Prediction of Columnar to Equiaxed Transition during Diffusion-Controlled Dendritic Alloy Solidification

A model is presented to predict the columnar to equiaxed transition (CET) in alloy castings. The model is based on a multiphase approach and accounts for heat and solute diffusion, as well as for grain nucleation, growth, and morphology. The model equations are applicable to both columnar and equiaxed dendritic solidification, thus offering an efficient single-domain formulation. A fixed grid, fully implicit finite-difference procedure is employed in the numerical solution, and a novel front tracking technique is incorporated that is also implicit in nature and readily applies to multidimensional situations. Calculations are performed for one-dimensional (1-D) and two-dimensional (2-D) castings of Al-Cu and Sn-Pb alloys. The calculated CET positions are compared with previous measurements in a (1-D) ingot cast under well-controlled conditions, and good agreement is found. The effects of various casting parameters on the CET are numerically explored.