# Numerical Simulation and Analysis of the Manufacturing Process of Pre-Bulged Rupture Discs
## 2 Materials and Methods
### Experimental Implementation of the Bulge-Forming Process and Theoretical Methods for Evaluation  
In this research work, rupture discs with a nominal diameter DN of 80 mm with three different initial thicknesses \(t_{0}\) of the circular blanks are investigated. The corresponding main dimensions can be identified with the help of Figure 5 and Table 1. This is a widely used nominal pipe size with disc thicknesses that are frequently encountered in process engineering systems. The same applies to the material used in this study, namely AISI 316L, which is known as EN 1.4404 in Europe. This is discussed in more detail in Section 2.3 when modeling the elastic-plastic material behavior. The bulge-forming process for the production of rupture discs is usually carried out using a hydraulic workshop press or a clamping device with a screw connection to ensure static equilibrium between the force due to the acting working pressure and the reaction load on the upper clamping device. Within this research project, a Knuth KNNP 60 HM hydraulic press was used to carry out the tests. A sketch of the test setup is shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Bulge** & **Disc** & **Bending** & **Initial** & **Bursting** & **Effective Pressure \(p\) in MPa at Specific Degree of Bulging \(\eta\)** \\
**Diameter** & **Diameter** & **Radius** & **Thickness** & **Pressure \(p_{\text{B}}\)** & **Pressure \(p_{\text{B}}\)** & **Effective Pressure \(p\) in MPa at Specific Degree of Bulging \(\eta\)** \\ \(d_{\text{B}}\) in mm & \(d_{\text{D}}\) in mm & **R in mm** & **t\({}_{\text{0}}\) in mm** & **In MPa** & **\(\eta=0.2\)** & **\(\eta=0.4\)** & **\(\eta=0.6\)** & **\(\eta=0.8\)** & **\(\eta=0.95\)** & **\(\eta=0.99\)** \\ \hline \multirow{4}{*}{88.9} & \multirow{4}{*}{123} & & 0.102 & 2.39 & 0.48 & 0.96 & 1.43 & 1.91 & 2.27 & 2.37 \\  & & & 0.343 & 7.43 & 1.49 & 2.97 & 4.46 & 5.94 & 7.06 & 7.36 \\ \cline{1-1}  & & & 0.480 & 10.66 & 2.13 & 4.26 & 6.40 & 8.53 & 10.13 & 10.55 \\ \hline \end{tabular}
\end{table} 
Table 1: Test matrix for the bursting and pre-bulging tests carried out with six different degrees of bulging \(\eta\) (\(=p/p_{\text{B}}\)) on rupture discs with a nominal diameter DN of 80 mm. Pressure values given as gauge pressure to ambient pressure. It is important that the hold-down force is sufficiently high to ensure the required sealing of the working space on the one hand and to provide a sufficient frictional force between the contact partners on the other. This should enable the rupture disc to be guided safely and concentrically during plastic shaping and also prevent unwanted wrinkling. It should be noted that the hold-down force is limited at the top by the yield point of the rupture disc material, as the edge of the rupture disc should not undergo pressure forming. When recording the flow curve (representation of true stress-true plastic strain behavior) by means of a bulge test, this problem is often solved by using a so-called lock bead. However, this is generally not performed in the industrial production of rupture discs, as the local plastic deformation of the edge around the bead can have a negative effect on the sealing behavior during subsequent operation of the rupture disc. Furthermore, unnecessary plastic straightening processes on a safety-relevant component should be avoided. The hydraulic adjustment was set in such a way that an average contact pressure \(p_{\text{c}}\) of around 120 MPa was achieved in the contact zone between the edge of the rupture disc and the clamping device. This corresponds to around 40% of the yield stress of the rupture disc material and leads to a hold-down force of around 600 kN, which must be provided by the cylinder force \(F_{\text{cyl}}\). This configuration led to consistently very good forming results and was therefore used to ensure comparability of the results across the entire test program.