Theoretical Study of the Conditions and the Mechanism of Shear Crack Acceleration towards the Longitudinal Wave Velocity

The question about physically admissible velocity of dynamic crack growth is of significance to safety engineering as well as to earthquake dynamics. Recent researches including numerical simulations, experimental observations and the analysis of strong earthquakes have shown a possibility of propagation of shear cracks in supershear regime, namely at velocities comparable with dilatational wave speed. The present paper is devoted to the theoretical (numerical) study of some fundamental aspects of this problem. It is shown that development of a sub Raleigh shear crack is connected with a vortex traveling ahead of the crack tip at a shear wave velocity. The stress concentration area ahead of the crack tip revealed by different authors (Burridge, Andrews, Geubelle, Rosakis and others) is connected with this vortex. Acceleration of a shear crack towards the longitudinal wave velocity is concerned with formation of a daughter crack by the mechanism of shearing (the daughter crack is formed in the center of vortex). Analysis of sub Raleigh to intersonic transition has shown that development of shear cracks is self-similar and depends on dimensionless parameters.