Mechanics of crack—microcrack interactions

Abstract

The paper summarizes recent work done by the authors on the mechanics of two- and three-dimensional crack-microcrack interactions. The mechanics of interactions of a crack with large numbers of microcracks (crack–“damage” interactions) is analyzed by directly solving the interaction problem for a number of sample microcrack arrays—realisations of certain microcrack statistics. Statistical aspects of the problem are examined. It is found that the “short range” interactions (several microcracks closest to the main crack tip) play a dominant role. The interaction effects produced by them are highly sensitive to the exact positions of microcracks. The impact of this dominant “short range” zone on the main crack cannot be adequately reproduced by modelling the zone by an “effective” elastic material of reduced stiffness. Due to a high sensitivity effects to the exact positions of microcracks in the “short range” zone, the interaction effects fluctuate, even qualitatively (from shielding to amplification) from one realization of a given microcrack statistics to another; in 3-D configurations, they also fluctuate along the main crack front. Thus, no statistically stable effect of shielding is found (at least, for the microcrack statistics considered which assume random locations of the microcrack centers). The mechanism of “toughening by microcracking”, if exists, may be due to expenditure of energy on nucleation of new microcracks, rather than interactions with them or due to a statistics of the microcrack centers which is “biased” towards shielding configurations. Stochastic asymmetries in the microcrack field produce noticeable “secondary” modes on the main crack (mode II component on the main crack under mode I loading conditions): this may be partially responsible for crack kinking and irregular crack path in brittle microcracking materials. The interaction effects in 3-D are weaker than in 2-D.