Plane Stress Crack Tip Field Around a Rapidly Growing Ductile/Rigid Interface Crack

Abstract

Plane stress dynamic crack growth along a ductile/rigid interface is investigated. The ductile material is taken to be ideally plastic and obey the J2 flow theory of plasticity. Under steady-state conditions, the asymptotic structure of the crack-tip stress, velocity and strain fields has been obtained. The study reveals that two types of crack-tip sectors exist, namely uniform and nonuniform plastic sectors and that the stress, strain and velocity fields are bounded (nonsingular) in all sectors. In a uniform sector, the rectangular Cartesian components of the stress, strain and velocity fields are constant, and there is no plastic strain accumulation. In a nonuniform sector, the stress, strain and velocity components at a point depend on the angular position of the point in the crack-tip polar coordinate system and are governed by a system of simultaneous ordinary differential equations. This is a sector plastic strains can accumulate. A general crack-tip sector assembly is obtained for a practical range of crack growth speeds. Several nontrivial families of admissible solutions of the crack-tip fields based on this general assembly of uniform and nonuniform crack-tip sectors are presented and discussed.