Evolution of Lüders banding under axial loading and reverse loading

Abstract

Low slenderness steel rods that exhibit Lüders banding are used to examine the evolution of localized deformation when a specimen is unloaded and reverse loaded. Special attention is given to how a specimen behaves when the initial loading is interrupted with part of it Lüders deformed and the rest still elastic. Digital image correlation revealed that both parts unload elastically, but on reverse loading the previously elastic zone yields and develops Lüders strain of the opposite sign. By contrast, the plastically deformed zone follows the usual Bauschinger rounding. Thus, the specimen behaves as a structure with its overall response being a combination of the two distinctly different stress-strain histories, and depends on the length of each zone. The experiments are simulated using finite element analysis coupled to a custom combined isotropic-kinematic hardening plasticity model with a partially softening branch spanning the Lüders stress plateau. The analysis reproduces the measured responses and evolution of localized deformation quite accurately demonstrating the fidelity of the constitutive model adopted. The results also demonstrate that the propagation of the Lüders zone has a more complex three-dimensional profile than that reported for thin strips. Overall, the study provides a guide on how Lüders banding can be treated in structures that undergo loading and reverse loading.