# Impact of Die Radius in a Streamlined Die during Wire Drawing
## 5 Discussion
As shown in Figure 14, the grid of the wire, especially at the surface area, was distorted from the rectangular shape in the deformation zone during wire drawing, and the amount of distortion of the grid increased as the die angle increased or the die radius decreased. That is, the wire around the surface area had a shearing strain or internal distortion due to the conical shape of the die during the wire drawing process, which is related to the redundant work. The redundant work increased with decreasing die radius. A higher redundant effect at the surface area with increasing \(I_{\text{DR}}\) value led to a higher \(S\!I\!F\) value, effective stress at the surface area, damage value at the center area, temperature rise, and drawing force as shown in Figure 12. In contrast, a greater frictional effect at the surface area with decreasing \(I_{\text{DR}}\) value led to a higher temperature rise and drawing force. Therefore, the optimum combination of die design can be derived from the \(I_{\text{DR}}\) value by optimizing the effects of metal flow and \(l_{\text{c}}\). For instance, the temperature rise increased with increasing \(l_{\text{c}}\) in a small \(I_{\text{DR}}\) region due to the greater frictional effect, and then decreased with decreasing \(l_{\text{c}}\) in a medium \(I_{\text{DR}}\) region owing to the smaller frictional effect, followed by increased with decreasing \(l_{\text{c}}\) in a higher \(I_{\text{DR}}\) region due to the higher redundant work effect. Figure 15 shows a schematic of the variations in various design factors with \(I_{\text{DR}}\) value. The \(S\!I\!F\) value, maximum shear stress, maximum effective stress, maximum damage value, temperature rise, and drawing force must be minimized by optimizing the design factors. Based on the results in Figure 15, the optimum \(I_{\text{DR}}\) values ranged from 0.14 to 0.18, indicating that a streamlined die with a radius of 70 to 90 mm was most suitable in the present process condition using Equation (8). That is, the optimum die radius varied with wire size, but suitable die radius can be determined regardless of wire size using Equation (8). Interestingly, we can reduce the damage value of the wire in this range of die radii compared to the conventional die (Figure 9b). The damage value was highly dependent on the highest tensile stress of the wire, as shown in Equation (7), because the normalized Cockcroft and Latham fracture criterion [40] was used in this study. It is known that the principal stress in the center area is the tensile stress state during wire drawing, and the stress in the center area is higher than that of the surface area [43], indicating that the center area exhibited the higher damage value, as shown in Figure 8. As the die angle decreased or the die radius increased, the strain distribution was more uniform along the radial direction of the wire, as shown in Figure 7. This means that the principal stress was also uniform with increasing die radius, leading to the low damage value in the center area of the wire. Overall, the damage value increased with decreasing die radius or increasing \(I_{\text{DR}}\), as shown in Figure 12d. The proposed design concept can provide process engineers with practical seeding ideas to select the optimal die design for high-quality drawn wire, which can be beneficial for industrial plants. The practical strategy was valid for most metals because it was derived from the general conditions of plastic deformation. In addition, it is noted that the effects of a streamlined die on the residual stress of the wire during wire drawing should be considered to obtain a wire with higher fatigue resistance. In this respect, further research is necessary. Figure 12: Variations in (**a**) _SIF_ value, (**b**) maximum shear strain, (**c**) maximum effective stress, (**d**) maximum damage value, (**e**) temperature rise, and (**f**) drawing force of a wire with \(I_{\text{DR}}\). Figure 13: Calculated contact length of wire and die with die angle in the conventional die used in this study.