Multi-phase field lattice Boltzmann model of columnar-to-equiaxed transition in entire welding molten pool

Columnar-to-equiaxed transition (CET) often occurs during the solidification of the weld. Moving molten pool and strong fluidity are two notable characteristics in this process. The former causes the deflective epitaxial growth of columnar dendrites, while the latter makes the equiaxed dendrites grow asymmetrically and continuously move, collide and coalesce in the melt. This paper proposed a multi-phase field lattice Boltzmann model to simulate the CET in the entire molten pool. The model can characterize the polycrystalline growth, compute the fluid flow, and simulate the solid motion, collision, and coalescence. It also combined the transient growth condition model and the continuous nucleation model to reproduce the moving molten pool and define heterogeneous nucleation respectively. It further combined the initial grain structure of the base metal to provide a more realistic condition for epitaxial growth. The proposed model was verified by simulating the pure motion of dendrite in lid-driven flow, the free fall of single dendrite in static flow, and the single-dendrite growths in lid driven and channel flow. The CET in the entire molten pool was simulated under different conditions, including considering or ignoring the fluid flow and gravity, the columnar and equiaxed dendrites growing simultaneously or sequentially. In these simulations, settlement, collision, and coalescence of equiaxed dendrites were reproduced successfully. Clear asymmetric growth, dendrite aggregation effect, and solute vortex were found. Significant differences in the size, symmetry, dendrite spacing, dendrite morphology, and solute distribution were found when the melt flow was considered or ignored. The dense equiaxed dendrite belt was found in the later stage of CET. They gathered in front of columnar dendrites and dominated the following solidification. The typical mixed structure that consists of columnar and equiaxed grains was obtained after complete solidification.