Steady-state motion of a Mode-III crack on imperfect interfaces

The aim of the present paper is to analyse the behaviour of the stress and displacement fields in the vicinity of the tip of a crack moving along a bi-material interface. For simplicity, we consider a straight interface of infinite extent. We assume that the two phases are separated by a thin layer which is either ‘soft’ or ‘stiff’ compared to the other two phases. We derive the transmission conditions which take into account the material properties of the layer and model the way the load is transferred across the layer from one phase to the other. We assume that the point of interchange in the boundary/transmission conditions coincides with the crack tip that moves along the interface boundary with a constant speed. We develop an integral equation formulation and derive asymptotic formulae for the out-of-plane displacement and the Mode-III stress intensity factor associated with such a motion of the crack inside the interphase layer. The theoretical results are illustrated by numerical examples.