Two coplanar griffith cracks under shear loading in an infinitely long elastic layer

Abstract

We consider the problem of determining the stress distribution in an infinitely long isotropic homogeneous elastic layer containing two coplanar Griffith cracks which are opened by internal shear stress acting along the lengths of the cracks. The faces of the layer are rigidly fixed. The cracks are located in the middle plane of the layer parallel to its faces. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations with a cosine kernel and a weight function. The triple integral equations are solved exactly. Closed form analytical expressions are derived for the stress intensity factors, shape of the deformed crack, and the crack energy. Solutions to some particular problems are derived as limiting cases. Numerical results are presented in the form of graphs.