In conventional studies of a semi-infinite crack in an unbounded homogeneous medium subjected to a spatially uniform traction distribution acting on crack faces, the complete solution is obtained by integral transform methods together with a direct application of the Wiener-Hope technique and the Cagniard-de Hoop method of Laplace inversion. If the loading is replaced by a nonuniform distribution having a characteristic length, then the straightforward application of the Wiener-Hope method is not successful. Freund studied the problem of an elastic solid containing a half-plane crack subjected to concentrated loadings on the crack faces at a finite distance from the crack tip. The exact solution of this problem was obtained by an indirect approach based on the superposition of moving dislocations. Basing his procedure on this method, Brock and Ma and Hou analyzed a series of problems of a semi-infinite crack in an homogeneous medium subjected to impact loading.

A stationary crack lying along an interface between dissimilar isotropic materials subjected to static loading was first considered by Williams for plane strain condition. In the field of propagating interface cracks, Willis investigated the energy release rate of a steadily extending interface crack by means of the local form of the Griffith virtual work argument. Yang, Suo and Shih have analyzed the problems of steadily propagating interface cracks in dissimilar isotropic and orthotropic bimaterials. They solved the crack-tip fields by the method of Stroh formulation and discussed the singularities for anti-plane and in-plane deformations carefully. To avoid mathematical complexity and difficulty, many investigators mentioned above have investigated only for the near tip fields. However, the transient full-field solutions for the problem of a propagating crack in a homogeneous material or in a bimaterial are rear to find.

In this paper, the transient problem of an interface crack in an infinite medium is considered. At time t = 0, the crack is at rest and an anti-plane dynamic body force loading acts at the medium. The incident wave will be reflected by the interface crack faces and diffracted from the crack tip. A new fundamental solution is proposed in this study and it is successfully applied towards solving the problem. The fundamental problem is the problem of applying an exponentially distributed traction on the interface crack faces in the Laplace transform domain and is demonstrated as an efficient methodology to solve similar problems. The transient full-field stresses and the dynamic stress intensity factor for the problem considered are obtained and expressed in a closed form. Numerical results for the transient problem are evaluated in detail.