Elastic wave scattering by a circular crack in a transversely isotropic solid

The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.