# The Study of Multi-Stage Cold Forming Process for the Manufacture of Relief Valve Regulating Nuts
## 2 Materials and Methods
### The Hardness Analysis  
During cold forging, the hardness and strength of the workpiece may increase due to the plastic flow. Figure 6 shows the average hardness (measured in Vickers hardness) of the workpiece cross-section at each stage by experiment. The red dot in the Figure is the position where the maximum hardness was measured. The hardness of the initial billet was almost the same and evenly distributed (about 142 HV), as shown in Figure 6, except for the higher hardness at both ends (about 173 and 194 HV) due to shear deformation. The average hardness overall of the initial billet was 158.6 HV. In the first stage, the hardness of the flatting and centering zones of the workpiece was larger than in the middle zone where the deformation was small, which was consistent with the effective strain distribution in Figure 5. The overall hardness of the workpiece (172.6 HV in average) was greater than the initial billet. The highest hardness of 247.6 HV was inspected in the bottom cross-section of the workpiece due to the centered forming. For the second stage of the backward extrusion over the die pin, the hardness in the upper end and the region of the backward extrusion forming was greater than in the middle region, which agreed with the effective strain distributions shown in Figure 5. The hardness distribution in the workpiece was relatively uneven, as shown in Figure 6. The hardness distribution around the inner wall of the lower cavity was obviously high (approx. 250 HV in average) due to the severe structure deformation. The average hardness overall the workpiece was 164.6 HV. The highest hardness was 290.9 HV, which was identified at the center of the section, immediately above the lower cavity of the workpiece, indicated by the red dot in Figure 6, due to the large plastic flow of the backward extrusion forming. In the third stage, the hardness in the upsetting zone of the workpiece, where the higher distribution of the effective strain is shown in Figure 5, was higher than in the middle region. The hardness distribution around the inner wall of the lower cavity, formed by the previous stage, remained high (approx. 248 HV in average). The overall hardness in the workpiece (203.6 HV in average) was greater than the initial billet and the previous two stages. The highest hardness was 290.9 HV, which was identified in the middle section of the thin wall, shown by the red dot in Figure 6.  
For the fourth stage of the backward extrusion over the moving punch to form a hexagonal cavity, the hardness in the backward extrusion forming zone was obviously  
Figure 6: The hardness (in HV) and gran flow lines in workpieces for five stages. higher, as shown in Figure 6. Due to the large amount of extrusion, the hardness in the extruded inner wall area was relatively large (about 222 HV in average), and a higher distribution of effective strain was also shown in Figure 5. The highest hardness was 264.2 HV, which was observed closest to the inner wall of the second section from the top of the workpiece (red dot in Figure 6). The overall hardness in the workpiece was averaged at around 205.9 HV, which was larger than the initial billet and the previous three stages, while the difference from the third stage was relatively small. In the fifth stage, the piercing of a hole in the internal cavity, the high hardness was distributed around the inner wall of the hole and in the piercing waste, as shown in Figure 6. The hardness around the inner wall of the hole was relatively large (about 240 HV in average), which agreed with the effective strain distributions shown in Figure 5. The highest hardness was 266.7 HV, which was observed closest to the inner wall of the middle section of the workpiece (red dots in Figure 6). The overall hardness of the workpiece (207.6 HV in average) was the highest among the five stages, increasing by 31% compared to the initial billet. The hardness of the workpiece increased with the forming stages, and the strain-hardening effect was obvious.