Lüders and Portevin–Le Chatelier Bands at the Stage of Elastoplastic Transition: Nucleation and Propagation

Abstract

The work is devoted to the theoretical study of the nucleation and propagation of Lüders bands on the yield plateau and of moving Portevin–Le Chatelier bands of type A (solitary waves of plastic flow) at the stage of parabolic hardening during strain aging. The proposed model considers collective deformation modes on the spatiotemporal meso- and macroscales. Strain aging changes the state of a deformable medium on the mesoscale. Deformation of a medium under constant-rate uniaxial tension is described by a system of two coupled nonlinear parabolic equations for dynamic order parameters. The coefficients of these equations depend on the impurity concentration. On the yield plateau, solutions of the equations in the form of a switching wave describe the nucleation (at the yield drop stage) and propagation of Lüders bands. Depending on the temperature and rate of deformation during strain aging, a yield drop may be repeated on the yield plateau. Its formation changes the mode of Lüders band propagation from constant-velocity continuous to discrete one. At the strain hardening stage, the nucleation and propagation of the Portevin–Le Chatelier band are described by solutions in the form of a traveling autosoliton (a solitary wave of plastic flow).