A phase-field approach to nonequilibrium phase transformations in elastic solids via an intermediate phase (melt) allowing for interface stresses

Abstract

A phase-field approach for phase transformations (PTs) between three different phases at nonequilibrium temperatures is developed. It includes advanced mechanics, thermodynamically consistent interfacial stresses, and interface interactions. A thermodynamic Landau–Ginzburg potential developed in terms of polar order parameters satisfies the desired instability and equilibrium conditions for homogeneous phases. The interfacial stresses were introduced with some terms from large-strain formulation even though the small-strain assumption was utilized. The developed model is applied to study the PTs between two solid phases via a highly disordered intermediate phase (IP) or an intermediate melt (IM) hundreds of degrees below the melting temperature. In particular, the β ↔ δ PTs in HMX energetic crystals via IM are analyzed. The effects of various parameters (temperature, ratios of widths and energies of solid–solid (SS) to solid–melt (SM) interfaces, elastic energy, and interfacial stresses) on the formation, stability, and structure of the IM within a propagating SS interface are studied. Interfacial and elastic stresses within a SS interphase and their relaxation and redistribution with the appearance of a partial or complete IM are analyzed. The energy and structure of the critical nucleus (CN) of the IM are studied as well. In particular, the interfacial stresses increase the aspect-ratio of the CN. Although including elastic energy can drastically reduce the energy of the CN of the IM, the activation energy of the CN of the IM within the SS interface increases when interfacial tension is taken into account. The developed thermodynamic potential can also be modified to model other multiphase physical phenomena, such as multi-variant martensitic PTs, grain boundary and surface-induced pre-melting and PTs, as well as developing phase diagrams for IPs.