Abstract
Numerical simulation of solute trapping during solidification, using two phase-field model for dilute binary alloys developed by Kim et al. [Phys. Rev. E, 60, 7186 (1999)] and Ramirez et al. [Phys. Rev. E, 69, 05167 (2004)] is presented here. The simulations on dilute Cu-Ni alloy are in good agreement with one dimensional analytic solution of sharp interface model. Simulation conducted under small solidification velocity using solid-liquid interface thickness (2λ) of 8 nanometers reproduced the solute (Cu) equilibrium partition coefficient. The spurious numerical solute trapping in solid phase, due to the interface thickness was negligible. A parameter used in analytical solute trapping model was determined by isothermal phase-field simulation of Ni-Cu alloy. Its application to Si-As and Si-Bi alloys reproduced results that agree reasonably well with experimental data. A comparison between the three models of solute trapping (Aziz, Sobolev and Galenko [Phys. Rev. E, 76, 031606 (2007)]) was performed. It resulted in large differences in predicting the solidification velocity for partition-less solidification, indicating the necessity for new and more acute experimental data.
Highlights
During low velocity solidification of alloys the solid-liquid interface atomic diffusion is much faster the movement of interface
The objective of the present work is to compare 2 phase field models for dilute binary alloys presented in the literature[6,7] and, from their validation against analytical solution of sharp interface model, to determine the value of K for Ni-Cu dilute alloy and to verify its vast lidity when applied to experimental data[8,9,10]
The results of present work on the solute (Cu) and phase field (φ) profiles along the y direction for the two dilute phase field models are presented in the Figures 1 and 2
Summary
During low velocity solidification of alloys the solid-liquid interface atomic diffusion is much faster the movement of interface. For alloys with solute partition coefficient (ratio between solute concentration at solid side of the interface and the maximum solute concentration in the liquid phase) smaller than one and solidified under low velocities, the liquid close to the solid-liquid interface will be enriched with solute, resulting in a well known segregation phenomena, which can be detrimental to the material properties[1]. In the limit of partition-less solidification, the solute concentration in both phase are equal, i.e., there is no segregation. This process is useful to obtain very fine structure with uniform properties. As an emerging RSP technology, direct strip casting is a continuous casting process for producing as cast metallic sheet of carbon and stainless steel, aluminium, magnesium, titanium and other alloys without any further thermo-mechanical processing
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