Analytical multicomponent microsegregation model for equiaxed globular growth with diffusion interaction between species
Résumé
In casting processes, the development of one solid phase from the liquid gives rise to microsegregation. The liquid is enriched in solute species that diffuse to/from the solid/liquid interface. In multicomponent alloys, this enrichment mainly controls the solidification path and plays a major role for the estimation of the nature and amount of secondary phases. While numerical models usually rely on few approximations [1], analytical models also remain of interest for coupling with large scale simulations of casting processes [2]. Several models have been proposed to predict microsegregation [3]. However, very few models have been applied to multicomponent alloys and coupled with thermodynamic equilibrium calculations [4]. Moreover, interaction between species (or cross diffusion phenomena) is always neglected.
We propose an analytical solution for a multicomponent microsegregation model with interaction between species. This paper relies on the approximation developed by Martorano et al. [3] initially proposed for binary alloys. The model is coupled with an energy balance and applied to simulate globulitic grain solidification in a ternary alloy during a cooling process. The influence of the cross-diffusion terms in the liquid diffusion matrix is demonstrated. A comparison is also provided with an exact solution using a front tracking method.
References
[1]Q. Chen, B. Sundman, Materials Transactions 43 (2002) 551-559
[2]H. Combeau, M. Zaloznik, S. Hans, P.-E. Richy, Metall. Mater. Trans. B 40 (2009) 289-304
[3]M.A. Martorano, C. Beckermann, Ch.-A. Gandin, Metall. and Mater. Trans. A 34 (2003), 1657-1673, 35A (2004) 1915
[4]H. Zhang, Ch. A. Gandin, H. Ben Hamouda, D. Tourret, K. Nakajima, J. He, ISIJ International 50 (2010) 1859-1866