Large strain responses of elastic-perfect plasticity and kinematic hardening plasticity with the logarithmic rate: Swift effect in torsion

A new Eulerian rate type elastic-perfectly plastic model has recently been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among the objective elastic-perfectly plastic models with all objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The finite simple shear response of this model has been studied and shown to be reasonable for both shear and normal stress components. On the other hand, a kinematic hardening plasticity model may be formulated by adopting the logarithmic rate. The objective of this work is to further study the large deformation responses of the foregoing two kinds of idealized models, in particular the well-known Swift effect, in torsion of thin-walled cylindrical tubes. A complete, rigorous analysis is made for the orders of magnitude of all stress components. A closed-form solution is obtained for the kinematic hardening plastic case, and an analytical perturbation solution is derived for the elastic-perfectly plastic case. It is shown that the simple idealized kinematic hardening model with the logarithmic rate, which uses only two classical material constants, i.e., the initial (tensile) yield stress and the hardening modulus, may arrive at satisfactory explanation for and reasonable accord with salient features of experimental observation.