On the Detachment of a Rigid Inclusion from an Elastic Matrix

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Abstract
In many materials, such as ductile metals and some polymers, nucleation of voids at weakly adhered inclusions and grains can initiate the fracture process. Accordingly, we consider a rigid spherical inclusion at the center of, and completely adhered to, a much larger sphere of linearly elastic isotropic material. The adhesive bond is assumed to be weak, and the matrix sphere is subject to uniform fixed radial stress on its outer surface. The criterion of detachment is investigated. Our approach follows that of the classical Griffith analysis for the centrally cracked plate, and our results appear to be new. In particular, a relation is derived giving the critical inclusion radius at which detachment is predicted to occur under a given stress. For example, this radius is found to depend inversely on the square of the applied stress.

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