# Numerical Simulation and Analysis of the Manufacturing Process of Pre-Bulged Rupture Discs
###### Abstract
**Reverse acting rupture discs** are also dome-shaped, but in contrast to forward acting rupture discs, their dome faces the process to be protected. Pressurization therefore causes compressive stresses in the bursting membrane. Due to the state of compression within the bursting membrane, the bursting mechanism involves a structural-mechanical stability problem in the sense of structural buckling. As the predefined bursting pressure of the rupture disc is reached, the bursting membrane enters a state of structural instability, forcing the dome to reverse back into a forward acting configu  
Figure 2: Flat rupture discs in multi-layer design with perforations in circumferential direction (**a**) and radial direction (**b**). The bottom row shows the closed configuration, while the upper row illustrates the burst/opened state. knife blade or multiple cutting edges. To ensure that the reverse acting rupture disc can still open safely during this process, the process medium must provide sufficient expansion energy. As a result, this type of rupture disc is unsuitable for purely incompressible media. However, the good structural behavior of the reverse acting rupture discs provides a very high operating ratio of around 90-95% [5] and favors their creep and fatigue behavior, making such types of rupture discs suitable for use at elevated temperatures and cyclic loading regimes. Figure 4 illustrates two exemplary types of reverse acting rupture discs. For all types of ruptures discs, the precise adjustment of the bursting pressure is extremely laborious and depends on a complex interaction of numerous parameters such as diameter, choice of specific material, material thickness, bulge height and curvature, notch geometry (for pre-notched bursting discs) or slotting geometry (for bursting discs with perforations) and thermal treatment. While the diameter and the specific material are often already determined by the piping system and the employed process fluid, respectively, the other parameters need to be set in the bulge-forming process. Due to its complexity, the  
Figure 4: Reverse acting rupture discs in single-layer design with knives on the back as well as C-shaped pre-notched diaphragm (**a**) and cutting edges on the back in combination with a non-notched membrane (**b**). The bottom row shows the intact front, while the upper row illustrates the back side in the burst/opened state. Figure 3: Forward acting rupture discs in multi-layer design with perforations in circumferential direction (**a**), single-layer design with a cross-shaped notch pattern (**b**) and multi-layer design with perforations in radial direction (**c**). The bottom row shows the closed configuration, while the upper row illustrates the burst/opened state. manufacturing process of rupture discs is still rather unsystematic, relying exclusively on the knowledge of experienced production engineers [6]. In the past, there have been several attempts to develop analytical as well as numerical approaches for describing the plastic deformation during the bulge-forming process. As early as 1948, [PERSON] studied the plastic deformation of circular diaphragms with edge clamping for small strains by means of local balance equations [7]. These balance equations need to be integrated along the meridian to come up with the stress and strain distribution as well as the overall deformation. However, a comparison with experimental results shows that the assumption of small deformations is disadvantageous for modeling the circular bulging of ductile metals with large plastic deformation capacity. Therefore, [PERSON] and [PERSON] extended [PERSON]'s model to large plastic deformations and also introduced a criterion for predicting the onset of instability in the pole of the membrane, above which the structure can no longer withstand any further increase in pressure, cf. [8]. However, their algorithm had numerical difficulties around the area of instability, so the solution had to be extrapolated to obtain results above this limitation.