Phase-field simulations of solidification in binary and ternary systems using a finite element method

TL;DR

This paper introduces adaptive finite element phase-field simulations for solidification in multicomponent alloys, capturing complex morphologies and dynamics in binary and ternary systems with high accuracy.

Contribution

The study develops a novel numerical scheme for phase-field modeling of non-isothermal multicomponent solidification using adaptive meshes, enabling detailed 2D and 3D simulations.

Findings

Morphology transition from dendritic to globular with increasing Cr

Simulation of oscillatory growth and topological changes in 3D

Insights into alloy composition effects on growth velocity

Abstract

We present adaptive finite element simulations of dendritic and eutectic solidification in binary and ternary alloys. The computations are based on a recently formulated phase-field model that is especially appropriate for modelling non-isothermal solidification in multicomponent multiphase systems. In this approach, a set of governing equations for the phase-field variables, for the concentrations of the alloy components and for the temperature has to be solved numerically, ensuring local entropy production and the conservation of mass and inner energy. To efficiently perform numerical simulations, we developed a numerical scheme to solve the governing equations using a finite element method on an adaptive non-uniform mesh with highest resolution in the regions of the phase boundaries. Simulation results of the solidification in ternary Ni$_{60}$Cu$_{40-x}$Cr$_{x}$ alloys are presented investigating the influence of the alloy composition on the growth morphology and on the growth velocity. A morphology diagram is obtained that shows a transition from a dendritic to a globular structure with increasing Cr concentrations. Furthermore, we comment on 2D and 3D simulations of binary eutectic phase transformations. Regular oscillatory growth structures are observed combined with a topological change of the matrix phase in 3D. An outlook for the application of our methods to describe AlCu eutectics is given.