*2.1. Experiment Using O*ff*-line Rolling Simulator*

In order to understand the thermal histories of the rod and plate with area, a simulator for the hot rolling process was used. The rolling simulator mainly consisted of a couple of rolls, guide for workpiece, roller conveyor, and reheating furnace, as shown in Figure 3. Prior to the hot rolling test, the workpiece with four thermocouples was placed in a box-type reheating furnace. An oxide scale formation on the surface of a workpiece was suppressed using nitrogen gas in the reheating furnace. When the workpiece was heated to the final temperature of 1150 ◦C, it stayed for an additional 20 min for a homogenization. Then, the workpiece was withdrawn from the reheating furnace and rolled without lubrication.

For the flat rolling test, a rectangular plate of 150 × 30 mm was selected for an initial workpiece and it was hot-rolled using the flat rolls, as shown in Figure 4a. The round specimen with a diameter of 50 mm was also hot-rolled using the oval groove, as shown in Figure 4b. The ductile casting iron (DCI) rolls of 400 mm in diameter were rotated at a speed of 10 RPM. Plain low carbon steel, AISI 1020, was used and the analyzed chemical composition in weight percent was Fe-0.2C-0.4Mn. The specific operating conditions are summarized in Table 1. The caliber roll was designed to have a reduction of area (RA) per pass of 20%, which is a general rolling condition in hot rod rolling industries. RA per pass was calculated using the following equation:

$$RA = \frac{A\_0 - A\_f}{A\_0} \times 100 (\%) \tag{1}$$

where *Ao* and *Af* are the areas of initial and final cross section, respectively. The reduction of height of a plate during flat rolling was selected to have a same average effective strain with the rod during shape rolling. The average effective strain of a rod during shape rolling was calculated using the model proposed by Lee et al. [24] that is based on the equivalent rectangle approximation method, which transforms a non-rectangular cross section shape into a rectangular shape, and the average effective strain (ε*p*) is calculated as follows:

$$
\varepsilon\_p = \left[\frac{2}{3} (\varepsilon\_1^2 + \varepsilon\_2^2 + \varepsilon\_3^2)\right]^{1/2} = \frac{2}{\sqrt{3}} \varepsilon\_2 \left[1 + \left(\frac{\varepsilon\_1}{\varepsilon\_2}\right)^2 + \left(\frac{\varepsilon\_1}{\varepsilon\_2}\right)\right]^{1/2} \tag{2}
$$

where ε<sup>1</sup> and ε<sup>2</sup> are simply obtained by calculating the reduction ratio of width and height in equivalent rectangle approximation, respectively. In case of plate rolling, the ratio of ε<sup>1</sup> and ε<sup>2</sup> is very small in nature, and thus the average effective strain is represented as follows:

$$
\varepsilon\_p = \frac{2}{\sqrt{3}} \varepsilon\_2 \tag{3}
$$

where ε<sup>2</sup> is calculated by the reduction ratio of height as follows:

$$\kappa\_2 = \ln \left( \frac{H\_i}{H\_f} \right) \tag{4}$$

where *Hi* and *Hf* are the height of initial and final plate, respectively. The final height of a plate was chosen using Equation (3), as shown in Figure 4a.

Figure 4a,b shows the schematic description of the measurement points of temperature using thermocouples in workpieces. Four points were measured at the each process using chromel–alumel (K-type) thermocouples with an Inconel sheath. The response time of the thermocouple was improved by decreasing its diameter; therefore, 1.0 mm diameter thermocouple was selected, although it was easily breakable during the experiment under the severe working conditions such as the hot rolling test. Thermocouples were embedded in the 70 mm deep hole drilled from the tail end of a workpiece, as shown in Figure 4c, to easily handle the workpiece during the rolling test and to minimize the thermal disturbance on the surface of a workpiece [23]. One thermocouple was located at the center, and three of them were placed as close the surface as possible, i.e., the thermocouples of the surface were located at 1.5 mm from the outer surface. A multi-channel data recorder gathered temperature data during the test with a sampling time of 0.2 s. Because the thermocouples that are embedded in the surface region were easy to burn out during the hot rolling test, each test was repeated three times to ensure reliability and repeatability.

**Figure 3.** Schematic description of the off-line hot rolling simulator in this study.

**Figure 4.** *Cont*.

**Figure 4.** Schematic description showing the roll design and the measurement points of temperature using thermocouples: (**a**) cross section of flat rolling, (**b**) cross section of rod rolling, and (**c**) cross section of the longitudinal direction of the rod.


**Table 1.** Process parameters of hot rolling test using the off-line simulator in this experiment.
