Semi-analytical and numerical modeling of microsegregation for solidifying metallic alloys

In this study, two semi-analytical models of microsegregation were developed to predict the concentration fields of solute in the liquid and solid regions for dendritic solidification of binary metallic alloys. Both models assume that the growing dendrites are cylindrical in shape. This assumption is more realistic compared to the common assumptions of plate-like dendrites that most of the earlier researchers employed in their microsegregation modeling study. The solute redistribution profile, in the developing solid layer, necessary to determine the back diffusion parameter was derived from Fick's second law for the model without coarsening. The application of this parameter in a wide range of conditions and the use of its basic form in the model with coarsening was verified. The concept of coordinate transformation and enhancement of back-diffusion Fourier number were used in deriving the model which took into account the coarsening of dendrites. The models are then extended to deal with rapid solidification, peritectic transformations and multi-component systems and the results were compared with relevant experimental data. A good agreement between the model predictions and experimental results was found.The second part of this study was focused on developing a fully numerical microsegregation model. The numerical model built upon a previously proposed phase change model which relied upon a coordinate transformation technique. The model was extended to deal with moving boundaries with solute diffusion. A suitable computational procedure was developed to solve the model equations which are strongly coupled to each other. To verify the accuracy of the present algorithm with regard to the capability of tracking the moving interfaces, analytical solution of the Stefan problem was used for verification purposes. A good agreement between the model predictions and the analytical solution was found. Evolution of concentration fields during solidification was calculated in the growing solid as well as in the shrinking liquid regions for rectangular, cylindrical and spherical dendrite geometries. The effects of various cooling conditions and relevant parametric values on microsegregation were analyzed and discussed