Configurational Stability of a Crack Propagating in Mixed-Mode I + II + III

Abstract

In some previous papers, we presented some linear stability analyses of the coplanar propagation of a crack loaded in mixed-mode I + III, using a propagation criterion combining a Griffith-type energetic condition and Goldstein and Salganik’s “principle of local symmetry”. In the last one, the local value of the fracture energy was no longer considered as a constant but heuristically permitted to depend upon the ratio of the local mode III to mode I stress intensity factors. As a result, a much improved agreement of theory and experimental observations was obtained for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar propagation becomes unstable. This analysis is extended here to the situation, of considerable practical significance, where a small additional mode II loading component is present in the initially planar configuration of the crack. This component induces a small, general kink of this crack from the moment it is applied. The main novelty resulting from its application is that the instability modes, present above the threshold, must drift along the crack front during its propagation. It is hoped that this prediction will be useful to theoretically interpret a number of experiments where such a drifting motion was indeed observed but left unexplained.