Cavitation instabilities in a power hardening elastic-plastic solid

For an infinite, remotely stressed elastic-plastic solid containing an isolated void a state may be reached, in which the void grows without bound, even though the remote stresses and strains are kept fixed. Such cavitation instabilities are determined here for power hardening elastic-plastic solids subject to axisymmetric stress states. The relatively simple analysis for a spherical void under spherically symmetric conditions is first briefly reviewed. Subsequently, the effect of an axisymmetric stress state is studied for the case of a cylindrical void, where the problem is also governed by ordinary differential equations. For a spherical void under axisymmetric stressing cavitation instabilities are determined by a numerical procedure, which couples a finite element solution for an inner region with a perturbation solution for an outer region. It is found that the critical stress levels are significantly increased by deformation hardening.