Ensemble averaged multi-phase Eulerian model for columnar/equiaxed solidification of a binary alloy: II. Simulation of the columnar-to-equiaxed transition (CET)

A new multi-phase Eulerian model for the columnar and equiaxed dendritic solidification has been developed. In this paper we first focus on the numerical simulation of quasi-steady solidification experiments in order to obtain corresponding CET maps. We have identified three main zones on the CET map: the pure columnar, the pure equiaxed zone and finally the mixed columnar+equiaxed zone. The mixed c/e zone was further quantified by means of a columnar fraction εc which quantifies in a rigorous way the two coexisting structures. Since it intrinsically includes the solutal and the mechanical blocking effects, the new ensemble model unifies the semi-empirical Hunt's approach (pure mechanical blocking mechanism) and the Martorano et al approach (pure solutal blocking mechanism). Secondly the present model was used to simulate unidirectional solidification experiments. It was found that the columnar front evolved in a quasi-steady state until a time very close to the critical CET moment. It is also found that the equiaxed nucleation undercooling is close to the maximum columnar dendrite tip undercooling and that the CET is virtually independent of the equiaxed zone ahead of the columnar front. If the equiaxed zone is not taken into account it is observed that the columnar front velocity exhibits a sudden increase at the beginning of the solidification followed by a quasi-plateau corresponding to a quasi-state at the columnar tips and finally, above a critical time, an oscillatory evolution. The beginning of the oscillatory evolution of the columnar front was well correlated with the CET position measured in the experiments. We also find that this oscillatory evolution of the columnar front is very favourable for the fragmentation of the columnar dendrites and thus for the CET. In this respect, it seems that the unsteady regime of the columnar front with respect to the local cooling conditions represents the main cause for the CET phenomena, at least for the non-refined alloys