Bending of steel tubes with Lüders bands

Inelastic bending of tubes made of steel which exhibits Lüders bands is being studied through a combination of experiment and analysis. Low carbon steel tubes with D/t of 27.2 were bent to failure under pure bending. The measured moment-curvature responses were found to have a relatively sharp transition from the elastic to the plastic regime followed by extended moment plateaus. The moment plateaus terminated by the occurrence of local collapse. Wrinkles appeared on the compressed side soon after the onset of inelastic deformation and simultaneously narrow Lüders bands emanated from the wrinkles. The bands were straight and oriented at ±(45–55°) to the axis of the tube. As bending progressed, the wrinkle amplitude grew and the bands lengthened, broadened and multiplied. The tubes eventually collapsed by local buckling induced by the wrinkles. Tube bending was modeled by considering a section of tube with initial axisymmetric imperfections. The domain was discretized with incompatible 3-D finite elements and a fine mesh. The material was modeled as an elastic-plastic solid with an up-down-up stress-strain response. The calculated moment-curvature responses reproduced measured results very well including the extended moment plateaus. While the moment plateau was traced, x-shaped banded patterns developed similar to those seen in the experiments. The bands were oriented at approximately ±55° to the axis of the tube. Thus, the simple unstable constitutive model adopted is capable of reproducing the main features of this problem.