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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.

We present a method of solution of a class of fracture problems in the theory of elasticity. The method can be applied to any problem reducible to Poisson's equation, e.g. heat conduction and mass diffusion in solids, theory of consolidation and the like. The novelty of the paper is that we address regions of layered composites with notches, or, in a particular case, with a crack. Within the framework of classical analysis, we apply Fourier and Mellin transforms, 'fit' them together, and reduce the problem to solving a singular integral equation with fixed singularities on a semi-axis. We show the existence and uniqueness of solutions of the equations under consideration, and justify the asymptotics necessary for applications. We show the practical usefulness of the method on the examples of an antiplane problem of fracture mechanics. From our solution, we are able to find the stress intensity factor in the case when a crack tip penetrates a layered composite consisting of 60 layers, and show the limits of applicability of the anisotropic model of such composites.