本文旨在探討含彈性薄層之半平面異向性裂紋體之問題，應用異向性Stroh理論公式，藉由連續差排密度模擬裂紋行為，推演以差排密度為未知函數之奇異積分方程式，其後利用數值方法求解未知差排密度函數，進而推得彈性薄層下之應力強度因子(KI、KII)，數值分析中針對裂紋面上受張應力和剪應力作用下探討了不同的幾何參數(如邊界條件、裂紋深度、材料角度、裂紋角度、彈性薄層厚度)對應力強度因子之影響，分析結果也應用了有限元素法進行比對。

The aim of this study is to investigate the cracked half-plane anisotropic solid bonded to a thin elastic layer. Employing the Stroh formalism to deal with anisotropic elastic materials and the concept of modeling the crack by a continuous dislocation density, a singular integral equation for the problem with dislocation density as the unknown function is deduced. The unknown dislocation density is determined by numerical method and the corresponding stress intensity factors(KI、KII) are directly obtained. Numerical analyses are performed for cracks subjected to tensile stress or shear stress and the effects of geometrical conditions (such as boundary condition, crack depth, material angle, crack angle, elastic layer character) on the stress intensity factors are discussed. Some of the presented results are also compared with those by Finite Element Method.

[1]Beghini, M., Bertini, L. and Fortanari, V., Stress Intensity Factors for an Inclined Edge Crack in a Semiplane. Engrg. Fracture Mechanics 62, 607-613,1999.
[2]Chow, W.T. and Atluri, S.N., Stress Intensity Factors as the Fracture Parameters for Delamination Crack Growth in Composite Laminates. Computational Mechanics,1-10,1998.
[3]Eshelby, J.D., Read, W.T. and Shockley, W., Anisotropic Elasticity with Applications to Dislocations Theory. Acta Metall 1,251-259,1953.
[4]Erdogan, F., Stress Intensity Factors. ASME J. Appl. Mech 50, 992-1002, 1983.
[5]Gerasoulis, A., The Use of Piecewise Quadratic Polynomials for the Solution of Singular Integral Equations of Cauchy Type. Comput. Math. With Applications. 8,15-22,1982.
[6]Higadhida, Y. and Kamada, K., Stress Fields around a Crack Lying Parallel to a Free Surface. Int J. Fracture 19,39-52,1982.
[7]Hasebe, N., and Qian, J., Fundamental Solutions for Half Plane with an Oblique Edge Crack. Engrg. Anal. With Boundary Elements 17, 263-267,1996.
[8]Stroh, A.N., Dislocations and Cracks on Anisotropic Elasticity. Philos. Mag 7,625-646,1958.
[9]Sung, J.C. and Liou, J.Y., An Internal Crack in a Half-Plane Solid with Clamped Boundary. Comput. Methods Appl. Engrg 121,361-372,1994.
[10]Sung, J.C. and Liou, J.Y., Analysis of a Crack Embedded in a Linear Elastic Half-Plane Solid. ASME J. Appl. Mech 62,78-86,1995.
[11]Ting, T.C.T., Explicit Solution and Invariance of the Singularities at an Interface Crack in Anisotropic Composites. Int J. Solids Structure 22,965-983,1986.
[12]Ting, T.C.T., Image Singularities of Green’s Functions for Anisotropic Elastic Half-Spaces and Bimaterials. Q. J. Mech. Appl. Math 45,119-139,1992.
[13]Ting, T.C.T. and Barnett, D.M., Image Force on Line Dislocations in Anisotropic Elastic Half-Spaces with a Fixed Boundary. Int J. Solids Struc 30,3,313-323,1993.
[14]Ting, T.C.T., Anisotropic Elasticity : Theory and Applications. Oxford University Press, New York,1996.
[15]Ting, T.C.T., Green’s Functions for a Half-Space and Two Half-Spaces Bonded to a Thin Anisotropic Elastic Layer. ASME J. Appl. Mech 75/051103-1,2008.
[16]劉鈞耀，雙層異向性材料介面附近裂紋之分析，國立成功大學土木工程研究所博士論文，1994。
[17]許智泰，具滑移邊界之半平面異向性材料內含裂紋之數值分析，國立成功大學土木工程研究所博士論文，2005。
[18]徐仲毅，半平面壓電裂紋材料之數值分析，國立成功大學土木工程研究所博士論文，2006。

[19]楊秉順，雙層介面完全結合之壓電裂紋解析，國立成功大學土木工程研究所博士論文，2008。
[20]愛發股份有限公司，ABAQUS實務入門引導，全華科技圖書股份有限公司 印行，2005。