Variational formulation based analysis on growth of yield front in high speed rotating solid disks

Abstract

The present study investigates the growth of elastic-plastic front in rotating solid disks of non-uniform thickness having exponential and parabolic geometry variation. The problem is solved through an extension of a variational method in elastoplastic regime. The formulation is based on von-Mises yield criterion and linear strain hardening material behavior. Assuming a series expression of the unknown variable, the solution of the governing equation is obtained using Galerkin’s principle. The approximate solution further needs an iterative method to locate the growth in the yield front. The paper reports von-Mises stress distribution in the disk at various load steps starting from the initiation of yielding till the attainment of fully plastic state. Effect of geometry parameters on the stress state of the disk is studied and the relevant results are reported in dimensionless form.

Keywords: Variational method, von-Mises stress, Yield front, Limit angular speed.