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.

Budreck, D. E., & Achenbach, J. D. (1989). Three-dimensional elastic wave scattering by surface-breaking cracks. The Journal of the Acoustical Society of America, 86(1), 395–406.