**3. Results**

#### *3.1. Flow Curves and Mean Flow Stress*

The torque-twist curves obtained were converted into stress-strain curves using Fields and Backofen formulation [18]. The stress–strain curves associated with the five-pass torsion simulation are displayed in Figure 2a. The peak stresses of the 1st (1100 ◦C) 2nd (1080 ◦C), 3rd (1060 ◦C), 4th (1040 ◦C), and 5th (1020 ◦C) passes are 83, 93, 98, 105, and 112 MPa, respectively. Although the increasing trend of peak stresses during cooling appears to be typical behavior of a material during cooling, note that the rate of increase from 1st pass going to the 2nd pass is about 0.5 MPa/◦C. This rate is higher than the ones in succeeding passes due to strain accumulation. For example, from 2nd to 5th pass, the average rate of increase from pass to pass is approximately 0.3 MPa/◦C. This is 40% lower than the rate of increase from the initial two passes. It appears that the low rate of peak stress increase indicates that dynamic softening is taking place in the material. To further analyze these observations from the stress–strain curves, the mean flow stresses (MFS) were calculated by measuring the area of the stress–strain curves, normalized by the amount of strain. The dependence of MFS on temperature and on the total applied strain is shown in Figure 2b. Note that the slope of the linear relation between the 1st and 2nd passes are considerably higher than the slope of the 3rd, 4th, and 5th passes. This is an indication of softening by combination of recrystallization and phase transformation occurring in the material during deformation.

**Figure 2.** (**a**) Roughing stress–strain curves determined according to the schedule of Figure 1 using pass strains of 0.3 applied at 1 s<sup>−</sup>1: (**b**) mean flow stresses (MFS) curve derived from the stress–strain curves of Figure 2a.

## *3.2. Microstrutural Results*

The microstructures before the 1st pass (Figure 3a), after the 1st pass (Figure 3b), after the 3rd pass (Figure 3c), and after the 5th (Figure 3d) are displayed in Figure 3. The martensite phase appears dark and characterized by needle-shape structures inside the grains, while ferrite is the lighter structure and commonly identified by its polygonal structure. Here the grain sizes before the initial deformation are quite large, which was measured to be around 54 ± 15 μm (see Figure 3a). These grain sizes are slightly smaller than the typical sizes of austenite phase in industrial plate rolling before applying the roughing passes. The phase consists of entirely martensitic structure (prior austenite phase at elevated temperature). Note that after the five-pass simulation (see Figure 3d), the grain sizes decreased to less than 10 μm, which suggests the occurrence of either static recrystallization (SRX), metadynamic recrystallization (MDRX), dynamic transformation (DT), or a combination of these softening mechanisms. Although a long interpass time of 10 s was employed, it is important to note that the presence of Nb can significantly delay SRX in-between passes. A more interesting observation is the presence of light structures (ferrite), which forms dynamically. It is well-known that ferrite is softer than austenite due to its higher stacking fault energy [19]. Therefore, the presence of dynamically transformed ferrite (in combination with DRX) can generate significant softening of the material.

(**a**) (**b**)

**Figure 3.** Optical microscopy images of steel subjected to the roughing simulation. The samples were quenched immediately: (**a**) Before the first pass; (**b**) after the first pass; (**c**) after the third pass and (**d**) after the fifth pass. Light regions are ferrite while the dark regions are martensite (prior austenite).

#### *3.3. Volume Fraction of Transformed Ferrite*

The volume fraction of ferrite was measured using the ImageJ software [20] to quantify the contribution of DT ferrite on the unusual behavior of the stress–strain curves, as shown above. The results are plotted and presented in Figure 4. The volume fraction of ferrite was measured based on the cumulative strain. Even though the reverse transformation of ferrite back into austenite can take place during the pass intervals, the amount of ferrite continously increases with applied strain. Note that the volume fraction of ferrite after the 2nd and 4th passes were interpolated. These values demonstrate that the rate of peak stress increase during cooling can be significantly affected by the occurrence of DT once the volume fraction of ferrite reached above 5%. This observation is consistent with the results of an earlier work of the present authors [13–15].

**Figure 4.** Dependence of the cumulative volume fraction of ferrite formed on the cumulative strain and temperature.

#### **4. Discussion**
