Deep drawing of pressure vessel end closures: finite element simulation and validation

The development of tooling for the deep drawing of pressure vessel end closures (PVECs) can be a time-consuming and expensive process. Finite element (FE) modeling of this process has the potential to reduce these costs. Accordingly, a parametric model of the forming of PVECs on a 500 t hydraulic press at C.E. MacPherson (a division of Conrex Steel) of Kingston, Ontario has been developed using the commercial FE software, MARC. The tooling is modeled as rigid surfaces. The workpiece is modeled as a deformable body using a quadrilateral axisymmetric element. The plastic stress–strain characteristics are based on tensile-test data fitted to the Ludwik–Hollomon hardening law. Isotropic material, isotropic hardening and the Prandtl–Reuss flow rule are assumed. A mesh-refinement study is conducted to determine the optimal FE mesh. Sensitivity studies of the effects of the Coulomb friction coefficient and the blank-holder gap are also conducted. The FE results for two sizes of PVECs are validated by comparison with in-process parameters (punch displacement, punch force, and blank-holder force) and post-process (part profile, thickness-strain distribution, and surface-strain distribution) forming data.