A possibility of the describing the elastic and elastic-plastic stages of the deformation process up to the beginning of disintegration of a body weakened by a crack in the form of a physical cut is considered. The model of the crack also includes the layer of the material lying on mental continuation of the physical cut in the continuous medium. It is assumed that a plastic region may exist within this layer during the loading process. In case of a normal separation, in contrast with Leonov-Panasuk-Dugdale's model, not only the stresses acting in a direction of the separation, but also in the direction orthogonal to it areconsidered on the crack continuation. To describe the behavior the material during the transition to the plastic region, the model ideally elastic-plastic body and a version of the deformation theory were used, assuming the volumetric change to be linearly elastic. For the model of the ideal elastic-plastic body, Tresca and Mises yield conditions were considered. The plastic region length - external load value relation was compared with the similar relation following from the model of Leonov-Panasuk- Dugdale. It is found, that accounting for elastic compressibility and stress of compression-tension along the direction of the cut results in considerable difference in the distribution of stresses and lengths of the plastic zones in the plane stressed and strained conditions that cannot be accounted for in the frame of Leonov-Panasuk-Dugdale's approach.When using the deformation theory, the elastic-plastic deformation process is assumed beam-like, the directing stress deviator tensor in each point of the layer was fixed by its value, attained at the moment of transition from the elastic to elastic-plastic stage. This assumption made it possible to reduce the problem to statically definable. The components of the pressure of the layer and the external wedging forces as a function of the plastic area length of the layer are determined, the effect of material hardening on the stressed-strained state of the crack trailer area is studied.
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