Scattering of elastic waves by a rectangular crack in an anisotropic half-space

Abstract

The scattering of elastic waves by a rectangular crack in a half-space of arbitrary anisotropy is considered. The application in mind is ultrasonic testing of thick-walled anisotropic components where the crack is close to a planar back surface. The orientation of the crack and the back surface may be arbitrary relative to the anisotropy. The scattering problem is formulated as a hypersingular integral equation for the crack-opening-displacement (COD) by means of the half-space Green’s tensor. The integral equation is solved by expanding the COD in a double series of Chebyshev functions with the correct behavior along the crack’s edges. Insertion into the integral equation and projection onto the same set of functions result in a linear system of equations for the expansion coefficients appearing in the representation of the COD. The transmitting transducer is modeled by the traction beneath it on the scanning surface and the incident field may then be calculated. An electromechanical reciprocity relation is used to model the receiving transducer. Numerical examples are included which show the influence of the anisotropy and especially the presence of a nearby planar back surface.