# Influence of Roll Diameter on Material Deformation and Properties during Wire Flat Rolling
## 4 Discussion  
The different behaviors of shape change, strain distribution, and damage value of the wire with the roll diameter during wire flat rolling must be evaluated. First, each strain imposed on the flat-rolled wire was compared with the direction. During the rolling process, the compressive stress imposed on the workpiece by the roll mainly deformed the workpiece in three directions (Figure 1), that is, the height, longitudinal, and transverse directions of the workpiece, which are typically known as reduction, elongation, and spreading, respectively. Figure 12 compares the strain contours in the three directions of the wire with the roll diameter. The reduction exhibited similar contours regardless of the roll diameter, and the spreading tended to concentrate on the center region with increasing roll diameter. Interestingly, the elongation decreased with increasing roll diameter. Figure 13 shows a comparison of the average elongation with the roll diameter. The decreased elongation with the roll diameter increased \(b\) and \(W\), resulting in a decrease in \(R_{A}\) with the roll diameter (Figure 7). The decreased elongation with the roll diameter also decreased the \(\epsilon_{min}\) of the wire at the free and contact surface regions, leading to an increase in \(SIF_{b}\) and \(SIF_{v}\) with the roll diameter (Figure 6). Accordingly, both the shape change and strain distribution of the specimen during wire flat rolling were associated significantly with the elongation of the wire during the process. The decreased elongation of the wire with the roll diameter was highly dependent on \(L\). The increased \(L\) with the roll diameter (Figure 10) rendered the frictional effect more prominent owing to the higher contact surface. That is, the increased contact area between the wire and roll resulting from the increased \(L\) increased the frictional effect along the longitudinal direction of the wire (\(F_{\text{ulength}}\)) compared with the transverse direction of the wire (\(F_{\text{ulwidth}}\)), as shown in Figure 14. The increased \(F_{\text{ulength}}\) decreased the elongation, leading to an increase in the spreading, including \(b\) and \(W\) owing to the conservation of volume during the plastic deformation. [PERSON] et al. (2017) reported that lateral spreading increases as the friction coefficient increases during the plate flat rolling process. Figure 11: Comparison of the (**a**) contour of the damage value in the wire, (**b**) profile of the damage value along the horizontal direction, and (**c**) the maximum damage value at free surface and center regions with the roll diameter. Meanwhile, it is known that a higher frictional effect concentrates the stress in the center region during the compression-type forming process. The rolling process mainly deformed the material under the compression stress state; therefore, the higher frictional effect with increasing roll diameter due to the higher \(L\) led to an increase in the \(\varepsilon_{max}\) at the center region of the wire. In other words, the strain concentration in the center region was stronger as the roll diameter increased, this is attributable to the high \(L\) during wire flat rolling. Figure 14: Schematic illustration of the frictional effect at the wire and roll interface with (**a**) small roll and (**b**) large roll during wire flat rolling. Figure 12: Comparison of the strain contours at three directions of the wire with the roll diameter. Figure 13: Comparison of the average elongation of the wire against roll diameter. rolling. [PERSON] and [PERSON] [1] revealed that the strain inhomogeneity of a flat-rolled wire increases as the friction coefficient at the interface between the wire and roll increases. As a result, the underlying cause of the strain distribution and shape change of the flattened wire was highly related to \(L\) during deformation.