Qualitative and quantitative analysis of the elastoplastic state of a rotating thin disk

Abstract

The task of a rotating disk with a constant small thickness, which is under the action of a uniformly distributed pressure along its contour, was considered. Total deformations are equal to the addition of elastic and plastic ones, since the deformations are quite small. Plastic deformations and stresses are interconnected by the plastic flow rule. A plastically incompressible isotropic body is considered. The condition of continuity of the plasticity function is satisfied. The stress and displacement vectors are continuous at the interface between elastic and plastic zones. When determining the plastic zones, depending on the external parameters, all possible modes of the plasticity condition of the maximum shear stress were considered. Analytical expressions are presented for the external parameters at which the nucleation of plastic zones occurs. The stress hodograph plots, presented in the paper, give a visual representation of the development of plastic zones.