Analytical Solution for Strain Gradient Plasticity of Rotating Functionally Graded Thick Cylinders

Abstract

The elastic-plastic deformation of rotating functionally graded (FG) cylinders is investigated based on strain gradient theory. The governing equations are obtained based on the modified von Mises yield criterion, linear work hardening and plane strain assumptions. An analytical solution for the obtained equations is presented by which the deformation, strain and stress components for any point of the cylinder can be obtained. After verification of the formulation by comparing the obtained results with the reported results in the literature, some studies are presented to investigate the effects of cylinder size on the stress distribution and elastic-plastic interface radius of the rotating FG cylinder under internal and external pressure. The effects of the strain gradient coefficient, angular velocity, and the heterogeneity constant of the material are investigated. The results show that increasing the heterogeneity constant of the material and decreasing the cylinder radius lead to increasing the strength of material and decreasing the elastic-plastic interface radius. Moreover, classical theory is compared with this study and the range of the sizes in which both the theories leading to the same results, are defined.