Separation at a circular interface under biaxial load

This paper is concerned with the plane problem of the decohesion of a smooth circular elastic inclusion from an unbounded elastic matrix subject to a remote biaxial load. The phenomenon of brittle decohesion is treated as a problem of bifurcation of equilibrium separation at the inclusion-matrix interface. In accordance with other cohesive zone type models the interface is characterized by a constitutive equation relating tractions across the interface to the displacement discontinuity that develops there. The specific form considered in this work is the physically based nonlinear force law of Ferrante, Smith and Rose that couples the normal component of displacement jump to the normal component of interface traction and which requires a characteristic length for its prescription. Under decreasing values of characteristic length to inclusion radius ratio, three types of separation behavior (ductile decohesion, brittle decohesion, closure) can occur provided the remote load, interface strength and elastic moduli of inclusion and matrix are within the required bounds. Within this context of interfacial separation, the phenomenon of void nucleation is briefly examined and a connection is made between the classical nucleation criteria of critical interfacial stress and critical energy release and the criteria for ductile and brittle decohesion. Interaction effects are analysed in an approximate way by considering the effects of decohesion on a hypothetical, rigidly bonded inclusion with the same elastic moduli as the matrix.