Modeling grain refinement for undercooled single-phase solid-solution alloys

A grain-refinement model for rapid solidification of undercooled single-phase solid-solution alloys was developed in which a combination of the model of dendrite fragmentation with the model of overall solidification kinetics allows dendrite fragmentation to occur along with the solidification process (e.g. during mushy zone solidification). Compared with Karma’s model, the dendrite break-up time as well as the time for the interdendritic liquid to be solidified completely can be predicted. Thus, the model can predict, in the absence of experimental data (e.g. the plateau duration), the microstructure transition. The model was applied to describe the rapid solidification of undercooled Ni–15 at.% Cu alloy, and a good agreement between the model predictions and the experimental results was obtained. On this basis, the effects of capillarity and back-diffusion on dendrite fragmentation during mushy zone solidification, as well as the effects of back-diffusion and cooling rate on the prediction of the microstructure transition, were found.