CHARACTERIZATION OF SHEET MATERIALS FOR STAMPING AND FINITE ELEMENT SIMULATION OF SHEET HYDROFORMING

Transcription

1 CHARACTERIZATION OF SHEET MATERIALS FOR STAMPING AND FINITE ELEMENT SIMULATION OF SHEET HYDROFORMING THESIS Presented in Partial Fulfillment of the Requirements for the Degree Masters in the Graduate School of the Ohio State University By Amin E. Al-Nasser, B.E ***** The Ohio State University 2009 Thesis Committee: Approved by Professor Taylan Altan, Advisor Associate Professor Jerald Brevick.. Advisor Industrial and Systems Engineering Graduate Program

2 Copyright by Amin Al-Nasser 2009

3 ABSTRACT The increase in using Advanced High Strength Steel (AHSS) and aluminum sheet materials is accompanied by many challenges in forming these alloys due to their unique mechanical properties and/or low formability. Therefore, developing a fundamental understanding of the mechanical properties of AHSS as compared to conventional Draw Quality Steel (DQS) is critical to successful process/ tools design. Also, alternative forming operations, such as warm forming or sheet hydroforming, are potential solutions for the low formability problem of aluminum alloys. Identifying potential difficulties in forming these materials early in the product realization process is important to avoid expensive late changes. Finite Element (FE) simulation is a powerful tool for this purpose provided that the inputs to the FE model, including the flow stress data, are reliable. However, obtaining the flow stress under near production condition (state of stress, strain rate, temperature) may be challenging especially if the flow stress is required at elevated temperature for warm forming applications. In this study, room temperature uniaxial tensile and biaxial Viscous Pressure Bulge (VPB) tests were conducted for five AHSS sheet materials; DP 600, DP 780, DP 780-CR, DP 780-HY, and TRIP 780, and the resulting flow stress curves were compared. Strain ratios (R-values) were also determined in the tensile test and used to correct the biaxial flow stress curves for anisotropy. The pressure vs. dome height raw data in the VPB test was extrapolated to the burst pressure to obtain the flow stress curve up to fracture. Results of this work show that flow stress data can be obtained to higher strain values under biaxial state of stress. ii

4 Moreover, it was observed that some materials behave differently if subjected to different state of stress. These two conclusions, and the fact that the state of stress in actual stamping processes is almost always biaxial, suggest that the bulge test is a more suitable test for obtaining the flow stress of AHSS sheet materials to be used as an input to FE models. An alternative methodology for obtaining the flow stress from the bulge test data, based on FE-optimization, was also applied and shown to work well for the AHSS sheet materials tested. Elevated temperature bulge tests were made for three aluminum alloys; AA5754- O, AA5182-O, and AA3003-O, using a special machine where the tools and specimen are submerged in a fluid heated to the required temperature. Several challenges were faced in the experiments such as leakage of the bulging fluid and sample pre-bulging in the clamping stage prior to the test. Moreover, it was originally planned to measure the dome curvature by using three LVDTs; one at the dome apex, and the others at different off-center locations. However, the probes slightly penetrated the soft sheet. Consequently, the off-center probes deflected and gave incorrect data. As a result of these challenges, the pressure and dome height data was not considered reliable to be used in determining the flow stress curves. Only the experimental data is included in this report for documentation purposes, while the calculated flow stress curves are not included. A Sheet Hydroforming with a Punch (SHF-P) process was successfully simulated using the FE software Pamstamp 2G The objective was to develop a fundamental understanding of the process to reduce the expensive experimental trial and error. A systematic methodology to design the process was suggested and applied using FE simulation. A considerable improvement in the thinning distribution in the part was achieved by properly selecting the blankholding and pot pressure curves. It was also found that SHF-P with a clamped flange (stretch iii

5 forming) is detrimental to the sheet thinning and that flange draw-in is required to benefit from this process. iv

6 Dedicated to my mother (Wafa Al-Khasawneh), father (Eyad Al-Nasser), and brothers (Said Al-Nasser, Ahmad Al-Nasser, Kamal Al-Nasser) v

7 ACKNOWLEDGEMENT I am sincerely grateful to my advisor, Prof. Taylan Altan for his supervision during my Masters studies at the Engineering Research Center for Net Shape Manufacturing (ERC/NSM). His intellectual support, encouragement, and guidance are the main factors for making this research work possible. I also thank my committee member Dr. Jerald Brevick for his continuous support and valuable feedback. Special thanks to the sponsors of this research; the Auto-Steel Partnership (A/S P), Dr. Mike Bzdok, and the United States Steel (USS), Dr. Ming Chen, for supporting the AHSS sheet characterization project. Special thanks to Interlaken Technology Corporation (ITC), Dr. Patrick Cain, and the Applied Engineering Solutions, LLC (AES), Dr. David Guza, for working with the ERC/NSM and providing technical support for the elevated temperature bulge testing. I also gratefully thank General Motors R&D, Dr. John Carsley, for supporting the sheet hydroforming project. I thank my colleagues and the visiting scholars of the ERC/NSM, Dr. Ajay Yadav, Dr. Partchapol Sartkulvanich, Dr. Hyunok Kim, Dr. Serhat Kaya, Dr. Yeon Sik Kang (Posco), Lars Penter (Dresden Germany), Gaetano Pittala (Prato Italy), Parth Pathak, Thomas Yelich, Nimet Kardes, Dario Braga (Brescia Italy), Yurdaer Demiralp, Adam Groseclose, and Soumya Subramonian for their assistance and encouragement. vi

8 VITA August 11, Born, Amman-Jordan B.E, Industrial Engineering The University of Jordan, Amman Jordan Graduate Research Associate Engineering Research Center for Net Shape Manufacturing (ERC/ NSM), Columbus- Ohio- USA Junior Industrial Consultant Abu-Ghazaleh and Co. Consulting (AGCON), Member of Talal Abu- Ghazaleh and Co. International (TAGI) Amman- Jordan vii

9 PUBLICATIONS Nasser A., Yadav A., Pathak P., Altan T., (2009), Determination of the Flow Stress of Five AHSS Sheet Materials (DP 600, DP 780, DP 780-CR, DP 780-HY and TRIP 780) using the Uniaxial Tensile and the Biaxial Viscous Pressure Bulge (VPB) Tests, Journal of Material Processing Technology, (In the progress of publication) Nasser A., Sung J., Kim H., Yadav A., Palaniswany H., (2009), Forming of Advanced High Strength Steels (AHSS) Chapter for ASM Sheet Metal Forming Handbook, Editor: Prof. Taylan Altan (In Progress) Nasser A., (2007), Supplier Evaluation and Selection Module for Arab Certified Quality Manager (ACQM), Arab Knowledge and Management Society (AKMS), 1 st Edition, Department of National Library, Amman, Jordan FIELD OF STUDY Major Field: Industrial and Systems Engineering (Manufacturing) viii

10 NOMENCLATURE Latin Letters d c h d h m,f and h m,s h s,f and h s,s M p ΔR R c Instantaneous cross sectional area (Tensile test) Original cross sectional area (Tensile test) Diameter of die cavity (Bulge test) Engineering strain in axial direction (Tensile test) The objective function to be minimized (Optimization Methodology) Instantaneous load (Tensile test) Clamping force (Bulge test) Dome height (Bulge test) The measured dome height at time t (Optimization Methodology) The simulation dome height at time t (Optimization Methodology) The measured dome heights at time t in the fast and slow tests, respectively (Optimization Methodology) The simulation dome heights at time t in the fast and slow simulations, respectively (Optimization Methodology) Strength Coefficient Instantaneous gauge length (Tensile test) Initial gauge length (Tensile test) Strain rate sensitivity exponent Number of datapoints used to apply the FE optimization methodology for the fast test at elevated temperature Strain hardening exponent Number of datapoints used to apply the FE optimization methodology at room temperature (or for the slow test at elevated temperature) Bulging pressure (Bulge test) Strain ratio (Plastic Anisotropy or Normal Anisotropy) Average strain ratio Planer anisotropy Strain ratio in the rolling direction Strain ratio 45 o to the rolling direction Strain ratio in the transverse direction Radii of curvature in the principle directions at the dome apex (Bulge test/non-axisymmetric) Die corner radius (Bulge test) ix

11 R d S t d Radius of curvature at dome apex (Bulge test) Engineering stress (Tensile test) Time point at which simulation and experiment were compared (Optimization Methodology) Initial sheet thickness (Bulge test) Instantaneous thickness at dome apex (Bulge test) Greek Letters and and Effective strain True (effective) strain rates before and after the jump in the Jump Rate Method (Tensile Test) True strain in axial direction (Tensile test) True strain in thickness direction (Tensile test, Bulge test) True strain in width direction (Tensile test) Principle strains in the sheet surface (Bulge test) Principle strain in the sheet thickness direction (Bulge test) True stress in axial direction (Tensile test) Effective stress Principal stresses in the sheet surface (Bulge test) Principal stress in the sheet thickness direction (Bulge test) True (effective) stress before and after the strain rate jump in the Jump Rate Method (Tensile Test) Effective stress corrected for anisotropy (Bulge test) Effective stress not corrected for anisotropy (Bulge test) x

12 TABLE OF CONTENTS ABSTRACT... ii ACKNOWLEDGEMENT... vi VITA... vii NOMENCLATURE... ix LIST OF FIGURES... xv LIST OF TABLES... xxi CHAPTER 1 INTRODUCTION AND MOTIVATION Sheet Metal Forming Deep Drawing Sheet Hydroforming High Strength and Light Weight Sheet Materials Advanced High Strength Steels (AHSS) Aluminum Alloys CHAPTER 2 OBJECTIVES AND APPROACH Objectives Rational of the Study Approach CHAPTER 3 BACKGROUND AND LITERATURE REVIEW Determination of the Flow Stress of Sheet Metals Uniaxial Tension Biaxial Tension/ Bulge test xi

13 3.2 Mechanical Properties of AHSS as related to Sheet Metal Forming Mechanical Properties of Aluminum Alloys as related to Sheet Metal Forming Strain Localization (Necking) in Sheet Metal Forming Principles of Sheet Hydroforming with a Punch (SHF-P) Overview of Deep Drawing Description, Advantages, and Disadvantages of SHF-P Process Process Window in SHF-P Process CHAPTER 4 DETERMINATION OF THE FLOW STRESS OF FIVE AHSS SHEET MATERIALS AT ROOM TEMPERATURE Experimental Setup-Uniaxial Tensile Test Experimental Setup-VPB Test Testing Matrix VPB Test (Combined FE - Membrane Theory Inverse Analysis) Isotropic Materials Anisotropic Materials VPB test (Combined FE - Optimization Inverse Analysis) Results Tensile Test VPB Test (Combined FE - Membrane Theory Inverse Analysis) VPB Test (Combined FE - Optimization Inverse Analysis) Comparison of Different Techniques Variation of Strain Hardening and the Suitability of the Power Law Fit CHAPTER 5 DETERMINATION OF THE FLOW STRESS OF ALLUMINUM SHEET MATERIALS AT ELEVATED TEMPERATURE Experimental Setup (Machine and Tool Design) Testing Matrix xii

14 5.3 Combined FE - Optimization Inverse Analysis at Elevated Temperature Results Problems Encountered and Solved Problems Encountered and not Solved Experimental data CHAPTER 6 A SYSTEMATIC METHODOLOGY FOR DESIGNING A SHF-P PROCESS USING FE SIMULATIONS Model Part and Tools Geometry Approach and Methodology for Designing SHF-P Process using FE Simulations General Approach Detailed Methodology FE Model using Pamstamp 2G Simulation Matrix Stretch Forming and hydroforming without Draw-In Preliminary Simulation of Deep Drawing and Hydroforming with Draw-In Deep Drawing and Hydroforming with Draw-In (According to the Proposed Methodology) Results Stretch Forming and hydroforming without Draw-In Preliminary Simulation of Deep Drawing and Hydroforming with Draw-In Deep Drawing and Hydroforming with Draw-In (According to the Proposed Methodology) CHAPTER 7 DISCUSSION, CONCLUSIONS AND FUTURE WORK Discussion and Conclusions Characterization of AHSS at Room Temperature xiii

15 7.1.2 Characterization of Aluminum Alloys at Elevated Temperature Design of SHF-P Process Future Work REFERENCES APPENDIX A AQUADRAW MODULE IN PAMSTAMP 2G xiv

16 LIST OF FIGURES Figure 1.1 Classification of metals manufacturing processes as related to this study... 2 Figure 1.2 Schematic showing the basic deep drawing operation [Marciniak et al, 2002]... 5 Figure 1.3 A non-axisymmetric part made by deep drawing [Palaniswany, 2007] 5 Figure 1.4 Schematic illustration of (a) the SHF-P process [Aust, 2001] (b) SHF-D process [Palaniswany, 2007]... 6 Figure 1.5 Example parts produced by (a) the SHF-P process [Maki, 2003] (b) the SHF-D process [Yadav, 2008]... 7 Figure 1.6 Example part (B-Pillar) usually made from higher strength AHSS grades [Fekete, 2006]... 8 Figure 1.7 Total Elongation vs. Ultimate Tensile Strength Banana Curve of automotive steels [World, 2009]... 9 Figure 1.8 Microstructure of DP steels [Sung et al, 2007]... 9 Figure 1.9 Microstructure of TRIP steels [Sung et al, 2007] Figure 3.1 Viscous Pressure Bulge (VPB) test tooling [Nasser et al, 2009] Figure 3.2 Geometrical features of the VPB test [Nasser et al, 2009] (nomenclature is before chapter 1) Figure 3.3 Variation of the instantaneous n-value with engineering strain for HSLA 350/450, DP 350/600, and TRIP 350/600 [World, 2009] Figure 3.4 Relationship between the r-value and the UTS of various steel Materials [Sadakopan et al, 2003] Figure 3.5 Variation of instantaneous strain hardening of DP 600 and TRIP 600 with sheet thickness [Sadakopan et al, 2003] Figure 3.6 Flow stress curves of TRIP 800 coming from different suppliers [Khaleel et al, 2005] Figure 3.7 Engineering Stress-strain curves of AA3003-H111 at different temperatures and a strain rate of sec -1 [Abbedrabbo et al, 2006-b] Figure 3.8 True stress-true strain curves of AA5754-O at different temperatures and a strain rate of sec -1 [Abbedrabbo et al, 2006-a] xv

17 Figure 3.9 Effect of strain rate on the flow stress of AA3003-H111 obtained by the tensile test at four temperatures; 25 o C, 93.3 o C, o C, and 260 o C. Jump-rate test was used (note that at 150 o C, the sample failed at 150 min -1. Thus, data is not available after that). [Abbedrabbo et al, 2006-b] Figure 3.10 Schematic illustration of the deep drawing process of a round cup [Kalpakjian et al, 2009] Figure 3.11 Schematic illustration of the variation of sheet thickness in deep drawing using flat-headed punch (left) and hemispherical-headed punch (right). (Thickness variation is exaggerated) [Johnson et al, 1973] Figure 3.12 State of stress (a) in the flange and (b) in the side wall during deep drawing of a cylindrical cup [Kalpakjian et al, 2003] Figure 3.13 Process window in the SHF-P Process [Palaniswany, 2007] Figure 4.1 A flow chart describing the FE-based inverse analysis methodology used to determine the flow stress curve of sheet materials [Gutscher et al, 2004] 50 Figure 4.2 (left) Schematic of the dome height evolution with time (or pressure). (right) Schematic showing how the calculated (simulation) dome height may deviate from the measured dome height if the simulation flow stress input is not correct [Penter et al, 2008] Figure 4.3 3D view of design space, showing objective function (response) obtained for each combination of K and n (design variables) [Penter et al, 2008] 54 Figure 4.4 A schematic showing the selected design points (red, big) and the computationally expensive full factorial points (black, small) [Penter et al, 2008] Figure 4.5 Minimization of objective function 'E' using RSM as applied to room temperature bulge test. In each iteration (set of 10 FE simulations), the margins for 'K' and 'n-value' keep shrinking to a smaller design space, until the objective function is minimized (the convergence criterion is met). (left) the result of the second iteration. (right) the result of the final iteration [Penter et al, 2008] Figure 4.6 Comparison of Engineering Stress - Engineering Strain curves of various AHSS grades obtained by the tensile test Figure 4.7 Comparison of True Stress - True Strain curves of various AHSS grades obtained by tensile test Figure 4.8 True Stress - True Strain curves of DP 780-HY at 0, 45, and 90 degrees with respect to rolling direction obtained by tensile test Figure 4.9 Uniform and Total Elongation of various AHSS grades (Gauge Length: 2 in) (Average values are shown) xvi

18 Figure 4.10 UTS and 0.2% Offset Yield Strength of various AHSS grades (Average UTS values are shown) Figure 4.11Experimental Pressure versus time curve for sample 1 of TRIP 780 steel sheet material Figure 4.12 Example tested specimens for TRIP 780 sheet material (a) sample burst (b) sample not burst Figure 4.13 Burst pressures of the five AHSS materials tested Figure 4.14 Experimental pressure versus dome height curves obtained from the VPB test for the five AHSS sheets materials tested (These curves are the measured curves without any extrapolation) Figure 4.15 Comparison of the flow stress curves of the five AHSS materials tested using the VPB test (these curves are neither corrected for anisotropy, nor extrapolated) Figure 4.16 Pressure versus dome height curve (for TRIP780, sample 6) extrapolated from last measured datapoint (212 bars) up to burst pressure (226 bars) using second order polynomial approximation Figure 4.17 The flow stress curve of TRIP 780 (sample 6) obtained from both experimentally measured and extrapolated pressure vs. dome height curves Figure 4.18 Optimization history of the design variables K and n for DP 600. Number of iterations to converge is Figure 4.19 Flow Stress curves of the five AHSS materials tested obtained using the combined FE-optimization methodology. Curves are plotted up to the last datapoint obtained from the combined FE-membrane theory methodology (also shown in the figure, the K-value in MPa and the n value) Figure 4.20 Comparison of True Stress- strain curves of DP 600 determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) Figure 4.21 Comparison of True Stress- strain curves of DP 780 determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) Figure 4.22 Comparison of True Stress- strain curves of DP 780-CR determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) Figure 4.23 Comparison of True Stress- strain curves of DP 780-HY determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) xvii

19 Figure 4.24 Comparison of True Stress- strain curves of TRIP 780 determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) Figure 4.25 Normalized Strain Hardening (NSH) vs. Strain for DP 600 obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve (Note that data for DP 600 was collected up to bursting since a sample accidentally burst during the test) Figure 4.26 Normalized Strain Hardening (NSH) vs. Strain for DP 780 obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve Figure 4.27 Normalized Strain Hardening (NSH) vs. Strain for DP 780-CR obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve Figure 4.28 Normalized Strain Hardening (NSH) vs. Strain for DP 780-HY obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve (Note that data for DP 780-HY was collected up to bursting since a sample accidentally burst during the test) Figure 4.29 Normalized Strain Hardening (NSH) vs. Strain for TRIP 780 obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve Figure 5.1 A schematic of the Fluid-based Elevated Temperature Biaxial Bulge Test Apparatus [Designed by the Applied Engineering Solutions (AES), LLC] Figure 5.2 Schematics showing the design and dimensions of (a) the tools, (b) lockbead (within the tools), designed to be suitable for the ET bulge test [Yadav, 2008] Figure 5.3 A schematic showing the clamped sheet during the bulging process and the LVDTs which were planned to be used to measure the dome height and sample curvature profile [Designed by the Applied Engineering Solutions (AES), LLC] Figure 5.4 A picture showing the arrangement designed to measure the sample bulge curvature profile without the need to submerge the LVDTs in the heated fluid [Designed by the Applied Engineering Solutions (AES), LLC] Figure 5.5 The fluid-based elevated temperature biaxial bulge test apparatus [Designed by the Applied Engineering Solutions (AES), LLC] Figure 5.6 (left) A schematic showing the fast (high pressurization rate) and slow (low pressurization rate) pressure curves. (right) a schematic showing the xviii

20 difference in dome height between two samples, one pressurized fast and the other pressurized slow Figure 5.7 Experimental Pressure vs. Dome height curves of AA3003-O at three temperatures; 200 o C, 230 o C, 260 o C, and two speeds; fast (2 in 3 /sec) and slow (0.2 in 3 /sec). Note that for the fast test, increasing the temperature from 200 o C to 230 o C, resulted in an increase in the pressure Figure 5.8 Experimental Pressure vs. Dome height curves of AA5182-O at three temperatures; 200 o C, 230 o C, 260 o C, and two speeds; fast (2 in 3 /sec) and slow (0.2 in 3 /sec) Figure 5.9 Experimental Pressure vs. Dome height curves of AA5754-O at three temperatures; 200 o C, 230 o C, 260 o C, and two speeds; fast (2 in 3 /sec) and slow (0.2 in 3 /sec) Figure 6.1 One quarter of the model part to be made by the SHF-P process Figure 6.2 2D sketch of the tools geometry and dimensions. The sketch shows the blank holder and the die with a lockbead. Another set of tooling similar to this, but without a lockbead, will also be used Figure 6.3 FE model of the SHF-P (a) without a lockbead (b) with a lockbead. Prepared using Pamstamp 2G 2007 (reverse punch and die corner radius are parts of the pressure pot) Figure 6.4 Schematics showing (a) the punch full stroke and (b) the locking stroke (if a lockbead is used) Figure 6.5 Flow Stress curve of AA5754-O (1 mm) obtained using the VPB test (data is not extrapolated) [Penter et al, 2008] Figure 6.6 Simulation matrix of stretch forming with and without pot pressure 98 Figure 6.7 Preliminary simulation matrix of deep drawing and SHF-P with drawin Figure 6.8 Simulation matrix of deep drawing and SHF-P with draw-in (according to the proposed methodology) Figure 6.9 BHF curves used in simulating the deep drawing process with 240 mm blank radius. Also shown (with a circle) the punch stroke at which the flange started to wrinkle in the simulation (details can be found in the Results section) Figure 6.10 Pot pressure curves used in simulating the SHF-P process with 240 mm blank radius and BHF curve 4 selected from deep drawing simulations plus an addition force to prevent blankholder lifting because of the pot pressure. The extra force applied is also shown for each curve xix

21 Figure 6.11 Comparison of the thinning distribution in stretch forming simulations with zero and 100 bars pot pressure, at a punch stroke of 13 mm. It can be seen that thinning at punch corner radius (point D) increases with pressure increase, indicating that SHF-P is detrimental if the sheet is totally clamped (stretch forming). Other pressure values were tried and shown to give similar results Figure 6.12 Effect of BHF on the thinning distribution in deep drawing simulation of mm radius sheet (Material: AA5754-O). Two BHF were used; 60, and 140 KN. Thinning was recorded at 20 mm stroke. Only thinning in the punch-die clearance is shown Figure 6.13 Effect of pot pressure on the thinning distribution in SHF-P simulation of mm radius sheet (Material: AA5754-O). Two pot pressure were used; 40, and 60 bars. 140 KN BHF was used in both simulations. Thinning was recorded at 20 mm stroke. Only thinning in the punch-die clearance is shown Figure 6.14 Sheet bulging (in the punch-die clearance) against the drawing direction in SHF-P simulations with two different pot pressures; 40 and 60 bars (Material: AA5754-O). Excessive pot pressure stretch forms (and thins) the sheet Figure 6.15 Comparison of thinning distribution at 20 mm stroke in deep drawing and SHF-P (40 bars pot pressure) obtained by FE simulations (Material: AA5754-O). The BHF in the two simulations is 140 KN. Thinning in SHF-P is lower than deep drawing. Two necks form in deep drawing, while only one forms in SHF-P Figure 6.16 Comparison of the thinning distribution at the end of the stroke between deep drawing (with selected BHF curve 4) and SHF-P with two different pressure curves (see simulation matrix). Note the considerable improvement in thinning distribution when using SHF-P xx

22 LIST OF TABLES Table 1.1 Sheet Metal Forming Process as a System [Sung et al, 2007]... 3 Table 1.2 Designation and general properties of Wrought Aluminum Alloys [based on Kalpakjian et al, 2009] Table 1.3 Temper designation of wrought and cast aluminum alloys [Stamping, Nov 2008] Table 3.1 Hardening parameters of three aluminum alloys as a function of temperature obtained by fitting the flow stress data obtained from the uniaxial tensile test. Materials are assumed to follow the Field and Backofen constitutive model [based on Abbedrabbo et al, 2006-a and Abbedrabbo et al, 2006-b] Table 3.2 Summary of possible defects in the SHF-P process, and corresponding causes and solutions. Reference is made to Figure Prepared based on [Kaya 2008, Palaniswany 2007, Yadav 2008] Table 4.1 The test matrix used for the tensile and VPB tests of the five AHSS sheet materials Table 4.2 Comparison of Anisotropy Ratios of various AHSS grades Table 4.3 Comparison of the K and n-values obtained using both the tensile and VPB tests (two methodologies) for the five AHSS materials Table 5.1 Testing matrix of AA5754-O, AA5182-O, and AA3003-O at elevated temperature Table 6.1 Summary of the parameters used in the deep drawing and SHF-P FE simulations Table 6.2 Simulation results of applying step 1 of the proposed methodology; Initial estimation of the blank radius. A preliminary BHF of 60 KN was used Table 6.3 Simulation results of applying step 2 of the proposed methodology; Initial estimation of the BHF curve Table 7.1 Comparison between the stress levels in the tensile and VPB tests (calculated using the combined FE-Membrane theory methodology) at a strain values equal to the true strain at the onset of necking in the tensile test xxi

23 Table 7.2 Comparison between the maximum true strain that can be obtained in the tensile test and that obtained in the VPB test (calculated using the combined FE-Membrane theory methodology) xxii

24 CHAPTER 1 INTRODUCTION AND MOTIVATION 1.1 Sheet Metal Forming Of the four families of metals manufacturing processes (see Figure 1.1), metal forming is a major family where the plasticity property of metallic materials is utilized to form them into useful shapes. Metal forming is classified into sheet forming and bulk forming. Sheet forming is a type of metal forming by which bends, shallow and deep recessed shapes are made from a sheet metal. The initial workpiece (sheet) has a large surface area to volume ratio, as opposed to the billet in bulk forming which has a low ratio. Another difference is that stretching (tensile stresses) is predominant in sheet forming processes, while compression is predominant in bulk forming. To successfully design or improve a sheet metal forming process, it should be considered as a system of components/ elements. A fundamental understanding of the relationships between process inputs (such as the sheet, the tools, sheet/tools interfaces, equipment) and process output (product) is extremely important. Typical components of the sheet metal forming process are shown in Table

25 In this study, we focus on three sheet metal forming processes; Drawing, Stretch forming, and Hydroforming. The first two are widely used, where the third is a non-conventional process used for special applications. The following sections describe these processes briefly. More details are given in the Background and Literature Review chapter. Figure 1.1 Classification of metals manufacturing processes as related to this study 2

26 Sheet material Tooling Condition at tool/material interface Deformation Zone Equipment used Product Flow stress (as a function of strain, strain rate, temperature and microstructure). Formability (forming limit diagrams, Stretch bend limits). Surface Texture. Initial conditions (composition, history/ prestrain). Plastic anisotropy. Blank size, location, and thickness. Tool geometry and forces. Surface conditions. Material / heat treatment / hardness. Temperature. Lubricant type and temperature. Insulation and cooling characteristics of the interface layer. Lubricity and frictional shear stress. Characteristic related to lubricant application and removal. Strain (kinematics), strain rate. Stresses (variation during deformation). Temperatures (heat generation and transfer). Speed / production rate. Cushion capabilities. Force / energy capabilities of press ram. Rigidity and accuracy. Geometry and failure. Dimensional accuracy/tolerances. Surface finish. Microstructure, metallurgical and mechanical properties. Table 1.1 Sheet Metal Forming Process as a System [Sung et al, 2007] 3

27 1.2 Deep Drawing Deep Drawing is a sheet metal forming process by which cylindrical or cylindrical-like shapes are made from a sheet metal blank. Figure 1.2 shows the basic deep drawing operation. Initially the sheet is held between the die and blank holder. After that, the punch moves down and draws the sheet into the die cavity. If the punch stroke is small with respect to the punch diameter, then the process is called Shallow Drawing. If the sheet is totally clamped in the flange region and not allowed to flow into the die cavity, then the process is called Stretch Forming. The most important defects observed in the deep drawing process are tearing in the side wall or wrinkling in the flange. Process parameters should be properly selected to eliminate defects. Usually deep drawing is performed at room temperature. However, for some materials, the sheet material may be heated in the flange region to improve the formability. Deep drawing is used to produce high variety of products, such as beverage cans, pans, sinks, containers, and automotive panels [Kalpakjian et al, 2009]. Figure 1.3 shows an example of a non-axisymmetric part produced by deep drawing. 4

28 Figure 1.2 Schematic showing the basic deep drawing operation [Marciniak et al, 2002] Figure 1.3 A non-axisymmetric part made by deep drawing [Palaniswany, 2007] 5

29 1.3 Sheet Hydroforming Sheet hydroforming (SHF) is similar to deep drawing except that either the punch or the die is replaced by a pressurized hydraulic medium. If the die is eliminated, then the process is called sheet hydroforming with a Punch (SHF-P) and the pressurized fluid forms the sheet around the punch (see Figure 1.4-a). If the punch is eliminated, then the process is called Sheet Hydroforming with a Die (SHF-P) or Hydro-Mechanical Deep Drawing (HMD) and the pressurized fluid forms the sheet in the die cavity (see Figure 1.4-b). Example parts produced by sheet hydroforming are shown in Figure 1.5. The improved drawability and the elimination of one piece of tooling are the main advantages of SHF. On the other hand, it is a slow process and only feasible for low production quantities of difficult-to-draw parts. Part of this study is concerned about simulating the SHF- P process. Therefore, a detailed description of this process, its mechanics, advantages and disadvantages, as compared to conventional deep drawing will be given in the Background and Literature Review Chapter. (a) (b) Figure 1.4 Schematic illustration of (a) the SHF-P process [Aust, 2001] (b) SHF-D process [Palaniswany, 2007] 6

30 (a) (b) Figure 1.5 Example parts produced by (a) the SHF-P process [Maki, 2003] (b) the SHF-D process [Yadav, 2008] 1.4 High Strength and Light Weight Sheet Materials Advanced High Strength Steels (AHSS) Fuel economy, environmental concerns, and crashworthiness are the main reasons for replacing conventional steels by the Advanced High Strength Steels (AHSS) in the automotive industry. It was reported that replacing mild steel with High Strength Steels (HSS) may result in 10-25% reduction in mass [Powers, 2000]. Figure 1.6 shows an example part (B-Pillar), critical for crash resistance of the car, usually made of higher strength AHSS grades. AHSS are multi-phase steels which contain martensite, bainite, and/or retained austenite in quantities sufficient to produce unique mechanical properties [Shaw et al, 2001-a]. This study is concerned about two types of AHSS; Dual Phase (DP) steels and Transformation-Induced Plasticity (TRIP) steels. Other types include Martensitic Steels (MS), Complex Phase (CP) steels, Hot Forming (HF) steels, and Twinning-Induced Plasticity (TWIP) steels. Some of these types 7

31 are shown in Figure 1.7. The microstructure of DP steels is composed of ferrite and martensite (see Figure 1.8), while the microstructure of TRIP steels is a matrix of ferrite, in which martensite and/or bainite, and more than 5% retained austenite exist (see Figure 1.9). Figure 1.6 Example part (B-Pillar) usually made from higher strength AHSS grades [Fekete, 2006] 8

32 Mild Steels AHSS HSS Figure 1.7 Total Elongation vs. Ultimate Tensile Strength Banana Curve of automotive steels [World, 2009] (a) SEM image of DP Steel (b) Schematic of the DP steel microstructure Figure 1.8 Microstructure of DP steels [Sung et al, 2007] 9

33 (a) SEM image of TRIP Steel (b) Schematic of the TRIP steel microstructure Figure 1.9 Microstructure of TRIP steels [Sung et al, 2007] The increased formability of AHSS is the main advantage over conventional HSS. Nevertheless, compared to Draw Quality Steels (DQS), AHSS steels have relatively low ductility [Nasser et al, 2009]. Figure 1.7 shows the relation between the total elongation (EL) and Ultimate Tensile Strength (UTS) for different automotive steels. This curve is usually referred to as the Banana Curve. This chart shows a dramatic drop in the EL with increased strength of the material. Moreover, it shows an overlap between different grades families, which suggests that classification based on this chart only is not sufficient [Sung et al, 2007]. In this study, the flow stress and strain ratios of five AHSS grades, of interest to the automotive industry, are determined using both the tensile and bulge test, to develop a fundamental understanding of the mechanical behavior of these materials as related to sheet metal forming. 10

34 1.4.2 Aluminum Alloys Similar to AHSS, fuel economy and environmental concerns are the two main reasons for the trend to replace conventional steels with light weight metals such as aluminum and magnesium alloys. However, the manufacturing of these alloys by conventional stamping is difficult, due to their limited formability at room temperature. To overcome this problem, non-conventional operations such as warm forming or SHF can be used. Table 1.2 shows the designation and general properties of Wrought Aluminum Alloys. Table 1.3 shows the temper designation of both wrought and cast aluminum alloys. Two series are related to this study; 3xxx and 5xxx. The former is softer and more formable. Three sheet alloys; AA5754-O, AA5182-O, and AA3003-O are tested at elevated temperature (200 o C to 300 o C) using the Viscous Pressure Bulge (VPB) test to obtain their flow stress curves. In addition, room temperature SHF-P of AA5754-O was simulated using the FE software Pamstamp 2G 2007 to understand the fundamentals of this relatively new process. 11

35 Designation Major alloying General properties elements 1xxx Pure Al Excellent corrosion resistance, high electrical and thermal conductivity, good workability, low strength, not heat treatable 2xxx Al, Cu High strength-to-weight ratio, low corrosion resistance, heat treatable 3xxx Al, Mn Good workability, moderate strength, generally not-heat treatable 4xxx Al, Si Lower melting point, forms an oxide film of dark grey to charcoal in color, generally nonheat treatable 5xxx Al, Mg Good corrosion resistance and weldability, moderate to high strength, non-heat treatable 6xxx Al, Mg, Si Medium strength, good formability, machinability, weldability, and corrosion resistance, heat treatable 7xxx Al, Zn Moderate to very high strength, heat treatable 8xxx others - Table 1.2 Designation and general properties of Wrought Aluminum Alloys [based on Kalpakjian et al, 2009] Temper Description Designation F As fabricated O Annealed H Strain hardened (wrought product only) W Solution heat treatment T Heat treated to produce stable tempers other than F, O, or H Table 1.3 Temper designation of wrought and cast aluminum alloys [Stamping, Nov 2008] 12

36 CHAPTER 2 OBJECTIVES AND APPROACH 2.1 Objectives The overall objective of this study is to determine the flow stress of AHSS and aluminum sheet materials, of interest to the automotive industry, at room and elevated temperatures, respectively. In addition, to optimize critical process parameters in the SHF-P process by using FE simulation. The detailed objectives of this study are to: 1) Determine the flow stress curves of five AHSS sheet materials; DP 600, DP 780, DP 780-CR, DP 780-HY, and TRIP 780, at room temperature. 2) Compare the flow stress curves obtained under balanced biaxial state of stress with those obtained under uniaxial condition for the AHSS materials tested. 3) Investigate the suitability, advantages and disadvantages of different inverse analysis methodologies for obtaining the flow stress curves of sheet materials tested using the VPB test. 4) Study the effect of anisotropy correction on the flow stress curves of the AHSS materials tested using the VPB test. 13

37 5) Investigate the strain hardening characteristics and formability of the AHSS materials tested, as related to sheet metal forming. 6) Extend the FE-based optimization methodology for determining the flow stress of sheet materials from the room temperature domain to elevated temperature. 7) Investigate the difficulties associated with testing sheet materials at elevated temperature using the hydraulic bulge test, as well as the challenges in analyzing the experimental data for obtaining the material properties. 8) Develop a fundamental understanding of the effect of various process parameters involved in the SHF-P process. 9) Investigate the capabilities of FE simulation in modeling the SHF-P process. 10) Develop a simple and systematic methodology for designing/ optimizing the SHF-P process using FE simulation. 11) Develop simple and applicable guidelines for designing/ optimizing the SHF-P process. 12) Quantify the improvement in the thinning distribution attained by replacing the deep drawing process by the SHF-P process. 14

38 2.2 Rational of the Study The following points emphasize the importance of this research work: 1) Crash worthiness, fuel economy, and environmental concerns are driving forces for the increased use of AHSS and aluminum sheet materials, especially in the automotive industry. 2) Determining the flow stress of AHSS and understanding the its unique mechanical properties as compared to conventional DDS are necessary for material selection and process/ tools design. 3) The low formability of aluminum alloys is a driving force for nonconventional processes such as warm forming and/or sheet hydroforming. 4) Determining the flow stress of sheet materials in the warm forming range under near-production state of stress is necessary for running reliable FE simulations. 5) Sheet hydroforming is a relatively new process. Thus, it is important to understand the process parameters and to develop guidelines for process design, in order to avoid expensive experimental trials. 15

39 2.3 Approach The following tasks were performed to achieve the objectives of the study: 1) Determination of the mechanical properties of the five AHSS materials using both the uniaxial tensile and biaxial VPB tests (Chapter 4). 2) Testing a promising methodology for determining the flow stress of sheet materials at elevated temperature by applying it initially to the AHSS room temperature VPB test (point 1) (Chapter 4). 3) Extending the methodology (point 2) to consider the strain rate effect in order to be applicable for the elevated temperature bulge test (Chapter 5). 4) Testing different aluminum alloys at elevated temperature using the bulge test and applying the elevated temperature methodology (point 3) to obtain the flow stress (Chapter 5). 5) Suggesting a methodology for designing process parameters (blank radius, pot pressure, blankholding force) in SHF-P of AA5754-O and using FE simulation to validate the methodology (Chapter 6). 16

40 CHAPTER 3 BACKGROUND AND LITERATURE REVIEW 3.1 Determination of the Flow Stress of Sheet Metals Uniaxial Tension Note: This section is prepared based on [Hosford et al 1993, Kalpakjian et al 2009, ASTM E , and ASTM E ]. In the sheet tensile test, the testing specimen (coupon) is usually prepared according to the dimensions specified in the ASTM standard; ASTM E614 [ASTM E646-07, 2007]. The method of preparing the specimen (blanking, wire EDM, ) should be reported since the edge quality may affect the testing results. The specimen is gripped from the two ends and loaded in the axial direction. It is common to use universal testing machines for the tensile test. The load is continuously increased until the specimen fails. Both the load and extension are measured. The specimen gauge length is the length of which the extension is measured. Usually, it is two inches and is measured using a device called the Extensometer. Sometimes, the extensometer is calibrated to directly give the engineering strain. The Engineering Strain (e) is defined as the change in the gauge length divided by the original gauge length: 17 Equation 1

41 Note: All nomenclatures are summarized before the beginning of chapter 1. The Engineering Stress (S) is defined as the instantaneous load divided by the original cross sectional area: Equation 2 The incremental true strain ( is defined at any moment during the test as the incremental change in gauge length divided by the instantaneous gauge length. Based on this definition, the total true strain ( can be calculated using: Equation 3 The true stress is defined at any moment during the test as the instantaneous load divided by the instantaneous cross sectional area: Equation 4 The relations between the true and engineering stress and strain are: Equation 5 Equation 6 The true stress-true strain curve of the material is commonly referred to as the Flow Stress curve. A material model may be fit into the flow stress curve of the material. The most common material model at room temperature is the Hollomon Power Law: Equation 7 At elevated temperatures where the strain rate sensitivity becomes more important, the Field and Backofen material model can be used: Equation 8 18

42 More than one method can be used to obtain the m-value in the tensile test. Only one method, called the Jump rate Method will be briefly described, since it will be referred to later in this chapter. In this method, the strain rate is suddenly increased during the test and the flow stress is recorded instantaneously before and after the jump. Using Equation 8, the following formula can be easily derived to calculate the m-value: Equation 9 An important mechanical property in sheet metal forming is the plastic anisotropy. Plastic anisotropy (also called normal anisotropy or strain ratio) is usually determined from the tensile test. It is defined as the ratio of the width true strain to the thickness true strain: Equation 10 The -value may change from time to time during the tensile test. Therefore, to compare different materials, the - value should be determined at the same axial strain. For convenience, the thickness strain is not measured. Instead, the axial and width strains are measured and the thickness strain is calculated from the principle of volume constancy: Equation 11 Note: the ASTM standard E [ASTM E517-00, 2006] states that the plastic component of the total strain should be used in calculating the strain ratio. 19

43 Subtracting the elastic strain from the total strain will not have a considerable effect on the R-values and therefore in this study, the total strain values were used in all calculations. The -value may also change from a direction to another in the plane of the sheet. Therefore, it is common to obtain the -value in the rolling direction (0 o ), transverse direction (90 o ), and 45 degrees to the rolling direction (45 o ) and report the average value: Equation 12 Materials having high deforms easier in the width direction compared to the thickness direction. This thickness change resistance is desirable when the sheet is used in deep drawing applications. More details will be given later. The variation of the - value from a direction to another in the plane of the sheet is not desirable in deep drawing since it will cause variation in the flow of the flange from a direction to another, resulting in what is called Earing. The tendency of the sheet material to ear when deep drawn is characterized by a parameter called the Planer Anisotropy ( : Equation Biaxial Tension/ Bulge test To determine the Flow Stress of sheet materials under biaxial state of stress, the bulge test can be used. At the ERC/NSM, a viscous material is used instead of the commonly used hydraulic fluid. Therefore, the name Viscous Pressure Bulge (VPB) test is used. This name will be used throughout this report. 20

44 Figure 3.1 is a schematic of the tooling used in the VPB test. The upper die is connected to the slide and the cushion pins support the lower die (the blank holder) to provide the required clamping force. The punch in the lower die is fixed to the press table and therefore stationary. At the beginning, the tooling is open and the viscous material is filled into the area on the top of the punch. When the tooling closes, the sheet is totally clamped [Figure 3.1-a] between the upper and lower dies using a lockbead to prevent any material draw-in, in order to maintain the sheet in a pure stretching condition throughout the test. The clamping force (the selected press cushion force) depends on the material and thickness tested. The slide then moves down together with the upper die and blank holder. Consequently, the viscous medium is pressurized by the stationary punch and the sheet is bulged into the upper die. Since the tools are axisymmetric, the sheet is bulged under balanced biaxial stress. Figure 3.2 shows the details of the geometrical features of the VPB test tooling. 21

45 Potentiometer Test Sample Upper die Lower die Viscous Medium (a) Before Forming Pressure Transducer Stationary Punch (b) After Forming Figure 3.1 Viscous Pressure Bulge (VPB) test tooling [Nasser et al, 2009] Figure 3.2 Geometrical features of the VPB test [Nasser et al, 2009] (nomenclature is before chapter 1) 22

46 The membrane theory is usually used to calculate the flow stress from the experimental data [Gutscher et al, 2000]. This theory assumes that the dome is spherical in shape and neglects bending stresses in the sheet. The relationship between membrane stresses and process parameters is: Equation 14 Under balanced biaxial tension, which is the case in the bulge test, the formula reduces to: Equation 15 The average compressive stress in the thickness direction is -p/2. Using Von- Mises yield criterion, the effective stress and effective strain can be calculated: Equation 16 Equation 17 Equation 18 Equation 19 It can be noticed from Equations 17 and 19 that the pressure, radius of curvature and thickness at the dome apex should be measured to be able to calculate the effective stress and strain. To reduce the number of measured parameters, different FE-based inverse analysis methodologies are used at the ERC/NSM where only two relatively easy-to-measure parameters are required. These are the bulging pressure, measured using a pressure transducer, and the dome 23

47 height, measured using a potentiometer. More details about these methodologies are given in the Chapter 4. [Hecht et al, 2005] conducted elevated temperature bulge test on magnesium AZ31-O and reported that at high dome heights (dome height/ die cavity diameter > 0.4), the shape of the dome near the apex is no longer spherical and that the best fit to the dome shape is a parabola. CCD cameras were used to instantaneously measure the radius of the dome. [Kaya, 2008] reported a similar result for the same alloy except that the spherical assumption was found to be valid up to a dome height/ die cavity diameter ratio of 0.2. [Koc et al, 2007] tested AA5754-O at elevated temperatures and was able, through controlling the flow rate of the pressurizing fluid, to maintain a nearly constant strain rate at the dome apex. Moreover, the strain at the dome apex was measured by using a noncontact sensor (ARAMIS). However, it was assumed that the dome is spherical in shape and the membrane theory equations were used. In this study, elevated temperature bulge test experiments were made on AA5754-O, AA5182- O, and AA3003-O. 3.2 Mechanical Properties of AHSS as related to Sheet Metal Forming This study is concerned about two types of AHSS, DP and TRIP steels. DP steels, have high initial strain hardening and a high Tensile-to-Yield Strength ratio, which accounts for the relatively high ductility, compared to conventional HSS [Chen et al, 2005 and Shaw et al, 2001-b]. The soft ferrite plastically flows before the hard martensite. The ferrite at the phase boundary encounters high stress concentration resulting in more plastic deformation. This explains the high initial 24

48 strain hardening of DP steels. When the martensite phase starts to deform plastically, the strain hardening rate decreases. TRIP steels retains its strain hardening to high strain values. This is due to the retained austenite-to-martensite phase transformation which takes place during plastic deformation. The formation of the hard martensite, and the stress concentration resulting from the volume expansion during phase transformation, increases the strain hardening of the material and thus both the uniform and total elongation [Sung et al, 2007]. Figure 3.3 Variation of the instantaneous n-value with engineering strain for HSLA 350/450, DP 350/600, and TRIP 350/600 [World, 2009] The variation of the strain hardening characteristic of a material with strain can be illustrated by plotting the instantaneous n-value (d ln /d ln ) vs. strain. Figure 3.3 shows how the instantaneous n-value changes for DP 600 and TRIP 600 as compared to a conventional HSS grade, High Strength-Low Alloy (HSLA) 25

49 steel. It can be seen that the n-value for HSLA steel decreases slightly with strain. The decrease for DP steels is more pronounced. For TRIP steel, the n-value at the beginning is low compared to DP steel. However, it is maintained at a relatively high value to a larger strain, and then drops at the end. The decrease in the n- value for DP 350/600 is explained by the martensite starting to deform plastically. The constant n-value of TRIP 350/600 is explained by the straininduced phase transformation. The following conclusions can be drawn from the discussion above. First, the power law ( which was used extensively to describe the behavior of many materials may not be valid for AHSS because of the variation of the n-value. Second, the fact that the hardening behavior of AHSS changes with time and is highly dependent on the microstructure evolution raises questions on the suitability of using extrapolated flow stress data to run FE simulations. Figure 3.4 shows a clear relationship between the average strain ratio ( ) and the UTS of the material. The stronger the material, the lower the and therefore the formability. A value, slightly below one, is asymptotically reached. The of DP and TRIP steels is close to or slightly less than one. 26

50 Figure 3.4 Relationship between the r-value and the UTS of various steel Materials [Sadakopan et al, 2003] It was reported [Sadakopan et al, 2003] that the mechanical properties of AHSS sheets, coming from the same supplier, may not be consistent. Variation in thickness, heat treatment, coil, and batch may result in different properties. Figure 3.5 shows the variation of instantaneous strain hardening of both DP 600 and TRIP 600 with sheet thickness. Variation in strain hardening behavior will affect the material formability. Figure 3.6 shows the flow stress curves of TRIP 800 sheets coming from different suppliers. It can be seen that strain hardening, uniform elongation and total elongation all are different for the three curves. 27

51 Figure 3.5 Variation of instantaneous strain hardening of DP 600 and TRIP 600 with sheet thickness [Sadakopan et al, 2003] Figure 3.6 Flow stress curves of TRIP 800 coming from different suppliers [Khaleel et al, 2005] 28

52 3.3 Mechanical Properties of Aluminum Alloys as related to Sheet Metal Forming Figure 3.7 shows the flow stress curve of AA 3003-H111 sheets tested by the tensile test in the temperature range from 25 o C to 232 o C. Convection heating was used. The strain rate in the test was sec -1. It can be seen that the UTS decreases from about 115 MPa to 55 MPa when increasing the testing temperature from room temperature to 232 o C. Also, the total elongation increases from about 33% to 50%. This increase in ductility when increasing the temperature is the main reason for the trend toward warm forming of aluminum magnesium alloys. [Abbedrabbo et al, 2006-a] showed similar behavior of AA5754-O and AA5182-O (see Figure 3.8). Figure 3.7 Engineering Stress-strain curves of AA3003-H111 at different temperatures and a strain rate of sec -1 [Abbedrabbo et al, 2006-b] 29

53 Figure 3.8 True stress-true strain curves of AA5754-O at different temperatures and a strain rate of sec -1 [Abbedrabbo et al, 2006-a] [Abbedrabbo et al, 2006-b] used the Jump-rate test to study the strain rate sensitivity of AA3003-H111 at several elevated temperature. Three strain rates; 10, 50, and 150 min -1, were used. Results are shown in Figure 3.9. It is clear that the strain rate effect is more important at elevated temperature. Strain rate sensitivity of AA5754-O and AA5182-O can be found in [Abbedrabbo et al, a]. 30

54 Figure 3.9 Effect of strain rate on the flow stress of AA3003-H111 obtained by the tensile test at four temperatures; 25 o C, 93.3 o C, o C, and 260 o C. Jump-rate test was used (note that at 150 o C, the sample failed at 150 min -1. Thus, data is not available after that). [Abbedrabbo et al, 2006-b] The equations in Table 3.1 [based on Abbedrabbo et al, 2006-a and Abbedrabbo et al, 2006-b] show how the three hardening parameters K, n and m change with temperatures for AA3003-H111, AA5754-O, and AA5182-O. The materials were assumed to follow the Field and Backofen constitutive model ( ) and the parameters were obtained by fitting the experimental data obtained in the uniaxial tensile test. It can be seen that K and n decrease linearly with temperature, while m increases exponentially with temperature. [Li et al, 2003] reported curves relating the n-value of AA5754+Mn and AA5182 with temperature. Trends and curves shapes are similar. 31

55 Hardening parameter K (T a ) in MPa n(t a ) m(t a ) AA3003-H111 AA5754-O AA5182-O *T (for T = o C) *T (for T = o C) *exp(0.0147*T) (for T = o C) *T (for T = o C) *T (for T = o C) *T (for T = o C) *T (for T = o C) *exp(0.0161*T) (for T = o C) *T (for T = o C) *T (for T = o C) *T (for T = o C) *T (for T = o C) *exp( *T) (for T = o C) Table 3.1 Hardening parameters of three aluminum alloys as a function of temperature obtained by fitting the flow stress data obtained from the uniaxial tensile test. Materials are assumed to follow the Field and Backofen constitutive model [based on Abbedrabbo et al, 2006-a and Abbedrabbo et al, 2006-b] a The temperature T is in o C [Li et al, 2003] attributed the increase in the total elongation of AA5754+Mn and AA5182 to the increase in post-uniform elongation. This is related to the higher m-value at elevated temperature which results in more resistance of the material to strain localization in the neck region (where strain rate is high) after instability. Moreover, it was shown that one order of magnitude increase in the strain rate, at elevated temperature, will dramatically reduce the total elongation of these two alloys. Another reason for forming 5xxx series aluminum at elevated temperature is the dynamic strain aging behavior at room behavior which results in Stretcher Strain marks/ Lueder s bands (serrated flow stress curve) [Abbedrabbo et al, 2006-a, Bolt et al, 2001, Sivakumar, 2006]. Lueder s Bands deteriorate the surface quality (results in coarse surface appearance) of the product and may cause difficulties in subsequent coating/ painting operations [Kalpakjian et al, 2009]. The migration 32

56 of the Magnesium solute atoms in 5xxx aluminum to dislocations explains this behavior [Abbedrabbo et al, 2006-a]. Another way of interpreting this phenomenon from the macroscopic perspective is the negative m-value of these alloys at room temperature. [Hosford et al, 1993] reported m-value of for 1 mm-thick AA5182-O sheets. [Abbedrabbo et al, 2006-a] reported that the serrated behavior disappears at temperatures above 93 o C for AA5182-O and above 121 o C for AA5754-O. 3.4 Strain Localization (Necking) in Sheet Metal Forming The formability in sheet metal forming processes highly depends on the resistance of the sheet material to strain localization (necking). In the simple uniaxial tensile test, two main types of necks form; The diffuse type, where the neck forms in the width direction, and the localized type, where it forms in the thickness direction (within the diffuse neck region). Among others, the strain and strain rate hardening of the sheet play an important role in postponing necking, thus increasing the sheet ductility. Strain rate effect will be discussed briefly at the end of this section and the strain hardening effect will be discussed in more details. The diffuse neck in the tensile test forms when the maximum force is reached, while the localized neck forms, in the post-uniform region, close to the fracture point. The criterion for plastic instability (diffuse necking) is [Hosford et al, 1993]: which is from the volume constancy 33

57 Thus the condition for instability in the tensile test is: Equation 20 This value which has to be equal to one in order for the diffuse neck to form is called the Normalized Strain Hardening (NSH) [Bird et al, 1981]. It is the instantaneous slope (strain hardening) of the flow stress curve divided (normalized) by the instantaneous stress. Before necking, the NSH is higher than one and it continuously decreases, even after diffuse necking, up to the fracture point. The localized neck forms when the NSH is about 0.5. The values at which necks form may vary depending on the strain rate sensitivity, the angle of the localized neck with respect to the loading direction, etc. [Bird et al, 1981]. Initial instability under balanced biaxial tension takes place when NSH equals to 0.5, while in plane strain (ex: side cup wall in deep drawing), instability starts at NSH equals to Throughout the tensile test, the cross sectional area continuously decreases, while the strength increases due to strain hardening. Before initial necking, the rate of increase in strength due to strain hardening is higher than the rate of area reduction, thus the load-carrying capacity of the sheet increases. This is why the engineering stress-strain curve increases up to the UTS. Since the slope of the flow stress curve decreases with strain (the material looses from its strain hardening characteristic), a point (instability point) is reached in the test where the rate of area reduction becomes equal to the rate of increase in strength due to strain hardening. At this point, the UTS is reached and the instability condition is started (the specimen will deform under a decreasing load). If the material follows the Hollomon Power Law,, then it can be easily shown using Equation 20 that the condition for necking is [Hosford et al, 34

58 1993]. This is not unexpected since the n-value is a measure of the slope of the flow stress curve (strain hardening behavior) and the necking phenomenon is closely related to strain hardening as described above. In the bulge test (balanced biaxial state of stress), the condition for instability (drop in the membrane force) is [Hosford et al, 1993]. Even at strain value higher than this value, localized neck will not form easily. The reason is that the formation of a localized neck should be accompanied by a local increase in the surface area, which will appear in the form of a local bulge on the dome. The radius of curvature in this local bulge is smaller than elsewhere in the test specimen. Therefore, according to Equation 17, the membrane stress will decrease locally and localized necking will be postponed. Many materials were tested in the Center for Precision Forming (CPF), formerly called the Engineering Research Center for Net Shape Manufacturing (ERC/NSM) using the biaxial bulge test. Experimental results validate the theoretical conclusion that flow stress data can be collected in the bulge test to much higher strain values than can be reached in the uniaxial tensile test. Flow stress data obtained using the bulge test can be found in [Nasser et al 2009, Nasser et al 2008, Nasser et al 2007, Sartkulvanich et al 2008, Penter et al 2008, Pathak et al 2008, Kim et al 2008, Kim et al 2007-a, Kim et al 2007-b, Palaniswamy et al 2007, Yadav et al 2007, Spampinato et al 2006, Bortot et al 2005, Kaya et al 2005, Braedel et al 2005, and Gutscher et al 2000]. Strain localization is more difficult in materials with positive strain rate sensitivity exponent (m). Once the neck forms, the strain rate (and thus the flow stress) in the neck region increases. This will result in more resistance for deformation in the neck region and will allow more deformation to take place in the rest of the specimen/ part. The resulting effect is more post-uniform elongation [Hosford et al, 1993 and Wagoner et al, 1996]. [Hosford et al, 1993] 35

59 argued that since a homogeneous material does not exist, higher m-value will resist early necking and thus increase the uniform elongation as well. 3.5 Principles of Sheet Hydroforming with a Punch (SHF-P) Overview of Deep Drawing Since Deep Drawing is a special case of Sheet Hydroforming with a punch (SHF- P), where the pot pressure is equal to zero (as will be described later), deep drawing principles and mechanics are described here. In the simplest Deep Drawing (DR) of a cylindrical flat-bottom cup, a round blank of initial thickness (T) and diameter (Do) is placed on a die with a round opening (cavity) and a die corner radius, Rd. An annular Blankholder (sometimes called a binder or hold-down ring) is used to hold the blank in place. A cylindrical punch, with a diameter Dp and corner radius Rp moves down to draw the sheet into die opening. The punch-die clearance (c) should be larger than the sheet thickness. Figure 3.10 is a schematic illustration of the deep drawing process. 36

60 Figure 3.10 Schematic illustration of the deep drawing process of a round cup [Kalpakjian et al, 2009] When the punch starts to move down, the sheet in the clearance region stretch bends around the punch and die corner radii. The sharper the radii, the higher the thinning the sheet will undergo. This initial stretching will strain harden the sheet in the clearance and increase it load-carrying capacity, but will also form two necks near the punch corner radius (see Figure 3.11). [Kaya 2008] called this part of the stroke the Critical Stroke and estimated it by Rp + Rd + T. As the punch travels more, the material in the flange (between die and blankholder) will be drawn in the radial direction and subjected to circumferential (hoop) compressive stresses (see Figure 3.12-a). If not held-down with enough Blankholder Force (BHF), compressive stresses in the flange will cause plastic buckling (wrinkling). The induced hoop stresses on elements moving toward the center and the friction forces at the tools-blank interface will resist material flow, thus subjecting the elements in the flange to tensile stresses in the radial direction 37

61 (see Figure 3.12-a). The hoop compressive stress is higher than the radial tensile stress. As a result, the sheet thickens as it flows in the flange region. Figure 3.11 Schematic illustration of the variation of sheet thickness in deep drawing using flat-headed punch (left) and hemispherical-headed punch (right). (Thickness variation is exaggerated) [Johnson et al, 1973] Figure 3.12 State of stress (a) in the flange and (b) in the side wall during deep drawing of a cylindrical cup [Kalpakjian et al, 2003] 38

62 The force required to draw the material in the die opening is transmitted to the flange through the cup side wall. Therefore, the wall is subjected to tensile stresses in the axial direction (see Figure 3.12-b). Since the sheet is stretched in the axial direction, it should contract in both the thickness and hoop direction. However, for cylindrical geometries with small clearances, the sheet will stick to the punch, which will prevent further hoop contraction, putting the sheet in this region in a plane strain condition with tensile hoop stresses (see Figure 3.12-b). Most of the energy requirement (deformation and friction) of the process is consumed in the flange. Therefore, the larger the flange region, the higher the punch force required (and the higher the axial stress in the side wall). If the axial stress in the side wall exceeds a critical value, tearing will occur. The ratio of the blank diameter and punch diameter is called the drawing ratio (DR). If the DR exceeds a critical value, called the Limiting Drawing Ratio (LDR), tearing will occur. The most important factor which affects the LDR is the Average Strain Ratio ( of the material. The higher the, the higher the LDR because of two main reasons: 1) Materials with high are easy to deform in the hoop direction in the flange. Thus, the required punch force is lower. 2) Materials with high are not easy to thin in the side wall. Thinning resistance will increase the load carrying capacity and enable more force to be transmitted to the flange without excessive thinning or tearing. Other factors which affect the LDR include: 1) Friction at the blank-blankholder and blank-die interface. The lower the friction, the higher the LDR. 39

63 2) Friction at the blank-punch interface. The higher the friction, the higher the LDR. As mentioned previously, the sheet usually necks around the punch corner radius. This neck makes strain localization (and tearing) in this region easier, especially if all the punch force is transmitted to the flange through this lower part of the cup. If the friction force between punch and the sheet is high, then part of the punch force will reach the flange through the upper portion of the cup side wall. As a result, the LDR increases. 3) Punch and die corner radii. The higher the radii, the higher the LDR. 4) Material strain hardening. Highly strain hardening materials have higher LDRs. The BHF is an important process design variable. Applying insufficient BHF will result in flange wrinkling, while BHF higher than required may result in side wall tearing. The punch-die clearance is usually 7 to 14% higher than the sheet thickness [Kalpakjian et al, 2009]. Too small a clearance will result in sheet ironing (in the clearance) and probable shearing (since the sheet thickens in the flange). Too high a clearance may cause side wall wrinkling. Warm forming (deep drawing) of aluminum alloys is usually done between 200 o C and 300 o C, in order to benefit from the increase in formability. The die and blankholder are usually heated, especially at the corners (for box-shaped parts) to reduce the flow stress and improve the formability. [Bolt et al, 2001] reported % increase in drawing depth of a box-shaped part of AA5754-O when the temperature was increased from 20 o C to 175 o C. They also reported about 70% increase in the drawing depth of a conical rectangular part when the temperature is increased from 20 o C to 250 o C. Moreover, the tendency for flange wrinkling was reduced. Straight parts of the flange may be cooled by circulating oil/ water to reduce metal flow in these regions, resulting in an effect similar to the draw 40

64 bead effect. Another interesting result is the very small reduction in the hardness of finished parts formed at 250 o C compared to parts formed at room temperature Description, Advantages, and Disadvantages of SHF-P Process Sheet Hydroforming with a Punch (SHF-P) process is similar to regular deep drawing (stamping) operation except that the sheet is drawn into the die cavity against a counter hydraulic pressure in a chamber usually called the pressure pot (see Figure 1.4-a). As mentioned previously, increasing the friction force between the sheet and the punch reduces side wall thinning by reducing the portion of the punch force transmitted to the flange region through the lower, critical, and highly thinned portion of the side cup wall. In SHF-P process, the pot pressure will push the sheet against the punch. The high contact pressure at the sheetpunch interface will increase the friction force, which will reduce the thinning and increase the LDR. Two main types of SHF-P exist. In the first, called the Passive SHF-P, the pressure is generated by the punch moving toward the pot which is full with a relatively incompressible fluid (usually water). The pot pressure profile (pressure vs. time) is controlled by a valve which regulates the fluid flow out of the pot to maintain the required pot pressure curve. In the second type, called the Active SHF-P, an external pump is used to generate the pot pressure. Following are the benefits of the SHF-P Process: 1) Higher LDR than conventional stamping, because: 41

65 a) The pot pressure separates the sheet from the die corner radius. Therefore, no friction energy is consumed at this location, which lowers the punch force and increases the LDR. b) Higher contact pressure between the sheet and punch reduces thinning and increases the LDR. 2) Pot pressure reduces/eliminates side wall wrinkling. 3) Better surface finish since there is no rubbing between the sheet and the die corner. 4) Although not convenient, small leakage of the pressurizing medium from the pot will reduce the friction coefficient between the sheet and die, and may increase the LRD. 5) Female die is not required since the pot pressure can form the sheet against impressions made in the punch. Thus, the cost of tools material, machining, and maintenance, as well as tools manufacturing lead time are all reduced. The disadvantages of SHF-P compared to conventional stamping are: 1) Higher cycle time/ lower production rate. 2) Pot pressure increases both the required ram and blankholder force (larger presses required) 3) Dimensional tolerances may not be attainable without a solid die. 42

66 3.5.3 Process Window in SHF-P Process In the SHF-P process, two main process parameters, the pot pressure and BHF, should be optimized to successfully form a part. The two parameters should be controlled together and can be varied with the punch stroke to produce defect free parts. The limits of the two parameters in which the process operates successfully are called the Process Limits and the region within the limit is called the Process Window (see Figure 3.13). Figure 3.13 Process window in the SHF-P Process [Palaniswany, 2007] Table 3.2 summarizes the possible defects in the SHF-P process, and explains corresponding reasons and solutions. This table can be used as a guideline for 43

67 trial and error experiments and/or FE simulation and will refer to hereinafter. Defects include tearing at upper and lower portions of the cup, bursting in the punch-die clearance, flange wrinkling, side wall wrinkling. [Meinhard et al, 2005] stated that small BHF should be applied at the beginning of the process and then increased toward the end of the process. The reason is that the sheet thickens as it flows in the flange and therefore parts of the flange loose contact with the tools at the end of the stroke and becomes easier to wrinkle. Moreover, higher BHF is required to generate the same moment about the die corner (in order to prevent lifting) at the end of the stroke where the flange width becomes smaller. [Yadav 2008, Kaya 2008, and Palaniswany 2007] used variable (increasing) BHF and pot pressure and showed an increase in the LDR. [Palaniswany, 2007] developed a sequential optimization technique combined with FE simulation to optimize the BHF and pot pressure curves in the SHF-P process. The stroke was divided into small increments. In each increment, the pot pressure and BHF were optimized by running FE simulations. Thinning at the end of the increment was the objective function to be minimized subjected to the constraint that no defects should be observed. After optimizing each increment, the output of the increment was used as an input to the next in a sequential manner, thus the name Sequential Optimization, until the end of the stroke. Although, highly automated, the complexity associated with the optimization makes this methodology difficult to apply in the industry. It was noticed from the work by [Yadav 2008, Palaniswany 2007] that the optimum pot pressure and BHF curves can be divided into three distinct regions where the curves are either constant or increasing (almost) linearly with the stroke. This idea will be utilized in this study to develop a simple FE-based methodology to optimize the process parameters in the SHF-P process. Details are explained in the methodology section. 44

68 # Defect (references to Figure 3.13) 1 Tearing in lower portion of the cup side wall (2) 2 Bulging against drawing direction followed by Bursting in the clearance (4, 5) 3 Leakage, and subsequently flange wrinkling (6) 4 Bursting in the upper portion of the cup side wall (8) 5 Side wall wrinkling Reasons BHF higher than required to prevent wrinkling/ leakage, or Pot pressure low (not fullybenefiting from SHF-P process) Note: pressure drop may be due to leakage (see point 3 below) Sheet bulges against the drawing direction (subsequently bursts) if high pot pressure is applied and the sheet is (almost) clamped due to high BHF (usually observed if the clearance is large/ at the beginning of the stroke for conical punches) Low BHF or high pot pressure High BHF Note: since no bulging against the drawing direction is observed, pot pressure is most probably suitable Clearance is large and pot pressure is low, or Solutions Reduce BHF (A A ) Increase pot pressure (A A ) Note: BHF should be slightly increased to avoid lifting and therefore wrinkling and leakage Reduce pot pressure (C C ) Note: BHF should also be reduced as well since (after reducing the pot pressure) it is higher than required First, Increase the BHF until leakage is eliminated. If the sheet excessively bulges against the drawing direction or burst in clearance, this means that both BHF and pot pressure are large go to point 2 above Note: proper sealing may eliminate/ reduce leakage Reduce the BHF (D D ) Note: The pot pressure may need to slightly reduced if lifting/wrinkling/ leakage was observed after reducing the BHF Increase pot pressure Low BHF flange wrinkling side wall wrinkling Increase BHF Table 3.2 Summary of possible defects in the SHF-P process, and corresponding causes and solutions. Reference is made to Figure Prepared based on [Kaya 2008, Palaniswany 2007, Yadav 2008] 45

69 CHAPTER 4 DETERMINATION OF THE FLOW STRESS OF FIVE AHSS SHEET MATERIALS AT ROOM TEMPERATURE 4.1 Experimental Setup-Uniaxial Tensile Test To eliminate edge effect problems associated with shearing operations, tensile test specimens were prepared by wire EDM process. For each of the five AHSS materials (DP 600, DP 780, DP 780-CR, TRIP 780, and DP 780-HY), at least three samples were prepared at each of the three orientations (0, 45 o, and 90 o ) with respect to the rolling direction. Specimen dimensions specified in the International Standard ASTM E [ASTM E646-07, 2007] were used. MTS 810 FlexTest Material Testing Machine, 100 KN in capacity, was used for testing. A hydraulic wedge grips and a 2-inch Epsilon extensometer were used in all the tests. Samples were loaded at a strain rate of 0.1 min -1 (1.67 Χ 10-3 sec -1 ) which is also according to the previously mentioned standard. Before starting the test, the specimen was properly aligned with the loading axis and gripped carefully to avoid twisting. Samples were loaded to an engineering strain of 8% (+ 0.5 %) where the test was stopped and the sample width was measured for the purpose of determining the Strain Ratio (only for DP 780-HY at 90 o, the test was stopped at about 7% since this grade at this direction has less uniform elongation). A micrometer with a minimum division of 0.01 mm (

70 mm) was used to measure the width at three locations within the gauge length (as recommended by the standard ASTM E 517 [ASTM E517-00, 2006]) and the average width was calculated. After measuring and recording the width, the sample is loaded again until failure. Throughout the test, both the load and the measured engineering strain were recorded to be used in calculating the true stress and strain. The test matrix is summarized in Table Experimental Setup-VPB Test For each of the five AHSS materials, at least six-10 in X 10 in square samples were sheared. All samples are 1 mm-thick and were prepared from the same sheets from which tensile testing coupons were prepared. Minster Tranemo DPA hydraulic press, 160 metric tons in capacity, was used for the test. Honeywell (S-model) pressure transducer and ETI (LCP 12 S-100 mm) potentiometer were used to measure the bulging pressure and dome height, respectively. National Instrument (SCXI) Data Acquisition System (Hardware: SCXI-1000 and software SCXI-1520) was used to collect the data. Measuring devices were calibrated before the test to ensure accurate measurements. The clamping force was set to 100 metric tons to ensure no draw-in of the sheet material in the die cavity. The die cavity diameter of bulge test tools available at the ERC/NSM is in (105.7 mm) and the die corner radius is 0.25 in (6.35 mm). The potentiometer used is a delicate device and cannot withstand impact loading at the burst of the specimen. Thus, for each material, at least one sample was burst without a potentiometer to know the bursting pressure. To avoid bursting 47

71 the other samples, they were pressurized to 90 to 95% of the burst pressure while the potentiometer was used to measure the bulge height. Pressure vs. dome height raw data, sheet thickness, and strain ratios at 0 o and 90 o were used as inputs to the excel macro to calculate the flow stress curve. To obtain the flow stress curve assuming the material is isotropic, value of one was used for both R0 and R90. Since it is not possible to obtain experimental data up to the burst pressure, and in order to get a rough estimate of the material formability under balanced biaxial condition, the data was extrapolated to the burst pressure using a higher order polynomial approximation. The extrapolated curve was then used in the excel macro to obtain the flow stress curve. The dome height of the burst samples can be used as a measure of material formability under balanced biaxial condition. However, since the main objective of the study was not to evaluate the formability, the number of samples burst and measured was not sufficient from the repeatability point of view. Thus, these results are not presented in this paper. Table 4.1 summarizes the test matrix for both the tensile and the VPB tests. 4.3 Testing Matrix Table 4.1 summarizes the tests performed to obtain the experimental data to be used in determining the flow stress of the five AHSS materials using the different techniques described above. 48

72 Number of samples tested # Material Thickness Tensile Test a VPB test 0 o 45 o 90 o Total Burst 1 DP mm DP mm DP 780-CR 1 mm DP 780-HY 1 mm TRIP mm Table 4.1 The test matrix used for the tensile and VPB tests of the five AHSS sheet materials a It was originally planned to test at least 3 samples for each condition. However, some samples were lost during the initial trials and therefore not included in this table 4.4 VPB Test (Combined FE - Membrane Theory Inverse Analysis) Isotropic Materials The methodology used for determining the flow stress of the sheet from the bulge test data assumes that the material follows the Hollomon power law (Equation 7). The effective stress and strain equations from the classical membrane plasticity theory are used (Equations 17 and 19). In addition to the bulging pressure which can be easily measured in the test, Equations 17 and 19 contain two other unknowns; the thickness and radius of curvature at the dome apex. To determine these unknowns, a series of FE simulations with different material properties (different n-value) were previously conducted at the ERC/NSM using the commercial FE software PAMSTAMP to generate a database. (Refer to [Nasser et al 2007, Gutscher et al 2004, Gutscher et al 2000]) This database shows how the thickness and radius of 49

73 curvature at the dome apex change with the dome height for different n-values. The Von-Mises yield criterion was used in the simulations. An excel macro was then developed to iteratively determine the flow stress curve of the material using both the database and the experimental pressure vs. dome height curve. A flow chart describing this FE-based inverse analysis methodology is shown in Figure 4.1. An initial guess of the n-value is made. Using the measured dome height and the database, the radius of curvature and thickness at the dome apex are calculated. Now that all the information needed are available, the membrane theory equations can be used to calculate the effective stress and strain. The power law is then used to represent the resulting curve. Another iteration is performed with a different n-value, and the process continues until the difference in the n-value between two subsequent iterations becomes less than or equal to At this moment, the iterations are stopped, and the flow stress curve is extracted and reported. Figure 4.1 A flow chart describing the FE-based inverse analysis methodology used to determine the flow stress curve of sheet materials [Gutscher et al, 2004] 50

74 4.4.2 Anisotropic Materials Since sheet materials are usually anisotropic (i.e. mechanical properties vary from one direction to another), the flow stress curve obtained in the bulge test may not be accurate if the material is assumed to be isotropic. Therefore in this study, the calculated flow stress curve using the methodology described in the previous section was corrected for anisotropy. While Von-Mises yield criterion is used in the methodology described above, Hill s anisotropic yield criteria is used in this section [Hill, 1990]. Following is the correction factor used to correct for anisotropy: (for more details, refer to [Bortot et al, 2005]) Equation 21 If the material does not have any planar anisotropy (i.e. R-value is the same in all directions), then Equation 21 simplifies to Equation 22: Equation VPB test (Combined FE - Optimization Inverse Analysis) This new optimization methodology is still based on the inverse analysis technique that was described above. The idea is that minimizing, thus the name optimization, the difference in dome height between the simulation and the experiment can be achieved only if the simulation flow stress input is very close, or equal, to the flow stress of the material tested. Therefore, the objective function to be minimized in this optimization is the difference between the experimental and measured dome heights, at selected pressure (or time) values, formulated in a least square sense. (see Figure 4.2 and Equation 23) 51

75 Figure 4.2 (left) Schematic of the dome height evolution with time (or pressure). (right) Schematic showing how the calculated (simulation) dome height may deviate from the measured dome height if the simulation flow stress input is not correct [Penter et al, 2008] The AHSS sheet materials were assumed to follow the Hollomon power law (Equation 7). The objective function used for the room temperature bulge test is: Equation 23 : the objective function to be minimized : time point at which simulation and experiment were compared : number of datapoints selected for the optimization : the measured dome height at time t : the simulation dome height at time t To apply the optimization methodology, the optimization software LS-OPT was used to generate FE simulation files with different combinations of the rheological parameters K and n. The FE software LS-DYNA was used to run the simulations. In each simulation, the sheet is pressurized with the same experimental pressure vs. time curve and the simulated dome height evolution 52

76 with time could be determined. As described above in the formulation of the objective function, the simulated and experimental dome heights at the selected points of time were compared. The inputs to the LS-OPT file are: 1. The experimental dome heights at the selected points of time. 2. The simulation times at which the simulated dome height should be extracted. 3. The formulation of the objective function based on (1) and (2). The Response Surface Methodology (RSM) was used in the optimization. The objective of applying the RSM is to find the combination of the two rheological parameters, called the Design Variables, which will minimize the objective function, called the Response. As applied in this study, the RSM can be described briefly as follows: 1. An initial guess of the ranges of K and n, is made (based on data in the literature) and used as an input to LS-OPT. These ranges define the Design Space. Within each range, a starting value is selected. The starting values define the Baseline Design. See 2. Figure Within the design space, LS-OPT will select certain combinations of the rheological parameters (each combination called a Design Point ), for which LS-DYNA files will be generated and run. The number of design points selected for room temperature bulge test was ten. See Figure From each LS-DYNA simulation file, the dome height will be extracted at the selected points of time. Using the simulated dome height and corresponding experimental dome heights, the objective function (response), hereinafter referred to with E, is calculated (See 5. Figure 4.3). 53

77 6. Having the value of E for each combination, a second order polynomial curve can be fit and the minimum value can be obtained. The minimum point is the closest to the correct (optimal) point. See 7. Figure 4.5 (left). If the K and n values used in the simulation are the correct values, then the calculated E value should ideally be equal to zero (i.e the simulation exactly matches the experiment). 8. A Sub-region within the initial design space is selected by LS-OPT. Within this new region, steps (2) to (4) above are repeated iteratively until the convergence criterion is met. The final K and n values are considered to be the optimal values. In this study, the optimization converges when the difference in the objective function and design variables between two subsequent iterations become less than and 0.01, respectively. See 9. Figure 4.5. Figure 4.3 3D view of design space, showing objective function (response) obtained for each combination of K and n (design variables) [Penter et al, 2008] 54

78 Figure 4.4 A schematic showing the selected design points (red, big) and the computationally expensive full factorial points (black, small) [Penter et al, 2008] Results for second iteration (FE simulations 11 through 20) Results for eighth (final) iteration (FE simulations 71 through 80) Figure 4.5 Minimization of objective function 'E' using RSM as applied to room temperature bulge test. In each iteration (set of 10 FE simulations), the margins for 'K' and 'n-value' keep shrinking to a smaller design space, until the objective function is minimized (the convergence criterion is met). (left) the result of the second iteration. (right) the result of the final iteration [Penter et al, 2008] 55

79 4.6 Results Tensile Test Figure 4.6 and Figure 4.7 show a comparison of the engineering and true stressstrain curves obtained by the tensile test, respectively. No considerable variation of the flow stress curves between different samples orientations was observed. Thus the flow stress curves for all materials and orientations are not presented. As an example, the true stress true strain curves of DP 780-HY for the three orientations are shown in Figure 4.8. Table 4.2 summarizes the strain ratios of the five AHSS materials in the three orientations, as well as, the average strain ratio and planar anisotropy. Figure 4.9 and Figure 4.10 compare the average values (0 o, 45 o, 90 o ) for the uniform elongation, total elongation, UTS, and 0.2% offset yield strength of the five AHSS tested by the tensile test. 56

80 True Stress (MPa) Engineering Stress (Mpa) TRIP 780 DP 780-CR DP 780-HY DP 780 DP Engineering Strain (%) Figure 4.6 Comparison of Engineering Stress - Engineering Strain curves of various AHSS grades obtained by the tensile test DP 780-HY DP 780 DP 780-CR TRIP 780 DP True Strain Figure 4.7 Comparison of True Stress - True Strain curves of various AHSS grades obtained by tensile test 57

81 True Stress (MPa) degrees 45 degrees 90 degrees True Strain Figure 4.8 True Stress - True Strain curves of DP 780-HY at 0, 45, and 90 degrees with respect to rolling direction obtained by tensile test 0 o 45 o 90 o ΔR DP DP DP 780- CR TRIP DP 780- HY Table 4.2 Comparison of Anisotropy Ratios of various AHSS grades 58

82 UTS/ 0.2% Offset Yield Strength (MPa) Uniform/Total Elongation (%) Uniform Elongation (%) Total Elongation (%) DP 600 DP 780 DP 780-CR TRIP 780 DP 780-HY Figure 4.9 Uniform and Total Elongation of various AHSS grades (Gauge Length: 2 in) (Average values are shown) % offset yield strength UTS DP 600 DP 780 DP 780-CR TRIP 780 DP 780-HY Figure 4.10 UTS and 0.2% Offset Yield Strength of various AHSS grades (Average UTS values are shown) 59

83 4.6.2 VPB Test (Combined FE - Membrane Theory Inverse Analysis) Figure 4.11 shows a sample pressure vs. time curve for TRIP 780 from which the burst pressure was obtained. The burst pressure was about 225 bars for sample 1 and 226 bars for sample 2. Figure 4.12 shows a picture of a burst sample (a) and a sample bulged but not burst (b) for TRIP 780. Since a large clamping force (100 metric tons) was used, no material draw-in was observed in all tests. Figure 4.13 compares the burst pressures, while Figure 4.14 compares the experimental pressure vs. dome height curves of the five AHSS materials obtained by the VPB test. The corresponding flow stress curves are compared in Figure The curves of both DP 600 and DP 780-HY were obtained up to bursting since a sample accidently burst during the test. As an example of experimental data extrapolation to the burst pressure, Figure 4.16 shows the pressure vs. dome height curve of TRIP 780 (sample 6) with and without extrapolation. Figure 4.17 shows the flow stress curve of TRIP 780 (sample 6) obtained from both experimentally measured and extrapolated pressure vs. dome height curves. 60

84 Pressure (bars) Burst pressure ~ 225 bar Time (seconds) Figure 4.11Experimental Pressure versus time curve for sample 1 of TRIP 780 steel sheet material (a) TRIP 780 (Sample 2) Burst (b) Sample 7 Figure 4.12 Example tested specimens for TRIP 780 sheet material (a) sample burst (b) sample not burst 61

85 Pressure (bars) Burst Pressure (bars) DP 600 DP 780 DP 780-CR DP 780-HY TRIP 780 Figure 4.13 Burst pressures of the five AHSS materials tested DP 780-CR 150 DP DP 780-HY TRIP 780 DP Dome Height (mm) Figure 4.14 Experimental pressure versus dome height curves obtained from the VPB test for the five AHSS sheets materials tested (These curves are the measured curves without any extrapolation). 62

86 Pressure (bars) True Stress (MPa) DP 780-CR TRIP DP 600 DP 780 DP 780-HY True Strain Figure 4.15 Comparison of the flow stress curves of the five AHSS materials tested using the VPB test (these curves are neither corrected for anisotropy, nor extrapolated) 250 Burst pressure = 226 bars Extrapolated Dome Height (mm) Figure 4.16 Pressure versus dome height curve (for TRIP780, sample 6) extrapolated from last measured datapoint (212 bars) up to burst pressure (226 bars) using second order polynomial approximation 63

87 True Stress (MPa) From Extrapolated data From Measured data From extrapolated data True Strain Figure 4.17 The flow stress curve of TRIP 780 (sample 6) obtained from both experimentally measured and extrapolated pressure vs. dome height curves VPB Test (Combined FE - Optimization Inverse Analysis) Figure 4.18 shows how the values of K and n converge to the optimal values for DP 600. The initial range for each material was selected based on the results obtained from the combined FE-membrane theory methodology. The number of simulation points in each iteration was selected to be 10 point. The average number of iterations until convergence was 8 iteration, with an average of 17 minutes per iteration. Figure 4.19 compares the flow stress curves of the five AHSS materials tested obtained from the optimization methodology. The curves are plotted from the optimal K and n values. Last datapoint on the curves is selected to be the same as the values reported for the combined FE-membrane theory methodology. 64

88 True Stress (MPa) (a) K-value (b) n-value Figure 4.18 Optimization history of the design variables K and n for DP 600. Number of iterations to converge is DP 780-CR (1346,0.14) TRIP 780 (1378, 0.174) DP 600 (980, 0.143) DP 780 DP 780-HY (1284,0.093) (1171,0.094) True Strain Figure 4.19 Flow Stress curves of the five AHSS materials tested obtained using the combined FE-optimization methodology. Curves are plotted up to the last datapoint obtained from the combined FE-membrane theory methodology (also shown in the figure, the K-value in MPa and the n value) 65

89 True Stress (MPa) Comparison of Different Techniques Figure 4.20 through Figure 4.24 compare the flow stress curves determined by the tensile and VPB tests (two methodologies) for the five AHSS materials tested. Table 4.3 shows the K and n-values obtained from the different tests and methodologies Tensile Test VPB-Membrane (with anisotropy correction) VBP-Membrane (without anisotorpy correction) VPB-Optimization True Strain Figure 4.20 Comparison of True Stress- strain curves of DP 600 determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) 66

90 True Stress (MPa) True Stress (MPa) Tensile Test VPB-Membrane (with anisotropy correction) VBP-Membrane (without anisotropy correction) VPB-Optimization True Strain Figure 4.21 Comparison of True Stress- strain curves of DP 780 determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) Tensile Test VPB-Membrane (with anisotropy correction) VBP-Membrane (without anisotropy correction) VPB-Optimization True Strain Figure 4.22 Comparison of True Stress- strain curves of DP 780-CR determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) 67

91 True Stress (MPa) True Stress (MPa) Tensile Test VBP-Membrane (with anisotropy correction) VBP-Membrane (without anisotropy correction) VPB-Optimization True Strain Figure 4.23 Comparison of True Stress- strain curves of DP 780-HY determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) Tensile Test VBP-Membrane (with anisotropy correction) VBP-Membrane (without anisotropy correction) VPB-Optimization True Strain Figure 4.24 Comparison of True Stress- strain curves of TRIP 780 determined by the Tensile test and VPB test (different methodologies) (Curves are not extrapolated) 68

92 Tensile test VPB-Membrane (w/o VPBcorrecting for Optimization anisotropy) K n a R 2b K n c R 2b K n Material (MPa) (MPa) (MPa) DP DP DP CR DP HY TRIP Table 4.3 Comparison of the K and n-values obtained using both the tensile and VPB tests (two methodologies) for the five AHSS materials a The n-value in the tensile test was obtained by fitting the power law in the range from the 0.2% offset yield point to the instability point b R 2 is the square of the Correlation Coefficient c The n-value in the VPB test was obtained by fitting the power law in the strain range from about 0.04 to the last datapoint available without extrapolation (note that the range in which the curve is fit affects the fit parameters) Variation of Strain Hardening and the Suitability of the Power Law Fit Figure 4.25 through Figure 4.29 show how the value of the Normalized Strain Hardening (NSH), calculated from bulge test flow stress data (without anisotropy correction), change with strain. In these charts, curves are calculated using both the original flow stress datapoints (as taken from the excel macro), and from the Hollomon Power law fit curves shown in Table 4.3. Comments on these charts can be found in the conclusions chapter. 69

93 NSH NSH From power law fit curve From experimental datapoints True Strain Figure 4.25 Normalized Strain Hardening (NSH) vs. Strain for DP 600 obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve (Note that data for DP 600 was collected up to bursting since a sample accidentally burst during the test) From power law fit curve From experimental datapoints True Strain Figure 4.26 Normalized Strain Hardening (NSH) vs. Strain for DP 780 obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve 70

94 NSH NSH From power law fit curve From experimental datapoints True Strain Figure 4.27 Normalized Strain Hardening (NSH) vs. Strain for DP 780-CR obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve From power law fit curve From experimental datapoints True Strain Figure 4.28 Normalized Strain Hardening (NSH) vs. Strain for DP 780-HY obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve (Note that data for DP 780-HY was collected up to bursting since a sample accidentally burst during the test) 71

95 NSH From power law fit curve From experimental datapoints True Strain Figure 4.29 Normalized Strain Hardening (NSH) vs. Strain for TRIP 780 obtained from both VPB flow stress data (combined FE-membrane theory methodology) and from the Power Law Fit Curve 72

96 CHAPTER 5 DETERMINATION OF THE FLOW STRESS OF ALLUMINUM SHEET MATERIALS AT ELEVATED TEMPERATURE 5.1 Experimental Setup (Machine and Tool Design) A fluid-based elevated temperature biaxial bulge system was designed and developed by Applied Engineering Solutions, LLC (AES) wherein the tested samples were submerged within a heated fluid. Die design was collaboratively accomplished with the CPF. Figure 5.1 shows a schematic of the machine design, which consists essentially of the tools (the forming die and seal plate/blankholder), heat transfer fluid, a heating system, fluid tank, fluid pressurization (fluid intensifier) system, and sensors to measure sample bulge deformation, bulging pressure, temperature, and the pressurizing fluid volume flow rate. All machine components were selected for elevated temperature applications. 73

97 LVDT Sensors Computer Controller Die Bulge Test Specimen Seal Plate Hydraulic Power Supply Hydraulic Ram Hydraulic Ram Heat Exchanger Fluid Tank Fluid Preheater Fluid Heater Fluid Pressure 2008 Applied Engineering Solutions, LLC Figure 5.1 A schematic of the Fluid-based Elevated Temperature Biaxial Bulge Test Apparatus [Designed by the Applied Engineering Solutions (AES), LLC] The test is divided into two main stages; clamping and bulging. The sample is first clamped between the die and blank holder to prevent the material from flowing into the die cavity during the test, thus maintaining a stretch forming condition. Critical to the clamping process is the lockbead design. A series of FE simulations of the clamping and bulging stages of the test, with various possible lockbead designs, were made with flow stress data from the literature, in order to select the design which prevents sheet draw-in [Yadav, 2008]. The design which properly clamps the sheets without excessive thinning or cracking in the clamping stage, and maintains the sheet clamped throughout the test was selected, taking into consideration the hold-down capacity of machine (25 tons). Figure 5.2 shows a schematic of the designed ET tools. While clamped, the intensifier pressurizes the sheet with the required volume flow rate of the 74

98 bulging fluid. Figure 5.3 shows schematically the clamped sheet during the bulging process. Two flow rates; 2 in 3 /second and 0.2 in 3 /second, were selected to result in a wide range of strain rates. Corresponding pressure vs. time can be measured using the pressure sensor and the resulting range of strain rates in the sheet can be estimated from the FE simulation. The criteria for the test machine design were: a) to provide a near-isothermal bulge condition at elevated temperatures, b) to control and measure the pressurizing fluid volume flow rate, and c) to measure the resulting pressure and sample deformation which are the key inputs to the optimization. In order to ensure the near-isothermal conditions of the test blank, the die, seal plate, and sample were submerged in a hot heat transfer liquid. To avoid heat transfer fluid oxidation, the heating system was divided into two components: 1) a fluidfilled tank used to submerge the sample and tools, and 2) a closed-loop external fluid heating unit and circuit. The heat transfer liquid inside the tank was heated via a heat exchanger located within the tank wherein heated heat transfer fluid was circulated via the external (closed loop) fluid heating unit located near the machine. The system was designed to reach controlled temperatures up to 300 o C. Three Linear Variable Differential Transducers (LVDTs) were used to capture real-time sample dome height (and shape) during the test. Due to the high temperatures required, no LVDTs capable of being submerged in a hot fluid were commercially available to allow their arrangement as originally proposed and depicted in Figure 5.3. Therefore, AES designed a remote method to sense dome height deformation using three sample contact probes which were connected to each of the three LVDTs via individual coaxial cables. This arrangement, as shown in Figure 5.4, allowed the measurement of the sample bulge curvature profile as a function of time. The applied fluid pressure was 75

99 measured using a pressure transducer within the intensifier unit, and the sample temperature was determined via a thermocouple located within the fluid tank. Figure 5.5 illustrates the constructed elevated temperature bulge test equipment and includes a photograph of a produced bulged sample. Center line Maximum available tonnage = 25 tons UPPER PLATE / DIE Ø (~ 4 ) Die entry corner radius (R) Sheet Lockbead required (a) LOWER PLATE (b) Figure 5.2 Schematics showing the design and dimensions of (a) the tools, (b) lockbead (within the tools), designed to be suitable for the ET bulge test [Yadav, 2008] Figure 5.3 A schematic showing the clamped sheet during the bulging process and the LVDTs which were planned to be used to measure the dome height and sample curvature profile [Designed by the Applied Engineering Solutions (AES), LLC] 76

100 Figure 5.4 A picture showing the arrangement designed to measure the sample bulge curvature profile without the need to submerge the LVDTs in the heated fluid [Designed by the Applied Engineering Solutions (AES), 2008 Applied Engineering 2008 Applied Engineering Solutions, 2008 Applied Engineering Solutions, Figure 5.5 The fluid-based elevated temperature biaxial bulge test apparatus [Designed by the Applied Engineering Solutions (AES), LLC] 77

101 5.2 Testing Matrix Table 5.1 is a summary of the tests performed at elevated temperature: Material Temperature # of Thickness Pressurization ( (mm) C) samples/ rate (in 3 /sec) condition AA5754-O and 2 3 AA5182-O and 2 3 AA3003-O and 2 3 Table 5.1 Testing matrix of AA5754-O, AA5182-O, and AA3003-O at elevated temperature 5.3 Combined FE - Optimization Inverse Analysis at Elevated Temperature Note: This section describes the difference between applying the optimization methodology to the elevated temperature and room temperature bulge test. At elevated temperatures, the material is strain rate sensitive. Thus, the material model to be used should be a function of the strain rate. [Abbedrabbo et al, a and b] showed that the Field and Backofen material model (Equation 8) is suitable to describe the behavior of AA5754-O, AA5182-O, and AA3003-H111. Since these are the materials of interest in this study (except the temper of AA3003), this material model will be used. Since the material at elevated temperature is strain rate sensitive, the deformation speed (pressurization rate) should be changed in the experiment to result in a wide range of strain rates in order to determine the m value. Thus, two samples, one pressurized fast (2 in 3 /second), and the other pressurized slow (0.2 78

102 in 3 /second) were tested and the resulting dome height evolutions were compared with FE simulations run with the corresponding pressure vs. time curves. Figure 5.6 shows schematically the fast and slow pressure curves and how the pressurization rate affects the dome height. The new objective function to be minimized should have two terms; one associated with the high pressurization rate test and the other associated with the low pressurization rate test and is formulated as follows: Equation 24 where; E: is the objective function to be minimized t: time point at which simulation and experiment were compared N and M: are the numbers of datapoints selected for the fast and slow tests, respectively hm,f and hm,s: are the measured dome heights at time t in the fast and slow tests, respectively hs,f and hs,s: are the simulation dome heights at time t in the fast and slow simulations, respectively 79

103 Figure 5.6 (left) A schematic showing the fast (high pressurization rate) and slow (low pressurization rate) pressure curves. (right) a schematic showing the difference in dome height between two samples, one pressurized fast and the other pressurized slow Instead of running FE simulations with two parameters; K and n, as was the case for room temperature, LS-OPT generates LS-DYNA FE simulations files for selected combinations of the three parameters; K, n, and m. In Each LS-DYNA file, two bulging processes (Fast and Slow) are simulated simultaneously and the dome height in each can be extracted. 16 design points were used for the elevated temperature bulge tests. In order to reduce the simulation time, time scaling was used where the time in the experimental pressure vs. time curve was divided by 100. Since the material is strain rate sensitive at elevated temperature, this will result in the strain rate approximately 100 times higher. Therefore, the Field and Backofen material model (Equation 8) should be modified as follows: Equation 25 80

104 5.4 Results Problems Encountered and Solved Following are the major problems encountered and solved in the elevated temperature bulge test experiments and simulations: Samples Pre-bulging in the Clamping Stage (AA5754-O and AA5182-O): The sheet specimen and the tools are totally submerged in warm oil. During the clamping stage, oil was entrapped between the specimen and male die, resulting in the sample pre-bulging prior to the test. This pre-bulging problem was solved by using a check valve to relieve the entrapped oil in the clamping stage. This problem was encountered while testing AA5754-O and AA5182-O. Pressure drop in the testing of AA-3003-O: After solving the problem described in section above, another problem resulted from using the check valve. The program controlling the machine was set to have a time delay between the clamping and bulging stages. Once the bulging stage starts, it was noticed that the pressure curve does not increase instantaneously and that the pressure may even drop at the beginning of the process. It was found later that the check valve required 81

105 some time to close after relieving the oil in the clamping stage. As a result, some leakage took place and was responsible for the pressure drop. To solve this problem, the time delay between the clamping and bulging stages was increased to give the check valve enough time to close; thus, prevent leakage. This problem was encountered while testing AA3003-O. It should be noted that enough testing materials and time were not available to repeat the experiment after solving the problems described above. Termination Errors in FE Simulations Some combinations of the three design variables (rheological parameters); K, n, and m may result in invalid simulation results (very large dome height); thus resulting in a termination error. To reduce the likelihood of termination errors, constraints were set on the dome height extracted from the simulation. The constraint is basically an upper-bound equal to 120% of the measured dome height. Thus, when selecting the design points (combinations K, n, and m), the optimization should select the combinations which do not cause the simulated dome height to deviate more than 20% from the measured dome. At least 7 design point (at room temperature), and 10 design points (at elevated temperature) are required to fit the second order polynomial curve. Therefore, loosing design points because of the reason described above may result in the number of point to become less than the minimum required. As a result, the optimization stops before the convergence criterion is met. 82

106 5.4.2 Problems Encountered and not Solved Uniqueness of Optimization Results It was noticed that the initial guess of the range of the design variable (K, n, and m) may affect the optimization results at elevated temperature. A slight shift of the initial range up or down, widening, or narrowing the range resulted in small difference in the optimal results. If the optimal value is relatively small (such as in the case of the m-value), the percentage variation in the optimal value due to selecting different initial range may be high. Measurement of sheet radius of curvature In room temperature bulge test, the shape of the dome may be assumed to be spherical and thus, the dome height is sufficient to characterize the dome evolution. However, this may not be the case at ET. The variation of the strain from one location to another in the sample and the effect of strain rate on the material flow stress will affect the strain distribution in the sample. This will change the deformation behavior of the sheet and may not result in a spherical bulge. To take this into consideration in the analysis, it was originally planned (as previously described) to measure the dome height at the center, and two different off-center locations to estimate the radius of curvature beside the dome apex height. This will provide additional 83

107 information to the analysis, resulting in more robust method for determining material properties. The three LVDTs were fixed on the machine, but a technical problem prevented the use of the off-center LVDTs. At ET, the material is relatively soft and the tip of the probes may slightly penetrate in the sheet. This caused a lateral deflection in the probes. As a result, only the center LVDT was used Experimental data Although not reliable, it was decided to include the experimental data for documentation purposes. Several trials were made to apply the optimization methodology. Results did not match the data in the literature and therefore are not included in this report. Figure 5.7 through Figure 5.9 shows the experimental pressure vs. dome height curves obtained at three temperatures; 200 o C, 230 o C, and 260 o C, and two pressurization rates; fast (2 in 3 /sec) and slow (0.2 in 3 /sec) for the three materials tested; AA5754-O, AA5182-O, and AA3003-O. 84

108 Pressure (MPa) o C 200 o C 260 o C Fast 200 o C 230 o C 260 o C Slow Dome Height (mm) Figure 5.7 Experimental Pressure vs. Dome height curves of AA3003-O at three temperatures; 200 o C, 230 o C, 260 o C, and two speeds; fast (2 in 3 /sec) and slow (0.2 in 3 /sec). Note that for the fast test, increasing the temperature from 200 o C to 230 o C, resulted in an increase in the pressure 85

109 Pressure (MPa) Pressure (MPa) Pressure (MPa) AA5182-O at 260 o C Dome height (mm) AA5181-O at 230 o C Dome height (mm) Fast Slow Figure 5.8 Experimental Pressure vs. Dome height curves of AA5182-O at three temperatures; 200 o C, 230 o C, 260 o C, and two speeds; fast (2 in 3 /sec) and slow (0.2 in 3 /sec) AA5182-O at 200 o C Dome height (mm) 86

110 Pressure (MPa) Pressure (MPa) Pressure (MPa) AA5754-O at 260 o C AA5754-O at 230 o C Dome Height (mm) Dome Height (mm) Fast Slow Figure 5.9 Experimental Pressure vs. Dome height curves of AA5754-O at three temperatures; 200 o C, 230 o C, 260 oc, and two speeds; fast (2 in 3 /sec) and slow (0.2 in 3 /sec) AA5754-O at 200 o C Dome Height (mm) 87

111 CHAPTER 6 A SYSTEMATIC METHODOLOGY FOR DESIGNING A SHF-P PROCESS USING FE SIMULATIONS 6.1 Model Part and Tools Geometry The model part used in this study to develop guidelines for designing SHF-P process is a flat-headed conical part with a round pocket in its base. This part was initial designed at General Motors R&D (the sponsor of this study). Sheet material to be formed is aluminum AA5754-O, 1 mm in thickness. For conical parts, the punch-die clearance is large at the beginning of the stroke and decreases with stroke. Thus, it is easier for the sheet to bulge against the drawing direction in such a geometry compared to a cylindrical part. This adds to the difficulty in designing the process, and usually makes it necessary to start with a small pot pressure and then increase it with the stroke. Moreover, thinning and side wall wrinkling observed in conventional deep drawing of conical parts is higher than cylindrical parts because of the suspended (unsupported) region in punch-die clearance. Therefore, one may appreciate using SHF-P process for conical parts more than for cylindrical parts. The initial clearance between the punch and blankholder (considering punch and blankholder corner radii) is mm and the conical angle is 84 o. Figure 6.1 shows the model part to be used in this study. 88

112 Flat base Die corner Tapered wall Pocket Punch corner Figure 6.1 One quarter of the model part to be made by the SHF-P process One objective of SHF-P is to eliminate the die in order to reduce tools cost. Alternatively, the punch should have the topographies required in the final part after. To study this, the punch was designed to have a round pocket in which the sheet will be formed. Stretch forming sheet in the pocket can be considered a Sheet Hydroforming with a Die (SHF-D) process. Since it may not possible to completely fill the pocket using the pot pressure, a reverse punch was designed to completely fill the pocket at the end of the stroke. Originally, tools were designed to have drawbeads in them. However, the clearance between the bead and the groove was very small (about 1.09 mm) which is very tight for a 1 mm thick sheet. Moreover, bead and groove corner radii were extremely small (about 3 mm and 2 mm, respectively). Simulations with the lockbead (see Results section) showed that it is impossible to draw the 89

113 sheet from the flange. Therefore, the bead used can be called a lockbead rather than a drawbead. In addition to these tools, another set of flat tools (flat die and blankholder) will be made to benefit from the SHF-P process and to avoid the complications associated with using a drawbead. Figure 6.2 is a 2D sketch of the tools geometry and dimensions. All dimensions are in mm Figure 6.2 2D sketch of the tools geometry and dimensions. The sketch shows the blank holder and the die with a lockbead. Another set of tooling similar to this, but without a lockbead, will also be used 90

114 6.2 Approach and Methodology for Designing SHF-P Process using FE Simulations Design criteria: Eliminate defects (see Table 1), minimize side wall thinning, and minimize material used. Design variables: blank size, pot pressure vs. stroke, BHF vs. stroke. General Procedure: trial and error FE simulations, experimental validation based on thinning distribution, punch force, and defects observed General Approach The blank radius will be initially estimated and may be changed later in the process. Small BHF and pot pressure will be used at the beginning of the stroke and will be increased toward the end of the process. The BHF will be held at a constant (low) value just sufficient to prevent wrinkling for about half the stroke (or more) and will be increased linearly (to simplify) after that, up to the end of the stroke. With respect to the pot pressure, the stroke is divided into three parts. In the first part, the critical stroke, where the sheet is being bent about the punch and die corner radii, and very little draw-in takes place, applying a high pot pressure will stretch form (and excessively thin) the sheet. Therefore, a small constant pressure value will be applied just to separate the sheet from the die corner radius (and also to slightly increase the contact pressure of the sheet with the punch). In the second part, the punch-die clearance decreases with the stroke and bulging 91

115 against the drawing direction becomes difficult. Therefore, the pot pressure will be increased linearly (to simplify) up to a maximum pressure reached at about half the stroke (more or less). The slope (how fast the pressure builds up) depends on how fast the clearance changes with the stroke. The maximum pressure reached also depends on other factors such as blankholder lifting. It should be noted that the higher the pot pressure, the higher the BHF should be to avoid lifting. The discussion above is for drawing and SHF-P processes where the sheet is allowed to draw-in from the flange. Another set of simulations will be made where the sheet is totally clamped. This stretch forming process will be simulated with different pot pressures to see how the maximum thinning in the part is affected. These simulations are not included in the detailed methodology below Detailed Methodology Step 1: Initial estimation of the blank radius Based on the principle of volume constancy and ignoring thickness change, the blank radius will be estimated using: Area initial = = Area final Note: The initial radius also depends on the BHF (the higher the BHF, the smaller the initial radius), µ (the higher µ, the smaller the initial radius), punch-die clearance (the higher the clearance, the smaller the initial radius), and on other factors. 92

116 Preliminary simulations will be made to check the suitability of the selected radius. Step 2: Initial estimation of BHF curve by simulating an equivalent deep drawing process (SHF-P with zero pot pressure) - Simulate half to two third of the stroke. Find minimum (constant) BHF to avoid flange wrinkling. - Simulate the rest of the stroke. Increase the BHF linearly until the end of the stroke. Find the minimum BHF (reached at end of stroke) without wrinkling. Step 3: Optimizing pot pressure and BHF curves by simulating the SHF-P process - Estimate the critical stroke from previous simulations (stroke in which the sheet only stretch bends about corner radii with very small flange draw-in). - Simulate the SHF-P process up to the critical stroke. Find the minimum pressure just to separate the sheet from the die corner radius. BHF should be increased to avoid lifting. - After the critical stroke, linearly increase the pressure up to a maximum value. The higher the maximum pressure reached, without defect (see Table 1), the better. Find the maximum pressure and the stroke at which it is reached. The earlier the maximum pressure is reached, without defects, the better. The BHF will have to be increased to prevent lifting. 93

117 - Simulate the rest of the process with a constant pressure. BHF from step 2 will have to be increased to prevent lifting. Step 4: Experimental Validation Run experiments with the same conditions (pot pressure and BHF) to validate simulation results. Compare the thinning distribution, punch force vs. stroke, and the defects observed. Step 5: Develop guidelines for designing SHF-P process, improve the suggested methodology for designing SHF-P process, Quantify the improvement in the thinning distribution attained by replacing the deep drawing process by the SHF-P process. 6.3 FE Model using Pamstamp 2G 2007 Pamstamp 2G 2007 commercial FE software was used to simulate the process. Since the tools are axisymmetric, only quarter geometry was modeled to reduce the simulation time (see Figure 6.3 a and b). Aquadraw module was used to model the SHF-P process (see Appendix A). The reverse punch and the die corner radius are modeled as parts of the pressure pot. Table 6.1 summarizes the parameters used in the FE model. 94

118 Punch Symmetry planes Blankholder Blank Binder Pot +reverse punch+die corner (a) Lockbead (b) Figure 6.3 FE model of the SHF-P (a) without a lockbead (b) with a lockbead. Prepared using Pamstamp 2G 2007 (reverse punch and die corner radius are parts of the pressure pot) 95

119 Blank Geometry Blank radius Varied (see section 6.4 for the simulation Matrix) Thickness 1 mm Mechanical Properties Flow stress/ AA5754-O (obtained by VPB test) See Figure 6.5 Young s Modulus (E) 70 GPa Poisson s ratio (ν) 0.33 R 0, R 45, R 90 1 (material assumed isotropic) Interface Condition Friction coefficient µ 0.1 (in deep drawing) (blank/binder and blank/ blank 0.06 (in Hydroforming) Holder) Friction coefficient µ (blank/ punch) 0.12 Mesh Element type Shell (Belytschko-Tsay ) Tools element size/ number of elements at radii 5 mm (6 element at radii) Initial sheet element size 2 mm Meshing Adaptive Meshing (max. level 3) Object type Blank Elastic, Plastic Tools Rigid Aquadraw (for Details of FE modeling using Aquadraw, see Appendix A) Medium (Bulk Modulus, K) Water (2.2 GPa) Pot Pressure Varied (see section 6.4 for the simulation Matrix) Locking stage (if exist) Blankholder stroke mm (see Figure 6.4-b) Hydroforming Stage BHF Varied (see section 6.4 for the simulation Matrix) Full punch stroke About 64.8 mm (see Figure 6.4 a) Table 6.1 Summary of the parameters used in the deep drawing and SHF-P FE simulations 96

120 (a) A schematic showing the punch full stroke (flat die and blank holder are shown) (b) A schematic showing the locking stroke for the tool set with a lockbead Figure 6.4 Schematics showing (a) the punch full stroke and (b) the locking stroke (if a lockbead is used) 97

121 True Stress (MPa) True Strain Figure 6.5 Flow Stress curve of AA5754-O (1 mm) obtained using the VPB test (data is not extrapolated) [Penter et al, 2008] 6.4 Simulation Matrix Stretch Forming and hydroforming without Draw-In # Blank radius (mm) BHF (KN) Blank holder fixed Pot Pressure (Bars) Zero Objective of running the simulation To investigate the possibility of excessive thinning in the clamping stage Blank holder fixed To study the effect of pot pressure on the stretch forming process by comparing with To study the effect of pot pressure on the stretch forming process by comparing with 1 Figure 6.6 Simulation matrix of stretch forming with and without pot pressure 98

122 6.4.2 Preliminary Simulation of Deep Drawing and Hydroforming with Draw-In # Blank radius (mm) BHF (KN) Pot Pressure (Bars) Objective of running the simulation Zero Study the effect of BHF Zero Study the effect of Pot pressure Compare deep drawing and SHF-P Study the effect of Pot pressure Compare deep drawing and SHF-P Figure 6.7 Preliminary simulation matrix of deep drawing and SHF-P with drawin 99

123 6.4.3 Deep Drawing and Hydroforming with Draw-In (According to the Proposed Methodology) # Blank radius (mm) BHF curve (KN) Pot Pressure curve (Bars) Objective of running the simulation Step 1: Initial estimation of the blank radius (constant) Zero To check the suitability of the calculated radius; 203 mm (constant) Zero To make sure a flange is left after forming (constant) Zero To increase thinning (on purpose) in order to see a considerable difference when running SHF-P simulations. Step 2: Initial estimation of BHF curve Deep Drawing Simulations BHF curve 1 a Zero To find minimum possible BHF BHF curve 2 a Zero (without wrinkling) in the first half to two third of the stroke BHF curve 3 a Zero To find minimum possible BHF BHF curve 4 a Zero curve to completely form the part (without wrinkling) Step 3: Optimizing the Pot Pressure and BHF curves SHF-P Simulations BHF curve 4 * + 50 KN to prevent lifting 35 (constant) BHF curve 4 * + 50 KN to prevent lifting BHF curve 4 * + 80 KN to prevent lifting Pressure curve 1 b Pressure curve 2 b Simulated up to the critical stroke to check the suitability of this pressure value. Critical stroke was estimated from previous simulations to be ~14 mm To find the most suitable pressure curve (which minimizes thinning) and BHF curve to prevent lifting due to the pot pressure Figure 6.8 Simulation matrix of deep drawing and SHF-P with draw-in (according to the proposed methodology) a For the BHF curves, see Figure 6.9 b For the pot pressure curves, see Figure

124 Pot Pressure (Bars) BHF (KN) BHF curve 1 BHF curve 2 BHF curve 3 BHF curve 4 No wrinkling Stroke (mm) Start of wrinkling Figure 6.9 BHF curves used in simulating the deep drawing process with 240 mm blank radius. Also shown (with a circle) the punch stroke at which the flange started to wrinkle in the simulation (details can be found in the Results section) P1 (extra BHF = 50 KN) P2 (extra BHF = 80 KN) Stroke (mm) Figure 6.10 Pot pressure curves used in simulating the SHF-P process with 240 mm blank radius and BHF curve 4 selected from deep drawing simulations plus an addition force to prevent blankholder lifting because of the pot pressure. The extra force applied is also shown for each curve 101

125 Thinning (%) 6.5 Results Stretch Forming and hydroforming without Draw-In At the end of the clamping stage, the maximum thinning observed in the lockbead region was about 6.5%, which indicates that cracking in this region is unlikely to occur. In the stretch forming stage (with and without pot pressure), no draw-in was observed in the simulation. Therefore, the geometry of the lockbead should be modified if sheet draw-in is required. Figure 6.11 compares the thinning distribution in simulations with zero and 100 bars pot pressure, at a punch stroke of 13 mm P=zero P=100 bars D C B E A Curvilinear Length (mm) Figure 6.11 Comparison of the thinning distribution in stretch forming simulations with zero and 100 bars pot pressure, at a punch stroke of 13 mm. It can be seen that thinning at punch corner radius (point D) increases with pressure increase, indicating that SHF-P is detrimental if the sheet is totally clamped (stretch forming). Other pressure values were tried and shown to give similar results 102

126 6.5.2 Preliminary Simulation of Deep Drawing and Hydroforming with Draw-In Preliminary simulations of the deep drawing and SHF-P processes of AA5754-O were made with a sheet mm in radius. The drawing ratio calculated from this radius is about The reason for selecting this small radius was to utilize the available tools (with lockbead) until a new tool set, without a lockbead, is manufactured at GM R&D. A sheet with this radius will not interfere with the lockbead. Because of the small drawing ratio, the process window in the deep drawing process was big. High BHF does not result in high sheet thinning and very low BHF is required to see wrinkling in the simulation. Moreover, the flange was small that the maximum possible punch stroke was about 20 mm. Two constant BHF; 60, and 140 KN were used in the deep drawing simulations. A comparison of the thinning distribution at 20 mm stroke in deep drawing is shown in Figure Since thinning in all cases is relatively low and to be able to see thinning reduction in the hydroforming process, the highest BHF (140 KN) was intentionally selected when running the SHF-P simulations. Figure 6.13 compares the thinning distribution at 20 mm stroke in SHF-P simulations run with two constant pot pressures; 40 bars, and 60 bars. Figure 6.14 shows the sheet bulging (in the punch-die clearance) against the drawing direction for the same pressure values. Figure 6.15 compares the thinning distribution (at 20 mm stroke) in deep drawing and SHF-P. The BHF in both simulations is 140 KN. 103

127 Thinning (%) Thinning (%) 4 BHF=60 KN BHF=140 KN 3 D 2 E Curvilinear Length (mm) Figure 6.12 Effect of BHF on the thinning distribution in deep drawing simulation of mm radius sheet (Material: AA5754-O). Two BHF were used; 60, and 140 KN. Thinning was recorded at 20 mm stroke. Only thinning in the punch-die clearance is shown 6 4 P= 40 bars P=60 bars D Curvilinear Length (mm) Figure 6.13 Effect of pot pressure on the thinning distribution in SHF-P simulation of mm radius sheet (Material: AA5754-O). Two pot pressure were used; 40, and 60 bars. 140 KN BHF was used in both simulations. Thinning was recorded at 20 mm stroke. Only thinning in the punch-die clearance is shown 104

128 Thinning (%) Punch Blankholder Punch Blankholder Die Die Small sheet bulging (a) Pot pressure = 40 bars Big sheet bulging (b) Pot pressure = 60 bars Figure 6.14 Sheet bulging (in the punch-die clearance) against the drawing direction in SHF-P simulations with two different pot pressures; 40 and 60 bars (Material: AA5754-O). Excessive pot pressure stretch forms (and thins) the sheet P=0 (Drawing) P=40 bars (SHF-P) D drawing D E drawing SHF-P Curvilinear Length (mm) Figure 6.15 Comparison of thinning distribution at 20 mm stroke in deep drawing and SHF-P (40 bars pot pressure) obtained by FE simulations (Material: AA5754-O). The BHF in the two simulations is 140 KN. Thinning in SHF-P is lower than deep drawing. Two necks form in deep drawing, while only one forms in SHF-P 105

129 6.5.3 Deep Drawing and Hydroforming with Draw-In (According to the Proposed Methodology) Following are the results organized according to the steps in the proposed methodology: Step 1: Initial estimation of the blank radius Based on the results shown in Table 6.2, a blank radius of 240 mm was selected to prevent the blank edge from moving past the die corner and also to see considerable thinning reduction when simulating the SHF-P process (same process but with a pot pressure). Although normally, the blank radius should be minimized, in this case and for research purposes, the maximum was selected. Ref. to Simulation Matrix Blank Radius (mm) BHF (KN) Pot Pressure (Bars) Wrinkling Punch corner Thinning (%) Zero No 3.77 Yes Zero No 4.1 No Zero No 10 No Blank moving past the die corner Table 6.2 Simulation results of applying step 1 of the proposed methodology; Initial estimation of the blank radius. A preliminary BHF of 60 KN was used. Step 2: Initial Estimation of the BHF Curve- Deep Drawing Simulations Based on the results shown in 106

130 Table 6.3, BHF curve 4 was selected since it is the minimum BHF curve (of the curves simulated) to completely form the part without wrinkling. For the selected curve, maximum thinning at the punch corner at the end of the stroke is 8.6%, while the maximum thinning in the pocket is 22.3%. Ref. to Simulation Matrix Blank Radius (mm) BHF curve (KN) Pot Pressure (Bars) Stroke at wrinkling (mm) BHF curve1 a Zero BHF curve2 a Zero BHF curve3 a Zero BHF curve4 a Zero No 8.6 Punch corner Thinning (%) [if no wrinkling] Table 6.3 Simulation results of applying step 2 of the proposed methodology; Initial estimation of the BHF curve. a For the BHF curves, refer to Figure 6.9 Step 3: Optimization of the BHF and Pot Pressure Curves The critical stroke was estimated from previous simulations to be about 14 mm. In the critical stroke, very small draw-in (~3.5 mm) was observed. 35 bars pot pressure was found to be suitable for lifting the sheet from the die corner without excessive bulging/ thinning. To prevent blank holder lifting due the pot pressure in the punch-die clearance, a BHF 50 KN higher than the BHF curve 4. According to the simulation matrix, simulations with two pressure curves were made. Figure 6.15 compares the thinning distribution at the end of the stroke for the two pressure curves, as well as zero pressure curve (deep drawing). 107

131 Thinning (%) BHF curve 4 (deep drawing) P1 P2 B-C (pocket corners) D (punch corner) Curvilinear Length (mm) Figure 6.16 Comparison of the thinning distribution at the end of the stroke between deep drawing (with selected BHF curve 4) and SHF-P with two different pressure curves (see simulation matrix). Note the considerable improvement in thinning distribution when using SHF-P 108

132 CHAPTER 7 DISCUSSION, CONCLUSIONS AND FUTURE WORK 7.1 Discussion and Conclusions Characterization of AHSS at Room Temperature Tensile Test Results Figure 4.6 shows that the engineering stress- strain curves of the five AHSS grades tested become almost flat around the UTS for a wide strain range, making it difficult to visually identify the instability point (Uniform elongation). Thus, these values that are clearly identified for low carbon steels are difficult to determine visually for AHSS. As seen in Figure 4.9, DP 600 has the highest post-uniform elongation (about 10%). Although DP 780-HY has the lowest uniform elongation, it has the second highest post-uniform elongation of about 9.5%. As seen in Table 4.2, DP 600 and DP 780-HY have the highest Average Anisotropy Ratio (Strain Ratio) of about 1.00, while TRIP 780 has the lowest value (about 0.7). TRIP 780 has the highest Planar Anisotropy (ΔR) of about 0.33, while DP 600 has the lowest value (about 0.001). Thus, non-uniform flow in the flange region (earing) when forming TRIP 780 sheet can be an issue. 109

133 One of the problems faced during tensile testing is that necking and failure for some materials at certain orientations occurred outside the gauge length. This was the case for some samples of DP 780 at 45 o and 90 o, TRIP 780 at 45 o, and both DP 780-CR and DP 780-HY in all orientations. Since deformation is uniform before the instability point and since the presented true stress- true strain curves are plotted up to this point, the data obtained from these samples was not discarded. For TRIP steels, strain hardening at the beginning takes place by the interaction of dislocations with second phases existing in the matrix. Later, when the material starts to loose its hardening characteristics, the retained austenite transforms to martensite (the strain at which phase transformation takes place depends mainly on the amount of carbon in the alloy) [9]. As a result, the alloy retains it hardening characteristic, which explains the delayed necking of TRIP 780 in uniaxial tensile test as compared to other DP steels with the same UTS (see Figure 4.7 and Figure 4.9). It can be seen from Figure 4.6 and Figure 4.7 that the flow stress curves of TRIP 780 have relatively low slope at lower strains compared to other grades with the same UTS. Still, this alloy has the largest values of both uniform and total elongation. This maybe attributed to the transformation mentioned above. It is reported that the austenite-to-martensite transformation of TRIP steels is easier under biaxial tension than under compression [9]. Thus, if used in drawing applications, TRIP steels shows relatively good performance since the transformation strengthens the side wall, while the flange region stays soft and easy to draw. 110

134 Bulge Test Results Figure 4.16 and Figure 4.17 show how much flow stress data is lost when ending the test at a pressure value slightly below the burst pressure. Moreover, these figures illustrate the high strain values which can be attained under balanced biaxial condition. The dome height at fracture (bursting) in the VPB test can be used as a measure of formability and therefore used as a quick and reliable acceptance test of incoming raw material in the stamping plant. However, not many samples were burst in this study so that burst height cannot be considered to be reliable in describing and/or comparing the formability of the different AHSS grades tested. The negligible variation in the dome height vs. pressure curves, and corresponding flow stress curves, among different samples of the same material, indicate the consistency in their deformation behavior. The combined FE-optimization methodology worked very well for the five AHSS materials tested using the VPB test at room temperature. Flow stress curves plotted from the K and n values obtained from LS-OPT output are compared in Figure Comparison of Different Techniques For all materials, stress levels obtained from the tensile test is lower than levels obtained from the VPB test. For DP 780-HY, the two tests gave close flow stress curves. Table 7.1 below compares the stress levels in the tensile test and the bulge test (calculated using the combined FE-Membrane theory methodology) at 111

135 a true strain value which corresponds to the instability point in the tensile test. This particular point was selected for comparison because the difference in the stress level between the two tests reaches it maximum at this point. It can be seen that the percentage difference in stress level between the VPB and the tensile tests can be as high as 17% as is the case for TRIP 780. True Strain at instability (in the tensile test) Maximum True Stress Level obtained in the Tensile Test (MPa) True Stress level in VPB test (MPa) (at a strain value equals to the instability strain in the tensile test) Maximum Percent difference between tensile test and bulge test DP 600 DP 780 DP780-CR TRIP % 12.3 % 8.3 % 17 % DP 780-HY % Table 7.1 Comparison between the stress levels in the tensile and VPB tests (calculated using the combined FE-Membrane theory methodology) at a strain values equal to the true strain at the onset of necking in the tensile test Depending on and, the corrected flow stress may increase, decrease, or stay the same. It can be seen from Figure 4.20 through Figure 4.24 that there is almost no difference between the anisotropy-corrected and uncorrected flow stress curves for both DP 780 and DP 780-HY, while the biggest difference is for TRIP 780. This illustrates how correcting for anisotropy may be important for some materials. 112

136 Theoretically speaking, the effective strain at instability under balanced biaxial loading is twice the instability strain under uniaxial loading. It can be seen from Table 7.2 below that data in the bulge test can be collected up to a very high strain values compared to the tensile test. This is an advantage of the bulge test, especially if the flow stress data is to be used for FE simulation, since no extrapolations is needed as is the case when using tensile data. Maximum true strain that can be obtained in tensile test (at instability point) Maximum true strain obtained in the bulge test (without extrapolation) DP 600 DP 780 DP780-CR TRIP Percent difference 254% 324% 137% 88% DP 780-HY % Table 7.2 Comparison between the maximum true strain that can be obtained in the tensile test and that obtained in the VPB test (calculated using the combined FE-Membrane theory methodology) Although we expect the percent difference in strain between the tensile and bulge tests to be about 100%, we can see that it can be as low as 88% (for TRIP 780) and as high as 564% (for DP 780-HY). This emphasizes the importance of the bulge test because of its capability to provide data for a bigger range of strain compared to the traditional tensile test. In addition, some materials may behave differently (especially from the formability point of view) under different loading conditions. DP 780-HY is an obvious example. It should be noted that the data lost because of ending 113

137 the test before bursting decreased the percentages shown in Table 5. Therefore, these percentages are not the maximum possible except for DP 600 and DP 780-HY since a sample accidentally burst while the potentiometer is in use. As shown in Figure 4.20 through Figure 4.24, and in Table 4.3, the combined FE-optimization methodology showed very similar results to the combined FE-Membrane theory methodology. Although working very well, it is not recommended to use the optimization methodology to determine the flow stress for the room temperature bulge test. The main reason is the long time required to run the optimization; more than two hours in this case, compared to few minutes in the combined FE- Membrane theory methodology. Moreover, the need for two software (FE and Optimization software) to apply this methodology makes this methodology difficult to apply in the industry. However, results shown in this study validates the optimization methodology when two design variables (K and n) are used, which is promising to extend the same approach to the elevated temperature bulge test, where strain rate becomes important and three design variables (K, n and m) are involved. The suitability of the Power Law Fit Power law fit, with R 2 values close to one, as is the case for all materials tested, may not capture the hardening behavior of the material. This is important because hardening is critical to predict thinning and necking in FE simulations. 114

138 A suggested quick test is to check the degree to which the NSH curve obtained from the fit data matches that obtained from the original data, especially in the range below NSH equals to 1 where various types of necking, for different states of stress, take place. The better the match, the more likely a simulation with the fit curve will accurately predict thinning and necking. For DP 780-HY (Figure 4.28), the two curves are close in the region from 1 to 0.5. For DP 780, the two curves matched very well in the region from 1 to 0.5, although this is not expected since the data is not available up to busting. However, fitting the power law to the extrapolated data gave n- value equals to which is close to the value used to generate Figure 4.26 (0.116). For TRIP 780 and DP 780-CR, a big amount of data was lost because of ending the test before the burst pressure. For these two materials, there is a big mismatch between the NSH curve obtained from the original data and fit data, especially if the true strain value is compared at NSH equals to 0.5. It is not intended by using the NSH curve to predict necking. However, it can be used to check whether the power law fit captures the hardening behavior of the material or not. It is observed that obtaining incomplete data results in a mismatch between the two curves. If this is the case, then the original data should be used in the simulation. The goodness of fit of the power law, as quantified by R 2, is not a good indicator of whether the power law describes the hardening behavior or not. This is because curves are usually fit to data by the least square method (by minimizing the difference in the stress level (not the curve slope)). This is clear when comparing the R 2 values in Table 4.3 which are all close to 1, with the degree to which the two curves in Figure

139 through Figure 4.29 match, especially in the region below NSH equals to one Characterization of Aluminum Alloys at Elevated Temperature The optimal K, n, and m values (and corresponding flow stress curves) obtained by applying the new methodology to the ET bulge test did not match with the flow stress data available in the literature [Abbedrabbo et al, 2006-a and Abbedrabbo et al, 2006-b]. This discrepancy may be due to different reasons. First, the Leakage and sample pre-bulging observed in the experiments. Second, data in the literature is a tensile data, while data in this study is a bulge test data. Third, the optimization methodology needs to be further improved. For AA3003-O, increasing the temperature from 200 o C to 230 o C resulted in a higher pressure which is not expected. The problems encountered in the experiment may be responsible for this. However, this may also be explained as follows. For strain rate-sensitive materials, the increase in strength due to high strain rate may be higher than the decrease in strength due to high temperature. This may take place in certain ranges of temperatures and strain rates. 116

140 7.1.3 Design of SHF-P Process Stretch forming and Hydroforming without Draw-In Since the sheet is totally clamped (no draw-in), the sheet in the punch-die clearance region is subjected to pure stretch forming. As a result, increasing the pot pressure was detrimental to sheet thinning in this region (see Figure 6.11). Thus, it is not recommended to use SHF-P if the sheet is totally clamped. Thinning in the punch base (between the pocket and punch corner radius) decreased in the SHF-P. This is because the contact pressure is higher in the presence of pot pressure, which increases the friction forces and prevents (reduces) sheet stretching. Preliminary Simulation of Deep Drawing and Hydroforming with Draw-In: It can be seen from Figure 6.12 that two necks form in the deep drawing process, one around the punch corner radius and the other around the die corner radius. As expected, the higher the BHF, the higher the thinning. As clear from Figure 6.13 and Figure 6.14, applying excessively high pot pressure at the beginning of the process, where the clearance is large, will bulge the sheet against the drawing direction in the punch-die clearance region. This will result in high sheet thinning. 117

141 Figure 6.15 shows one neck and lower thinning in the SHF-P simulation as compared to two necks and higher thinning in the deep drawing process. In the SHF-P process, the sheet is separated from the die corner radius. Thus, no neck forms at this region. Also, the sheet is pushed against the punch. Thus, lower thinning occurs at this region. As a result, thinning in the SHF-P is reduced and the neck shifts up the cup side wall. Simulation of Deep Drawing and Hydroforming with Draw-In (According to the Proposed Methodology): Step 1: Initial Estimation of the Blank Radius A blank radius of 240 mm was selected although the remaining flange after forming is larger than the case of 215 mm radius (more material waste). This was done on purpose, to increase thinning so that the effect of using the SHF-P process can be appreciated. Step 2: Initial Estimation of the BHF Curve It can be seen from Figure 6.9 and Table 6.3, that the required BHF to prevent wrinkling increases with the stroke (i.e the tendency for wrinkling increases with stroke). Therefore, applying an increasing BHF, instead of a constant and high BHF, will reduce thinning and increase the LDR. In this study, a simple BHF curve is suggested, where the force is constant up to 1/2 to 2/3 of the stroke and then increases linearly until the end of the process. BHF curve 4 (Figure 6.9) was selected and used in all SHF-P simulations. However, it should noted that the optimal (minimum) BHF curve in deep 118

142 drawing is not sufficient to prevent wrinkling in SHF-P because the pot pressure tends to lift the blankholder. Step 3: Optimizing the Pot pressure and BHF Curves It is observed from FE simulations that sheet draw-in in the flange is higher in SHF-P compared to deep drawing. 3.5 mm difference was observed between simulation 3-2 and 2-4 (see simulation matrix). This is because of the lower thinning in SHF-P. Therefore, when designing a SHF- P, the blank size should be slightly increased over the optimal size in deep drawing. At the beginning of the stroke, the punch-die clearance is large making it easy for the sheet to bulge against the drawing direction and thin. Therefore, only 35 bars was applied in the first 14 mm of the simulation, just to separate the sheet from the die corner. Two maximum pressures were reached; 200 bars and 100 bars (see Figure bars gave slightly better results indicating the 200 bars was causing extra stretching in the clearance region. Comparing deep drawing (simulation 4-2, see matrix) with SHF-P (simulation 3-2, see matrix), it was possible to reduce the thinning at the punch corner radius from 8.6% to 4.2% (about 51% reduction). This considerable reduction is mainly a result of the high contact force at the sheet-punch corner interface. The maximum thinning in the pocket was reduced from 26% to 15.5% (in practice, both values may cause fracture). When the reverse (solid) punch is used to fill the pocket, extra force is required to overcome friction. This force will be transmitted through the sheet and cause excessively thinning. It should be noted that the pocket filling with a hydraulic medium is similar to SHF-D process. Another advantage observed in the simulations for the SHF-P is that the sheet is taking the exact shape of the punch, where in deep drawing, a gap is left between the sheet and the punch. It was noticed in the deep drawing simulations that the sheet at the punch base, especially at the unsupported region under the pocket, thins slightly during the process even before stretch forming in the pocket. This 119

143 thinning history is another reason for the high thinning in the pocket in deep drawing. 7.2 Future Work Characterization of AHSS at Room Temperature: The engineering stress-strain curve of AHSSs around the UTS is almost flat. This means that a clear neck, and a change from a uniaxial to triaxial state of stress, may not occur immediately after the UTS is exceeded. It is interesting to check experimentally if the neck formation coincides with the UTS. This may change the way of determining and reporting the uniform elongation for this special steel family. To further check the suitability of the power law fit, a sheet forming process can be simulated with the original flow stress and with the power law fit, and the results compared with the experimental data. Characterization of Aluminum Alloys at Elevated Temperature: To repeat the elevated temperature bulge test experiments of AA5754-O, AA5182-O, and AA3003-O in order to get reliable data to be used as an input to the optimization methodology. To develop the capability to control the strain rate at the dome apex by controlling the flow rate of the pressurizing medium. To increase the tips radii of the probes used to prevent (reduce) sheet penetration and therefore prevent probe deflection. To simulate of the elevated temperature bulge test to understand the effect of the rheological parameters; K, n, and m on the strain, strain rate, and 120

144 thickness distribution in the dome, as well as the shape of the dome. This will help in selecting the best parameter to be measured and compared with the simulation in the inverse analysis methodology. The combined FE-optimization methodology is very promising for the elevated temperature bulge test. However, it should be improved to be more robust. Simulation of SHF-P Process: To run experiments at General Motors R&D to validate the simulation results. The conical punch has a very small conical angle, which makes it easier to design the process since applying high pressure cannot bulge the sheet in the punch-die clearance easily. Another punch with larger angle can be made to make the design process more challenging and closer to reality. 121

145 REFERENCES [Abbedrabbo et al, 2006-a] Abbedrabbo N., Pourboghrat F., Carsley J., (2007), Forming of AA5182-O and AA5754-O at elevated temperatures using coupled thermo-mechanical finite element models, International Journal of Plasticity, Vol. 23, pp [Abbedrabbo et al, 2006-b] Abbedrabbo N., Pourboghrat F., Carsley J., (2006), Forming of Aluminun Alloys at Elevated Temperature- Part 1: Material Characterization, International Journal of Plasticity, Vol 22, pp [ASM 14B, 2006] American Society for Metals (ASM), (2006), ASM Handbook Vol. 14B, Metal Working: Sheet Forming, Metals Park, Ohio [ASTM E646-07, 2007] ASTM Committee E28, Subcommittee E28.02, (Approved on December 2007), Standard Test Method for Tensile Strain-Hardening Exponents (n -Values) of Metallic Sheet Materials, ASTM E [ASTM E517-00, 2006] ASTM Committee E28, Subcommittee E28.02, (Approved on September 2006), Standard Test Method for Plastic Strain Ratio r for Sheet Metal, ASTM E [Aust, 2001] Aust M., (2001), Modified Hydromechanical Deep Drawing, Hydroforming of Tubes, Extrusions, and Sheet Metals, Edited by Siegert K., Vol. 2, pp [Bird et al, 1981] Bird J., Duncan J., (1981), Strain Hardening at High Strain in Aluminum Alloys and Its Effect on Strain Localization, American Society for Metals and the Metallurgical Society of AIME, Issue 2, Vol. 12, PP [Bolt et al, 2001] Bolt P.J, Lamboo N.A.P.M, Rozier P.J.C.M, (2001), Feasibility of Warm Drawing of Aluminum Products, Journal of Materials Processing Technology, Vol. 115, pp

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148 [Koc et al, 2007] Koc, M., Mahabunphachai, S., Usta, Y., (2007) "Determination of Lightweight Alloy Sheet Properties at Elevated Temperature using Hydraulic Bulge Test", Center for Precision Forming Report CPF-2.2b/2007/11 [Li et al, 2003] Li D., Ghosh A., (2003), Tensile Deformation Behavior of Aluminum Alloys at Warm Forming Temperature, Material Science and Engineering A, Vol. 352, pp [Maki, 2003] Maki T., (2003), Current Status of Fluid Forming in the Automotive Industry, Hydroforming of Tubes, Extrusions, and Sheet Metals, Edited by Siegert K., Vol. 3, pp [Marciniak et al, 2002] Marciniak, Z., Duncan J.L., Hu S.J., (2002), Mechanics of Sheet Metal Forming, 2 nd edition, Butterworth-Heinmann, Oxford [Meinhard et al, 2005] Meinhard B., Palaniswany H., Altan T., (2005), Estimation of Optimum Blank Holder Force and Pressure Trajectories in Sheet Metal Hydroforming with a Punch (SHF-P)-Hydromechanical Deep Drawing (HMD), CPF-4.2b/06/01 (ERC/NSM-05-R-21), The Center for Precision Forming (CPF), Columbus, Ohio [Nasser et al, 2009] Nasser A., Yadav A., Pathak P., Altan T., (2009), Determination of the Flow Stress of Five AHSS Sheet Materials (DP 600, DP 780, DP 780-CR, DP 780-HY and TRIP 780) using the Uniaxial Tensile and the Biaxial Viscous Pressure Bulge (VPB) Tests, Journal of Materials Processing Technology, (in the progress of publication) [Nasser et al, 2008] Nasser A., Pathak P., Yadav A., and Altan T., (2008), Determination of Flow Stress of Five AHSS Sheet Materials (DP600, DP780, DP780CR, DP780HY and TRIP 780) using the Uniaxial Tensile Test and the Biaxial Viscous Pressure Bulge Test, ERC/ NSM 08-R-03, the Center for Precision Forming (CPF), Columbus, Ohio, (Prepared for, and published with the permission of, the Auto-Steel Partnership A/S P) [Nasser et al, 2007] Nasser A., Yelich T., Yadav A., Palaniswamy H., Altan T., (2007), Summary Report: Flow Stress Determination and Formability Estimation in Sheet Materials using the Bulge Test, CPF / 07/ 01, The Center for Precision Forming, Columbus, Ohio [Palaniswany, 2007] Palaniswany H., (2007), Determination of Process Parameters for Stamping and Sheet Hydroforming of Sheet Metal Parts using 125

149 Finite Element Method, PhD Dissertation, Mechanical Engineering Department, The Ohio State University [Palaniswamy et al, 2007] Palaniswamy H., Mai J., Sung J., Kardes N., and Taylan Altan, (2007), Design of Tooling for Springback Studies in Forming AHSS Steels, CPF-1.4/07/03, The Center for Precision Forming (CPF), Columbus, Ohio [Pamstamp manual, 2007] Pamstamp 2G 2007 user manual, ESI group [Pathak et al, 2008] Pathak P., Yadav A., Penter L., Altan T., (2008), Determination of Flow Stress for Aluminum AA5754-O at Room Temperature using the Hydraulic Bulge Test at General Motors R&D, CPF-1.1/08/01, The Center for Precision Forming (CPF), Columbus, Ohio [Penter et al, 2008] Penter L., Yadav A., Cain P. and Altan T., (2008), Methodology for Flow Stress Determination using Biaxial Sheet Bulge Test using Commercial FEM code LS-DYNA & Optimization Tool LS-OPT - Part I: Room temperature, CPF-1.1/08/04, The Center for Precision Forming (CPF), Columbus, Ohio [Powers, 2000] Powers W., (May 2000), AUTOMOTIVE MATERIALS in the 21 st Century, Advanced Materials & Processes, Vol. 157, Issue 5, pp. 38 [Sadakopan et al, 2003] Sadakopan S., Urban D., (2003), Formability Characterization of a new Generation of High Strength Steels, American Iron and Steel Institute (AISI), Report TRP 0012 [Stander, 2007] Stander N., Roux W., Graig K. (2007), OPTIMIZATION THEORY, LS-OPT Training Class, Detroit [Sartkulvanich et al, 2008] Sartkulvanich P., Ma X., and Altan T., (2008), Finite Element Simulation of Instop Gasket Forming and Analysis of Fracture, ERC/NSM 08-R 01, The Center for Precision Forming (CPF), Columbus, Ohio [Shaw et al, 2001-a] Shaw J., Zuidema B., (October 2001), New High Strength Steels Help Automakers Reach Future Goals for Safety, Affordability, Fuel Efficiency and Environmental Responsibility, SAE

150 [Shaw et al, 2001-b] Shaw J., Watanabe K., Chen M., (March 2001), Metal Forming Characterization and Simulation of Advanced High Strength Steel, SAE [Sivakumar et al, 2006] Sivakumar R., Aue-u-Ian Y., Kaya S., Spampinato G., (2006), Flow Stress Database for Aluminum and Magnesium Alloys for Warm Sheet Forming, ERC/NSM-06-R-10, The Engineering Research Center for Net Shape Manufacturing (ERC/NSM), Columbus, Ohio [Spampinato et al, 2006] Spampinato G., Palaniswamy H., and Altan T., (2006), Warm Deep Drawing of Round Cups from Mg, Al, And SS - Non-Isothermal FE Simulations using LSDYNA, CPF-1.1/06/03, The Center for Precision Forming (CPF), Columbus, Ohio [Stamping, Nov 2008] Stamping Journal, (November 2008), Six Questions about Stamping Aluminum [Sung et al, 2007] Sung J., Kim H., Yadav A., Palaniswamy H., Altan T., Forming of Advanced High Strength Steel (AHSS), (2007), CPF-1.4/07/01, The Center for Precision Forming (CPF), Ohio State University, Columbus, Ohio [Wagoner et al, 1996] Wagoner R., Chenot J., (1996), Fundamentals of Metal Forming, John Wiley and Sons, Inc [World, 2009] World Steel Association, (2009), Advanced High Strength Steels (AHSS) Application Guidelines, [Yadav, 2008] Yadav A., (2008), Process Analysis and Design in Stamping and Sheet Hydroforming, PhD Dissertation, Industrial and Systems Engineering Department, The Ohio State University [Yadav et al, 2007] Yadav A., Gulisano G., Palaniswamy H., and Altan T., (2007), Summary Report: Sheet Hydroforming with Punch (SHF-P) Process, CPF- 4.2b/07/01, The Center for Precision Forming (CPF), Columbus, Ohio 127

151 APPENDIX A AQUADRAW MODULE IN PAMSTAMP 2G 2007 (This appendix is adapted entirely from [Pamstamp manual, 2007]) Aquadraw This option creates an aquadraw attribute for the blank which can be used to model the forming process illustrated in figure below. Note that the aquadraw process input data are not issued from a macrocommand, therefore the user must create all the necessary attributes and conditions for each component (object) of the process. For further information, please refer to the User's Guide. The process makes use of conventional deep drawing tools, but the die is filled with a relatively incompressible fluid such as water. Additional pumps and valves may be included to prebulge the sheet and/or to control the maximum 128

152 fluid pressure. During forming the pressure in the die cavity rises as the fluid is compressed until the resultant force acting on the sheet is sufficient to lift the blankholder. At this point fluid begins to escape via the gap between the binder and sheet, relieving the pressure and reducing friction on the die side. A continuous controlled lift of the blankholder during forming is generally desirable and is known as a stable aquadraw regime. i Dialog Box This dialog enables the user to define the parameters for the aquadraw attribute. 129

153 Curve Selection The button allows the user to gain access to the 2D curve plotter which is used to specify time varying pressure limits and flow rates into the cell. Fluid Bulk Modulus The Bulk modulus of fluid K is used to calculate the cell pressure p using the formula: where VC is the volume of the fluid cell and VF is the volume of the fluid contained in the cell when uncompressed. Normally the physical bulk modulus of the fluid should be specified, although in special applications such as superplastic forming with strain rate control, an artificial K value may be used. Very large values of K may lead to integration stabilities, particularly if the fluid cell volume is small. However, in normal applications with water or oil emulsions these problems seldom occur. If encountered they can be cured by reducing the time step factor. Volume Definition Ideally, the fluid cell should be defined as a closed volume with shell elements and the orientation of the elements should be such as to have their normal pointing inwards. Volume definition with: The volume is defined between the blank an object selected in this drop-down list, usually the die. Axis for volume definition: The direction of this axis is defined by a vector either by using the help of the wizard or by typing its components in the text fields. Warning, only one of the three main directions can be used (X-axis, Y-axis or Z- axis). The volume of the fluid cell is calculated by summing up the contributions of rectangular prisms drawn on each boundary segment with sides parallel to a specified integration direction, as illustrated in figure below. 130

154 Note Surface elements whose normals are perpendicular to the integration axis do not contribute to the volume sum and can be omitted. When symmetry has been exploited in the model, it is often convenient to leave out surface boundaries on symmetry planes, while choosing an integration axis which lies within them. : This drop-down list defines whether the axis definition is done in the Global or a user-defined system of axes. Initial volume: It can be defined by the user to avoid model positioning problem. Optional Volume flow rate curve: Select in the drop-down list the curve that defines the volume flow rate. Maximum fluid pressure curve: Represents the maximum pressure the system can develop within the fluid cell. Maximum velocity curve: The maximum sheet velocity should be limited to 10 m/s to avoid unwanted inertia effects. Note that the average sheet velocity Vs is related to the flow rate F by the approximate formula, where Am is the area of moving boundaries in the cell. 131