The Spread of Yield Zone from a Penny-Shaped Crack

Abstract

On the basis of the theory of continuous distribution of dislocations, the extent of spread of plasticity from the rim of a penny-shaped crack and the relative displacement of the two faces of the crack are determined and the analysis is reduced to a mixed boundary value problem in the potential theory. Solutions are obtained for a penny-shaped crack in an infinite elastic-plastic medium under the conditions of uniform tension perpendicular to the plane of the crack and uniform shear stress parallel to it. The change of energy of the system accompanying the infinitesimal crack extension is calculated and discussed. It is shown that if the cohesive force is taken into account we are able to get an unstable crack condition on the energy balance consideration.