IMPROVING THE FORMABILITY LIMITS OF LIGHTWEIGHT METAL ALLOY SHEET USING ADVANCED PROCESSES - FINITE ELEMENT MODELING AND EXPERIMENTAL VALIDATION-

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1 IMPROVING THE FORMABILITY LIMITS OF LIGHTWEIGHT METAL ALLOY SHEET USING ADVANCED PROCESSES - FINITE ELEMENT MODELING AND EXPERIMENTAL VALIDATION- DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Graduate School of The Ohio State University By Serhat Kaya, M.S. * * * * * The Ohio State University 2008 Dissertation Committee: Approved by Professor Taylan Altan, Adviser Associate Professor Jerald Brevick Assistant Professor Allen Yi Adviser Industrial and Systems Engineering Graduate Program

2 ABSTRACT Weight reduction is one of the major goals in the automotive, appliance and electronics industries. One way of achieving this goal is to use lightweight alloys such as aluminum and magnesium that have high strength to weight ratios. However, due to their limited formability at room temperature, advanced forming processes are needed. Room temperature and elevated temperature hydraulic bulge tests (using a submerged tool) were conducted for Al 5754-O and Mg AZ31-O to determine their mechanical properties. Experiments were conducted between room temperature and 225 C, at various approximate true strain rates. Strain values up to 0.7 were obtained under equi-biaxial state of stress at elevated temperatures. Flow stress curves were calculated using the membrane theory. Deep drawability of aluminum and magnesium alloys is investigated through experiments and process simulation at room temperature (using solid dies), against liquid pressure (hydroforming) and at elevated temperatures (warm forming). Limiting Draw Ratio (LDR) of Al 5754-O is increased from 2.1 (room temperature) to 2.4 when hydroforming is used as the drawing process. This value is increased to 2.9 when warm forming is used. Formability of Mg ii

3 AZ31-O is found to be limited at room temperature while LDR up to 3.2 is obtained at elevated temperatures. Warm forming experiments were conducted using a servo motor driven press and a heated tool set. The in-die dwelling concept is developed by using the flexibility of the servo press kinematics and blanks were heated in the tool set prior to forming. Temperature time measurements were made at various blank holder interface pressures in order to determine the required dwell time to heat the blank to the forming temperature. Several lubricants for elevated temperature forming were evaluated using the deep draw test and a PTFE based film was selected as a lubricant at elevated temperatures. Deep drawing tests were conducted to determine the process window (max. punch velocity as functions of blank size and temperature) for Al 5754-O and Mg AZ31-O. Maximum punch velocities of 35 mm/s and 300 mm/s were obtained for the Al and Mg alloys, respectively. Comparisons for the Mg alloy sheets from two different suppliers were made and significant differences in formability were found. Additional experiments were conducted in order to understand the effect of constant and variable punch velocity and the temperature on the mechanics of deformation. Variable punch velocity is found to improve the thickness distribution of the formed part and provide 60 % reduction in the drawing time. By calculating heat transfer coefficients using inverse optimization, computational models are iii

4 developed and experimental results are used to validate the predictions from the computational model. iv

5 Dedicated to my family v

6 ACKNOWLEDGEMENTS I wish to thank my adviser, Taylan Altan, for intellectual support, encouragement and enthusiasm which made this thesis possible, and for his patience in correcting both my stylistic and scientific errors. I thank my candidacy and dissertation committee members Professors Jerald Brevick, Ted Allen and Allen Yi for discussions and support. Most of this research was supported by a grant from the National Science Foundation. Finally, I sincerely thank to my mother Neriman Kaya, my father Ahmet Kaya, my sister Neslihan Kaya and my brother Ferhat Kaya for their unending support, encouragement and patience. vi

7 VITA July 07, Born Istanbul, Turkey Die Design Engineer, Turkey M.S., Mechanical Eng. Yildiz Technical University, Istanbul M.S., Industrial and Systems Eng. The Ohio State University 2002 present... Graduate Research Associate, The Ohio State University Research Publication Book Chapter PUBLICATIONS 1. William Thomas, Taylan Altan and Serhat Kaya, (2003) Handbook of Aluminum, Volume I, Physical Metallurgy and Processes, Chapter 18, pp , Marcel Dekker, Inc., New York, ISBN: Journal Papers 2. Taylan Altan, Serhat Kaya, Yingyot Aue-u-lan, (2007), Forming Al and Mg Alloy Sheet and Tube at Elevated Temperatures, Key Engineering Materials, vol.344, pp Serhat Kaya, Taylan Altan, Peter Groche, Christian Kloepsch, (2006), Determination of Flow Stress of Magnesium AZ31-O Sheet At Elevated Temperatures Using the Hydraulic Bulge Test, (accepted/in print - Special Issue of International Journal of Machine Tools and Manufacture) vii

8 Conference Papers 4. Taylan Altan, Serhat Kaya, Yingyot Aue-u-lan, (2007), Forming Al and Mg alloy Sheet and Tube at Elevated Temperatures, Shemet 07, 12th International Conference on Sheet Metal, April 1-4, Palermo, ITALY 5. Hariharasudhan Palaniswamy, Ajay Yadav, Serhat Kaya, Taylan Altan, (2007), New Technologies to Form Light Weight Automotive Components, 4th International Conference and Exhibition on Design and Production of Machines and Dies/Molds, DIEMOLD 2007, June 21-23, Cesme, TURKEY 6. Serhat Kaya, and Taylan Altan, (2006), Forming Limits of AZ31-O Magnesium Alloy Sheet at Elevated Temperatures, 2006 NSF Design, Service and Manufacturing Grantees and Research Conference, July 24-27, 2006, St. Louis, Missouri, USA 7. Taylan Altan, Yingyot Aue-u-lan, Hariharasudhan Palaniswamy, Serhat Kaya, (2005), State of the art-visions and priorities in research and development in metal forming, Proceedings of the 8th International Conference on Technology of Plasticity, ICTP 2005, ISBN X, pp.3-24, October , Verona, ITALY (Keynote Paper) 8. Taylan Altan, Yingyot Aue-u-lan, Serhat Kaya, (2004), Tube and Sheet Hydroforming-New Developments in Equipment, Tooling and Process Simulation, Society of Manufacturing Engineers, SME, 2nd Annual North American Hydroforming Conference, September 27-29, 2004, Ontario, CANADA FIELDS OF STUDY Major Field: Industrial and Systems Engineering Minor: Design / Mechanics of Materials Minor: Design of Experiments, DOE viii

9 TABLE OF CONTENTS Abstract..ii Dedication..v Acknowledgements.vi Vita...vii List of Tables..xii List of Figures xiv Chapters: 1. Introduction Objectives Mechanical properties of aluminum and magnesium alloys Forming behavior of Mg alloy sheet Strength asymmetry in Mg alloy sheets Determination of the flow stress of lightweight alloy sheet under equi-biaxial state of stress Introduction Experimental Setup Calculation of stresses and strains under equi-biaxial state of stress Membrane Theory Calculation of the radius of the bulge (dome) Calculation of the Thickness at the Top of the Dome Stress Strain relationship at elevated temperature for magnesium alloy sheet Experimental investigation Observations Test conditions and experimental matrix Measurement of initial sheet thickness ix

10 4.8.4 Sheet Draw-in During Bulging Pressure bulge height curves Analysis of the dome geometry Deviation from the original bulge shape Thickness distributions along the dome curvature Conclusions Deep drawing process at room temperature Drawability Criteria Critical Stroke in deep drawing Deep drawing of aluminum and magnesium at room temperature Hydroforming of sheet at room temperature Mechanics of SHF-P Process Prediction of the Initial Pressure Value SHF-P of a 90 mm round cup Deep drawing at elevated temperature Introduction Experimental Setup Servo press and its kinematics Design of the tooling Issues at the interface in forming at elevated temperature Heating the blank Effect of the interface pressure on the hardness and the surface roughness Hardness Measurements Surface roughness measurements Dome formation in the sheet under pressure Lubricant evaluation for warm deep drawing process Preliminary Experiments Process Optimization / Windows Effect of constant forming velocity and temperature on deformation Results for Al 5754-O Results for Mg AZ31-O (Supplier A) x

11 Results for Mg AZ31-O (Supplier B) Effect of Variable Forming Velocity Conclusions Modeling of non-isothermal deep drawing process Determination of the heat transfer coefficients Inverse Analysis Setup of the inverse analysis problem Non-isothermal deep drawing of Mg AZ31-O Mg AZ31-O flow stress in literature FE Modeling in LS-Dyna3D Plastic-thermal material model available in LS-Dyna Thermal contact definition Simulation matrix Comparison of FE predictions and experimental results Non-isothermal deep drawing of Al 5754-O Yield criterion adopted in the FE model for the Al 5754-O Flow stress curves for aluminum Comparison of numerical predictions with experimental measurements Non-isothermal modeling of SHF-P Conclusions Determination of drawability using fracture criterion Cockcroft & Latham ductile fracture criterion Approach Setup of the FE model for tensile test and deep drawing Results and discussion Determining the Critical Damage Value Deep drawing analyses Conclusions Summary and conclusions Bibliography xi

12 LIST OF TABLES Table 3.1 List of wrought Mg alloys and their product range [Avedesian et al. 1999] Hensel coefficients obtained from elevated temperature forming of magnesium sheets in tensile test [Droeder, 1999] Experimental matrix for high formability sheets (strain rate values are approximate) Experimental matrix for low formability sheets (strain rate values are approximate) Thickness measurements for high and low formability sheets Comparison of radius values (R 1 & R 2 ) obtained by using 5 and 3 points Measured and calculated thickness values at the apex Curvilinear length and percentage stretch of the sheet in the sheet radius zone according to Figure 6.7 (pressure curve: P4) Friction coefficients used in the FEA Hardness (Brinell) measurements of Al 5052-H Hardness (Brinell) measurements of Mg AZ31-O (Supplier A) Hardness (Brinell) measurements of Mg AZ31-O (Supplier B) List of lubricants and experimental conditions Summary of the preliminary screening experiments for Al 5754-O, Al H32 and MgAZ31-O Experimental results for Al 5754-O xii

13 7.7 Experimental results for Mg AZ31-O (Supplier A) Experiments at 225 o C Experiments at 250 o C and lower velocities Significant savings in drawing time is obtained through the use of variable forming velocity AZ31B-O simulation matrix Summary of input data used for AZ31B-O simulations List of input parameters to the FE model (Al 5754-O) Simulation matrix for the deep drawing analysis Summary of obtained drawability through the use of different manufacturing processes A.1 Calculated flow stress values and related process parameters A.2 Press characteristics.182 B.1 Mesh Density Windows (same values used in S1, S2 and S3).194 B.2 Flow stress data of St C.1 Stainless steel blank dimensions used for the drawability investigation (D B = blank diameter, D P = punch diameter) C.2 Blank dimensions and process conditions xiii

14 LIST OF FIGURES Figure 3.1 a) Uniform and post-uniform strains vs. temperature for different strain rates and b) variation of total elongation with temperature and strain rate for alloy 5182-O [Ayres, 1977] Temperature dependent flow stress of Mg AZ31B alloy determined by tensile test [Doege et al. 2001] Flow stress at different temperatures for Mg AZ31B sheet with different temper [Doege et al. 2001] Stress-strain data for AZ31B plate deformed in in-plane tension (IPT) and compression (IPC) and through-thickness compression (TTC) [Agnew, et.al., 2002] Compression flow curves as a function of testing temperature. The transverse (open symbol) samples are stronger than the rolling (closed symbols) at all temperatures A comparison of experimental (symbols) and simulated (curves) compressive flow behavior at a) RT, b) 150 C, c) 175 C and d) 200 C Measured (symbol) and predicted tensile r-values Plot of the variation in r-values after compression (strain ~0.11) at different temperatures. (symbols are experiments curves are predictions) [Jain, 2005] Initial (left) and the deformed sheet (right) in the hydraulic bulge test Geometrical and process related parameters Elevated temperature Hydraulic Bulge Tooling (PtU, TU Darmstadt) Hoop ( σ 1 ) and Transverse ( σ 2 ) Stresses and Dome Radii in a Membrane.22 xiv

15 4.5 Comparison of Hensel Model and Experimental Data [Droeder, 1999] Thickness measurement along Rolling Direction (RD), and Transverse Direction (TD) (dimensions in mm) Pressure-bulge height curves at the approximate strain rate of 0.25s Pressure-bulge height curves at the approximate strain rate of s Measurement points on the bulged sheet Comparison of calculated and measured bulge radius values Radius difference using 5 and 3 points Residual plots for sample at h d =14.7 mm Residual plots for sample at h d =21.7 mm Residual plots for samples at h d =33.9 mm Thickness distribution along the RD (bulge height (h)=~21mm and h 33 mm) Schematic representation of the strain rate and flow stress gradients in the bulged sample True stress and true strain curves at 0.25 s True stress and true strain curves at s True stress true strain curve with possible errors at 225 C (0.025 s -1 ) Axisymmetric Top view of drawn sheet Stress on an Thickening of the sheet in the flange area xv

16 5.5 Definition of cup height (h) for a cup with a flange and without a flange Deep drawn cup with ears Schematic view of the critical stroke (S cr ) before (left) and after (right) RT drawing of Al 5754-O RT drawing of Mg AZ31-O SHF-P process a) without leakage; b) with leakage Important tool parameters that influence the SHF-P process During a hydromechanical deep drawing process the sheet loses contact with the die Maximum thinning around the cup bottom radius at two different values of the punch stroke Position of the slab in the sheet radius zone (a) and equilibrium of the forces in the slab (b) Pressure-stroke curves used in the critical stroke Initial (a) and final (b) length of stretch in the sheet used to evaluate the material stretching in the sheet radius zone Fluid pressure determined based on the critical stroke Thinning distribution along the 45 cup wall Open (left) and closed (right) condition of the tool AIDA servo-mechanical press drive mechanism Ram motion of the servo press (TDC: top dead center, BDC: Bottom dead center) Schematic view and the dimensions of the tool (dimensions are in mm).. 76 xvi

17 7.5 Warm forming with in-die dwelling process sequence Open warm forming tooling (top die set on the left, bottom die set on the right) [Kaya, et.al., 2006] Assembled tooling on the Aida servo press ton Aida Servo Press Top view of the fixture used to determine the dwell time necessary to heat the blank (thickness 3mm) Schematic view of the experimental setup with the affected interfaces Temperature-time curves obtained with the test fixture for different interface (blank holder) pressures (tool temperature=300 o C) Punch and knockout pin temperatures at tool temperatures of 250 o C, 275 o C and 300 o C R a values for 5754-O and 5052-H R a values for Mg AZ31-O (Supplier A) and Mg AZ31-O (Supplier B) BHP dome height at T=300 C Change in the sheet diameter with respect to the BHP (Sheet Diameter: 100 mm) Thickness distributions for different lubricants under same process conditions [Kaya, et.al., 2006] Cup with Lube A after drawing [Kaya, et.al., 2006] Al cups formed with Lube C, Lube B and Lube A (from left to right) Mg cups formed with Lube C, Lube B and Lube A (from left to right) Adopted methodology for preliminary experimentation xvii

18 7.22 Variation of LDR with punch velocity (Mg AZ31-O, T=250 o C) Variation of LDR with punch velocity (Mg AZ31-O, T=275 o C) Variation of LDR with punch velocity (Mg AZ31-O, T=300 o C) Process window for the Mg AZ31-O alloy Process window for the Al 5754-O alloy Effect of temperature on thickness distribution (5 mm/s, DR 2.5) Effect of temperature on thickness distribution (15 mm/s, DR 2.5) Punch load stroke curves at 5mm/s for different temperatures Punch load stroke curves at 15mm/s for different temperatures Change in cup bottom temperature at 5 mm/s (Punch temp ~55 o C, 65 o C, 73 o C) Change in cup bottom temperature at 15 mm/s (Punch temp: ~55 o C, 65 o C) Effect of temperature on thickness distribution (5 mm/s, DR 2.5) Effect of temperature on thickness distribution (15 mm/s, DR: 2.5) Effect of temperature on thickness distribution (50 mm/s, DR: 2.5) Effect of forming velocity on thickness distribution (250 o C, DR: 2.5) Effect of forming velocity on thickness distribution (275 o C, DR: 2.5) Effect of forming velocity on thickness distribution (300 o C, DR: 2.5) Punch load stroke curves at 5mm/s for different temperatures Punch load stroke curves at 15mm/s for different temperatures Punch load stroke curves at 50mm/s for different temperatures xviii

19 7.42 Change in cup bottom temperature at 5 mm/s Change in cup bottom temperature at 15 mm/s Change in cup bottom temperature at 50 mm/s Pictures of the formed cups from Al 5754-O (left) and Mg AZ31-O (Supp.A) (right) Effect of blank temperature and punch velocity upon wall thinning at the bottom corner of the drawn cup for the Al 5754-O alloy Effect of blank temperature and punch velocity on thinning at the bottom corner of the drawn cup for the Mg AZ31-O alloy Effect of variable forming speed on the thickness distribution of the drawn Al cups Effect of variable forming speed on the thickness distribution of the drawn Mg cups Experimental and calculated temperature-time curves Schematic view of the FE model Modeling of the measurement fixture with the temperature measurement point Calculated heat transfer coefficients Graphical representation of the database for Magnesium AZ31 Tensile tests conducted at different strain rates and temperatures [Sivakumar, et al, 2006] FE model for non-isothermal simulations of deep drawing of round cups Contact-Forming card used to define mechanical and thermal contact parameters xix

20 8.8 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction Comparison of experimental yield loci and those predicted by the Von Mises, Hill, Tresca, Logan-Hosford and Barlat criteria under biaxial stress condition for Al 5083-O alloy sheet [Naka, et.al., 2003] Extrapolated flow stress versus temperature for different strain rates(original data from Boogard, 2001) Elimination of the softening behavior from the stress-strain curve xx

21 8.19 Comparison of punch load predictions using various heat transfer coefficients (HTC: kw/m 2 C) with experiment (5 mm/s at 250 o C) Predicted thickness distribution comparison with various heat transfer coefficients (5 mm/s at 250 o C) Comparison of punch load prediction with experiment (5 mm/s at 275 o C) Predicted thickness distribution comparison with experiments (5 mm/s at 275 o C) Comparison of punch load prediction with experiment (5 mm/s at 300 o C) Predicted thickness distribution comparison with experiments (5 mm/s at 300 o C) Comparison of punch load prediction with experiment (15 mm/s at 275 o C) Predicted thickness distribution comparison with experiments (15 mm/s at 275 o C) Predicted thickness distribution comparison with experiments (5 mm/s at 300 o C) Predicted thickness distribution comparison with experiments (5 mm/s at 300 o C) Interfaces in elevated temperature SHF-P process Pressure and BHF used in the simulations Temperature distribution of the sheet at the end of the stroke Temperature distribution of a sheet formed using SHF-P Temperature distribution of a deep drawn sheet Flow stress curve of Al 5754-O obtained from the bulge test xxi

22 9.2 Geometry of the tensile specimen (ASTM, E 8M-04) Flow stress curves used in the FEA Point of instability in the load-stroke curve during the tensile test CDV (when necking starts during 3D tensile test simulation) for Al 5754-O is CDV (when necking starts during 3D tensile test simulation) for Al 6061-T6 is Maximum CDV obtained for the successfully deep drawn Al 5754-O (LDR: 2.1) cup is Max CDV reaches 0.42 for the unsuccessfully deep drawn Al 5754-O (LDR: 2.2) cup Maximum CDV obtained for Al 6061-T6 (LDR: 1.6) is Maximum CDV obtained for Al 6061-T6 (LDR: 1.5) is A.1 Flow stress curves of the tested aluminum alloys. 181 A.2 Thinning measurements are done in Direction 1-3 and Direction A.3 Comparison of the predicted and measured pressure values for O.185 A.4 Thinning comparison in Direction 1-3; at corner 1 the difference is 14 (%) while at corner 3 it is 11 (%) A.5 Thinning comparison in Direction 2-4;at corner 2 the difference is 10 (%) while in the corner 4 is 1.5 (%) A.6 Pressure comparison; max pressure for simulation is 199 (Bar) while measured pressure value from the experiments is 208 (Bar) xxii

23 A.7 Thinning comparison in Direction 1-3; at corner 1 the difference is 2 (%) while at corner 3 it is 7 (%) A.8 Thinning comparison in Direction 2-4; at corner 2 the difference is 3 (%) while at corner 4 it is 2 (%) A.9 Pressure comparison; max pressure for simulation is 192 (Bar) while measured pressure value from the experiments is 218 (Bar) A.10 Thinning comparison in Direction 1-3; at corner 1 the difference is 4 (%) while at corner 3 it is 10 (%) B.1 Mesh Density Windows for the blank holder B.2 Mesh Density Windows for the die-ring B.3 Predicted elastic deflection is shown with the dashed line. 197 B.4 Predicted elastic deflection is shown with the dashed line [Kaya, et.al., 2004] C.1 Limiting DR - Die/BH temperature (forming velocity 2.5 mm/s) 202 C.2 Geometrical parameters (height and external diameter) of the cups drawn at different conditions C.3 Thinning distribution along rolling and transverse direction for cup A and cup B.203 C.4 Thinning distribution along rolling and transverse direction for cup C and cup D. 204 C.5 Limiting DR - Die/BH temperature (forming velocity 25 mm/s).205 C.6 Limiting DR - Die/BH temperature (forming velocity 50 mm/s).206 xxiii

24 CHAPTER 1 INTRODUCTION Weight reduction while maintaining functional requirements is one of the major goals of engineering design and manufacturing so that materials, energy, and costs are saved and environmental damage is reduced. Magnesium (Mg) and Aluminum (Al) alloys offer great potential to reduce weight by displacing the most commonly used materials, i.e. steel and polymers, because of their high strength to weight ratio. Other important factors in selecting Mg and Al alloys for engineering applications, compared to other engineering materials include their thermal properties, damping capacity, fatigue properties, dimensional stability and easy machinability [Avedesian et al. 1999, Naka et al. 2001]. Besides Al and Mg, it is important to mention weight reduction can also be achieved by using thinner gauge steels (high strength steel, stainless steel) and forming them using advanced forming processes. The use of forming technology for Al and Mg alloy sheet is restricted because of the low formability of these materials especially at room temperature. Therefore, advanced forming methods are needed in order to improve their formability. Some improvement is believed to be obtained when 1

25 drawing these materials against pressure (sheet hydroforming) and at elevated temperatures (warm forming). Investigation of the formability limits of aluminum and magnesium sheet is done by using these advanced forming techniques. This study focuses on 1) the design and development of forming process with emphasis on a) material properties, b) deformation mechanics c) the forming temperatures, d) the interface condition (friction, lubrication and heat transfer), e) the tool temperature, f) tooling/ equipment design, and g) constant and variable forming speed (or strain rate); 2) the influence of the forming equipment (servo motor driven press) on the process and the final product and 3) computational modeling of the process. Al and Mg alloys show increased formability especially at temperature range of 200 o C to 300 o C. Currently formed Al alloy components find applications only as shallow parts in automobile body panels and chassis applications because of their low room temperature formability. Warm forming technology for Al alloys has been investigated by Bolt et al., 2001a, Bolt et al., 2001b, Boogard et al., 2001a, Boogard et al., 2001b, Wu et al. 2001, Taylor et al. 1980, Naka et al. 2001, Shehta et al. 1978, Li et al., 2000, Groche They have found that 5xxx series and 6xxx series Al alloys show increased formability at the range of 250 o C to 300 o C. However, there is a lack of 2

26 sufficient knowledge on warm sheet forming processes which limited the practical use of these alloys. 3

27 CHAPTER 2 OBJECTIVES The overall objective of the proposed research is to increase the formability (drawability) limits of aluminum and magnesium using advanced forming methods. Thus the major specific objectives of this study are; 1. Determine elevated temperature mechanical properties of magnesium sheet under equi-biaxial state of stress using hydraulic bulge test 2. Determine the influence of the process parameters in hydroforming of Al and Mg sheet (SHF-P / Sheet hydroforming with punch) and increase the drawability 3. Investigate the use of a servo motor driven press for in-die-dwelling using a warm deep drawing tool to improve warm drawability of aluminum, magnesium and stainless steel alloys 4. Determine the effect of process parameters (punch velocity, lubrication, temperature, interface pressure) and geometrical parameters (punch and die radii, initial blank size) on metal flow in deep drawing round Al and Mg alloy cups. 4

28 5. Develop FE models of the deep drawing and hydroforming process by applying the appropriate pressure, temperature, interface and velocity boundary conditions under isothermal and non-isothermal conditions, and compare predictions with experimental data. 6. Develop a methodology to minimize experimentation to determine the drawability of aluminum sheet. 5

29 CHAPTER 3 MECHANICAL PROPERTIES OF ALUMINUM AND MAGNESIUM ALLOYS Most common testing methods to investigate the formability are uniaxial tension, plane strain tension, bending, Limiting Dome Height (LDH) test and drawing test. Tensile test provides information that characterizes material s potential in formability and delivers qualitative information on the yield point and the stress levels at the onset of necking in uniaxial state of stress. However, most of the deformation in real forming operations occurs mostly in biaxial even in triaxial state of stress. It is possible to improve the formability of lightweight alloys through forming operations at elevated temperatures. [Taylor et. al, 1976] conducted their investigations using tensile test in the strain rate range of 7x10-4 sec -1-3 sec -1 for alloys 5182-O, 5085-H11 and 5090-H34, and found a substantial increase in the tensile elongation at a temperature of 473 o K. In particular, their results indicated that the work hardening rate and uniform elongation decreased but the strain rate sensitivity and total elongation increased with increasing temperature. In other words, the increase in the total elongation is exclusively contributed by the post-uniform elongation. Figure 3.1 shows the results obtained by [Ayres, 1977] for Al alloy 5182-O. It is clear from Figure 6

30 3.1a that, as temperature increases, the post-uniform strain increases while the uniform strain decreases, and this trend is enhanced by decreasing strain rate. Since the increase in the post-uniform strain dominates that in the uniform strain, the total elongation increases with temperature at various strain rates (Figure 3.1b) for temperatures of 373 o K and higher. 7

31 Figure 3.1: a) Uniform and post-uniform strains vs. temperature for different strain rates and b) variation of total elongation with temperature and strain rate for alloy 5182-O [Ayres, 1977] 3.1 Forming behavior of Mg alloy sheet Mg is the lightest of all commonly used structural metals with a density of approximately 2/3 that of aluminum. Commercially available Mg alloy is classified as zirconium containing alloys and zirconium free alloys. A comprehensive list of Mg wrought alloys is shown in Table

32 Zirconium free alloys Zirconium containing alloys Mg-Al-Mn-Zn alloy system Mg-Zn-Cu alloy system Mg-Li alloy system Mg-Zn-Zr alloy system Forging M1A-F, AZ31B-F, AZ61A-F, AZ80A-T5, AZ80A-T6 Extruded bars and tubes M1A-F, AZ10A-F, AZ31B-F, AZ61A-F, AZ80A-T5 Sheet AZ31B ZM21-F ZC71-T6, ZM21-F ZM21 Currently under investigation ZK31-T5, ZK60A-T5, ZK61-T5 Currently under investigation ZK21A-F, ZK31-T5, ZK60A-T5 Currently under investigation. Table 3.1: List of wrought Mg alloys and their product range [Avedesian et al. 1999] The limited formability of Mg sheet at room temperature is due to the hexagonal closed pack (hcp) lattice structure that has three slip systems compared to the twelve slip systems in face centered cubic (fcc) and body centered cubic (bcc) lattice structures. Therefore it is better to form Mg alloys at elevated temperatures ( o C), which activates additional slip planes thereby improving the material formability. Mg alloy sheets, AZ31B and ZM21, which are commonly produced, are hot rolled at temperatures of 315 o C o C to the final thickness. The amount of work hardening remaining in the material and the amount of annealing that takes place during and after final pass rolling is critical in forming applications. 9

33 [Doege et al., 2001] conducted exhaustive investigation on the plastic material properties of Mg alloy sheet AZ31B at room temperature by conducting uniaxial tensile tests. The Mg alloy showed an elongation of 17% and strain hardening coefficient of On the other hand, Mg alloy sheet (AZ31B) shows remarkable increase in the formability in tensile test at temperatures above 200 o C as shown in Figure 3.2. The effect of rolling condition on the flow stress decreases with increase in the temperature as shown in Figure 3.3. [Takuda et.al., 2005] has conducted uniaxial tensile tests at constant crosshead velocities (0.02 mm/s, 0.2 mm/s, 2 mm/s and 20 mm/s) between 150 o C and 300 o C and obtained strain values up to 0.7. Most of the available literature on the formability of Mg is on the uniaxial testing. Pneumatic bulge tests conducted at IFU of the University of Stuttgart also showed significant formability increase in the Mg alloy sheet [Siegert, 2003] and [Siegert, 2004]. However, information on properties of Mg alloy sheet obtained at elevated temperatures under equi-biaxial state of stress is very limited. Also the geometrical evolution of the dome under equi-biaxial state of stress, various temperatures and strain rates has not been studied. 10

34 Figure 3.2: Temperature dependent flow stress of Mg AZ31B alloy determined by tensile test [Doege et al. 2001] Figure 3.3: Flow stress at different temperatures for Mg AZ31B sheet with different temper [Doege et al. 2001] 3.2 Strength asymmetry in Mg alloy sheets Magnesium alloy sheets tend to exhibit asymmetric behavior in yielding (much higher yield stress during in-plane tension than compression) due to different 11

35 metallurgical mechanisms, which operate under different loading conditions [Agnew et al, 2002] (Figure 3.4). Asymmetric deformation behavior is a characteristic of materials having a non-cubic crystal structure and does not exist in polycrystalline cubic materials, due to their more symmetric structure. The phenomenon is generally associated with mechanical twinning [Agnew, et al, 2001]. [Klimanek, et.al., 2002] has investigated the microstructure evolution under compressive plastic deformation of magnesium at different temperatures and strain rates and provided stress-strain curves obtained under compression. In the case of magnesium alloy sheet, a relatively soft deformation twinning mechanism operates during in-plane compression, while only dislocation slip (in poorly oriented grains) is possible during tension. Hence, the yield stress in compression is much lower than in tension. It is important to note that twinning is more common at high strain rates and low temperatures [Meyers et al, 1999]. Early studies show that for Mg alloys (HM21A-T8, HK31A-H24 and HM31A-T5) tensile yield strengths are considerably higher than compressive yield strengths at room temperature. However, at 204 C, the differences between tensile and compressive yield strengths decrease to an average value of 7.5 MPa. Above 315 C, the tensile and compressive yield strengths are equal [Fenn, 1961]. 12

36 Figure 3.4: Stress-strain data for AZ31B plate deformed in in-plane tension (IPT) and compression (IPC) and through-thickness compression (TTC) [Agnew, et.al., 2002] Figure 3.5 shows the flow curves obtained from rolling direction (RD) and transverse direction (TD) compression tests at different temperatures using Mg alloy AZ31-H24. The samples were strained to strain of 1.0 or failure, whichever occurred first. It is clear to see that the TD samples are stronger at every temperature, as was observed in the tensile tests conducted by [Duygulu, et.al., 2005]. At 250 o C, the difference in the flow curves from RD and TD is extremely small. Strong sigmoidal hardening is observed at room temperature and mildly elevated temperature tests, while essentially no hardening is observed at the higher temperatures (200 o C & 250 C). Significantly, there is no 13

37 softening in the initial yield stress with an increase in temperature up to 200 C, in fact there is a slight increase in strength. Figure 3.5: Compression flow curves as a function of testing temperature. The transverse (open symbol) samples are stronger than the rolling (closed symbols) at all temperatures Figure 3.6 shows the experimental flow behavior obtained at normal direction (ND), RD and TD compression and TD and RD tension of Mg AZ31 alloy at room temperature, 150 o C, 175 o C and 200 o C. Experimental findings can be summarized as; i) The flow stress curve obtained from ND compression is different than the TD and RD compression curves, 14

38 ii) At 200 o C, the variation in the flow stress curves obtained at RD, TD and ND is smaller than the ones obtained at 175 o C. (a) (b) (c) (d) Figure 3.6: A comparison of experimental (symbols) and simulated (curves) compressive flow behavior at a) RT, b) 150 C, c) 175 C and d) 200 C 15

39 [Duygulu, et.al., 2005] has determined the r-values in uniaxial tension along the RD and TD using the Mg AZ31-H24 alloy. Figure 3.7 shows that the r-value along the TD are higher (up to 5) than the ones in the RD (up to 2) and it decreases with temperature. In contrast with these observations of high r- values during in-plane tension, same samples compressed within the rolling plane exhibit very low r-values (Figure 3.8). Although the strengths along the three directions become quite similar at the highest temperature T = 250 C, the r-values remain distinct at all temperatures [Jain, 2005]. Figure 3.7: Measured (symbol) and predicted tensile r-values 16

40 Figure 3.8: Plot of the variation in r-values after compression (strain ~0.11) at different temperatures. (symbols are experiments curves are predictions) [Jain, 2005] 17

41 CHAPTER 4 DETERMINATION OF THE FLOW STRESS OF LIGHTWEIGHT ALLOY SHEET UNDER EQUI-BIAXIAL STATE OF STRESS 4.1 Introduction Properties of Mg alloys at elevated temperatures have been determined by various researchers around the world. However, information on properties obtained at elevated temperatures under equi-biaxial state of stress using hydraulic bulge test is limited. Materials are often tested using the standard uniaxial tensile test. Stress conditions in stamping, however, are not uniaxial as they are in the tensile test. Therefore, it is necessary to obtain material properties under biaxial deformation conditions (Figure 4.1). In this test, the sheet is clamped between the lower and the upper die. When the fluid in the lower chamber is pressurized, the sheet is bulged into the cavity of the upper die. The clamping force between the lower and upper die has to be high enough to prevent sliding of the sheet between the dies. Often, a lockbead is used to prevent the movement of the sheet in the clamped region. Thus, the sheet will only be stretched and no draw-in will occur. When the deformation of the material exceeds its formability limit, the bulged sheet will fracture. In this test, the deformation is not affected by friction. Thus, the reproducibility of the test results is good. 18

42 Bulged Sheet Initial Sheet p Pressurized Fluid Upper Die Lower Die Figure 4.1: Initial (left) and the deformed sheet (right) in the hydraulic bulge test The main geometrical and process related parameters of the hydraulic bulge test are shown in Figure 4.2. F c d c F c t d R d h d p R c t 0 Figure 4.2: Geometrical and process related parameters t 0 initial thickness of the sheet t d thickness at the top of the dome h d dome height R d radius at the top of the dome d c diameter of the cavity R c radius of the fillet of the cavity F c clamping force 19

43 p hydraulic pressure The elevated temperature bulge tests were conducted in co-operation with the PtU of the University of Darmstadt that has the appropriate apparatus available. The specific objectives in conducting these tests were to; a) gain experience and observe difficulties/advantages of using hydraulic bulge test tooling submerged in heated heat transfer liquid and check the applicability of the unique submerged testing concept b) obtain the mechanical properties of Mg AZ31-O alloy at various temperatures and approximate strain rates under equi0biaxial state of stress. 4.2 Experimental setup Figure 4.3 shows the elevated temperature hydraulic bulge tooling used in this study. In this unique set-up, the die, the blankholder and the sheet are submerged in the heated pressure medium. Thus the temperature variations in the tool and the sheet are reduced. The pressure medium is heated via a) cartridge heaters located at the bottom of the tool (Figure 4.3), b) cartridge heaters in an outside tank and c) circulation pump equipped with heaters. A potentiometer is used to record the bulge height while the medium pressure is measured with a pressure transducer. A constant 90 bar blank holder pressure 20

44 (BHP) was applied to lock the sheet to prevent the draw-in of the sheet into the die cavity. The die corner radius (R c ) of the die was 4 mm. The heated pressure medium used was Multidraw Hydrofluid HT 400 and it had a flash point of 280oC. While the tool/liquid temperature was 275 o C at the bottom of the tool, the maximum sheet temperature was 225 o C. Therefore, for safety reasons, experiments were conducted up to sheet temperatures of 225 o C. Figure 4.3: Elevated temperature Hydraulic Bulge Tooling (PtU, TU Darmstadt) In this test set-up the constant strain rate (estimated at the apex of the bulge) could be reached only approximately, by controlling the appropriate flow rate of the pressure medium [Groche et.al., 2002]. 21

45 4.3 Calculation of stresses and strains under equi-biaxial state of stress In hydraulic bulge test, equi-biaxial state of stress is achieved at the apex during bulging. By using the membrane theory, which assumes that the thickness stress is neglected, and by calculating the hoop and transverse stresses, it is possible to obtain the effective stress values (Figure 4.4). The parameters necessary for the calculation of the stresses are a) pressure (obtained from experiment), b) instantaneous dome (bulge) radius (R 1 =R 2 ) and c) instantaneous thickness. Dome radius and thickness values are measured from the bulged samples at various bulge heights. Since the capability of measuring the dome radius and thickness measurements instantaneously did not exist, analytical models were used to calculate the dome radius and thickness. There is also a need to understand the applicability of these models (membrane theory) at elevated temperature conditions. σ 2 σ 1 R 2 R 1 Figure 4.4: Hoop ( 1 σ ) and Transverse ( 2 σ ) Stresses and Dome Radii in a Membrane 22

46 4.4 Membrane theory To determine the flow stress curve by using the hydraulic bulge test, the most common theory used is the membrane theory [Panknin 1959], [Gologranc 1975]. The membrane theory neglects bending stresses. Thus, it is only applicable for thin sheets. The following equation (1) represents this theory: σ 1 σ 2 + R R 1 2 = p t d (1) Where σ 1 and σ 2 are the principle stresses on the sheet surface, R 1 and R 2 are the corresponding radii of the curved surface, p is the hydraulic pressure, and t d is the sheet thickness. (Figure 4.2) For the axi-symmetric case of the hydraulic bulge test, σ 1 =σ 2 and the radius at the top of the dome is R d = R 1 = R 2. Therefore, equation (1) can be simplified to: 2σ R p = d t d (2) σ = pr 2t d d (3) 23

47 In hydraulic bulge testing, pressure is applied on the internal sheet surface. No normal forces acting on the outer sheet surface. Therefore, the average stress in the sheet normal to the sheet surface is approximately: σ n = p + 0 = 2 p 2 (4) The effective stress can be calculated by Tresca s plastic flow criterion, since Traesca and Von Mises criteria are the same at equi-biaxial state of stresses: σ = σ max σ min = pr 2t d d p 2 (5) p R d σ = t d (6) The effective strain (thickness) is: ε = ε t t = ln t d 0 (7) 4.5 Calculation of the radius of the bulge (dome) The radius at the top of the dome can be calculated by [Hill 1950] assuming that the dome is spherical and that there is no fillet in the cavity of the die: 24

48 R d = 2 dc + 4h 8h d 2 d (8) Considering that there is a die radius R c, and assuming that the dome is spherical, the radius of the dome can be calculated by [Hill 1950]: R d dc 2 = + R c 2 + h 2h d 2 d 2R c h d (9) [Panknin 1959] investigated the hydraulic bulge test experimentally. He measured the radius at the top of the dome of the deformed samples with radii gages. He also calculated the radius at the top of the dome using the dome height. He assumed that the dome is a part of a sphere and considered the fillet in the cavity of the die. [Gologranc 1975] had similar results with his experiments. Besides, he detected that for small dome heights the radius of the dome is up to 10 % larger than the calculated ones. Equation 9 is an analytical formula that can be used to calculate the bulge radius at various bulge heights. 4.6 Calculation of the thickness at the top of the dome [Hill 1950] developed analytical methods to describe the deformation in the hydraulic bulge test. For his calculations, he assumed that the shape of the 25

49 bulge is spherical. With this assumption, the thickness at the top of the dome can be calculated by the following equation: t d 1 = t 0 2hd 1 + d c 2 2 (10) 4.7 Stress Strain relationship at elevated temperature for magnesium alloy sheet For the description of flow behavior, it is necessary to express the flow stress mathematically as a function of the relevant parameters true strain ε, true strain rate ε& and temperature T. For a given material and microstructure, the flow stress can be expressed as: ( ε,ε& ) σ = f,t (11) At room temperature forming, Equation 11 can be described with the law of Hollomon σ n ( ε ) K ε = (12) where K is a material specific constant factor, called strength coefficient. Parameter n describes increasing hardening of the material with increasing strain and is therefore called strain hardening exponent. In some cases, when 26

50 deformation takes place at higher temperatures (200 o C-300 o C) and at lower strain rates, straining may continue with decreasing stress, i.e. work-softening may occur. Using tensile tests conducted at elevated temperatures, several approaches for describing both the softening effect and the influence of strain rate were considered by [Brand 1998] in the following as; m3 ( ) ( ) & σ ε ε mt 1 m2 m4 T = K T e e ε (13) This approach expresses the true strain dependent hardening behavior with the additional term m 4 ε e, in which e is the base of natural logarithms. In order to evaluate the accuracy of this approach tensile tests at elevated temperatures were conducted at IFUM for magnesium sheet alloy AZ31B, (thickness t 0 =1.3 mm) [Brand, 1998], [Droeder, 1999] and [Doege, 2001b] have also used this model in their studies. Comparison of experimentally obtained flow stress curves for AZ31-O with those of equation (13) are shown in Figure 4.5 for a temperature range of T= 150 C to T= 235 C. 27

51 Yield Stress [MPa] True strain ε Figure 4.5: Comparison of Brand model and experimental data [Droeder, 1999] Coefficients m1, m2, m3 and m4 were derived from experimental data using a regression analysis. (Table 4.1) Exponents m1 and m2 appeared to be constant while m1 provides a measure for dependence of flow stress on forming temperature. Constant m2 shows the dependence of flow stress on strain rate. As in the power law, exponent m3 is the same as the hardening coefficient n. In addition, exponent m4 indicates an additional dependence of the flow stress in function of strain. As it is seen from Table 4.1, m4 is negative when softening takes place. At T= 150 C (m4=0) therefore no softening is 28

52 present and an almost constant strain hardening occurs. Dependence of the K value on temperature is also seen from Table 4.1. Temperature [ C] Constant K [MPa s] Exponent m 1 [-] 18x x x10-4 Exponent m 2 [-] Exponent m 3 [-] Exponent m 4 [-] Table 4.1: Brand coefficients obtained from elevated temperature forming of magnesium sheets in tensile test [Droeder, 1999] 4.8 Experimental investigation Observations Approximately 1.2 mm thick (5% thickness tolerance) square sheet samples (260mm 260mm) were provided by Salzgitter A.G., Germany. Rolling directions were marked on each specimen. Thickness measurements were made on specimens to check the uniformity of thickness. The location of each sample (260mm 260mm) in the original rolled sheet before cutting was not known. Following observations were made before and during the experiments: a) Specimens were difficult to etch with grids and some of the specimens exhibited corrosion after the tests. 29

53 b) Before the tests, the specimens were not all flat and they exhibited approximately 5 % variation in thickness (nominal thickness was 1.2 mm) c) The tests showed considerable differences in formability (as measured by bulge height at bursting) among the samples that were obtained from the same coil. Furthermore, samples were separated as low and high in formability. They exhibited color difference in surface. d) In between tests, it was necessary to compensate for temperature losses by using a circulation pump to circulate the pressure medium. e) The temperature of the sheet was measured manually by a thermocouple before the test. It was not possible to monitor the temperatures during the test. f) When the sample fractured, in some selected tests, due to impact at bursting, the fixture holding the potentiometer hit the apex of the bulged sheet. This impact created a dent at the apex, which is not very important since the sheet is already burst. However, the impact might damage the potentiometer or reduce its life Test conditions and experimental matrix Due to a) the difficulty in pressure/temperature control and long test cycles; b) unexpected material property variations and waste of samples c) time 30

54 delay because of excessive smoke generation at elevated temperatures, experimentation is quite slow. Results of experiments will be explained in the upcoming sections. Table 4.2 and Table 4.3 give a summary of the conducted experiments for the high and the low formability sheets, respectively. It is seen that, the test temperatures vary, because it is difficult to control the sheet temperature precisely. Three samples were used for most of the test conditions. Temperature ( o C) Strain Rate (s -1 ) Table 4.2 : Experimental matrix for high formability sheets (strain rate values are approximate) 31

55 Temperature ( o C) Strain Rate (s -1 ) Table 4.3: Experimental matrix for low formability sheets (strain rate values are approximate) Measurement of initial sheet thickness Figure 4.6 shows the measurement directions for the as-rolled sheets. Thickness measurements were made for randomly selected three high formability and three low formability sheets. Measurements are made at every 20 mm increments along A-B and C-D using a micrometer and are shown in Table 4.4. Figure 4.6: Thickness measurement along Rolling Direction (RD), and Transverse Direction (TD) (dimensions in mm) 32

56 High Formability Sheets Low Formability Sheets Sheet1 Sheet 2 Sheet3 Sheet 4 Sheet 5 Sheet 6 A-B C-D A-B C-D A-B C-D A-B C-D A-B C-D A-B C-D O-center Avg Table 4.4: Thickness measurements for high and low formability sheets It is seen from Table 4.4 that maximum and minimum thickness values measured from the high formability sheets are 1.19 mm (sheet 1) and 1.14 mm (sheet3), which corresponds to almost a 5% difference. When the average thickness values are compared, variation can easily be seen between sheet 1, sheet 2 and sheet 3. Thickness values are pretty close in A-B and C-D directions for almost every sheet Sheet draw-in during bulging During hydraulic bulging, the sheet is held in order to prevent draw-in by using either a lockbead or applying higher clamping forces. In the set-up that was used, there was no lockbead in the tool due to lower forming loads at elevated temperatures. Therefore, all the square sheets (260 mm 260 mm) 33

57 side length was measured to check whether draw-in occurred during deformation. As a result of measurements, it is seen that no draw-in to the die cavity happened Pressure bulge height curves Figure 4.7 shows the pressure-bulge height curves at various temperatures for the approximate strain rate of 0.25 s -1. It is seen that at temperatures above 180 C, bulge height increases with decreasing pressure. This is possibly a sign of thermal/work softening effect. Three samples were bulged at the same condition for understanding the experimental repeatability. The variation between these curves was within 8% of the measured data. Figure 4.7: Pressure-bulge height curves at the approximate strain rate of 0.25s -1 34

58 Figure 4.8 shows the pressure-bulge height curves at various temperatures for the approximate strain rate of s -1. The effect of possible thermal/work softening is clearly seen above 165 C. The difference between Figure 4.7 and Figure 4.8 is that, samples in Figure 4.8 show higher bulge heights, lower pressure values and extended pressure drops (possible softening behavior). Figure 4.8: Pressure-bulge height curves at the approximate strain rate of s Analysis of the dome geometry The bulge shape obtained in equi-biaxial bulging is actually not a perfect sphere, although to simplify the analysis, most researchers assume that the experimental bulge is a perfect sphere. In order to investigate this in elevated 35

59 temperature forming of Mg AZ31-O alloys, several pressurized sheets (without fracture) were selected for determining the bulge geometry. The bulge geometries were measured using a Coordinate Measurement Machine with a 0.98 mm probe tip. Measurements were made along the rolling direction (RD) and transverse direction (TD) by obtaining 21 points (10 points on each side of the apex). It is entirely possible that there was some small amount of springback, especially at the lower range of the forming temperatures that were investigated. However, in this study, it was not possible to determine the magnitude of springback which can be expected to be small at elevated temperature forming. The radius of the bulge was calculated by using 5 points (near the apex) and 21 points for the entire bulge. 5 points were used because, it is believed that a 3 point fit (at apex) might lead to erroneous radius values due to possible local imperfections at the apex of the bulge while 5 points around the apex will provide more realistic data. Least Squares Circle Fit (LSCF) was conducted to fit the 5 and 21 points to the best circle by minimizing the residuals through an optimization routine. Figure 4.9 shows the schematic of the measurement points. 36

60 Figure 4.9: Measurement points on the bulged sheet Figure 4.10 shows the obtained radius values along RD using a) 5 point LSCF b) 21 point LSCF and c) analytical solution with Eq.9 for samples having bulge heights of 14.7mm, 21.7mm and 33.9 mm, respectively. It is seen that radius values calculated analytically are closer to the radius values obtained using 5 points at the apex, rather than those obtained using 21 points. Differences between predictions made with Eq.9 and the radii obtained using 5 point LSCF for bulge heights of 14.7 mm, 21.7 mm and 33.9 mm, are 1.5 %, 3 % and 6 %, respectively. However, as shown in Figure 4.11, by selecting a 5 point fit (points 2,3,4,5 & 6) we know that the fitted circle is not going to pass from points (1 and 7) at the edges of the bulge. Therefore, a comparison between the 37

61 radius obtained from the 5 point (points 2,3,4,5 & 6) and a 3 point (points 1, 4 & 7) fit was done to determine the amount of change in the bulge radius. For this purpose, two samples with different bulge heights (21.7 mm and 33.9 mm) were selected. Calculated R 1 & R 2 values (Figure 4.11) are given in Table 4.5. Figure 4.10: Comparison of calculated and measured bulge radius values In both cases, it is clear that R 1 is larger than R 2. However, the difference is limited to a maximum of 2.5 % for the sample with the higher bulge height. As a conclusion, a 5-point Least Squares Circle Fit (LSCF) is assumed to be an acceptable approximation for obtaining the radius at the apex of the bulge. 38

62 pt. LSCF 3 pt. 3 5 R 2 1 R 1 7 Figure 4.11: Radius difference using 5 and 3 points 5-point 3-point Bulge LSCF LSCF Difference Height RD (mm) RD (mm) [%] (mm) -R R < Table 4.5: Comparison of radius values (R 1 & R 2 ) obtained by using 5 and 3 points Deviation from the original bulge shape Figure 4.12, Figure 4.13, and Figure 4.14 show the difference (residuals) between the original measured points and the fitted circles using 5 and 21 points for bulge heights of 14.7 mm, 21.7 mm and 33.9 mm, respectively. These bulge heights were selected to demonstrate the evolution of change from the lowest to the highest bulge height. 39

63 Figure 4.12: Residual plots for sample at h d =14.7 mm In Figure 4.12 and Figure 4.13 symmetric distribution of residuals on each side of the apex for h=14.7 and 21.7 mm are seen. While residuals around the apex are very close to zero, they are larger near the edges of the bulges. The residuals in Figure 4.13 are slightly higher compared to those in Figure 4.12, but the maximum value is under 0.5 mm. For a larger bulge height, (Figure 4.14), the symmetric distribution is not seen and the value of residuals around the edges increase up to 4 mm. It is also seen that the residuals are higher around the apex when 21 points are used. 40

64 Figure 4.13: Residual plots for sample at h d =21.7 mm Figure 4.14: Residual plots for samples at h d =33.9 mm The residuals seen in Figure 4.12, Figure 4.13 and Figure 4.14 and other results of measurements indicate that the bulge shape does not deviate from the 41

65 assumed sphere shape until the bulge height to diameter ratio h d /d c is approximately larger than 0.2. Below this ratio, the maximum residuals remained under 0.5 mm. It is clearly seen from Figure 4.14 that the residuals are not symmetric, which possibly indicates that material becomes unstable at that high deformation Thickness distributions along the dome curvature Thickness measurements were conducted for samples that were pressurized to approximately same bulge heights at different approximate strain rates and temperatures. Measurements and predictions, made using Eq.10 were compared. Figure 4.15 shows the thickness distributions in the rolling direction along the curvilinear lengths of the bulges formed to 21 mm height. As expected, due to volume constancy, at approximately the same bulge height (~21 mm) there is not a significant thickness difference for samples that were bulged at the same strain rate (0.25 s -1 ) but at different temperature. Table 4.6 shows the measured and the calculated thickness values at the apex of the bulges shown in Figure The error percentage using Eq.10 is up to 4% and 8 % for bulge heights around 21 mm and 33.9 mm, respectively. 42

66 Figure 4.15: Thickness distribution along the RD (bulge height (h)=~21mm and h 33 mm) It is clear from Figure 4.15 that for samples formed at ~0.025 s -1, the lowest measured thickness is not at the apex. For samples formed at ~0.25 s -1, at least three of the same thickness values are seen between curvilinear lengths of 40 mm and 80 mm. In most samples at high temperature and low strain rate, fracture was as big as the tip of a needle. Sheets formed to higher bulge heights also clearly show the unusual thickness distribution (Figure 4.15). It was first thought that the unexpected thickening at the apex may be due to the weight or the temperature of the bulge height sensor. (The contact between the sensor and the apex is a point contact) However, the weight of the bulge height sensor is extremely low, and its tip is also submerged under the hot liquid. Therefore it is not likely that the sensor could have caused the unexpected thickness distribution. 43

67 Bulge Height (mm) Temp. ( o C) Strain Rate (s -1 ) t d (measured at apex) (mm) t d (Eq.4) (mm) Table 4.6: Measured and calculated thickness values at the apex At room temperature hydraulic bulging of sheets, the minimum thickness values are always observed at the apex. Furthermore, the fracture takes place at the apex of the bulge. The thickness distribution plots, seen in Figure 4.15, are clearly different from the thickness distributions observed at room temperature hydraulic bulging of sheets. Most probably, this observation is due to the strain rate effect during the deformation. During hydraulic bulging at elevated temperatures, even though obtaining an approximate true constant strain rate is possible at the apex by controlling the flow rate, there is a strain rate gradient along the contour of the bulged sheet. In Figure 4.16, a schematic representation of the strain rate distribution is shown. Consequently, at isothermal conditions, there is also a flow stress gradient in the bulged sheet. As a result, the sheet might fail at a location where a combination of low flow stress and high strain (low thickness) is present. 44

68 Pneumatic bulging of Mg AZ31-O alloys conducted at elevated temperatures show also that the fracture does not take place at the apex. [Siegert, 2001] a a σ, & b b a ε a c c d σ, & d b ε b & ε > & ε > & ε > & ε > & ε σ > σ > σ > σ > σ e e σ, & c ε c σ, & d ε d σ, & e ε e Figure 4.16: Schematic representation of the strain rate and flow stress gradients in the bulged sample Figure 4.17 and Figure 4.18 show the calculated true stress (Eq.6) and true strain (Eq.7) curves at approximate strain rate values of 0.25 s -1 and 0.025s - 1 at various temperatures. At 0.25s -1, a slight drop in stress takes place at 221 C. However, at s -1, the drop in stress is clearer at temperatures of 190 C, 214 C and 225 C. Maximum strain values of 0.45 and 0.7 are reached at strain rates of 0.25 s -1 and s -1 respectively, while the achievable strains using the tensile test are approximately 0.3 at the same strain rate values. [Groche et al, 2002] 45

69 True Stress (MPa) T: o C True Strain ε / s Figure 4.17: True stress and true strain curves at 0.25 s -1 As discussed earlier, there is an error in radius and thickness predictions when membrane theory is used. This error was up to 6 % in radius and 8% in thickness predictions for the highest obtained bulge height. For samples with h d /d c ratios lower than 0.2, radius and thickness predictions were acceptable since the shape of the bulge is nearly spherical, as assumed in analytical calculations. In order to demonstrate the introduced error, the sample in Figure 4.18 that was formed at 225 C was selected. The same curve was plotted with possible errors after (h d /d c )>0.2, which corresponds to a strain of ~0.4. Therefore, the error plots are shown after 0.4 strain (Figure 4.19). 46

70 True Stress (MPa) T: o C ε / s True Strain Figure 4.18: True stress and true strain curves at s -1 In Figure 4.18, the flow stress curve of the sample formed at 225 C and at the strain rate of s -1 show certain amount of crossing of the data. In other words, the flow stress value for 225 C at a true strain rate of s -1 is larger than the corresponding value at 210 C. This observation may be due to the effect of recrystallization and microstructure changes or experimental errors. These observations must be investigated in the future and the flow stress data obtained in this study must be compared with data from other investigations in order to clarify this seemingly perplexing observation. A similar behavior is also seen in the elevated temperature tests conducted by [Takuda et.al., 2005]. In that study, the flow stress curve at the highest temperature 300 C, and at the lowest forming speed (0.2 mm/s), show the same crossing behavior at lower strains. 47

71 True Stress (MPa) True Strain 225 C/0.025 s -1 Figure 4.19: True stress true strain curve with possible errors at 225 C (0.025 s -1 ) 4.11 Conclusions 1) Submerged hydraulic tool concept for conducting bulge test offers homogeneous temperatures in the deformed sample. However, repeatability of the experimental conditions is difficult to achieve. Temperature control was one of the most difficult issues. It was nearly impossible to have exact temperatures on the sheet when experiments had to be repeated at the same temperature. 2) Variation of properties within the same batch of material is a serious issue. Some sheets that were from the same coil unexpectedly showed low formability. This might be due to varying processing conditions 48

72 during rolling of the sheet. Therefore, it is expected that data, obtained for the same material but by different investigation (using different material lots) may have variations. 3) It is observed that at elevated temperatures, depending on the strain rate work softening behavior might take place along with work hardening. 4) By using elevated temperature hydraulic bulge system, strains up to 0.7 were obtained at a strain rate of s -1 at 225 C. 5) It was observed that almost up to 25 mm bulge height, (for the die diameter of 115 mm used in this study) dome radius and thickness predictions at the apex were acceptable. Above a certain bulge height, (~25mm) it is clear that, the dome shape is not spherical and starts to deviate from a sphere. The effect of strain rate is believed to have effect on the dome geometry. 6) Minimum thickness values were found to be closer to the apex but not at the apex. This is believed to be due to the strain rate and flow stress gradient along the dome. 49

73 CHAPTER 5 DEEP DRAWING PROCESS AT ROOM TEMPERATURE Before investigating the warm deep drawing of light alloys (Al, Mg) it is appropriate to examine first the details of this process at room temperature. Deep drawing is used for the mass production of parts used in automotive, aerospace and appliance industries. In this process, a sheet metal is drawn into a die cavity by a moving punch. Figure 5.1 shows a deep drawn sheet that is divided into six regions. (A-B/ B-C/ C-D/ D-E/ E-F and F-G). At each region, the sheet metal experiences different state of stress, therefore the sheet thickness is not uniform. Figure 5.2 shows the top view of a drawn sheet, where A is the edge of the deformed sheet and C is the point where sheet is entering the die cavity. At point A, there is a free surface and the radial stress σ r =0, therefore the dominant stress state is compressive, which causes the thickening of the sheet. At point B, the stress state is both compressive and tensile and the sheet thickness will remain unchanged. At point C, the radial stress will be very high and the sheet will thin. Figure 5.3 shows the stresses on an element at a radius r. 50

74 Figure 5.1: Axisymmetric Deep Drawing Figure 5.2: Top view of drawn sheet Figure 5.3: Stress on an element at radius r [Marciniak, et al, 2002] Figure 5.4: Thickening of the sheet in the flange area The metal at point A (Figure 5.4) is moving towards the points A, B and C where the perimeter and surface area over the die are smaller. Since the metal is incompressible, the material in region A thickens, as seen in Figure 51

75 5.4. In most analytical calculations the thickness is assumed to be uniform in order to simplify the calculations [Lange, K., 1985]. However, in reality the thickening of the sheet creates elastic stresses and deflections on the blank holder and the die. 5.1 Drawability Criteria In literature, deep drawability of an alloy is indicated by the Limiting Draw Ratio (LDR). LDR is defined by the ratio of initial sheet diameter (D) to the punch diameter (D p ) (Figure 5.5). Maximum LDR refers to the cup that can be drawn without fracture or other defects. The higher is the maximum LDR that can be deep drawn for a material, the higher is the drawability of that material. LDR is a function of many parameters such as the tool geometry, lubricant, blank holder force which means it can change when any of these is changed. Therefore, it is a criterion that heavily depends on the given experimental setting. When LDR is mentioned, it is possible that the drawn cup may or may not have a flange left. A deep drawn cup might be drawn with or without a flange. If a cup is drawn with flange, using LDR as drawability criterion does not reflect accurate forming severity. Another criterion and a better parameter to indicate the deep drawability is the ratio of the height of drawn cup (without defects) to the punch diameter is determined and called as the Cup Height to Punch Diameter ratio (HDR) (h/d p ). (Figure 5.5) It is believed 52

76 that this criterion represents the drawability better if the drawn cup has flange left. Figure 5.5: Definition of cup height (h) for a cup with a flange and without a flange Some drawn cups can experience earing due to the anisotropy that exists in the incoming sheet material. For better accuracy, while determining the HDR for cups with ears, cup height is decided to be the h min as shown in Figure 5.6. Therefore, both LDR and HDR are used based on the definitions provided here. Figure 5.6: Deep drawn cup with ears 53

77 5.2 Critical Stroke in deep drawing Based on the conducted FEA and observations in the mechanics of drawing, it is seen that the bending of the sheet takes place around the punch and the die corner during the initial part of the drawing process. The sheet thins during the initial bending. Therefore we can say that the cause of thinning is due to a) continuous bending of the sheet b) stretching of the sheet around punch corner. Bending of the sheet continues until the punch reaches a critical stroke (S cr ) which is defined as: Scr=rD+rP+t where, r D : Die corner radius, r p : Punch corner radius, t: Sheet thickness. When the punch is exactly at the end of the critical stroke, centers of the die ring radius and the punch radius are aligned (Figure 5.7). When the punch travels within the critical stroke, the sheet is tangent both to the blank holder and the punch corner radius. Both tangency point positions change until the punch travels the whole critical stroke. After the punch completes traveling the critical stroke, the sheet is mostly in contact with the punch wall and tangent to the blank holder. The critical stroke concept will be used later on with the hydroforming and the warm deep drawing processes. 54

78 Figure 5.7: Schematic view of the critical stroke (S cr ) before (left) and after (right) 5.3 Deep drawing of aluminum and magnesium at room temperature Drawability limits of Al 5754-O and Mg AZ31-O at room temperature is determined experimentally. Figure 5.8 and Figure 5.9 show that LDR of 2.1 (HDR:0.84) is obtained for the Al 5754-O alloy at room temperature. It is clearly seen that Mg AZ31-O alloy experienced early fracture and was not drawn successfully. A nylon film was used as a lubricant. Figure 5.8: RT drawing of Al 5754-O Figure 5.9: RT drawing of Mg AZ31-O 55

79 CHAPTER 6 HYDROFORMING OF SHEET AT ROOM TEMPERATURE A variety of innovative metal forming processes are being developed for forming lightweight materials. Among these processes, hydroforming of sheet is quite significant. Sheet hydroforming can be done with a stationary die (SHF- D) or with a moving punch (SHF-P). SHF-D is pressurization of a sheet to a die that has certain geometry. Therefore, it is a combination of less drawing and more of a stretching process. Research on SHF-D has shown that excessive thinning is seen in the deformed sheets, especially at the die corner areas, and therefore it is not very beneficial. Summary of some results for SHF-D process is given in Appendix A. However, sheet hydroforming with punch (SHF-P) provides better thickness distribution and offers great potential for low and medium volume production. In this process, instead of using two hard dies as done in conventional drawing, a single die or even no die is used. A viscous or liquid medium applies pressure to the sheet metal that is deformed and pressed against the punch that has the part geometry (Figure 6.1). Increased formability, high surface finish and reduction in the number of tools are the main advantages of SHF. However, compared to conventional deep drawing, control of liquid medium pressure and the blank holder force (in time and in 56

80 space) become critical in order to prevent leaking and wrinkling. Also higher machine capacity is required due to the forming that takes place against pressure. A fundamental understanding of the mechanics of sheet hydroforming process, including the effect of elastic deformation of tools that affect the process robustness, can lead to wide application of this technology for cost effective production of lightweight components. Appendix B shows some results of elastic deflection analysis conducted using FEA in deep drawing operation. If the pressure is high, a reaction force (F LIFT ) is generated that acts against the BHF (F BH ) (Figure 6.1). If F LIFT > F BH, then leakage takes place as it is shown in (Figure 6.1b). If F LIFT < F BH then perfect sealing takes place, like it is shown in (Figure 6.1a) By using SHF-P, higher LDR s can be obtained due to a) eliminated frictional forces at the sheet-die corner interface b) reduced drawing stresses at the cup wall due to pressure and increased frictional forces between sheet and punch. The fluid pressure profile is an important factor and it influences the sheet formability. 57

81 a) b) Figure 6.1: SHF-P process a) without leakage; b) with leakage Experimental results for SHF-P process of soft 70/30 brass round cups with a LRD equal to 3.44 are presented by [Sebaie et al., 1973]. Yossifon and Tirosh studied and developed an analytical model that provided a pressure path relative to the punch stroke that took wrinkling and fracture into account [Yossifon et.al., 1985a] and [Yossifon et.al., 1985b]. Their formulation is based on the classical theory of plasticity (with simple Power-Law hardening ( σ = n Kε ) and Mises-Hill normal anisotropic yielding) assuming plane strain tensile failure. This study concluded that in hydroforming, wrinkling occurs at the unsupported cup wall sheet close to the die corner [Yossifon et.al., 1984] and [Yossifon et.al., 1988]. The authors defined a Maximum Drawing Ratio 58

82 (MDR) as the highest drawing ratio before wrinkling and fracture takes place. They concluded that the MDR is increased as the anisotropy parameter (R) and wall thickness (t) are increased for a given strain-hardening exponent (n). They determined that MDR reaches its minimum between the strain hardening exponent n= , but increases moderately beyond this range [Yossifon, 1990]. Most of the research and analysis has been conducted for SHF-P using interchangeable dies. SHF-P with uniform pressure on the flange is an alternative to hydroforming with dies. In this process, the die is eliminated and the sheet metal is placed in the pressure pot. A brief state of the art of hydromechanical deep drawing has been summarized by [Thiruvarudchelvan et.al. 2003]. The effect of anisotropy and pre-bulging on mild steels has also been investigated by [Zhang et.al., 2003]. Main objective is to determine an approximate pressure profile, which provides a defect-free (no wrinkling or early fracture) cup with a high LDR while preventing leakage throughout the process. The pressure profile curve is a function of both the sheet material and the tool dimensions (Figure 6.2). The punch corner radius (r p ), the die ring corner radius (r D ) and the clearance between punch and blank holder (c) affect the SHF-P process. A too small value of the punch corner radius and the die ring corner radius could tear the sheet. Bulging of the sheet between the punch and the blank holder could 59

83 happen if a too large clearance (c) between punch and blank holder exist. These aspects are analyzed for a 90 mm round cup tool geometry provided by Schnupp Hydraulik of Bogen, Germany. Blank holder c Punch Rp Die rp rd Sheet Figure 6.2: Important tool parameters that influence the SHF-P process 6.1. Mechanics of SHF-P process In SHF-P, the cause of thinning is due to a) continuous bending of the sheet b) stretching of the sheet around punch corner due to counter pressure. When the punch travels within the critical stroke, the sheet is tangent both to the blank holder and the punch corner radius. Both tangency point positions change until the punch travels the whole critical stroke. After the punch travels the critical stroke, the sheet is always in contact with the punch wall and tangent to the blank holder. If the fluid pressure doesn t change, the tangency point between sheet and blank holder remains the same. 60

84 Therefore, after the critical stroke, the sheet radius is constant if the fluid pressure is constant. Higher pressure causes the tangent point (distance H in Figure 5.7) to shift in the direction of +x. (Figure 5.7) When this point shifts in the direction of +x, it causes more sheet area to be in contact with the blank holder. In return, higher blank holder force is needed. Therefore, the higher the fluid pressure, the smaller the sheet radius and the larger the BHF required to avoid leakage. It is seen from the previous FE Analyses that, it is very important to determine the pressure curve. As it is seen in Figure 6.3, if the pressure is high enough at the beginning of the process than the sheet loses contact with the die corner. Figure 6.3: During a hydromechanical deep drawing process the sheet loses contact with the die 61

85 Max thinning happens at an early stage of the drawing at the punch corner and stays almost constant until the total punch stroke is completed (Figure 6.4). In order to demonstrate this phenomenon, the mechanical deformation of the sheet has been observed from FEA. It is seen from Figure 6.4 that, at punch strokes of 20 mm and 70 mm, for the same given conditions (pressure, BHF, etc..) maximum thinning percentages are approximately 15 %. This shows that once the max thinning percentage is reached at initial stroke levels, it remains the same the rest of the process. Thinning distribution (Punch Stroke = 20 mm) Thinning distribution (Punch Stroke = 70 mm) Thinning percenta 20% 15% 10% 5% 0% -5% -10% -15% -20% C C B A A Curvilinear Ditance [mm] Figure 6.4: Maximum thinning around the cup bottom radius at two different values of the punch stroke 62

86 6.2. Prediction of the initial pressure value Since it is beneficial that the sheet has to be lifted from the die corner to eliminate the frictional forces, the issue is to find the first approximate pressure value that we need to have in the pressure pot that will lift the sheet from the die corner. Therefore, in order to determine this pressure value, slab analysis was conducted to find an approximate relationship between the pressure, sheet corner radius, thickness of the sheet, circumferential and radial stress components. FBH BLANK HOLDER Rp R DIE rd rs PUNCH Y X (a) (b) Figure 6.5: Position of the slab in the sheet radius zone (a) and equilibrium of the forces in the slab (b) Equation (1) shows the obtained relationship from the global equilibrium of the slab. This equation provides an initial guess for the pressure value to 63

87 start with if the circumferential and the radial stresses are assumed to be the yield stress of the material. The calculated pressure later was slightly altered using FEA to optimize the movement of the sheet around the die corner. σ r σϑ p = t + rs R (1) where: p: pressure in the pressure pot; σ r : radial stress; σ θ : circumferential stress; r s : instant sheet radius; R: distance from the centerline of the punch to the slab. The pressure inside the die pot (p) is a function of the yield stress (σ y ) and the sheet geometry during the process (instant radius of the sheet (r s ) and distance from the center of the punch to the slab (R)) (Figure 6.5). By using this equation, the starting pressure that needs to be in the pressure pot approximately calculated to be around 100 bars for low carbon steel. Low carbon steel was selected due to the previously availability of experimental data to validate the FE model [Kaya et.al., 2004] [Contri et.al., 2004]. From trials with FEA, it is observed that this pressure cannot remain constant within the critical stroke and needs to increase as the process proceeds. A linear 64

88 increase until the critical stroke is generally found to be satisfactory. The need for the increase in the pressure is due to the strain hardening in the sheet. Effect of various pressure curves (P1, P2, P3 and P4) on thinning behavior was investigated using FEA (Figure 6.6). Following conclusions can be drawn from this investigation; a) When P1 was used, 20% thinning was obtained at the end of the critical stroke due to excessive stretching. b) After observing the deformation in P1, it was decided to start with a lower pressure value and increase gradually (P2). The thinning percentage at the end of the critical stroke was around 17%. c) In order to quantify the effect of P1 on thinning, a constant 100 bar pressure was input. (P3) After the punch traveled half of the critical stroke, it was observed that the sheet started rubbing the die corner. Therefore, the pressure curve needed to be updated to eliminate this problem d) Finally, when P4 was used, the sheet was never in contact with the die corner and it was kept at a minimum distance from the die corner in order to eliminate more stretching. By coupling the FEA with the slab analysis P4 was later modified to increase linearly (the initial flat part of 65

89 the curve until 6 mm stroke is eliminated based on observation in FEA) within the critical stroke while lifting the sheet off the die corner. Pressure [bar] P1 P2 P3 P P P2 150 P P Punch Stroke [mm] Figure 6.6: Pressure-stroke curves used in the critical stroke It is of interest to know whether the material is stretching during the critical stroke, since it is directly related to thinning. Therefore, the amount of stretching in the sheet radius zone has been evaluated (Figure 6.7). As Table 6.1 shows, the stretching of material increases with the punch stroke. Material stretching at the end of the critical stroke is around 15%. 66

90 Blank holder Punch Blank holder Punch A Die B Sheet Die A B (a) (b) Sheet Figure 6.7: Initial (a) and final (b) length of stretch in the sheet used to evaluate the material stretching in the sheet radius zone Punch Stroke [mm] Curvilinear length [mm] Stretching percentage [%] Table 6.1: Curvilinear length and percentage stretch of the sheet in the sheet radius zone according to Figure 6.7 (pressure curve: P4) 6.3. SHF-P of a 90 mm round cup Experienced obtained using steel is applied to investigate the attainable LDR for Al 5754-O. In this section, results of computer simulations are 67

91 presented for Al 5754-O. For 90 mm diameter round cup with flat die and blank holder surfaces was analyzed. Material properties are taken from [Boogard 2001] and friction coefficients are taken based on previous modeling and experimental experience [Table 6.2] [Contri, et al., 2004]. Friction coefficients were validated with available experimental data from Schnupp Hydraulik. In order to reduce computation time, quarter of each die set was modeled. Friction coefficients, m Sheet/Punch (µ sp ) 0.12 Sheet/Die (µ sd ) 0.08 Sheet/Blank holder 0.08 (µ sb ) Table 6.2: Friction coefficients used in the FEA Figure 6.8 shows the pressure curve. Initial pressure value of 60 bars is determined from the slab analysis. A linear increase in the pressure curve is found to be acceptable until 300 bars, since above this pressure value the sheet is bent severely and excessive thinning was observed. Results showed that an LDR of 2.4 is obtained with a maximum thinning percentage of 12 % for the Al 5754-O alloy (Figure 6.9). It is already known that bendability of Mg at room temperature is limited. Therefore, modeling of Mg with SHF-P process is not conducted. 68

92 Figure 6.8: Fluid pressure determined based on the critical stroke Thinning percenta 20% 10% 0% -10% -20% -30% D E F C % A B Curvilinear Distance [mm] Figure 6.9: Thinning distribution along the 45 cup wall 69

93 CHAPTER 7 DEEP DRAWING AT ELEVATED TEMPERATURE 7.1 Introduction The use of conventional forming technologies for Al and Mg alloy sheet is restricted because of the low formability of these alloys at room temperature. Increasing demand in weight reduction requires the development of innovative forming techniques for forming difficult-to-form alloys. Studies in the past have shown that the formability of Al & Mg alloys increases with temperature. The rather complex mechanical deformation that takes place in deep drawing process becomes more complicated when the effect of temperature and strain rate is introduced. In elevated temperature deep drawing, the die and the blank holder are generally heated, however the punch is cooled. When the sheet first touches the cooled punch, its temperature decreases and therefore part of the sheet in contact with the punch will be cooler than the rest of the sheet. This means that the sheet closer to the punch corner can withstand more stress and it will stretch less. Since the deformation is continuous, the portion of the drawn cup in contact with the punch continues to cool. However, the sheet that is under the heated dies has a higher temperature which helps the material flow easier. 70

94 In order to develop a rational R&D strategy for warm forming of Al and Mg alloys and to establish research priorities, it is important to consider the warm sheet forming process as a system. The incoming material shape and properties, the forming temperature, the interface condition (friction and heat transfer), the tool temperature, forming speed (or strain rate), and the forming equipment influence the final product shape and properties as well as the economics of the process. A fundamental understanding of the relationship between the input and output variables of the system is essential for developing a robust, productive and economical manufacturing process [Altan et al. 1983]. Thus, the development of warm forming process for sheet metal requires critical consideration of: (a) material flow behavior of Mg and Al alloy sheet at elevated temperature (b) lubrication system at the tool/blank interface (c) tool design with temperature control, and (d) warm forming process design, experimentation and numerical modeling using finite element method (FEM). A warm deep drawing tool was designed and Figure 7.1 shows the schematic of the designed tool in open and closed condition. 71

95 Figure 7.1: Open (left) and closed (right) condition of the tool In this study, the focus was on a) the effect of interface pressure on the dwell time and on the surface roughness, b) selection of the best performing lubricant among the available lubricants manufactured for elevated temperature forming conditions c) the effect of forming temperature and velocity (constant and variable) on the deformation mechanics d) process optimization of the warm forming process. 72

96 7.2 Experimental setup Servo press and its kinematics The most obvious benefit of the servo press is the flexibility it offers. This flexibility comes from the ability to program the speed and motion of the slide in an infinite number of ways, with a constant load available throughout the stroke at any speed. In warm deep drawing process, the servo press allows the workpiece to be heated in the tool, through the ability to dwell. Therefore, it eliminates the extra equipment necessary for heating and transferring the sheet to the die. The schematic drive system of the 110 ton AIDA Servo press, used in this study, was shown in Figure 7.2. The key feature of this design is the company s proprietary high torque, low RPM servomotor. This motor is mounted directly to the driveshaft, eliminating the need for linkage systems. In this design, the need for mechanism to multiply the torque and therefore the flywheel, clutch, and drive motor are all eliminated. The drive shaft drives the main gear, which in turn, is connected to an eccentric drive mechanism. 73

97 Figure 7.2: AIDA servo-mechanical press drive mechanism The eccentric drive mechanism facilitates the movement of the top ram. The capacitor stores power in the non-working portion of the stroke, helping to reduce the power consumption to levels comparable to standard mechanical presses. The press is equipped with an air operated blank holding system to provide the blank holder force (BHF). 1-2 Fast approach 2-3 Slower approach reduces impact and vibrations. Both tools are in contact at Dwell (heating of the blank) 4-5 Slower punch velocity for forming sharp corner radii. 5-6 Higher velocity for faster forming 6-7 Slower exit from the tool 7-8 Faster return to TDC Figure 7.3: Ram motion of the servo press (TDC: top dead center, BDC: Bottom dead center) 74

98 7.2.2 Design of the tooling Figure 7.4 gives a schematic view of the warm forming tooling. The operation of the designed tool set is illustrated in Figure 7.5. In the proposed process sequence, initially the blank is placed on the bottom die/blank holder. The top ram moves down till it touches the blank and dwells. During this dwell time, the blank is heated to the required temperature by the heated die and blank holder. After the dwelling period, the top ram moves further down against the stationary punch and the sheet is formed. The servomotor driven press allows infinite freedom in programming the velocity characteristics i.e. initially move rapidly to touch the blank, dwell for the desired time and finally form the sheet at desired forming velocity. A stroke vs. time profile that can be used for the warm deep drawing process is shown in Figure 7.3. The die and the blank holder are heated with cartridge heaters (up to 310 o C) while the punch is cooled approximately to room temperature (up to 65 o C) with water circulation. The die and blank holder temperatures are measured and controlled. Glass fiber insulators are located on top and bottom, between the tool plates and the die ring holder. The tool set is equipped with a load cell and a displacement transducer to measure the punch force and ram displacement during the process. Figure 7.6 shows the tool in open condition. Figure 7.7 and Figure 7.8 show the tool in the press and the whole view of the 75

99 servo press with the temperature controller and the punch cooling unit, respectively. 22,3 R 6 DIE R 4 20 PUNCH Figure 7.4: Schematic view and the dimensions of the tool (dimensions are in mm) Figure 7.5: Warm forming with in-die dwelling process sequence 76

100 Figure 7.6: Open warm forming tooling (top die set on the left, bottom die set on the right) [Kaya, et.al., 2007] Top die Bottom springs Bottom die Figure 7.7: Assembled tooling on the Aida servo press 77

101 Programming interface Temperature controller Punch cooling water tank Figure 7.8: 110 ton Aida Servo Press 7.3 Issues at the interface in forming at elevated temperature It is well known that heat transfer at the tool-blank interface is affected by the surface roughness of the blank/tool, lubricant and the amount of interface pressure. Lubrication is more important in warm forming than in cold forming of Al and Mg alloys because the likelihood of galling increases with the increase in temperature [Avedesian et al. 1999]. Lubricant performance depends primarily on the forming temperature. For temperatures up to 120 o C (250 F), oil, grease, tallow, soap and wax are generally used in warm forming of metals. A soap solution is acceptable for temperatures of up to 230 o C. When 78

102 the forming temperature exceeds 230 o C the choice of lubrication is restricted to molybdenum disulphide, colloidal solution of graphite, and Teflon. These lubricants should be cleaned from Mg parts as soon as possible to avoid corrosion [Avedesian et al. 1999], [Dow, 1962]. Although a limited number of lubricants exist that can be used for warm forming of metals (up to 300 o C), no extensive lubricant evaluation has been done for warm forming processes. Therefore, investigation on the performance of these lubricants in Al and Mg alloy sheet forming is of utmost importance. To evaluate the performance of lubricants closer to production conditions, the deep drawing test at room temperature was used by [Meiler, M., et al, 2005], [Meiler, M., et al, 2004], [Pfestorf, M., 2002], [Wagner, S., et al, 2002]. [Semiatin et.al.,1987] have conducted experiments to measure the change in temperature under different pressures in forging processes. However, the effect of interface pressure on heat transfer in rolled sheet metal has not been studied. 7.4 Heating the blank In hot forming, heat transfer is affected by the interface pressure, [Semiatin et.al.,1987]. In order to determine the necessary dwell time and the effect of interface pressure on temperature increase, experiments were conducted by using a designed aluminum fixture (Figure 7.9). Four holes (each 2 mm in diameter) vertical to the thickness direction were drilled towards the 79

103 center of the fixture. Depths of these holes were designed to be 20 mm, 25 mm, 30 mm and 40 mm, with respect to the tool dimensions. As the top view of the fixture is seen in Figure 7.9, 40 mm hole touches the center of the fixture. In this type of experiment, one of the difficulties is to have the sheet touch the heated upper and the lower dies at the same time. In order to minimize this, the servo press was programmed to operate at the highest velocity between points 1 and 3. (Figure 7.3) Therefore, once sheet/fixture was located on the lower die, approximately after one second the upper and lower tools were both in contact with the sheet/fixture before the dwell stage started. Interface C q DIE P q Interface A Thermocouple PUNCH q P BLANK HOLDER q Interface B Figure 7.9: Top view of the fixture used to determine the dwell time necessary to heat the blank (thickness 3mm) Figure 7.10: Schematic view of the experimental setup with the affected interfaces Experiments were conducted by inserting an E-type thermocouple into the 40 mm hole, in order to make temperature measurements at the center of the 80

104 fixture, while the fixture was under different interface pressures. Figure 7.10 shows the schematic view of the attached thermocouple and the affected interfaces. Figure 7.11 shows the experimentally measured temperature-time curves at various interface pressures (Blank Holder Pressure, BHP) when the tool temperature is at 300 o C. BHP levels were selected in such a way that the range of 1.5 MPa 4 MPa would fall into the range that was required in the deep drawing experiments. As it is seen from Figure 7.11, when the fixture was under 26 MPa of BHP, it reached to 250 o C 7 seconds before than the test that was conducted with 1.5 MPa of BHP. Figure 7.11: Temperature-time curves obtained with the test fixture for different interface (blank holder) pressures (tool temperature=300 o C) During these measurements the variation in the temperatures of the punch and the knock-out pin (used to take the drawn cup out of the tool) were 81

105 also recorded. Figure 7.12 shows the temperature range plots at 250 o C, 275 o C and 300 o C. Figure 7.12: Punch and knockout pin temperatures at tool temperatures of 250 o C, 275 o C and 300 o C Effect of the interface pressure on the hardness and the surface roughness Surface roughness of the material affects the heat transfer, which would at the same time affect the dwell time necessary for heating the sheet in warm deep drawing. Along with the surface roughness, change in the hardness of the material after operating at elevated temperatures, is also of interest for further practical applications. Therefore, in this experimental analysis, hardness and surface roughness values were measured for each sample (Al 5052-H32, Mg AZ31-O (Supplier A), Mg AZ31-O (Supplier B)) before and after the experiments at two locations. Al 5754-O is not used because it is already at the O heat treatment condition. (One point in the center and the other point ~10 82

106 mm off the edge of the sheet). The reason for conducting the measurements at two points is because of the slight variation of the sheet temperature between the center and the edge of the sheet. The center of the sheet is relatively cooler compared to the side of the sheet, because it is open to air. Tool temperature was set to 300 o C and the dwell time was selected to be 90 seconds to make sure that the whole sheet reaches approximately to the same temperature. Diameter of the samples was 100 mm Hardness Measurements Hardness measurements in Brinell scale (500 kg weight) were made using a 1/16 ball. Table 7.1, Table 7.2 and Table 7.3 show the hardness values of the sheets before and after the experiments. Results indicate that there is a decrease in the hardness values of Al 5052-H32 sheet both at the center and at the side. For Mg materials, there is a slight increase in the hardness. The reason for this increase might be related to the decrease in the surface roughness. Local plastic deformations on the surfaces might have hardened the surface of these materials. As it is seen from the tables, hardness measurements for the highest BHP values could not be made at the center. Because, during the experiments, with increasing BHP, axisymmetric domes were observed at the centers of the sheets (open to air from both sides). Due to the formation of these domes, flatness is 83

107 lost at the center of the sheets; therefore hardness measurements were not possible. Al 5052-H32 BHP (psi) Before Exp. After Exp Center Side Center Side Table 7.1: Hardness (Brinell) measurements of Al 5052-H32 Mg AZ31-O (Supplier A) BHP (psi) Before After Center Side Center Side Table 7.2: Hardness (Brinell) measurements of Mg AZ31-O (Supplier A) 84

108 Mg AZ31-O (Supplier B) BHP (psi) Before After Center Side Center Side Table 7.3: Hardness (Brinell) measurements of Mg AZ31-O (Supplier B) Surface roughness measurements Figure 7.13 and Figure 7.14 show the as received surface roughness conditions of the sheets along the rolling and the transverse directions (RD and TD). It is interesting to note that the surface roughness values for the Mg AZ31-O (Supplier A) are the highest and they differ significantly from the Supplier B. Figure 7.13: R a values for 5754-O and 5052-H32 85

109 Figure 7.14: R a values for Mg AZ31-O (Supplier A) and Mg AZ31-O (Supplier B) Dome formation in the sheet under pressure Figure 7.15 shows the dome heights at 90 psi, 270 psi, 750 psi and 1740 psi for tests conducted at 300 o C, with a sheet diameter of 100 mm. Figure 7.16 shows the change in the diameter of the sheets. Diameters were measured before and after the test. It is interesting to note that, as the dome height increases, change in diameter (contraction towards center) also increases. 86

110 Figure 7.15: BHP dome height at T=300 C Figure 7.16: Change in the sheet diameter with respect to the BHP (Sheet Diameter: 100 mm) 87

111 7.5 Lubricant evaluation for warm deep drawing process Selection of lubricants for elevated temperature deep drawing is one of the most important issues. On the other hand, development of lubricants for elevated temperatures is at its preliminary stage, therefore there are not many lubricants available commercially. Four lubricants were evaluated for their applicability in the warm deep drawing process. Table 7.4 gives the list of lubricants and the experimental condition. Evaluation method is using the existing deep drawing tool and keeping every process parameter constant and changing the lubricant. Therefore, deep drawing tests were conducted under the same temperature, draw depth, forming speed and using the same die corner radius. Measurement criteria are; a) flange draw-in, b) thickness distribution c) visual inspection of the blank surface. Lube Description PTFE Film Lube A 600 % elongation 327 o C melting temp. Forgeease 02 Lube B AIS Binder III 7.5% Boron Nitride Lube C Forgeease 02 AIS Binder III Al 5754-O Sheet Diameter: 112 mm Punch velocity:5 mm/s Dwell time is 30 sec. T= 250 o C Environment temperature: 25 o C Relative Humidity: 55 % BHF=4.4kN 8.8 kn (linear increase) Lube C dries faster than Lube B (20 min.drying time) Lube D Dry Lubricant (info N/A) Table 7.4: List of lubricants and experimental conditions 88

112 Figure 7.17 shows that Lube A (Vac-Pak HT-620, Richmond Aircraft Products) provides a more uniform thickness distribution in the cup, compared to the other lubricants. This is due to Lube A s high stretchability. During drawing it did not tear and therefore eliminated a metal to metal contact. Figure 7.18 shows the cup tested with Lube A. Visual analysis of the cup surfaces also indicate that the scratches arise from drawing is not seen when Lube A is used. (Figure 7.19 and Figure 7.20) After experimenting with Lube B (Fuchs) and Lube C (Fuchs), dried (possibly burned) lubricant accumulation was seen on the tools, which required some cleaning after consecutive tests. Fourth lubricant (Lube D, Lubrizol), did not perform well and was eliminated at the very first stage of tests. Lube A is used in the vacuum molding of composite materials in aircraft applications where high temperatures are involved. Therefore, a new use of a PTFE film (Lube A) was found as a lubricant at elevated temperatures and successfully used first time. Therefore, in the rest of the experimental study, Lube A was used as lubricant. Figure 7.19 shows the pictures of the cups that were tested using the lubricants. It was observed from the experiments that cups that were tested with Lube B and Lube C needed to be cleaned right after the test (when they were hot) in order to be able to take the residue from the lubricants. It was difficult to take the lubricant residue off the cups once they cooled down. 89

113 Figure 7.17: Thickness distributions for different lubricants under same process conditions [Kaya, et.al., 2007] Figure 7.18: Cup with Lube A after drawing [Kaya, et.al., 2007] 90

114 Figure 7.19: Al cups formed with Lube C, Lube B and Lube A (from left to right) Figure 7.20: Mg cups formed with Lube C, Lube B and Lube A (from left to right) 91

115 7.6 Preliminary Experiments A set of preliminary screening experiments were conducted to investigate the maximum attainable LDR for Al 5754-O, Al 5052-H32 and MgAZ31-O using the lubricant A. As preliminary experiments, part of the methodology shown in Figure 7.21 was followed to determine the maximum LDR that can be reached for Al 5754-O at a particular die temperature. Similar approach was used to find the maximum LDR that can be reached for Aluminum 5052-H32 and Magnesium AZ31B-O. The objective is to find the highest possible LDR by adjusting the process parameters and obtaining some numerical values about the process. Figure 7.21: Adopted methodology for preliminary experimentation 92

116 Table 7.5 gives the obtained LDR and HDR values As a result of the experiments, LDR values of 2.9, 2.9 and 3.2 were obtained for Al5754-O, Al5052-H32 and MgAZ31-O, respectively (Table 7.5). In order for the LDR to be accurate, the cup has to be fully drawn. It is seen in Table 7.5 that all cups from Al5754-O and Al5052-H32 are fully drawn. For Mg AZ31-O, LDR 2.6 is fully drawn but LDR of 3.2 has some flange. In order to be more accurate we also used the Cup Height/Punch Diameter Ratio (HDR), explained earlier which represents the drawability better when there is a flange. Al 5754-O Al 5052-H32 Mg AZ31-O Left to right LDR HDR Left LDR HDR Left LDR HDR to to N/A N/A right right Table 7.5: Summary of the preliminary screening experiments for Al 5754-O, Al 5052-H32 and MgAZ31-O 93

117 Through these preliminary experiments, the designed and assembled tool with temperature controller, heating system, tool temperatures, thermocouples and punch cooling system was also checked and verified for further experiments. 7.7 Process optimization / windows Using the lubricant A and a dwell time of 90 sec. to heat the blanks, a series of tests were conducted to determine the best blank temperature and constant punch velocity for the Al 5754-O and the Mg AZ31-O (Supplier A) alloy. Experiments were also conducted using SS304 since it is possible to reduce weight using a thinner gauge material. Results of these experiments are given in Appendix C. Figure 7.22 through Figure 7.24 show variations of LDR with punch velocity at various blank temperatures, including when some of the drawn samples were fractured for the Mg AZ31-O alloy sheet. Three to four samples were formed under each condition. Figure 7.25 shows the process window (temperatures and punch velocities for successful cup drawing) for Mg AZ31-O alloy for the tool geometry, used in this study. The numbers in boxes at each point in Figure 7.25 show the maximum thinning (in percent) obtained in the drawn cups. Figure 7.26 shows the corresponding data (formed and fractured cups) for the Al 5754-O alloy. 94

118 Figure 7.22: Variation of LDR with punch velocity (Mg AZ31-O, T=250 o C) Figure 7.23: Variation of LDR with punch velocity (Mg AZ31-O, T=275 o C) 95

119 Figure 7.24: Variation of LDR with punch velocity (Mg AZ31-O, T=300 o C) Figure 7.25: Process window for the Mg AZ31-O alloy 96

120 Figure 7.26: Process window for the Al 5754-O alloy Results show that punch velocities up to 300 mm/s are possible to obtain for the Mg alloy sheet while maximum punch velocity remains at 35 mm/s for the Al alloy. The effect of the blank size is obvious on the attainable punch velocity Effect of constant forming velocity and temperature on deformation Experiments are conducted using a 100 mm diameter sheet (draw ratio of 2.5) for both Al 5754-O and Mg AZ31B-O. The objective is to understand the effect of constant (5 mm/s, 15 mm/s and 50 mm/s) and variable punch velocity and temperature (250 o C, 275 o C and 300 o C) on the forming behavior of Al 97

121 5754-O and Mg AZ31-O cups. These velocity and temperature ranges were obtained by the preliminary experiments that were conducted. During the experiments, punch load and the temperature at the cop bottom are also measured Results for Al 5754-O Table 7.6 shows the summary of the conducted experiments. At various temperatures and forming velocities, formed and fractured cups along with their heights and flange diameters are given. Min. and max. blank holder Draw Ratio Dwell time (sec) force/pressure (kn/mpa) / / 1.5 Punch Velocity (mm/s) Cup Height / Flange Diameter of the drawn cup (mm) Temperature ( C) / 53.1 Cup fractured 48 / / / / 53.3 Cup fractured Cup fractured Cup fractured Table 7.6: Experimental results for Al 5754-O 98

122 Figure 7.27 and Figure 7.28 show the thickness distributions for the aluminum cups. Plots indicate that higher temperature helps reduce thinning at the punch corner, which is the location of maximum thinning. 2.5) Figure 7.27: Effect of temperature on thickness distribution (5 mm/s, DR: 99

123 Figure 7.28: Effect of temperature on thickness distribution (15 mm/s, DR: 2.5) Figure 7.29 and Figure 7.30 show the punch load-stroke measurements at various temperatures (250 o C, 275 o C and 300 o C) and punch velocities (5 mm/s and 15 mm/s). 100

124 Figure 7.29: Punch load stroke curves at 5mm/s for different temperatures Figure 7.30: Punch load stroke curves at 15mm/s for different temperatures It is important to obtain the temperature change in the cup as forming process proceeds. This data could be helpful in order to inversely obtain more accurate heat transfer coefficients at the sheet-punch interface through finite element analysis. Therefore, design modifications were made in the tooling in order to record the temperature change at the center of the sheet during the dwelling and the forming stage. Figure 7.31 and Figure 7.32 show the cup bottom temperature change curves for 5 mm/s and 15 mm/s punch velocities, at various tool temperatures. (250 o C, 275 o C and 300 o C) As it is seen, the sheet starts cooling once it is in contact with the cold punch. The pattern of the curves and the amount of temperature drop at the cup bottom is determined by the forming velocity. 101

125 Figure 7.31: Change in cup bottom temperature at 5 mm/s (Punch temp: ~55 o C, 65 o C, 73 o C) Figure 7.32: Change in cup bottom temperature at 15 mm/s (Punch temp: ~55 o C, 65 o C) It is seen from Figure 7.31 and Figure 7.32 that the sheet temperatures are lower than the set tool temperatures. Possible reasons for this could be a) the temperature gradient within the heated die block. Die surface temperatures 102

126 are usually ~15-20 o C lower than the set temperature b) the center of the sheet (~ 45 mm in diameter) is open to air from both sides, which causes some heat loss Results for Mg AZ31-O (Supplier A) Table 7.7 shows the summary of the conducted experiments and provides cup heights and flange diameters. At various temperatures and forming velocities, all cups are fully formed and there is no flange left. Magnesium sheets were also cut to be 100 mm in diameter, which corresponds to a draw ratio of 2.5. All the process conditions were kept exactly the same. It is important to notice the difference in cup heights of aluminum (Table 7.6) and magnesium (Table 7.7). Under same conditions aluminum cups are generally 4 mm deeper than the magnesium cups. This shows that aluminum cups are stretched more than the magnesium cups. This observation is also backed by the lower thickness distribution of the aluminum cups. Figure 7.33, Figure 7.34 and Figure 7.35 show the thickness distributions for the magnesium cups at constant punch velocities (5 mm/s, 15 mm/s, 50 mm/s) but at different temperatures. (250 o C, 275 o C, 300 o C) Plots indicate that at constant velocity, temperature does not change the thickness distribution significantly. Figure 7.36, Figure 7.37 and Figure 7.38, show the thickness 103

127 distributions for the magnesium cups at constant temperatures but at different velocities. The effect of velocity in thickness distribution is clearer in the plots. Min. and max. blank holder Draw Ratio Dwell time (sec) force/pressure (kn/mpa) / / 1.5 Punch Velocity (mm/s) Cup Height / Flange Diameter of the drawn cup (mm) Temperature ( C) / / / / / / / / / 44.8 Table 7.7: Experimental results for Mg AZ31-O (Supplier A) 104

128 Figure 7.33: Effect of temperature on thickness distribution (5 mm/s, DR: 2.5) Figure 7.34: Effect of temperature on thickness distribution (15 mm/s, DR: 2.5) 105

129 Figure 7.35: Effect of temperature on thickness distribution (50 mm/s, DR: 2.5) Figure 7.36: Effect of forming velocity on thickness distribution (250 o C, DR: 2.5) 106

130 Figure 7.37: Effect of forming velocity on thickness distribution (275 o C, DR: 2.5) Figure 7.38: Effect of forming velocity on thickness distribution (300 o C, DR: 2.5) 107

131 Figure 7.39, Figure 7.40 and Figure 7.41 show the punch load-stroke measurements at various temperatures and forming velocities for the Mg (Supplier A). As expected, punch load decreases with temperature and increases with velocity. Punch loads for magnesium are approximately 10 kn lower compared to the ones in the aluminum experiments. Figure 7.39: Punch load stroke curves at 5mm/s for different temperatures 108

132 Figure 7.40: Punch load stroke curves at 15mm/s for different temperatures Figure 7.41: Punch load stroke curves at 50mm/s for different temperatures 109

133 Temperature change at the center of the sheet during the dwelling and the forming stage was also recorded. Figure 7.42, Figure 7.43 and Figure 7.44 show the cup bottom temperature change curves for 5 mm/s, 15 mm/s and 50 mm/s forming velocities, at various tool temperatures. (250 o C, 275 o C and 300 o C) Same temperature change patterns were observed for the magnesium cup, and the patterns are determined by the punch velocity. Figure 7.42: Change in cup bottom temperature at 5 mm/s 110

134 Figure 7.43: Change in cup bottom temperature at 15 mm/s Figure 7.44: Change in cup bottom temperature at 50 mm/s 111

135 Figure 7.45: Pictures of the formed cups from Al 5754-O (left) and Mg AZ31-O (Supp.A) (right) Figure 7.45 show the pictures of the formed aluminum and magnesium cups. Wrinkling was seen in the rolling direction in almost every formed magnesium cup. As a summary, Figure 7.46 and Figure 7.47 show the effects of temperature and punch velocity on the maximum thinning values obtained at the cup bottom corner (critical location for design) for the Al and Mg alloy respectively. 112

136 Figure 7.46: Effect of blank temperature and punch velocity upon wall thinning at the bottom corner of the drawn cup for the Al 5754-O alloy Figure 7.47: Effect of blank temperature and punch velocity on thinning at the bottom corner of the drawn cup for the Mg AZ31-O alloy 113

137 Plots indicate that the amount of thinning in Mg alloy is lower compared to aluminum, which might be due to high anisotropy values seen in magnesium sheets Results for Mg AZ31-O (Supplier B) Experiments were conducted in order to investigate the difference in material properties of magnesium AZ31-O sheet from a different supplier. Same experimental conditions were repeated in Table 7.6 and Table 7.7. No cups were formed successfully. Experiments were repeated with a lower velocity and a lower temperature. The reason for this was, due to various mechanical property tests available in literature that uses the AZ31-O from supplier B shows less formability above 235 o C. Therefore, tool temperature was decreased to 225 o C. This change also did not provide successful cups. (Table 7.8) Velocity (mm/s) Temperature (225 o C) Not Formed Not Formed Table 7.8: Experiments at 225 o C Successful cups were obtained at 250 o C and at 1 mm/s and 2.5 mm/s. (Table 7.9) At the cup formed at 2.5 mm/s, cracks were seen in the area that was bent around the punch. Since all the experiments were conducted under 114

138 same conditions, this result shows that there is significant difference in the mechanical behavior of the material from different suppliers. Velocity (mm/s) Temperature (250 o C) Formed Formed Table 7.9: Experiments at 250 o C and lower velocities 7.8 Effect of variable forming velocity It was mentioned earlier that the most obvious benefit of the servo press is the flexibility it offers. This flexibility comes from the ability to program the speed and motion of the slide in an infinite number of ways. Figure 7.3 provided an explanation for a general ram motion that can be used in warm deep drawing process. So far path ( ) shown in Figure 7.3 is used, which means that a constant velocity was set between points 4 and 6. It is mentioned earlier that in deep drawing, severe deformation takes place around the punch and the die corner. Therefore, as it is seen in Figure 7.3, a variable velocity could also be set between points 4-5 and 5-6. For example, a slower velocity between 4 and 5 for forming around the punch and the die corner radii, and a faster velocity between points 5 and 6 to complete the forming stroke. The main unknown in the path is the amount of stroke needed to apply the slower velocity between points 4 and 5. In order to come up with an approximate estimate the critical concept mentioned earlier is used. 115

139 In the existing tool, r D is 6 mm, r P is 4 mm and the sheet thickness, t, is 1.3 mm. Therefore the critical stroke is calculated to be ~12 mm. Based on this; experiments were conducted to look at the effect of variable velocity on the thickness distribution for Al 5754-O and Mg AZ31-O. Experiments were repeated for two cups. Figure 7.48 shows that while an aluminum cup cannot be formed at 40 mm/s, it can be formed by using a variable velocity profile (5/40 mm/s or 10/40 mm/s). In these graphs, for example; 5/40 mm/s means that the cup was drawn at 5 mm/s during the first 12 mm of stroke and the rest of the stroke was completed with 40 mm/s. Figure 7.49 shows the results for the Mg alloy. The difference in the thickness of the cup formed at 40 mm/s is lower compared to the 5 mm/s. However, there is significant similarity in the thickness distributions of cups formed at 5 mm/s and 5/40 mm/s. Therefore, instead of forming the cup at 5 mm/s, results show that it can also be formed using 5/40 mm/s. The benefit of this is shown in Table

140 Figure 7.48: Effect of variable forming speed on the thickness distribution of the drawn Al cups Figure 7.49: Effect of variable forming speed on the thickness distribution of the drawn Mg cups 117

141 Punch Velocity (mm/s) Drawing time (s) 5 5 / =3.4 sec 1.1 sec 5.6 sec saving per part Table 7.10: Significant savings in drawing time is obtained through the use of variable forming velocity 7.9 Conclusions The following conclusions can be drawn from these deep drawing experiments conducted at elevated temperatures: a) The dwell time needed to heat blank is reduced with increasing interface pressure, i.e. Blank Holder Pressure (BHP). b) Surface roughness (R a ) values decrease with increasing interface pressures. The decrease was found to be 13 %, 30 % and 65 % for Al5052-H32, MgAZ31-O (Supplier A), MgAZ31-O (Supplier B), respectively. c) Hardness measurements before and after the experiments revealed that, hardness (Brinell scale) of A5052-H32 decreased from 60 to 55 in 118

142 average. However, both magnesium alloys showed a small increase in hardness values. d) During the dwell time when heating the blank, a slight dome was formed in the free center of the blank. As the interface pressure increased, the height of the dome also increased, for all investigated materials. This might be due to the limitation of the radial thermal expansion of the material because of higher interface pressures. Therefore, expansion can happen at the center of the sheet since it is open to air from both sides. e) Three lubricants out of a total of four investigated were successful in drawing a cup. However, only the PTFE based lubricant provided good thinning distribution and best surface conditions. The other successful lubricants left a residue on the formed cup and the tool. f) Experiments showed that for Al5754-O, higher temperature helps to reduce thinning at the punch corner. g) Significant variations in the deformation of the same magnesium alloy blank, from two suppliers, is observed. h) At constant velocity but at different temperatures (250 o C, 275 o C and 300 o C), there is no significant difference in wall thickness distribution 119

143 of the cups formed from Mg AZ31-O. However, at constant temperature, slight increase in thinning is seen with increasing velocity. i) The effect of variable punch velocity (slower at the initial stages of drawing) was found to be significant. Instead of forming with a slower constant velocity for the full stroke, a slower velocity within the critical stroke and a faster velocity after this stroke can be used if the press can provide this type of velocity control. In our experiments, 60 % reduction in the drawing time was achieved. 120

144 CHAPTER 8 MODELING OF NON-ISOTHERMAL DEEP DRAWING PROCESS Traditionally, metal forming processes have been developed based on expensive experimental trials. In recent years, finite element (FE) simulations have been extensively used to reduce the amount of experiments and trial and error involved in the process development. However, reliable results can be expected only if the material properties and related process parameters input to the FE simulations are accurate. Due to the highly non-linear nature and coupling of variables in warm forming of Mg and Al, experimental determination of variables such as material properties, friction, etc., are difficult and expensive, but necessary for a reliable analysis. To understand the complex interactions between material properties, temperature and punch velocity (strain rate), it is necessary to model the process using FEM. However, this modeling requires reliable input data, i.e. a) material properties in function of strain, strain rate and temperature, b) heat transfer coefficients at the die/blank interface and at the punch/cup bottom interface, c) coefficient of friction in function of interface pressure and temperature. 121

145 In non-isothermal sheet forming processes, the temperature of the sheet during forming is not constant. In other words, different locations in the sheet are subject to different temperatures during the operation. In the existing experimental setup, the punch was cooled in order to increase the strength of the material in the punch corner area while the flange was kept at higher temperature to promote easy flow of the material. Having the right temperature distribution in the part is then the key factor for the success of the process Determination of the heat transfer coefficients In order to perform more accurate FE analysis of non-isothermal processes, the user needs to approximately know the interface Heat Transfer Coefficient. When conducting FEA, it is a common practice to assume a constant value for the HTC. This simplification can reduce the accuracy of FEA. Therefore instead of picking an average value from literature it was decided to determine the heat transfer coefficients through the temperature measurements conducted. Various researchers, mostly in the forging area, have experimentally demonstrated that the interface HTC is a function of interface pressure and interface temperature [Semiatin et.al, 1987]. Pressure and temperature conditions generate microscopic changes in the contact area conditions 122

146 (roughness and micro-welding) and significantly affect the heat transfer phenomena Inverse Analysis In order to determine the HTC values under different temperatures and interface pressures an FEM based inverse optimization method [Kim, et.al., 2001] has been implemented into Deform2D V9.0. In order to conduct this analysis, temperature time curves given in Figure 7.11 were used as input. Prior to the inverse analysis, heat transfer analysis was conducted by selecting constant heat transfer coefficients and predicted temperature-time curves were plotted against the experimental ones. Figure 8.1 shows the measured and calculated temperature time curves. Figure 8.1 Experimental and calculated temperature-time curves 123

147 Setup of the inverse analysis problem Figure 8.2 shows the fixture in contact with the blank holder and the die. Only the fixture was modeled and the areas where die and blank holder are in touch with the fixture were selected and assigned as heat exchange areas (Figure 8.3). The temperature measurement locations in the FE model of the fixture are decided in correspondence with the location that the experimental measurements were conducted. Experimentally measured temperature-time curves (target functions for the optimization) are provided in tabular form for the calculation. thermocouple location Areas of heat exchange Figure 8.2: Schematic view of the FE model Figure 8.3: Modeling of the measurement fixture with the temperature measurement point The last step in the model setup is to assign an initial guess value to the HTC and a certain number of temperature control points (a minimum of two control points are required). The optimization program, after each iteration changes the 124

148 value of the HTC in order to obtain a closer match with the target function. The solution provides the variation of the HTC with respect to temperature. Figure 8.4 shows the calculated heat transfer coefficients with changing interface pressure. The calculated values were compared with the only available data in [Groche et.al., 2002]. Figure 8.4: Calculated heat transfer coefficients 8.2. Non-isothermal deep drawing of Mg AZ31-O Mg AZ31-O flow stress in literature Among the commercially available magnesium alloys, AZ31B is, by far, the most used for sheet forming applications. In the past, many researchers, 125

149 interested in sheet forming of lightweight materials, have studied the properties of this alloy. A comprehensive literature study to collect flow stress data obtained by different researchers at various temperatures and strain rate conditions was conducted. As a result of the study a flow stress database, for the AZ31 sheet material was created [Sivakumar, et al, 2006]. Graphical representation of this database is reported in Figure 8.5. Due to the observation in the property variation of Mg AZ31-O in the bulging and drawing experiments, it was decided not to use the literature data. Therefore, the flow stress obtained from the hydraulic bulge test was used. 126

150 A, Jager Chen S, Jager Hecht Takuda 05 Agnew Yi Doege Xu Doege Chastel Behren Figure 8.5 Graphical representation of the database for Magnesium AZ31 Tensile tests conducted at different strain rates and temperatures [Sivakumar, et al, 2006] FE modeling in LS-Dyna3D LS-Dyna is commonly used to model isothermal sheet metal forming processes. There is almost no experience in conducting non-isothermal analysis therefore it is more of a challenge to understand how to conduct a nonisothermal forming process analysis. Once the first model was built, a series of trial-and-error simulations were conducted to better understand the significance of some input parameters and to make sure the model was working properly. The aim of the present work is to discuss two main issues encountered during the setup of the FE simulation; namely: 127

151 flow stress data implementation, definition of the thermal contact, Die Sheet Punch Blank holder Figure 8.6 FE model for non-isothermal simulations of deep drawing of round cups Plastic-thermal material model available in LS-Dyna For warm forming under non-isothermal conditions, material models are needed where the equivalent plastic stress is defined in function of equivalent strain, equivalent strain rate and temperature. Only three plastic-thermal material models are available in LS Dyna. These are: Mat 004 (*MAT_ELASTIC_PLASTIC_THERMAL) Mat 015 (*MAT_JOHNSON_COOK) Mat 106 (*MAT_ELASTIC_VISCO_PLASTIC_THERMAL) 128

152 Moreover, only the last two can include strain rate effects. They are discussed briefly, below. MAT 015 (*MAT_JOHNSON_COOK) The Johnson-Cook material is strain and temperature sensitive plasticity; it is usually used for problems where the strain rates vary over large ranges and temperature increases due to plastic deformation. Johnson and Cook express the flow stress as: m & εε& eq T T & ε T T n eq 1 (, & ε& eq, T) = ( A+ B ) 1+ c ln 1- σ ε ε ε eq eq eq eq where: A, B, c, n and m are input constants. ε& 0 is set to 1 s -1 by default. MAT 106 (*MAT_ELASTIC_VISCO_PLASTIC_THERMAL) Mat 106 was selected in our study to input flow stress data in LS-Dyna. This model was preferred over the others since it gives the user more flexibility in fitting the experimental data for different values of temperatures and strain rates. The flow stress, in function of strain, strain rate, and temperature is calculated using the formula below: ε& 0 ε& 0 129

153 I II III ε& & ε eq σeq ( εeq, ε& & ε eq, T) = MFS( εeq ) SF( T) 1+ CT ( ) Mater Flow Effect of Effect of Effect of Stress temperature Viscous component strain temperatu Effect of strain rate 1 PT ( ) I. The first component in the formula is the master flow stress, (MFS). It is in the form of a table where stress and strain values are inserted as data-points. It is suggested to use the flow stress of the material at room temperature as the master flow stress. II. III. The second component, SF, scales the masters flow stress values to account for temperature effects. SF(T) is input in tabular form. The last component is the viscous component, which includes strain rate dependency. The viscous parameters C and P are used to take into account strain rate effects. C(T) and P(T) are input in tabular form. At the end, a total of four tables need to be input: MFS( P(T). These tables are used in the above formula to give flow stress value for each value of strain, strain rate and temperature. The fact that aluminum and magnesium material data can satisfactorily be fit using material model 106, does not imply that every flow stress data can by fitted using *MAT106. If the hardening of the material varies too much with temperature and/or stain rate, the accuracy of the fitting could be very poor. 130 ε eq ), SF(T), C(T) and

154 Therefore, problems in fitting were encountered where there is slight work softening in the flow stress. Through experience it is realized that it is better if the flow stress data could be inserted entirely in data-point format Thermal contact definition Thermal contact definition plays an essential role in the simulation of non-isothermal warm forming process since it determines the amount of heat that is transferred between the objects in contact. During forming, the heated sheet comes in contact with the punch (at room temperature) and looses heat. The region of the sheet metal in contact with the punch has lower temperature compared to the sheet in contact with the die. The lower temperature in the wall and higher temperature in the flange are essential in warm deep drawing because, increase in the flow stress due to decrease of temperature enables the cup wall at the punch corner to support more stress. It must also be considered that, for given interface conditions (materials, lubricants, surface finish), the heat transfer (or thermal contact) depends on interface pressure that may vary within the entire contact area between sheet and tool. 131

155 In LS-Dyna, the thermal contact can be activated from the same card used to define the mechanical contact (see Figure 8.7). The algorithm accounts for the possibility of having a gap of fluid between the sliding surfaces. Since in our case there is no fluid between the objects, the only significant parameters to input are: HTC = heat transfer coefficient (h cont ). GCRIT = Critical gap (l min ) GMAX = no thermal contact if gap is grater than this value (l max ) LS-Dyna uses (h cont ) for gaps in the range of 0<l gap <l min ; l gap is recalculated every step by the code based on deformation. With the use of GMAX=GCRIT, and CF=FRAD=0 the assumption of no fluid is modeled. 132

156 mechanical contact definition thermal contact definition Figure 8.7 Contact-Forming card used to define mechanical and thermal contact parameters. Values of GCRIT of about one tenth of the sheet thickness have been used in simulations. A reasonable value of this parameter was found by trial and error. If lower values are used, the heat transfer between bodies could, depending of the mesh size, become null. The effect of the interface pressure on the heat transfer coefficient (HTC) cannot be modeled due to the selected contact model Simulation matrix Table 8.1 shows the matrix of the conducted simulations. Comparisons with experiments were done for there different die temperatures and forming 133

157 velocities from 2 mm/s to 35 mm/s. The drawing ratio of the cups varied from 2.7 to 3.0. Name Simulations Matrix Drawing Ratio (DR) Die/BH temperature Forming velocity M mm/s M C 10 mm/s M mm/s M mm/s 275 C M mm/s M mm/s M C 12 mm/s M mm/s Table 8.1 AZ31B-O simulation matrix A summary of the most important thermal and mechanical parameters used in simulations is given in Table 8.2. Friction coefficient value of 0.04 was used. This value is relatively lower than what is normally reported in literature (form 0.1 to 0.16) because of the low friction PTFE film lubricant used during experiments. Our previous experience shows that the friction coefficient can be in the range of 0.04 when PTFE film type lubricants are used. 134

158 Thermo-mechanical data used for simulations thermal conductivity 77 W m -1 C -1 specific heat 1020 J kg -1 C -1 Interface heat transfer coefficient (HTC) Fraction of mechanical work converted to heat 95 % sheet-punch 5000 W m -2 C -1 Friction coefficient, µ sheet-die 1000 W m -2 C -1 sheet-punch 0.04 sheet-binder 1000 W m -2 C -1 sheet-die 0.04 sheet-environment 50 W m -2 C -1 sheet-binder 0.04 Table 8.2 Summary of input data used for AZ31B-O simulations Comparison of FE predictions and experimental results Figure 8.8 to Figure 8.15 show the comparison between calculated and experimental punch load vs. stroke curves and thinning distributions for the eight selected cases. It is noticeable that punch loads have always been overestimated. Depending on the forming conditions, calculated loads are, in fact, 20% to 50% higher than in experiments. This was not a surprising result. It is known that magnesium behavior is different in flange (where compressive stresses are dominant) than in tensile so the material flows much easily in reality than in simulation. Another possible reason is also the different yield surface of magnesium. It is also known that anisotropy of magnesium alloy sheet varies 135

159 between the rolling and the transverse direction under tensile and compressive stresses. Thinning distribution trends matched experimental measurements for forming velocity up to 10 mm/s. In two cases where forming velocity was relatively higher, 25 mm/s (Figure 8.11) and 35 mm/s (Figure 8.13), FE predictions showed very high thinning compared with experiments. Sim # : M1 Punch load [kn] Drawing Ratio (DR) Die/BH Temperature forming velocity C 10 mm/s 10 Exp EXP 5 SIM Stroke [mm] SIM. Thinning EXP TD EXP RD SIM 20 mm 60 mm Curvilinear length [mm] Figure 8.8 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) 136

160 Sim # : M2 Drawing Ratio (DR) Die/BH Temperature Punch load [kn] forming velocity Exp EXP SIM C 10 mm/s Stroke [mm] SIM. Thinning EXP TD EXP RD SIM 20 mm 75 mm Curvilinear length [mm] Figure 8.9 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Sim # : M3 Punch load [kn] Drawing Ratio (DR) Die/BH Temperature forming velocity C 2 mm/s SIM. 10 EXP 5 Exp SIM Stroke [mm] Thinning EXP TD EXP RD SIM 20 mm 70 mm Curvilinear length [mm] Figure 8.10 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) 137

161 Sim # : M4 Drawing Ratio (DR) Die/BH Temperature forming velocity Exp SIM C 25 mm/s EXP SIM Stroke [mm] Thinning EXP TD EXP RD SIM 20 mm 65 mm Curvilinear length [mm] Figure 8.11 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Sim # : M5 Drawing Ratio (DR) Die/BH Temperature Punch load [kn] forming velocity EXP SIM SIM. Exp C 10 mm/s Stroke [mm] Thinning mm 75 mm EXP TD EXP RD SIM Curvilinear length [mm] Figure 8.12 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) 138

162 Sim # : M6 Punch load [kn] Drawing Ratio (DR) Die/BH Temperature forming velocity Exp SIM C 35 mm/s EXP SIM Stroke [mm] Thinning EXP TD EXP RD SIM 20 mm 65 mm Curvilinear length [mm] Figure 8.13 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) Sim # : M7 Drawing Ratio (DR) Die/BH Temperature Punch load [kn] forming velocity SIM. Exp C 12 mm/s EXP SIM Stroke [mm] Thinning mm 65 mm EXP TD EXP RD SIM Curvilinear length [mm] Figure 8.14 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction) 139

163 Sim # : M8 Drawing Ratio (DR) Die/BH Temperature Punch load [kn] forming velocity SIM. Exp C 5 mm/s EXP SIM Stroke [mm] Thinning EXP TD EXP RD SIM 20 mm 75 mm Curvilinear length [mm] Figure 8.15 Experimental and computed punch load vs. stroke curves (left) and cup thinning distributions (right). (RD=rolling direction; TD=transverse direction 8.3. Non-isothermal deep drawing of Al 5754-O FE modeling of the non isothermal deep drawing process of aluminum is conducted and numerical predictions are compared with the experimental measurements using DEFORM 2D. Due to the inconveniences encountered using LS-Dyna, analysis was conducted with Deform 2D. Because Deform2D allowed to input a) flow stress parameters to be input as data points, rather than using a material model and b) heat transfer coefficients as function of pressure. Over all Deform2D is designed for non-isothermal forging process therefore it is believed to perform better in non-isothermal analysis. Table 8.3 provides the list of process parameters, thermal and mechanical properties of 140

164 the Al alloy sheet. The flow stress data used in this study is obtained from [Boogard, 2001] Geometry Thermal and Mechanical properties Punch shoulder radius (mm) r p 4 Punch diameter (mm) D p 40 Die shoulder radius (mm) r d 6 Die inner diameter (mm) D d 44.6 Initial sheet thickness s 0 (mm) 1.3 Thermal conductivity (sheet) (N/(sec C)) Heat capacity (sheet) (N/(mm 2 C)) Thermal conductivity (tool) (N/(sec C)) Heat capacity (tool) (N/(mm 2 C)) Interface heat transfer coefficient (N/(sec mm C)) 140 (Incropera, et.al., (2002) 2.40 (Incropera, et.al., 2002) 60.5 (Incropera, et.al., 2002) 3.41 (Incropera, et.al., 2002) Initial die / BH temperature ( C) 250/275/300 Initial sheet temperature ( C) 250/275/300 Initial punch temperature ( C) 60 Young s modulus, E (GPa) Poisson s ratio, ν (room temp) Flow stress curve [Boogard, 2001] Friction coefficient, µ 0.04 Table 8.3: List of input parameters to the FE model (Al 5754-O) In Table 8.3, the effect of temperature on the thermal conductivity and the effect of radiation is neglected since the percentage change is approximately 2% for Al and steel alloys. The effect of temperature on the heat capacity is also 141

165 negligible within the studied temperature ranges. It is known that E-Modulus also changes with temperature; however, in our FEA we have neglected this effect since the deformation dominantly takes place in the plastic range. Selection of the friction coefficient is based on a) previous experimental experience on testing PTFE based lubricants b) through acceptable comparison with the FE predictions Yield criterion adopted in the FE model for the Al 5754-O Von Mises yield criterion is widely accepted in plasticity and it represents the deformation of steels to a great accuracy. For Al alloys various yield surface models have been proposed by researchers. [Barlat et.al., 2003] is widely accepted and implemented in various FE codes. [Naka et.al., 2003] has investigated the effects of temperature on the yield locus for 5083 aluminum alloy sheet in forming operations. He suggests that Logan-Hosford and Barlat criteria can well describe the yield loci and the equivalent stress-strain curves for the Al-Mg alloy sheet at various temperatures. [Figure 8.16] shows the experimentally determined yield loci for the aluminum alloy sheet at various temperatures and those predicted by various suggested models. It is seen from [Figure 8.16] that the Logan-Hosford and Barlat models fit better, however Von Mises yield surface is also acceptable since the difference might be negligible and Al 5754-O is isotropic. Therefore, in the present study, the Von Mises yield 142

166 locus is adopted to conduct the non-isothermal analysis of deep drawing process. Thickness distributions and punch load predictions were compared with the experimental measurements. Figure 8.16: Comparison of experimental yield loci and those predicted by the Von Mises, Hill, Tresca, Logan-Hosford and Barlat criteria under biaxial stress condition for Al 5083-O alloy sheet [Naka, et.al., 2003] Flow stress curves for aluminum Flow stress data for the Al 5754-O alloy sheet, used in this study, was obtained from [Boogard, 2001]. Data in the mentioned reference is obtained through tensile tests up to 250 o C with strain rates of 0.1 1/s, /s and /s. Therefore the data for 275 o C and 300 o C were obtained by extrapolation as shown in Figure In the definition of flow stress curves, softening behavior was not taken into account. In other words, once the maximum stress point was reached in the 143

167 flow stress curve that maximum stress level was kept constant with respect to the strain. [Figure 8.18] Flow Stress MPa y = E-08x E-03x E-01x E y = E-03x E-01x E Strain rate Strain rate 0.02 Strain rate 0.1 Poly. ( Strain rate 0.02) Poly. (Strain rate 0.002) Poly. (Strain rate 0.1) 0.1 y = E-06x E-03x E-01x E Temperatur C True Stress True Strain Max. stress points Figure 8.17: Extrapolated flow stress versus temperature for different strain rates(original data from Boogard, 2001) Figure 8.18: Elimination of the softening behavior from the stressstrain curve 144

168 Comparison of numerical predictions with experimental measurements FEA of the experimental cases given in Table 7.6 was conducted. Initially various constant heat transfer coefficients were used to investigate their effect on the process. It was found that when constant HTC values of 2 kw/m 2 C and 3 kw/m 2 C were used the cup fractured at the first 15 mm of the stroke. Punch load and thickness distribution curves are shown in Figure 8.19 through Figure 8.26, for various cases. It is seen that the predictions for 5 mm/s are acceptable except the case with 15 mm/s. This is mostly due to the lack of flow stress data at higher strain rates. Results indicate that the adopted Von Mises yield criterion provides acceptable accuracy. The maximum difference in punch load was obtained for 250 o C with 5mm/s is around 10%. Differences in the other cases are relatively lower. Figure 8.27 and Figure 8.28 show the comparison of results for one case when the heat transfer coefficient is input as function of interface pressure given in Figure 8.4. There is a slight improvement in the thickness distribution. 145

169 Figure 8.19: Comparison of punch load predictions using various heat transfer coefficients (HTC: kw/m 2 C) with experiment (5 mm/s at 250 o C) Figure 8.20: Predicted thickness distribution comparison with various heat transfer coefficients (5 mm/s at 250 o C) Figure 8.21: Comparison of punch load prediction with experiment (5 mm/s at 275 o C) Figure 8.22: Predicted thickness distribution comparison with experiments (5 mm/s at 275 o C) 146

170 Figure 8.23: Comparison of punch load prediction with experiment (5 mm/s at 300 o C) Figure 8.24: Predicted thickness distribution comparison with experiments (5 mm/s at 300 o C) Figure 8.25: Comparison of punch load prediction with experiment (15 mm/s at 275 o C) Figure 8.26: Predicted thickness distribution comparison with experiments (15 mm/s at 275 o C) 147

171 Figure 8.27: Predicted thickness distribution comparison with experiments (5 mm/s at 300 o C) Figure 8.28: Predicted thickness distribution comparison with experiments (5 mm/s at 300 o C) 8.4. Non-isothermal modeling of SHF-P Experience obtained from modeling the SHF-P (at room temperature) and the deep drawing under non-isothermal conditions is combined for modeling the non-isothermal SHF-P process. Heat transfer takes place in four interfaces in elevated temperature SHF-P in which appropriate inputs to the model is needed (Figure 8.29). 148

172 Interface C V PUNCH q BLANK HOLDER F q q Interface A Interface D q P q DIE q Interface B Liquid Figure 8.29: Interfaces in elevated temperature SHF-P process As an initial modeling exercise, some assumptions are made. These are; a) Non-isothermal analysis is conducted (heat transfer at the sheet-die, sheetblank holder and sheet-punch interfaces) b) Pressure is applied to the complete sheet (additional force generated due to pressure is added to the blank holder force) c) Initial sheet and liquid temperature are the same (275 o C) Assumption: no heat transfer between liquid and sheet. Figure 8.30 shows the pressure curve, the blank holder force curve and the related process conditions used in the analysis. Figure 8.31 shows the sheet temperature at the end of the drawing process in the analysis. It is noticeable that there is no gap between the sheet and the punch. Difference in sheet temperature using SHF-P and deep drawing is clearly seen in Figure 8.32 and Figure 8.33, respectively. 149

173 Al 5754-O Punch temperature: 60 o C Sheet temperature: 275 o C Die temperature: 275 o C Blank holder temperature: 275 o C Punch speed: 5 mm/s Friction coefficient, µ= 0.04 Figure 8.30: Pressure and BHF used in the simulations Figure 8.31: Temperature distribution of the sheet at the end of the stroke 150

174 Figure 8.32: Temperature distribution of a sheet formed using SHF-P Figure 8.33: Temperature distribution of a deep drawn sheet 151

175 Conclusions a) Non-isothermal cup drawing simulations of magnesium AZ31-O have been conducted using commercial FE software LS-Dyna. Difficulties in the method of inputting the flow stress are encountered. At this point, the need for inputting the flow stress as data points became obvious. b) FEA of Al 5754-O cups were conducted using Deform 2D. Effect of the heat transfer coefficient was found to be significant in the thickness distribution of the cups. Heat transfer coefficients of ~11 kw/m 2 C and 6 kw/m 2 C were found to be better at the sheet-punch and sheet-tool interfaces, respectively. An overall heat transfer coefficient of 6 kw/m 2 C is also found to be satisfactory. 152

176 CHAPTER 9 DETERMINATION OF DRAWABILITY USING FRACTURE CRITERION The LDR of a material is usually determined through experimentation, which requires extensive resources. Therefore, there is a need for a quick and approximate methodology to determine the LDR of a material by using the available stress-strain curve and FEA. Thus, the objective is to predict an approximate LDR (if possible) for aluminum (Al 6061-T6), with FEA by using the flow stress (stress-strain curve) of this material and a fracture criterion Cockcroft & Latham ductile fracture criterion The application of ductile fracture criteria for predicting the forming limit of a sheet material has been studied by various researchers using formability tests such as uniaxial tensile test, plane-strain tension test etc. [Takuda, 1999 et al.] conducted FEA on deep drawing of various steel sheet by using various ductile fracture criteria and compared the predictions with the experimental findings. He concluded that Cockroft & Latham criterion could be used effectively for various materials as a ductile fracture criterion. Based on Takuda s work, in this study, the Cockcroft & Latham criterion will be used to determine the drawing limits of an aluminum alloy. By using this 153

177 criterion, the Critical Damage Values found using the Cockcroft & Latham criterion, will be determined through FEA of uniaxial tension test and applied in the deep drawing analysis. Cockcroft & Latham criterion is given in Eq.(1); ε 0 * σ d ε = C σ Eq. (1) * where, σ is the maximum normal stress, σ is the equivalent stress, ε is the fracture strain and C is a material constant called Critical Damage Value (CDV) Approach For this purpose, hydraulic bulge tests were conducted to determine the flow stress of the Al 5754-O at room temperature. The flow stress curve of Al 5754-O is given in Figure 9.1. Through additional drawing experiments, the LDR of Al 5754-O was determined to be 2.1 using the designed deep drawing tooling described in previous chapters. This available experimental data will be used to obtain the Critical Damage Value (CDV) by FEA and will be applied in the FEA of deep drawing Al 6061-T6 alloy. Same tool geometry will be used as given in Figure

178 Flow Stress Data from the Bulge test Stress (MPa Bulge test Strain Figure 9.1: Flow stress curve of Al 5754-O obtained from the bulge test The following steps will be carried out to validate the LDR/HDR for the Al 5754-O alloy and determine the LDR/HDR for the Al 6061-O alloy through FEA. a) Conduct 3D FEA of uniaxial tension test using Al 5754-O to determine the Critical Damage Value (CDV) The CDV under uniaxial tensile state of stress, through modeling the tensile test, will be determined by using the flow stress data given in Figure 9.1. The tensile specimen geometry used in the simulations is given in Figure

179 A= 50 mm (gage length) W= 12.5 mm R= 12.5 mm L= 200 mm C= 20 mm Figure 9.2: Geometry of the tensile specimen (ASTM, E 8M-04) b) Conduct FEA of deep drawing Al 5754-O Through FEA it is necessary to show that a cup with LDR=2.1 can be deep drawn for validation of the FE model. We will also check that in this FEA, the normalized CDV obtained from step (a) corresponds to that determined in this task. In other words, the objective in this task is to validate through FEA the same experimentally determined LDR of 2.1. c) Conduct 3D FEA of uniaxial tension test using Al 6061-T6 to determine the CDV The CDV will be determined under uniaxial state of stress through 3D modeling of the tensile test by using the flow stress data given in Figure 9.3. Flow stress data for the Al 6061-T6 is obtained from the literature [Padmanabhan, 1997]. d) Conduct FEA to determine the LDR of Al 6061-T6 using the CDV from step (c) 156

180 Various initial sheet diameters corresponding to various LDR s (such as 1.5 and 1.6) will be modeled to simulate the deep drawing operation for Al 6061-T6. In the simulations, drawn cup will be considered to fracture when the normalized CDV calculated anywhere in the cup wall reaches the CDV determined in step (c) Setup of the FE model for tensile test and deep drawing The tensile test specimen geometry is obtained from [ASTM, E 8M-04], Figure 9.2. Flow stress curves given in Figure 9.3 are used both in modeling the tensile test and the deep drawing analysis for Al 5754-O and the Al 6061-T6. Figure 9.3: Flow stress curves used in the FEA 157

181 Both tensile test and deep drawing simulations are conducted at room temperature (for Al 5754-O bulge test data and for Al 6061-T6 tensile data were used). The friction coefficient in the deep drawing analysis is selected to be 0.04 based on previous experience. Due to the limitations in the blank holding system of the press, blank holder force increased linearly from 4.4 kn to 8 kn during the experiments. Therefore, in order to accurately conduct the analysis, same linear increase is modeled in the FEA. Simulation matrix for Al 5754-O and Al 6061-T6 is shown in Table 9.1. Material LDR modeled in FEA Al 5754-O Al 6061-T Table 9.1: Simulation matrix for the deep drawing analysis 9.4. Results and discussion Determining the Critical Damage Value It is known that in uniaxial tension, load increases until the point when necking starts and decreases post necking. Until necking, uniform elongation takes place, therefore necking is usually considered to be the instability point. This phenomenon is illustrated in Figure

182 Max. Load Load (F) Uniform elongation Stroke (s) Figure 9.4: Point of instability in the load-stroke curve during the tensile test In the FEA of uniaxial tension, the CDV at the instability point (i.e. at the point when necking starts) will be taken as the CDV for the analyzed material. Based on this, Critical Damage Values of and are obtained for Al 5754-O and Al 6061-T6, respectively (Figure 9.5 and Figure 9.6). The length of stroke before necking starts (i.e. at the end of uniform elongation) is found to be 18 mm for Al 5754-O and 5 mm Al 6061-T6. It is clearly seen that, the deformation of Al 6061-T6 is noticeably low. 159

183 Figure 9.5: CDV (when necking starts during 3D tensile test simulation) for Al 5754-O is Figure 9.6: CDV (when necking starts during 3D tensile test simulation) for Al 6061-T6 is Deep drawing analyses Initially, the deep drawing analysis is conducted for the Al 5754-O (LDR=2.1) for checking whether the drawing will be successful and the obtained CDV from the drawing analysis will be under Figure 9.7 shows that for Al 5754-O the draw is successful and the maximum CDV is and it is located at the cup bottom corner. Based on this result, a secondary deep 160

184 drawing analysis is conducted using a LDR of 2.2 for extra validation because it was not possible experimentally to draw a LDR 2.2 cup. Figure 9.8 shows that the obtained maximum CDV is 0.42 and the location is again at the cup bottom corner. The cup reaches the CDV (for LDR of 2.2) at the early stage of the draw (17 mm). Further drawing of this cup showed excessive thinning which indicates fracture at the cup bottom corner. These results show that the adopted methodology for determining the LDR works well, based on the validation of Al 5754-O. Figure 9.7: Maximum CDV obtained for the successfully deep drawn Al 5754-O (LDR: 2.1) cup is Figure 9.8: Max CDV reaches 0.42 for the unsuccessfully deep drawn Al 5754-O (LDR: 2.2) cup Same methodology used in the analysis of Al 5754-O is applied to Al 6061-T6. Figure 9.9 and Figure 9.10 show that the cup reaches the Critical Damage Values of and at around the 3 mm stroke for LDR s of 1.6 and

185 respectively and both values are higher than LDR of 1.4 was also tried and the CDV was found to be around Results show that the sheet fractures during the bending that takes place around the punch corner. Therefore, it is concluded that for the existing tool dimensions and process conditions it is not possible to draw Al 6061-T6. It is believed that this result makes sense because for this material the maximum strain at fracture obtained from the tensile test is only 0.1. On the other hand the maximum strain at fracture (in tensile test) for Al 5754-O is around 0.3. It is also known that Al 6061-T6 has one of the lowest formability due to its alloying and heat treatment conditions. As a preliminary study with aluminum alloys, an idea about the drawability of an alloy can be obtained using the methodology explained above. Further experimentation will be beneficial with different materials and tool geometries in order to establish the methodology. 162

186 Figure 9.9: Maximum CDV obtained for Al 6061-T6 (LDR: 1.6) is Figure 9.10: Maximum CDV obtained for Al 6061-T6 (LDR: 1.5) is Conclusions Following conclusions can be drawn from this study; c) The adopted methodology for determining the LDR for a given material by using the flow stress data and FEA is tested and found out to be working satisfactorily. d) With the existing tooling, it is not possible to draw Al 6061-T6 to any degree, due to early fracture at the cup bottom corner. It is believed that this result makes sense because for this material the maximum strain at 163

187 fracture obtained from the tensile test is only 0.1. On the other hand the maximum strain at fracture (in tensile test) for Al 5754-O is around

188 CHAPTER 10 SUMMARY AND CONCLUSIONS Aluminum and magnesium components are being increasingly used by major automotive and electronics companies. Current automotive magnesium applications are mostly die castings, such as instrument panel beam, transfer case, steering components and radiator support. Some aluminum sheet applications can be seen in body panels of cars. The average magnesium content in a typical 2003 model year family sedan built in North America was only about 0.3% of the total vehicle weight, which compares to about 10% for aluminum and 8% for polymers and polymer-based composites [ Aluminum and especially wrought magnesium alloys and their manufacturing processes are receiving increasing attention. As especially magnesium is expanding from interior components to more critical applications in chassis and body areas, there is a great need for developing wrought magnesium products and manufacturing processes to provide improved mechanical and physical properties, crash performance and corrosion resistance. In the present study, formability limits of aluminum and magnesium alloy sheet are investigated through a) mechanical property 165

189 determination tests at room and at elevated temperatures (hydraulic bulging) and b) deep drawing processes conducted at room temperature, against liquid pressure (SHF-P) and at elevated temperatures. Major accomplishments can be listed as; a) Elevated temperature mechanical properties of Mg alloy sheet under equibiaxial state of stress were determined using the submerged hydraulic bulge test. This concept is found to be best in obtaining close to uniform temperature distribution in the sheet. True stress - true strain curves were obtained using the membrane theory. Strain values up to 0.7 were obtained under equi-biaxial state. b) FE simulations illustrated that SHF-P process improved the drawability of Al 5754-O from LDR of 2.1 (room temperature deep drawing) to LDR of 2.4. This was obtained by the application of minimum pot pressure during the critical stroke and increasing the pressure during the rest of the stroke. c) Table 10.1 summarizes the improvement in the drawability of aluminum and magnesium when warm forming process (with heated tools) is used. 166

190 Manufacturing Process Material Deep Drawing (RT) SHF-P (RT) Warm Forming Al 5754-O Mg AZ31-O N/A N/A 3.2 Table 10.1: Summary of obtained drawability through the use of different manufacturing processes d) Due to the high thermal conductivity and low heat capacity of Al and Mg, it is shown that through the use of a servo motor driven press, the in-die-dwelling concept is applicable. With this method, the need for a furnace and a transfer system is eliminated. e) For obtaining a sound product, the maximum punch velocity was decreased with increasing initial sheet diameter. Punch velocities of 35 mm/s and 300 mm/s were obtained for aluminum and magnesium respectively. Up to 50 mm/s forming velocity, it is seen that temperature improved the thinning behavior of aluminum significantly. However, the same behavior was not seen in magnesium. f) A foil type product was used as lubricant in warm forming and was found to perform well. It provided scratch free cups, cleaner tools and a smoke-free experimental environment. 167

191 g) Computational models of deep drawing and SHF-P at room and at elevated temperatures (non-isothermal) were developed successfully. Interface properties (heat transfer and friction coefficients) were obtained through experimentation and inverse optimization methods. Heat transfer coefficient was modeled as function of pressure and an improvement in thickness distributions was obtained. h) A methodology was used to determine the drawability limits of aluminum alloys at room temperature through the use of Cockcroft & Latham ductile fracture criterion. The validity of this approach was demonstrated by computational modeling and experimental validation. It was demonstrated that in some cases drawing experiments can be eliminated and an approximate LDR value for a given material can be estimated, using material properties and deep drawing conditions. 168

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202 APPENDIX A MODELING AND EXPERIMENTAL INVESTIGATION OF SHEET HYDROFORMING WITH DIE (SHF-D) 179

203 The objectives of this study are to : a) determine the flow stress of Al 3003-H14, 3003-O, 5052-H32, 5052-O and 6061-O alloy sheets at room temperature using the hydraulic bulge test b) conduct SHF-D experiments and Finite Element Analysis with 3003-O, H32 and 6061-O using an asymmetric die and compare the results to investigate the feasibility of this process. 1) Flow stress results from the hydraulic bulge test The equation used to describe the flow stress is the law of Hollomon given as; n σ = K ε where, K is a material specific constant factor, called strength coefficient and n describes increasing hardening of the material with increasing strain and is therefore called strain hardening exponent. Table A.1 shows all the results, obtained from the hydraulic bulge tests. Max.Bulge Height (mm) Burst Pressure (bar) Max thinning (%) K (MPa) Material Thickness (mm) n R H O H O O Table A.1: Calculated flow stress values and related process parameters 180

204 Table A.1 shows that 3003-O gives the highest bulge height of 36.1 mm compared to all other alloy sheets. [Explanation of R 2 : Let s assume that we have a simple regression model, y=a*x 1 +b*x 2, where y is a dependent variable and x 1 and x 2 are explanatory variables. The usual interpretation of R 2 (coefficient of determination) is as the relative amount of variance of the dependent variable y, explained or accounted for by the explanatory variables x1, x2,.. For example, if R 2 = 0.83 we say that the explanatory variables (x1, x2) "explains" 83 % of the variance of y]. Figure A.1 shows the calculated flow stress curves for the tested alloys. Figure A.1: Flow stress curves of the tested aluminum alloys 181

205 2. SHF-D experiments and numerical predictions 2.1 Press and tooling characteristics The experimental press was a 160 ton hydraulic Minster press. The characteristics of the press are listed in [Table A.2]. Type Minster Tranemo DPA Slide Force 160 metric tons (176.4 tons) Cushion Force 100 metric tons (110.3 tons) Ejector Force 15 metric tons (16.5 tons) Slide Speed 90 mm/s maximum (3.54 in/s) Total Daylight 800 mm ( ) Slide Stroke 500 mm ( ) Cushion Stroke 190 mm (7.480 ) Ejector Stroke 250 mm (9.843 ) T-Slots 5 slots, 6 apart (152.4 mm) Table A.2: Press characteristics Aluminum alloys 6061-O, 3003-O and 5052-H32 were tested and the initial sheet geometry was a square sheet with a 241 mm side length. Thickness measurements are conducted along 1-3 and 2-4 directions (Figure A.2). 182

206 Figure A.2: Thinning measurements are done in Direction 1-3 and Direction Comparison of the experiments and the FEA Predictions Results of the FEA and the experiments are compared for 6061-O, 3003-O and 5052-H32 alloy sheets. The validation of the sheet hydroforming interface Aquadraw in the commercially available finite element software Pam-Stamp 2K is made through comparison. It is important to note the following; a) The comparison criteria between the FEA and the experiments were 1) maximum pressure values and 2) the thinning distributions across the part corners. b) In the simulations the material was considered to be isotropic. 183

207 c) The lubricant that was used in the experiments was a highly viscous lubricant. The friction coefficient for this lubricant was not available experimentally. Therefore a friction coefficient of 0.1 was assumed in the FEA Aluminum alloy 6061-O The different behavior in pressure curves is well seen in Figure A.3. In the experiment, the viscous medium used for pressurization has a transitory phase (until 4 Sec) in which it is compressed and for this reason the pressure doesn t increase. After this point (> 4 Sec) the pressure starts to increase which means the medium has been compressed. The final value is consistent with the one predicted by the FEA. The predicted and measured thinning percentage curves along 1-3 and 2-4 are shown in Figure A.4 and Figure A

208 Figure A.3: Comparison of the predicted and measured pressure values for 6061-O Figure A.4: Thinning comparison in Direction 1-3; at corner 1 the difference is 14 (%) while at corner 3 it is 11 (%) 185

209 Figure A.5: Thinning comparison in Direction 2-4;at corner 2 the difference is 10 (%) while in the corner 4 is 1.5 (%). 186

210 Aluminum alloy 3003-O Figure A.6: Pressure comparison; max pressure for simulation is 199 (Bar) while measured pressure value from the experiments is 208 (Bar) 187

211 Figure A.7: Thinning comparison in Direction 1-3; at corner 1 the difference is 2 (%) while at corner 3 it is 7 (%) 188

212 Figure A.8: Thinning comparison in Direction 2-4; at corner 2 the difference is 3 (%) while at corner 4 it is 2 (%) 189

213 Aluminum alloy 5052-H32 Figure A.9: Pressure comparison; max pressure for simulation is 192 (Bar) while measured pressure value from the experiments is 218 (Bar) 190

214 Figure A.10: Thinning comparison in Direction 1-3; at corner 1 the difference is 4 (%) while at corner 3 it is 10 (%) 191

215 APPENDIX B MODELING OF ELASTIC DEFLECTION IN DEEP DRAWING 192

216 In computational modeling of deep drawing process, the tools (blank holder, die and punch) are generally assumed to be rigid. This saves computation time since the calculations are pretty acceptable. However, when assumed rigid these tools do not adjust to the thickness changes that take place in the sheet during a drawing operation. The blank holder and the die touch the sheet metal where the thickness is a maximum and apply pressure only at these points where uniform pressure on the sheet metal is desired. Many studies have shown that the combined rigidity of the dies and the press has a great influence on the accuracy in precision blanking and deep drawing. Elastic deflections of press and tooling are difficult to predict and control. Thus, they affect the quality of the parts and are undesirable. An elastically deforming blank holder and die that adjusts itself to the sheet thickness can provide a uniform distribution of the blank holder pressure at the flange area. This will result in uniform metal flow during deep drawing and ultimately in improved quality of the parts. However, the amount of elastic deflection is always an unknown. In this study, computational modeling of the deep drawing process is conducted in which the die and the blank holder is modeled elastic instead of rigid bodies in order to determine the maximum amount and location of elastic deflection. 193

217 1. Modeling of sheet, punch, die-ring and blank holder To predict the elastic deflection in the blank holder and the die-ring over the whole stroke, die-ring and blankholder were modeled as elastic objects. The sheet is modeled as plastic and the punch as rigid body. In order to obtain higher accuracy and less computation time, variable meshing densities were used at different parts of the die-ring and the blank holder. Table B.1 gives an overview of the mesh density windows, which are shown in Figure B.1 and Figure B.2, respectively. Number of elements Density window #1 Density window #2 Density window #3 Blank holder (Binder) Die-ring Table B.1: Mesh Density Windows (same values used in S1, S2 and S3) 2 1 Figure B.1: Mesh Density Windows for the blank holder 194

218 3 1 2 Figure B.2: Mesh Density Windows for the die-ring 2. Sheet and tool material St14 steel is used as the sheet material and tool material was determined to be H13. The elastic tool material data is described by using Hooke s Law. To describe the plastic behavior of St14, Law of Hollomon is used. σ = Kε with K (strength coefficient) and n (strain hardening exponent). Table B.2 shows the material properties for St14. Material K n St Table B.2: Flow stress data of St14 Since experimental data was not available, after conducting couple of simulations, it was found that 15 kn as blank holder force is an adequate constant blank holder force value. The friction conditions on the sheet-blank holder, sheet-die and sheet-punch, were modeled using the Coulomb friction n 195

219 model with a value of This value was selected based on previous experience. 3. Results and discussion Figure B.3 shows the elastic deflection of the die and the blank holder in conventional deep drawing schematically. In Figure B.3, continuous (ABCDE) line is the initial flat die geometry and the dashed line (AB 1 C 1 D 1 E) is the elastically deflected die geometry. It is seen that AB is deflected in the negative Y direction and DE is deflected in the positive X direction. At the die corner (BCD), maximum deflection happens at CC 1. Therefore, we can see that the elastic deflection varies from A thru E. It should also be noted that deflection also changes with stroke, H. The blank holder (binder) deflects in the positive Y direction. Figure B.4 shows the punch load and the die ring deflection plots calculated from the numerical analyses. 196

220 Figure B.3: Predicted elastic deflection is shown with the dashed line Punch-Load Die-Corner-Deflection mm 40 mm 60 mm Load [kn] Deflection [µm] Stroke [mm] 0 Figure B.4: Predicted elastic deflection is shown with the dashed line [Kaya, et.al., 2004] 197

221 APPENDIX C WARM FORMING OF STAINLESS STEEL (SS)

222 1. Warm forming of austenitic steel Among austenitic stainless steels, Type 304 is superior in formability and is most commonly used in parts for household appliances. However, the austenitic phase is unstable and gets transformed into martensite during forming. This transformation of austenite to martensite is a function of strain, strain rate (punch velocity) and temperature. Martensite enhances the strain hardening, thus delaying the onset of necking in sheet metal. Delayed necking is desirable for high formability/drawability. However, martensitic phase raises the forming loads, reduces formability and decreases corrosion resistivity. For further deformation, an annealing operation is required. These intermediate annealing operation(s) slow down production and increase cost. To eliminate the intermediate annealing operations and avoid martensitic transformation, warm forming process of stainless steels is explored. 2. Blank dimensions The 304 stainless steel sheet material used for the investigations was provided by Elkay Manufacturing Company. A total of 80 round samples (20 for each draw ratio) were used for the tests. (Table C.1) 199

223 Material: SS 304 Thickness 0.87 mm (0.035 in) Diameter, D B [mm] DR (D B /D P ) Table C.1: Stainless steel blank dimensions used for the drawability investigation (D B = blank diameter, D P = punch diameter) 3. Experimental procedure The mechanical servo press was programmed in order to run at the constant velocity of 2.5 mm/s (this is the value Elkay Manufacturing requested us to perform the investigation) and the following procedure has been used to determine the limiting draw ratio (LDR) at various die temperatures. step 1) a smaller blank has been drawn at room temperature (Note: during experiments, this BHF value has been increased every time the formed cup showed wrinkles) step 2) the blank size has been increased until a fractured cup was obtained consistently. The last cup that was formed successfully is used to determine the LDR at room temperature. 200

224 step 3) the initial temperature of the dies has been increased and the same procedure described in step 2 has been applied. Table C.2 shows the blank dimensions and the experimental conditions. Forming condition Dies/BH Temperature [C] LDR forming velocity [mm/s] dwell time [s] Blank Holder Force [ kn] A B C D Table C.2: Blank dimensions and process conditions 4. Experimental results Results show that the formability of SS304 increases when the temperature of the dies is increased (up to 150 C) [Figure C.1]. When the temperature was set at 150 C, it was possible to form the cup with a 2.5 draw ratio consistently. The remaining blanks were later used to repeat the same study with higher forming velocities. 201

225 2.6 Limiting Drawing Ratio A B C D Die and BH temperature [C] Figure C.1: Limiting DR - Die/BH temperature (forming velocity 2.5 mm/s) Cups showed in Figure C.2 were cut and the thickness distribution along the rolling direction (RD) and the transverse direction (TD) were measured. Cup A Cup B Cup C Cup D DR: 2.1 DR: 2.3 DR: 2.4 DR: 2.5 Height: 32 mm Height: 40 mm Height: 40 mm Height: 45 mm Diameter: 45 mm Diameter: 45 mm Diameter: 45 mm Diameter: 45 mm Figure C.2: Geometrical parameters (height and external diameter) of the cups drawn at different conditions 202