Elastic-plastic analysis of rotating solid shaft by maximum reduced stress yield criterion

An elasto-plastic rotating solid cylinder under plane strain condition is investigated. The analysis is based on infinitesimal strain theory, maximum reduced stress yield criterion, its associated flow rule and perfectly plastic material behavior. It is assumed that angular velocity is monotonically increasing from 0 to the maximum value and then is monotonically reducing down to 0. In this investigation both loading and unloading phases are considered. It is assumed that angular velocity varies slowly with time, so angular acceleration can be neglected. Under above mentioned assumptions, there is only one non-trivial equilibrium equation in a cylinder.
It is established that with increasing angular velocity four plastic regions appear in a cylinder. The last one forms at angular velocity which exceeds fully-plastic limit. Stresses image points of plastic regions lie on different sides and corners of yield surface. As the angular speed decreases, the whole cylinder behaves elastically again. At particular value of angular velocity secondary plastic flow may starts at the center of cylinder. Replasticization is possible only for sufficiently high maximum angular speed and the entire cylinder may be replasticized. Four secondary plastic regions may appear in the cylinder under unloading. The stresses image points in primary and secondary regions lie on opposite sides and corners of yield surface. In the present analysis it is assumed that the entire cylinder becomes replasticized just at stand-still. In this case only two secondary plastic regions emerge.
Exact solutions for all stages of deformation are obtained. The systems of algebraic equations for determination of integration constants and border radii are formulated. The obtained results are illustrated by the distributions of stresses and plastic strains in the cylinder rotating at different speeds. Presented solutions are compared with known analytical solutions based on Tresca's criterion.