Quasistatic problem of a non-homogeneous elastic layer containing a crack

A nonhomogeneous elastic layer is weakened by an infinite, rectilinear crack separating two layers of different elastic materials. The boundary surfaces of the layer are rigidly clamped, and the crack surfaces are loaded by arbitrary forces satisfying the conditions of antiplane state of strain. Two cases are considered - namely, the case where the crack and its load propagate at a constant velocity along the horizontal axis, and the case where the load is a harmonic function of time. In both cases exact values of the stress intensity factor for arbitrary loading (arbitrary load amplitude) of the crack are given. In the limiting cases, solutions of static problems are obtained. The results are illustrated by particular solutions concerning the cases where the crack edge load (or its amplitude) is constant along its entire length.