Previous researchers have investigated anti-plane problems of a crack terminating at an interface within an infinite domain. This study is devoted to the theoretical analysis of these crack terminating problems for a circular composite material with a finite radius. Detailed solutions for a composite with a crack terminating at the interface under anti-plane loading were derived by employing a double transform that consists of the finite Mellin and Laplace transforms. Using the proposed method, related problems of anti-plane shearing can be solved in a straightforward manner. According to these solutions, stress intensity factors are obtained and discussed. Based on the problems studied with the maximum shear stress criterion, the crack may be interfacial debonded or may penetrate through the interface, but it cannot be reflected back.
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