## 3 Results
### Simulated Deformation When Tube Forming in a Closed Die  
The simulation results are used to select the optimum technological step for the part. When the upsetting is done in one step, the part becomes folded at its top, due to instability of the workpiece, as shown in Figure 4. The deformed mesh begins to overlap, and eventually the parts are folded into the wall of the tube due to this instability. The process of deformation shows the workpiece starting to lose stability at the transition region between the head and body of the part. After the forming of the tube head, the final thickness of the shaped part is S\({}_{1}\) = 3.65 mm. The thickness of the mold after flow forming is S\({}_{0}\) = 1.95 mm, and the ratio S\({}_{1}\)/S\({}_{0}\) = 1.871. If the technological steps of forming are divided into two steps, each step can be split, as shown in Table 1.  
Figure 4 shows the simulation of the part-forming process by one step, on a die, from the dimensions D\({}_{0}\), S\({}_{0}\), and H\({}_{0}\) to those (D\({}_{1}\), S\({}_{1}\), and H\({}_{1}\)) shown in Figure 3. The simulation shows that mesh folding starts happening due to instability; then overlapping mesh causes errors during the simulation. Hence, the deformed mesh is folded, which will obviously cause defects in the fabrication process. However, the deformed mesh shown in Figure 5 is uniform, without deflection, and contains no folding defects. When forming with two steps, the parts meet production requirements, i.e., the products are free from defects, and the deformed mesh is not overlapped or cracked. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Step**} & **Thickness of** & **Thickness of** & **Ratio** \\  & **Next Steps (mm)** & **Previous Step (mm)** & **S1/S0** \\ \hline
1 & 1.95 & 2.70 & 1.386 \\
2 & 2.77 & 3.65 & 1.352 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thickness distribution of the forming steps. Figure 4: Simulation of the forming process via one step. By numerical simulation, the number of stamping steps to change the workpiece dimensions (D\({}_{0}\), S\({}_{0}\), H\({}_{0}\)) to the part dimensions (D\({}_{1}\), S\({}_{1}\), H\({}_{1}\)) is determined. It is therefore necessary to take a two-step process with the ratio S\({}_{1}\)/S\({}_{0}\), as shown in Table 1. Figure 5 shows that it will not cause defects between non-overlapping mesh steps. At the corners of the parts, the metal flow through region I (shown in Figure 5) is very difficult, especially for the thin-walled tubular parts. This consideration of the non-overlapping mesh ensures the conditions to avoid forming instability. The remaining issue to consider is whether the values of stress and deformation during forming process exceed the allowable values so that defects do not occur. A comparison of the stress, strain, and material flow values in two cases is performed, including (1) single-step stamping and (2) two-step stamping for the part head forming tasks. Numerical simulations are performed, and a comparison of the principal stress values in the \(z\)-direction and the equivalent stresses, respectively, for one- and two-step stamping, is shown in Figures 6 and 7. It can be seen that the high-stress area in Figures 6a and 7a occurs at the defect location, and, although these stresses do not reach a value that causes material destruction, they create a non-uniform stress distribution. Figures 6b and 7b show uniform stress where the maximum stress does not reach a destruction value and, thus, no defect is found in the parts. In Figure 8a, irregular plastic strain is observed between the points in the angular region and the straight wall inside the tube. The differences in plastic strain between these points are so great that the material no longer satisfies the continuity condition. Moreover, the plastic strain distribution with two steps, as seen in Figure 8b, shows that no defects appear in the part. For defects to not occur in the part, the flow of material during forming should not experience turbulence.