Phase-field Study Of The Dendrite Growth In Solidification Of Pure Metal

Computer modeling and numerical simulations of dendritic crystal growth plays an important role in prediction and improving material properties to establish the relationship of material properties and material processing with material microstructure. This work aimed at simulating dendritic growth during solidification of undercooled melt of pure metal under different condition by using phase-field micro-modeling. The mechanism of dendritic growth in undercooled melt is discussed.First, based on the Wheeler 2-D model, a 2-D phase-field model was derived in light of anisotropy thermal diffusivity, different thermal diffusivity in solid state and liquid state, structural fluctuation and energetic fluctuation. The model consists of 2-D phase-field equations and thermal transportation equations. The governing equation is discretized using standard second order central finite difference method with uniform grids, except that (?)~2φis discretized using a nine-point method to reduce the grid anisotropy of the nearest and the second nearest neighbors. The dimensionless temperature fields u are time-stepped using an Alternative Direction Implicit Iteration.Based on the model, effect of undercooling on dendritic side-branching during solidification of melt of pure metal is studied, and the effect of the magnitude of structural fluctuation and energetic fluctuation on undercooled melt of pure metal is discussed. The study results indicate that, structural fluctuation and energetic fluctuation can result in the growth of secondary branches, but they do not influence the steady state growth of the tip. As the level of structural fluctuation and energetic fluctuation increases, dendrite morphology is transformed to dendritic 'seaweed' morphology. The relationship between the percentage of secondary branches and the magnitude of structural fluctuation and energetic fluctuation can be written as: S = 0.076 ln(0.32ξ_R) + 0.34. The Study results also indicate that by holding structural fluctuation and energetic fluctuation level constant, dendrite morphology self-reproduces with the increase of undercooling during a small undercooling degree. However, as the undercooling increases more, secondary branches occur near the dendrite tip. This also depends on the level of kinetic undercooling at the tip. Morphology changes dramatically when secondary branches begin to occur within 1-2 radii of the tip, which leads to the shrink of the dendrite trunk. The trunk ruptures and morphology gives rise to spontaneous grain refinement under convection. This process can be used to explain many of the observed features of spontaneous grain refinement in deeply undercooled metallic melts. It is also found that, as the undercooling increases, the secondary branches grow fast and the percent of secondary branches is proportional to the level of structural fluctuation and energetic fluctuation.Finally the effect of the ratio of thermal conductivity in solid state to that in liquid state on side-branching of undercooled melt is studied. The results indicate that, as the ratio increases, the secondary branches get suppressed and the portion of secondary branches decreases. Meanwhile, the smaller the crystal RMS spacing, the weaker anisotropy becomes. The effect of thermal diffusivity on dendrite growth in undercooled pure metal is also studied. The relationship of undercooling, velocity and radius of dendrite tip with dimensionless time has been established at several thermal diffusivity levels. It is found that the dendrite steady-state tip undercooling and velocity are roughly in proportion to thermal diffusivity while radius of the tip is inversely proportional to thermal diffusivity.