Dynamic branching, arresting of rupture and the seismic wave radiation in self-chosen crack path modelling

Abstract

We simulate spontaneous mode II crack propagation for which the path is dynamically self-chosen. Our main interests are in the formation of the branching path under the influence of self-radiating wave stresses, and in the resultant seismic wave radiation. For these purposes, we adopt the elastodynamic boundary integral equation method (BIEM), which does not impose any constraints on the crack path. We consider a crack subjected to biaxial compression, on which Coulomb friction acts and we determine the extension and the direction of crack growth from a critical shear stress criterion. Our analysis shows that the crack tip bifurcates into two branches at the high-speed propagation stage due to the stress wave localization near the crack tip. Each of the two branches is generated in compressive and tensile stress regions around the propagating tip. Under the same friction coefficient different normal stresses cause different friction levels on them and that results in increasing their bending angles asymmetrically. If the angle of bending exceeds a threshold under biaxial compression, the stress to be released on the curved crack branch becomes negative. Therefore, the growth of such branch is arrested after increasing the bending angle. We then synthesize its waveforms to find phases associated with the dynamic branching. We compare them with those emitted by two planar crack models for which the growths are arrested by inhomogeneities in the fracture strength or the pre-stress state: little effect appeared from the branching characteristics in the waveforms. This is because the curved branches themselves make little contribution to the wave radiation due to the negligible slip velocity.