Thermodynamically consistent phase-field model for pressure-induced multiphase phase transformation of metals under intensive dynamic loading

Understanding the pressured-induced multiphase phase transformation (MPT) of metals at high strain rate is of great technical and scientific interest. Despite of several decades of studies, the pressured-induced MPT of metals at high strain rate is far from well understood because the deformation at high strain rate is so complex that present in situ diagnostic techniques or atomistic simulations cannot provide the details of the MPT at high strain rate. In the current work, a multiphase phase-field (MPF) model for the dynamic phase transformation (PT) of metals is developed, in which the volume fraction of each phase is chosen as the order parameter. The driving force of the MPT consists of the Gibbs free energy, the gradient energy and the penalizing energy. In particular, a smooth and normalized interpolation function is introduced to establish the Gibbs free energy at the multiphase junction. With the aid of this interpolation function, the explicit forms of the kinetics equation and constitutive relations of the MPT at the multiphase junction are also derived. It is demonstrated that the model satisfies all seven criteria of a consistent MPF model. Compared to previous models, the thermodynamic stability of this model is improved significantly. When applied to address the MPT of bismuth subjected to ramp-wave loading (RWL), the model can quantify the connection between the microstructural evolution of multiple phases and the experimentally measured multiwave structures.Moreover, new insights concerning the MPT-related thermodynamic paths of bismuth at elevated temperatures and the metastable phase during dynamic MPT are gained.