A phase-field model is proposed for the simulation of microstructure and solute concentration during the solidification of Fe-C-P-Mn quaternary alloys. In this paper, a study is presented to analyze both the effects of partition coefficient and solute diffusivity on the microstructural evolution during solidification simulation. Partition coefficient and diffusivity are very important from a practical standpoint, because both parameters exert a strong influence on the dendrite morphology. Additionally, the proposed model is applied for quaternary alloys to the analysis of the time-dependent solidified fraction. Simulations permit to conclude that the solidified fraction is proportional to the square root of time, as expected for any diffusion-controlled growth process. Phase-field simulations on non-isothermal dendrite growth are also examined. Two-dimensional simulation results exhibit different dendrites in multicomponent alloys for different solute concentrations. Changes in the carbon concentration seem to affect the dendrite morphology, due to its higher concentration and its lower equilibrium partition coefficient. Changes in the phosphorus concentration affect the dendrite morphology and the interface velocity, when its content is increased from 10-3mol%P. Higher manganese content slows down the solidification kinetic, while the dendrite morphology remains unchanged.
Numerical simulation of multicomponent alloy solidification demands accuracy of thermophysical properties in order to obtain a numerical representation as close as possible to the physical reality. Some alloy properties are only seldom found in the literature. In this paper, a solution of Butler’s formulation for surface tension is presented for Al-Cu-Si ternary alloys, allowing the Gibbs-Thomson coefficient to be calculated as a function of Cu and Si contents. The importance of the Gibbs-Thomson coefficient is related to the reliability of predictions furnished by predictive microstructure growth models and of numerical computations of solidification thermal variables that will be strongly dependent on the values of the thermophysical properties adopted in the calculations. A numerical model based on Powell hybrid algorithm and a finite difference Jacobian approximation was coupled with a ThermoCalc TCAPI interface to assess the excess Gibbs energy of the liquid phase, permitting the surface tension and Gibbs-Thomson coefficient for Al-Cu-Si hypoeutectic alloys to be calculated. The computed results are presented as a function of the alloy composition.
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