Diffraction of Antiplane Shear Waves by an Edge Crack

Abstract

The diffraction of time harmonic antiplane shear waves by an edge crack normal to the free surface of a homogeneous half space is considered. The problem is formulated in terms of a singular integral equation with the unknown crack opening displacement as the density function. A numerical scheme is utilized to solve the integral equation at any given finite frequency. Asymptotic solutions valid at low and high frequencies are obtained. The accuracy of the numerical solution at high frequencies and of the high frequency asymptotic solution at intermediate frequencies are examined. Graphical results are presented for the crack opening displacement and the stress intensity factor as functions of frequency and the incident angle, Expressions for the far-field displacements at high and low frequencies are also presented.