## 3 Results and Discussions
### Analysis of DE Optimization Parameters  
The DE optimization technique enables arriving at the optimal combinations to achieve the objective of minimizing the response variables. The billet size ratio (\(z\)), reduction ratio (\(r\)) were maintained as independent parameters with practical intuition for which the optimal values of punch face angle (\(a\)-deg) and land height (\(h\)-mm) were determined for AISI 1010, 1018, and 1045 steel. The optimal punch angle at different reduction and billet size ratios for AISI steels is illustrated in Figure 12. The optimal punch angle obtained through the DE technique was 170\({}^{\circ}\) for \(r\) = 0.3 for AISI 1010, 1018, and 1045, irrespective of the billet size ratio. However, the optimal punch angle was leaning towards 160\({}^{\circ}\) until approximately \(z\) = 0.6 and reversed thereafter for different AISI grades steel. The optimal punch angle was also observed to be striding to 170\({}^{\circ}\) for AISI 1045 rather than 1010 and 1018 for the given reduction and billet size ratio, substantiating the effect of carbon content in the cold forging process of various steels. Subsequently, optimal land height (h) values for different reduction ratios with varying billet size ratios for AISI 1010, 1018, and 1045 steel have been plotted in Figure 13. A similar trend was witnessed for optimal land height on the punch, where the optimal land height values were seen to be close to 4 mm for low carbon steel and descended to 2 mm for AISI 1045 steel. The reason was probably because of friction during metal flow and contact conditions during cold forming. Comparison of Steel for Optimal Response Factors  
The optimal combinations of control factors, billet size ratio (\(z\)), reduction ratio (\(r\)), punch angle (\(a\)), and land height (\(h\)), obtained from the DE technique have resulted in the optimal responses for effective stress, strain, strain rate, and punch force. The optimal forming responses were compared through plots generated by keeping the billet size (\(z\)) and reduction ratios (\(r\)) as independent input variables. Figure 12: Comparison of optimal values of punch face angle (\(a\)) for different steels. * Optimal response factor comparison: effective stress The optimal effective stress \(\left(\sigma_{eff. }\right)\) curves for the reduction ratios (\(r\) = 0.3, 0.4, 0.5, and 0.6) with varying billet size ratio (\(z\)) from 0.3 to 1.2 was observed to be increased until \(z\) = 0.6 and further remained almost stagnant thereafter, up to \(z\) = 1.2 for all steel grades, as illustrated in Figure 14. However, it is evident from the plots that though the optimal effective stress trend was similar for AISI 1010, 1018, and 1045 steels; the stress values increased with varying carbon content. It was also apparent that the effective stress values for the particular grade steel was slightly increased with reduction ratio, while, overall, there was little variation in between AISI1010 and AISI1018 as compared to AISI 1045. This 2 to 4% deviation observed was probably due to the carbon presence in the steel, which largely dictated the formability. The AISI 1045 steel contains a larger % of carbon than the other two AISI grade steels. * Optimal response factor comparison: effective strain Since the amount of deformation remained similar for different steel grades for the given billet size and reduction ratio, there was marginal deviation observed in the plots of the optimal effective strain among AISI steels, as shown in Figure 15. However, optimal effective strain values were increased with a billet size ratio (\(z\)) up to 0.6 for all steel grades, subsequently, no significant rise was observed. The optimal effective strain values for AISI 1045 were slightly leading until \(z\) = 0.6 and marginally held-back until \(z\) = 1.2 compared to that of AISI 1010 and 1018 steel, possibly because of residue elasticity that affects more with volume.