Kaya Serhat

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IMPROVING THE FORMABILITY LIMITS OF LIGHTWEIGHT METAL ALLOYSHEET 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 EngineeringGraduate Program


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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


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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


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developed and experimental results are used to validate the predictions from

the computational model.


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Dedicated to my family


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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.


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VITA

July 07, 1973 Born Istanbul, Turkey

1998... Die Design Engineer, Turkey

1999 M.S., Mechanical Eng.Yildiz Technical University, Istanbul

2001 M.S., Industrial and Systems Eng.The Ohio State University

2002 present... Graduate Research Associate,The Ohio State University

PUBLICATIONS

Research Publication

Book Chapter

1. William Thomas, Taylan Altan and Serhat Kaya, (2003) Handbook of

Aluminum, Volume I, Physical Metallurgy and Processes, Chapter 18, pp.837-880, Marcel Dekker, Inc., New York, ISBN: 0-8247-0494-0

Journal Papers

2. Taylan Altan, Serhat Kaya, Yingyot Aue-u-lan, (2007), Forming Al andMg Alloy Sheet and Tube at Elevated Temperatures, Key EngineeringMaterials, vol.344, pp.317-323

3. Serhat Kaya, Taylan Altan, Peter Groche, Christian Kloepsch, (2006),Determination of Flow Stress of Magnesium AZ31-O Sheet At ElevatedTemperatures Using the Hydraulic Bulge Test, (accepted/in print - Special

Issue of International Journal of Machine Tools and Manufacture)


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Conference Papers

4. Taylan Altan, Serhat Kaya, Yingyot Aue-u-lan, (2007), Forming Al andMg alloy Sheet and Tube at Elevated Temperatures, Shemet 07, 12thInternational 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 ofMachines and Dies/Molds, DIEMOLD 2007, June 21-23, Cesme, TURKEY

6. Serhat Kaya, and Taylan Altan, (2006), Forming Limits of AZ31-OMagnesium Alloy Sheet at Elevated Temperatures, 2006 NSF Design, Serviceand Manufacturing Grantees and Research Conference, July 24-27, 2006, St.Louis, Missouri, USA

7. Taylan Altan, Yingyot Aue-u-lan, Hariharasudhan Palaniswamy, SerhatKaya, (2005), State of the art-visions and priorities in research anddevelopment in metal forming, Proceedings of the 8th InternationalConference on Technology of Plasticity, ICTP 2005, ISBN 88-87331-74-X, pp.3 -24, October 9-13 2005, Verona, ITALY (Keynote Paper)

8. Taylan Altan, Yingyot Aue-u-lan, Serhat Kaya, (2004), Tube and SheetHydroforming-New Developments in Equipment, Tooling and ProcessSimulation, Society of Manufacturing Engineers, SME, 2nd Annual NorthAmerican 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


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TABLE OF CONTENTS

Abstract..ii

Dedication..v

Acknowledgements.vi

Vita...vii

List of Tables..xii

List of Figuresxiv

Chapters:

1. Introduction ....................................................................................................... 1

2. Objectives........................................................................................................... 4

3.Mechanical properties of aluminum and magnesium alloys ........................... 6

3.1Forming behavior of Mg alloy sheet ...................................................... 8

3.2Strength asymmetry in Mg alloy sheets............................................... 11

4.Determination of the flow stress of lightweight alloy sheet under equi-biaxialstate of stress........................................................................................................ 18

4.1 Introduction.......................................................................................... 184.2 Experimental Setup.............................................................................. 204.3 Calculation of stresses and strains under equi-biaxial state of stress. 224.4 Membrane Theory................................................................................ 234.5 Calculation of the radius of the bulge (dome)..................................... 244.6 Calculation of the Thickness at the Top of the Dome......................... 254.7 Stress Strain relationship at elevated temperature for magnesium

alloy sheet ............................................................................................................ 264.8 Experimental investigation .................................................................. 29

4.8.1 Observations.............................................................................. 294.8.2 Test conditions and experimental matrix ................................ 304.8.3 Measurement of initial sheet thickness.................................... 32


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4.8.4 Sheet Draw-in During Bulging.................................................. 334.8.5 Pressure bulge height curves .................................................... 34

4.9 Analysis of the dome geometry............................................................ 354.9.1 Deviation from the original bulge shape .................................. 39

4.10 Thickness distributions along the dome curvature........................... 424.11Conclusions ........................................................................................48

5. Deep drawing process at room temperature .................................................. 50

5.1 Drawability Criteria.............................................................................. 525.2 Critical Stroke in deep drawing........................................................ 54

5.3 Deep drawing of aluminum and magnesium at room temperature.... 55

6. Hydroforming of sheet at room temperature .................................................. 56

6.1 Mechanics of SHF-P Process................................................................ 606.2 Prediction of the Initial Pressure Value............................................... 636.3 SHF-P of a 90 mm round cup .............................................................. 67

7. Deep drawing at elevated temperature ........................................................... 70

7.1 Introduction.......................................................................................... 707.2 Experimental Setup.............................................................................. 73

7.2.1 Servo press and its kinematics ................................................. 737.2.2 Design of the tooling .................................................................75

7.3 Issues at the interface in forming at elevated temperature ................. 787.4 Heating the blank ................................................................................. 79

7.4.1Effect of the interface pressure on the hardness and the surfaceroughness ............................................................................................................. 82

7.4.1.1 Hardness Measurements................................................. 837.4.1.2 Surface roughness measurements .................................. 857.4.1.3 Dome formation in the sheet under pressure................. 86

7.5 Lubricant evaluation for warm deep drawing process........................ 887.6 Preliminary Experiments ..................................................................... 927.7 Process Optimization / Windows......................................................... 94

7.7.1 Effect of constant forming velocity and temperature ondeformation..........................................................................................................97

7.7.1.1 Results for Al 5754-O...................................................... 987.7.1.2 Results for Mg AZ31-O (Supplier A) ............................ 103


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7.7.1.3 Results for Mg AZ31-O (Supplier B)............................. 1147.8 Effect of Variable Forming Velocity................................................... 1157.9Conclusions ........................................................................................118

8. Modeling of non-isothermal deep drawing process ..................................... 121

8.1 Determination of the heat transfer coefficients................................. 1228.1.1 Inverse Analysis......................................................................1238.1.2 Setup of the inverse analysis problem ................................... 124

8.2 Non-isothermal deep drawing of Mg AZ31-O................................... 1258.2.1 Mg AZ31-O flow stress in literature....................................... 125

8.2.2 FE Modeling in LS-Dyna3D .................................................... 1278.2.2.1 Plastic-thermal material model available in LS-Dyna.. 1288.2.2.2 Thermal contact definition ........................................... 131

8.2.3 Simulation matrix ...................................................................1338.2.4 Comparison of FE predictions and experimental results....... 135

8.3 Non-isothermal deep drawing of Al 5754-O ..................................... 1408.3.1 Yield criterion adopted in the FE model for the Al 5754-O...1428.3.2 Flow stress curves for aluminum ........................................... 1438.3.3 Comparison of numerical predictions with experimental

measurements .................................................................................................... 1458.4 Non-isothermal modeling of SHF-P................................................... 148

8.4.1 Conclusions............................................................................. 152

9. Determination of drawability using fracture criterion ................................. 153

9.1 Cockcroft & Latham ductile fracture criterion................................... 1539.2 Approach............................................................................................ 1549.3 Setup of the FE model for tensile test and deep drawing ................. 1579.4 Results and discussion....................................................................... 158

9.4.1 Determining the Critical Damage Value................................. 1589.4.2 Deep drawing analyses ...........................................................160

9.5 Conclusions........................................................................................163

10. Summary and conclusions.......................................................................... 165

Bibliography....................................................................................................... 169


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LIST OF TABLES

Table

3.1 List of wrought Mg alloys and their product range [Avedesian et al. 1999].. 9

4.1 Hensel coefficients obtained from elevated temperature forming ofmagnesium sheets in tensile test [Droeder, 1999]........................................... 29

4.2 Experimental matrix for high formability sheets (strain rate values areapproximate)........................................................................................................... 31

4.3 Experimental matrix for low formability sheets (strain rate values areapproximate)........................................................................................................... 32

4.4 Thickness measurements for high and low formability sheets...................... 33

4.5 Comparison of radius values (R1 & R2) obtained by using 5 and 3 points.... 39

4.6 Measured and calculated thickness values at the apex ................................... 44

6.1 Curvilinear length and percentage stretch of the sheet in the sheet radiuszone according to Figure 6.7 (pressure curve: P4)........................................... 67

6.2 Friction coefficients used in the FEA.................................................................. 68

7.1 Hardness (Brinell) measurements of Al 5052-H32 ........................................... 84

7.2 Hardness (Brinell) measurements of Mg AZ31-O (Supplier A)...................... 84

7.3 Hardness (Brinell) measurements of Mg AZ31-O (Supplier B)...................... 85

7.4 List of lubricants and experimental conditions................................................. 88

7.5 Summary of the preliminary screening experiments for Al 5754-O, Al 5052-H32 and MgAZ31-O.............................................................................................. 93

7.6 Experimental results for Al 5754-O..................................................................... 98


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7.7 Experimental results for Mg AZ31-O (Supplier A)......................................... 104

7.8 Experiments at 225 oC .......................................................................................... 114

7.9 Experiments at 250 oC and lower velocities..................................................... 115

7.10 Significant savings in drawing time is obtained through the use of variableforming velocity ................................................................................................... 118

8.1 AZ31B-O simulation matrix................................................................................ 134

8.2 Summary of input data used for AZ31B-O simulations................................ 135

8.3 List of input parameters to the FE model (Al 5754-O)................................... 141

9.1 Simulation matrix for the deep drawing analysis........................................... 158

10.1 Summary of obtained drawability through the use of differentmanufacturing processes.................................................................................... 167

A.1 Calculated flow stress values and related process parameters........180

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 St14...195

C.1 Stainless steel blank dimensions used for the drawability investigation (DB= blank diameter, DP = punch diameter)....200

C.2 Blank dimensions and process conditions...201


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LIST OF FIGURES

Figure

3.1 a) Uniform and post-uniform strains vs. temperature for different strainrates and b) variation of total elongation with temperature and strain ratefor alloy 5182-O [Ayres, 1977] .............................................................................. 8

3.2 Temperature dependent flow stress of Mg AZ31B alloy determined by

tensile test [Doege et al. 2001]............................................................................. 11

3.3 Flow stress at different temperatures for Mg AZ31B sheet with differenttemper [Doege et al. 2001].................................................................................... 11

3.4 Stress-strain data for AZ31B plate deformed in in-plane tension (IPT) andcompression (IPC) and through-thickness compression (TTC) [Agnew,et.al., 2002] ............................................................................................................. 13

3.5 Compression flow curves as a function of testing temperature. Thetransverse (open symbol) samples are stronger than the rolling (closed

symbols) at all temperatures................................................................................ 14

3.6 A comparison of experimental (symbols) and simulated (curves)compressive flow behavior at a) RT, b) 150C, c) 175C and d) 200C........ 15

3.7 Measured (symbol) and predicted tensile r-values.......................................... 16

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

4.1 Initial (left) and the deformed sheet (right) in the hydraulic bulge test...... 19

4.2 Geometrical and process related parameters.................................................... 19

4.3 Elevated temperature Hydraulic Bulge Tooling (PtU, TU Darmstadt)......... 21

4.4 Hoop ( 1 ) and Transverse ( 2 ) Stresses and Dome Radii in a Membrane . 22


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4.5 Comparison of Hensel Model and Experimental Data [Droeder, 1999]....... 28

4.6 Thickness measurement along Rolling Direction (RD), and TransverseDirection (TD) (dimensions in mm) ................................................................... 32

4.7 Pressure-bulge height curves at the approximate strain rate of 0.25s-1........ 34

4.8 Pressure-bulge height curves at the approximate strain rate of 0.025 s-1 .... 35

4.9 Measurement points on the bulged sheet.......................................................... 37

4.10 Comparison of calculated and measured bulge radius values.................... 38

4.11 Radius difference using 5 and 3 points ........................................................... 39

4.12 Residual plots for sample at hd=14.7 mm....................................................... 40

4.13 Residual plots for sample at hd=21.7 mm....................................................... 41

4.14 Residual plots for samples at hd=33.9 mm..................................................... 41

4.15 Thickness distribution along the RD (bulge height (h)=~21mm and h33

mm) .......................................................................................................................... 43

4.16 Schematic representation of the strain rate and flow stress gradients in thebulged sample ........................................................................................................ 45

4.17 True stress and true strain curves at 0.25 s-1 .................................................. 46

4.18 True stress and true strain curves at 0.025 s-1 ................................................ 47

4.19 True stress true strain curve with possible errors at 225 C (0.025 s-1).... 48

5.1 Axisymmetric ......................................................................................................... 51

5.2 Top view of drawn sheet ...................................................................................... 51

5.3 Stress on an............................................................................................................. 51

5.4 Thickening of the sheet in the flange area ........................................................ 51


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5.5 Definition of cup height (h) for a cup with a flange and without a flange.. 53

5.6 Deep drawn cup with ears.................................................................................... 53

5.7 Schematic view of the critical stroke (Scr) before (left) and after (right)...... 55

5.8 RT drawing of Al 5754-O ..................................................................................... 55

5.9 RT drawing of Mg AZ31-O................................................................................... 55

6.1 SHF-P process a) without leakage; b) with leakage......................................... 58

6.2 Important tool parameters that influence the SHF-P process........................ 60

6.3 During a hydromechanical deep drawing process the sheet loses contactwith the die............................................................................................................. 61

6.4 Maximum thinning around the cup bottom radius at two different values ofthe punch stroke .................................................................................................... 62

6.5 Position of the slab in the sheet radius zone (a) and equilibrium of theforces in the slab (b).............................................................................................. 63

6.6 Pressure-stroke curves used in the critical stroke............................................ 66

6.7 Initial (a) and final (b) length of stretch in the sheet used to evaluate thematerial stretching in the sheet radius zone .................................................... 67

6.8 Fluid pressure determined based on the critical stroke ................................. 69

6.9 Thinning distribution along the 45 cup wall .................................................. 69

7.1 Open (left) and closed (right) condition of the tool......................................... 72

7.2 AIDA servo-mechanical press drive mechanism ............................................. 74

7.3 Ram motion of the servo press (TDC: top dead center, BDC: Bottom deadcenter) ...................................................................................................................... 74

7.4 Schematic view and the dimensions of the tool (dimensions are in mm).. 76


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7.5 Warm forming with in-die dwelling process sequence .................................. 76

7.6Open warm forming tooling (top die set on the left, bottom die set on theright) [Kaya, et.al., 2006] ...................................................................................... 77

7.7Assembled tooling on the Aida servo press...................................................... 77

7.8110 ton Aida Servo Press ..................................................................................... 78

7.9 Top view of the fixture used to determine the dwell time necessary to heat

the blank (thickness 3mm) .................................................................................. 80

7.10 Schematic view of the experimental setup with the affected interfaces... 80

7.11 Temperature-time curves obtained with the test fixture for differentinterface (blank holder) pressures (tool temperature=300 oC) ..................... 81

7.12 Punch and knockout pin temperatures at tool temperatures of 250 oC, 275oC and 300 oC .......................................................................................................... 82

7.13 Ra values for 5754-O and 5052-H32 ................................................................. 85

7.14 Ra values for Mg AZ31-O (Supplier A) and Mg AZ31-O (Supplier B) ....... 86

7.15 BHP dome height at T=300 C........................................................................ 87

7.16 Change in the sheet diameter with respect to the BHP (Sheet Diameter:100 mm) .................................................................................................................. 87

7.17 Thickness distributions for different lubricants under same processconditions [Kaya, et.al., 2006]............................................................................. 90

7.18 Cup with Lube A after drawing [Kaya, et.al., 2006]...................................... 90

7.19 Al cups formed with Lube C, Lube B and Lube A (from left to right)....... 91

7.20 Mg cups formed with Lube C, Lube B and Lube A (from left to right)...... 91

7.21 Adopted methodology for preliminary experimentation ............................. 92


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7.22 Variation of LDR with punch velocity (Mg AZ31-O, T=250o

C) ................ 95

7.23 Variation of LDR with punch velocity (Mg AZ31-O, T=275 oC) ................ 95

7.24 Variation of LDR with punch velocity (Mg AZ31-O, T=300 oC) ................ 96

7.25 Process window for the Mg AZ31-O alloy ...................................................... 96

7.26 Process window for the Al 5754-O alloy......................................................... 97

7.27 Effect of temperature on thickness distribution (5 mm/s, DR 2.5)............. 99

7.28 Effect of temperature on thickness distribution (15 mm/s, DR 2.5)......... 100

7.29 Punch load stroke curves at 5mm/s for different temperatures............. 101

7.30 Punch load stroke curves at 15mm/s for different temperatures........... 101

7.31 Change in cup bottom temperature at 5 mm/s (Punch temp ~55 oC, 65 oC,73 oC)...................................................................................................................... 102

7.32 Change in cup bottom temperature at 15 mm/s (Punch temp: ~55 oC, 65oC) ........................................................................................................................... 102

7.33 Effect of temperature on thickness distribution (5 mm/s, DR 2.5)........... 105

7.34 Effect of temperature on thickness distribution (15 mm/s, DR: 2.5)........ 105

7.35 Effect of temperature on thickness distribution (50 mm/s, DR: 2.5)........ 106

7.36 Effect of forming velocity on thickness distribution (250 oC, DR: 2.5) .... 106

7.37 Effect of forming velocity on thickness distribution (275 oC, DR: 2.5) .... 107

7.38 Effect of forming velocity on thickness distribution (300o

C, DR: 2.5) .... 107

7.39 Punch load stroke curves at 5mm/s for different temperatures............. 108




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7.42 Change in cup bottom temperature at 5 mm/s............................................. 110

7.43 Change in cup bottom temperature at 15 mm/s........................................... 111

7.44 Change in cup bottom temperature at 50 mm/s........................................... 111

7.45 Pictures of the formed cups from Al 5754-O (left) and Mg AZ31-O(Supp.A) (right) .................................................................................................... 112

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............................. 113

7.47 Effect of blank temperature and punch velocity on thinning at the bottomcorner of the drawn cup for the Mg AZ31-O alloy........................................ 113

7.48 Effect of variable forming speed on the thickness distribution of thedrawn Al cups ...................................................................................................... 117

7.49 Effect of variable forming speed on the thickness distribution of thedrawn Mg cups..................................................................................................... 117

8.1 Experimental and calculated temperature-time curves................................ 123

8.2 Schematic view of the FE model....................................................................... 124

8.3 Modeling of the measurement fixture with the temperature measurementpoint ....................................................................................................................... 124

8.4 Calculated heat transfer coefficients ................................................................ 125

8.5 Graphical representation of the database for Magnesium AZ31 Tensiletestsconducted at different strain rates and temperatures [Sivakumar, et al,2006]. ..................................................................................................................... 127

8.6 FE model for non-isothermal simulations of deep drawing of round cups................................................................................................................................. 128

8.7 Contact-Forming card used to define mechanical and thermal contactparameters. ........................................................................................................... 133


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8.8 Experimental and computed punch load vs. stroke curves (left) and cupthinning distributions (right). (RD=rolling direction; TD=transversedirection)............................................................................................................... 136





8.13 Experimental and computed punch load vs. stroke curves (left) and cupthinning distributions (right). (RD=rolling direction; TD=transverse

direction)............................................................................................................... 139


8.15 Experimental and computed punch load vs. stroke curves (left) and cupthinning distributions (right). (RD=rolling direction; TD=transversedirection ................................................................................................................ 140

8.16 Comparison of experimental yield loci and those predicted by the Von

Mises, Hill, Tresca, Logan-Hosford and Barlat criteria under biaxial stresscondition for Al 5083-O alloy sheet [Naka, et.al., 2003].............................. 143

8.17 Extrapolated flow stress versus temperature for different strainrates(original data from Boogard, 2001) .......................................................... 144

8.18 Elimination of the softening behavior from the stress-strain curve......... 144


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8.19 Comparison of punch load predictions using various heat transfercoefficients (HTC: kW/m2 C) with experiment (5 mm/s at 250 oC)............. 146

8.20 Predicted thickness distribution comparison with various heat transfercoefficients (5 mm/s at 250 oC)......................................................................... 146

8.21 Comparison of punch load prediction with experiment (5 mm/s at 275 oC)................................................................................................................................. 146

8.22 Predicted thickness distribution comparison with experiments (5 mm/s at275 oC).................................................................................................................... 146

8.23 Comparison of punch load prediction with experiment (5 mm/s at 300 oC)................................................................................................................................. 147


8.25 Comparison of punch load prediction with experiment (15 mm/s at 275oC) ........................................................................................................................... 147

8.26 Predicted thickness distribution comparison with experiments (15 mm/sat 275 oC) ............................................................................................................... 147



8.29 Interfaces in elevated temperature SHF-P process...................................... 149

8.30 Pressure and BHF used in the simulations................................................... 150

8.31 Temperature distribution of the sheet at the end of the stroke................. 150

8.32 Temperature distribution of a sheet formed using SHF-P ......................... 151

8.33 Temperature distribution of a deep drawn sheet ........................................ 151

9.1 Flow stress curve of Al 5754-O obtained from the bulge test...................... 155


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9.2 Geometry of the tensile specimen (ASTM, E 8M-04).................................... 156

9.3 Flow stress curves used in the FEA.................................................................. 157

9.4 Point of instability in the load-stroke curve during the tensile test........... 159

9.5 CDV (when necking starts during 3D tensile test simulation) for Al 5754-Ois 0.428................................................................................................................... 160

9.6 CDV (when necking starts during 3D tensile test simulation) for Al 6061-T6

is 0.148................................................................................................................... 160

9.7 Maximum CDV obtained for the successfully deep drawn Al 5754-O (LDR:2.1) cup is 0.352................................................................................................... 161

9.8 Max CDV reaches 0.42 for the unsuccessfully deep drawn Al 5754-O (LDR:2.2) cup.................................................................................................................. 161

9.9 Maximum CDV obtained for Al 6061-T6 (LDR: 1.6) is 0.175...................... 163

9.10 Maximum CDV obtained for Al 6061-T6 (LDR: 1.5) is 0.165.................... 163

A.1 Flow stress curves of the tested aluminum alloys.181

A.2 Thinning measurements are done in Direction 1-3 and Direction 2-4.183

A.3 Comparison of the predicted and measured pressure values for 6061-O.185

A.4 Thinning comparison in Direction 1-3; at corner 1 the difference is 14 (%)while at corner 3 it is 11 (%)....185

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

A.6 Pressure comparison; max pressure for simulation is 199 (Bar) whilemeasured pressure value from the experiments is 208 (Bar).....187


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

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

A.9 Pressure comparison; max pressure for simulation is 192 (Bar) whilemeasured pressure value from the experiments is 218 (Bar).....190

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

B.1 Mesh Density Windows for the blank holder.....194

B.2 Mesh Density Windows for the die-ring.........195

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]....197

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 drawnat different conditions...202

C.3 Thinning distribution along rolling and transverse direction for cup A andcup B.203

C.4 Thinning distribution along rolling and transverse direction for cup C andcup 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


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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


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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 200oC to 300oC. 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 2001 .

They have found that 5xxx series and 6xxx series Al alloys show increased

formability at the range of 250 oC to 300 oC. However, there is a lack of


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sufficient knowledge on warm sheet forming processes which limited the

practical use of these alloys.


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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.


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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.


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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 materials

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 oK. 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


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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 oK and higher.


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Figure 3.1: a) Uniform and post-uniform strains vs. temperature for differentstrain rates and b) variation of total elongation with temperature and strain ratefor 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 3.1.


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ForgingExtruded bars and

tubesSheet

Mg-Al-Mn-Znalloy system

M1A-F, AZ31B-F,AZ61A-F, AZ80A-T5,

AZ80A-T6

M1A-F, AZ10A-F,AZ31B-F, AZ61A-F,

AZ80A-T5AZ31B

Mg-Zn-Cualloy system

ZM21-F ZC71-T6, ZM21-F ZM21Zirconiumfree alloys

Mg-Li alloysystem

Currently underinvestigation

Currently underinvestigation

Currentlyunder

investigationZirconiumcontaining

alloys

Mg-Zn-Zralloy system

ZK31-T5, ZK60A-T5,ZK61-T5

ZK21A-F, ZK31-T5,ZK60A-T5

.

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 (200-300 oC), 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 oC - 370 oC 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.


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[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 0.177. On the other hand, Mg alloy sheet (AZ31B)

shows remarkable increase in the formability in tensile test at temperatures

above 200 oC 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 oC and 300

oC 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.


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Figure 3.2: Temperature dependent flow stress of Mg AZ31B alloy determinedby 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


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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].


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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 oC, 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 oC & 250C). Significantly, there is no


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softening in the initial yield stress with an increase in temperature up to 200

C, in fact there is a slightincrease 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 oC, 175 oC and 200 oC.

Experimental findings can be summarized as;

i) The flow stress curve obtained from ND compression is different than

the TD and RD compression curves,


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ii) At 200o

C, the variation in the flow stress curves obtained at RD, TD

and ND is smaller than the ones obtained at 175 oC.

(a)

(b) (c) (d)

Figure 3.6: A comparison of experimental (symbols) and simulated (curves)compressive flow behavior at a) RT, b) 150C, c) 175C and d) 200C


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[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 = 250C, the r-values remain distinct at all temperatures

[Jain, 2005].

Figure 3.7: Measured (symbol) and predicted tensile r-values


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

2005]


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CHAPTER 4

DETERMINATION OF THE FLOW STRESS OF LIGHTWEIGHT ALLOY

SHEET UNDER EQUI-BIAXIAL STATE OF STRESS

4.1Introduction

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.


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p

Lower Die

Upper Die

Pressurized

Fluid

Initial Sheet

Bulged Sheet

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.

phd

dc

td

t0

Rc

Rd

Fc Fc

Figure 4.2: Geometrical and process related parameters

t0 initial thickness of the sheet t

dthickness at the top of the dome

hd dome height Rd radius at the top of the dome dc diameter of the cavity Rc radius of the fillet of the cavity Fc clamping force


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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.

4.2Experimental 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 tankandc) 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


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(BHP) was applied to lock the sheet to prevent the draw-in of the sheet into the

die cavity. The die corner radius (Rc) 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 275oC at the bottom of the tool,

the maximum sheet temperature was 225oC. Therefore, for safety reasons,

experiments were conducted up to sheet temperatures of 225oC.

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].


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4.3Calculation 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 (R1=R2) 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.

12

R1R2

Figure 4.4: Hoop ( 1 ) and Transverse ( 2 ) Stresses and Dome Radii in a

Membrane


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4.4Membrane 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:

dt

p

RR=+

2

2

1

1

(1)

Where 1 and 2 are the principle stresses on the sheet surface, R1 and R2 are

the corresponding radii of the curved surface, p is the hydraulic pressure, and

td is the sheet thickness. (Figure 4.2) For the axi-symmetric case of the

hydraulic bulge test, 1 =2 and the radius at the top of the dome is

Rd = R1 = R2. Therefore, equation (1) can be simplified to:

dd t

p

R

2=

(2)

d

d

t2

pR=

(3)


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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:

2

p

2

0pn

=

+=

(4)

The effective stress can be calculated by Trescas plastic flow criterion, since

Traesca and Von Mises criteria are the same at equi-biaxial state of stresses:

2

p

t2

pR

d

dminmax

==

(5)

+= 1

t

R

2

p

d

d

(6)

The effective strain (thickness) is:

==

0

dt

t

tln

(7)

4.5Calculation 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:


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d

2d2cd

h8h4dR +=

(8)

Considering that there is a die radius Rc, and assuming that the dome is

spherical, the radius of the dome can be calculated by [Hill 1950]:

d

dc

2

d

2

cc

d

h2

hR2hR2

d

R

+

+=

(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.

4.6Calculation 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


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bulge is spherical. With this assumption, the thickness at the top of the dome

can be calculated by the following equation:

2

2

c

d

0d

d

h21

1tt

+

=

(10)

4.7Stress Strain relationship at elevated temperature for magnesiumalloy 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 ,

true strain rate &

and temperature T. For a given material and

microstructure, the flow stress can be expressed as:

( )Tf ,, &= (11)

At room temperature forming, Equation 11 can be described with the law of

Hollomon

( ) nK = (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


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deformation takes place at higher temperatures (200o

C-300o

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;

( )31 2 4

( )mm T m m

T K T e e

= &

(13)

This approach expresses the true strain dependent hardening behavior

with the additional term4me , 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 t0=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= 150C to T= 235C.


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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= 150C (m4=0) therefore no softening is

True strain

Y

ieldStress[MPa]


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present and an almost constant strain hardening occurs. Dependence of the K

value on temperature is also seen from Table 4.1.

Temperature [C] 150 200 235

Constant K [MPa s] 190 141 112

Exponent m1 [-] 18x10-4 18x10-4 18x10-4

Exponent m2 [-] 10-4 10-4 10-4

Exponent m3 [-] 0.12 0.103 0.072

Exponent m4 [-] 0 -0.52 -0.62

Table 4.1: Brand coefficients obtained from elevated temperature forming ofmagnesium sheets in tensile test [Droeder, 1999]

4.8Experimental investigation

4.8.1 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.


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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.

4.8.2 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


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32

Temperature (

oC) Strain Rate (s

-1)

179 0.25

206 0.25

191 0.025

206 0.025

Table 4.3: Experimental matrix for low formability sheets (strain rate values areapproximate)

4.8.3 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), andTransverse Direction (TD) (dimensions in mm)


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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

1 1.1938 1.1938 1.1684 1.1811 1.143 1.1684 1.16841.18111.1684 1.1938 1.1684 1.1938

2 1.1938 1.1938 1.1684 1.1684 1.143 1.1684 1.16841.16841.1684 1.1811 1.1684 1.1938

3 1.1938 1.1938 1.1684 1.1684 1.143 1.143 1.18111.16841.1684 1.1811 1.1684 1.1938

4 1.2065 1.1938 1.1684 1.1684 1.143 1.143 1.16841.16841.1684 1.1684 1.1684 1.1938

5 1.1938 1.1938 1.1684 1.1684 1.143 1.143 1.16841.16841.1684 1.1684 1.1684 1.1938

O-center 1.1938 1.1938 1.1684 1.1684 1.143 1.143 1.16841.16841.1684 1.1684 1.1938 1.1938

6 1.1938 1.1938 1.1684 1.1684 1.1557 1.143 1.16841.16841.1811 1.1684 1.1938 1.1938

7 1.1811 1.1938 1.1684 1.1684 1.1684 1.143 1.19381.16841.1938 1.1684 1.1938 1.1938

8 1.1938 1.1938 1.1684 1.1684 1.143 1.143 1.19381.19381.1938 1.1684 1.1938 1.1938

9 1.1938 1.1811 1.1684 1.1557 1.1557 1.143 1.19381.19381.1938 1.1684 1.1938 1.1938

10 1.1938 1.1684 1.1684 1.1557 1.143 1.143 1.20651.19381.1938 1.1684 1.1938 1.1938

Avg. 1.1938 1.1903 1.1684 1.1672 1.1476 1.1476 1.17991.17651.1788 1.173 1.1823 1.1938

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.

4.8.4 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)


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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.

4.8.5 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


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Figure 4.8 shows the pressure-bulge height curves at various

temperatures for the approximate strain rate of 0.025 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 0.025s-1

4.9Analysis 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


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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.


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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


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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 R1 & R2 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 R1 is larger than R2. 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.


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R1

R2

5 pt. LSCF3 pt.

1

4

5

6

7

3

2

Figure 4.11: Radius difference using 5 and 3 points

Bulge

Height

(mm)

5-point

LSCF

RD (mm)

-R1-

3-point

LSCF

RD (mm)

- R2-

Difference

[%]

21.7 90.7 89.9


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Figure 4.12: Residual plots for sample at hd=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.


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Figure 4.13: Residual plots for sample at hd=21.7 mm

Figure 4.14: Residual plots for samples at hd=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


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assumed sphere shape until the bulge height to diameter ratio hd/dc 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.

4.10 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 4.15. The error percentage using Eq.10 is up to

4% and 8 % for bulge heights around 21 mm and 33.9 mm, respectively.


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Figure 4.15: Thickness distribution along the RD (bulge height (h)=~21mmand h33 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.


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BulgeHeight(mm)

Temp.(oC)

StrainRate(s-1)

td(measured

at apex)(mm)

td(Eq.4)(mm)

21.7 180 0.25 0.96 0.9221.6 207 0.25 0.95 0.9221.2 194 0.025 0.92 0.9333.9 214 0.025 0.73 0.67

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.


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0

50

100

150

200

250

300

350

0 0.1 0.2 0.3 0.4 0.5

221

205

180168

145

T:oCT

rueStress(MPa)

True Strain

s/125.0

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

hd/dc 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 (hd/dc)>0.2, which corresponds to a strain of ~0.4.

Therefore, the error plots are shown after 0.4 strain (Figure 4.19).


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0

50

100

150

200

250

300

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

225210

190

165

25

T:oCT

rueStress(MPa)

True Strain

s/1025.0

Figure 4.18: True stress and true strain curves at 0.025 s-1

In Figure 4.18, the flow stress curve of the sample formed at 225 C and

at the strain rate of 0.025 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 0.025 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.


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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

100

105

110

115

120

125

130

135

140

145

150

155

160

TrueStress(MPa)

True Strain

225 C/0.025 s-1

Figure 4.19: True stress true strain curve with possible errors at 225 C (0.025s-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


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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 0.025 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 d

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