# Influence of Roll Diameter on Material Deformation and Properties during Wire Flat Rolling
## 2 FE Analysis and Model Validation  
### FE Analysis and Boundary Conditions  
During wire flat rolling, the workpiece exhibits three-dimensional (3D) deformation behavior owing to the initial round shaped wire [15]. Accordingly, FE analysis was conducted using the commercial software, DEFORM 3D version 11.0(Scientific Forming Technologies Corporation, Columbus, OH, USA) to evaluate the deformation behavior of the workpiece during wire flat rolling.  
The 13 mm-diameter wire was reduced to a 9.1 mm-thick flattened wire by flat rolls with diameters of 150, 400, 800, and 1600 mm at room temperature (RT, 24 \({}^{\circ}\)C), as schematically shown in Figure 1. Hereafter, the flat-rolled wires fabricated using rolls with diameter of 150, 400, 800, and 1600 mm are referred to as \"150-wire\", \"400-wire\", \"800-wire\", and \"1600-wire\", respectively. During the process, the reduction in height (\(R_{h}\)) and reduction in area (\(R_{A}\)) of the workpiece were calculated using the following equations:  
\[R_{h}=\frac{h_{0}-h_{1}}{h_{0}}\times 100\ (\%) \tag{1}\]  
\[R_{A}=\frac{A_{0}-A_{1}}{A_{0}}\times 100\ (\%) \tag{2}\]where \(h_{0}\) and \(h_{1}\) represent the initial and final heights of the workpiece; and \(A_{0}\) and \(A_{1}\) indicate the initial and final areas of the workpiece, respectively. The nominal strain (\(\varepsilon_{n}\)) of the workpiece was calculated using the height of the workpiece as follows:  
\[\varepsilon_{n}=ln\frac{h_{0}}{h_{1}} \tag{3}\]  
According to the equations above, the \(R_{h}\) and \(\varepsilon_{n}\) values in the present study were 30% and 0.36, respectively.  
Friction plays a crucial role in determining the deformation behavior of a workpiece during the rolling process because friction is the main reason for the rolling process to take place. Although a Tresca model (shear friction factor) is preferable in high-pressure bulk forming processes [20], the Coulomb friction model was applied at the roll and wire interfaces because it is known that the shear friction model cannot predict the sticking region near the neutral point during plat flat rolling [21]. Accordingly, in this study, the Coulomb friction model was applied as follows:  
\[\tau=\mu p \tag{4}\]  
where, \(\tau\), \(\mu\), and \(p\) are the frictional stress, coefficient of friction, and normal pressure, respectively. In the present study, a constant friction coefficient of 0.15 was used because [PERSON] and [PERSON] [22] well predicted the roll force during wire flat rolling using the friction coefficient of 0.17 although it is known that the friction coefficient in the roll bite varies with the rolling [23] and width [24] directions of the workpiece during rolling. In addition, the friction coefficient of 0.15 was a reasonable value for the cold rolling process without lubrication.  
The influences of temperature increase and rolling speed were not considered during the process because the rolling velocity was set to 5 rpm, that is, a low strain rate or forming speed. The roll was considered to be a rigid body because the plastic deformation of the workpiece was relatively large, i.e., \(R_{h}\) of 30%. In such a case, the elastic deformation of roll can be ignored.  
Owing to the double symmetry condition in both the reduction and spreading directions during wire flat rolling, only a quarter of the full geometry of both the wire and roll were modeled. Hence, a significant reduction in computational costs was achieved.