Plastic waves of combined stress based on self-consistent slip models

Abstract

A computational procedure for obtaining the macroscopic, rate-independent stress-strain behavior of a polycrystalline metal from the plastic flow characteristics of the slip systems of a large number of randomly oriented single crystals is extended to cases of combined stress loading. The procedure, based on the simplex method of linear programming, is applied to the computation of simple wave solutions for combined longitudinal and torsional plastic wave propagation in thin-walled cylindrical tubes. Solutions based on self-consistent slip models for independent, isotropic and latent hardening of FCC metals are compared with experimental results reported previously for the case of aluminum tubes subjected to static torque followed by longitudinal impact. These comparisons indicate considerably better agreement between theory and experiment than has been obtained previously for theories based on plasticity models that incorporate smooth yield surfaces, normality, and a hardening law. For step loading, such theories predict a solution consisting of a fast simple wave followed by an intermediate constant state region, a slow simple wave, and a final constant state region. The principal new feature of solutions based on selfconsistent slip models is that there is no intermediate constant state region, in agreement with the results of experiments.