Abstract
A directional solidification experiment of a Ti-Al-Nb-B-C alloy by power down method is simulated using a Bridgman furnace front tracking model. The effect of varying the dendritic growth parameters; C, the columnar dendrite growth coefficient, and n, the undercooling exponent, is investigated. A matrix of growth coefficients and undercooling exponents - at three levels each, based around a growth law for Ti-46wt.%Al - is applied in simulations, and the effect on columnar dendrite tip temperature, tip velocity, and tip temperature gradient is observed. The simulation results show that the dendrite tip velocity and temperature gradient at the tip are practically unaffected by the use of different growth parameters. However, the predicted columnar dendrite tip undercooling did vary to give the required dendrite tip velocity. This finding has implications for the analysis of microstructural transitions, such as the Columnar to Equiaxed Transition (CET). In conclusion, it is suggested that, for transient solidification conditions, a CET prediction criterion based on tip undercooling is preferable to one that uses growth velocity.
Highlights
Many practical analytical models of dendritic growth use the Ivantsov parabolic model [1] to treat diffusion of heat and solute at the dendrite tip
In the analysis carried out by Lapin et al [10] it was discovered that, for the sample cooled at 30 °C/min, the columnar to equiaxed transition (CET) occurred at a position approximately 76 mm from the cold end of the sample
A sensitivity study using the model showed that the predicted growth velocity and temperature gradient at the dendrite tip were insensitive to changes in the dendrite kinetics growth parameters
Summary
Many practical analytical models of dendritic growth use the Ivantsov parabolic model [1] to treat diffusion of heat and solute at the dendrite tip. Notable models include; marginal stability theory models based on the work Langer and Müller-Krumbhaar [2], such as the Lipton–Glicksman–Kurz (LGK) [3] model for equiaxed growth at small undercoolings, the Kurz–Giovanola–Trivedi (KGT) [4] model for columnar growth, and microsolvability theory models, as outlined by Kessler and Levine [5], where surface energy anisotropy is accounted for In any such models, a velocity–undercooling relationship can be determined and it is possible to fit results to a power law curve so that the growth model can be more readily applied in subsequent numerical simulations. Lapin et al [10] reported on preliminary results from the experiment carried out at a cooling
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