Collapse of tubes with Lüders bands under bending
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In several practical applications hot-finished pipe that exhibits Lüders banding over part of its plastic deformation regime must be bent to strains of 2-3%. Lüders banding is a material instability associated with localized deformation. Bending induces ovalization to the tube that leads to a limit load instability and subsequently to collapse. For thinner walled pipes, the limit load is preceded by wrinkling that precipitates local kinking and collapse. This thesis uses experiments and numerical modeling to investigate how Lüders banding influences these modes of collapse. Carbon steel tubes with D/t ratios of 24.3 and 18.9 were heat-treated in order for the Lüders banding to develop. The tubes were then bent to failure under curvature control. The tubes tested exhibited moment plateaus associated with the development of inclined Lüders bands on the tension and compression sides of the tubes. Concurrently, bending was observed to localize over part of the tube, with the higher curvature zone gradually spreading over the whole length of the tube. Subsequently the lower D/t tubes exhibited a stable regime characterized by increasing moment and uniform curvature, which lead to a moment maximum and diffuse local ovalization. By contrast, tubes with D/ t = 24.2 did not exhibit a stable branch. The moment plateau terminated with the tube collapsing by localized diffuse ovalization. Tube bending was simulated using a finite element model in which the tube was assigned small initial geometric imperfections. The material behavior was modeled as elastic-plastic with an up-down-up stress-strain response over the range of the Lüders banding behavior. The model reproduced the major characteristics of the experiments. This includes the moment plateau, its extent, the coexistence of two curvature regimes, and the subsequent return to uniform deformation followed by collapse. A parametric study conducted with the model developed showed that the interaction of structural instabilities with Lüders banding depends of the tube D/t.