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 pla stic models with all objective corotational stress rates and other known ob jective stress rates by virtue of the self-consistency criterion: the hypoe lastic formulation intended for elastic behaviour must be exactly integrabl e to deliver a hyperelastic relation. The finite simple shear response of t his model has been studied and shown to be reasonable for both shear and no rmal 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 foreg oing two kinds of idealized models, in particular the well-known Swift effe ct, in torsion of thin-walled cylindrical tubes. A complete. rigorous analy sis 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 plast ic case. It is shown that the simple idealized kinematic hardening model wi th the logarithmic rate, which uses only two classical material constants, i.e., the initial (tensile) yield stress and the hardening modulus, may arr ive at satisfactory explanation for and reasonable accord with salient feat ures of experimental observation. (C) 2001 Elsevier Science Ltd. All rights reserved.