Alloy solidification: Assessment and improvement of an easy-to-apply model

Abstract

• The Gong-Chen model requires no experimental parameters and is easy to apply. • It can be used as a generic solidification model up to the solid fraction (fs) of 0.9. • When fs > 0.9, its applicability depends on both solute diffusion and partition coefficient. • The Gong-Chen model requires f s Lever > 1, which has been examined and justified. • The Won-Thomas model provides the most practical predictions but requires experimental input. It has been a central task of solidification research to predict solute microsegregation. Apart from the Lever rule and the Scheil-Gulliver equation, which concern two extreme cases, a long list of microsegregation models has been proposed. However, the use of these models often requires essential experimental input information, e.g. , the secondary dendrite arm spacing ( λ ), cooling rate ( T ˙ ) or actual solidification range ( Δ T ). This requirement disables these models for alloy solidification with no measured values for λ, T ˙ and Δ T . Furthermore, not all of these required experimental data are easily obtainable. It is therefore highly desirable to have an easy-to-apply predictive model that is independent of experimental input, akin to the Lever rule or Scheil-Gulliver model. Gong, Chen, and co-workers have recently proposed such a model, referred to as the Gong-Chen model, by averaging the solid fractions ( f s ) of the Lever rule and Scheil-Gulliver model as the actual solid fraction. We provide a systematic assessment of this model versus established solidification microsegregation models and address a latent deficiency of the model, i.e., it allows the Lever rule solid fraction f s to be greater than one ( f s > 1). It is shown that the Gong-Chen model can serve as a generic model for alloy solidification until f s reaches about 0.9, beyond which ( f s > 0.9) its applicability is dictated by both the equilibrium solute partition coefficient ( k ) and the solute diffusion coefficient in the solid ( D s ), which has been tabulated in detail.