STABLE AND UNSTABLE SOLUTIONS FOR BRIDGED CRACKS IN VARIOUS SPECIMENS

This paper reviews the formulation of the problem of a bridged crack in an elastic medium as an integral equation, noting explicit forms for specimens of various common shapes. Numerical methods are provided for the convenient and efficient self-consistent solution of the integral equation when the bridging tractions, p, are a function of crack opening displacement, u, rather than an explicit function of position in the crack. Methods are presented for determining physically and computationally unstable crack configurations for various forms of p(u), including functions possessing a peak. Knowledge of both stable and unstable solutions is essential to demarking the transition from noncatastrophic (or ductile) failure to catastrophic (or brittle) failure.