臺灣博碩士論文加值系統

延伸有限元素法 (Extended Finite Element Method; XFEM) 改善了傳統的有限元素法，它擁有傳統有限元素法的優點，但是在處理裂縫成長時所產生的不連續(discontinuity)或奇異(singularity)問題時，不需再重新網格化及重新定義裂縫軌跡，且在裂縫成長時，不需要定義明確的裂縫表面。利用這種方法，可以更快速且有效的求得準確的數值解。
本論文利用延伸有限元素法模擬在一個基材/薄膜系統下，一存在於基材靠近介面處之裂縫。探討整個薄膜受平均應力時，裂縫是否會穩態成長；以及薄膜與基材系統在不同的材料的情況下，對於裂縫穩態成長時深度的影響。
接著探討在四點彎矩試片模型下，使用不同材料系數以及不同裂縫長度比時的應力強度因子與能量釋放率，並與理論值比較其誤差。

The extended finite element method (XFEM) keeps the merit of classical finite element method (FEM) and can be used to solve discontinuity and singularity problems without re-meshing
The case of a substrate crack in a thin film/substrate system subjected to a uniform stress applied to the film is firstly considered. The effect of material properties on the steady-state crack location is studied.
The interface crack in a bi-material system subjected to symmetric or asymmetric four-point bending is considered next. The computed stress intensity factors and energy release rates are benchmarked against analytic solutions. In addition, the effects of material property and crack length on mixed-mode stress intensity factor are discussed.

ABSTRACT i
ACKNOWLEDGMENT iii
Nomenclature iv
Table of Content viii
List of Tables ix
List of Figures x
CHAPTER 1 INTRODUCATION 1
1.1 Background 1
1.2 Fracture Mechanics 1
1.3 Literature Review 3
1.4 Objective 5
CHAPTER 2 FUNDAMENTAL THEOREMS OF XFEM 8
2.1 Finite Element Approximations 8
2.2 Finite Element Approximations with Local Enrichment 8
2.3 Discontinuous Enrichment 9
2.4 Near-Tip Enrichment 10
2.5 Stress Intensity Factors 11
2.6 Crack Growth Simulation in a Linear Elastic Solid 14
CHAPTER 3 CRACK GROWTH IN A FILM/SUBSTRATE SYSTEM SUBJECTED TO A UNIFORM TENSION 20
3.1 The Model 20
3.2 Analytic Solutions 20
3.3 XFEM Solutions in Substrate Cracking 21
CHAPTER 4 THE CRACK LYING ON BIMATERIAL INTERFACE 30
4.1 Analytic Solutions 30
4.1.1 Symmetric Geometry Configuration 31
4.1.2 Asymmetric Geometry Configuration 32
4.2 Results and Discussions 33
CHAPTER 5 Conclusions and Discussions 45
References 46
Appendix A 49
Appendix B 62

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