Diffraction of elastic waves by a sub-surface crack (in-plane motion)

Abstract

A rigorous theory of the diffraction of time-harmonic elastic waves by an arbitrarily oriented, cylindrical, stress-free crack of finite width embedded in a semi-infinite elastic medium is presented. The incident wave is taken to be either a P wave, an SV wave, or a Rayleigh wave. The resulting boundary-value problems for the unknown jump in the particle displacement across the crack are solved by employing the integral-equation method in combination with the Galerkin method. Numerical results are presented in the form of scattering cross sections, normalized power scattering characteristics, dynamic stress intensity factors, and Rayleigh wave transmission and reflection coefficients, for a range of geometrical parameters.