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

TL;DR

This paper introduces a comprehensive non-isothermal phase field model that simulates coupled displacive and diffusive microstructural transformations under thermal loading, incorporating thermodynamic consistency and advanced numerical methods.

Contribution

It develops a unified thermodynamic framework with novel numerical approaches to accurately model phase boundary energies and transformations under thermal conditions.

Findings

Model qualitatively reproduces microstructural evolution in alloys.

Numerical scheme effectively handles high-order spatial derivatives.

Results show potential for controlling microstructure development.

Abstract

A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible constitutive relationships and on the coupling of the numerous physical processes that are active. Phase changes are driven by temperature-dependent free-energy functions that become non-convex below a transition temperature. Higher-order spatial gradients are present in the model to account for phase boundary energy, and these terms necessitate the introduction of non-standard terms in the energy balance equation in order to satisfy the classical entropy inequality point-wise. To solve the resulting balance equations, a Galerkin finite element scheme is elaborated. To deal rigorously with the presence of high-order spatial derivatives associated with surface energies at phase boundaries in both the momentum and mass balance equations, some novel numerical approaches are used. Numerical examples are presented that consider boundary cooling of a domain at different rates, and these results demonstrate that the model can qualitatively reproduce the evolution of microstructural features that are observed in some alloys, especially steels. The proposed model opens a number of interesting possibilities for simulating and controlling microstructure pattern development under combinations of thermal and mechanical loading.