A General Solution of the Problem of Elastic-Wave Scattering by a Plane Crack

The 3D problem of elastic-wave scattering by cracks in a homogeneous isotropic medium is considered. Using the method of Green’s function and specially introduced auxiliary functions (potentials), it is shown how, in the general case, for plane cracks, the boundary conditions can be divided into two independent parts, one of which is a system of two differential equations, the solution of which leads to Rayleigh waves on the crack surfaces, and the second of which includes one differential equation, reduced to a similar equation for acoustic-wave scattering by an absolutely rigid inclusion. Using as an example scattering by a disk-shaped crack, it is shown that the expressions for the scattered fields can be reduced to quadratures, which is important, e.g., for the study of crack detection by ultrasonic methods of flaw detection.