*4.2. Shape of Flat-Rolled Wire with Roll Design*

To apply the shaped rolls to the flat rolling process, the effect of the roll design on the shape of the final product needs to be considered. Figure 7 shows the variation in *b* and *W* values with *IRD* after the second pass. Both values decreased linearly with *IRD*, indicating that the lateral spreading of the wire decreased when using the oval-grooved roll with a small radius, because the spreading in the free surface area of the wire was highly restricted by the roll shape and curvature, as shown in Figure 1b. In contrast, the spreading in the surface area increased during the rolling process with the cambered roll due to the reduced restriction of the metal flow in the free surface area, as shown in Figure 1c. These results practically imply that the size of the initial wire needs to be changed when using the shaped roll during the flat rolling of wire due to the different wire spreading results with roll designs.

**Figure 7.** Variations in the *b* and *W* values with *IRD*.

#### *4.3. Design Concept for a High-Quality Flat-Rolled Wire*

To make high-quality flat-rolled wires, a practical strategy was designed, as shown in Figure 8, based on the results achieved in the above comparative study. The strain on the flat surface of the wire

increased with decreasing *IRD*, while the strain inhomogeneity in the cross-section of the wire was slightly reduced with decreasing *IRD*, meaning that we can produce higher quality flat-rolled wire products using a cambered roll with a small radius. In contrast, the use of an oval-grooved roll is not a good idea when fabricating a flat-rolled wire. The proposed design concepts can provide process designers with seeding ideas to choose the optimal process conditions for high-quality flat-rolled wires. This is beneficial for industrial plants because a cambered roll can be easily applied in flat rolling plants. It is worth noting that the proposed practical strategy was valid for most materials, since it was derived from the general plastic forming conditions. However, the effects of the kinematic hardening, the strain rate sensitivity in the material, and the friction coefficient should be considered to obtain more reliable results. In addition, it should be noted that the effects of the roll design on the *b* and *W* values should be considered to obtain a wire with accurate dimensions and tolerance (Figure 7). For mass production, the wear issue needs to be considered when applying the cambered roll in the flat rolling of wire. Additionally, the present results need to be confirmed by experimental data, such as a hardness analysis and microstructure evolution data. In this respect, additional research is necessary.

**Figure 8.** Schematic description of the effective strain on the flat surface and shape of a flat-rolled wire with *IRD*.
