# Influence of Roll Diameter on Material Deformation and Properties during Wire Flat Rolling
## 3 Results
### Contact Area and Pressure Distribution with Roll Diameter  
The contact area and its pressure distribution in the workpiece and roll interface have a great effect on the product shape, roll force, temperature drop, surface properties, production costs, and roll wear during the rolling process. Therefore, the evaluation of the contact pressure in the roll bite is essential to gain a better understanding of the wire flat rolling process. It is known that the distribution of the contact pressure during the rolling process depends on \(R_{h}\), friction at the workpiece and roll interface, and material properties [5; 27; 28; 29; 30; 31]. Figure 8 shows the distribution of the normal contact pressure on the wire surface with the roll diameter. The contour of the normal contact pressure on the wire exhibited similar patterns regardless of the roll diameter. The contact pressure showed higher values at the entry, edge, and exit zones of the contact area. This shape of the contact pressure distribution was reported in earlier studies [32; 33]. Summarizing the literature above, the higher contact pressures in the entry and edge zones of the contact area are explained by the restrictions caused by the more rigid surrounding material that deforms elastically. In addition, the higher contact pressure on the exit zone of the contact area is attributable to the strain hardening effect of the metal during the process. Figure 9 shows a comparison of the effective stress distribution of the wire along the rolling direction. The similar effective stress distributions of the wire, regardless of the roll diameter, partially supported the present similar contact pressure distributions.  
Figure 8: Comparison of the normal contact pressure on the wire surface with the roll diameter during wire flat rolling.  
Figure 9: Comparison of the effective stress along the rolling direction of the wire with the roll diameter during wire flat rolling.  
Meanwhile, the contact area increased with the roll diameter owing to the increased contact length (\(L\)) of the workpiece and roll. Figure 10a shows the contact angle (\(\alpha\)) with the roll diameter. The value of \(\alpha\) was derived based on the geometrical condition of the wire flat rolling process (Figure 1) as follows:  
\[\alpha=\cos^{-1}\left(\frac{D-\Delta h}{D}\right) \tag{8}\]  
where \(\Delta h\) indicates the height reduction, i.e., \(h_{0}-h_{1}\). Figure 10b compares \(L\) with the roll diameter. Although \(\alpha\) decreased with the roll diameter, \(L\) increased gradually with the roll diameter owing to the increased roll size. During the plate or strip flat rolling process, it was reported that \(L\) increases with the roll diameter and \(R_{h}\) as follows [18]:  
\[L=\sqrt{\frac{1}{2}D\cdot R_{h}} \tag{9}\]  
Figure 10b also shows a comparison between the geometrically derived \(L\) and the \(L\) value obtained using Equation (9). The equation above predicted the \(L\) of the wire well during wire flat rolling. Obviously, \(L\) increased with increasing roll diameter during wire flat rolling.