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Abstract
Abstract The solidification of metals and alloys and the resulting microstructures, which as a function of thermal and solutal parameters can evolve as planar, cellular and dendritic, are important from a practical point of view, since they strongly influence the properties and quality of the final product. In many practical situations it is impracticable to develop analytical solutions permitting reliable predictions of microstructural growth during unsteady-state solidification conditions. The Phase Field method has become very popular and effective in modeling complex solid/liquid interfaces due to its ability to simulate the interface kinetics and the formation and evolution of different morphologies along the solidification process. In this work, a numerical analysis of the microstructural evolution during the transient solidification of dilute alloys of the Al-Cu-Si system is developed, which uses a phase-field approach for the simulation of ternary alloys. The phase-field, energy and solute concentration equations were numerically solved for the correspondent ternary system, varying the mesh parameters, temperature and alloy composition. The analysis performed were confronted with existing theoretical models and the results obtained are in agreement with the solidification theory.
Highlights
Understanding the solidification process and the main microstructures arising from it, are extremely important from a practical standpoint, given that they exert a strong influence on the resulting properties of the products
The Lever Rule equation can be written in terms of solute concentration and solid fraction as, Cs kC0 (1− k) where, k is the equilibrium partition coefficient, C0 is the initial concentration, Cs concentration of the solid phase and fs is the solid fraction
Regarding the situation where no solute diffusion in the solid phase occurs, infinite diffusion in the liquid phase takes place and equilibrium exists at the solid-liquid interface
Summary
Understanding the solidification process and the main microstructures arising from it, are extremely important from a practical standpoint, given that they exert a strong influence on the resulting properties of the products. The phase-field models were developed mainly for simulating solidification of pure materials, being subsequently extended to the solidification of binary, ternary and quaternary alloys. The mechanical properties of as-cast alloys are strongly influenced by the microstructures resulting from the solidification process. As described by Ode et al.[6] for ternary alloys, the influences the material properties, the morphology governing equations for a quaternary non-isothermal phase of the structure itself, such as dendrites and cells, and field model for dilute alloys consists in the following set of inclusions, porosities and segregation, as discussed by chemical potential equations, Paradela et al.[11]. The set of governing equations for the phase-field, solute diffusion and energy transport are the following:. In this study the energy equation is assumed as a first order time discretization scheme, that is, T= n+1 − T n δt k cP
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