A quantitative phase-field model combining with front-tracking method for polycrystalline solidification of alloys

Abstract

As the orientation of an individual crystal is constant in solid and diffusive interface layer, a sharp interface model can be coupled to calculate the orientation in phase-field simulation of polycrystalline growth. Here, a two-dimensional phase-field model in combination with the front-tracking method is provided for simulating polycrystalline growth during solidification. In this model, the quantitative phase-field formulations for slow solidification of dilute binary alloys are employed to describe the dynamical evolution of diffusive solid–liquid interface while the front-tracking method is utilized to track the spatial dependent orientation of each grain. Because of the high computing efficiency that is resulted from only one order parameter used to depict the phase transformation during solidification, the model overcomes the disadvantage of reported phase-field approaches for polycrystalline growth. The built model was firstly solved to simulate a free equiaxed dendrite with different orientations growing from undercooled melt for benchmarking. The comparison results indicate that the model is able to compute the orientation exactly. Secondly, the model was extended to simulate the solidification with many equiaxed dendrites. The growth behaviors of the simulated crystals were characterized and analyzed, which demonstrate that the model is feasible to quantitatively and efficiently predict growth dynamics of crystals in a large number and scale during solidification of alloys.