Development of a CALPHAD-coupled Phase-field Model for Predicting Microstructure Evolution in Fe–C Steels

Takumi Morino; Machiko Ode; Yusuke Matsuoka; Shoichi Hirosawa

doi:10.2355/tetsutohagane.tetsu-2025-086

Journal article Development of a CALPHAD-coupled Phase-field Model for Predicting Microstructure Evolution in Fe–C Steels

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Takumi Morino, Machiko Ode, Yusuke Matsuoka, Shoichi Hirosawa. Development of a CALPHAD-coupled Phase-field Model for Predicting Microstructure Evolution in Fe–C Steels. Tetsu-to-Hagane. 2026, 112 (6), TETSU-2025-086. https://doi.org/10.2355/tetsutohagane.tetsu-2025-086

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To predict the microstructures of steels, direct coupling of phase-field method and Calculation of Phase Diagrams (CALPHAD) databases is desirable. However, such direct coupling is challenging even for the binary Fe-C system. The first difficulty is that the local equilibrium condition becomes an implicit function, resulting in extremely high computational costs. The second difficulty is that the relationship between phase composition used in phase-field method and site fraction employed in CALPHAD method is nonlinear. In this study, a phase-field model for the Fe-C system is developed by combining Direct CALPHAD Coupling (DCC) model, which explicitly solves the local equilibrium condition, with a chain-rule formulation that links phase composition to site fractions. Numerical tests for phase solidification and phase peritectic transformation demonstrated that the proposed model satisfies the local equilibrium condition with errors small enough to have no impact on the simulation results and accurately reproduces phase diagram at equilibrium condition. The developed approach provides a framework for simulating microstructure evolution directly coupled with CALPHAD database for steels containing interstitial elements such as carbon and nitrogen.

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