Development of Plastic Strips in the Process of Shear Deformation of a Body with Narrow Rectangular Slot

Abstract

We obtain analytic solutions of the antiplane problems for a body with semiinfinite rectangular slot in the elastic and elastoplastic (single-strip model of the zone) statements. The load is given in the form of the asymptotics of stresses at infinity equal to the asymptotics of a semiinfinite crack of longitudinal shear expressed via the stress intensity factor. It is established that the development of plastic strips starts in the direction of continuation of the bisectors of the notch angles. Their lengths of the plastic strips are found as functions of the stress intensity factor.To decrease the hazard of sudden fracture and provide the reliable operation of mechanical structures under high loads, it is customary to use materials characterized by the presence of plastic deformations. Hence, it is of interest to investigate the elastoplastic stress-strain state (SSS) of bodies and structural elements. At present, the main efforts of the researchers in the field of fracture mechanics are focused on the analysis of the SSS of bodies weakened by cracks, which are, as a rule, modeled by mathematical cuts. It is assumed that, prior to loading, the distance between the crack faces is equal to zero and the faces do not interact. The crack tip is regarded as a cuspidal point. An important continuation of these investigations is connected with the study of the distributions of elastoplastic strains near rectangular slots, which turn into a classical crack in the case of infinitesimally small width [1,2].In the present work, we study the development of plastic strips from the vertices of a narrow rectangular slot under the influence of shear loads applied at a great distance from its end faces. To analyze the SSS near the vertices of the slot, we assume that it is semiinfinite. The problem of development of continual plastic zones from the vertex of a semiinfinite rectangular notch was solved in [2]. In the cited work, the authors determined in particular, the shape of the plastic zones. Moreover, it was shown that, in the initial stage, the length of the zone is maximal on the continuation of the bisector of the notch angle, and its direction gradually approaches the axis of the notch as the load increases.We determine the direction of propagation of a single plastic strip from the vertices of a semiinfinite slotin an infinite body and investigate its development under quasistatically increasing shear loads (Fig. 1). The material of the body is assumed to be perfectly elastoplastic with yield limit in shear k .