On the elastic-viscoplastic proportional combined twist and stretch of a circular bar of rate-sensitive material

The elastic-plastic behaviour of a solid circular bar made of a homogeneous, isotropic and nonhardening material but of a rate-dependent type, subjected to different proportional deformation programmes of twist and stretch, is analysed. In this investigation the material is assumed to yield according to the von Mises criterion and then to follow a rate-dependent post-yield constitutive law of the Perzyna type. Four radial paths in the angte-of-twist and axial-stretch plane were investigated. For each deformation path the numerical solution of the governing system of quasi-linear partial differential equations gave the corresponding loading path and the radial variation of the stress field at selected times. This study complements that of S. A. Meguid and J.D. Campbell (1979) which considered mainly nonproportional deformation paths. In this work residual stress profiles were also calculated, based upon instantaneous unloading after various amounts of deformation. Comparison with predictions of a rateindependent theory for a limiting state, where elastic strains are negligible, is made. Over a considerable range, the loading paths beyond the initial yield were nearly straight, at the elastic slope. The load trajectory then bends over and approaches a point on the limit-state locus. The results showed that the approximate procedure of increasing the flow stress by an empirically determined factor corresponding to a mean plastic strain-rate gave a good estimate for the limit-state stresses.