Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks

Abstract

Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks are considered. The work extends the earlier analysis of 2-D crack-microcrack interactions to the 3-D configurations.

After analysing simple “elementary interaction events” (involving only one microcrack) we solve the interaction problem for a number of sample arrays (containing up to 50 microcracks)-realizations of certain microcrack statistics.

Statistical aspects of the problem are examined. The interaction effects are found to fluctuate, even qualitatively (from shielding to amplification) along the crack front: the intervals of reduced stress intensity factors (SIFs) alternate with local peaks of SIFs that enhance local front advances. Thus, no statistically stable effect of stress shielding is found (at least, for the microcrack statistics considered): the “toughening by microcracking”, if it exists, may be due to a statistics of the microcrack centers which is “biased” towards shielding configurations or to expenditure of energy on nucleation of new microcracks, rather than elastic interactions with them. Similarly to the 2-D case, stochastic asymmetries in the microcrack field produce noticeable “secondary” modes on the main crack (i.e., modes II and III under mode I loading); this may be partially responsible for crack kinking and an irregular crack path.

The “short range” interactions (several microcracks closest to the main crack tip) play a dominant role. Their impact on the main crack is quite sensitive to the individual microcrack locations and cannot be adequately reproduced by modelling the “short range” microcracking zone by an “effective” elastic material of reduced stiffness.

The interaction effects in 3-D are found to be weaker than in 2-D.