Periodic crack problems for an elastic layer

Abstract

The problems of periodic mode I 3 D cracks for an elastic layer are reduced to an integro-differential equation (IDE). The principal part of the IDE is the same as in the classical Griffith problem for one crack in an elastic full space. The periodic system of elliptic cracks, featuring equal spaces between neighboring cracks, lies in the middle plane of the layer. Each crack is parallel to the layer’s faces. Four types of boundary conditions are considered on the layer’s faces (sliding or rigid support, stress-free state, sliding support in between elastic layers). The regular asymptotic method has been applied to solving the problems as it proves effective for some fairly big spaces between cracks as well as for relatively thick layers. The stress intensity factor (SIF) has been calculated for a variety of geometric and mechanical parameters. It was compared to that for the well-known case of a single crack in a layer. It has been shown that the SIF for the crack system can be smaller or greater than that for a single crack depending on the boundary conditions on the layer’s faces.