A pseudo-front tracking technique for the modelling of solidification microstructures in multi-component alloys

Abstract

A two-dimensional model for the simulation of microstructure formation during solidification in multi-component systems has been developed. The model is based on a new pseudo-front tracking technique for the calculation of the evolution of interfaces that are governed by solute diffusion and the Gibbs–Thomson effect. The diffusion equations are solved in the primary solid phase and in the liquid using an explicit finite volume method formulated for a regular hexagonal grid. Volume elements located in the liquid phase undergo a transition to interfacial (or mushy) cells before being incorporated in the solid phase. This layer of interfacial elements, which always separates the solid from the liquid sub-domains, permits to handle the displacement of the interface in agreement with the flux condition at the interface. The interface curvature is obtained from the field of the signed distance to the interface, as reconstructed with a PLIC (piecewise linear interface calculation) technique. The concentrations at the solid–liquid interface are calculated using thermodynamic data provided by the phase diagram software Thermo-Calc [Sundman et al. CALPHAD 1987;9:153] . Different coupling strategies between the microstructure model and Thermo-Calc have been developed, in particular a computationally-efficient direct coupling using the TQ-interface of Thermo-Calc. After testing the accuracy of the model with respect to curvature calculation, comparisons are made with predictions obtained with the marginal stability theory, a one-dimensional front-tracking method and two-dimensional phase-field simulations of dendritic growth in binary alloys. The model is then used to describe the formation of several grains in an Al–1%Mg–1%Si alloy, as a function of the heat extraction rate and inoculation conditions. It is shown that the model is capable of reproducing the transition between globular and dendritic morphologies.