Note on the Energy Release Rate of Simple Crack Models with Finite Jump Discontinuities

Abstract

A spherical flaw model in linear viscoelasticity and a simple double cantilever model were proposed by Williams and Freund respectively, with the hope that they would lead to a qualitatively similar phenomenon as a common crack model. Although both models were very simple, they had jump discontinuities of stress at the crack tip (or the like) at any time. In this paper, a general expression for the energy release rate in such crack models is derived and is evaluated for each model. Also, Nuismer's modified interpretation of Williams' model is discussed. Furthermore, the expressions of a partition for the energy release rate into the usual quasi-static part and a dynamic contribution are evaluated in Freund's model.