Three-dimensional elastic wave scattering by surface-breaking cracks

Abstract

Scattering of time-harmonic elastic waves by a surface-breaking crack of arbitrary shape, which is normal to the traction-free surface of a half-space, is investigated by the boundary integral equation method. The use of full-space Green’s functions requires a discretization of the free surface near the crack mouth. Convergence of the crack-opening displacements with successively larger regions of discretization of the free surface is demonstrated. The crack-opening displacements are used to calculate the farfield amplitude spectra of scattered longitudinal and transverse body waves. The required representation integral makes use of the farfield expansions of the half-space Green’s functions. Solutions of both symmetric and antisymmetric problems are obtained by considering two special angles of incidence of a transverse wave field. Numerical results, in the form of crack-opening displacements and scattered farfield amplitude distributions, are presented for scattering by a semicircular normal-edge crack of radius a. A breakdown of contributions to the farfield amplitudes, by ray cases, provides insight as to the relative strengths of the signals radiating from the crack along the various ray paths.