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

Studies of the post-bifurcation behaviour and imperfection-sensitivity of elastic–plastic tubes under internal pressure are carried out. When increasing enclosed volume is prescribed, the first critical bifurcation mode for cylindrical tubes is an axisymmetric non-cylindrical mode occurring shortly after the maximum pressure point.

Thereafter, bifurcation into a non-axisymmetric mode occurs, leading to localized necking of the tube wall in the hoop direction. A 2-D membrane analysis based on a conventional (local) plasticity theory shows the bifurcations into the axisymmetric and non-axisymmetric modes. However, a full 3-D analysis is required to give an accurate description 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 development is reduced to a 2-D plane strain problem. In the present work, the 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 scale based on the current thickness of the tube wall.

In the case of post-necking behaviour of stretched thin sheets, this has been found to give a good approximation of the real 3-D post-necking behaviour. Results for the post-bifurcation behaviour of the tube under internal pressure are presented.