Mass-conserved morphological evolution of hypocycloid cavities: a model of diffusive crack initiation with no associated energy barrier

Abstract
An analytic proof is developed for an energy variation theorem which states that in a homogeneous isotropic linear elastic solid under equibiaxial loading, a cusp-shaped hypocycloid cavity satisfying the Griffith condition G ≽ 2γ can be formed through mass-conserved shape evolution with no associated energy barrier. In this process, the sum of the strain energy and the surface energy continuously decreases as the hypocycloid changes from a perfectly circular hole to an array of cusp cracks. The hypocycloid evolution provides a unified model of diffusive crack formation from Griffith cracks to cycloid surfaces; the latter has been used recently to model stress driven surface evolution in heteroepitaxial thin films. A number of interesting observations are made regarding features that are common to the entire hypocycloid family. It is shown in Appendix A that the assumption of a finite energy release rate at diffusive crack initiation leads to the conclusion that the only kind of geometric singularities which may be formed by stress controlled surface diffusion is a mode I cusp crack exactly satisfying the Griffith equality G = 2γ. If thermal nucleation of dislocations has not occured when such a cusp crack is formed, it is only logical to assume cleavage decohesion at a tension cusp and diffusive trapping of dislocations at a compression cusp.

This publication has 16 references indexed in Scilit: