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研究生： 維佳達
Alief - Wikarta
論文名稱： 含直線或圓形界面多層異質與裂紋交互作用之彈性問題解析
Interaction between a Crack and Multi-Layered Media with Straight or Circular Boundary for Plane Elasticity
指導教授： 趙振綱
Ching-Kong Chao
口試委員: 馬劍清
Chien-Ching Ma
吳光鐘
Kuang-Chong Wu
陳東陽
Tungyang Chen
胡潛濱
Chyanbin Hwu
黃榮芳
Rong-Fung Huang
學位類別： 博士
Doctor
系所名稱： 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 141
中文關鍵詞： 多層異質 、其應力集中因子 、藉由複變函 、對數對奇異積分方程式
外文關鍵詞： multi-layered media, stress intensity factors, complex potential functions, logarithmic singular integral equations
相關次數： 點閱：247  下載：1 
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    • 本論文主要以線彈性破壞之觀點，針對直線或圓形多層異質與裂紋在受一遠端均勻負載下之反平面與平面彈性的問題，求其應力集中因子。
    本文求解的過程可分為兩大部分，第一部分，藉由複變函數理論結合解析連續法與交替技巧，求得在多層異質系統受差排作用下之全場應力函數之級數解。第二部分，利用此差排沿著裂紋邊界積分配合疊加法求得奇異積分方程式。接著，再利用差排密度函數之數值，求得其應力集中因子。
    本論文亦考慮多層直線或圓形異質界面與裂紋之交互作用問題。在不同材料性質與幾何形狀下，其應力集中因子與無因次裂紋長度之關係，並以圖解表示。由數值結果顯示本研究所使用之方法可提供一可靠的結果並呈現一快速收斂之級數閉合解。本文所採用方法亦可求解多層橢圓異質或偏心塗層異質之相關問題。

    In this study, the solution of a crack interacting with multi-layered composite under a remote uniform load for anti-plane or in-plane elasticity is provided. The study can be achieved by determination of the stress intensity factors that allow the characterization of interaction from the point of view of linear elastic fracture mechanics.
    The solution procedures for solving this problem consist of two parts. In the first part, based on the method of analytical continuation in conjunction with the alternating technique, the complex potential functions of dislocation interacting with multi-layered composites are obtained. The second part consists of the derivation of logarithmic singular integral equations by introducing the complex potential functions of dislocation along the crack border together with superposition technique. The stress intensity factors are then obtained numerically in terms of the values of the dislocation density functions of the logarithmic singular integral equations.
    Several different problems of multi-layered composite with straight or circular boundaries interacting with a crack are considered. The stress intensity factors as a function of the dimensionless crack length for various material properties and geometric parameters are shown in graphic form. In all problems, this approach obviously provides a reliable result and demonstrates that the series form solution is rapidly convergent. Another merit is that the solutions obtained remain valid regardless of the shape and number of medium such as elliptically layered media and eccentrically coated circular inclusion.

    摘要 i Abstract ii Acknowledgments iii Table of Contents iv Nomenclature vii List of Figures ix List of Tables xiv Chapter 1 Introduction 1 1.1 Background 1 1.2 Literature Study 2 1.3 Objective 4 1.4 Organization of Dissertation 5 Chapter 2 Principles of Complex Potential and Singular Integral Equations 6 2.1 Displacement and Resultant Force Equations 6 2.2 Homogeneous Solution 7 2.3 Analytical Continuation 9 2.4 Superposition Techniques 9 2.5 Numerical Treatment 10 2.6 Stress Intensity Factors 12 Chapter 3 Interaction between a Crack and an Isotropic Tri-Material Media in Anti-plane Elasticity 14 3.1 Problem Statement 14 3.2 Complex Potential Formulation 14 3.3 Singular Integral Equation 17 3.4 Numerical Examples 19 Chapter 4 Interaction between a Crack and a Three-Phase Composite with an Eccentric Circular Inclusion in Anti-plane Elasticity 25 4.1 Problem Statement 25 4.2 Complex Potential Formulation 25 4.2.1 Screw dislocation in infinite matrix 26 4.2.2 Screw dislocation in core inclusion 29 4.3 Singular Integral Equation 30 4.4 Numerical Examples 32 4.4.1 Crack in infinite matrix 32 4.4.2 Crack in core inclusion 34 Chapter 5 Interaction between a Crack and an Elliptically Cylindrical Layered Media in Anti-plane Elasticity 50 5.1 Problem Statement 50 5.2 Complex Potential Formulation 51 5.3 Singular Integral Equation 56 5.4 Numerical Examples 57 Chapter 6 Solutions of a Crack Interacting with a Tri-material Media in Plane Elasticity 64 6.1 Problem Statement 64 6.2 Complex Potential Formulation 64 6.2.1 Edge dislocation in region S1 64 6.2.2 Edge dislocation in region S2 66 6.3 Singular Integral Equation 67 6.3.1 Crack in region S1 67 6.3.2 Crack in region S2 69 6.4 Numerical Examples 70 Chapter 7 Solutions of a Crack Interacting with a Circularly Cylindrical Layered Media in Plane Elasticity 85 7.1 Problem Statement 85 7.2 Complex Potential Formulation 85 7.2.1 Edge dislocation in infinite matrix 86 7.2.2 Edge dislocation in core inclusion 88 7.3 Singular Integral Equation 90 7.3.1 Crack in infinite matrix 90 7.3.2 Crack in core inclusion 93 7.4 Numerical Examples 96 Chapter 8 Conclusion & Future Study 113 References 115 About the Author 120

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