Dynamic Shear Fracture at Subsonic and Transonic Speeds in a Compressible Neo-Hookean Material Under Compressive Prestress

Abstract

A crack driven by shear forces translating on its surfaces grows in an isotropic compressible neo-Hookean material that is initially in uniform compression. The material replicates a linear isotropic solid at small deformations, and preserves as a limit case for all deformations the incompressibility that occurs in the linear case when Poisson’s ratio becomes 1/2. A plane-strain steady state is assumed such that the crack and surface forces move at the same constant speed, whether subsonic, transonic, or supersonic. An exact analysis is performed based on superposition of infinitesimal deformations upon large, both for frictionless crack surface slip, and slip resisted by friction. The pre-stress induces anisotropy and increases the Rayleigh, rotational and dilatational wave speeds from their classical values. A positive finite fracture energy release rate arises for crack speeds below the Rayleight value and at two transonic speeds. In contrast, the transonic range in a purely linear analysis exhibits only one speed. It is found that friction enhances fracture energy release rate, and that compressive pre-stress enhances the rates for small crack speeds, but decreases it for speeds near the Rayleigh value.