Dendritic tip selection during solidification of alloys: Insights from phase-field simulations

In this paper, the effect of undercooling △T and the interface energy anisotropy parameter ε 4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys. It was found that the tip radius ρ increases and the tip shape amplitude coefficient A 4 decreases with the increase of the fitting range for all cases. The dendrite tip shape selection parameter σ * decreases and then stabilizes with the increase of the fitting range, and σ * increases with the increase of ε 4. The relationship between σ * and ε 4 follows a power law function σ * ∝ ε 4 α, and is independent of but dependent of the fitting range. Numerical results demonstrate that the predicted σ * is consistent with the MST curve for ε 4 ＜ 0.02, and σ * obtained from our phase-field simulations is sensitive to the undercooling when ε 4 is fixed.