Evaluation of Formability and Determination of Flow
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EVALUATION OF FORMABILITY AND DETERMINATION OF FLOW STRESS CURVE OF SHEET MATERIALS WITH DOME TEST THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Ji You Yoon Graduate Program in Mechanical Engineering The Ohio State University 2012 Master's Examination Committee: Taylan Altan, Advisor Jerald Brevick Copyright by Ji You Yoon 2012 Abstract Determination of flow stress curve of sheet material is important for designing stamping process efficiently. Entering accurate flow stress curve to FE simulations is necessary to obtain reliable results from simulations. Furthermore, in most Advanced High Strength Steels (AHSS), material properties may vary from coil to coil and that can affect to product quality. The dome test is a material test to evaluate formability and determine the flow stress curve of the sheet materials. The dome test is a biaxial test which consequently achieves greater maximum true strain without localized necking compared to that of uniaxial tensile test. As a result, the flow stress curve obtained from the dome test can be determined up to larger strains than in tensile test. This reduces possible errors from extrapolation of flow stress curve obtained from tensile test. FE simulations are performed in order to understand the deformation process in the dome test and to develop database for computer program, PRODOME, (MATLAB). With PRODOME, flow stress curve is calculated (determining K and n values in Hollomon’s Law (σ=Kεn)) by inputting dome test outputs of punch force vs. stroke. It is calculated by using inverse analysis method. From the dome test, JAC 590R (t = 1.6 mm), JAC 780 TRIP (thickness = 1.0 mm) and Al 6022 (t = 1.0 mm) are tested. Lubrication system is developed from the dome test. With lubrication system, samples are evaluated how much they deviate from the apex of the dome by having percentage error they have in the flow stress curve. ii Dedication This document is dedicated to my parent, my sister and friends iii Acknowledgements Thanks God, I barely finish my study without Your help and Your strength that comes from You. To be able to accomplish this study, I have been supported and supervised by many people that God sent to me. To my family, I cannot express my gratitude enough. I am indebted to my family and my friends who helped me a lot during my school period. I believe that I would not be able to name everyone separately and to thank for everything that they did for me, however, I would like to express a few words of thanks from the bottom of my heart. I would like to express my deepest gratitude to: Prof. Taylan Altan for his great support and his valuable suggestions which make me strong to step up beyond my deficiency. His intellectual support, advice and guidance make me possible to accomplish this research works. I thank my committee member Dr. Jerald Brevick for support. I thank my colleagues of the CPF, Eren Billur, Dr. Hyun-Sung Son, Soumya Subramonian, Tingting Mao, Xi Yang, Adam Groseclose, Niranjan Rajagopal for their assistance. I also want to express great thanks to HRA, Jim Dykeman and Ben Flocken for their support. Specially, I would like to thank my parents and my sister for their endless encouragement, inspiration, advice and support. I would like to thank all those too numerous to mention here, who have assisted and encouraged to complete of my work. iv Vita February 2006 ............................................ Se-Hwa Girls’ High School 2010 ........................................................... B.S. Mechanical Engineering, Hanyang University 2011 to present .............................................. Graduate Research Associate, Department of Mechanical Engineering, The Ohio State University Fields of Study Major Field: Mechanical Engineering v Table of Contents Abstract ................................................................................................................... ii Dedication .............................................................................................................. iii Acknowledgements ................................................................................................ iv Vita .......................................................................................................................... v CHAPTER 1 INTRODUCTION ............................................................. 1 CHAPTER 2 BACKGROUND ............................................................... 3 2.1 Uniaxial Tensile Test .................................................................... 4 2.2 Biaxial Tension Test ................................................................... 16 2.2.1 Cupping tests ......................................................................... 16 2.2.2 Limiting Dome Height (LDH) Test ....................................... 17 2.2.3 Bulge Test .............................................................................. 20 2.2.4 Dome Test (extension of LDH test) ....................................... 24 CHAPTER 3 OBJECTIVES AND APPROACH .................................. 25 3.1 Objectives .................................................................................... 25 3.2 Approach ..................................................................................... 25 CHAPTER 4 INVERSE ANALYSIS METHODOLOGY .................... 30 vi CHAPTER 5 EXPERIMENTAL WORK AND RESULTS ................. 33 5.1 Experiments and Tooling ............................................................ 33 5.2 Test Procedure ............................................................................. 34 5.3 Output from the Dome Tests ....................................................... 35 5.4 Test Parameters and Selection of Materials ................................ 36 5.5 Test Results ................................................................................. 39 CHAPTER 6 FE SIMULATIONS ......................................................... 41 6.1 Simulation Parameters ................................................................ 41 6.2 Computer Program “PRODOME” Using MATLAB ................. 43 6.2.1 General concepts of computer program using MATLAB ..... 43 6.2.2 Running the PRODOME ....................................................... 44 CHAPTER 7 RESULTS AND DISCUSSION ...................................... 47 7.1 Determination K and n Values of the Sheet Materials ................ 47 7.2 Anisotropy Correction ................................................................. 48 7.3 Comparison of the Flow Stress Curves ....................................... 49 7.3.1 Tensile test vs. dome test ....................................................... 49 7.3.2 VPB test vs. Dome test from DEFORM and PAMSTPMP ... 51 7.4 Zero Point Adjustment ................................................................ 53 7.5 Lubrication System ..................................................................... 55 vii 7.5.1 Preliminary Evaluation Lubricant Test .................................. 55 7.5.2 Measurement of angle of fractures ........................................ 56 CHAPTER 8 SUMMARY AND CONCLUSIONS .............................. 64 REFERNECES ..................................................................................................... 68 APPENDIX A: Lubricants list .............................................................................. 72 APPENDIX B: Evaluation lubricant tests for high formability material (JSC 270F, t = 0.8 mm) ................................................................................................. 73 viii List of Tables Table 1. Dome test experiment matrix [Dykeman 2011, POSCO 2012].............. 33 Table 2. Material properties evaluated by tensile test provided by Honda ........... 37 Table 3. Test parameters of the dome test ............................................................ 38 Table 4. K & n values and of the materials with isotropic assumption ( = 1) ........................................................................................................................... 47 Table 5. Normal anisotropy of the materials (provided by Honda) ...................... 49 Table 6. Determined parameters from VPB test (w/o considering anisotropy), DEFORM and PAMSTAMP ................................................................................ 52 ix List of Figures Figure 1. Tensile test specimen, according to ASTM E8 [Altan 2012, ASTM 2011] ....................................................................................................................... 4 Figure 2. Schematic of a fixture used in a tensile test [Altan 2012] ....................... 5 Figure 3. The schematic of the force vs. elongation curve obtained from tensile test [Altan 2012] ..................................................................................................... 5 Figure 4. Engineering stress vs. engineering strain curve [Kalpakjian 2008] ........ 7 Figure 5. Comparison stress vs. strain curve between engineering state and true state [Hosford 2007] ............................................................................................... 8 Figure 6. True stress and true strain curve of Al 1100-O, plotted on log-log scale [Hosford 2007, Altan 2012] .................................................................................... 9 Figure 7. Some of the flow curve equations used in plastic deformation studies [Marciniak 2002, Altan 2012]: (a)