A nonlocal two-dimensional analysis of instabilities in tubes under internal pressure

Studies of the post-bifurcation behaviour and imperfection-sensitivity of e lastic-plastic tubes under internal pressure are carried out. When increasi ng enclosed volume is prescribed, the first critical bifurcation mode for c ylindrical tubes is an axisymmetric non-cylindrical mode occurring shortly after the maximum pressure point. Thereafter, bifurcation into a non-axisym metric mode occurs, leading to localized necking of the tube wall in the ho op direction. A 2-D membrane analysis based on a conventional (local) plast icity theory shows the bifurcations into the axisymmetric and non-axisymmet ric modes. However, a full 3-D analysis is required to give an accurate des cription of the neck development on one side of the tube wall. If the axial variation in the deformation pattern is neglected, the analysis of neck de velopment is reduced to a 2-D plane strain problem. In the present work, th e 3-D post-bifurcation behaviour is approximated by a 2-D nonlocal membrane finite element analysis. The third dimension (the thickness direction) is taken into account in the continuum description by an incorporated length s cale based on the current thickness of the tube wall. In the case of post-n ecking behaviour of stretched thin sheets, this has been found to give a go od approximation of the real 3-D post-necking behaviour. Results for the po st-bifurcation behaviour of the tube under internal pressure are presented. (C) 1999 Elsevier Science Ltd. All rights reserved.