Dark energy in crystals: prediction of stored energy in polycrystalline aggregates

During the plastic deformation of metallic materials, part of expended mechanical energy diffuses as heat. The fraction of plastic work converted into heat is called the Taylor–Quinney Coefficient (TQC), which is often assumed to be a constant parameter of about 0.9. The remaining portion of the plastic work is called stored energy. The stored energy is known as the main driving force for dynamic or static recovery and recrystallization. Therefore, numerical predictions and experimental measurements of the stored energy and TQC are essential to optimize thermomechanical material processing. An adequate prediction of the stored energy and the TQC using existing crystal plasticity models in line with the experimental measurements remains a challenging problem. In this work, a thermodynamic class of crystal plasticity models is used to predict the stored energy and TQC of copper and aluminum single crystals. Then, the numerical stored energy predictions are extended to polycrystalline austenitic steel 316L and compared with the experimental measurements from the literature. An ad-hoc factor is introduced in the numerical expression of stored energy in order to compensate for the difference with the experimental measurement. To this end, the contributions of statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) for the stored energy prediction are analyzed to understand the physical origin of the ad-hoc factor. The contribution of GNDs to stored energy and enhanced hardening is accounted for by means of a strain gradient plasticity model. The present systematic finite element crystal plasticity simulations also include specific interface conditions at grain boundaries. The presented computational analysis indicates that, compared to the experiment, there remains dark energy in the evaluation of energy storage as predicted by the proposed thermodynamically consistent crystal plasticity framework.