The Portevin–Le Chatelier Effect as a Nonlinear Wave Process in Deformable Alloys

Abstract

The instability mechanism of plastic deformations in crystalline alloys is studied on the basis of the autowave approach. A mathematical model is proposed for the serrated flow behavior and localization of the plastic flow in the form of deformation bands—the Portevin–Le Chatelier effect, which manifests itself in a wide range of positive Celsius temperatures. A stationary solution of the initial system of equations at a constant load is found within the framework of the proposed model; the solution is the wave front of the plastic strain rate and is interpreted as a Lüders band. The numerical analysis of the initial model shows that the irregular variations of deforming stress and the spatial wave solutions take place in the instability region determined by the N-shaped dependence of the dislocation deceleration force on the dislocation velocity. This nonlinearity of the deceleration force is due to the peculiarities of the interaction of the dislocations with impurity atoms. The critical dimensionless parameters responsible for the variety of wave solutions of the equation system are determined. For the specific values of these parameters, the irregular oscillation waveform of deforming stress is found, as well as the shape and periodicity of the bursts in plastic strain rate with the oscillation waveform and bursts being strictly correlated and forming the Portevin–Le Chatelier bands, which can be relatively uniform or randomly distributed along the length of the crystal.