On the nucleation of cavities in planar elasticity

Cavity formation at an inhomogeneity is examined by analysing the problem of a plane circular elastic inclusion embedded in an unbounded elastic matrix subject to remote equibiaxial, tensile or pure shear loading. Within the framework of infinitesimal strain kinematics, nonlinear behaviour is confined to an interfacial cohesive zone characterized by a nonlinear interface force-interface separation law requiring a characteristic length for its prescription. Equilibrium solutions for symmetric and non-symmetric cavity shapes (and their associated interfacial tractions) are sought by approximation of the governing interfacial integral equations derived from the Boussinesq-Flamant solution to the problem of a point force operative at a point of a boundary. For an interval of values of characteristic length-inclusion radius ratio only a symmetric cavity will form under increasing remote load. For other parameter intervals the existence of a non-symmetric cavity is studied by performing a local bifurcation analysis about the symmetrical equilibrium state. A global, post bifurcation analysis is carried out by analysing the approximate equations computationally. Stability of equilibrium states is assessed according to the Hadamard stability definition. The complexity of cavity nucleation phenomena is revealed through the prediction of a diversity of behaviour ranging from the gradual formation of a symmetrical cavity to the gradual or abrupt formation of a non-symmetrical cavity coincident with the rigid displacement of the inclusion within the cavity. A brief, critical examination of the classical nucleation criteria (critical interfacial stress, critical energy release) is undertaken as well in light of the results of the analysis.