## 3 Results and Discussion  
### Fem Results  
Before this extensive work could be undertaken, it was necessary to validate the FEM setup and assess whether the novel Vo-CAP die design would give better results compared to VE. To achieve this, the FEM model was validated against the study conducted by [PERSON] et al. using identical material properties, boundary conditions, and process parameters for the AA1050 workpiece [24]. As shown in Figure 10, there is excellent agreement between the simulation results obtained in this study and the reference data at different twist angles (\(30^{\circ}\), \(90^{\circ}\), and \(180^{\circ}\)). This clearly confirms the reliability of the FEM  
Figure 9: Tensile test sample. (**a**) Geometrical dimensions. (**b**) Prepared round test specimen. setup designed for this study. Furthermore, as is clearly evident in the figure, the Vo-CAP method consistently achieves both higher strain values and more homogeneous effective strain distributions compared to VE. To systematically investigate the effects of geometric parameters on the Vo-CAP process performance, twenty-seven different die configurations were analyzed using FEM. Table 3 presents the comprehensive results of these analyses, showing the relationship between design variables (\(\beta\), \(\mathrm{T_{L}}\), and \(\mathrm{T_{CL}}\)) and objectives (\(\overline{\varepsilon}\), ML, and CV\(\varepsilon\)p). The results demonstrate that the twist angle (\(\beta\)) has a significant impact on effective strain values. Higher twist angles tend to increase the effective strain but also result in greater maximum pressing loads. Furthermore, increasing the channel length (\(\mathrm{C_{L}}\))  
Figure 10: Validation of the FEM setup and comparison of the VE and the Vo-CAP at different twist angles [24]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case Num. **} & \multicolumn{3}{c}{**Variables**} & \multicolumn{3}{c}{**Objectives**} \\ \cline{2-7}  & \(\beta\) & \(\mathrm{T_{L}}\) & \(\mathrm{TCL}\) & \(\overline{\varepsilon}\) & \(\overline{\mathrm{ML}}\) & \(\mathrm{CV\varepsilon p}\) \\ \hline case 1 & 30 & 10 & 10 & 11.84 & 12.79 & 0.4  
improves strain homogeneity; however, it negatively affects the effective strain. These opposing effects of the design variables on the different objectives highlight the complexity of the optimization problem. Therefore, a comprehensive multi-objective optimization approach was necessary to identify the optimal design parameters that balance these competing factors. To better understand the process mechanics, Figure 11 shows both the deformation patterns and the load-stroke curve during the Vo-CAP process. The process can be divided into three zones. Each zone shows a specific characteristic behavior. In the VE zone, a rapid pressing load increase was observed from 0 to 5.6 mm of the stroke. This is due to the fact that the material has been forced into the vortex-shaped channel. And the result is torsional deformation, which necessitates considerable pressing load. In the TC zone, the pressing load was relatively constant from about 5.8 mm to 15.1 mm of the die stroke. So, this zone has, therefore, acted as a bridge between the VE and ECAP regions. As the material flows through a straight channel without much deformation, the force was stable in this TC zone. In the final ECAP zone, at approximately 15 mm of the die stroke, the pressing load was suddenly increased. As the material entered the third and final ECAP section, it was subjected to high shear deformation due to the sharp rotation. As the fluidity of the material increases at this point and the resistance exerted by the die decreases, the pressing load was reduced slightly between the 35 and 40 mm range of the stroke. To ensure that the material achieved the desired vortex shape, the experiment was paused, and the die was opened to inspect the deformation progress.