Mathematical modeling of microsegregation in binary metallic alloys

A mathematical model was developed to calculate microsegregation in binary metallic alloys. This model utilized the mathematical techniques of the method of lines combined with invariant imbedding (MOL/II) to solve the problem of combined heat and mass transfer during and after solidification. Model predictions were compared to experimental measurements in the Al-Cu system and to other microsegregation models. The MOL/II model predicted nonequilibrium second-phase contents within ±3 pct at low and intermediate cooling rates, when dendrite-arm coarsening was included in the model. It also was able to reproduce concentration profiles reasonably well. The analytical models commonly used (equilibrium cooling, Scheil equation, Brody/ Flemings model, Clyne/Kurz model, Solari/Biloni model, and Basaran equation) in micro-segregation calculations were shown to be considerably less accurate than the numerical models (MOL/II and the Ogilvy/Kirkwood model).

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