Elastic–plastic analysis of rotating disks having non-linearly variable thickness: residual stresses by overspeeding and service stress state reduction

Abstract

Two models for evaluation of elastic and elastic–plastic stress and strain in non-linear variable thickness rotating disks, either solid or annular, subjected to such a rotational speed to determine stresses beyond yielding are presented. The first model regards the elastic field and the second concerns the elastic–plastic field, assuming that material hardening is isotropic and follows a most general hardening power-law. In the elastic region, a non-homogeneous hypergeometric differential equation is obtained. Such differential equation, which solves the elastic problem in closed form for non-linear variable thickness disks, with thickness given by the power of a linear function which may define a fourfold infinity of profiles, is integrated in closed form. As concerns the elastic–plastic analysis, first of all the introduction is made of a correlation between equivalent plastic strain and equivalent stress according to Von Mises, which is more general than those known from literature. In the case of isotropic hardening a second-order, non-homogeneous, non-linear differential equation is found, which governs the stress state in the plastic region of the disk. The procedure allows to calculate stress and displacement states in the two regions—plastic and elastic—of the disk subjected to prestressing by overspeeding. Several examples of disks, also prestressed by overspeeding, are considered (annular and solid, convex or concave, and linear tapered disks); the matching of results of the theoretical model and those obtained by means of FEA is very good. Lastly, the residual stress state can be found in a prestressed disk by overspeeding and the stress state in the actual operating condition in the same disk is evaluated.