Crack-microcrack interactions in dynamical fracture

We address the interaction of fast moving cracks in stressed materials with microcracks on their way, considering it as one possible mechanism for fluctuations in the velocity of the main crack (irrespective whether the microcracks are existing material defects or they form during the crack evolution). We analyze carefully the dynamics (in two space dimensions) of one macrocrack and one microcrack, and demonstrate that their interaction results in a large and rapid velocity fluctuation, in qualitative correspondence with typical velocity fluctuations observed in experiments. In developing the theory of the dynamical interaction we invoke an approximation that affords a reduction in mathematical complexity to a simple set of ordinary differential equations for the positions of the crack tips; we propose that this kind of approximation has a range of usefulness that exceeds the present context.