A coupled phase-field and crystal plasticity model for understanding shock-induced phase transition of iron

Abstract

In the current work, we propose a chemical-potential-based phase-field model coupled with dynamic crystal plasticity based on a unified energy framework with the aim of understanding the shock-induced α–ϵ–α phase transition (PT) of iron. The plasticity is coupled with the PT through controlling the shear strain energy and the entropy rise during the dynamic deformation. In contrast with previous models, the PT pressure in this model is not a constant but obeys the Gaussian distribution with the applied stress, which is in accordance with the hysteresis effect observed in quasi-static experiments. Moreover, the contribution of multivariants to PT can be distinguished based on reaction-pathway theory. The proposed model quantitatively reproduces the split of the three-wave structure and the “loop” features of the plasticity wave and the phase transition wave, which agree well with the shock loading experiments of polycrystalline and monocrystalline iron, and cannot be well captured by previous models. Furthermore, many new insights in shock wave physics are gained. PT kinetics is found to be influenced by plasticity via the hysteresis effect and the newly generated stress wave induced by the dynamic deformation. First, the rarefaction wave induced by plastic deformation, as well as that by the growth of the child phase, behind the shock front reduces the PT plateau in the wave profile. Second, the plasticity controls the PT driving force and influences the PT hysteresis effect behind the shock front. As yield stress increases, less strain energy is plastically dissipated, and more strain energy drives the PT behind the shock front more efficiently, which results in a sharper slope of the P2 wave.