## 3 Results
### Slip System Activity  
Representative experimental data obtained using the DSR method are presented to provide an overview of the process leading to the final result, which is the confirmation of the activation of the [112]\(<\)111\(>\) slip system (Figure 7). The DSR method is known to involve differential rolling speeds, where the upper roll operates at a higher speed than the lower roll. This speed difference is expected to induce shear effects, making it plausible that the activation of the slip system under these conditions would occur, a configuration supported by VPSC simulations [10]. Additional experimental data include several cases where the active slip system predicted by calculations aligns precisely with experimental  
Figure 6: ODF maps (\(\varphi 1\) (0 to 90\({}^{\circ}\)), \(\Phi\) (0 to 90\({}^{\circ}\)), and a constant \(\varphi 2\) of 45\({}^{\circ}\)) of (**a**) lubricated and (**b**) non-lubricated sample. The highlighted textures are those commonly found in a metal sheet after rolling deformation. observations. All these cases involve grains exhibiting shear texture, as identified by their positions in the ODF [24] and within individual grains. The slip system activity was statistically estimated for the following orientations: \(\{001\}<\overline{11}0>\), \(\{001\}<\overline{11}0>\), \(\{111\}<\overline{11}0>\), \(\{111\}<\overline{12}1>\), \(\{111\}<\overline{01}1>\), and \(\{111\}<\overline{11}2>\) and for grains with other orientations (referred to as \"others\"). All repeated observations (five repetitions for each condition) were averaged, and these averages were then compared. Figure 7 provides insights into the fraction of grains with these specified orientations and the proportion activating the \(\{112\}<111>\) slip system under plane strain or plane strain + shear strain conditions. Texture fraction was calculated as the ratio of each specific texture's fraction to the total texture fraction within a single map. Several conclusions can be drawn from this analysis. The first dataset, represented by the orange columns, indicates the fraction of grains with the orientation shown in the top left corner of each subfigure. Figure 8a,b illustrate that the fraction of red color-coded orientations is nearly identical between the two samples, as indicated by the similar mean values and consistent labels (all labeled \"a\") from the Tukey post hoc test. In contrast, Figure 8c-f show that the dominant blue color-coded textures differ between the samples. Once again, it was confirmed statistically that the lubricated sample is primarily characterized by \(\{111\}<\overline{11}0>\), \(\{111\}<0\overline{1}1>\), and a minor fraction of \(\{111\}<\overline{11}2>\), whereas the non-lubricated sample is defined by \(\{111\}<1\overline{2}1>\) and \(\{111\}<0\overline{1}1>\). Additionally, the fraction of grains classified as \"others\" (Figure 8g) is higher in the non-lubricated sample than in the lubricated sample. Figure 7: Three representative datasets providing an overview of the current method. Both experimental and theoretical rotation axes demonstrate the activation of the [112]\(<\)111\(>\) slip system under plane strain and shear conditions. The second dataset, represented by the green columns, shows the fraction of grains with the orientations indicated in the top left corner that activated the {112}\(<\)111\(>\) slip system under plane strain mode. Although the overall fraction of grains activating the slip system is small, activation is not strictly proportional to grain orientation. For instance, while grains classified as \"others\" appear in higher counts, they show close to the lowest fraction of grains activating the single {112}\(<\)111\(>\) slip system. Interestingly, grains with {111}\(//\)ND orientations activating the single {112}\(<\)111\(>\) slip system occur more frequently than those with {001}\(//\)ND orientations, indicating that {001}\(//\)ND grains are more likely to support multiple slip systems.