Interface crack loaded by a time-harmonic plane wave

In this paper, the two-dimensional problem of a finite crack along the interface between two dissimilar solids loaded by a plane wave is considered. Through use of the Fourier transform method, the boundary value problem of wave scattering is reduced to a vectorial Cauchy singular integral equation for the dislocation density on the crack face. A Jacobi polynomial technique is then used to solve the integral equation numerically. Crack opening displacements and stress intensity factors are obtained for various incident frequencies and incident angles. It is found that the crack faces interpenetrate each other near the crack-tips, and the crack-tip singular fields are oscillatory. The oscillatory index is the same as that for an interface crack under static loading, which can be expressed by the second Dundurs bimaterial constant. For practical purposes, an engineering approximation is proposed to remedy these pathological behaviors near the crack tips.