temperature at the tool / sheet interface remains almost constant throughout the test. In the case B the maximum temperature reaches about 40 °C. The higher temperature in the case B is because of a shorter test duration and higher coefficient of friction compared to the case A.

Time (s) for the case B 0 1 2 3 4 5 6 45 Case A: (Highest TCT factor) 40 Contact pressure: 70 MPa 35 Sliding velocity: 11.5 mm/sec

Lubricant coating weight: Fully C) ° 30 flooded

25 20 Case B: (Lowest TCT factor) Contact pressure: 200 MPa 15 Sliding velocity: 23 mm/sec 2 Temperature ( Temperature Lubricant coating weight: 1 g/m 10 5 0 0 10 20 30 40 50 60 Time (s) for the case A

4. Discussions - Comparison of the CDT and the TCT 4.1. Contact pressure

In the CDT the predicted contact pressure around the die corner radius was between 160 MPa and 500 MPa. The TCT results showed that increasing the contact pressure to about 200 MPa reduces the accuracy of the test result. The TCT was not successful when 200 MPa contact pressure were used with 34.5 mm/sec sliding velocity. Considering the CDT as an example of actual stamping operation, results indicate that the range of the contact pressure which the TCT can provide reliable results is not close to the contact pressure that the material experiences in real stamping operation. High contact pressure around the die corner radius provides a severe interface condition, which can cause the lubricant film breakdown.

4.2. Sliding velocity

The maximum sliding velocity in the CDT is directly related to the deformation speed (press speed). In this study, for the CDT, the maximum predicted sliding velocity around the die corner radius was about 225 mm/sec. The maximum sliding velocity used for the TCT was 34.5 mm/sec which is significantly lower than the sliding velocity in the CDT with mechanical press. In the

TCTs, even with sliding speed of 34.5 mm/s, in two cases of 1 g/m2 and 2 g/m2 lubricant coating weight, lubricant breakage happened before the contact pressure reaches to the target value of

200 MPa.

4.3. Temperature

In metal stamping, plastic deformation and frictional work are two sources of heat generation.

Results show that in the cup draw test, 90% of the heat generated at the part is due to the plastic deformation. In the TCT, there is no plastic deformation of the specimen and all the heat

44 generated is due to the friction work. Therefore, the maximum temperature at the tool / sheet interface in the TCT is significantly lower than the temperature at the part in the CDT. In this study the maximum predicted temperature at the tool / sheet interface for the CDT was about 100

°C while the maximum temperature predicted in the TCT was about 40 °C.

In this study, the temperature increase is predicted for only one forming cycle. In our previous study (Fallahiarezoodar et al., 2016) it was shown that in deep drawing of AHSS, the temperature increase due to multi-forming operations can be significant and should not be neglected.

5. Conclusions

The twist compression test and the cup drawing test, two laboratory tribotests, are compared for evaluation of metal stamping lubricants. The cup drawing test can provide similar testing conditions relative to an actual deep drawing process. However, this test needs more complex tooling than the TCT. Also a press, cushion, and relatively large blank size are required for the

CDT. In comparison, conducting twist compression test is faster and easier and the required tools and machinery are less complicated. However, the testing conditions i.e. the contact pressure, the sliding velocity, and the temperature in the TCT are not similar to the conditions of actual deep drawing process. Therefore, the CDT is a more reliable test method for evaluation and selection a proper lubricant for a deep drawing process, while TCT is useful for evaluating lubricants with various additives and compositions.

CHAPTER 4: TEMPERATURE INCREASE IN FORMING OF

ADVANCED HIGH STRENGTH STEELS (AHSS)- EFFECT OF RAM

SPEED USING A SERVO DRIVE PRESS

Note: This chapter was submitted for publication to the Journal of Manufacturing Science and Engineering on January 15, 2016; accepted for publication on June 27, 2016. doi:10.1115/1.4033996

1. Introduction

Light-weight design has become essential for automotive industry due to its considerable economic and ecological benefits (i.e., higher fuel economy and lower emission). High strength and lightweight materials are introduced for a wide range of body panels and structural parts. In addition to Al alloys, Advanced and Ultra High Strength Steels (A/UHSS) are increasingly used in automotive manufacturing. Therefore, to minimize the part failure and tool wear, press speed during part deformation often needs to be reduced. Electro-mechanical servo drive presses provide precision ram position and velocity control during the stroke, Figure 4.1. This allows improvement of drawability by only reducing the ram velocity during the part deformation stage, without significantly reducing the production rate (Altan and Tekkaya 2012c).

Figure 4.1: Servo drive press provide flexible slide motion control (Miyoshi, 2004)

In sheet forming of AHSS, the heat generated due to friction and plastic deformation can reach up to about 100-200 °C depending to process type and speed (Kim et al., 2009; Pereira and Rolfe

2014). As reported by Farren et al. (1925), approximately 90% of the work done for the plastic deformation is converted into heat and the remaining 10% is used up in increasing the internal energy of the material. For material with temperature dependent flow stress, temperature raise during the deformation can affect the stiffness of the material and lowering the flow stress data.

This softening can increase the real area of contact resulting in higher adhesion. It has been reported that adhesion starts to rise at approximately 125-150 °C (Gaard et al., 2010).

From the tribological point of view, temperature rise during the deformation can affect the properties of the lubricant and influence the lubrication performance. Organic based lubricants, which often used in sheet metal stamping, can be used below 250 °C without significant thermal

47 degradation (Wilson, 1997). Therefore, it is important to accurately determine the fraction of deformation work which goes to increasing the temperature of the material during the sheet forming process. There are a few studies that investigated the temperature generation in forming of AHSS and aluminum alloys using numerical or experimental procedures (Kim et al., 2009;

Pereira and Rolfe 2014; Kim et al., 2011; Ju et al., 2015b). Kim et al., (2009), investigated the shear fracture at die corner radius in draw bending test of DP 980 and they concluded that the deformation-induced heating, in the order of 75 °C, has a dominant effect on the occurrence of shear failure.

In order to determine the temperature, cost and time could be greatly reduced by using computer simulations rather than running experiments with a try-out press in the die shop. FE simulations were used for temperature prediction in metal forming process (Kim et al., 2009; Pereira and

Rolfe 2014; Kim et al., 2011; Ju et al., 2015b).

In published literature, the temperature at the part / tool interface is predicted after a single forming operation. However, it is important to estimate how the temperature increases after several numbers of forming operations, especially in forming of AHSS materials. In the current study, first a simulation of U-channel drawing is conducted to validate the methodology and assumptions used in the thermo-mechanical simulation model, by comparing the predictions with experimental results available in the literature. Then, a similar thermo-mechanical FE model for deep drawing of industrial scale non-symmetric panel is developed. The temperature rise in sheet and tools is determined for two different AHSS materials (1.4 mm CP800 and 1.4 mm DP590).

The simulation results are validated with experimental results in terms of thinning distribution.

Effect of coefficient of Friction (COF) and lubrication performance on temperature generation at tool / sheet interface is investigated. Simulations of multi-forming operation of U-channel

48 forming and deep drawing process were conducted to investigate the effect of the ram speed

(SPM) on temperature rise at the tool surface after several consecutive forming operations.

2. Material Model and Element Type

In the present study, three different AHSS materials, complex phase grade steel CP800 (1.4 mm), and dual phase grade steels DP590 (1.4 mm), and DP780 (2mm), are examined. Tensile properties for DP780 were obtained from literature (Pereira and Rolfe 2014), and for CP800 and

DP590 tensile tests, in rolling direction, were conducted at Honda R&D department of Honda

America. Hill 48 plasticity law with isotropic material model was used for simulating the plastic behavior of the sheet. The flow stress for CP800 and DP590 materials were obtained from the

Viscous Pressure Bulge (VPB) test and are shown in Figure 4.9. The detail information about

VPB test can be found in previous publications (Altan and Tekkaya 2012a; Gutscher et al.,

2004). The flow stress data obtained from the VPB test then were extrapolated up to true strain values equal to 1 using the Hollomon’s equation (휎 = 퐾휀푛). The calculated K and n values, along with the other properties obtained from the tensile test, are summarized in Table 4.1.

Table 4.1. Mechanical properties of sheet materials used in this study. Data for DP780 is from reference (Pereira and Rolfe 2014)

Tensile test Bulge test Material Yield Tensile Young’s Strength coefficient Strain hardening stress stress modulus (K) exponent (n) (MPa) (MPa) (MPa)

DP780 (2 mm) 587 884 210 (assumed) 1332 0.11 DP590 (1.4 mm) 355 600 180 1311 0.27 CP800 (1.4 mm) 770 900 230 1325 0.11

Thermal properties of the sheet and the tools are selected based on the data available in the literature (Pereira and Rolfe 2014; Gaard et al., 2010; Kim et al., 2011). Due to unavailability of the thermal data for the materials used in this study, the thermal properties for sheet material are based on the properties of low carbon steel. Using the actual thermal properties for each specific material will increase the accuracy of the predictions. However, in the current study, the predicted temperature for U-channel drawing is compared with available experimental results and it is observed that the predicted temperature for given boundary conditions and process parameters is in a good agreement with experimental measurements. Therefore, the prediction error for using the thermal properties of low carbon steel in forming AHSS materials can be considered to be negligible. For the tools, the relevant thermal properties for the tool steel were utilized using the data available in the PAM-STAMP database and reference (Pereira and Rolfe

2014). The thermal data used for the sheet and the tools are summarized in Table 4.2. The dissipation factor, 훼, describes the percentage of internal work which will be converted to temperature. 훽 shows the fraction of friction work dissipation converted into heat. In simulations, it is assumed that the heat generated due to the friction is equally distributed into the tools and sheet surface.

Table 4.2. Thermal properties used in the thermo-mechanical FE simulation. Thermal properties for sheet are for low carbon steel and are from previous publication by Pereira, et al., (2014)

tools Sheet Density (kg/mm3) 7.7×10-6 7.9×10-6 Heat conductivity (J/s m °C) 22 52 Heat convection with air (W/m2 °C) 50 - Specific heat capacity (J/kg °C) 460 480 Surface heat transfer coefficient (J/s m2 °C) 20 20 Expansion coefficient (1/°C) 12×10-6 12×10-6 Friction energy heat dissipation factor (훼) 0.9 - Friction heat distribution factor (훽) 0.5 - In elastic heat fraction - 0.9 Initial temperature (°C) 20 20

It is known that the Surface Heat Transfer Coefficient (SHTC) is a function of gap and pressure between the sheet and the tool surfaces. However, due to simplicity, this parameter was considered as a constant value. In simulation of multi-forming operations, the heat convection between the tool surface and the air, a factor that influences temperature reduction during the die opening and transformation stages, is also considered. The initial temperature of the sheet and the tools were considered 20 °C in all simulations.

The sheet material was simulated using shell elements with five integration points through thickness direction. The initial element size was selected based on the minimum sliding radius in each die set. In simulations of deep drawing process “mesh refinement” option was activated as suggested by PAM-STAMP V15.1 manual. This option allows the software to more accurately calculate the flow of the material by automatically reducing the element size at locations where severe deformation occurs. The elastic deflection of the tools is neglected. The tools are simulated as surfaces (not volume) to reduce the simulation time. Six thermal points were considered in the thickness direction for the tools. The prediction error due to use of surface element instead of solid element is not investigated in this study.

3. U-Channel Drawing 3.1. Simulation setup and validation of Thermo-mechanical FE Model

3-D coupled thermo-mechanical finite element (FE) model is developed to analyze the U- channel forming of DP780 (2 mm). Figure 4.2 shows the geometrical parameters of the die and specimen. The commercial software PAM-STAMP-V15.1 with explicit solver was used. The die geometry and tooling setup is similar to what was used in experiments to be able to validate the accuracy of the simulation model and results by comparing with experimental results (Pereira and Rolfe 2014). The model consists of die, punch, blankholder, ejector pin, and sheet. The punch was fixed in all three directions. Blankholder and die were fixed in X and Y directions and allowed to move in the Z direction which was considered as the forming direction. 27 kN constant force was applied on the blankholder and the ejector pin. The distance between the die and the blankholder was checked in several forming strokes to ensure the closure of the blankholder. The die movement is specified by speed vs time curve. The same speed pattern used in the experiment was applied to the die representing the motion of the single-action mechanical press with 1 Stroke Per Minutes (SPM) ram speed (Pereira and Rolfe 2014). Based on the geometry of the press, the crank rotational speed and the drawing depth used in the experiment, the deformation starts at about 8 mm/s and reduces to 0 mm/s at the end of 40 mm forming stroke. The total forming duration was about 9 sec. The temperature at the die / sheet interface was predicted and compared with experimental results.

Figure 4.2: Schematic cross section of the simulation setup and the geometrical parameters used for simulation of U-channel forming (Pereira and Rolfe 2014).

3.2. Results of U-channel drawing and validation of thermo-mechanical FE model

Several assumptions were made in the simulations due to unavailability of the required data.

These assumptions, discussed below, can limit the accuracy of the simulation results: a) The accurate thermal properties of the sheet material used in this study were not available. So, the properties of low carbon steel were used from literature; b) The heat transfer coefficient which determines the amount of the heat transferred from sheet to the dies was considered as a constant value. However, as determined experimentally, this value is a function of the gap and pressure between the sheet and the die (Ju et al., 2015b; Billur, 2013); c) The sheet and the tools are simulated as surface elements and thermal integration points through the thickness were considered to analyze the heat conduction inside the tools; d) A constant value of the coefficient of friction is considered in all simulations and it is known that the COF is not constant in all locations in the die during stamping.

Figure 4.3 shows the predicted maximum temperature generated at the die / sheet interface compared to the experimental results. Simulation results are in good agreement with

53 experimental measurements from Pereira and Rolfe (2014). The maximum predicted temperature at the die / sheet interface goes up to about 45 °C (25 °C temperature rise) after about 3 sec. of drawing (about 22 mm drawing depth) and drops to about 33 °C at the end of deformation.

Similar trend was observed in experiments. The temperature rise in terms of value and trend follows the experimental measurement very well. Therefore, the prediction error as a result of using thermal properties of low carbon steel instead of the real values for the specific sheet material used in the experiment can be considered to be negligible. Also, it can be concluded that the methodology and the boundary conditions used to develop the thermo-mechanical FE models in this study can predict the temperatures close to that encountered in the real stamping operations.

Some inconsistency of the simulation results compared to the experiment can be observed at about 2 to 3 sec after the deformation starts. Since the temperature and pressure can affect the lubrication condition and COF, assuming a constant value of COF in simulation causes some errors in predictions. However, do to unavailability of data for variable COF in function of pressure and temperature for the lubricant used in the study, it was not possible to use a variable

COF in the simulations.

4. Deep drawing of non-symmetrical industrial size panel 4.1. Experimental procedure

Figure 4.4 shows a schematic of the die geometry used for deep drawing process in this study.

The die was manufactured by SHILOH industries. 1.4 mm CP800 and DP590 sheet materials were used in the experiments. The tensile test and the bulge test results showed DP590 is more formable than CP800, by comparing the uniform elongation and bulge height. Therefore, the total drawing depths 70 mm and 48 mm were selected for DP590 and CP800, respectively.

Rectangular sheets (600*395 mm for CP800, and 640*435 mm for DP590) were used. In case of

DP590, the corners of the sheet were chamfered by 100*75 mm to reduce the possibility of wrinkle and improve the drawing process.

Parameter Notation Value (mm) Concave side radius 푅1 601.5 Convex side radius 푅2 598.5 푅3 51.5 Cavity corner radii 푅4 56.5 푅5 61.5 푅6 66.5 Die corner radius 푅7 10 Punch corner radius 푅8 10

Figure 4.4: Schematic of the non-symmetric industrial scale die used in this study for deep drawing process (die set built by Shiloh Industries).

The sheets samples were cleaned by acetone and then lubricated in both sides. Cup Drawing Test

(CDT) as a regular lubrication test in sheet metal stamping (Kim et al., 2009, Ju et al., 2015a) was used for the evaluation of lubricants. Ten different lubricants suggested by lubricant companies, for deep drawing of AHSS, were tested. In cup drawing lubrication test, sheets are lubricated on both sides and then formed up to a predefined drawing depth using a constant blankholder force. The tests were performed at about 30 mm/sec ram speed using 160-ton hydraulic press. Then the flange perimeter of the cups was measured and the lubricants were ranked based on the length of the flange perimeter. The flange length, as a function of lubrication performance, is smaller when the cup draw-in is more and it is an indication of better lubrication performance. The selected lubricant used in this study, polymer synthetic, was provided by

IRMCO Company and was one of the best ranked lubricants from the cup drawing tests.

A 300-ton Aida servo drive press with 25-ton servo hydraulic cushion was used. This press provides accurate control of ram displacement/speed and blankholder force during the deformation process. The press speed, at the stroke position when the punch touched the sheet, was about 75 mm/sec. A constant blankholder force was used. Preliminary simulation results showed that 200 kN and 250 kN constant blankholder forces were sufficient to maintain closure of the blankholder and avoid creation of wrinkles for the sheet size used to form DP590 and

CP800, respectively. Three samples from each material were used in the tests. However, due to the difficulty of cutting the materials for thickness measurement, only two samples from each material were measured.

4.2. FE Model of Deep Drawing Process and Prediction of Thinning

3D thermo-mechanical simulation model of deep drawing process for CP800 and DP590 with

1.4 mm thickness was developed using the die geometry shown in Figure 4.4. The model consists of die, punch, blankholder, pad, and sheet. The boundary conditions are set similar to what was used in the experiments. The punch was fixed in all three directions. Blankholder, pad, and die were fixed in X and Y directions and allowed to move in the axial Z direction (forming direction). A constant 250 and 200 kN blankholder force were applied on the opposite direction of the die movement for CP800 and DP590, respectively. A 2 kN force was also applied on the pad to avoid the separation of the sheet from the top of the punch. The tools were modeled using surface elements and considered as rigid body. Similar thermal and mechanical properties as described in section 2 for the tools and sheets are used.

As mentioned in section 4.1, due to the different formability of DP590 and CP800, different sheet sizes and drawing depths were used for each of these materials in the experiments.

Therefore, a simulation model, with drawing depth and blankholder force according to the experimental set-up, is developed for each material.

In order to be able to investigate the effect of the material properties on temperature rise at the tool / sheet interface, simulation with similar forming conditions and sheet dimensions used for

CP800 was also conducted for DP590. In this way, the only difference that provides different temperature predictions in the simulation models is the sheer material properties.

In order to determine the COF from the CDT test, several simulations of cup drawing process with different COF values were conducted with similar boundary conditions used in the lubrication evaluation tests. The COF value which provides the similar flange length as measured from the experiment is selected as the COF for that lubricant, COF=0.08. Then this calculated

COF value is used as initial COF in simulations of deep drawing process. The predicted load- stroke curves from the simulations with COF=0.08 were compared with that obtained from the experiments. It was observed that the predicted load-stroke curves were slightly lower than experimental results. Therefore, the initial COF (0.08) was modified and increased to the value

(COF=0.12) that the predicted load-stroke curves match with experiments.

4.3. Results of deep drawing process using nonsymmetrical die geometry and comparison with experimental results

Similar assumptions, mentioned in section 3.2, are also considered for simulations of deep drawing process. However, as discussed in section 3.2, these assumptions are not significantly affecting the accuracy of simulation results in terms of temperature prediction. Comparison of simulation results with experimental measurements in terms of both temperature prediction and thinning distribution shows that the FE model and the boundary conditions used in the current study are reasonably reliable.

4.3.1. Prediction of thinning distribution and validation of the FE model

Thinning distribution along the curvilinear length at the corner of the panel where the maximum thinning is predicted in simulation, Figure 4.5, is compared with experimental measurements,

Figure 4.6 and Figure 4.7 for CP800 and DP590, respectively. For CP800, the maximum predicted thinning on the part is about 13%, Figure 4.5. However, the maximum thinning value calculated along the curvilinear line is about 9%, Figure 4.6. The reason is that the curvilinear line where the thinning values are measured in experimental samples is not passing through the element which shows the maximum thinning in simulation. For CP800, results showed the predicted thinning is in the same range of the thinning measurement from the experiments except at location number 4. The nominal sheet thickness was about 1.4 mm and the real initial thickness was not measured before the test. A small difference between the nominal and real thickness (even about 0.05 mm) for a sheet in range of 1.4 mm thickness cause about 3% different in thinning measurement. The differences between the prediction and experimental thinning measurements in this study are less than 3%.

Similar results are illustrated in Figure 6 for DP590 formed up to 70 mm drawing depth using

200 kN blankholder force. For this material also the maximum difference between the predicted thinning value and the experimental measurement is about 4%.

4.3.2. Effect of the COF on temperature rise at die / sheet interface

Once the accuracy of the simulation results are validated by comparing the thinning predictions with experimental measurements, temperature rise at the tool / sheet interface is investigated for

CP800 and DP590 used in this study. The COF used in the deep drawing simulation is initially determined by CDT and then modified by comparing the load stroke curves of the simulations and experiments, as described in sections 4.1 and 4.2. The reason for calculating different COF in deep drawing process compared to the CDT can be described due to different pressures and temperatures at die / sheet interface in these two different forming processes. The CDT was performed at about 30 mm/sec ram speed but the deep drawing process was conducted at about

75 mm/sec. In the deep drawing process, the forming speed is about two times faster and the die corner radius is smaller (10 mm compared to 16 mm) compared to the CDT. Smaller die corner radius and more complexity of the die cavity compared to the cup drawing cause higher strains at the part and consequently increase the deformation induced heating. Also, the faster ram speed in deep drawing experiments reduces the time of heat distribute through the tools by conduction.

So, the temperature at the tool / sheet interface was higher in deep drawing process compared to

CDT. This higher temperature can affect the lubrication performance and increase the COF.

Also, the different pressure between the tools and the sheet in the CDT and the deep drawing operations can be another reason for different COF values. As reported in several previous publications (Wilson, 1997; Wilson et al., 1995; Sun et al., 1987), assuming a constant COF for whole model is not accurate. FE model with variable COF as a function of temperature, and pressure can increase the accuracy of the simulation results. However, variable COF values as functions of pressure and temperature are not available at this moment.

Temperature rise at the die / sheet interface is predicted for two different COF values (0.08 and

0.12) during the forming of 1.4 CP800 up to 48 mm. Temperature rise versus stroke is shown in

Figure 4.8. As expected, the maximum temperature for lower COF is lower. Changing the COF from 0.08 to 0.12 increases the maximum temperature at die/ sheet interface at 48 mm stroke from about 80 °C to 91 °C. Therefore, using accurate COF is necessary for accurate prediction of temperature in the simulation of sheet metal stamping.

4.3.3. Effect of the material properties on temperature generation

It is known that the deformation-induced heating is proportional to the deformation energy, i.e. the area below the flow stress curve of the material. The flow stress data developed by VPB test for the materials used in this study are shown in Figure 4.9.

Figure 4.9: Flow stress data for 1.4 mm CP800 and DP590 obtained from the viscous pressure bulge test

The nominal thickness for both materials (CP800 and DP590) is 1.4 mm. Therefore, for a given forming conditions (COF, sheet size, blankholder force, drawing depth, and forming speed) the temperature generated at the part for CP800 must be higher. The predicted maximum temperature is approximately 33% higher for CP800 than for DP590. Comparison of the tensile strengths of both materials shows that the ultimate tensile stress for CP800 is about 30% higher than DP590. These results show the effect of material strength on temperature generation during the deep drawing process. Also, for higher strength material the forming load and contact pressure in forming is higher and it is known that the COF is a function of pressure. Therefore, the COF value is different during the forming of different materials with different strengths and consequently the temperature generation due to friction work is different. However, since a constant COF is considered in the simulations the effect of the material properties on friction work is not considered in this study.

The FE simulation of deep drawing process for DP590 with the conditions used in the experiment (640*435 mm rectangular sheet, 200 kN blankholder force, and 70 mm drawing depth) is also conducted, to predict the temperature in the part and tool / sheet interface at similar conditions to what the material was tested. The location of the maximum temperature at 70 mm stroke was in the same location shown in Figure 4.10, but the value reached up to about 130 °C.

The maximum temperature calculated at the die / sheet interface at this stroke was about 110 °C.

Currently, metal manufacturers and automotive companies are investigating the development and production of materials with tensile strength of about 1500 MPa. Based on the simulation results presented in this study, the temperature at the part for these ultrahigh strength materials can reach to up to 200 °C. This high temperature can affect the lubrication performance, the material properties, and the surface quality of the part and the tooling.

Figure 4.10: Temperature predicted in panels formed up to 48 mm depth with 250 kN blankholder force and 75 mm/sec ram speed; top) 1.4 mm CP800, bottom) 1.4 mm DP590.

5. Multi-Stroke Forming Operations 5.1. Simulation set-up

Similar methodology used for the single forming operation was used to simulate the multi- forming operation of the U-channel-forming and the deep drawing processes. The temperature rise at the die / sheet interface was predicted immediately after when the deformation stage was finished and also before starting the next steps.

For U-channel drawing, two different forming speeds, 5 SPM and 30 SPM were considered. The ram (punch) speed during deformation was calculated using the well-known equations for slider- crank mechanism of the press (Altan et al., 2005).

The information, used in the simulation of multi-stroke forming operations of U-channel drawing was as follows:

 For press speed at 5 SPM, the ram speed at contact was 41 mm/sec, the duration of

forming was 2 sec., and the transfer time between 2 strokes was 10 sec.

 For press speed at 30 SPM, the corresponding values were 250 mm/sec (ram speed at

contact), 0.32 sec (duration of forming), and 2 sec (transfer time between 2 consecutive

strokes).

The material data for 1.4 mm CP800 is only used in simulation of multi-stroke deep drawing operations. Crank diameter of the servo press used in the experiment, 400 mm, was utilized to create the ram speed versus stroke curve. As a particular characteristic of the servo drive presses, the selected ram speed versus stroke, Figure 4.11, allows the press to move at 6 SPM before and after touching the material while during the material deformation the ram speed remains constant, 75 mm/sec. The total duration from the start of one forming operation to the next was considered about 10 sec (6 SPM). The forming duration was about 0.64 sec (75 mm/sec and 48 mm drawing depth) and 9.36 sec was considered for die opening and part transformation.

5.2. Results and discussion

Servo-drive presses, compared to mechanical presses of similar capacity, can be run 50 to 100% faster, in terms of SPM. However, it is not completely clear how temperature at the tool sheet interface increases at multi-forming steps at different forming speeds. Therefore, in the current study the simulation of multi-forming operations of U-channel drawing and deep drawing were investigated as two examples.

Figure 4.12 shows the increase of maximum temperature predicted at die / sheet interface for 2 mm DP780 after several operations of U-channel drawing with two different forming speeds (5 and 30 SPM). At 5 SPM ram speed the maximum temperature at die / sheet interface increased from 41°C to 46 °C after 8 operations. At 30 SPM, maximum temperature increased from 100 °C

68 to 117 °C after 9 operations. However, the temperature rise at die / sheet interface does not increase significantly (less than 1 °C) after nine operations and reach almost steady state condition. As expected, using faster forming speed and transfer time, the temperature at the die / sheet increased significantly. Faster forming operation reduces the time of heat transfer from the tools surface into the air and therefore the temperature rise after several operations was more significant when using a faster ram speed.

Figure 4.13 shows the max temperature rise at die / sheet interface for several forming operations of deep drawing process for CP800 at 6 SPM production rate. The maximum temperature increased 6 °C after seven forming operations. The temperature rise from the sixth to the seventh operation is about 2 °C and the temperature rise does not reach steady state condition after seven operations. However, the main objective of this study is to show how temperature rises during the deformation of AHSS. The calculation of the maximum temperature when steady state condition reached is out of the scope of this study. Therefore, to save computation time, the model was developed to predict the temperature only up to seven strokes.

Below is a summary of the results obtained from the simulation of both U-channel forming and deep drawing:

a) the die/sheet interface temperature increases with increasing deformation speed, as

indicated by SPM

b) the die surface temperature continues to increase slightly during multiple successive

forming operations, until a near steady state surface temperature is reached

Temperature rise at U-channel multi-forming operation of 2 mm DP780

C) Forming time: 2 sec ° Transfer time: 10 sec One complete single operation time: 12 sec (5 SPM) 50 45 40 35 30 25 20 15 10 5 0 F1 T1 F2 T2 F3 T3 F4 T4 F5 T5 F6 T6 F7 T7 F8

0 10 20 30 40 50 60 70 80 90 100

Time (s) Max. temperature rise temperature Max. sheet atrise die interface ( Forming stage Transfer stage (A)

Temperature rise at U-channel multi-forming operation of 2 mm DP780 Forming time: 0.32 sec Transfer time: 1.68 sec One complete single operation time: 2 sec (30 SPM)

140

C) ° 120

100

F1 T1 F2 T2 F3 T3 F4 T4 F5 T5 F6 T6 F7 T7 F8 T8 F9 0 0 2 4 6 8 10 12 14 16 18

Max. temperature rise at die sheet interface ( Time (s) Forming stage Transfer stage (B)

Figure 4.12: Calculated temperature rise at die / sheet interface in U-channel drawing with: A) 5 SPM and B) 30 SPM forming speed, F: forming stage; T: transfer stage.

Temperature rise at multi-forming operation (deep drawing) of 1.4 mm CP800

Forming time: 0.64 sec (ram speed 75 mm/sec) C) ° Transfer time: 9.36 sec One complete single operation time: 10 sec (6 SPM) 100 90 80 70 60 50 40 30 20 10 Max. temperature rise at die sheet interface ( F1 T1 F2 T2 F3 T3 F4 T4 F5 T5 F6 T6 F7 0 0 10 20 30 40 50 60 70 Time (s) Forming stage Transfer stage

Figure 4.13: Temperature rise at die / sheet interface at deep drawing of 1.4 mm CP800 in consecutive multiple forming, F: forming stage; T: transfer stage.

6. Summary and Conclusions

The objective of the study, discussed in this paper, was to understand and explain how die/sheet

interface temperatures can be predicted for given forming conditions. The knowledge of the

interface temperatures are expected to help in evaluating lubricant performance and, possibly, in

understanding die wear and galling issues.

Two forming examples were studied: (1) U-channel drawing of 2 mm thick DP780 and (2) Deep

drawing of DP590 (1.4 mm) and CP800 (1.4 mm) in a nearly rectangular die. FE models were

developed for both applications to predict die / sheet interface temperatures. In case of U-channel

drawing, the predictions were compared with experimental data from the literature and

reasonable agreement between predictions and measurements were found. In case of deep

71 drawing, the thinning in the part and temperatures were estimated. The effect of press speed and temperatures upon friction was discussed. Forming in single as well as in multiple-consecutive press strokes was considered.

This study illustrated that it is possible to estimate temperatures at the die/sheet interface, using

FE simulation. The temperature prediction and thinning distribution were in good agreement with experimental results. In U-channel drawing the temperature increases with increasing forming stroke and then decreases toward the bottom dead center. The location where the temperature at the tool / sheet interface starts to decrease is dependent of the geometry and the forming speed. On the other hand, in deep drawing operations, the temperature in the part as well as the die / sheet interface keeps increasing with forming stroke. The COF used in the FE simulation can significantly affect the prediction of the temperature. Therefore, for accurate temperature prediction, it is necessary to use a COF value that is closed to the COF value which is present in the experiment.

The information presented in the current study helps to predict the temperature for a specific forming process for given process conditions. Using this information the effect of temperature upon lubricant performance in stamping can be better understood so that for a given application, lubricants may be selected, based on quantitative information. Furthermore, prediction of interface temperatures will also lead to understanding and possible prediction of tool wear in stamping.

CHAPTER 5: SPRINGBACK IN SHEET METAL FORMING –

BACKGROUND AND FUNDAMENTALS

1. Introduction

Automotive companies are moving to develop lighter vehicles by replacing carbon steels with

Advanced High Strength Steels (AHSS) and aluminum alloys. One of the major challenges of using AHSS and aluminum alloys is their high tendency to springback, as seen in Figure 5.1.

Springback defined as the elastic recovery that a part exhibit upon unloading and is the result of heterogeneous redistribution of strains and stresses in sheet thickness. The higher strength of

AHSS results higher bending moment and stress distributions during the cold forming process.

Higher stresses results more elastic recovery and consequently higher springback. In aluminum alloys, the lower elastic modulus compared to low carbon steels is responsible for higher springback.

In assembly lines, most of the joints between components are handled by automatic robotic arms and this requires geometrical tolerances to be increasingly strict. Also, considering the demands for a very short lead time required by automotive companies, springback is one of the most serious problems for tool and die designer for press forming of AHSS.

Figure 5.1: Schematic of typical engineering stress-strain graph for three materials describing the effect of E-modulus and strength of the material on elastic recovery (springback)

2. Fundamentals of bending and springback

Bending operation defined as a sheet forming operation to produce angled parts, is widely used in sheet metal forming where parts require simple or complex bent profile. A sheet material is bent by an imposed moment, by stretching over a cylindrical form, or by combination of both moment and tension. In bending of a sheet material, area around the bending radius experiences simultaneous tension-compression loading state. In plane strain bending, a nonlinear strain distribution across the sheet thickness is introduced as (Pourboghrat and Chu, 1995):

푡푟푢푒 r y ε푋 = ln = ln⁡(1 ± ) (5-1) Rn Rn where Rn is the radius of the neutral axis and y is the distance from the neutral axis.

The amount of the stresses developed on the sheet during the forming process determines whether the area is in pure elastic or elastoplastic strain state Figure 5.2. Under plane strain condition, using Hooke’s law, the elastic stress component can be calculated as:

E E y σx = 2 εx = 2 (5-2) (1−ν ) (1−ν ) Rn where E is Young’s modulus and ν is Poisson’s ratio. The stress component for plastic deformation depends on the complexity of the material hardening model. For the Swift’s law

n (σ̅ = K(ε0 + ε̅) ), using Hill’s yield index F, the bending stress can be described as:

ε −εe σ = KFn+1[ 0 0 + ε ]n (5-3) x F x

Where:

1+R̅ F = (5-4a) √1+2R̅

ε̅ = Fεx (5-4b) and

σx = Fσ̅ (5-4c) e R̅ is the normal anisotropy, ε0 is yield strain, K is the hardening coefficient, and n is the hardening exponent.

Figure 5.2: stress distribution in bending theory.

The integration of the bending stresses through the sheet thickness provides the internal bending moment per width. The bending moment can also be divided into the elastic (Me)⁡and plastic

(Mp) bending moment. This bending moment can be calculated as:

t M = M + M = σ ydy (5-5) e p ∫0 x where εe Me = ∫ σxydy (5-6) −εe and −εe εmax Mp = ∫ σxydy + ∫ σxydy (5-7) εmin εe

Based on the classic elastic bending theory, the unloading moment can be expressed as:

1 1 M = ( − )E′I (5-8) r r′

76 where E′ = E⁄(1 − ν2) is the plane strain modulus, I is the second moment of area about the

wt3 middle axis (I = ), r and r′ are the radius of curvature of the sheet metal before and after 12 springback. E′I describes the stiffness of the bent sheet. If it is assumed that the unloading moment has the same magnitude but opposite sign to the applied bending moment the change in curvature due to springback is:

1 1 M 12(1−ν2) ( − ) = unloading = (M + M ) (5-9) r r′ E′I⁡ wt3E e p

Substituting equation 5-2 and 5-3 into the above relations, it can be seen that the springback is a function of material properties, sheet thickness, bend radius, and the stress-strain state at the part.

It should be noted that all of the equations above, corresponds to specific section of the sheet.

Therefore, the total springback is calculated as the summation of all the incremental springback angles of each individual section.

3. Mechanical properties affecting springback

Regarding the material properties, equation 5-9 shows that the springback is highly dependent on

E-modulus and the flow stress data of the material. Generally:

a) Springback is more in material with higher yield stress, work hardening, and anisotropy

due to greater resistance to plastic yielding

b) Springback is more in materials with lower E-modulus as the resistance to elastic bending

increases with E-modulus.

3.1. Effect of Stress-strain data and Constitutive model on springback prediction

During forming process the sheet metal experiences stretch bending, stretch unbending, and reverse bending. Researchers have shown that the stress-strain response of sheet metal under

77 cyclic tension and compression loading is complex and may not follow a linear isotropic hardening rule. Figure 5.3 represents a schematic of stress-strain behavior of a sheet metal under tension-compression loading. The Bauschinger effect, transient behavior, work hardening stagnation, and permanent softening, are the four main characteristics indicated in Figure 5.3.

Therefore, the classical isotropic hardening law cannot accurately predict stress and strain magnitudes and distributions, during reverse loading.

Figure 5.3: Schematic of stress-strain response of a sheet metal under tension-compression loading.

There are extensive research studies on developing material models that are able to capture the characteristics illustrated in Figure 5.3. The main focus of these models is the yield function and hardening behavior of the material. In materials with work hardening characteristic, once yield occurs, the stress needs to be continually increased in order to drive the plastic deformation. In multiaxial loading case, the initial yield surface is usually defined as:

푓(휎푖푗) = 0 (5-10)

However, in materials with strain hardening behavior, the size, the shape, and the position of the yield surface can be changed during the plastic deformation. Therefore, the yield surface can be described by:

푓(휎푖푗, 퐾푖) = 0 (5-11)

where, 퐾푖 represents one or more hardening parameters which determine the evolution of the yield surface. Different hardening models are shortly discussed in the next sub-sections.

3.1.1. Isotropic Hardening (IH)

In isotropic hardening model, the shape and position of the yield surface remains unchanged but expands with increasing stress, Figure 5.4. In this model, the yield function is described as:

푓(휎푖푗, 퐾푖) = 푓0(휎푖푗) − 퐾 = 0 (5-12)

where, 푓0(휎푖푗) determines the shape and the size of the initial yield, and the hardening parameter

퐾 controls the expansion of the yield surface.

Figure 5.4: Schematic of yield surface expansion in isotropic hardening model.

Most sheet metals are anisotropic as the result of rolling process used in making the sheets. It means that the properties of the sheet material are dependent to the direction that the property is measured with respect to the rolling direction. Therefore, anisotropic yield surfaces are introduced to more accurately represent the plastic behavior of the material. Hill’s quadratic yield function (Hill, 1948) and Barlat non-quadratic Yld2000-2d (Barlat et al., 2003) are two conventional anisotropic yield functions used in simulation of sheet metal forming.

The Hill’s quadratic yield function can be expressed as:

2 2 2 2 푓(휎) = 퐹(휎2 − 휎3) + 퐺(휎1 − 휎3) + 퐻(휎1 − 휎2) = 휎̅ (5-13)

where 퐹, 퐺, and 퐻 are constants and 휎1, 휎2, and 휎3 are the principal stresses whose vectors are parallel to rolling direction, transverse direction, and the thickness direction, respectively. It can be shown that, 푟푅퐷 = 퐻/퐺, and 푟푇퐷 = 퐻/퐹.

The Barlat non-quadratic Yld2000-2d is described as:

′ ′ 푎 ′′ ′′ 푎 ′′ ′′ 푎 1/푎 휎̅ = [1/2(|푋 1 − 푋 2| + |2푋 2 + 푋 1| + |2푋 1 + 푋 2| )] (5-14)

′ ′′ Where 푎 is an exponent associated with crystal structures. 푋 푖 and 푋 푖 (𝑖 = 1, 2) are the

′ ′′ principal values of the deviatoric stress tensor (푋̃ 푘 and 푋̃ 푘, 푘 = 1~3) by the following linear transformation:

′ ′ ′ 푋 푥푥 퐿 11휎푥푥 + 퐿 12휎푦푦 ′ ′ ′ ′ [푋 푦푦] = [퐿 21휎푥푥 + 퐿 22휎푦푦] = [푋̃ 푘] (5-15) ′ ′ 푋 푥푦 퐿 33휎푥푦

And

′′ ′′ ′′ 푋 푥푥 퐿 11휎푥푥 + 퐿 12휎푦푦 ′′ ′′ ′′ ′′ [푋 푦푦] = [퐿 21휎푥푥 + 퐿 22휎푦푦] = [푋̃ 푘] (5-16) ′′ ′′ 푋 푥푦 퐿 33휎푥푦

The tensor [퐿′] and [퐿′′] represent linear transformations of the stress tensor, which are expressed with anisotropic coefficients.

3.1.2. Kinematic Hardening (KH)

In the isotropic hardening model the yield surface is symmetric about the stress axes, and remains equal as it develops with plastic strain. Therefore, it implies that the yield strength in tension and compression are the same. However, in reverse loading the behavior of material may not be identical in tension and compression stress state, i.e. Bauschinger effect and similar responses. Kinematic hardening is mainly of interest in cases where a hardening in tension will lead to a softening in a subsequent compression. In Kinematic hardening model, the yield surface remains the same shape and size but translates in stress space, Figure 5.5.

The general form of the yield function in kinematic hardening model can be described as:

푓(휎푖푗, 퐾푖) = 푓0(휎푖푗 − 훼푖푗) = 0 (5-17)

The hardening parameter 훼푖푗, known as back-stress, determines the relative motion of the yield surface to the stress space axes. In kinematic hardening model, the material yields earlier in subsequent compression after tension loading, compared to the isotropic hardening model.

Figure 5.5: Schematic of yield surface translation in kinematic hardening model.

3.1.3. Combined isotropic and Kinematic Hardening (IH+KH)

Neither the isotropic nor the kinematic hardening model can describe accurately the behavior of sheet material in cyclic tension compression loading state. Therefore, more complex hardening rules such as combined isotropic-kinematic hardening (IH+KH) model are introduced (Krieg,

1975; Jiang and Sehitoglu 1996; Yoshida et al., 2002; Fredrick and Armstrong 2007). The

IH+KH model combines features of both the isotropic and kinematic hardening models and the yield function takes the general form:

푓(휎푖푗, 퐾푖) = 푓0(휎푖푗 − 훼푖푗) − 퐾 = 0 (4-18)

Multi surface hardening models are the improved versions of the IH+KH model. In a multi surface hardening model, there are two surfaces: the yield surface and the bounding surface. The bounding surface expands and also slightly moves with increasing plastic strain. The yield surface moves within the bounding surface. The Yoshida-Uemori (Y-U) model is one of the conventional two surface (yield surface and boundary surface) plasticity hardening models

(Yoshida et al., 2002). In this model the relative kinematic motion of the two surfaces is a function of the difference between their sizes and the yield surface never crosses the bounding surface, Figure 5.6.

The plastic strain rate is determined by the associated flow rule, for both the IH and KH models, as:

휕푓 휀̇ = 휆̇ (5-19) 푝 휕휎

The associate flow rule for the yield surface is given by:

3 푓 = ⁡(푠 − 훼): (푠 − 훼) − 휎 2 = 0 (5-20) 2 0

Where 푠 and 훼 are Cauchy stress deviator and center of the yield surface, respectively, and 휎0 is the size of the yield surface.

The flow rule for bounding surface is as follow:

3 퐹 = ⁡(푠 − 훽): (푠 − 훽) − (퐵 + 푅)2 = 0 (5-21) 2

Where 훽 is the center of the bounding surface (back stress deviator) and 퐵 and 푅 are the initial yield stress of the bounding surface and the isotropic hardening, respectively. The Bauschinger effect is expressed by 훼∗which is calculated by:

훼∗ = 훼 − 훽 (5-22)

훼∗ is the relative motion of the yield surface with respect to the bounding surface and its evolution can be expressed by:

2 훼̅ 훼̇ = √ 푐푎 (푛 − √ ∗ 푛 ) 푝̇ (5-23) ∗ 3 푝 푎 ∗

푎 is a material parameter that controls the rate of the kinematic hardening. 푛푝 and 푛∗ are the unit vectors and can be expressed as:

푠−훼 푛 = (5-24) 푝 ‖푠−훼‖

훼∗ 푛∗ = (5-25) ‖훼∗‖

The parameters 푝̇, 훼̅∗, and 푎 in equation (5-23) can be calculated as:

2 푝̇ = √ ‖휀̇ ‖ (5-26) 3 푝

2 훼̅ = √ ‖훼 ‖ (5-27) ∗ 3 ∗ and

푎 = 퐵 + 푅 − 휎0 (5-28)

휀̇푃and 푝̇ denotes the plastic strain rate and effective plastic strain rate, respectively.

The kinematic hardening and isotropic hardening of the boundary surface is expressed as follows:

2 훽̇ = 푚( 훼휀̇푃 − 훼푝̇) (5-29) 3

푅̇ = 푚(푅푠푎푡 − 푅)푝̇ (5-30)

In the equations above, m and Rsat are material parameters.

Komgrit et al. (2016) used the Y-U material model to predict the springback in U-bending of

980Y high strength steel with additional bending with counter punch to reduce the springback.

They investigated the effect of the counter punch force on springback reduction and showed that the springback predictions are more accurate in all testing conditions when using Y-U model

85 compared to pure isotropic hardening model. Ogawa and Yoshida (2011) investigated the effect of the bottoming in reduction of springback in U-shaped bending process of 590MPa high stress steel material. They concluded that the Y-U model can appropriately predict the bending moment and springback in FE simulation of bottoming.

3.1.4. Distortion yield function

In order to simulate the Bauschinger effect and other similar behavior of the material in cyclic tension-compression loading state, a new model called Homogeneous yield function-based

Anisotropic Hardening (HAH), is presented by Barlat et al. (2011). In this model there is only one yirld surface. A fluctuating term in the yield function causes a smooth change of the yield surface shape during loading. The fluctuating term, called the microstructure deviator, memorizes the loading history and controls the continuous evolution of the yield surface distortion when strain path changes during the deformation. If the material is subjected only to monotonic loading, the stress-strain behavior of the material is same in HAH and isotropic hardening. The homogeneous yield function consists of two components, 휙 and 휙ℎ as:

푞 푞 1/푞 푓 = [휙 + 휙ℎ ] − 휎̅ = 0 (5-31)

휙 is a stable component describes the general anisotropic yield function and can be any isotropic or anisotropic yield function of degree one. 휙ℎ is the fluctuating component and is described as:

푞 푞 푞 푞 ̂푠 ̂푠 푞 ̂푠 ̂푠 휙ℎ = 푓1 |ℎ : 푆 − |ℎ : 푆|| + 푓2 |ℎ : 푆 − |ℎ : 푆|| (5-32)

Where S is the stress deviator, ĥs is the microstructure deviator. q is an exponent that determines the shape of the yield surface. The microstructure deviator, ĥs, memorizes the previous deformation history and is defined as the normalized traceless tensor as:

hS ĥs = (5-33) 8 √ hS:hS 3

Initially, hS corresponds to the stress deviator 푆 and remains constant as long as the loading direction is not changed. When the loading is changed, hS ≠ 푆, hS evolves as:

If 푆: ĥs ≥ 0,

푑ĥs 8 = 푘 [푆̂ − ĥs(푆̂: ĥs)] (5-34) 푑휀̅ 3

If 푆: ĥs < 0,

푑ĥs 8 = 푘 [−푆̂ + ĥs(푆̂: ĥs)] (5-35) 푑휀̅ 3

푆̂ is the normalized of 푆 in the manner of Eq. (5-33). By these evolution laws, ĥs rotates from its initial value toward 푆̂ corresponding to the new loading at a rate controlled by 푘. f1 and f2 in Eq.

(5-32) are functions of two state variables g1 and g2, which physically represent the ratio of the current flow stress to that of the isotropic hardening.

1 −푞 푞 f1 = [g1 − 1] (5-36)

1 −푞 푞 f2 = [g2 − 1] (5-37)

In the HAH model, while the loading direction is not changed, there is no contribution of the fluctuating component and therefore, f1 = f2 = 0. When the material is plastically deformed, the state variables evolution described as:

If 푆: ĥs ≥ 0,

푑푔 퐻(0) 1 = 푘 (푘 − 푔 ) (5-38) 푑휀̅ 2 3 퐻(휀̅) 1

푑푔2 푔3−푔2 = 푘1 (5-39) 푑휀̅ 푔2

푑푔 4 = 푘 (푘 − 푔 ) (5-40) 푑휀̅ 5 4 4

If 푆: ĥs < 0,

푑푔1 푔4−푔1 = 푘1 (5-41) 푑휀̅ 푔1

푑푔 퐻(0) 2 = 푘 (푘 − 푔 ) (5-42) 푑휀̅ 2 3 퐻(휀̅) 2

푑푔 3 = 푘 (푘 − 푔 ) (5-43) 푑휀̅ 5 4 3

In the equations above, 푘1~푘5 are material parameters. The 퐻(휀)̅ is the classical isotropic hardening curve. 푔3 and 푔4 are two additional state variables to include permanent softening behavior of the material. When 푘4 = 1, or 푘5 = 0 and 푔3 = 푔4 = 1, no permanent softening is predicted by the model. The coefficients f1 and f2 control the distortion of the yield surface in stress space. For instance, if the material is initially loaded in the x direction (푆: ℎ̂푠 ≥ 0) and the permanent softening is ignored, only 푔1 evolves according to the Eq. (5-38). Then f1 evolves but f2 remains equal to zero. The yield surface corresponding to this state is described by the curve B in Figure 5.7, in which the shape of the yield surface is kept unchanged near the loading direction (controlled by 푓2) but flattened far from the loading direction (controlled by 푓1). If the load is reversed in the –x direction (푆: ℎ̂푠 < 0), the state variables evolve according to Eqs. (4-

41) and (4-42). In this case, 푔2 starts to evolve as well as 푔1. Then the yield surface near the

88 reverse loading direction tends to recover its original shape while the opposite side flattens as the curve C in Figure 5.7.

In order to describe the material behavior with the HAH model, proper experiments are required to determine the required coefficients. These coefficients are:

 Coefficients for isotropic hardening curve 휎̅ = 퐻(휀)̅ . For instance 퐾, 푛, and 휀0, for the

푛 swift law, i.e., 휎̅ = 퐾(휀0 + 휀)̅ .

 Coefficient for the isotropic or anisotropic yield function 휙.

 Exponent 푞 which controls the flatness of yield surface far from the loading direction.

 Coefficient 푘 which controls the evolution rate of microstructure deviator.

 Coefficients 푘1, 푘2, and 푘3which control the evolution of the reloading flow stress and

hardening (푔1 and 푔2).

 Coefficients 푘4 and 푘5 which control the evolution of permanent softening (푔3 and 푔4).

The coefficients for the isotropic hardening curve and the stable yield function can be determined using uniaxial tension tests in various loading directions and balanced biaxial tests. Other coefficients 푘1~푘5 can be determined from a forward-reverse loading test, and the coefficient 푘 requires a cross-loading test such as uniaxial tension followed by tension at 60°.

Barlat et al., (2011) demonstrated the capability of the HAH model to capture the material behavior in reverse loading. They showed that the curves calculated with the HAH model reproduce the measured stress-strain data and all the characteristics observed in reverse loading.

Lee at al. (2012a) investigated the prediction of springback in the U-Channel draw/bending test for DP590 and TRIP590 steel blank materials. They compared the springback predictions for three hardening models, Chaboche IH+KH, HAH, and isotropic hardening, and concluded that the springback predictions with HAH and IH+KH models are more close to experimental measurement compared to isotropic hardening model.

Lee et al., (2012b) used the HAH model for springback prediction of virgin and pre-strained

DP780 for the NUMISHEET93 U-channel benchmark. They used the HAH model combined with a non-quadratic anisotropic yield function and showed a good agreement between the FE result and experimental springback measurement (Lee at al., 2012b).

3.2. Effect of E-modulus

In addition to the flow stress of the material, the E-modulus (Young’s modulus) is the other material property that significantly affects the springback. In fact, unloading elastic modulus that determines the elastic recovery of the material after load removal is responsible for springback.

In practice, the unloading elastic modulus is always assumed to be the same as the E-modulus of the material. Researchers have shown that the unloading elastic modulus of material is not

90 constant and is a function of plastic strain. Morestin and Boivin (1996) discussed the effect of work hardening on E-modulus and implementation of accurate E-modulus in elastic-plastic FE simulation of metal forming.

A detail discussion of the effect of the unloading elastic modulus on springback prediction is presented in chapter 6 of this study. Also, the challenges in determination of the unloading elastic modulus are described.

CHAPTER 6: EFFECT OF E-MODULUS VARIATION ON SPRINGBACK

AND A PRACTICAL SOLUTION

Note: This chapter is accepted for publication to the SAE International on December 2017

1. Introduction

The usual practice is to simulate the forming operation using a Finite Element (FE) technique, then using the simulation result to modify the initial die design for springback compensation.

The die is then manufactured and the final modification of the tool geometry is performed through successive trials. These additional trials lead to an increase in development cost and time. For this reason, accurate springback prediction through FE simulation is necessary.

A review of FE technique and constitutive modeling for springback prediction can be found in

Wagoner et al. (2013). Material models play an important role in simulating sheet metal stamping and springback. Some materials such as AHSS exhibit behaviors such as Bauschinger effect, transient behavior, work hardening stagnation, and permanent softening when they are formed under reverse loading condition. Therefore, the conventional isotropic hardening model may not accurately predict such phenomena. Regarding the material model, parameters which significantly affect the springback prediction are:

1) Flow stress data, which relates the stress state of each element in the formed part to its

strain value

2) E-modulus, which determines the proportion of elastic and plastic deformation and

amount of elastic recovery

3) Hardening rule, which represents complex behaviors of material such as Bauschinger

effect, transient behavior, work hardening stagnation, and permanent softening

2. Effect of E-modulus on springback prediction

In plasticity, the elastic recovery of material after plastic deformation is usually assumed to be linear with stiffness equal to E-modulus. Therefore, an accurate E-modulus or unloading elastic modulus is necessary for accurate springback prediction (Morestin and Boivin, 1996). Figure 6.1 shows the results of a loading-unloading-loading tensile test, one of the conventional methods for determining the unloading elastic modulus. Conventional methods have the following challenges determining the elastic unloading modulus:

1) The elastic unloading behavior of material is nonlinear

2) The average elastic unloading modulus is a function of plastic strain (not constant)

3) The elastic unloading modulus is strain path dependent

Figure 6.1: [a] Example of a loading-unloading tensile test result for determining E-modulus variation with plastic strain. [b] Expanded view of the last unloaded cycle indicating the nonlinear elastic unloading behavior of the material. 퐸25⁡% and 퐸50⁡% are the calculated E- modulus using the line which connects the point of maximum stress before unloading and the point of 25% and 50 % of that maximum stress value. [c] E-modulus variation with plastic strain; Test results from (Xue et al., 2016).

2.1. Nonlinear elastic unloading behavior

Experimental observations show that dislocations pile-up and relaxation cause nonlinear unloading behavior in metals (Sun and Wagoner, 2011; Perez et al., 2005; Xue et al., 2016).

Nonlinearity of the unloading behavior makes determining the unloading elastic modulus not to be accurate. Figure 6.1b shows an example of nonlinear loading and unloading elastic behavior of DP780 steel. One can see that determining the E–modulus is with some approximation depends on the stress points selected along the unloading curve. The E25⁡% and E50⁡% are the calculated E-moduli using the lines which connect the point of maximum stress before start of unloading and the points of 25% and 50% of that maximum stress. Several approaches have been suggested to describe the elastic unloading behavior of the material using the tensile test. Most of the practical approaches propose an average E-modulus obtained using a chord line that connects two points obtained from the start of unloading and the end of unloading (Yoshida et al., 2002).

Sun and Wagoner, (2011) have introduced a new strain component named Quasi-Plastic-Elastic

(QPE) strain in addition to the elastic and plastic strains to describe the nonlinearity of elastic unloading. They implemented the QPE to a multi surface yield function approach (combined kinematic and isotropic hardening) for DP980 material and observed improvement in springback prediction using the new model compared to the simulations with standard model or with variable E-modulus.

2.2. Variation of unloading elastic modulus with plastic strain

In addition to the nonlinearity of the unloading elastic modulus, the average unloading modulus decreases with increasing the plastic strain (Xue et al., 2016; Kim et al., 2013). As shown in

Figure 6.1c, the reduction of the unloading elastic modulus with plastic strain can be determined

95 through the loading-unloading tensile test using the chord line. For many types of steel, the unloading elastic modulus decreases rapidly with increasing the plastic strain, though this effect tends to saturate at a strain of about 0.2 (Lee at al., 2012). As an example shown in Figure 6.1c, when unloading at about 0.09 plastic strain, the unloading elastic modulus of the DP780 material is about 157 GPa. This is about 25% less than the original value (207 GPa) and could potentially produce more springback compared to using the standard E-modulus of 207 GPa.

Although the constitutive model with the QPE strain component shows some potential to describe more accurately the elastic behavior of the material, for practical modeling, it is easier to define the elastic portion of the deformation using a constant E-modulus. Yoshida et al. (2002) suggested to use an average E-modulus, Eav, using a chord line during the unloading process.

They introduced the following equation to express the variation of E-modulus with plastic strain:

푃 퐸푎푣 = 퐸0 − (퐸0 − 퐸푎)[1 − exp(−휉휀0 )] (1)

Where 퐸0 and 퐸푎 are the E-modulus for virgin and approximately large pre-strained materials, respectively, and 휉 is a material constant.

2.3. Strain path dependency of unloading elastic modulus

Xue et.al. (2016) investigated the effect of the loading path on elastic unloading behavior of dual-phase steels. They used three test methods: uniaxial loading-unloading test, biaxial loading- unloading test, and three-point bending test. They concluded that the initial and the degradation of the elastic modulus depend on the loading strategy. Therefore, an E-modulus determined with the tensile test may not be sufficient for accurate springback prediction when the strain state at the part is not uniaxial.

3. Inverse analysis method for determination of an apparent E-modulus

Considering the important role of the E-modulus on springback prediction and the challenges reviewed in previous section regarding the determination of the E-modulus through the tensile test, it is desirable to develop a simple practical method for obtaining a value of the E-modulus which can provide more accurate springback prediction. In the current study, inverse analysis method, Figure 6.2, is introduced for determining an average apparent E-modulus for a given material, thickness, and a bending operation. This E-modulus can provide reliable springback prediction. The assumption is that a constant apparent value of the E-modulus over the entire part can provide accurate springback prediction. This apparent E-modulus represents the average of the actual values of the E-moduli at different locations in the part.

Figure 6.2: Flowchart describing the inverse analysis method for the determination of an apparent E-modulus which can be used to obtain springback values, comparable to experimental measurement.

To investigate the possibility of improving the springback prediction using the inverse analysis method, the method is applied to three forming / bending operations listed in Table 6.1. First it is tested in wipe bending which is a simple plane strain bending operation without reverse loading.

Then the accuracy of springback prediction is investigated in U-drawing process which the

97 material is bent while it is under stretch force. Finally, it is studied whether a constant value of E- modulus can predict springback in crash forming of a real production part.

The wipe bending test was conducted at the Center for Precision Forming (CPF) in the Ohio

State University. The experimental details of the U-drawing process are obtained from the

NUMISHEET 2011 benchmark report (Chung et.al. 2011). The die design and the experimental result of the crash forming test is provided by Die Cad Group.

AutoForm implicit code was adopted for numerical simulation of bending and springback in all three bending operations. The bending tools were assumed to be completely rigid and the blanks were simulated using triangular shell elements with 11 integration points in thickness direction.

Anisotropy behavior of materials was considered using the r-value. The Hill 48 yield function was used in all simulations to account for the anisotropic elastic-plastic property of the blank.

The Swift equation was employed for the flow stress evolution of the materials:

n σ̅ = K(ε0 + ε̅) (2)

Material constants K, n, and ε0 for each material are listed in Table 6.1.

Wipe bending U-drawing Crash forming Final part

Material MP980 (1.2 mm) DP780 (1.4 mm) DP980 (1 mm) Flow stress ε0 = 0.0013 ε0 = 0.0008 ε0 = 0.007 Swift law n = 0.082 n = 0.146 n = 0.135 σ̅ = 퐾 = 1485⁡(푀푃푎) 퐾 = 1280⁡(푀푃푎) 퐾 = 1299⁡(푀푃푎) n K(ε0 + ε̅) r-Value 0.67 0.78 0.74 Initial E- 207 (GPa) 199 (GPa) 210 (GPa) modulus E-modulus 퐸0 = 207⁡퐺푃푎 퐸0 = 199⁡퐺푃푎 퐸0 = 210⁡퐺푃푎 variation 퐸푎 = 180⁡퐺푃푎 퐸푎 = 167⁡퐺푃푎 퐸푎 = 183⁡퐺푃푎 constants 휉 = 40 휉 = 97 휉 = 40 (Eq.1)

E-modulus 220 variation 210 DP980 200 MP980

190 DP780

180 E (GPa) E 170

160

150 0 0.025 0.05 0.075 0.1 0.125 0.15

True Strain

4. Wipe-bending 4.1. Experiment and FE-simulation

Wipe bending test was performed on 1.2 mm MP980 sheet steel using a 5500 series Instron machine with 50kN capacity. Information about the geometry and dimensions of the tooling is presented in Figure 6.3. Rectangular blanks with dimensions of 70 mm × 100 mm were used.

Each blank was clamped between the blank holder and the die using four M10 screws. A punch stroke of 30 mm with a velocity of 10 mm/min was used to bend the material to 90°. No forming lubricant was used. A preliminary study was conducted to investigate the effect of the friction coefficient on springback prediction in wipe bending. Results showed that, in wipe bending operation, effects of friction and lubrication on springback can be neglected. To ensure accuracy, each wipe bending test was replicated three times. These trial were averaged together to produce the final measurement. During each trial, the bending angle was measured under load, and again after unloading. The springback was calculated as the difference between the angle under load and the final angle of the sheet metal, after unloading.

In the numerical model, a friction coefficient of 0.1 between the sheet surface and the tools was assumed. An E-modulus of 207 GPa was measured from the tensile test and used as the initial value in the simulation. The simulated results were compared with experimental results. A series of simulations with different E-moduli were conducted to determine the apparent E-modulus that provides an accurate springback prediction for a given combination of material and bending operation.

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Figure 6.3: A schematic view of tools and dimensions used in the wipe bending tests

4.2. Results and discussion for wipe bending Figure 6.4 compares the simulated results of springback with the experimental observations. This

figure indicates that the simulated results which have an apparent E-modulus of 183 GPa, are

fairly accurate, whereas the simulation with E-modulus of 207 GPa (obtained from the tensile

test of the virgin material) underestimates springback. Also, the simulation with combined

101 isotropic and kinematic hardening and variable E-modulus (shown in Table 6.1) overestimates springback. Results indicate that in a wipe bending operation where the sheet material is not subjected to the cyclic loading, an isotropic work hardening model with an accurate apparent E- modulus can predict the springback with reasonable accuracy.

) ° 14

13 Springback ( Springback 12

10 Experiment IH+ E-modulus= 207 GPa IH+ E-modulus=183 GPa IH+KH+variable E

Figure 6.4: Comparison of springback predictions with experimental measurement in wipe bending operation

5. Draw bending (U-drawing or Hat-shape bending) 5.1. Experiment and FE simulation

2-D draw bending (U-drawing) was used to evaluate the accuracy of the springback prediction with apparent E-modulus in a bending operation where the sheet material is subjected to tensile loading. The experimental procedures for U-drawing are originally provided in the Numisheet

2011 benchmark problem (Chung et.al. 2011 and Lee et al., 2012b). The main procedure is summarized here.

The blank material was Dual Phase (DP) 780 steel with a thickness of 1.4 mm. Information about the geometry and dimensions of the tooling used is presented in Figure 6.5. The blank was

102 rectangular with the dimension of 30 mm × 324 mm. A blank holder force of 2.94 kN was used with a maximum punch stroke of 71.8 mm and speed of 1.0 mm/s. P-340N (rust-preventive oil) was used as a forming lubricant. For accuracy, three replications were considered. The E- modulus variation with plastic strain was obtained from a loading-unloading tensile test and results are shown in Table 6.1.

Figure 6.5: A schematic view of tools and dimensions for the U-draw bending (Lee et al., 2012b).

The simulation model of this process consists of two steps: (1) drawing and (2) unloading.

According to the benchmark committee recommendation the coulomb friction law with a coefficient of 0.1 is used for all contacts between tool and blank. An E-modulus of 199 GPa

(virgin material) was used along with isotropic work hardening as the reference simulation. Also, simulation with combined kinematic and isotropic hardening model along with variable E- modulus (Table 6.1) was conducted. AutoForm default values for AHSS were selected to define the kinematic hardening behavior of the material.

In order to determine the apparent E-modulus through inverse analysis method, several iterations of the simulation were conducted with different E-moduli. After each iteration the predicted springback was compared to the experimental measurement.

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5.2. Results and discussion for U-Drawing

In U-drawing process, springback changes the geometry in die and punch corner radii as well as the wall of the part. In the corner radii, springback opens the bending area, while in the wall area it causes curl. Comparison of the experimental springback with predicted results using different hardening models and E-moduli are illustrated in Figure 6.6. Similar to what was observed in the wipe bending test, in the U-drawing process, the simulation with isotropic hardening and

E=198.8 GPa (virgin material), cannot accurately predict the angle opening and the side wall curl. This is because the simulation did not consider the E-modulus degradation with plastic strain. Also, in U-drawing, when the punch is moving down, the sheet is bent around the die corner and then unbent to form the wall of the part. This provides the reverse loading condition and therefore, an isotropic hardening model alone may not be sufficient to define the actual material behavior.

A combined kinematic and isotropic hardening model along with the variable E-modulus significantly improves the simulation results in both springback of angle opening and side wall curl. The apparent E-modulus calculated from the inverse analysis method for this combination of material and bending operation was about 170 GPa. Simulation results with isotropic hardening model and E=170 GPa shows a significant improvement of springback prediction compared to the simulation results with E=199 GPa.

Figure 6.6b, shows an expanded view of the area around the side wall curl. This results clearly show that the simulation with apparent E-modulus and the one with combined hardening model and variable E-modulus predict the side wall curl more accurately compared to the simulation

104 with isotropic hardening model and E=199 GPa. The side wall curl in simulation with the apparent E-modulus is slightly better than the simulation with combined hardening model. Also, regarding the flange angle, simulation with apparent E-modulus predicts more accurate angle opening compared to the experiment than the simulation with combined hardening model.

In U-drawing process, the material is compressed between the die and the blank holder. Friction between the material and the tool surface controls the draw-in of the material. Therefore, the friction condition (coefficient of friction in simulations) affects the strain distribution at the part and consequently the springback. The assumption of a constant value for the friction coefficient over the entire tool / sheet interface may not appropriately represent the complex frictional behavior in forming operation. Several experimental reports have shown that the friction coefficient is a function of contact pressure, sliding velocity, and the temperature (Han et al.

2011; Wang et al. 2016). In this study, a constant friction coefficient of 0.1 is used and the effect of contact pressure and sliding velocity on coefficient of friction is neglected. This can be one of the reasons for difference between the predicted springback in simulations and experiment.

Wang et al. (2016) compared the effect of constant and variable friction coefficients on springback in U-drawing of a DP780 material and concluded that the variable friction coefficient significantly improves the springback prediction.

105

70 [b]

Experiment 40

IH+ E-modulus=199 GPa Y Y (mm) 30 IH+ E-modulus=170 GPa

10 25 30 35 40 45 50 55 X (mm)

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6. Crash forming (real production part) 6.1. Experimental set-up and FE simulation

Crash forming is a sheet forming operation that creates hat-shaped profiles similar to U-drawing.

In contrast to U-drawing, crash forming does not use a blank holder, so the sheet material is not stretched during the deformation. Figure 6.7 shows a 2-D cross section of the tooling and the final part. The tooling consists of three main components; the upper die, the punch, and the pad.

The total upper die stroke was 60 mm. An 80 kN force were applied by the pad to hold the blank in contact with the top surface of the punch during the deformation. DP980 sheet steel with 1 mm thickness was used. After unloading and springback, the part was scanned to compare with simulations. The mechanical properties of the sheet material were obtained from the tensile test.

The stress-strain data is approximated using the Swift law (Eq. 2) and the constants are shown in

Table 6.1.

A 3-D finite element model of the process was developed using AutoForm. E=210 GPa was used as the E-modulus of the material at zero plastic strain. A Friction coefficient of 0.12 was assumed between the sheet material and the tool interfaces. A series of simulations with different

E-moduli were performed and springback predictions were compared with the 3-D scan of the part to determine the apparent E-modulus that provides the most accurate result. Simulation with combined isotropic and kinematic hardening along with variable E-modulus (Table 6.1) was also conducted. Autoform default values for AHSS were used to define the kinematic hardening of the material.

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Figure 6.7: (left) 2-D section of the schematic of the tool set-up, (right) schematic of the final part geometry.

6.2. Results and discussion Simulation results with various E-moduli indicate that 180 GPa is the apparent E-modulus for this combination of material and bending operation. Figure 9 shows the normal distance between simulation results and the 3-D scan of the part. In this figure, the simulation results are superimposed on the 3-D scan of the part using the AutoForm. The values of normal distance between the simulation results and the experimental measurement at four corners of the part are summarized in the table in left side of Figure 6.8.

The maximum normal distance between the simulation results and the scan data of the part was

2.68 mm for simulation with the isotropic hardening model and E=210 GPa. This value is 1.78 mm and 1.73 mm for simulations with combined hardening model and apparent E-modulus, respectively. Although in general, the springback prediction improves by using either the combined hardening model or the apparent E-modulus, the improvement in springback prediction is not consistent over the entire part. Results show that springback prediction is more accurate at location 1 and 2, when the isotropic hardening model with E=210 GPa is used.

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Figure 6.8: Comparison of normal distance between the simulation results and 3-D scan of the part after springback.

7. Conclusions

Modifying dies to compensate for springback requires re-cutting the die several times, based on experience, trial and error. This is expensive and time consuming. Accurate springback prediction using FE simulations can significantly reduce the number of times the die must be recut. The accuracy of FE simulations is determined by the material properties, material hardening model, boundary conditions, and numerical procedures. Accurate material properties and reliable material models can significantly improve the springback prediction. Of the material properties, the E modulus and the flow stress data are of particular concern, since they are the most important properties affecting the springback.

The conventional method used to determine the E-modulus is the tensile test. Researchers have shown that the elastic behavior of materials is nonlinear and that the elastic modulus decreases when plastic strain increases (Xue et al., 2016; Kim et al., 2013). Also the nonlinear elastic

109 modulus is sensitive to loading path (Xue et al., 2016). Nonlinearity of elastic behavior of sheet metals, the reduction of the E-modulus with plastic strain, and strain path dependency of the E- modulus indicates that the calculation of E-modulus through the tensile test is always with some approximation.

This study used a methodology called “inverse analysis” to determine the average E-modulus from a bending test and improve the springback prediction. This method is used in three different bending operations, Wipe bending, U-drawing, and crash forming. Results show improvement in springback prediction in all three forming/bending operations when the apparent E-modulus is used compared to the simulation results using an E-modulus value obtained through a tensile test.

The inverse analysis method cannot be used to predict springback in die design stage before manufacturing the die. However, this method provides the possibility to reduce the number of die trials by predicting springback using the apparent E-modulus after the first tryout. Figure 6.9 describes how the inverse analysis method can help to reduce the number of die re-cutting process. Another potential of the inverse analysis is, once the apparent E-modulus is determined for a selected material and thickness, this value can be recorded in the company database and be used in simulations as the initial value of the E-modulus for that material when a new die is designing for this material.

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Figure 6.9: [a] conventional die manufacturing method; [b] New proposed procedure for reducing the number of die re-cut by improving the springback prediction.

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CHAPTER 7: DETERMINATION OF VARIABLE E-MODULUS

THROUGH WIPE BENDING TEST AND APPLICATION TO

SPRINGBACK PREDICTION

Note: This chapter is submitted for publication to the International Deep-Drawing Research

Group Conference (IDDRG) on February 2018.

1. Introduction

The effect of the nonlinear elastic behavior of material and degradation of elastic modulus with plastic strain on springback has been ignored in most industrial forming applications, i.e., the elastic modulus has usually been assumed constant. Also, despite considerable research on explanation and constitutive description of nonlinear elastic behavior of material, there are not many studies that investigate the appropriate technique for measuring the unloading elastic modulus. The conventional method for determining the unloading elastic modulus is the uniaxial

Loading-Unloading-Loading (LUL) test. In this test, the specimen is loaded to achieve a certain amount of plastic strain (similar to a normal tensile test) and then unloaded. After the unloading the material is reloaded to achieve a new amount of plastic strain. This procedure is repeated at several different plastic strain levels.

The objective of this chapter is to introduce a practical method for calculating the unloading elastic modulus degradation with plastic strain using a wipe bending test.

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2. Experiments

Wipe bending tests were performed using a 5500 series Instron machine. Schematic of the tool geometry and dimensions are shown in Figure 7.1. A MP980 steel sheet with 1.2 mm thickness was considered and its basic mechanical properties were provided by General Motors. The flow

n stress data obtained from the tensile test was fitted by Swift law, σ̅ = K(ε0 + ε̅) . The degradation of unloading elastic modulus with plastic strain was initially determined by the uniaxial loading-unloading-loading test. The experimental data was fitted by Y-U model (퐸0=

207 GPa, 퐸푎= 156 GPa, 휉 = 15).

The bending specimens were waterjet cut to 70×100 mm rectangular geometry with two extra flange areas which allows measuring the bending angle under load using a digital protractor.

Blank holder force was applied by four M10 screws and it was carefully controlled during the test that the blank holder does not move upward due to reaction force. No lubricant was applied on the specimen surfaces. Specimens were subjected to wipe bending with a punch speed of 10 mm/min. A clearance of 1.85 mm (54% of sheet thickness) was present between the punch and the die.

Due to the nature of the wipe bending operation, during the deformation, a horizontal reaction force is applied to the punch. Therefore, a punch guide was designed to eliminate the elastic deflection of the punch and keep the clearance between the die and the punch constant throughout the deformation. The elastic deflections of the tools were measured using dial indicators and it was confirmed that the elastic deflection of the tools is small enough to be neglected in the computer simulation. Seven different punch displacement strokes i.e. 3 mm, 5 mm, 10 mm, 15 mm, 20 mm, 25 mm, and 30 mm were considered to provide seven different bending angles. Bending angle versus punch stroke data obtained from the experiment is shown

113 in Figure 7.2. The maximum punch stroke considered in the test was 30 mm which provides 90 degree bending angle. Any punch stroke more than 30 mm does not increase the bending angle.

After each test, the springback was calculated as the difference between the bending angle under load and angle after unloading. Three tests were repeated for each punch stroke and it was confirmed that the results were reproducible.

Figure 7.1: A schematic view of tools and dimensions used in the wipe bending tests.

100

90 80 70 60 Experiment 50 Simulation - DEFORM 40 30 20

Bending under Bending (deg) angle load 10 0 5 10 15 20 25 30 35 Punch Stroke (mm) Figure 7.2: Bending angle under load for seven different punch strokes considered in this study.

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3. FE simulations of springback and inverse analysis 3.1. Simulation setup

A FE model for wipe bending was constructed in DEFORM, following the geometry shown in

Figure 7.1. The blank was modeled using 4-node solid elements with 12 elements through the thickness direction. The tools were modeled using rigid analytical surfaces. In order to reduce the computational cost, the plane strain condition was imposed which means strain in the transverse direction was eliminated. The effect of material anisotropy was neglected and the von Mises yield criterion was used. A constant E-modulus measured from the tensile test was used as the initial value in the simulation. The Coulomb friction law was used with a coefficient of 0.1 for all contacts between tool and blank. The flow stress data of material were defined using the Swift law. No movement was allowed to the die and blank holder. A constant speed was input for the punch to move downward and form the part. Simulations were stopped at punch strokes similar to the experiment and springback was predicted at each punch stroke. The predicted bending angle under load at each punch stroke was compared with the experimental measurement to validate the simulation model, Figure 7.2. Results showed that the simulation model predicted the bending angle underload with less than ±2 degree variation.

In addition to the simulation model with constant E-modulus, two other simulation models were also conducted with variable E-modulus as a function of plastic strain. One model is based on the data obtained from the loading-unloading-loading tensile test and the other model is based on the data obtained from the inverse analysis method described in next section. Results of springback predicted by these three simulation models are compared with experimental measurements for all seven different punch strokes.

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3.2. Inverse analysis method

The inverse analysis method is used to determine an apparent E-modulus for a given punch stroke which can provide accurate springback prediction, Figure 7.3. In this method, the springback predicted from the simulation model with the constant E-modulus, was compared with experimental measurement. Based on the comparison result, the E-modulus in the simulation was adjusted to predict the springback more accurately. The value of the E-modulus which can provide accurate springback prediction for a certain punch stroke / bending angle under load was considered as the apparent E-modulus for that punch stroke.

Figure 7.3: Inverse analysis method used to determine the apparent E-modulus for each punch stroke / bending angle under load.

3.3. Calculation of the E-modulus variation through the Inverse analysis method

The inverse analysis method was used to determine an apparent E-modulus for each punch stroke. To correlate the punch stroke to strain, and determine the variation of E-modulus as a function of strain, average strain in the part at each punch stroke was calculated as:

∑ 휀̅ 휀̅ = 푖 ⁡⁡⁡⁡⁡⁡(𝑖 = 1 − 푛) (7-1) 푎푣 푛

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th where 휀푖̅ is the effective strain of the 𝑖 element and 푛 is the total number of the elements which have strain value more than zero. The average strain in the part rose up until the punch strokes reaches to 20 mm and then by continuing the punch movement, the average strain is reduced.

4. Results and discussion 4.1. Elastic modulus degradation with plastic strain

Figure 7.4 shows the selected apparent E-modulus for each punch stroke. In general, by increasing the punch stroke the apparent E-modulus decreases and reaches a saturation value.

This is consistent with the results of the LUL tensile test. The reduction of E-modulus by increasing the punch stroke is due to increase of plastic strain. The minimum calculated apparent

E-modulus, 155 GPa, was considered as the saturation value 퐸푎 in the Y-U model.

200 180

160 modulus (GPa) modulus - 140 120

100 Apparent Apparent E 3 5 10 15 20 25 30 Punch stroke (mm) Figure 7.4: Selected apparent E-modulus through the inverse analysis at each punch stroke

The apparent E-modulus calculated for each punch stroke, Figure 7.4, was used to create the variable E-modulus versus strain curve. Since the average strain at the part starts to decrease after about 20 mm punch stroke, the apparent E-modulus for the strokes more than 20 mm is eliminated from the data. Figure 7.5 shows the comparison between the Y-U curve obtained from the wipe bending test and the inverse analysis method and the curve obtained from the LUL tensile test. The saturated value of the E-modulus (퐸푎) was about 155 GPa in both methods.

However, the reduction rate of the E-modulus with strain (휉) is more abrupt in the model

117 obtained from the inverse analysis method than the model obtained from the LUL tensile test. In order to investigate the improvement in springback prediction using the variable E-modulus, the calculated curves from the inverse analysis method and the LUL method were applied in the simulations and results were compared with experimental measurements.

220 210 Inverse analysis method 200 LUL method 190 180 170

160

modulus (GPa) modulus -

E 150 140 130 120 0 0.05 0.1 0.15 0.2 0.25 Plastic strain Test method 퐸0 (GPa) 퐸푎 (GPa) 휉 LUL Method 207 156 15 Inverse analysis 207 155 120 method Figure 7.5: Comparison of the E-modulus versus plastic strain calculated from the inverse analysis method and the LUL method.

4.2.Improvement in springback prediction using the variable E-modulus

Figure 7.6 shows the springback prediction at each punch stroke from three simulation models i.e. with constant E-modulus, with variable E-modulus that is obtained from the LUL method, and with variable E-modulus that is obtained from the inverse analysis method. In all three simulation models, springback increases by increasing the punch stroke similar to the experimental results. The most accurate prediction results were obtained when the variable E- modulus from the inverse analysis method was used. Using the variable E-modulus from the

LUL test improved the prediction results compared to the case of using the constant E-modulus.

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16 14 12

Experiment

10 8 Variable E-modulus (Inverse analysis method) 6 Variable E-modulus (LUL method)

Springback (deg) 4 2 Constant E-modulus of 207 GPa 0 3 5 10 15 20 25 30 Punch stroke (mm)

Figure 7.6: comparison of springback prediction results obtained from simulation models with different E-modulus and experimental measurement.

5. Conclusions

E-modulus determines the stiffness of the material and the amount of elastic strain during the deformation. Therefore, it is one of the most important material properties affecting the springback prediction. The elastic deformation of some steel materials is not linear and this makes determination of the E-modulus difficult. Also, researchers have shown that the E- modulus is strain path dependent and an E-modulus obtained from uniaxial test may not accurately represent the material stiffness in multiaxial forming process.

In the current study, the inverse analysis method was used to determine the variation of E- modulus with plastic strain. The wipe bending test was considered as the experiment which provide plane strain condition. Results showed that using the variable E-modulus versus plastic strain obtained from the inverse analysis method significantly improves the springback prediction compared to the case of using the constant E-modulus, or variable E-modulus from the LUL test.

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Calculation of strain in the wipe bending test was performed by averaging the strain values of all elements of the part. Since the strain distribution in the part during the wipe bending operation is not uniform, taking the average of strains reduces the accuracy of the inverse analysis method for prediction of springback. Determination of E-modulus degradation with plastic strain through a bending operation which can provide a pure bending condition at the part can increase the accuracy of the method.

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CHAPTER 8: SPRINGBACK REDUCTION IN U-CHANNEL DRAWING

OF AL 5182-O BY USING A SERVO PRESS AND A SERVO HYDRAULIC

CUSHION

Note: This chapter is submitted for publication to the Numerical Simulation of 3D Sheet Metal

Forming Processes Conference (NUMISHEET) on March 2018.

1. Introduction

During the past decade, springback predictions have been conducted using numerical solutions and Finite Element (FE) methods. The accuracy of the prediction result is affected by several parameters such as material properties, material model, Coefficient of Friction (COF), numerical procedures, and element type and size. In terms of material properties, flow stress data of sheet material and E-modulus are two most important properties affecting the prediction of springback.

Regarding to material model, plastic constitutive equations (Komgrit et al., 2016; Lee et al.,

2012a) and degradation of unloading elastic modulus (Yu 2009; Xue et al., 2016) significantly affect the simulation results. The influence of COF on springback is also investigated by several researchers (Gil et al., 2016; Wang et al., 2016).

In addition to the parameters mentioned above, there are some other phenomena which can significantly affect the springback of the part in an industrial stamping operation. Owing to their complexity, it is practically impossible to consider these parameters in simulation. Examples of such phenomena are elastic deflection of tools and presses during the forming process (Eggertsen and Mattiasson 2012) or the inertia and response time of the machine.

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Regarding control and reduction of springback, in general, there are two practical ways

(Wagoner et al., 2013): a) Obtain the final part within geometric tolerances after compensating for springback by altering

the geometry of tooling b) Applying additional stretch/tension forces to the part during the forming operation

Tooling geometry compensation is based on simulated prediction of springback as well as trial

and error (Gan and Wagoner 2004). Effects of additional tension on reduction of springback has

been shown both experimentally and numerically (Ayres 1984; Liu et al., 2002). Sidewall curl

springback produced from drawing process (process where the draw-in of the sheet material into

die cavity is controlled by blank holder and material is under stretch force during the

deformation) causes assembly difficulties and the post stretching method has been used to reduce

the side wall curl. In this method, the sheet material undergoes extra stretching toward the end of

deformation. This extra tension reduces the heterogeneous distribution of stresses through the

sheet thickness at the wall area and consequently reduces springback.

To reduce the springback by post stretching there are two ways:

a) Design the tooling with drawbeads which start to contact the sheet toward the end of the

deformation process

b) Use of Servo Hydraulic Cushion (SHC) to control of Blank Holder Force (BHF) during the

deformation cycle and induce post stretching

In the present study, the use of SHC for reduction of springback in a U-channel part is

investigated experimentally and numerically. The effect of elastic deflection of the tools and

COF on springback prediction is also investigated.

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2. Reduction of springback by post-stretching – use of servo hydraulic cushion

2.1. Servo hydraulic cushion During the deep drawing process, the sheet material is restrained at the periphery of the BHF.

Generally, the BHF is generated by pneumatic cushions, nitrogen cylinders, or hydraulic cushions. Hydraulic cushions allow for computer numerical control of the BHF by regulating the oil flow to the cushion cylinders. The main advantage of the SHC compared to other types of cushions is that the SHC allows controlling the BHF during the deformation.

2.2. Experiments U-channel drawing of 1.2 mm Al5182-O was conducted to investigate the possibility of reduction of springback using the post stretching method by applying blankholder force with an

SHC. A 300-metric ton servo press with 100 metric-ton SHC was used. Information about the geometry and dimensions of the tooling is presented in Figure 8.1. The blank was rectangular with the dimension of 720 mm × 120 mm and it was drawn to stroke of approximately 66 mm.

Blanks were coated by dry lubricant. Two constant blank holder forces (100 kN and 400 kN) and one variable with time (100 kN to 700 kN) were used, Figure 8.2. The values of the BHFs are selected based on simulation predictions to avoid excessive thinning at the part. For the case of variable BHF, deformation starts with constant 100 kN BHF and then at stroke of 60 mm the

BHF starts to raise up and reach to 700 kN at stroke of 65 mm. The variable BHF is selected to provide the post stretching condition for reduction of springback. Three replications were considered to ensure repeatability of the results.

During the test, the blank holder and the die displacements were recorded. This information was used to determine the exact final stroke and elastic deflection of the tools for each BHF.

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Figure 8.1: A schematic of tools and dimensions for the U-draw bending.

2.3. FE simulation

3-D FE simulation of the U-channel drawing process was developed using the AutoForm software package. The blank was created using shell elements and tools were modelled using rigid analytical surfaces. The flow stress of the material was determined from a tensile test and the true stress- true strain data was used directly in simulations. An E-modulus of 70 GPa was used as an initial estimate. By comparing the springback prediction and experimental measurement, the E-modulus was adjusted until the predicted springback matched measurements. To determine the COF for each testing condition, flange length of the part was measured. Then simulations with different values of COF were conducted and the value of the

COF that predicted a similar flange length to the measured value was assumed to be the COF for that test condition. For each testing condition (BHF value) the simulation was stopped at a punch stroke similar to the experiment and springback was predicted.

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2.4. Results and discussion

Figure 8.3 shows the profiles of the parts obtained from the experiments and the simulations. As shown in this figure, there is a large side wall curl in the part for both constant 100 kN and 400 kN BHFs. The side wall curl is significantly reduced with the variable BHF (post stretching method). The predicted stress distribution along the sheet thickness at the wall area is shown in

Figure 8.4 for the cases of constant 100 kN and variable BHFs. In the case of variable BHF all the compression stresses on the wall are converted to tension. It clearly describes how the post stretching method reduces the heterogeneous stress distribution at the wall area, leading to a reduction in springback.

Figure 8.3: Experimental results and simulation predictions of springback for 3 different BHF values.

125

Figure 8.4: Stress distribution along the sheet thickness at wall area for two different BHF values.

3. Effect of coefficient of friction on springback prediction

The effect of the COF on simulation results is more significant for higher Blank holder forces.

The COF calculated for the 400 kN BHF used in this study was about 0.04. This value is calculated by comparing the flange length in simulation and experiment. However, to investigate the effect of BHF on springback, additional simulation with higher COF were also conducted.

Results show that with 400 kN BHF, failure results if the COF is higher than 0.07. Figure 8.5 shows the springback prediction for two different COFs, 0.04 and 0.07, compared to the experimental measurement.

Figure 8.5: Effect of COF on springback prediction.

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4. Elastic deflection of the tools

The die displacement was continuously measured during the experiment to accurately determine the elastic deflection of the tools and the final stroke at each testing condition (BHFs). Figure 8.6 shows the profile of the die motion (ram motion) versus time and the magnified view close to bottom dead center. Using the servo press provides the capability to significantly reduce the die speed when it starts to touch the sheet material to avoid the shock. After the soft touch the speed increases immediately to avoid increasing the forming cycle time. Results show that the total die displacement was not same in all testing conditions and the BHF affects the amount of die displacement. The die displacement is reduced by increasing the BHF. The die displacement in the case of variable BHF where the maximum BHF close to the bottom dead center reached to

700 kN was about 0.5 mm less than the die displacement when 100 kN constant BHF was used.

Figure 8.6: Die displacement versus time for three different tested BHFs.

5. Conclusions

Results of this study indicate that the side wall curl in drawn aluminium parts can be significant.

Servo hydraulic cushion provides the capability to control the BHF through the die stroke and springback can be controlled significantly by applying the post stretching method. There are some limitations and the actual BHF is not always the same as the CNC target value. Some

127 parameters such as the forming speed, the range of BHF, the size of the cushion, and the speed of the closing and opening of the hydraulic valves can affect the accuracy of the actual force compared to the CNC target value.

Coefficient of friction is an important parameter significantly affects the springback prediction.

Also, elastic deflection of the tools can affect the test conditions. The elastic deflection of the tools is more critical when forming with a higher blank holder force.

128

REFERENCES

Abspoel, M., Scholting, M.E., Droog, J.M.M., 2013. A new method for predicting forming limit curves from mechanical properties. Journal of Materials Processing Technology. 213 (5), 759-769.

Allen, S.J. and Mahdavian S.M., 2008. The effect of lubrication on die expansion during the deep drawing of axisymmetrical steel cups. Journal of materials processing technology. 199, 102-107.

Altan, T., Ngaile, G., Shen, G., 2005. Cold and hot forging- fundamentals and applications. ASM international. Ch. 11 Presses and hammers for cold and hot forging, pp. 115-140.

Altan, T., Tekkaya, A.E., 2012a. Sheet metal forming- fundamentals. ASM international. Ch. 4 Plastic deformation- Flow stress, Anisotropy, and Formability. 33-52.

Altan, T., Tekkaya, A.E., 2012b. Sheet metal forming- fundamentals. ASM international. Ch. 7 Friction and lubrication. 89-104.

Altan, T., Tekkaya, A.E., 2012c. Sheet metal forming- fundamentals. ASM international. Ch. 11 Electromechanical Servo-Drive Presses. 160-180.

Amaral, R., Santos, A.D., Lopes, A.B., 2017. Mechanical properties determination of dual-phase steels using uniaxial tensile and hydraulic bulge test. Ciencia & Technologia dos Materiais. 29, 239-243.

Arrieux, R., Bedrin, C., Boivin, M., 1982. Determination of an intrinsic forming limit stress diagram for isotropic metal sheets. In: Proceedings of the 12th Biennial Congress IDDRG, pp. 61–71.

Arrieux, R., 1995. Determination and use of the forming limit stress diagrams in sheet metal forming. Journal of Materials Processing Technology. 53, 47–56.

AS/P 2009. "Advanced high strength steel (AHSS) application guidelines Version 4.1." The World Steel Association.

Ayres, R.A., 1984. SHAPESET: a process to reduce sidewall curl springback in high strength steel rails. Journal of Applied Metalworking. 3(2), 127-134.

Banabic, D., 2010. Sheet metal forming process: constitutive modeling and numerical simulation. Springer. Chapter 2, 27.

Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H., Chu, E., 2003. Plane stress yield function for aluminium alloy sheets - Part 1: theory, International Journal of Plasticity. 19, 1297-1319.

129

Barlat, F., Gracio, J.J., Lee, M.-G., Rauch, E.F., Vincze, G., 2011. An alternative to kinematic hardening in classical plasticity. International Journal of Plasticity. 27 (9), 1309–1327.

Bhushan, B., 2002. Introduction to Tribology, John Wiley and Sons.

Billur, E., Altan, T., 2010. Challenges in forming advanced high strength steels. In proceedings of New Developments in Sheet Metal Forming. May 2-4. Stuttgart, Germany. 285-304.

Billur, E., 2013. Fundamentals and Applications of Hot Stamping Technology for Producing Crash-Relevant Automotive Parts. Ph.D. thesis. The Ohio State University, Columbus, OH. Billur, E., Altan, T., 2013. Three generations of advanced high-strength steels for automotive applications, Part I. Stamping Journal. Nov-Dec, 16-17.

Cayssials, F., 1998. A new method for predicting FLC. In: Proceedings of the 20th IDDRG Congress, Brussels, Belgium, pp. 443–454.

Cayssials, F., Lemoine, X., 2005. Predictive model of FLC (Arcelor model) upgraded to UHSS steels. In: Boudeau, N. (Ed.), Proceedings of the 24th International Deep- Drawing Research Group Congress. Besanc¸ on, France.

Chaboche, J.L., Dang-Van, K., Cordier, G., 1979. modelization of the strain memory effect on the cyclic hardening of 316 stainless steels. SMiRT-5, Div. L,. Paper No. L. 11/3. Chen, K., Scales, M., Kyriakides, S., 2018. Material hardening of a high ductility aluminum alloy from a bulge test. International Journal of Mechanical Sciences. 138-139, 476- 488. Chung, K., Kuwabara, T., Verma, R.K., Park, T., 2011. Numisheet 2011 Benchmark 4: Pre- strain effect on springback of 2D draw bending. In: Huh, H., Chung, K., Han, S.S., Chung, W.J. (Eds.), The 8th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes. Seoul, Korea, 171–175. Cleveland, R. M., and Ghosh, A. K. 2002. Inelastic effects on springback in metals. International Journal of Plasticity. 18, 769-785.

Dohda, K., Boher, C., Rezai-aria, F., Mahayotsanun, N., 2015. Tribology in metal forming at elevated temperature. Friction. 3, 1-27

Eggertsen, P.A., Mattiasson, K., 2012. Experiences from experimental and numerical springback studies of a semi-industrial forming tool. Int. J. Mater. Form. 5, 341-359.

Fallahiarezoodar, A., Groseclose, A., Appachu, S., Altan, T., 2014. Evaluation the lubrication performance of ten different lubricants in forming of AHSS (DP590 and DP980) using the Cup Drawing Test. CPF internal report. CPF-2.3/14/01.

130

Fallahiarezoodar, A., Altan, T., 2015. Determining flow stress data by combining uniaxial and biaxial bulge tests. Stamping Journal, Sep-Oct, 16-17.

Fallahiarezoodar, A., Peker, R., Altan, T., 2016. Temperature increase in forming of advanced high strength steels – effect of ram speed using a servo drive press. Journal of Manufacturing Science and Engineering.138, 094503-1-7.

Farren, W., Taylor. G., 1925. The heat developed during plastic extension of metals. Proceedings of the royal society of London, Series A. 107, 422-451.

Figueiredo, L., Ramalho, A., Oliveira, M.C., Menezes, L.F., 2011. Experimental study of friction in sheet metal forming. Wear. 271, 1651-1657.

Frederick, C.O., Armstrong, P.J., 2007. A mathematical representation of the multiaxial Bauschinger effect. Materials at High Temperatures. 24:1, 1-26

Fridlyander, I.N., Sister, V.G., Grushko, O.E., Berstenev, V.V., Sheveleva, L.M., Ivanova, L.A., 2002. Aluminum alloys: promising materials in the automotive industry. Metal science and heat treatment. 44 (9), 365-370.

Gaard, A., Hallback, N., Krakhmalev, P., Bergstrom, J., 2010. Temperature effects on adhesive wear in dry sliding contacts. Wear. 268, 968-975.

Gan, W., Wagoner, R.H., 2004. Die design method for sheet springback Int. J. Mech. Sci. 46 1097-1113.

Gau, J. T., and Kinzel, G. L. 2001. A new model for springback prediction in which the Bauschinger effect is considered. International Journal of Mechanical Sciences. 43, 1813-1832.

Geng, L. M., Shen, Y., and Wagoner, R. H. 2002. Anisotropic hardening equations derived from reverse-bend testing. International Journal of Plasticity 18, 743-767.

Gerlach, J., Kessler, L., Köhler, A., 2010. The forming limit curve as a measure of formability— is an increase of testing necessary for robustness simulations? In: Kolleck, R. (Ed.), Proceedings IDDRG 50th Anniversary Conference. 479–488.

Gil, I., Mendiguren, J., Galdos, L., Mugarra, E., Argandona, E., 2016. Influence of the pressure dependent coefficient of friction on deep drawing springback predictions. Tribol. Int. 103, 266-273.

Gong, H., Lou, Z., Zhang, Z., 2004. Studies on the friction and lubrication characteristics in the sheet steel drawing process. Journal of materials processing technology. 151, 328-333.

Grueebler, R. and Hora, P., 2009. Temperature dependent friction modeling for sheet metal forming. Int. J. Mater. Form. 2, 251-254.

131

Gutscher, G., Wu, H.C., Ngaile, G., Altan, T., 2004. Determination of Flow Stress for Sheet Metal Forming Using the Viscous Pressure Bulge (VPB) Test. Journal of Materials Processing Technology. 146, 1-7.

Haddad, A., Arrieux, R., Vacher, P., 2000. Use of two behaviour laws for the determination of the forming limit stress diagram of a thin steel sheet: results and comparisons. Journal of Materials Processing Technology. 106, 49–53.

Han, S.S., Kim, D.J., 2011. Contact pressure effect on frictional characteristics of steel sheet for autobody. AIP Conference Proceedings. 1383, 780-783.

Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond. A193, 281.

Jiang, Y., Sehitoglu, H., 1996. Modeling of cyclic ratchetting plasticity. Part I: Development of constitutive relations. Journal of Applied Mechanics. 63, 720–725.

Ju, L., Mao, T., Malpica, J., Altan, T., 2015a. Evaluation of lubricants for stamping of Al 5182-O aluminum sheet using cup drawing test. Journal of manufacturing science and engineering. 137,051010-1-051010-8.

Ju, L., Patil, S., Dykeman, J., Altan, T., 2015b. Forming of Al 5182-O in a servo press at room and elevated temperatures. Journal of manufacturing science and engineering. 137, 051009-1-0510097.

Keeler., S.P., Brazier, S.G., 1977. Relationship between laboratory material characterization and press-shop formability. In: Proceedings of Microalloying, vol. 75, New York, pp. 517– 530.

Kim, H., Sung, J., Goodwin, F., Altan, T., 2008. Investigation of galling in forming galvanized advanced high strength steels (AHSSs) using the twist compression test (TCT). Journal of Materials Processing Technology. 205, 459-468.

Kim, H., Altan, T., Yan, Q., 2009. Evaluation of stamping lubricants in forming advanced high strength steels (AHSS) using deep drawing and ironing tests. Journal of Materials Processing Technology. 209, 4122-4133.

Kim, J.H., Sung, J.H., Piao, K., Wagoner, R.H., 2011. The shear fracture of dual-phase steel. International journal of plasticity. 27, 1658-1676.

Kim, H., Kim, C., Barlat, F., Pavlina, E., Lee, M.G., 2013. Nonlinear elastic behaviors of law and high strength steels in unloading and reloading. Materials Science & Engineering. A 562, 161–171.

Kirkhorn, L., Frogner, K., Andersson, M., Ståhl, J.E., 2012. Improved tribotesting for sheet metal forming. Procedia CIRP. 3, 507–512.

132

Knockaert, R., Chastel, Y., Massoni, E., 2002. Forming limits prediction using rate-independent polycrystalline plasticity. International Journal of Plasticity. 18, 231–247.

Koistinen, D., 1978. Mechanics of sheet metal forming. Chapter 7 friction and lubrication in sheet metal forming. pp. 157-177.

Komgrit, L., Hamasaki, H., Hino, R., Yoshida, F., 2016. Elimination of springback of high- strength steel sheet by using additional bending with counter punch. Journal of Materials Processing Technology. 229, 199–206.

Krieg, R.D., 1975. A practical two surface plasticity theory. Journal of Applied Mechanics. 47, 641–646.

Kumar, S., Date, P.P., Narasimhan, K., 1994. A new criterion to predict necking failure under biaxial stretching. Journal of Materials Processing Technology. 45, 583-588.

Kuroda, M., Tvergaard, V., 2000. Effect of strain path change on limits to ductility of anisotropic metal sheets. International Journal of Mechanical Sciences. 42, 867–887.

Lee, J. W., Lee, M. G., Barlat, F., 2012a. Finite element modeling using homogeneous anisotropic hardening and application to springback prediction. International Journal of Plasticity. 29, 13–41.

Lee, J. Y., Lee, J. W., Lee, M. G., Barlat, F., 2012b. An application of homogeneous anisotropic hardening to springback prediction in pre-strained U-draw/bending. international journal of solids and structures. 49, 3562–3572.

Liu, G., Lin, Z., Bao, Y., Cao, J, 2002. Eliminating springback error in U-Shaped part forming by variable blankholder force. J. Mater. Eng. Perform. 11(1), 64-70.

Ma, X., de Rooij, M., Schipper, D., 2010. A load dependent friction model for fully plastic contact conditions. Wear. 269, 790–796.

Marciniak, Z., Kuckzynski, K., 1967. Limit strains in the process of stretch-forming sheet metal. Int. J. Mech. Sci., 9, 609-620.

Miyoshi, K., 2004. Current trens in free motion presses. Proceedings of the 3rd Japan Society for Technology of Plasticity (JSTP), International Seminar on Precision Forming.

Morestin, F., Bovin, B., 1996. On the necessity of taking into account the variation in the Young’s modulus with plastic strain in elastic-plastic software. Nuclear Engineering and Design. 162, 107-116.

Nakazima, K., Kikuma, T., Hasuka, K., 1968. Study on the formability of steel sheets. Yawata Iron and Steel Publications, Yawata technical report no. 264.

133

Nine, H.D., 1978. Draw bead forces in sheet metal forming. Proceedings of a Symposium on Mechanics of Sheet Metal Forming: Behaviour and Deformation Analysis, Plenum Press, Warren, Michigan, 179–211.

Ogawa, T., Yoshida, F., 2011. Springback analysis of U-bending with Bottoming. AIP Conference Proceedings. 1383, 1129.

Osakada, K., Mori, K., Altan, T., Groche, P., 2011. Mechanical servo press technology for metal forming. CIRP Annals – Manufacturing Technology. 60, 651-672.

Pereira, M.P., Rolfe, B.F., 2014. Temperature Conditions During ‘Cold’ Sheet Metal Stamping. J. Mater. Process. Technol. 214(8), 1749-1758.

Pérez, R., Benito, J.A., Prado, J.M., 2005. Study of the inelastic response of TRIP steels after plastic deformation. ISIJ Int. 45, 1925–1933. Pourboghrat, F., Chu, E., 1995. Springback in plane strain stretch/draw sheet forming. Int. J. Mech. Sci. 36 (3), 327-341

Raghavan, K.S., Van Kuren, R.C., Darlington, H., 1992. Recent Progress in the Development of Forming Limit Curves for Automotive Sheet Steels. SAE Technical Paper 920437.

Sanchez, L.R. and Weinmann K.J., 1996. An analytical and experimental study of the flow of sheet metal between circular drawbeads. Journal of Engineering for industry. 118, 45- 54.

Sanchez, L.R., 1999. Characterisation of a measurement system for reproducible friction testing on sheet metal under plane strain. Tribol. Int. 32, 575–586.

Schey, J.A., 1996. Speed effects in drawbead simulation. Journal of materials processing technology. 57, 146-154.

Shi, M.F., Gelisse, S., 2006. Issues on the AHSS forming limit determination. In: Santos, A.D., Barata de Rocha, A. (Eds.), Proceedings IDDRG International Deep Drawing Research Group 2006 Conference. Porto, Portugal, 19–25.

Sigvant, M., Mattiasson, K., Vegter, H., Thilderkvist, P., 2009. A viscous pressure bulge test for the determination of a plastic hardening curve and equibiaxial material data. International journal of Material forming. 2, 235-242.

Sigvant, M., Pilthammar, J., Hol, J., Wiebenga, J.H., Chezan, T., Carleer, B., van den Boogard, A.H., 2016. Friction and lubrication modeling in sheet metal forming simulations of the Volvo XC90 inner door. Numisheet. Journal of Physics: Conference Series 734, 032090

Sun, D. C, Chen, K. K., and Nine, H. D., 1987. Hydrodynamic lubrication in hemispherical punch stretch forming—modified theory and experimental validation. Int. J. of Mech. Set. 29, 761-776.

134

Sun, L., Wagoner, R.H., 2011. Complex unloading behavior: Nature of the deformation and its consistent constitutive representation. International Journal of Plasticity. 27, 1126–1144.

Taherizadeh, A., Ghaei, A., Green, D. E., and Altenhof, W. J. 2009. Finite element simulation of springback for a channel draw process with drawbead using different hardening models. International Journal of Mechanical Sciences. 51, 314-325.

Tong, L., Hora, P., Reisser, J., 2002. Prediction of forming limit with nonlinear deformation paths using modified maximum force criterion. NUMISHEET. Toyohashi, Japan

Trzepiecinski, T. and Fejkiel, R., 2017. On the influence of deformation of deep drawing quality steel sheet on surface topography and friction. Tribol. Int. 115, 78-88.

Vermeulen, M. and Scheers, J., 2001. Micro-hydrodynamic effects in EBT textured steel sheet. International Journal of machine tools & manufacture. 41:1941-51.

Wang, W., Zhao, Y., Wang, Z., Hua, M., Wei, X., 2016. A study on variable friction model in sheet metal forming with advanced high strength steels. Tribol. Int. 93, 17-28.

Wang, C., Ma, R., Zhao, J., Zhao, J., 2017. Calculation method and experimental study of coulomb friction coefficient in sheet metal forming. Journal of manufacturing processes. 27, 126-137.

Wagoner, R.H., Lim, H., Lee, M.G., 2013. Advanced issues in springback. International journal of plasticity. 45, 3-20. Werber, A., Liewald, M., Nester, W., Grunbaum, M., Wiegand, K., Simon, J., Timm, J., Hotz, W., 2013. Assessment of forming limit stress curves as failure criterion for non- proportional forming processes. 7, 213-221.

Wilson, W. R. D., Hsu, T.C., Huang, X. B., 1995. A Realistic friction model for computer simulation of sheet metal forming processes. Transaction of the ASME. 117, 202-209.

Wilson, W. R. D., 1997. Tribology in cold metal forming. Journal of Manufacturing science and engineering. 119, 695-698.

Wu, P.D., Graf, A., Jain, M., MacEwen, S.R., 2000. On alternative representation of forming limits. Key Engineering Materials. 177–180, 517–522.

Wu, P.D., Jain, M., Savoie, J., MacEwen, S.R., Tugcu, P., Neale, K.W., 2003. Evaluation of anisotropic yield function for aluminum sheets. International Journal of Plasticity. 19, 121–138. Wu, P.D., Graf, A., MacEwen, S.R., Lioyd, D.J., Jain, M., Neale, K.W., 2005. On forming limit stress diagram analysis. International Journal of Solids and Structures. 42, 2225-2241. Xue, X., Liao, J., Vincze, G., Pereira, Antonio., Barlat, F., 2016. Experimental assessment of nonlinear elastic behaviour of dual-phase steels and application to springback prediction. International Journal of Mechanical Sciences. 1–15.

135

Yang, T.S., 2008. Prediction of surface topography in lubricated sheet metal forming. Int. J. Mach. Tools & Manufacture. 48, 768-777.

Yoshida, F., Uemori, T., Fujiwara, K., 2002. Elastic-plastic behavior of steel sheets under in- plane cyclic tension-compression at large strain. International journal of plasticity. 18, 633-659.

Yoshida, F., and Uemori, T. 2003. A model of large-strain cyclic plasticity and its application to springback simulation. International Journal of Mechanical Sciences. 45, 1687-1702.

Yu, H.Y., 2009. Variation of elastic modulus during plastic deformation and its influence on springback. Mater Des. 30, 846-850.

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