The study of Widmanstätten ferrite in Fe–C alloys by a phase field model coupled with anisotropic elasticity

• A model assuming elastic anisotropy for the growth of ferrites is formulated.
• The elastic anisotropy is sufficient to generate acicular Widmanstätten ferrites.
• The direction of the plate thickness features a parabolic thickening.
• The direction of the plate tip characterizes a linear lengthening.
• The calculated aspect ratio and growth rate are in good agreement with experiments.

A phase field model accounting for anisotropic elastic energy has been formulated to investigate the morphology and growth kinetics of a Widmanstätten microstructure during the isothermal austenite to ferrite transformation in binary Fe–C. Physically realistic parameters are employed, for which the thermodynamic functions and the diffusional mobilities are from the literatures that were assessed via the Calphad technique and from experimental results respectively. The simulation results suggest that the anisotropy of elastic energy, resulting from the lattice distortion between the ferrite precipitate and the austenite matrix in the phase transformation, is sufficient to generate a plate-like Widmanstätten structure. The growth of the ferrite precipitate follows completely different dynamic laws in different directions, i.e., parabolic thickening in the direction of the plate thickness and linear lengthening in the direction toward the plate tip. The chief reason for the former is that the moving of the plate broad sides may be regarded as a migration of straight interfaces in the diffusion-controlled phase transformation; the latter is because that the plate tip can maintain a constant radius of curvature during the phase transition after a transient initial stage. Furthermore, the aspect ratio and the lengthening rate of the Widmanstätten ferrite plate simulated by our analyses are in good agreement with the experimental observations.

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