An exact transient analysis of plane wave diffraction by a crack in an orthotropic or transversely isotropic solid

Abstract

A transient plane strain analysis of diffraction of plane waves by a semi-infinite crack in an unbounded orthotropic or transversely isotropic solid is performed. The waves approach the crack at a general oblique angle, and are of two types, a normal stress pulse and a shear stress pulse, i.e. a P- and an SV-wave, respectively, in the isotropic limit. A class of materials that includes this limit and beryl, cobalt, ice, magnesium and titanium is chosen for illustration, and exact solutions are obtained for the initial/mixed boundary value problems. In contrast to related work, a factorization in the Laplace transform space is used to simplify the solution forms and the Wiener-Hopf component of the solution process, and to yield a more compact expression for the Rayleigh wave speed. Calculations for this speed, the two allowable, direction-dependent, plane wave speeds, and quantities related to the Mode I and Mode II dynamic stress intensity factors are given for the five anisotropic materials mentioned.