Fig. 1. Temperature programs employed in the current work: (a) different holding temperatures, (b) various durations at a given temperature for isothermal austenite-to-ferrite transformation.

Fig. 2. (a) Schematic depicting that a ferrite grain α nucleated at the GBs of austenite is considered as a sphere growing in a fictitious and concentric austenite matrix γ with radius of Dγ,0, and (b) geometry of the α grain with a probe plane A (parallel to the GB plane) used for the calculation of its extended area or volume.

Fig. 3. Contiguity ratio Cα/α as a function of the volume fraction transformed $\int_V^α$ for isothermal decomposition of austenite to ferrite in a hypo-eutectoid steel, the open circles denoting stereological measurement from Ref. [49], the solid line and the dashed line denoting Cα/α=$(\int_V^α)^ξ$ with ξ = 0.5 and 1, respectively.

Fig. 4. Measured relative length change by dilatometer as a function of the relative time during the different isothermal holding (Tγ→α = 740, 760, 780 and 800 °C) of Fe-0.17C-0.91Mn-1.03Si alloy as sketched in Fig. 1(a).

Fig. 5. SEM micrograph of Fe-0.17C-0.91Mn-1.03Si alloy after going through the temperature paths sketched in Fig. 1(a), (a) Tγ→α = 740 °C, (b) Tγ→α = 760 °C, (c) Tγ→α = 780 °C and (d) Tγ→α = 800 °C. F is polygonal ferrite and B is bainite.

Fig. 6. Optical micrograph of Fe-0.17C-0.91Mn-1.03Si alloy after going through the temperature program sketched in Fig. 1(b), (a) tγ→α = 60 s, (b) tγ→α = 120 s, (c) tγ→α = 360 s and (d) tγ→α = 600 s at 760 °C F is polygonal ferrite and M(γ) is martensite transformed from the untransformed austenite.

Fig. 7. Isopleth section of phase diagram for Fe-C-0.91Mn-1.03Si alloy calculated by Thermo-Calc with TCFE8 database. The initial concentration and the experimental results are also included.

Fig. 8. (a) Calculated Gibbs energy dissipation and the available chemical driving force $ΔG_m^{chem}$ for different Rα as functions of the interface (or growth) velocity v, (b) the calculated $ΔG_m^{chem}$ and v as functions of the corresponding Rα, and (c) Rα as a function of t-τ, for the growth of single ferrite grain in austenite matrix at 760 °C in the Fe-0.17C-0.91Mn-1.03Si alloy.

Fig. 9. (a) $\int_V^α$ from the present model prediction (solid line), from the model calculation assuming plane interface growth regardless of nucleation [30] (dashed line), and from the experimental measurement (scatter + line) as function of time, (b) the phase interface area $S_V^{γ/α}$ and the interfacial area between ferrite grains $S_V^{α/α}$ per unit volume as function of $\int_V^α$, and (c) the calculated <Dα> associated with the quantitative metallography as a function of time, for the isothermal austenite-to-ferrite transformation of Fe-0.17C-0.91Mn-1.03Si alloy at 760 ℃.

Fig. 10. (a) $\int_V^α$ from the dilatation measurement of Fig. 4 (scatters) and from the present model prediction (lines) as a function of time for the isothermal austenite-to-ferrite transformation of Fe-0.17C-0.91Mn-1.03Si alloy at T = 740, 760, 780 and 800 °C. (b) The calculated final-state Dα associated with the quantitative metallography and the corresponding shape factor gα as a function of the holding temperature, where the model calculation assuming gα = 1 is also included.

Fig. 11. Calculated QMeff as a function of the normalized driving forceΔGchem/$ΔG_{chem}^{initial}$ for interface migration (or growth) during the isothermal austenite-to-ferrite transformation of Fe-0.17C-0.91Mn-1.03Si alloy.

Fig. 12. Ferrite grain-size distributions (bars) of Fe-0.17C-0.91Mn-1.03Si alloy in the final state of isothermal annealing. Lines show the lognormal fit according to Eq. (34).