Reviewed in this paper are mathematical analyses for prediction of segregations and chemical compositions change of nonmetallic inclusions during solidification of steels. The studies conducted by the present author are used to construct the main stream of this article, and the author’s view is delivered by introducing the related studies by other researchers and in comparisons among them.
In order to predict segregations of solutes during solidification of steels with more precision than previous microsegregation models such as Flemings-Brody equation and Clyne-Kurz equation, finite difference method was utilized to solve the Fick’s law of solute diffusion in combination of thermodynamic equilibrium calculation at the solid/liquid interface. Stemming from the work, various attempts were conducted for its modifications, improvements and extensions of applicability. In order to control the chemical compositions of nonmetallic inclusions preferable to properties of steel products, mathematical analyses were done for the prediction of their chemical compositions change during solidification of steels. It utilized a microsegregation model by Clyne and Kurz and the assumption of equilibrium throughout the residual liquid including nonmetallic inclusions. In the most universal calculation method developed by the present author et al. simulation softwares developed in the field of calculation of phase diagram were fully utilized. An improved simulation method for solidification path analysis was introduced, which utilized a finite difference method to solve the solute diffusion between adjacent finite segments and equilibrium calculation in each finite segment to solve transformation.
The author’s view for the future task in these field is summarized at the end. Development of mathematical models are highly promising, which consider macroscopic transport of solute and nonmetallic inclusions if necessary among the segments consisting the system interested and appropriate reaction models in each segment.