SAFEBUCK JIP: Local Buckling Limit State for Seamless Linepipe
Authors: Carr Malcolm , MacRae Ian , Bruton David A.S. 
Published: May 2011

Abstract
The SAFEBUCK JIP was initiated to develop methodologies to deliver a safe and effective pipeline design that admits lateral buckling. A key limit state for designing to accommodate lateral buckling is local buckling. Local buckling is driven by the high imposed bending in combination with internal and external pressure. Relatively little work has addressed the effect of these combined loads for the D/t (diameter/thickness) range of interest to submarine pipelines (between 10 and 45). Further, little attention has been paid to the importance of Lüder banding. This type of behaviour is normal in seamless linepipe, which is used for most in-field flowlines, and can be extremely detrimental to the local buckling capacity of a pipe.
To address this, the SAFEBUCK JIP performed a combination of full-scale testing and numerical modelling to investigate the local buckling behaviour of seamless linepipe. The work showed that the local buckling response is fundamentally influenced by the Lüder plateau. Pipes with a low D/t ratio buckle at strains far above the Lüder strain and have a high buckling capacity. However, pipes with a high D/t ratio may buckle below the Lüder strain, in which case there is essentially no beneficial effect of strain hardening and the pipe has a very low buckling capacity. This work looked at buckling capacity across a wide D/t range, including the D/t transition zone where the behaviour changes from one response to the other.
Current design equations do not capture the influence of the Lüder plateau, and the design margin implied by the equation varies considerably over the range of parameters considered.

Introduction
The SAFEBUCK JIP was initiated to develop methodologies to deliver a safe and effective pipeline design that admits lateral buckling. The bending loads in a lateral buckle are high and usually involve straining beyond the elastic limit of the pipe; these strains can be high enough to induce local buckling of the pipe wall. Within this paper, and in most design codes, the buckling capacity is defined by the limit point - the position of maximum moment in the moment-curvature response. Although this is not the point at which the pipe loses all structural resistance, beyond this point softening and severe strain localisation occurs; accurate calculation of the structural response is extremely involved and influenced by parameters which are not well controlled or known. Consequently, the curvature associated with the limit point is taken to represent the buckling capacity of the section.
The local buckling response within the buckled pipeline can either be assessed using a moment limit or a curvature limit. The two extremes of imposed loading are generally termed load controlled or displacement controlled. For bending dominated deformations this implies moment controlled bending or curvature controlled bending. For curvature control, the curvature developed in the pipe does not depend upon its bending resistance, because the bending process will always result in the same curvature, irrespective of the pipe moment-curvature relationship. A typical example of this is the bending of a pipe to fit the radius of a former. However, real structures are rarely truly displacement controlled or load controlled - they tend to exhibit elements of both. The application of these approaches to a typical pipeline response is illustrated in Figure 1.
Once yielding of the cross-section becomes established, the moment-curvature response is very flat; so that there is significant increase in curvature with little increase in moment. As a result of the flat response, any moment limit must be defined before significant plasticity has developed. This is appropriate if the imposed moment is not self limiting - since failure can quickly result if the design value is exceeded. During lateral buckling, the bending will exceed the elastic limit of the pipeline; this is an inevitable consequence of the buckling behaviour in all but the most benignly loaded systems. This means that a moment limit may well be too onerous to apply to this condition.