A penny-shaped crack in a material which is ideally elastic-plastic has been envisaged with the assumption that the plastic zone forms a very thin layer surrounding the crack. The Dugdale hypothesis has been adapted and thus the problem has been reduced to that uf an elastic semi-space with properly modified boundary conditions. The entire energy absorbed in the process of creation of a new surface is associated with the work expanded in irreversible plastic deformation, the work of cohesive forces being neglected. The displacements of the crack surfaces are calculated as well as the plastic energy dissipation and the fracture criterion is discussed.
The shape uf the crack, obtained here, differs considerably from !hat predicted by the theory of elasticity, particularly at the crack tip. The differences in the values of the critical pressure calculated from the Griffith--Sack-Sneddon formula and those obtained by use of the equations derived here are also significant. It is shown that for macro-cracks when crack radius I~ is not too small the following formula holds Pcrit = [ffE(dWp/dA)crit/2(1 -k'2)'~] Y2 which agrees with the Orowan--Irwin modification of Griffith's theory; (dWp/dA)cri t denotes the plastic work per unit area uf new surface, dissipated in the course of loading before fracture.
The results of this paper hold for the so called 'quasi-brittle' solids. Two schemes of loading are considered: 1. pressure applied on the crack surfaces and 2. applied at infinity. Attention is paid to a slightly different mechanism of fracture in buth the cases.