Sensitivity analysis of dendritic growth kinetics in a Bridgman furnace front tracking model

Abstract

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. IntroductionMany 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. Rebow and Browne [6] demonstrated an example of this where the predicted growth velocity, V, was fitted to various levels of dendrite tip undercooling, T, by the power law; V=CT n , where C (the growth coefficient) and n (the undercooling exponent) were the fitted variables for directional solidification of Al-4wt.%Cu and Al-2wt.%Si. In a similar way, the KGT model was used by Rebow et al. [7] to model columnar