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A non-isothermal phase field model that captures both displacive anddiffusive phase transformations in a unified framework is presented. The modelis developed in a formal thermodynamic setting, which provides guidance onadmissible constitutive relationships and on the coupling of the numerousphysical processes that are active. Phase changes are driven bytemperature-dependent free-energy functions that become non-convex below atransition temperature. Higher-order spatial gradients are present in the modelto account for phase boundary energy, and these terms necessitate theintroduction of non-standard terms in the energy balance equation in order tosatisfy the classical entropy inequality point-wise. To solve the resultingbalance equations, a Galerkin finite element scheme is elaborated. To dealrigorously with the presence of high-order spatial derivatives associated withsurface energies at phase boundaries in both the momentum and mass balanceequations, some novel numerical approaches are used. Numerical examples arepresented that consider boundary cooling of a domain at different rates, andthese results demonstrate that the model can qualitatively reproduce theevolution of microstructural features that are observed in some alloys,especially steels. The proposed model opens a number of interestingpossibilities for simulating and controlling microstructure pattern developmentunder combinations of thermal and mechanical loading.

Phase field model for coupled displacive and diffusive microstructural processes under thermal loading