## 2 Development of an Advanced SR-JOINT (SR-II)
### Finite Element Analysis
#### 2.1.2 Finite Element Analysis of SR-Joint (SR-II)  
A finite element analysis was performed on the conventional pipe crimping process to analyze the validity of the finite element analysis program. Analysis modeling was performed using AFDEX V20, a commercial finite element analysis program, to analyze the conventional SR-joint molding behavior. Although finite element analysis is typically performed with 3D modeling in principle, because the pipe had the same revolved section based on the central axis, a two-dimensional axisymmetric finite element model was constructed instead. The conventional SR-joint is a structure in which a metal ring and a rubber ring are adjacent to each other between the SR-joint that has completed the expansion process and the pipe that has not been processed; furthermore, they are fitted as shown in Figure 4. An image showing only the 270\({}^{\circ}\) view to visualize the inside of the material is shown in Figure 4a, and the cross-sections of the pressure jig, pipe, metal ring, and rubber ring, and two fitted pipes are shown in Figure 4b. The fitted shape after compression and finite element analysis is shown in Figure 4c. The shape considered in this study is a stainless-steel pipe with a diameter and thickness of 114 and 2 mm, respectively. The rubber ring has a circular cross-section and a diameter of 7 mm, and the metal ring \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **SUS304 (Stainless Steel)** & **EDPM (Rubber)** \\ \hline \(k\) [MPa] & 1426 & 6.018 \\ \(\varepsilon_{0}\) [\(-\)] & 0.029 & 0.001 \\ \(n\) [\(-\)] & 0.502 & 1 \\ Young’s Modulus [GPa] & 207 & 15 \\ Poisson’s ratio [\(-\)] & 0.28 & 0.49 \\ Yield Stress [MPa] & 215 & 0.0058 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of SUS304 and ethylene propylene diene monomer rubber (EPDM). Figure 3: Specim shapes and true stress–true strain curves of SUS304 and EPDM. has a rectangular cross-section and 8.35 mm and 3 mm in width and length, respectively. Finite element modeling for pipes, SR-joints, metal rings, and rubber rings was made using 4-node elements of about 1020, 770, 210, and 920, respectively. Since the plastic deformation of the metal ring and rubber ring is relatively large during compression, many elements are placed. In the order mentioned above, the minimum element size for each part is 0.666 \(\times\) 1.065, 0.349 \(\times\) 0.663, 0.141 \(\times\) 0.141, and 0.136 \(\times\) 0.136 mm\({}^{2}\), respectively. Since the difference in pipe diameter before and after the actual compression process was 8.8 mm, the pressure jig stroke was set to 4.4 mm, which was half the measured value in consideration of the axisymmetric shape in the \(x\)-axis direction. The speed of the pressure jig was \(-1\) mm/s in the \(x\)-axis direction. Considering the analysis time and convergence, the pressure jig was assumed to be a rigid body. The finite element analysis results of the conventional SR-joint are as shown in Figure 5, and the maximum molding load was 340.8 kN. The maximum pressure applied to the pressure jig was calculated using Equation (2) based on the load applied per unit area, where \(P\) denotes the pressure, \(F\) denotes the load [N], and \(A\) denotes the cross-sectional area [mm\({}^{2}\)]. \[P=F/A \tag{2}\]  
Figure 4: Geometry and FE modeling of a conventional stainless ring (SR)-joint (SR-I). (**a**) overall mesh design (**b**) detailed dimensions for each part (**c**) deformed shape of each part after compression. Figure 5: Numerical load–stroke curves of the conventional SR-joint (SR-I). After the finite element analysis, the contact area between the pressure jig and SR-joint was measured using a 3D-computer aided design (CAD) program, and the calculated contact area was 154.54 cm\({}^{2}\). If the maximum load value of 340.8 kN and a contact area of 154.54 cm\({}^{2}\) derived through finite element analysis are substituted into Equation (2), then the pressure obtained will be 22.05 MPa at 2.205 kN/cm\({}^{2}\).