A qualitative comparison of flow rules of pressure-dependent plasticity under plane stress conditions

Abstract

The stresses and strains in a partly plastic hollow disc inserted into a rigid container and subject to thermal loading are obtained under plane stress conditions according to the associated and non-associated flow rules. Both the yield criterion and plastic potential are represented by a conical surface in a three-dimensional space where the principal stresses are taken as Cartesian coordinates. In general, the yield criterion and plastic potential are not identical. Assuming that the yield criterion is given the effect of the plastic potential on the radial distribution of strains is revealed. The associated flow rule and plastically incompressible material are considered as special cases of the general solution. The residual stresses and strains are determined as well. It is shown that reversed plastic flow can occur and the effect of the plastic potential on the radial distribution of residual strains is more pronounced as compared to that at the end of loading.