Quantitative three-dimensional phase-field modeling of dendritic solidification coupled with local ensemble transform Kalman filter

Prediction of dendrite growth during alloy solidification is important for controlling the microstructures and mechanical properties of alloys. To this end, quantitative phase-field (QPF) models have been developed to accurately predict dendrite growth. However, a comprehensive method to calibrate the parameters of the QPF models has not been established. In this study, QPF modeling of dendritic solidification coupled with a data assimilation method based on the local ensemble transform Kalman filter (LETKF) is proposed. This modeling could simultaneously estimate multiple parameters and improve the prediction of dendrite growth. The modeling was applied to simulations of isothermal dendritic solidification in Fe-C-Mn ternary alloys. The results show that the solid-liquid interfacial energy and diffusion coefficients of solute atoms in a liquid phase can be estimated from the shapes of the growing dendrites. The accuracy of parameter estimation depends on the growth rate of the primary dendrite arm instead of the dendrite shape. This study demonstrates that LETKF-based data assimilation improves the prediction of solute concentration fields. The proposed QPF modeling paves a promising way to improve the prediction accuracy of conventional QPF models and derive new knowledge from the experimental data obtained by in-situ observations of growing dendrites.