Comparison of Johnson–Mehl–Avrami–Kologoromov (JMAK) kinetics with a phase field simulation for polycrystalline solidification

Abstract

Polycrystalline solidification in binary alloys proceeding by nucleation and subsequent anisotropic growth is studied by a newly developed phase field model. Simulation results show that, although the growth rates at different locations of the dendrite arm are diverse and cannot be correlated through a multiplicative factor, the time dependence of the dendritic growth area also satisfies a certain simple power function as in the case of linear growth or parabolic growth of a convex particle, but the growth exponent is different from those cases. Through phase field simulation it can be obtained that the growth exponent in two dimensions approximately equals 2 for the dendrite with well-developed side branches and 1.5 for one without side branches. The transformation kinetics of polycrystalline solidification obtained by phase field simulation is compared with the Johnson–Mehl–Avrami–Kologoromov (JMAK) theory based on analyzing the growth kinetics of a single dendrite. For the dendrites grow without side branches, it is found that the JMAK model will overestimate the transformed fraction because of the neglecting of the blocking effect. For the impingement of dendrites with fully developed side branches, the blocking effect is negligible because of the small anisotropy of the dendrictic envelope shape.