On the macroscopic description of yield surface evolution by means of distortional hardening models: Application to magnesium

Abstract

Texture evolution in polycrystals due to rotation of the atomic lattice in single grains results in a complex macroscopic mechanical behavior which cannot be reasonably captured only by classical isotropic or kinematic hardening in general. More precisely and focusing on standard rate-independent plasticity theory, the complex interplay at the microscale of a polycrystal leads to an evolving macroscopic anisotropy of the yield surface, also known as distortional or differential hardening. This effect is of utmost importance, if non-radial loading paths such as those associated with forming processes are to be numerically analyzed. In the present paper, different existing distortional hardening models are critically reviewed. For a better comparison, they are reformulated into the modern framework of hyperelastoplasticity, and the same objective time derivative is applied to all evolution equations. Furthermore, since the original models are based on a Hill-type yield function not accounting for the strength differential effect as observed in hcp metals such as magnesium, respective generalizations are also discussed. It is shown that only one of the resulting models can fulfill the second law of thermodynamics. That model predicts a high curvature of the yield function in loading direction, while the opposite region of the yield function is rather flat. Indeed, such a response can be observed for some materials such as aluminum alloys. In the case of magnesium, however, that does not seem to be true. Therefore, a novel constitutive model is presented. Its underlying structure is comparably simple and the model is thermodynamically consistent. Conceptually, distortional hardening is described by an Armstrong–Frederick-type evolution equation. The predictive capabilities of the final model are demonstrated by comparisons to experimentally measured data.