Cyclic bending of steel tubes with Lüders bands

Abstract

Preceding experiments and analyses revealed that bending of tubes whose material exhibits Lüders banding leads to the progressive nucleation of inclined bands of higher strain organized into periodic diamond clusters. The diamonds cover both the tensioned and compressed sides of the tube with the affected length developing a higher curvature than the unaffected section. Between the diamond patterns are elastic zones required for each periodic domain to conform to the curvature of the tube (Hallai and Kyriakides, 2011a,b). The present work examines how this inhomogeneously deformed structure behaves on unloading, reverse bending, and curvature symmetric cycling. The inelastic behavior of the material is modeled through a combined isotropic/kinematic hardening constitutive model. The model incorporates partial softening over the extent of the Lüders strain and uses nonlinear kinematic hardening for reverse loading. A tube of virgin material is bent until the whole length is Lüders deformed and is in uniform curvature. The curvature remains uniform during unloading with the strain in the diamonds gradually being erased, but simultaneously a secondary set of local higher strain patterns emerge in the hitherto elastic zones between the original diamonds. During reverse bending to the symmetric negative curvature, the secondary patterns continue to grow in intensity. The tube is unloaded again and bent back to positive curvature completing the cycle. In the course of the second half cycle, localized strain patterns evolve in the reverse order to that of the first half cycle. The secondary patterns are gradually erased, and the diamond patterns reappear now concurrently reaching the same intensity as that acquired progressively during the bending of the virgin material. The same appearance, erasure, and reappearance of localized deformation take place in subsequent cycles. Once past the initial bending, the structure bends uniformly.