# Predicting the Effect of Processing Parameters on Caliber-Rolled Mg Alloys through Machine Learning
## 3 Results and Discussion  
Table 1 summarizes the side length of caliber cross-section (s) measured by a micrometer, accumulated reduction in area (\(r\)), and equivalent strain (\(\varepsilon_{eq}\)) per MPCR deformation pass. The relation between the latter parameters is expressed as follows:  
\[\varepsilon_{eq}=-\ln\Bigl{(}1-\frac{r}{100}\Bigr{)} \tag{2}\]  
Increasing the number of MPCR passes imposed an increasing amount of plastic deformation, leading to the positive correlation between the \(\varepsilon_{eq}\) value and pass number. However, these calculations are insufficient to describe the precise trends of plastic deformation for two reasons. First, the results assume the uniform distribution of strains on the cross-sectional area, which is not applicable to the present case. Complex three-dimensional stress states induced by the MPCR process caused a significant difference in deformation behavior [32]. Second, the actual strain is remarkably higher than the theoretical \(\varepsilon_{eq}\) value as the latter cannot consider the redundant strain [17]. Such a disparity was confirmed in various materials including both steels [18; 32] and nonferrous alloys [23; 33]. FEA provided deeper insight into the two drawbacks of theoretical calculation mentioned above (Figure 3). The FEA-based \(\varepsilon_{eq}\) values were remarkably higher than the theoretical value calculated using Equation (2) (1.29), as aforementioned. Furthermore, the eight-pass MPCR process gave rise to a significant inhomogeneity of \(\varepsilon_{eq}\) values on the cross-section. The \(\varepsilon_{eq}\) value for the corner sections (2.08) was significantly higher than that for the center (1.78). This type of \(\varepsilon_{eq}\) distribution arose from the MPCR process, rather than from the material, because the similar distribution was reported from 0.15C-0.3 Si-1.5 Mn-0.01P-0.0025 steel subjected to the MPCR process [18]. Specifically, diamond calibers led to \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Pass \({}^{\ddagger}\)** & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline \(s\) **(mm)** & 5.30 & 4.91 & 4.56 & 4.17 & 3.89 & 3.50 & 3.29 & 3.04 & 2.79 \\ \(r\) (\%) & 0 & 13.6 & 26.6 & 37.7 & 46.4 & 56.8 & 61.8 & 67.5 & 72.4 \\ \(\varepsilon_{eq}\) & 0 & 0.15 & 0.31 & 0.47 & 0.62 & 0.84 & 0.96 & 1.12 & 1.29 \\ \hline \hline \end{tabular} \({}^{\ddagger}\) The number of applied MPCR passes.  
\end{table} 
Table 1: \(\varepsilon_{eq}\) and shape factors for its calculation for each deformation pass of MPCR process. Figure 2: Graphical scheme of GAN-aided ANN model developed in the present study. the given \(\varepsilon_{eq}\) distribution [18, 23]. The FEA also demonstrated the significant local strain at the interface between the rod surface and roll, as shown in Figure 3b. Conversely, oval and circular calibers accumulate strain on the center, leading to different \(\varepsilon_{eq}\) distribution [32, 33]. Vickers microhardness values were measured along the transverse direction on the cross-sectional areas (Figure 4). The hardness increased with increasing amounts of MPCR deformation from the first to fourth pass (Stage I). It became steady at ~83 HV from the fourth to sixth pass (Stage II), and then increased again up to the eighth MPCR pass (Stage III). The suppressed hardness increment between the fourth and sixth passes can be understood using microstructural evolution. Dynamic recrystallization occurs during the MPCR process for Mg alloy, which consists of (i) the formation of fine arrays surrounded by low-angle grain boundaries and (ii) the conversion of them into recrystallized grains with high-angle grain boundaries [13]. Stages I and II correspond to these steps, respectively. The first dynamic recrystallization was completed in Stage II, leading to the steady state of microhardness. Further straining in Stage III induced the second dynamic recrystallization including the subgrain refinement, and thus increased the hardness again. [PERSON] et al.