Restrictions of Physical Properties on Solidification Microstructures of Al-based Binary Alloys by Cellular Automaton

Abstract

Fig. 1. Dendrite tip growth kinetics predicted by the GGAN model, i.e. Eq. (6), the simplified expressions based on KGT model (Refs. 14), 15)) and the present simplified expression based on GGAN model (Eq. (8)).by CA-FD coupling model. The related physical properties for Al-3mass%Si and Al-3mass%Cu alloy are shown in Tables 1 and 2, others can be found in Ref. 1). A seen, the latent heat of the solidification is regarded as the functions of the solute concentration in order to fit with Kobayashi's model. 8)The cooling rate in intermediate position Ṫ is set as 0.7, 2.3 and 5.0 K/s. The heat transfer coefficient h corresponding to each alloy and Ṫ is obtained beforehand through several attempts. Since this work mainly discusses the influences of the physical properties on the solidification morphologies, most of the nucleation parameters are fixed, such as n V *ϭ200ϫ10 4 m Ϫ2 , DT S ϭ1 K, DT S,s ϭ0.1 K, and DT V,s ϭ 0.1 K, except the nucleation undercooling in the bulk of liquid DT V and the nucleation density at the surface n S *. The former one is changed for the determination of the critical range for the CET, and the latter one is determined by the primary arm spacing, i.e. n S *ϭ1/l 1 , which is related to the cooling rate at the surface, as seen in Table 1.The heat transfer equation combined with microsegregation model and energy balance is adopted to obtain the temperature field. The temperature is then interpolated into CA ISIJ International, Vol. 50 (2010), No. 12 1837 © 2010 ISIJ Table 1. Thermophysical properties of Al-3mass%Si and Al-3mass%Cu alloy. cells. The Gaussian distribution is adopted for the nucleation procedure, the GGAN model for predicting the dendrite tip growth rate of Al-Si and Al-Cu alloys and the decentred square growth algorithm are used for the grain growth procedure. Physical Properties Influencing Heat TransferHeat transfer is the basic stage for the solidification and evolution of the morphologies. Figure 2 plots the cooling curves for Al-3mass%Si and Al-3mass%Cu alloy in the same cooling rate in intermediate position Ṫ. The curves show the same tendency that the slope of the curve becomes smaller temporarily due to the appearance of the primary phase and the eutectic phase. After the completion of the solidification, the slope returns to the original state. Here the cooling rates at the three positions (intermediate, center and surface) are defined by the ratio of the temperature decrease to the solidification time.With different solute in Al melt, the solidification interval is different due to their different slope of the liquidus and different eutectic temperature. As illustrated in the cooling curves in Fig. 2, since the slope of the liquidus for Al-3mass%Si alloy is larger than that for Al-3mass%Cu alloy, with the same solute concentration, the liquidus temperature for Al-3mass%Si alloy is lower. And the eutectic temperature of Al-3mass%Si alloy (577°C) is higher than that of Al-3mass%Cu alloy (548°C). So the solidification interval, resulting from both the decrease of the ...

Methodological Progress for Computer Simulation of Solidification and Casting

“…It is noticed that the limit condition DT s →0 K in Thevoz et al's continuous model corresponds to the instantaneous nucleation model. Gandin et al 29,30) and Nakajima et al [54][55][56] adopted this continuous model in several of their CA simulations. Futhermore, judged the activation level (nucleation probability) of each CA cell by using Eq.…”