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Abstract

This work explores the possibility that quick deviations of cracks loaded in mode I+III from coplanarity may be greatly facilitated by inevitable fluctuations of the fracture toughness. The idea is that such fluctuations must induce in-plane undulations of the crack front resulting, because of the presence of the mode III load, in nonzero values of the local stress intensity factor of mode II, implying future local out-of-plane deviations of the crack which might be "unstable" in Cotterell and Rice's sense if the local nonsingular stress parallel to the direction of propagation is positive. Exploration of this idea implies evaluation of the variations of the local stress intensity factors and nonsingular stresses arising from a slight but otherwise arbitrary in-plane perturbation of a semi-infinite crack. These quantities were calculated in works of Gao and Rice, but the evaluation of the nonsingular stresses was incomplete, and is supplemented here by using the theory of 3D weight functions due to Rice and Bueckner. Inspection of the results shows that for in-plane sinusoidal undulations of the crack front of sufficient (though still small) amplitude, the conditions of nonzero local stress intensity factor of mode II and positive local nonsingular stress parallel to the direction of propagation are simultaneously met on some parts of the front, implying the possibility of future local deviations of the crack from coplanarity that are "unstable" in Cotterell and Rice's sense, and thus confirming the idea investigated.

Crack Front Segmentation and Facet Coarsening in Mixed-Mode Fracture

“…While the present results show that the subcritical propagation of segmented cracks is theoretically possible, they do not identify the mechanism and scale of subcritical facet formation. As suggested by a recent LEFM analysis, materials imperfections may contribute to this process [39]. However, this scenario, and even more fundamentally the ability of LEFM to model subcritical facet formation, remain to be explored both computationally and experimentally.…”