Elastic-Plastic Tension-Torsion in a Circular Bar of Rate-Sensitive Material

A theoretical and numerical investigation is made of the behavior of a circular bar of elastic-viscoplastic material subjected to either proportional or nonproportional straining in tension and torsion. The tensile properties of the material are assumed to be adequately represented by the empirical formula of Bodner and Symonds, which is based on experimental results for mild steel. The analysis employs Perzyna’s generalization of von Mises’ yield criterion, and the associated plastic flow rule. Elastic compressibility is taken into account. The stresses, strains, and loading paths are determined for four prescribed straining paths; the results were obtained by solving numerically, using Crout’s method with partial pivoting, a system of six simultaneous quasi-linear partial differential equations of hyperbolic type. Closed-form analytical solutions are also obtained for the stresses, load, and torque corresponding to fully plastic conditions; interaction curves are plotted relating load and torque under these conditions, for quasi-static straining and for a range of finite effective strain rates.