*4.2. E*ff*ect of Heat Generation due to Plastic Deformation*

The heat generation by the plastic deformation during rolling process affects the thermal behavior of a workpiece, which means that the temperature distribution of workpiece depends on the strain distribution of a workpiece with area. The temperature rise by plastic deformation was typically described as the following equation [38]:

$$
\Delta T = \frac{\Delta Q}{\rho \mathbb{C}\_p} = \frac{\beta}{\rho \mathbb{C}\_p} \int\_{\varepsilon\_1}^{\varepsilon\_2} \sigma d\varepsilon \tag{7}
$$

where β and Δ*T* are the fraction coefficient between deformation work and heat energy and temperature rise, respectively. As given in Table 2, the fraction of deformation energy converted to heat energy is generally assumed to be 0.9 because only a small amount of deformation energy is stored within the workpiece as elastic energy. Because the temperature rise of a workpiece is highly related to the amount of plastic deformation according to Equation (7), the effective strain distribution of both plate and rod was evaluated, as shown in Figure 10a,b. It was clearly shown that the strain distribution of the plate was more homogeneous than that of the rod. Additionally, the pattern of effective strain distribution was totally different between the two processes. In the plate, the surface area had the maximum strain value and the center area had the minimum [39]. On the other hand, the center area had the maximum strain and the surface area had the minimum during shape rolling, which was well described in the profiles of effective strain along the horizontal and vertical directions of the two processes (Figure 10c). The higher effective strain in the center area of the rod during shape rolling can make a higher temperature rise in the center area, as shown in Figure 5b. Meanwhile, the relatively lower effective strain in the center area of the plate during flat rolling induced the lower temperature rise in the center area (Figure 5a). Comparing the distribution of effective strain in the plate, the rod had a higher temperature deviation with area because the temperature rise in the center area of the rod was higher than that of the plate. Overall, the center temperature of the rod became higher by the temperature rise due to the higher plastic deformation, whereas the surface temperature of the rod became lower by the hard contact with roll. This can make a higher temperature deviation of the rod with area during the shape rolling process. In contrast, strain distribution of the plate during flat rolling contributed to the uniformity of temperature distribution of the plate with area because the surface area had a higher effective strain during the flat rolling process.

The frictional stress in the roll–workpiece interface also increased temperature of a workpiece during the forming process, and the amount of temperature rise can be different between the two processes. Further experiments are necessary to reveal the frictional effect on temperature rise with rolling process, which is one of the valuable research topics in the field of forming industries. Overall, the higher temperature deviation of the rod along the circumferential and radial directions can induce the surface defects such as surface flaw, abnormal grain growth, and decarburization during the shape rolling process. In contrast, the influence of temperature deviation of the plate on surface defects is relatively weak during the flat rolling process.

**Figure 9.** Contour maps of effective stress of (**a**) plate and (**b**) rod during the hot rolling process.

**Figure 10.** Contour maps of effective strain of (**a**) plate, (**b**) rod, and (**c**) comparison of profiles of effective strain along the horizontal and vertical directions of a workpiece.
