An idea to treat the dendritic morphology in mixed columnar–equiaxed solidification

To treat mixed columnar–equiaxed solidification with dendritic morphology, five phase regions have been distinguished: extradendritic melt, interdendritic melt and solid dendrites in equiaxed grains, interdendritic melt and solid dendrites in columnar arrays of dendrites. These five phases are quantified by their volume fractions, and characterized by different volume-averaged solute concentrations. The equiaxed grains and columnar dendrites are confined by their envelopes, whose shapes are described by morphological parameters. The evolution of the envelopes is derived based on recent growth theories: the growth of primary columnar dendrite tips by the Kurz–Giovanola–Trivedi (KGT) model, the growth of secondary dendrite tips in radial direction of columnar trunk and the equiaxed dendrite tips by the Lipton–Glicksman–Kurz (LGK) model. The solidification of the interdendritic melt is governed by diffusion in the interdendritic melt region. Preliminary modelling results on a benchmark casting (Al–4·7wt-% Cu) show the potentials of the model.