Configurational stability of a crack propagating in a material with mode-dependent fracture energy -- Part II: Drift of fracture facets in mixed-mode I+II+III

TL;DR

This paper extends previous stability analyses of mixed-mode crack propagation by including a small mode II component, predicting drift of fracture facets along the crack front, which aligns with experimental observations.

Contribution

It introduces the analysis of crack front drift caused by a small mode II load in mixed-mode I+II+III propagation, enhancing understanding of fracture facet behavior.

Findings

Instability modes drift along the crack front with mode II presence.

Heuristic dependence of critical energy-release-rate on mode III/I ratio improves theory.

Prediction of crack facet drift matches experimental observations.

Abstract

In earlier papers (Leblond et.al., 2011, 2019), we presented linear stability analyses of the coplanar propagation of a crack loaded in mixed-mode I+III, based on a "double'' propagation criterion combining Griffith (1920)'s energetic condition and Goldstein and Salganik (1974)'s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the "threshold'' value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.