Stress singularity near a crack tip terminating at a nonideal interface

Modelling problems for a semi-infinite crack terminating at a bimaterial interface are considered. Instead of the "ideal contact" interfacial conditions, usually done, we have introduced a thin intermediate zone between the materials, and we model it as a thin elastic region the width of which changes according to an exponential law. Depending on parameters defining the thickness of the intermediate zone, we discuss the displacement distribution and stress field at the neighbourhood of the crack tip. It is shown that the geometry of the thin region influences essentially the state of strain and stress not only qualitatively (the character of the stress singularity near the crack tip), but also quantitatively (the increase of a number of singular terms in the asymptotics).