Stress gradient plasticity theory development for cyclic and monotonic loading of thin-walled structures: Back-stress, size effect, passivation effect

Abstract

Small scale plasticity behaviour is modelled by strain or stress gradient plasticity models. The stress gradient plasticity theory, proposed by Chakravarthy and Curtin, is a constitutive consideration of the stress gradient that affects the initial flow as well as strain hardening rate. We apply the lower-order stress gradient plasticity model to different monotonic problems and cyclic torsion, under small strain and rotation assumption. The stress gradient can be due to the problem geometry and loading and/or due to passivation. Passivation is considered in different monotonic loadings of classical problems. To use the stress gradient plasticity model in cyclic loading problems, a back-stress model is used and the kinematic hardening is considered. The developed model in microscale plasticity considers dislocation pile-ups, grain size, and dislocation density. The Bauschinger effect is also considered during reverse loading by the consideration of the kinematic hardening. The cyclic torsion of thin copper wires of different diameters is modelled by the developed model. Comparisons with the experimental results and distortion strain gradient plasticity model are also performed. It is shown that the simple developed model can capture the essential microscale plasticity behaviour of metals, with only one length scale parameter.