The transient response of a semi-infinite crack in an anisotropic layered medium is presented in this study. The individual layers are anisotropic and homogeneous. The number of reflections and diffractions of stress waves that are generated from the interfaces of the layered medium and the crack are infinite. It will cause extreme difficulties in analyzing this problem. A modified linear coordinate transformation is introduced to reduce the anisotropic layered medium problem to an equivalent isotropic problem with a similar geometry configuration. Besides, a useful fundamental solution is proposed and the solution can be determined by superposition of the fundamental solution in theLaplace transform domain. The Cagniard method of Laplace inversion is used to obtain the analytical transient solution in the time domain. The final results for the stress intensity factor are expressed in compact formulations and are valid for an infinite length of time. Numerical calculations are also evaluated and discussed in detail.

The transient analysis of dynamic anti-plane propagation in an anisotropic layered medium is investigated in this study. The complete effects of reflections and diffractions of stress waves that are generated from the interfaces of the anisotropic layered medium and the crack are considered. A modified linear coordinate transformation is introduced and it is successful in reducing the anisotropic layered medium problem to an equivalent isotropic problem with a similar geometry configuration. Besides, a useful fundamental solution is proposed and the solution can be determined by superposition of the fundamental solution in the Laplace transform domain. The influence of the reflected waves generated from interface boundaries on the propagating crack tip is analyzed. Analytical transient solutions for dynamic stress intensity factors of the propagating crack are expressed in compact formulations and are valid for an infinite length of time. Numerical results indicate that the reflected waves have significant influence on the stress intensity factors of propagating cracks.