Effect of Magneto-Mechanical Synergism in the Process-Structure Correlation in Fe-C Alloys: A Phase-Field Modeling Approach

Abstract

Applied magnetic fields can alter phase equilibria and kinetics in steels; however, quantitatively resolving how magnetic, chemical, and elastic driving forces jointly influence the microstructure remains challenging. We develop a quantitative magneto-mechanically coupled phase-field model for the Fe-C system that couples a CALPHAD-based chemical free energy with demagnetization-field magnetostatics and microelasticity. The model reproduces single- and multi-particle evolution during the alpha to gamma inverse transformation at 1023 K under external fields up to 20 T, including ellipsoidal morphologies observed experimentally at 8 T. Chemically driven growth is isotropic; a magnetic interaction introduces an anisotropic driving force that elongates gamma precipitates along the field into ellipsoids, while elastic coherency promotes faceting, yielding elongated cuboidal or ``brick-like" particles under combined magneto-elastic coupling. Growth kinetics increase with C content, and decrease with field strength and misfit strain. Multi-particle simulations reveal dipolar interaction-mediated coalescence for field-parallel neighbors and ripening for field-perpendicular neighbors. Incorporating field-dependent diffusivity from experiment slows kinetics as expected; a first-principles-motivated anisotropic diffusivity correction is estimated to be small (<2%). These results establish a process-structure link for magnetically assisted heat treatments of Fe-C alloys and provide guidance for microstructure control via chemo-magneto-mechanical synergism.

Figures (12)

• Figure 1: Optical micrographs of Fe–0.4 mass% C aged at 1023 K, showing microstructure formation: (a) without applied magnetic field; (b) with a vertically applied magnetic field. Black and white regions correspond to the martensite (transformed from $\gamma$) and $\alpha$ phases, respectively. The $\gamma$ phase transforms into martensite during quenching. Taken from Ohtsuka et al.ohtsuka2000alignment. Ellipsoidal grains nucleated in samples with an applied field: (c) microstructures of Fe–0.1%C alloy subjected to the inverse transformation under magnetic field of 8T. Dark spots are $\gamma$ particles and the gray matrix is $\alpha$ phase maruta2002magnetic; (d) scanning electron micrographs of steel specimen showing the nucleation of $\alpha$ particles inside a $\gamma$ grain. shimotomai2003formation. Ellipsoidal particles are outlined in red.
• Figure 2: Fitted Gibbs free energies of the $\gamma$ and $\alpha$ phases obtained from CALPHAD databases naraghi2014thermodynamicsgustafson1985thermodynamic.
• Figure 3: (a)-(b) Representative sections of the microstructures (shown in Fig. \ref{['fig:experiment']}(c)) obtained from the experimental report by Maruta et al.maruta2002magnetic for Fe-0.1 %C under 8T magnetic field. (c) Simulated morphology for the same system with similar experimental conditions and misfit strain of $0.3\%$. The simulated morphology displays an elliptical shape under these condition, which agrees well with the experimental observation.
• Figure 4: Microstructural evolution of an austenite precipitate within a ferrite matrix in a Fe-0.4 wt%C system: (a) initial configuration; (b) shape resulting from chemical effects alone, showing an isotropic profile; (c–e) evolution under 1 T, 10 T, and 20 T magnetic fields, transitioning from a lens shape at 1 T to a perfectly elliptical morphology at higher fields; (f) profile arising from combined chemical and elastic interactions, yielding a cuboidal precipitate; (g–i) combined magneto-elastic effects at 20 T, evolving from a faceted ellipse at low misfit strain to a brick-like morphology at higher misfit strain.
• Figure 5: Power spectrum analysis (b,e,h,k) and angular power distribution (c,f,i,l) for austenite precipitates (a,d,g,j) in a Fe-0.4 wt%C system for (a-c) chemical effects along, (d-e) elastic‐only interactions with $\epsilon_{ls} = -0.03$, (g-i) magnetic interaction with $B^{ext} = 20$ T, and (j-i) under combined magnetic and elastic interactions with $\epsilon_{ls} = -0.03$ and $B^{ext} = 20$ T.