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

The effect of undercooling Delta T and the interface energy anisotropy parameter epsilon(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 rho 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 sigma* decreases and then stabilizes with the increase of the fitting range, and sigma* increases with the increase of epsilon(4). The relationship between sigma* and epsilon(4) follows a power-law function sigma(& lowast; )proportional to epsilon(alpha)(4) , and alpha is independent of Delta T but dependent on the fitting range. Numerical results demonstrate that the predicted sigma* is consistent with the curve of microscopic solvability theory (MST) for epsilon(4) < 0.02, and sigma* obtained from our phase-field simulations is sensitive to the undercooling when epsilon(4) is fixed.