A phase field model for spontaneous grain refinement in deeply undercooled metallic melts

The origin of spontaneous grain refinement in deeply undercooled metallic melts has been of enduring interest within the solidification literature. Here we present the results of phase field simulations of dendritic growth into pure undercooled melts, at growth velocities up to 35 m s−1. We find that, at low growth velocities, dendrite morphologies are broadly self-similar with increasing growth velocity. However, above ≈15 m s−1 the initiation of side-branching moves closer to the dendrite tip with increasing growth velocity. This appears to be related to the level of kinetic undercooling at the tip. Once side-branch initiation begins to occur within 1–2 radii of the tip, profound morphological changes occur, leading to severe thinning of the dendrite trunk and ultimately repeated multiple tip-splitting. This process can be invoked to explain many of the observed features of spontaneous grain refinement in deeply undercooled metallic melts.