Some Problems of Stability and Bifurcation in the Propagation of Plane Cracks

Abstract

This paper addresses some stability and bifurcation problems arising in the study of plane cracks of arbitrary shape. In brittle fracture, when Griffith's law of crack propagation is adopted, the governing equations of the quasi-static extension of a plane crack can be given in the same spirit as in standard plasticity. The description of the rate problem of crack propagation leads to a mathematical formulation of stability or non-bifurcation criteria as in the theory of plastic buckling. This discussion is illustrated analytically here by the example of circular and tunnel cracks in the debonding of a thin film on a rigid substrate.