A semi-in® nite crack in a layered medium subjected to antiplane dynamic loading is investigated. In analyzing this problem, the fact that the re¯ections and diffractions of stress waves by the interface boundary and by the crack will generate an in® nite number of waves must be taken into account. A useful fundamental solution is proposed, and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the application of exponentially distributed traction (in the Laplace transform domain) on the crack faces. Cagniard's method for Laplace inversion is used to obtain the transient solution in time domain. The ® nal formulations for the stress intensity factor are expressed explicitly and the dynamic effect of each wave is presented in a closed form. The results are valid for an in® nite number of waves that are scattered from the crack tip and re¯ected by the interface. Numerical calculations of dynamic stress intensity factors are evaluated and discussed in detail.

In transversely isotropic elastic solids, there is no surface wave for anti-plane deformation. However, for certain orientations of piezoelectric materials, a surface wave propagating along the free surface (interface) will occur and is called the Bleustein-Gulyaev (Maerfeld-Tournois) wave. The existence of the surface wave strongly influences the crack propagation event. The nature of anti-plane dynamic fracture in piezoelectric materials is fundamentally different from that in purely elastic solids. Piezoelectric surface wave phenomena are clearly seen to be critical to the behavior of the moving crack. In this paper, the problem of dynamic interfacial crack propagation in elastic-piezoelectric bi-materials subjected to uniformly distributed dynamic anti-plane loadings on crack faces is studied. Four situations for different combination of shear wave velocity and the existence of MT surface wave are discussed to completely analyze this problem. The mixed boundary value problem is solved by transform methods together with the Wiener-Hopf and Cagniard-de Hoop techniques. The analytical results of the transient full-field solutions and the dynamic stress intensity factor for the interfacial crack propagation problem are obtained in explicit forms. The numerical results based on analytical solutions are evaluated and are discussed in detail.

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