Plastic Collapse Assessment of Thick Vessels Under Internal Pressure According to Various Hardening Rules

Abstract

This paper aims to deal with plastic collapse assessment for thick vessels under internal pressure, thick tubes in plane strain conditions, and thick spheres, taking into consideration various strain hardening effects and large deformation aspect. In the framework of von Mises’ criterion, strain hardening manifestation is described by various rules such as isotropic and/or kinematic laws. To predict plastic collapse, sequential limit analysis, which is based on the upper bound formulation, is used. The sequential limit analysis consists in solving sequentially the problem of the plastic collapse, step by step. In the first sequence, the plastic collapse of the vessel corresponds to the classical limit state of the rigid perfectly plastic behavior. At the end of each sequence, the yield stress and/or back-stresses are updated with or without geometry updating via displacement velocity and strain rates. The updating of all these quantities (geometry and strain hardening variables) is adopted to conduct the next sequence. As a result of this proposal, we get the limit pressure evolution, which could cause the plastic collapse of the device for different levels of hardening and also hardening variables such as back-stresses with respect to the geometry change.