Lüders banding and its effects on structures under tension/compression and cyclic bending loads



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Lüders banding is a material instability that leads to localized deformation during the initial yielding of the material. This research project investigates how this material instability affects the response of tubular structures under bending and cyclic bending. Tension/compression experiments are first performed on steel rods exhibiting Lüders banding. Special attention is given to how a specimen behaves when the initial loading is interrupted with part of it Lüders deformed and the rest of the specimen still remaining elastic. Digital image correlation reveals that both sections unload elastically, but upon reverse loading, the previously elastic zone develops Lüders strain of the opposite sign, while the plastically deformed zone traces Bauschinger rounding. A custom constitutive model is developed to capture this complex behavior, encompassing a J2-type softening material response and nonlinear kinematic hardening for reverse loading. The constitutive model is subsequently used to study the effect of Lüders banding on tubes under cyclic bending. Under bending, tubes progressively develop inclined bands of higher strain organized in periodic diamond-shaped patterns. Upon unloading, the diamond patterns gradually disappear, but simultaneously local secondary patterns of higher strain develop in the hitherto elastic zones between the original diamonds. When completing the cycle, the secondary patterns are progressively erased and the diamond patterns reappear. The sensitivity of this structural behavior to several problem variables including the extent of Lüders strain, the level of Lüders stress, and diameter-to-thickness ratio of the tube is examined in parametric studies. The constitutive model is subsequently implemented in a large-scale numerical analysis of the winding/unwinding of a pipeline with Lüders bands on a large diameter reel. During winding, inclined Lüders bands organize into clusters separated by elastic sections. During unwinding and straightening, the intensity of Lüders patterns is gradually reduced and secondary patterns develop in the previously undeformed zones. This appearance, erasure, and reappearance of Lüders patterns is repeated in subsequent wind/unwind cycles. Ovality accumulates during each cycle and may lead to local buckling and collapse. The effect of problem variables such as the level of back tension, reel diameter, extent of Lüders strain, steel yield strength and diameter-to-thickness ratio is examined in a parametric study.


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