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

Artikel i vetenskaplig tidskrift, 1992

The scattering of arbitrary elastic waves by a circular crack in a transversely 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 tp the plane of the crack. A Fourier-Hankel representation of 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 openaing 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 the crack opening displacement for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.