Use of elastic follow-up to study the effect of displacement controlled loading on plastic collapse pressures for circumferentially cracked pipes

Structural integrity assessments of pressurised pipes consider plastic collapse as a potential failure mode. This paper uses finite element analysis to explore the effect of the pipe end boundary conditions on the collapse pressure. Two end conditions are considered: a fixed axial load and a fixed axial displacement. The fixed axial displacement condition represents a long-range axial residual stress. In the R6 structural integrity assessment procedure long-range residual stress is associated with elastic follow-up. However, no guidance is given on whether the level of elastic follow-up is sufficient to justify treating long-range residual stress as a primary stress. In this paper, a method is proposed to estimate elastic follow-up of an internally pressurised pipe containing a fully circumferential crack. It is found that the elastic follow-up is related to the length of the pipe. A short pipe that contains a fully circumferential crack, subjected to a displacement induced axial stress, has a global collapse that is not modified by the fixed displacement condition. The short pipe corresponds to a small elastic follow-up factor, Z. However, as the elastic follow-up factor increases, the presence of long-range residual stress starts to make a contribution to global collapse. When elastic follow-up is significant, a long-range residual stress has the same effect on global collapse as does a mechanical stress.