Localization and propagation of curvature under pure bending in steel tubes with Lüders bands

The paper examines the plastic bending of steel tubes exhibiting Lu¨ders bands through a combination of experiments and analyses. In pure bending experiments on tubes with diameter-to-thickness ratio of 18.8 tested under end-rotation control, following the elastic regime the moment initially traced a somewhat ragged plateau. At the beginning of the plateau Lu¨ders bands appeared on the tension and compression sides of the cross section and simultaneously the curvature localized in one or two short zones while the rest of the tube maintained a much lower curvature. As the rotation of the ends was increased, one of the higher curvature zones spread at a nearly steady rate, affecting an increasingly larger part of the tube. When the whole tube was deformed to the higher curvature, the moment started to gradually increase while the tube deformed uniformly. A moment maximum was eventually attained and the structure failed by localized diffuse ovalization without any apparent effect from the initial Lu¨ders bands-induced propagating instability. The problem was analyzed using 3D finite elements with a fine mesh. The material was modeled as an elastic–plastic solid with an up–down–up response over the extent of the Lu¨ders strain, followed by hardening. The calculated response reproduced all major structural events observed experimentally including the initiation of the Lu¨ders deformation, the moment plateau that followed, its extent, and the curvature localization and propagation associated with it. As in the experiments, once the high curvature extended over the whole tube length, the response of the tube became stable and the curvature uniform. With further bending the increasing ovalization induced a limit moment at a very high curvature.