Stress and Strain Analysis of Rotating Annular Disks Obeying a Pressure-Dependent Yield Criterion

Abstract

The Drucker - Prager yield criterion is used in conjunction with its associated flow rule to find the elastic/plastic stress and strain distributions within the rotating annular disks under plane stress conditions. The main distinguished feature of the model, as compared to typical models used for analysis of rotating disks, is that the material is plastically compressible. Also, in contrast to many models used for analysis of rotating disks, the constitutive equations involve strain rates rather than strains. However, using an approach proposed elsewhere the solution for strain rates is reduced to one non-linear ordinary differential equation and two linear ordinary differential equations. These equations can be solved one by one, which significantly simplifies the numerical treatment and increases the accuracy of numerical solution. The strain solution requires a numerical technique to evaluate ordinary integrals. An example is presented to illustrate the general solution. The primary objective of this paper is to examine the effect of the parameter that controls the deviation of the Drucker-Prager yield criterion from the von Mises yield criterion and the geometric parameter that controls the profile of hyperbolic discs on the stress distribution at loading and the residual stress distribution.