On the effect of Lüders bands on the bending of steel tubes
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In several practical applications, hot-finished steel pipe that exhibits Lüders bands is bent to strains of 2-3%. Lüders banding is a material instability that leads to inhomogeneous plastic deformation in the range of 1-4%. This work investigates the influence of Lüders banding on the inelastic response and stability of tubes under rotation controlled pure bending. It starts with the results of an experimental study involving tubes of several diameter-to-thickness ratios in the range of 33.2 to 14.7 and Lüders strains of 1.8% to 2.7%. In all cases, the initial elastic regime terminates at a local moment maximum and the local nucleation of narrow angled Lüders bands of higher strain on the tension and compression sides of the tube. As the rotation continues, the bands multiply and spread axially causing the affected zone to bend to a higher curvature while the rest of the tube is still at the curvature corresponding to the initial moment maximum. With further rotation of the ends, the higher curvature zone(s) gradually spreads while the moment remains essentially unchanged. For relatively low D/t tubes and/or short Lüders strains, the whole tube eventually is deformed to the higher curvature entering the usual hardening regime. Subsequently it continues to deform uniformly until the usual limit moment instability is reached. For high D/t tubes and/or materials with longer Lüders strains, the propagation of the larger curvature is interrupted by collapse when a critical length is Lüders deformed leaving behind part of the structure essentially undeformed. The higher the D/t and/or the longer the Lüders strain is, the shorter the critical length. This class of problems is analyzed using 3D finite elements while the material is modeled as an elastic-plastic solid with an “up-down-up” response over the extent of the Lüders strain, followed by hardening. The analysis reproduces the main features of the mechanical behavior provided the unstable part of the response is suitably calibrated. The uniform curvature elastic regime terminates with the nucleation of localized banded deformation. The bands appear in pockets on the most deformed sites of the tube and propagate into the hitherto intact part of the structure while the moment remains essentially unchanged. The Lüders-deformed section has a higher curvature, ovalizes more than the rest of the tube, and develops wrinkles with a characteristic wavelength. For every tube D/t there exists a threshold of Lüders strain separating the two types of behavior. This bounding value of Lüders strain was studied parametrically.