Title Page

Contents

Abstract 14

Chapter 1. Motivations and Objectives 16

1.1. Research motivations 16

1.2. Research objectives 18

Chapter 2. A Brief Review of Theoretical Background 19

2.1. Hardening models 19

2.1.1. Hardening behavior of metals 19

2.1.2. Isotropic hardening 21

2.1.3. Kinematic hardening 22

2.1.4. One-surface model: Mixed isotropic-kinematic hardening 23

2.1.5. Two-surface model: Yoshida-Uemori model 27

2.2. Ductile damage models 30

2.2.1. Damage plasticity 30

2.2.2. Damage modeling approaches 32

2.2.3. Macroscopic models 35

2.2.4. Microscopic models 37

2.2.5. Summary of damage variables and criteria 41

2.3. Material formability 42

2.3.1. Introduction 42

2.3.2. Forming limit curve 42

Chapter 3. New Constitutive Models 44

3.1. Methodology and hypothesis 44

3.2. One-surface model 47

3.3. Two-surface model 51

3.4. Numerical Implementation 55

Chapter 4. Validation and Evaluation of Proposed Models 58

4.1. Model validation in terms of damage models 58

4.1.1. Uniaxial tensile test at elevated temperature 58

4.1.2. Materials parameters 61

4.1.3. Evaluation of damage models 64

4.2. Model application in terms of damage models 68

4.2.1. Hydroforming description 68

4.2.2. Experimental test 69

4.2.3. Finite element model 70

4.2.4. Results and discussions 72

4.3. Model validation in terms of hardening models 78

4.3.1. Uniaxial tension-compression-tension test 78

4.3.2. Materials parameters 79

4.3.3. Evaluation of hardening models 82

4.4. S-rail deep drawing 83

4.4.1. Introduction 83

4.4.2. Finite element analysis 84

4.4.3. Results and discussions 88

4.5. Validation of proposed models 90

4.5.1. Cyclic loading test 90

4.5.2. Material parameters 92

4.5.3. Evaluation of proposed models 97

4.6. Incremental forming 101

4.6.1. Introduction of incremental forming 101

4.6.2. Experimental test 103

4.6.3. Finite element model 107

4.6.4. Results and discussions 107

Chapter 5. Conclusions 111

5.1. Summary 111

5.2. Future work 112

References 113

Fig. 2.1. Concept of isotropic, kinematic hardening 20

Fig. 2.2. Isotropic hardening, in which the yield surface expands with plastic deformation,... 21

Fig. 2.3. Reversed loading with isotropic hardening showing (a) the yield surface and (b) the... 22

Fig. 2.4. Kinematic hardening showing (a) the translation and (b) the resulting stress-strain... 22

Fig. 2.5. Mixed hardening model 24

Fig. 2.6. Bauschinger effect, transient behavior and permanent softening 25

Fig. 2.7. Schematic diagram of Zang's model 26

Fig. 2.8. Schematic illustration of Yoshida-Uemori model 29

Fig. 2.9. Tensile force stages 32

Fig. 2.10. Schematic diagram of the damage containing solid and matrix material 34

Fig. 2.11. The growth of voids in micro-mechanical model 37

Fig. 2.12. Illustration of Rice-Tracey model 39

Fig. 2.13. Schematic of forming limit curve 43

Fig. 3.1. Schematic of research hypothesis 46

Fig. 3.2. Illustration of cyclic hardening behavior integrating with damage accumulation 48

Fig. 3.3. Illustration of Y-U model integrating with damage accumulation 52

Fig. 4.1. Two views of the environmental chamber with a specimen loaded in the grips. 59

Fig. 4.2. Shape of tensile specimen for AA5754-O 59

Fig. 4.3. Load-stroke curve at elevated temperature 60

Fig. 4.4. Yield stress and UTS at elevated temperature 60

Fig. 4.5. Strain at break at elevated temperature 60

Fig. 4.6. Fitting results of AA5754-O before UTS 61

Fig. 4.7. Parameters curve of the Swift model for AA5754-O 62

Fig. 4.8. Fitting results of AA5754-O at different temperature 64

Fig. 4.9. Numerical analysis coupling with damage model when stroke is 15㎜ at 220℃ 65

Fig. 4.10. Numerical analysis without damage model when stroke is 15㎜ at 220℃ 66

Fig. 4.11. Deviation of damage models at different temperature 67

Fig. 4.12. Loading sequences in the free bulge test 69

Fig. 4.13. Free bulge tests with respect to the specified loading paths. 70

Fig. 4.14. Initial set-up of free bulge test for finite element simulation 71

Fig. 4.15. Damage distributions of Lemaitre model 72

Fig. 4.16. Damage distributions of B&W model 72

Fig. 4.17. Damage distributions of R&T model 73

Fig. 4.18. Strain measurement region for FLC 75

Fig. 4.19. Major strain and minor strain in different paths (B&W model) 75

Fig. 4.20. FLC obtained by different damage model 76

Fig. 4.21. Comparison of FLC between experiment and FE analysis 76

Fig. 4.22. Parameter study on friction coefficient for FLC 77

Fig. 4.23. Set-up of uniaxial tension-compression-tension test for AISI-1045 78

Fig. 4.24. True stress-strain curve obtained from tension-compression-tension (TCT) tests 79

Fig. 4.25. Young's modulus vs. equivalent plastic strain in cyclic loading tests 80

Fig. 4.26. True stress-strain comparison between FE analysis and experiment 81

Fig. 4.27. Initial setup and blank shape of S-rail 84

Fig. 4.28. Fitting curve of material model for MSLA 85

Fig. 4.29. Beginning of forming in S-rail drawing process 86

Fig. 4.30. End of forming in S-rail drawing process 86

Fig. 4.31. Spring-back in S-rail drawing process 86

Fig. 4.32. Punch force in forming process 87

Fig. 4.33. Cross-section line through point I and point E 88

Fig. 4.34. Spring-back of IE cross-section in FE analysis 88

Fig. 4.35. Spring-back profile in IE cross-section (BHF＝10kN) 89

Fig. 4.36. Spring-back profile in IE cross-section (BHF＝200kN) 89

Fig. 4.37. Loading histories of cyclic loading test 91

Fig. 4.38. FE model for cyclic loading test 91

Fig. 4.39. Three mesh size for mesh sensitivity testes 92

Fig. 4.40. Mesh test results for four loading histories 93

Fig. 4.41. Deviation of each mesh test case for four loading histories 93

Fig. 4.42. Comparison of deviation of damage models for critical strain verification 94

Fig. 4.43. Numerical results from one-surface model 96

Fig. 4.44. Numerical results from two-surface model 96

Fig. 4.45. Deviation of each damage model for different loading path in one-surface model 97

Fig. 4.46. Damage comparison from one-surface model 98

Fig. 4.47. Deviation of each damage model for different loading path in two-surface model 99

Fig. 4.48. Damage comparison from two-surface model 100

Fig. 4.49. Configuration of incremental forming 102

Fig. 4.50. Schematic representation of the details of acting stresses in thickness direction. 102

Fig. 4.51. Experimental setup for incremental forming 104

Fig. 4.52. Measuring apparatus of final shape and thickness 105

Fig. 4.53. Measuring positions of final shape and thickness 105

Fig. 4.54. Initial set-up of incremental forming test for FE simulation 105

Fig. 4.55. Local necking distribution in experiment (68° drawing angle) 108

Fig. 4.56. Local necking distribution in FE analysis (68° drawing angle) 108

Fig. 4.57. Measuring positions of the thickness and outside diameter profile 108

Fig. 4.58. Comparison of thickness and outside diameter profile 109

Fig. 4.59. Deviation comparison of thickness and outside diameter profile 110

Fig. 4.60. Comparison of proposed model and isotropic hardening model 110

In real forming process, since the complex and large plastic deformation is not been evaluated accurately, there are many defects exist such as wrinkling, fracture and spring-back. To correct these defects, material constitutive models and their implementation into finite element analysis is required. Based on FE analysis, the formability of materials in forming process can be predicted accurately and the optimal design for the forming process can be taken effectively.

In the thesis, constitutive models for extremely large plastic strain range are put forward and their implementation in FE analysis is accomplished. More specifically, integrating ductile damage models into hardening models, the proposed constitutive models are used to describe the metal behavior completely and predict the metal formability and damage distribution precisely in extremely large plastic strain range.

The fracture initiation in ductile materials is caused by damage accumulation along the plastic loading path. Thus, the suitable damage model is necessary to describe the accumulation. In this dissertation, non-linear damage models are adopted and integrated into constitutive model to characterize the damage accumulation with respect to the plastic strain and describe the material deterioration under extremely large deformation.

However, the sheet or tube metals are often performed by loading, unloading, and reverse loading in real forming process, so the Bauschinger effect will appear. It means the formability prediction will be limited and imprecise if the constitutive model is comprised with ductile damage model and isotropic hardening model. In this dissertation, the sophisticated hardening models: mixed isotropic-kinematic hardening (MIK) one-surface model and Yoshida-Uemori (YU) two-surface model are used to describe the Bauschinger effect such as transient behavior and permanent softening. Therefore, the plastic deformation and damage accumulation under complex and large loading condition can be described and predicted completely.

According to the proposed constitutive models, numerical implementation is carried out to evaluate the formability of sheet metal aluminum alloy AA5754-O at elevated temperature, predict the formability of tubular metal JIS-SS400 in hydroforming forming and sheet metal in incremental forming and predict the spring-back of High-strength low-alloy steel (HSLA) following with the NUMISHEET 96 S-rail benchmark problem.

In a word, the thesis focuses on constitutive modeling which combines hardening model and ductile damage model together and formability predicting in forming processes. It can be concluded that the constitutive models constitutes can be used for material behavior description under complex and large deformation effectively. The formability prediction by the constitutive models is reasonable and precise through various tests and applications.