**2. Materials and Methods**

A Nb-microalloyed steel was investigated in the present work. This material was provided by EVRAZ North America in the form of hot-rolled plates. The complete chemical composition of the material (in wt%) is displayed in Table 1. The orthoequilibrium and paraequilibrium Ae3 temperatures were identified by employing the FSstel database of the FactSage thermodynamic software 7.1 [17]. For the present analysis, the orthoequilibrium Ae3 temperature will be considered, where both the substitutional and interstitial atoms are assumed to participate during phase transformation. The hot-rolled plates were machined into torsion samples with diameters and gauge lengths of 10 mm and 20 mm, respectively. The cylindrical axis of all the samples were parallel to the rolling direction of the plate. The torsion experiments were carried out using a Gleeble 3800 thermomechanical simulator (Dynamic Systems Inc. Poestenkill, NY, USA) with a Hot Torsion Mobile Conversion Unit (MCU). The samples were heated by flowing alternated current to the desired reheat temperature. This ensured that each deformation occurred at the proper temperature simulated by that rotation step. Thermal gradients in the sample were controlled by making the specimen solid in the torsion span and hollow on both sides to minimize gradients in the sample that would otherwise develop due to non-uniform current densities in the shoulders versus the reduced center

section of the sample. A thermocouple was welded to the sample to accurately track the deformation temperatures at every pass.

**Table 1.** Chemical composition (mass%) and equilibrium transformation temperatures (◦C).


The thermomechanical schedule of the present work is shown in Figure 1. The torsion samples were heated to 1200 ◦C at a rate of 1 ◦C/s and were isothermally held for 5 min to attain a single-phase austenite microstructure. The samples were then cooled to 1100 ◦C at a rate of 1 ◦C/s. The first deformation was applied after 60 s at 1100 ◦C, followed by controlled cooling at a rate of approximately 2 ◦C/s. The succeeding deformations (from 2nd pass up to the 5th pass) were applied during continuous cooling conditions with an interpass time of 10 s, mimicking the actual plate rolling process. The deformation temperatures were 1080 ◦C (2nd), 1060 ◦C (3rd), 1040 ◦C (4th), and 1020 ◦C (5th). Note that the samples were strained to 0.3 during each pass applied at a strain rate of 1 s−1. A strain higher than the critical stains for the onset of DT [9–15] was selected so as to allow for DT to take place. Water spray quenching after R1, R3, and R5 were performed at minimum rate of 500 ◦C/s using the Gleeble high flow quenching system. All experiments were performed under argon atmosphere to minimize the oxidation and decarburization, which can affect the results. Additionally, the experiments were repeated three times to validate the results. In general, less than 3% difference in the level flow curves was observed.

**Figure 1.** Thermomechanical schedule employed in the Gleeble torsion simulations of roughing passes. The deformation temperatures were 1100, 1080, 1060, 1040, and 1020 ◦C, strain of 0.3 was employed in each pass and interpass time of 10 s.

The deformed samples were water quenched before the 1st pass, and after 1st, 3rd, and 5th pass to accurately track the evolution of microstructure during multi-pass rolling simulation. The deformed and quenched torsion samples were sectioned longitudinally to reveal the changes in grain shape that accompany straining for microscopy analysis. These analyses were carried out at about 150 μm below the surface of the samples so as to avoid the oxidized outer layer. A conductive hot phenolic resin was used to mount the samples. These were polished using SiC grits 400, 600, 800, and 1200 lubricated with water. The final polishing was carried out using 3 and 1 μm diamond suspensions. The polished surfaces were etched with 2% nital (to reveal the microstructure) followed by 10% aqueous metabisulfite (Na2S2O5) solution (to provide contrast between ferrite and martensite).
