Deformation of an Isotropic Plate with Periodic System of Curvilinear Holes and Plasticity Bands

Abstract

By the method of singular integral equations, we solve a plane elastoplastic problem of fracture mechanics for an isotropic plane with an infinite series of curvilinear holes and plasticity bands at their tips. We study the influence of the shapes of smooth holes and the radii of rounding of the contours at their tips on the opening displacements and lengths of the plasticity bands. The solutions of the corresponding problems for semiinfinite bilateral rounded notches whose tips serve as the origins of plasticity bands are obtained by the limit transition in the case where the relative distance between the holes tends to zero. On the basis of the deformation criterion of fracture and solutions of the periodic elastoplastic problem, we approximately determine the strength of rectangular specimens with bilateral U-shaped notches.