Stress gradient effects on the nucleation and propagation of cohesive cracks

Abstract

International audienceThe aim of the present work is to study the nucleation and propagation of cohesive cracks in two-dimensional elastic structures. The crack evolution is governed by Dugdale’s cohesive force model. Specifically, we investigate the stabilizing effect of the stress field non-uniformity by introducing a length l which characterizes the stress gradient in a neighborhood of the point where the crack nucleates. We distinguish two stages in the crack evolution: the first one where the entire crack is submitted to cohesive forces, followed by a second one where a non-cohesive part appears. Assuming that the material characteristic length dc associated with Dugdale’s model is small in comparison with the dimension L of the body, we develop a two-scale approach and, using the methods of complex analysis, obtain the entire crack evolution with the loading in closed form. In particular, we show that the propagation is stable during the first stage, but becomes unstable with a brutal crack length jump as soon as the non-cohesive crack part appears. We also discuss the influence of the problem parameters and study the sensitivity to imperfections

Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method

“…A major issue in fracture mechanics is how to model the initiation of a crack in a sound material, see [1][2][3][4]. If one uses Griffith criterion like in [5,6] or cohesive force models like in [7,8], the main difficulty is to compute with a good accuracy mechanical quantities like the energy release rate associated with a crack of small length which appears at the tip of a notch, see [9][10][11]. The classical finite element method leads to inaccurate results because of the overlap of two singularities (one due to the tip of the notch, the other due to the tip of the crack) which cannot be correctly captured, see [12][13][14].…”