# Numerical Simulation and Analysis of the Manufacturing Process of Pre-Bulged Rupture Discs
###### Abstract
In 1964, [PERSON] discretized the axially symmetrical geometry of the membrane into circular ring segments and calculated the material response in the form of stresses and plastic strains in the membrane plane during the pressure increase iteratively from increment to increment and from segment to segment [9]. With this approach, he demonstrated the non-constant curvature along the meridian, which is caused by the influence of the edge restraint. However, all models assume a rigid-plastic material behavior without elastic effects and neglect the bending stiffness for thin membranes. Furthermore, their theories lead to extremely extensive and time-consuming calculations. More recent approaches make use of finite element methods in order to describe the plastic deformation. [PERSON] and [PERSON] implemented a shell model with edge clamping, including nonlinear material behavior and large deformations for the computer simulation of rupture disc design and the prediction of bursting pressure [10]. They created models in two different FE-codes (Ansys and I-DEAS) and compared their results with experimental references for nickel rupture discs. Inaccurate assumptions, such as the fact that they assumed the achievement of ultimate tensile strength in the membrane pole as a failure criterion, led to some considerable deviations in the results. [PERSON] et al. employ a finite element model for the structural analysis of superficially grooved rupture discs within the Ansys FE-code [11]. For the material model, uniaxial tensile tests of 316L stainless steel are used with a simple bi-linear fit of the experimental results. The simulation results were not validated by experiments considering the bulge-forming process. [PERSON] et al. provide the most promising approach for modeling the manufacturing process of rupture discs, cf. [12]. The authors model the frictional contact between the membrane and the clamping unit in Abaqus and fit their constitutive model to experimental data from biaxial tensile tests with 316L stainless steel. They investigated the influence of the loading rate as well as the variation in friction on the forming of the bulge. The simulations were validated with experimental observations from a hydro-forming process. However, the modeling of the geometry of the upper clamping tool was greatly simplified by neglecting the bending radius. In addition, the authors did not consider the entire production process of rupture membranes, including the relaxation of the clamping unit, which means that the effects of elastic spring-back as well as the residual stresses introduced into the structure by elastoplastic deformation cannot be analyzed. All of the above-mentioned approaches have at least one of the following deficits:  
* insufficient modeling of the nonlinear material behavior;
* missing or inadequate modeling of the contact zone (incl. bending radius) between the membrane and the clamping tool;
* inadequate discretization of the geometry of the membrane;
* incomplete modeling of the production process: clamping, pre-bulging, unclamping (with elastic spring-back and deformation history);
* incomplete analysis and evaluation of the structural-mechanical relationships;* lack of experimental validation. The objective of this manuscript is to close these research gaps and provide comprehensive insight into all relevant aspects of the manufacturing process of pre-bulged rupture discs. For this reason, the present contribution provides a thorough finite element-based approach involving large deformations, nonlinear frictional contact to the clamping devices, the entire production process in terms of clamping, bulging and unclamping as well as an experimentally validated state-of-the-art material model. All simulation results are validated by extensive experiments from an industrial pneumatic bulge-forming setup.