Phenomenological theory of Lüders bands

Abstract

The constitutive functions of deformation, work hardening rate,H, and deceleration,D, are specialized for various deformation paths, and related to the evolution of dislocation structure. Based on the variation with deformation ofH andD it is shown that two modes of tensile deformation may be defined: a destabilizing mode which leads to the normal homogeneous deformation behaviour terminated by necking and rupture, and a stabilizing mode which gives rise to Lüders band formation and subsequent homogeneous deformation. The conditions for Lüders banding are established and a simple mathematical description based on these concepts is given. A detailed discussion shows that with theories using only one structure parameter it is not possible to understand the Lüders phenomenon.