本文探討一線剛性異質物於二維異向性全平面彈性體內受到無限遠處外力作用下，異質物兩端產生Z型分叉行為，此問題可視為將兩個子問題線性疊加後之結果。子問題一為彈性體內含一異質物受無限遠處外力作用；子問題二為彈性體內含一異質物受兩個未知的差排函數作用，疊加二子問題使其符合邊界條件–分叉裂紋位置之曳引力為零。透過已知的位移函數及應力函數，並利用差排密度函數模擬裂紋，將此問題離散化後轉換成奇異積分方程組，藉由數值積分求解差排函數，進而求得分叉裂紋尖端之應力強度因子，文中對於不同受力狀況、分叉裂紋角度變化以及分叉裂紋長度變化在不同異向性程度下之應力強度因子有詳細的討論。

The behaviours of Z-branch extending from the tip of rigid line inclusion in an anisotropic elastic material are investigated in this thesis. The problem can be analyzed by superposition of two simple problems. One is an elastic material containing a rigid line subjected to far field uniform stress. The other is an elastic material containing a rigid line applied by unknown distributed edge dislocations. The traction-free condition is applied on the positions of two branches. Eshelby-Stroh formalism is used to establish the Cauchy-type singular integral equations. A numerical method is employed to solve these equations. Then unknown distributed edge dislocations and stress intensity factors (SIFs) at the branch tip can be obtained. In this thesis, three kinds of far field stresses are considered: uniform tension, in-plane shear and out-of-plane shear. The influences of degree of anisotropy, angle of Z-branch, and length of Z-branch on the SIE at branch tip are investigated and the results are discussed.

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