Explicit transient solutions for a mode III crack subjected to dynamic concentrated loading in a piezoelectric material

Abstract

In this study, the transient response of a semi-infinite crack subjected to dynamic anti-plane concentrated loading in a hexagonal piezoelectric medium (6 mm) is investigated. The crack surfaces are assumed to behave as though covered with a conducting electrode. In order to give an insight into the effect of the electrode boundary condition, a simple half-plane problem is also discussed in the paper. A new fundamental solution for piezoelectric materials is proposed and the transient solution for the cracked body is determined by superposition of the fundamental solution in the Laplace transform domain. The fundamental solution to be used is the problem of applying exponentially distributed traction on the crack faces in the Laplace transform domain. Exact analytical transient solutions for the dynamic stress intensity factor, the dynamic electric displacement intensity factor, and the dynamic energy release rate are obtained by using the Cagniard method of Laplace inversion and are expressed in explicit forms. Finally, numerical results for the transient solutions are evaluated and discussed in detail.