本文旨在探討異向性材料主裂紋與微裂紋共線下之互制情形，主裂紋考慮成半無限長裂紋。應用Stroh異向性彈性體之理論公式，首先介紹差排作用於全平面半無窮長裂紋之基本解，其次利用基本解以差排密度模擬微裂紋推演問題之奇異積分方程式，利用數值方法探討異向性材料為等向性材料、正交異性材料或一般異向性材料三種不同材料下，微裂紋與主裂紋共線下之互制情形。

This thesis investigates the interactions of the collinear micro-macro cracks in anisotropic materials. The length of the macro-crack is assumed to be semi-infinite. Employing the Stroh formalism for anisotropic elastic materials, the fundamental solution due to dislocation acting on full plane with a semi-infinite crack embedded is first introduced. The fundamental solution is adopted to simulate the micro-crack. By distributing unknown dislocation density on the micro-crack faces, a system of singular integral equation for the problem is then deduced. The numerical method is used to study the interactions of the collinear micro-macro cracks in anisotropic materials. Numerical results are presented for isotropic material, orthotropic material and anisotropic material.

Broberg K.B., Cracks and fracture. Academic Press. San Diego. 1999.

Chen B.J., Xiao Z.M., and Liew K.M., A line dislocation interacting with a semi-infinite crack in piezoelectric solid. International Journal of Engineering Science, Vol. 42,1-11. 2004.

Gong S.X., On the main crack - microcrack interaction under mode III loading. Engineering Fracture Mechanics, Vol. 51, No.5. 753-762. 1995.

Gong S.X., and Horii H., General solution to the problem of microcracks near the tip of a main crack. J. Mech. Phys. Solids, Vol. 37, No. 1. 27-46. 1989.

Gerasoulis, A., The use of piecewise quadratic polynomials for the solution of singular integral equations of cauchy type. Computers & Mathematics with Applications, Vol. 8, No. 1,15-22. 1982.

Hills D.A., Kelly P.A., and Dai D.N., Korsunsky A.M., Solution of Crack Problems: the distributed disclocation technique. Kluwer Academic Publishers. Dordrecht. 1996.

Liou J.Y., and Sung J.C., On the Barnett Lothe tensors for anisotropic elastic materials. European Journal of Mechanics A/Solids Vol. 27,1140-1160. 2008.

Lee S.B., General solution of screw dislocations near an interfacial crack. Materials Science and Engineering, A176, 335-340. 1994.

Lam K.Y., and Wen C., Interaction between microcracks and a main crack in a semi - infinite medium. Engineering Fracture Mechanics, Vol. 44, No. 5,753-761. 1993.

Majumdar B.S., and Burns S.J., Crack tip shielding an elastic theory of dislocation and dislocation arrays near a sharp crack. Acta Metallurgica, Vol. 29,579-588. 1980.

Ohr S.M., Dislocation crack interaction. J. Phys. Chem. Solids Vol. 48, No. 11,1007-1014. 1987.

Tupholme G.E., Mode III crack in an isotropic elastic half-space. International Journal of Engineering Science, Vol. 27,No. 2,123-129. 1989.

Wang X., and Zhong Z., Interaction between a semi-infinite crack and a straight dislocation in a decagonal quasicrystal. International Journal of Engineering Science, Vol. 42,512-538. 2004.

徐國城, 異向性多裂紋體之分析. 國立成功大學土木工程研究所碩士論文. 2003.

葉庭恩, 異向性界面裂紋分叉行為之研究. 國立成功大學土木工程研究所碩士論文. 2005.

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碩士論文. 2005.