Plane strain solution and cross-section flattening analysis in tube bending with linear hardening law

Abstract

Formulae based on plane strain assumption are deduced to calculate principal stresses, von Mises stress and cross-section flattening ratio of tubes subjected to combined bending and additional tension. The analysis shows that additional tensile force causes movement of neutral layer toward bending center and makes deformation behavior under rotary draw bending different with that under pure bending. The principal stresses and the von Mises stress are proportional to yield stress, linear hardening factor and the neutral layer movement and inversely proportional to centerline radius/diameter ratio. With radial displacement at tube’s extrados taken into consideration, the von Mises stress increases with greater neutral layer movement but reduces with larger centerline radius/diameter ratio. Analytical and numerical von Mises stresses distribute nonuniformly in the cross section, and large von Mises stresses localize at the tube’s extrados. Both the maximum values of the two results localize on the outermost surface of the tube. In addition, the variation tendencies of analytical, numerical and experimental change rates of minor axis of the distorted cross section are in good agreement, increasing with smaller centerline radius/diameter ratio. The analytical results are greater than the numerical results but smaller than the experimental results.