Combined Analytical and Numerical Front Tracking Approach to Modeling Directional Solidification of a TiAl-Based Intermetallic Alloy for Design of Microgravity Experiments

Abstract

Abstract.A three-step combined analytical and numerical approach to thermal modelling of a twoheater power-down furnace for controlled directional solidification of an intermetallic alloy is proposed. An analytical sensitivity analysis of the thermal model is carried out to show the effect of adiabatic zone length, and both hot-zone and cold-zone heater temperatures, on the initial thermal gradient in the sample and on the length of melt in the adiabatic zone. The subsequent axisymmetric front tracking method (FTM) simulations of directional solidification of a binary intermetallic Ti46at.%Al alloy show that temperature gradient in the melt declines and velocity of the solid-liquid front increases with time, thus promoting good conditions for a columnar to equiaxed transition. The proposed analytical calculations combined with full-scale numerical FTM simulations provide a convenient and predictive optimization tool for the two-heater power-down furnace design and growth conditions for the future microgravity experiments.

Conditions for CET in a gamma TiAl alloy

“…The growth of columnar grains in alloy 455 is estimated using the dendrite growth model of Kurz et al [15] (KGT model) using the liquidus slope and partition coefficient of a constitutionally similar binary alloy, namely: Ti-46at.%Al, (after Rebow et al [16]). Using this approach, the following power law curve fit relates columnar growth rate (v tip ) to columnar dendrite tip undercooling (ΔT tip ):…”

A phase-field study on the formation of the intermetallic Al2Au phase in the Al–Au system

“…Monte Carlo [12] and front-tracking [13,14] methods have been used for the study of intermetallic alloys. A review concerning first principle as well as molecular dynamic investigations on intermetallic compounds can be found in Ref.…”

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

“…A matrix of values for the growth coefficient C, and undercooling index n, were chosen to give a wide variation in growth rate versus undercooling based about central baseline values taken from the KGT columnar growth model power law fit for TiAl [7]. This range of values represents a 38% variation in C and a 35% variation for n, about the central values (C 2 and n 2 ) in Table 1.…”

“…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 growth of Ti-46wt.%Al, where the stability parameter * was set at 0.0506, i.e. twice the normal value used under the marginal stability criterion.…”