Mode III interfacial crack in the presence of couple stress elastic materials

Abstract

In this paper we are concerned with the problem of a crack lying at the interface between dissimilar materials with microstructure undergoing antiplane deformations. The micropolar behaviour of the materials is described by the theory of couple-stress elasticity developed by Koiter (1964). This constitutive model includes the characteristic lengths in bending and torsion and thus it is able to account for the underlying microstructure of the two materials. We perform an asymptotic analysis to investigate the behaviour of the solution near the crack tip. It turns out that the stress singularity at the crack tip is strongly influenced by the microstructural parameters and it may or may not show oscillatory behaviour depending on the ratio between the characteristic lengths.