•The heat and mass transfer process in weld pool for various conditions was studied.•The solidification conditions along the trailing pool boundary were analyzed.•The morphological evolution of solidification structures was simulated by CA model.•We discussed the formation mechanisms for different weld grain structures. The heat and mass transfer and the morphological evolution of the various weld solidification structures for the entire weld were simulated through the macro-micro modeling which combined the welding process and the solidification structures in the weld pool. The weld profiles were calculated for different welding conditions, and the effects of the welding parameters on the solidification conditions were analyzed along the trailing pool boundary. The formation mechanism of the axial columnar structure and the equiaxed grains in the weld were studied by the developed model. The results indicate that the temperature gradient G, solidification rate Rw, and the ratio G/Rw along the trailing pool boundary are related with the location in the weld and the welding parameters. If there does not exist heterogeneous nuclei in the weld pool, the axial columnar structure forms in the central region of the weld at low welding speeds owing to the anisotropic kinetics of the dendritic structure. When the heterogeneous nucleation occurs in the weld pool, the weld structure is directly determined by the competitive growth between the columnar and new nucleated grains. At low welding speeds, the preferential orientations of the survival grains get closer to the welding direction with the decrease of the distance to the weld centerline. With the increase of the welding speed and welding current, more grains form in the weld pool, and the new nucleated grains also become more competitive. The columnar grains from the fusion line are blocked by the equiaxed grains. The continuous equiaxed grain zone forms in the weld, and the columnar to equiaxed transition (CET) occurs.