Instability and axisymmetric bifurcation of elastic-plastic thick-walled cylindrical pressure vessels

This article presents a theoretical and numerical investigation of the instability and bifurcation of metallic thick-walled cylindrical pressure vessels loaded by combinations of large pressure and axial force. A general bifurcation theory is developed considering elastic-plastic material behavior with non-linear isotropic hardening. The constitutive law is based on applying the von Mises yield criterion in association with the normality rule. Instability limit loads and deformations are obtained and compared with those associated with axisymmetric bifurcation. The developed theory is validated by comparing the theoretically obtained results with those obtained numerically using nonlinear finite element simulations. It is shown that axisymmetric bifurcation occurs at descending loads after the instability limit has been reached. The unstable regular deformation, which continues under descending loads prior to bifurcation, is more evident in shorter cylinders where the delay of bifurcation after instability depends on the loading combination. While in some cases, bifurcation immediately follows instability, leading to catastrophic failure, in some other cases axisymmetric bifurcation is delayed so much that it does not occur at all, even after extremely large unstable regular deformations have developed under descending loads, which provides the opportunity for further energy absorption through unstable, albeit regular plastic deformations. This investigation addresses and provides a solution for a long-standing unresolved problem. The findings provide valuable information in the safety design of extremely loaded pressure vessels.