Evolution of cylindrical void and elastoplastic constitutive description

Assuming the voids in a pearlitic steel are cylindrical, a cylindrical void-cell model is presented. From the analysis of the void-cell model a void evolution equation is obtained. Defining a new intrinsic time and the softening function related to the void evolution, and introducing them into an endochronic constitutive equation, the constitutive equation involving void evolution is derived. The corresponding numerical algorithm and the finite element approach are offered, which are applied to analyse the stress and porosity distributions of the unnotched and notched cylindrical specimens of a pearlitic steel. The analytical result of the unnotched specimen shows that the porosity of the specimen increases with the increase of its plastic deformation, which is consistent with the experimental data. The analytical result of the notched specimen reveals that the stress of considering void evolution is larger than that of no considering void evolution. Both the stress and porosity reach their maximum at the notch root. The latter agrees with the experimental result.