Modeling of dynamic branching of a longitudinal shear crack at an inclusion

Abstract

Mathematical modeling of branching of the leading edge of a longitudinal shear crack on a porous inclusion is proposed. The leading edge of the crack is approximated by the δ-neighborhood of the plastic deformation of the material with the front of longitudinal or shear waves, at which the longitudinal or transverse velocities break when passing through the leading edge of the crack. Expressions are obtained and graphs of the relative intensity of the leading edges of the reflected cracks of longitudinal and transverse shear and the conditions for the generation of reflected cracks depending on the angle of intersection of the crack with inclusion and physical parameters of the material are constructed.