Simulation of the thermal history dependence of primary spacing during directional solidification

Thermal history dependent primary dendrite spacing during directional solidification was investigated using a combined cellular automaton-finite difference model. This model simulates the key phenomena occurring during dendritic growth, including overgrowth and branching. The dependence of primary spacing upon the thermal history during columnar dendritic growth was studied for a range of thermal gradient from 1 to 18 K mm^-1 and constant pulling velocity. Changes in primary spacing through both branching and overgrowth mechanisms were quantified. It was found that a range of stable spacings were possible for any given growth condition, with the maximum spacing about 3 times the minimum spacing. Further, for a monotonic increase in thermal gradient the spacing always stayed at the upper bound, whilst for a monotonic decrease the lower bound was followed. It was also found that the incubation period for dendrite branching at the upper limit was longer than that for overgrowth. The influence of having a range of spacings upon the propensity for equiaxed grains to nucleate ahead of the columnar dendrites was also investigated, revealing for the same thermal conditions, fine primary spacings are less prone to freckle formation.