Reeling of pipe with Lüders bands

Bending of tubes with a material that exhibits Lüders banding results in banded, localized deformation organized in diamond-shaped pockets on the tensioned and compressed sides of the tube. Furthermore, the Lüders-deformed section exhibits higher ovalization and curvature than the rest of the structure. Under deformation controlled bending, the higher deformation and curvature tend to propagate until the whole length of the structure is so deformed. The present study examines the behavior of a pipe as it is gradually wound on a large diameter reel. The material is modeled as a finitely deforming, elastic–plastic solid undergoing isotropic hardening/softening calibrated to a stress–strain response with a negative slope over the extent of the Lüders deformation. The reeling process is modeled with finite elements with a mesh that is fine enough to capture the evolution of Lüders banding that develops.During reeling with some back tension, Lüders banding again produces inclined bands of localized deformation, but the bands are organized in clusters with distinctly different spatial distribution than that of pure bending. The clusters are now separated by sections of pipe free of Lüders bands. For realistic pipe and reel geometries, the average bending strain imposed by the curvature of the reel is lower than the strain induced by Lüders banding. Accordingly, the clusters are separated by relatively undeformed sections so that the bending strain averages out to the value imposed by the reel. Because of the applied tension the bands on the compressed side are somewhat more diffuse and exhibit a more regular distribution along the length. Reeling induces ovalization of the pipe cross section, which is intensified by the application of back tension. It is demonstrated that as a consequence of the clustering of Lüders bands, the ovalization develops axial undulations. Such undulations can act as imperfections in subsequent, particularly compressive, loadings of the structure. Problem variables like the Lüders strain, the applied tension, the ratio of the reel diameter to that of the pipe, and the pipe diameter-to-thickness ratio all influence the amplitude and spatial distribution of localized deformation patterns that develop. The influence of each of these was examined in a detailed parametric study.