On the thermodynamically consistent modeling of distortional hardening: A novel generalized framework

Abstract

Many important physical effects of materials undergoing plasticity at the macroscale cannot be captured realistically by isotropic and kinematic hardening only. For instance, the evolution of the texture in polycrystals results macroscopically in a distorted yield surface. This paper deals with adequate hardening models for such a distortion. To be more precise, a novel general frame for finite strain plasticity models is elaborated. To the best knowledge of the authors, it is the first one combining the following features: (1) proof of thermodynamical consistency; (2) decomposition of distortional hardening into dynamic hardening (due to currently active dislocations) and latent hardening (due to currently inactive dislocations); (3) difference of the yield surface’s curvature in loading direction and in the opposite direction. The cornerstone of this model is a new plastic potential for the evolution equations governing distortional hardening. Although this type of hardening is characterized through a fourth-order tensor as internal variable, the structure of the aforementioned potential is surprisingly simple. Even though the final model is rather complex, it requires only few model parameters. For these parameters, in turn, physically sound bounds based on the convexity condition of the yield surface can be derived. Three different examples demonstrate the predictive capabilities of the novel framework.