Diffraction of transient horizontal shear waves by a running crack at the interface of two bonded dissimilar elastic solids.

Abstract

This paper deals with the problem of diffraction of horizontally polarized shear waves of arbitrary profile by a running crack located at the interface of two-bonded dissimilar elastic solids. A set of moving coordinate systems attached at the center of the running crack and a new time parameter are employed to obtain the basic equations of motion for two dissimilar elastic half spaces. By the use of Laplace and Fourier transforms we reduce the problem to a pair of dual integral equations. The solution to the dual integral equations is expressed in terms of a pair of Fredholm integral equations of the second kind having the kernel of a finite integration. Dynamic stress intensity factor for an incident wave with a step function profile is obtained as a function of the speed of crack propagation, the angle of incidence, the material properties, and time, and is shown graphically.