臺灣博碩士論文加值系統

本論文探討複合材料系統之彈塑力學和黏彈力學的反應，應用有限元素數值方法，計算兩種複合材料系統在不同狀態下的力學性質，一種是含孔洞或第二相內含物環形盤 之熱彈塑力學行為。另一種是由高分子和金屬形成的高阻尼和高勁度（HDHS）複合系統之等效黏彈性質。複合環形盤假設具有溫度相依的材料性質，並比較完美彈塑性 與硬化彈塑性模型。在溫度加載下，計算複合盤的彈性不可逆溫度（EIT）和塑性崩壞溫度(PCT)，並分析溫度加載卸載後的殘餘應力。當材料具有溫度相依的特性時， 導致EIT和PCT比沒有溫度相依的狀態顯著減少，且預測的殘餘應力較小。此外，本文亦探討希爾正交異性塑性模型，對殘餘應力的影響，異向性塑行可以顯著改變殘餘應力的分佈狀態。至於高阻尼和高勁度複合材料系統，本文研究含有不同體積百分比的聚胺內含物在鋼鐵材料中的有效黏彈性質。以實驗數據反算廣義Maxwell模型的參數， 並用於後續的有限元素計算中，評估複合系統的等效黏彈性質，此種複合材料系統的設計，可以大幅提高整體勁度和阻尼。

The elastoplastic and viscoelastic responses of composite material systems are studied via the finite element numerical method. Specifically, two systems are analyzed in this work. One is the annular disc containing a hole or a second phase inclusion under thermal loading. The other is a type of high damping and high stiffness (HDHS) composite system that is formed by polymer and metal. As for the annular disc problem, it is assumed that the material properties are temperature dependent, and elastoplastic models with or without hardening are considered. Upon temperature increasing, the elastic irreversible temperature (EIT) and plastic collapse temperature (PCT) of the composite disc are determined. Residual stresses under thermal loading and unloading have been analyzed. Considerations of material properties being temperature dependent may lead to significant reduction of the EIT’s and PCT’s. Furthermore, the magnitudes of residual stresses may be smaller when temperature dependent material properties are considered. In addition, effects of Hill’s orthotropic plasticity in the development of residual stresses are analyzed. It is found that anisotropy in plasticity may significantly change the distribution of residual stresses. As for the HDHS composite system, I study the effective viscoelastic properties of a steel cube containing polyamide inclusion with various volume fraction. By using experimental data, the parameters of the generalized Maxwell model are determined for estimating the effective properties of the composite system in the finite element calculations. It is found the overall stiffness and damping can be largely increased vis such design of composite material system.

CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1 Goals and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Inelastic process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Plane disc under thermal loading . . . . . . . . . . . . . . . . . . . . . 3
1.2.3 Energy dissipation and HDHS system . . . . . . . . . . . . . . . . . . 5
1.2.4 Damping calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Theory of plasticity (Rate independent responce) . . . . . . . . . . . . . . . . . 11
2.1 Elastic domain and yield condition . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Hardening rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Perfect plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Linear isotropic hardening . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 Kinematic hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Plastic flow rule (Loading/Unloading conditions) . . . . . . . . . . . . . . . . 16
2.4 The yield criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.1 General quadratic model . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 Plane strain, classical J2 (isotropic/kinematic hardening) . . . . . . . . 21
3 Theory of linear viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 One - Dimensional rheological model . . . . . . . . . . . . . . . . . . . . . . 24
3.1.1 Generalized Maxwell Model (GMM) . . . . . . . . . . . . . . . . . . 26
3.2 Three - Dimensional Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Thermodynamic Theory . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Considerations of computational inelasticity . . . . . . . . . . . . . . . . . . . . 30
4.1 Finite element methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Return-Mapping algorithms with plastic hardening . . . . . . . . . . . . . . . 31
4.2.1 Algorithmic form from the loading/unloading conditions (Trail state) . 33
4.2.2 The closet point project . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.3 General Return Mapping algorithm for linear Isotropic/Kinematic Hardening
plasticity model . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.4 Return mapping for J2 Plasticity (Nonlinear Isotropic/Kinematic Hardening)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Finite-Element Implementation and discrete Variational Formulation . . . . . . 40
5 Theory of elasticity and plasticity for circular disc . . . . . . . . . . . . . . . . . 43
5.1 Orthotropic disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.1.1 Elastic solution for the orthotropic disc . . . . . . . . . . . . . . . . . 43
5.1.2 Plastic solution for the orthotropic disc . . . . . . . . . . . . . . . . . 46
5.2 Isotropic disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2.1 Elastic solution for isotropic disc . . . . . . . . . . . . . . . . . . . . 49
5.2.2 Plastic solution for isotropic disc . . . . . . . . . . . . . . . . . . . . . 51
6 Composite system 1: Plastic behavior of circular disc under thermal loading . . 55
6.1 Isotropic composite disc under uniform thermal loading [78] . . . . . . . . . . 55
6.1.1 Theoretical and numerical aspects . . . . . . . . . . . . . . . . . . . . 56
6.1.2 Temperature-dependent material properties . . . . . . . . . . . . . . . 59
6.1.3 Two-dimensional analysis – plane strain . . . . . . . . . . . . . . . . . 60
6.1.4 Two-dimensional analysis – plane stress . . . . . . . . . . . . . . . . . 61
6.1.5 Three-dimensional analysis – long cylinder . . . . . . . . . . . . . . . 62
6.1.6 Three-dimensional analysis – thin disc . . . . . . . . . . . . . . . . . . 63
6.2 Isotropic composite disc under thermal loading and unloading [79] . . . . . . . 68
6.2.1 Theoretical and numerical aspects . . . . . . . . . . . . . . . . . . . . 68

6.2.2 Temperature loading/unloading profile and temperature-dependent ma-
terial properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.3 Plastic strain after unloading . . . . . . . . . . . . . . . . . . . . . . . 75
6.2.4 Effects of hardening rules . . . . . . . . . . . . . . . . . . . . . . . . 76
6.2.5 Discussions on other stress components . . . . . . . . . . . . . . . . . 79
6.2.6 Verification by the analytical solution . . . . . . . . . . . . . . . . . . 81
6.3 Orthotropic composite cylinder under thermal loading and unloading [80] . . . 85
6.3.1 Theoretical and Numerical Considerations . . . . . . . . . . . . . . . . 86
6.3.2 Effects of selective TD material properties on residual stress . . . . . . 91
6.3.3 Residual stress analysis with linear hardening . . . . . . . . . . . . . . 92
6.4 Summary of composite system 1 . . . . . . . . . . . . . . . . . . . . . . . . . 94
7 Composite system 2: Viscoelastic behavior of novel viscoelastic dampers under dynamic loading.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.1 Modeling behavior of viscoelastic materials . . . . . . . . . . . . . . . . . . . 100
7.1.1 Calculation of damping and stiffness . . . . . . . . . . . . . . . . . . . 100
7.1.2 Mathematical model of viscoelastic materials . . . . . . . . . . . . . . 102
7.2 Experimental and numerical material properties characterization . . . . . . . . 105
7.2.1 Viscoelastic properties of the polyamide . . . . . . . . . . . . . . . . . 105
7.2.2 VSP damper samples preparation . . . . . . . . . . . . . . . . . . . . 106
7.2.3 Viscoelastic properties of the VSP dampers . . . . . . . . . . . . . . . 107
7.2.4 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.3.1 Polyamide Shear modulus and relaxation time characterization . . . . . 109
7.3.2 Polyamide damping and Young’s modulus calculation . . . . . . . . . 111
7.3.3 Viscoelastic parameter of VSP dampers . . . . . . . . . . . . . . . . . 114
7.3.4 VSP as a HSHD damper . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.4 Summary of composite system 2 . . . . . . . . . . . . . . . . . . . . . . . . . 117
8 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
APPENDICES
Appendix A: Viscoplastic analysis of steel polymer (VSP) damper . . . . . . . . . 130
Appendix B: Checking thermal warping in composite disc . . . . . . . . . . . . . 134
Appendix C: Presentation slide . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

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