Chemo-elastic phase-field simulation of the cooperative growth of mutually-accommodating Widmanstätten plates

Abstract

A comprehensive understanding of the phase transformations is of primary importance to optimize the properties of a material. In the present study, a novel and thermodynamically consistent chemo-elastic multiphase-field model is formulated to simulate phase transformations which yield unique needle-like patterns, referred to as Widmanstätten structure. Owing to the critical role of the curvature in the growth of the Widmanstätten structure, the model is devised to recover the sharp interface solutions, despite the introduction of a diffuse interface. This condition is fulfilled by formulating the chemical and the elastic driving force based on the grand potential density and the mechanical jump conditions, respectively. Additionally, to render a quantitative chemical driving force, parameters from CALPHAD-database (TCFE8) are incorporated. The current work, through the multicomponent multiphase-field simulations, shows that at high temperatures, when the chemical driving force is insufficient to actuate the growth of a plate, the Widmanstätten structure evolves by the co-operative growth of self-accommodating plates. Furthermore, the growth of a single Widmanstätten plate at low temperature is also simulated, and the growth kinetics of the transformations are verified through existing analytical predictions.