**1. Introduction**

The thermomechanical processing of steels is carried out primarily within the austenite phase field. Previous work has shown that hot rolling produces partial phase transformation of austenite into ferrite in the roll bite inside the single austenite phase field [1,2]. This has been referred to as dynamic transformation (DT) and was first investigated by Yada and co-workers in the 1980's [3,4]. In their study, fine grains of ferrite were produced when three plain carbon were strained during compression testing above the Ae3 temperature.

In order to provide real-time evidence for the occurrence of DT, Yada and co-workers returned to its study in early 2000s. They used the in-situ X-ray diffraction technique coupled to a torsion machine and deformed three Fe-C alloys above the Ae3 temperature [5]. They captured the diffraction patterns associated with α-ferrite during deformation. Chen and Chen [6] performed experiments in 2003 by using a laser dilatometry technique and observed the reverse transformation of dynamically transformed ferrite into austenite at temperatures above the Ae3. Liu et al. [7] performed tests

in a Gleeble thermomechanical simulator in 2007 on a low-carbon steel and obtained similar metallographic results. In 2008, Sun et al. also employed a laser dilatometer in order to follow the reverse DT both below and above the Ae3 [8]. The former authors deformed a 0.17% C plain carbon steel using a Gleeble thermomechanical simulator above the Ae3. They confirmed the existence of both the forward and reverse transformation at temperatures up to 115 ◦C above the Ae3.

In 2010, Basabe and Jonas [9] conducted torsion tests on a 0.036% Nb microalloyed steel in order to study the effects of strain, strain rate, and temperature on DT. They concluded that the reverse transformation was retarded by the addition of niobium in comparison with a plain C steel. This phenomenon was a result of dislocation pinning and solute drag of the niobium carbonitride precipitates and Nb in solution, respectively.

In 2013, Ghosh et al. [10], showed that DT ferrite can be formed as high as 130 ◦C above the Ae3. In their work, they allowed for the inhomogeneous distribution of dislocations, leading to driving forces for ferrite formation as high as 197 J/mol when their materials were submitted to large strains. In 2015, Aranas et al. [1,11,12], presented a new approach involving thermodynamic features to explain the occurrence of DT as much as 500 ◦C above the Ae3. The driving force for DT was redefined to consist only of the softening that takes place during transformation due to the applied stress. The free energy barrier against the driving force for DT consists of the Gibbs free energy difference between the phases as well as the lattice dilatation work and shear accommodation work. According to this model, DT takes place when the driving force overcomes the total barrier preventing its formation.

More recently, Rodrigues et al. [13–15], investigated the phenomenon of DT under various industrial plate rolling simulation conditions. They found that the application of roughing passes under isothermal conditions can lead to the presence of around 8% of transformed ferrite after deformation. The occurrence of DT above the Ae3 temperature during thermomechanical processing is known to generate lower rolling loads and mean flow stresses (MFS) [16]. Moreover, the volume flow rate (as the bar passes through a rolling mill) increases due to formation of less dense ferrite. This type of transformation involves carbon partitioning, which can generate undesirable volume fractions of martensite. Thus, an accurate account of phases during high temperature deformation leads to better mechanical properties of the material.

Nevertheless, the phenomenon of DT has not been studied under the cooling stage of roughing rolling simulation, which represents more realistic industrial conditions. Thus, the present study represents an advance over the previous investigations in that the DT behavior of a Nb-microalloyed steel is investigated under continuous cooling condition of 2 ◦C/s, comparable to industrial roughing rolling schedules. The results obtained are described and discussed in following sections.
