The affect of interfacial shear on cavity formation at an elastic inhomogeneity

Abstract

Cavity formation at an inhomogeneity is examined by analyzing the problem of a plane circular elastic inclusion embedded in an unbounded elastic matrix subject to remote equibiaxial loading. Nonlinear behavior is confined to an interfacial cohesive zone characterized by normal and tangential interface forces which generally depend on interfacial displacement jump components and which require a characteristic length, an interface strength, and a shear stiffness parameter for their prescription. Infinitesimal strain equilibrium solutions for rotationally symmetric and nonsymmetric 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 normal and tangential point force operative at a point of a boundary. For fixed constitutive parameters and relatively small remote loads only rotationally symmetric cavities will form. For other parameter regions the existence of nonsymmetric cavities is studied by performing a local bifurcation analysis about the rotationally symmetric equilibrium state. A global, post bifurcation analysis is carried out by analyzing the approximate equations computationally. Stability of equilibrium states is assessed according to the Hadamard stability definition. Results indicate that increasing the interfacial shear stiffness can (1) under certain circumstances transform brittle nucleation to ductile nucleation and (2) delay the formation of a nonsymmetrical cavity. However, nonsymmetrical growth cannot be completely suppressed, i.e., ultimately a nonsymmetric cavity will form coincident with the rigid displacement of the inclusion within it.