Interaction of SH-waves with a finite crack in a half-space

Abstract

The diffraction of time harmonic antiplane shear waves by a finite length crack embedded in a half-space is considered. Based on the qualitatively similar features of cracks and dislocations, with the aid of image method, the dislocation density function as well as the stress field due to such dislocations are expressed by a system of singular integral equations. These equations with kernels containing Bessel functions can be solved by Galerkin numerical scheme. As the crack is nearly in contact with the free surface, the problem can be regarded as the diffraction of elastic waves by an edge crack. The difference between numerical solutions for two types of boundary conditions, free of traction and clamped surface, is examined. Graphical results for the dynamic stress intensity factors as functions of waves number, angle of incidence and position of the crack are presented.