Constant-speed propagation of a penny-shaped interface crack under pure torsion

Abstract

A transient problem of propagation of a penny-shaped crack in the plane interface between two different media is solved. The body is twisted by a torque at infinity that tends to shear the bond between the two media. A small initial flaw is assumed to expand uniformly in the plane of the interface at a speed less than the smaller of the SH wave speeds of the two media. The solution is carried out by a combination of two methods: a method of rotational superposition of two-dimensional solutions and the Smirnov-Sobolev method of self-similar potentials for twodimensional problems. The dynamic stress intensity factor and the crack tearing displacement are determined. It is found that the stress field near the crack tip has a square root singularity. The maximum crack-tearing displacement is found to occur at close to three-fourths of the way from the crack origin to the running crack tip.