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研究生：	康鈺京 Kang, Yu-Jing
論文名稱：	被夾於兩層不同彈性材料之無窮平板且含有單一被固定於中央之嵌入式有限長度裂縫之功能梯度材料面內問題破壞分析 In-plane Fracture Analysis of an Embedded Central Crack in Functionally Graded Strip Bonded by Two Homogeneous Half Planes
指導教授：	褚晴暉 Chue, Ching-Hwei
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2010
畢業學年度：	98
語文別：	英文
論文頁數：	47
中文關鍵詞：	裂縫、功能梯度材料、奇異積分方程式、面內、應力強度因子、應變能密度因子
外文關鍵詞：	Crack, Functionally graded material, Singular integral equation, In-plane, Stress intensity factor, Strain energy density factor
相關次數：	點閱：173 下載：3
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查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

本論文主要研究目的在於探討被夾於兩層不同彈性材料之無窮平板且含有單一被固定於中央之嵌入式有限長度裂縫之功能梯度材料的面內破壞問題。材料梯度假設為指數型函數。利用 Fourier 轉換法可將問題轉換成一組奇異積分方程式，再藉由 Gauss-Chebyshev 積分公式進行數值求解，並從數值解中探討裂縫長度以及非均質材料參數對於無因次化應力強度因子和無因次化應變能密度因子的影響。
第I型與第II型之無因次化應力強度因子的大小皆與裂縫長度成正比。對均質材料而言，裂縫會沿著應變能密度相對極小值發生的角度開始成長，若此結論也適用於非均質材料，則本研究也發現裂縫會沿著材料較弱的地方開始成長。同時，我們也可預測出裂縫開始成長的角度。

This dissertation investigates the in-plane fracture problem of an embedded central crack in the FGM strip bonded by two dissimilar homogeneous half planes under in-plane loads. The material gradient is assumed to be in an exponential form. By using the Fourier transform, the problem can be formulated into a system of singular integral equations which is then solved by applying the Gauss-Chebyshev integration formula. The effects of the crack length and the inhomogeneous material parameter on the normalized stress intensity factors and the normalized strain energy density factor are discussed.
The magnitudes of both the normalized stress intensity factors of Mode I and Mode II are proportional to the crack length. If the conclusion in strain energy density theory that the crack propagation occurs at the angle of Smin in homogeneous medium is also valid for inhomogeneous materials, the direction of the crack extension can be predicted in the problem of this dissertation. The result, which shows that the angle of Smin decreases from 0 degree to negative values when the values of beta*h increase from 0, indicates that the crack would propagate along the direction where the material is softer.

摘要							   I
Abstract						  II
誌謝							 III
Table of contents					  IV
List of tables						  VI
List of figures						 VII
Nomenclatures						VIII
Chapter 1 Introduction					   1
        1.1 Introduction				   1
        1.2 Functionally graded materials		   2
        1.3 Literature survey				   3
        1.4 Problem statements				   3
        1.5 Outline of the dissertation			   3
Chapter 2 Formulation of the problem			   5
	2.1 Geometry of the problem			   5
	2.2 Constitutive equations			   5
	2.3 Cracked functionally graded strip		   7
	2.4 Uncracked homogeneous half plane		  10
	2.4.1 Upper half plane				  10
	2.4.2 Lower half plane				  11
	2.5 Boundary conditions				  13
Chapter 3 Singular integral equations and solutions	  15
	3.1 Development of singular integral equations	  15
	3.1.1 Boundary and continuous conditions	  15
	3.1.2 Dislocation density functions		  16
	3.1.3 Mixed boundary conditions			  17
	3.2 Evaluation of singularities and expressions for stress intensity factors				  18
Chapter 4 Numerical procedures				  20
	4.1 Singular integral equations of the first kind 20
	4.2 Gauss-Chebyshev integration formulas	  21
	4.3 Strain energy density theory		  24
Chapter 5 Results and discussions			  26
Chapter 6 Conclusions					  39
References						  41
Appendix A						  42
Appendix B						  45
Appendix C						  47
                                    

Delale, F., and Erdogan, F., Crack problem for a nonhomogeneous plane. Journal of Applied Mechanics, Transactions ASME 50, 609-614, 1983.
Delale, F., and Erdogan, F., On the mechanical modeling of the interfacial region in bonded half-planes. Journal of Applied Mechanics, Transactions ASME 55, 317-324, 1988.
Erdogan, F., and Gupta, G. D., On the numerical solution of singular integral equations. Quarterly of Applied Mathematics 30, 525-534, 1972.
Erdogan, F., Gupta, G. D., and Cook, T. S., Numerical solution of singular integral equations. In: Sih, G. C. (ed.), Mechanics of Fracture 1: Method of analysis and solution of crack problem. Noordhoff International Publishing, Leyden, The Netherlands, 368-425, 1973.
Jiang, L. Y., and Wang, X. D., On the dynamic crack propagation in an interphase with spatially varying elastic properties under inplane loading. International Journal of Fracture 114, 225-244, 2002.
Lee, W. Y., Stinton, D. P., Berndt, C. C., Erdogan, F., Lee, Y. D., and Mutasim, Z., Concept of functionally graded materials for advanced thermal barrier coating applications. Journal of the American Ceramic Society 79, 3003-3012, 1996.
Muskhelishvili, N. I., Singular integral equations. Noordhoff International Publishing, Groningen, The Netherlands, 1953.
Nissley, D. M., Thermal barrier coating life modeling in aircraft gas turbine engines. Journal of Thermal Spray Technology 6, 91-98, 1997.
Rivlin, T. J., The Chebyshev polynomials. Wiley, New York, 1974.

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