Determination of the stress intensity factors at the ends of two collinear transverse shear cracks under steady vibrations

Abstract

The solution is obtained by using a method proposed in [2]. The problem reduces to a singular integral equation of the first kind for the complex amplitude of the crack-edge displacement, which is then solved by using the "method of moments" [5]. To improve the convergence of the solution, the behavior of the desired function (the displacement) in the neighborhoods of the crack tips under dynamic loading is taken into account in selecting the kind of basis functions, and the shape of the crack edge shift under the static effect of the load is also taken into account. i. Let us consider an infinite elastic isotropic plane containing two identical collinear slits (cracks) on whose edges a skew-symmetric shear load xGT(x)e ~s' acts (Fig. i). It is assumed that the crack edges are not in contact, there are no volume forces, and T(x) is an even function of x. During the solution it is necessary to satisfy the radiation conditions at infinity and the mixed boundary conditions at y = 0