Abstract
An analytical model is proposed to predict as-cast grain size of inoculated aluminum alloys during isothermal and non-isothermal solidification. The model is derived from a unified nucleation ceasing criterion which takes into account two stifling effects resulted from recalescence and solute segregation. The theoretical framework adopted by Greer et al. is utilized to account for the phase transformation kinetics during both isothermal and non-isothermal solidification. The proposed analytical model is able to predict maximum nucleation undercooling and hence the as-cast grain size. With some rational assumptions, the model yields a novel relationship between grain size and diffusivity-weighted Grain Restriction Factor, U. The model predictions on grain size for a variety of binary alloys has been compared with that from the reported semi-empirical relation, numerical solution and experimental measurements, and good agreements have been achieved. Unlike previous analytical models, all the input parameters of the present model are physically meaningful, including thermo-physical properties, alloy composition, cooling and inoculation conditions. Therefore the model can be applied directly to various alloys systems. It is concluded that the proposed model is valuable in identifying alloy composition and processing parameters to optimize as-cast grain size.