The diffraction of time harmonic antiplane shear waves by a finite-length crack embedded in a half-space was considered. On the basis of the qualitatively similar features of cracks and dislocations, and with the aid of the image method, the dislocation density function as well as the stress field due to such dislocations were expressed as a system of singular integral equations. These equations, with kernels which contained Bessel functions, could be solved by using Galerkin methods. As the crack was almost in contact with the free surface, the problem could be regarded as involving the diffraction of elastic waves by an edge crack. The difference between the numerical solutions for two types of boundary condition (traction-free, clamped-surface) was examined. Graphical results were presented for the dynamic stress intensity factor as a function of the wave-number, of the angle of incidence and of the position of the crack.

Interaction of SH-Waves with a Finite Crack in a Half-Space. J.Y.Huang: Engineering Fracture Mechanics, 1995, 51[2], 217-24