Fig. 1 Profiles of η and the free energy (f s , f s + f e ) across the unrecrystallized (UnRex, η 1) and recrystallized (Rex, η 2) grains

Fig. 2 Flow stresses as functions of strain during hot rolling at T = 900 °C and \(\dot{\varepsilon }\) = 1.0 s-1 for C-Mn steels. The model prediction compares with experimental measurements

Fig. 3 Initial undeformed microstructure

Fig. 4 Increase in grain boundary area with increasing strain ?. S 0 is the original grain boundary area and S d is the grain boundary area after deformation

Fig. 5 Simulated microstructural evolution during the austenite SRX after hot deformation under different pre-strains of a ε = 0.2, b ε = 0.3, c ε = 0.4, d ε = 0.5

Fig. 6 Variations of the SRX grains number with time under different pre-strains

Fig. 7 Average SRX grain size d aver as a function of time under different pre-strains

Fig. 8 Average grain size ln(d rex) with the respect to ln ?

Fig. 9 Simulated SRX kinetics under different pre-strains and a comparison with the predictions by the JMAK model

Fig. 10 Relation between ln t 0.5 and ln ?

Fig. 11 Average interface velocity 〈v〉 as a function of time