Simulation of the history dependence of primary dendrite spacing in directional solidification

Primary dendrite spacing (lambda(1)) in directionally solidified alloys is dependent not only on processing parameters, i.e. temperature gradient and pulling velocity, but also on the processing history, including seed density and acceleration/deceleration of the pulling velocity. A cellular automaton model of grain growth was combined with a finite difference model of solute diffusion (CA-FD) to simulate the dendritic solidification of binary alloys. Constitutional and curvature undercoolings are considered to calculate the velocity of the solid/liquid interface. Crystallographic anisotropy of cubic metal is accounted for by an adapted implementation of the decentred square/octahedron growth technique developed by Gandin and Rappaz [I]. The model was also extended into three dimensions. Simulation results show that a range of stable values of lambda(1) exists for columnar dendrites at each growth velocity, depending on their nucleation/thermal history. The upper limit of the distribution of lambda(1) is about three times of the lower limit under conditions of constant temperature gradient and pulling velocity. The factor is reduced to two when the pulling velocity is perturbed about an average value.