Decohesion at a circular interface

The present investigation is concerned with the problem of the decohesion of a plane circular elastic inclusion from an unbounded elastic matrix subject to a remote biaxial load. Brittle decohesion is treated as a problem of the bifurcation of equilibrium displacement jump 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 which develops there. The specific form considered in this work is a physically based exponential force law which couples the normal component of displacement jump to the normal component of interface traction and, which requires a characteristic length for its prescription. Bifurcation of equilibrium can be shown to occur for decreasing values of the ratio of characteristic length to inclusion radius provided the remote load, interface strength and elastic moduli of inclusion and matrix are within certain bounds. By studying the character of the displacement discontinuity at the interface, as well as matrix and inclusion stress and deformation fields, a more detailed understanding of the mechanics of stress redistribution during the debonding process may be obtained.