Cellular automaton modeling for dendritic growth during laser beam welding solidification process

Abstract

A modified non-equilibrium cellular automaton (CA) model is proposed to simulate the dendrite growth along the fusion boundary under transient conditions during the solidification process of laser beam welding (LBW) pool. The main non-equilibrium solidification effects, including solute trapping, deviation of the liquidus line slope, and kinetic undercooling, are taken into consideration in this modified CA model. The evolution of dendrite morphology, concentration field, and velocity field was investigated. Four growth periods, i.e., the initial stable period, the instability period, the competitive growth period, and the short-term stable period, were observed during the solidification process of LBW pool. The dendrite growth patterns were different in these periods due to the transient solidification conditions. The solute distribution predicted by this modified CA model showed similar trends to that predicted by the previous phase field model. The dendrite tip velocity was significantly influenced by the thermal undercooling and constitutional undercooling in the LBW pool, and the tip velocity field can be divided into three stages, i.e., the planar growth stage, competitive stage, and short-term steady growth stage. In addition, further comparison between the simulated dendrite morphology and experimental dendrite morphology was performed. Results showed that the simulated morphology of dendrites agreed well with the experimental results. In particular, the primary dendrite arm spacing predicted by this model was in good agreement with that obtained from experiments.