Macroscopic modeling of distortional hardening in polycrystals: application to magnesium alloys

Abstract

Texture evolution in metals due to rotation of the atomic lattice results in a complex macroscopic mechanical behaviour which cannot in general be reasonably captured by only classical isotropic or kinematic hardening. Focusing on standard rate-independent plasticity, the evolution of microstructure leads to an evolving macroscopic anisotropy of the yield surface, also known as distortional or differential hardening. This effect is very important, particularly if non-radial loading paths such as those associated with forming processes are to be numerically analyzed. In the present work, different existing distortional hardening models are critically reviewed. They are reformulated into the modern framework of hyperelastoplasticity and the same objective time derivative is applied to all evolution equations for a better comparison. Furthermore, since the original models are based on a yield function not accounting for the different mechanical responses between tension and compression as observed in metals showing a close-packed atomic structure, respective generalizations are also discussed. It is shown that only one of the extended models can fulfill the second law of thermodynamics. That model predicts a high curvature of the yield surface in the loading direction, while the opposite region of the yield surface is rather flat. Such a response can indeed be observed for some materials. In the case of magnesium alloys, however, that does not seem to be true. Therefore, a new constitutive model is presented. Its underlying structure is surprisingly simple and the model is not only thermodynamically consistent but also variationally consistent. Conceptually, distortional hardening is described by an Armstrong-Frederick-type evolution equation. The calibrated new model is implemented in a finite element framework and its predictive capabilities are demonstrated. Makroskopische Modellierung der formativen Verfestigung in Polykristallen: Anwendung auf Magnesiumlegierungen