Fig. 1 Schematic diagram for the planar interface ($\text{I}$) upon austenite reverse transformation, which separates the austenite ($\gamma$) and the ferrite ($\alpha$) and moves toward the ferrite with the velocity $v$ along the direction normal to the γ/α interface. Note that a single closed system is considered because there is no solute fluxed at the interface of the austenite ($\text{L}$) and the ferrite ($\text{R}$), which is different from the inner interface ($\text{I}$), the austenite ($\gamma$) and the ferrite ($\alpha$) with concentration ($u_{\alpha }^{i},u_{\gamma }^{i},u_{\alpha }^{{i*}},u_{\gamma }^{{i*}}$), solute fluxes ($J_{\alpha }^{i}$, $J_{\gamma }^{i},J_{\alpha }^{{i*}},J_{\gamma }^{{i*}}$), and chemical potential ($\mu _{\alpha }^{i},\mu _{\gamma }^{i},\mu _{\alpha }^{{i*}},\mu _{\gamma }^{{i*}}$). The lengths of $\text{LI}$ and $\text{LR}$ are $l$ and $S$, respectively

Fig. 2 Concentration profiles of a carbon and b manganese are plotted at different time: the initial time t = 0, an intermediate time t, and the infinite time t=$\infty$ when the austenite-ferrite equilibrium is reached

Fig. 3 Microstructure of the specimen before the ART. a An EBSD map filled with lath martensite before the heat treatment, in Fe-0.92C-8.06Mn (in at.%) alloy. b Counts of different lath widths in a, where the mean width is 1.01 μm

Fig. 4 Evolution of the calculated phase transformation dynamics. a Dilatation of the sample as a function of temperature. b Variation of austenite fraction with transformed time at 620, 640, 660 ℃ calculated by the current model and the Kuang’s model. c, d C and Mn diffusion profiles at various time at 660 ℃, respectively. Note that the $\gamma$ phase grows from the left to the right in the cell of the $\alpha$ phase

Fig. 5 Evolution of experimental phase transformation dynamics. a Dilatation of the samples as a function of time at 620, 640, 660 ℃, respectively. b XRD patterns of the samples treated for 30 min at different temperatures. c Volume fraction of austenite treated at different temperatures for 30 min. d Calculated evolution and experimental evolution of γ fraction as functions of time

Fig. 6 Changes in Gibbs free energy of phases. a Gibbs free energy of the austenite phase as a function of temperature and carbon content. b Gibbs free energy of the ferrite phase as a function of temperature and manganese content (Thermo-Calc)

Fig. 7 Evolution of the thermodynamic driving force, the kinetic energy barrier, and generalized stability. a Evolution of thermodynamic driving force and the kinetic energy barrier as a function of the isothermal temperature. b Variation of the driving force and generalized stability with isothermal temperature and transition fraction

Fig. 8 Mechanical properties: a engineering stress-strain curves of the ART620-180, ART620-600, ART620-1200, and ART620-1800 samples, b summary of yield strength and uniform elongation