Crystal plasticity simulation of the hydrostatic bulge test

In this article the finite-strain deformation of a membrane under hydrostatic pressure is investigated using a rate-dependent polycrystal plasticity formulation based on Taylor assumptions, where each material point in the sheet is considered to be a polycrystalline aggregate of a large number of grains. A finite element program is developed for arbitrary die aperture geometries and numerical results are generated for a circular specimen using parallel computing features. The plane stress assumption is invoked at the macro level, since the sheet thickness is small compared to the surface dimensions of the specimen. The deformation gradient is computed with the requirement that the two shearing strains along the sheet normal are explicitly enforced to be zero. The effect of deformation-induced anisotropy is examined for a single crystal as well as for different polycrystalline materials, with and without initial orthotropy. Using the maximum stress criterion for the rate-dependent material model employed, the onset of instability for the membrane is examined for succesive localization modes. First, the onset and development of biaxial straining localized around the pole, and then the onset of an instability at this region involving localized necking (similar to the forming limit diagrams), are demonstrated and discussed from numerical examples.