Title Page
Abstract
Contents
Chapter 1. Introduction 10
1.1. Study Background 10
1.2. Purpose of Research & Thesis Overview 14
Chapter 2. Homogenization Methodology 18
2.1. Lippmann Schwinger Homogenization 19
2.2. Cluster-based LS Homogenization 22
2.2.1. Domain Decomposition 24
2.2.2. Interaction tensor 27
2.2.3. Cluster-based Iterative Self-consistent Analysis 27
2.3. Mori-Tanaka Homogenization 31
2.4. Improved Mori-Tanaka Homogenization 34
2.4.1. Mori-Tanaka Homogenization with Interface Damage 34
2.4.2. Mori-Tanaka Homogenization with random wavy fiber 38
2.4.3. Mori-Tanaka Homogenization with plasticity and ductile damage 42
2.5. Comparison of LS homogenization and Mori-Tanaka Homogenization 51
Chapter 3. Multiscale Homogenization for SCA composites 58
3.1. Multistep Analytical Homogenization 58
3.1.1. 1st Homogenization[이미지참조] 59
3.1.2. 2nd Homogenization[이미지참조] 61
3.1.3. 3rd Homogenization[이미지참조] 64
3.2. Multiscale cluster based SCA homogenization 66
Chapter 4. Results 73
4.1. Results of analytical homogenization 73
4.1.1. Effects of interfacial damage 73
4.1.2. Effects of plasticity and ductile damage 74
4.2. Results of multistep homogenization for SMC 79
4.2.1. Model Validation with literatures 79
4.2.2. Effect of overlapping 82
4.2.3. Effect of waviness and orientation 83
4.2.4. The SMC micromechanics model under cyclic loading 85
4.3. Results of multiscale cluster based SCA simulation 86
4.3.1. Validation of multiscale cluster based SCA simulation 86
4.3.2. The effect of waviness and orientation 89
4.3.3. The comparison of multiscale SCA simulation and multistep homogenization of SMC 91
Chapter 5. Conclusions 93
Bibliography 94
Abstract in Korean 103
Table 1. Material properties of plasticity simulation 75
Table 2. Material parameters of fiber chips 80
Table 3. Results comparison of fiber chip 80
Table 4. Comparison of effective elastic properties of SMC composites for the proposed method and literatures 80
Table 5. Material parameters of fiber and matrix 86
Figure 1. Periodic boundary condition application in ABAQUS 26
Figure 2. (a) spring layer modeling of interphase (b) tangential component of discontinuous displacement (c) normal component of the traction 35
Figure 3. Modeling of wavy fiber with interface damage 39
Figure 4. (a) unidirectional aligned wavy CNT distribution (b) randomly oriented wavy CNT distribution 42
Figure 5. Scheme of Mid-Point Rule 46
Figure 6. Return Mapping Algorithm 48
Figure 7. In & Output of Newton Raphson's Iteration 49
Figure 8. Convergent of multivariable Newton Iteration 49
Figure 9. Scheme of micromechanics Mori-Tanaka model 51
Figure 10. 2D Fiber reinforced composites RVE with (a). Lippmann Schwinger homogenization, (b). cluster-based Lippmann Schwinger homogenization, (c). Mori-... 53
Figure 11. Flowchart of Homogenization Methods 54
Figure 12. Input & Output Comparison of Homogenization Methods 56
Figure 13. Comparison of stress and strain curve of fiber reinforced composites 56
Figure 14. Representation of random fiber waviness 60
Figure 15. The micromechanics modeling of wavy fiber chip 61
Figure 16. Defining the angles of fiber chips' orientation 61
Figure 17. Overlapping parts of chips and mapping to the upper layer 63
Figure 18. (a) The contents of SMC composites (b) the normal distribution in terms of aspect ratio (AR) for overlapping parts 63
Figure 19. Effect of the number of overlapping phases on the effective elastic modulus 64
Figure 20. Flowchart of multi-step homogenization 65
Figure 21. (a) FE model for fiber-reinforced composites (b) Fiber-reinforced composites model after PBC 67
Figure 22. Cluster distribution of fiber-reinforced composites model with (a) 4 clusters (b) 64 clusters (c) 128 clusters (d) 256 clusters 68
Figure 23. The effect of number of clusters 68
Figure 24. Multiscale model for fiber-reinforced composites 70
Figure 25. Process for multiscale fiber-reinforced composites simulation 70
Figure 26. Data transform of multiscale SCA model for SMC 71
Figure 27. Effective properties with various interface damage 73
Figure 28. (a) Longitudinal and (b) transverse effective Young's modulus with varying orientation, waviness and damage parameter α and β 74
Figure 29. The effect of p on strain release energy Y 75
Figure 30. Plasticity and damage evolution with various aspect ratio 75
Figure 30. The influence of volume fraction on plastic and damage evolution 76
Figure 31. The effect of volume fraction (Interfacial damage: α=0.3, β=0; Aspect Ratio: 0.01) 77
Figure 32. The effect of volume fraction (Interfacial damage: α=0.3, β=0; Aspect Ratio: 0.1) 77
Figure 33. The effect of tangential damage (Volume Fraction: 0.1; Aspect Ratio: 0.1) 78
Figure 34. The effect of normal damage (Volume Fraction: 0.1; Aspect Ratio: 0.01) 78
Figure 35. CNT nanocomposites elasto-plastic simulation (Waviness: 0, α=0.3, β=0) 79
Figure 36. Comparison of multistep homogenization for SMC 81
Figure 37. Effect of overlapping parts 83
Figure 38. The stress-strain curves (a) the influence of the waviness on SMC chip and (b) the influence of the orientation on SMC composites 84
Figure 39. The change of chip orientation with an increment of k 84
Figure 40. Periodic boundary condition application in ABAQUS 85
Figure 41. Cyclic stress-strain responses (a) waviness (b) orientation distribution 85
Figure 42. Comparison of various homogenization methods 87
Figure 43. Validation of random orientation 89
Figure 44. Rotate transformation of multiscale SCA model 89
Figure 45. The effect of (a) waviness and (b) orientation 90
Figure 46. Layered SMC composites 91
Figure 47. (a) SMC chip distribution (b) Stress contour of macroscale SMC composites 91
Figure 48. (a) Cluster distribution of microscale model (b) Comparison of multistep homogenization and multiscale clustering-based SCA 92