Structural-mechanical model for describing the Portevin–Le Châtelier effect

Despite nearly 200 years having passed since its discovery, the Portevin–Le Châtelier (PLC) effect—the phenomenon of discontinuous plastic flow observed in most alloys under specific deformation conditions—remains an active research area for both mechanicians and physicists. Current studies encompass experimental investigations and theoretical developments, leading to various mathematical models, a brief review of which is presented in this work. Given the stochastic nature of the PLC effect, including the spatiotemporal distribution of slip bands and response variations during monotonic loading (as evidenced by physical and numerical experiments on various alloy specimens), mathematical description and analysis methods for these phenomena are of particular scientific interest.
During the model development stage, we carried out a thorough analysis of the physical mechanisms underlying the PLC effect. Two primary mechanisms were identified: (1) the formation of impurity atom clusters around temporarily arrested dislocations at obstacles, and (2) the capture of alloying element atoms by slowly moving dislocations. For modeling this effect, we propose a structural-mechanical approach to describe uniaxial tensile loading of rod specimens under kinematic control. The formulation includes fundamental constitutive and evolutionary relations based on the physical mechanisms of dislocation-impurity interactions.
A novel two-stage model identification procedure is introduced, incorporating statistical analysis and wavelet transform methods. The paper presents application results of the identified model for describing the PLC effect in Al–Mg alloy specimens, demonstrating its effectiveness in capturing the key features of discontinuous plastic flow.