A comparison of rate sensitive constitutive equations under plane stress conditions

Abstract

Numerical dynamic solutions of the circular hole enlargement problem for a thin plate, due to a constant acceleration imposed at the hole boundary, have been used for comparing different models for describing rate sensitive visco-plastic materials. In the constitutive equations that have been compared, the visco-plastic part of the strain rate is an exponential, linear, cubic and fifth power function of the overstress above the static stress-strain curve. Stress histories and the variation of the plate thickness, at the hole radius, have been computed for different rates of loading, and for a wide range of the parameter describing the visco-plastic behaviour of the material. The relative usefulness of the different models, for a complex state of stress and strain, has been assessed by comparing the numerical solutions for the different models.