M. Lebyodkin

Spatio-temporal dynamics of the Portevin–Le Chatelier effect: experiment and modelling

Abstract The temporal and spatial features of the Portevin–Le Chatelier plastic instabilities in single and polycrystals of Al–Mg alloys were investigated systematically, with special emphasis being put on the character of the statistical distributions of the stress drops. The effect of strain rate, temperature and the microstructural state of the alloy was studied experimentally. It was shown that an experimentally accessible quantity, the flow stress, governs to a large extent the observed correlation between the variation of the type of serrations and of the stress drop distributions. Computer simulations of the Portevin–Le Chatelier effect were carried out using a simple spatial coupling model. It was demonstrated that the salient features of the complex spatio-temporal behaviour observed experimentally for different microstructural states are adequately reproduced by the model. A comparison between the experimental data and the simulation results suggests that the spatial coupling stems from plastic strain incompatibilities.

Spatial coupling in jerky flow using polycrystal plasticity

A multiscale approach including a finite element framework for polycrystal plasticity is used to model jerky flow, also known as the Portevin-Le Chatelier effect. The local constitutive behavior comprises the standard description of the negative strain rate sensitivity of the flow stress in the domain of instability. Due to stress gradients inherent to the polycrystal formulation, the spatial coupling involved in the spatio-temporal dynamics of jerky flow is naturally accounted for in the model, without using any ad hoc gradient constitutive formulation. For the first time, the static, hopping and propagating band types are recovered in constant strain-rate tests, as well as the temporal properties of the stress serrations. The associated dynamic regimes are characterized and found consistent with recent experimental evidence of both chaos and self-organized criticality in Al-Mg polycrystals.

Statistical behaviour and strain localization patterns in the Portevin-Le Chatelier effect

Abstract Statistics of the stress drops associated with the Portevin-Le Châtelier effect in an AlMg alloy were studied both experimentally and theoretically. It was shown that the character of the statistics changes from a peaked distribution of the stress drop magnitudes to a monotonically decreasing one as the imposed strain rate or the temperature are increased. A discrete model based on a micromechanically founded local constitutive equation combined with spatial coupling between the elements of the system was shown to reproduce the observed statistical behaviour. The mechanism of spatial coupling is connected with elastic stresses due to local plastic incompatibilities. The model was further applied to simulate spatial deformation patterns including propagative deformation bands. The systematics of the bands reported in the literature as well as the observed dependence of the band velocity on the imposed deformation rate were recovered. It was concluded that the model proposed provides an adequate description of both the statistics of stress discontinuities and the spatial features of the Portevin-Le Châtelier effect.

Multifractal Burst in the Spatiotemporal Dynamics of Jerky Flow

The collective behavior of dislocations in jerky flow is studied in Al-Mg polycrystalline samples subjected to constant strain rate tests. Complementary dynamical, statistical, and multifractal analyses are carried out on the stress-time series recorded during jerky flow to characterize the distinct spatiotemporal dynamical regimes. It is shown that the hopping type B and the propagating type A bands correspond to chaotic and self-organized critical states, respectively. The crossover between these types of bands is identified by a large spread in the multifractal spectrum. These results are interpreted on the basis of competing scales and mechanisms.

The hidden order behind jerky flow

Jerky flow, or the Portevin-Le Chatelier effect, is investigated at room temperature by applying statistical, multifractal and dynamical analyses to the unstable plastic flow of polycrystalline Al-Mg alloys with different initial microstructures. It is shown that a chaotic regime is found at medium strain rates, whereas a self-organized critical dynamics is observed at high strain rates. The cross-over between these two regimes is signified by a large spread in the multifractal spectrum. Possible physical mechanisms leading to this wealth of patterning behavior and their dependence on the strain rate and the initial microstructure are discussed.

Influence of second-phase morphology and topology on mechanical and fracture properties of Al-Si alloys

Mechanical behaviour of eutectic Al-Si alloys with different Si particle topology and morphology modified by heat treatment has been studied. The alloy chosen was a model system for understanding the influence of morphological and topological features on macroscopic mechanical properties. The heat treatment was used to transform a percolated structure of Si platelets and needles into an ensemble of well separated spheroidised particles. Different modes of fracture were observed depending on the particle morphology and on the testing temperature. The as-cast specimens appeared to be softer and showed higher ductility than those with spheroidised particles.

Statistical and multifractal analysis of the Portevin–Le Chatelier effect

Abstract The stress time series associated with the Portevin–Le Chatelier (PLC) effect in Al–2.5%Mg polycrystals deformed in constant applied strain rate have been analyzed by statistical and multifractal methods. The objective was to check the conjecture that jerky flow should exhibit distinct dynamical regimes. Statistical distributions of stress drops and drop durations exhibit a well-defined sequence as the applied strain rate increases. Peaked distributions are followed by monotonically decreasing ones at higher strain rate. For a large grain size, the high strain rate distributions are consistently fitted by power laws suggesting a self-organized critical (SOC) dynamics. At smaller grain sizes, a multifractal fit of the distributions is more appropriate. Multifractality increases with strain rate. A sharp upturn is observed at the boundary between type B and type A PLC bands. The correlation between independant statistical and multifractal analyses suggests a fundamental crossover of the underlying dynamics. It is also an indication that the multifractal analysis has the ability to provide sensible quantitative characterizations of jerky flow.

Kinetics and statistics of jerky flow: experiments and computer simulations

Abstract The paper presents an overview of experimental and theoretical studies of the Portevin-Le Chatelier effect with regard to the statistics of stress discontinuities and spatio-temporal behaviour of strain localisations. It is shown that the statistics of stress drops changes progressively from peak-shaped to monotonie distributions when the strain rate or temperature are increased. A mesoscopic model accounting for strain inhomogeneity and spatial coupling is proposed to explain the statistical behaviour observed. The model reproduces the character of deformation curves and the corresponding deformation band kinetics. It also predicts the caracteristics of the bands for both constant strain rate and constant stress rate experiments.

Statistical aspects of low temperature discontinuous deformation

Abstract To summarize we point out the following. 1. (i) There is an analogy in macroscopic stress behaviour of discontinuous flow associated with thermomechanical instability or Portevin-Le Chatelier effect. It may be suggested that statistics of these types of plastic instability do not depend on the particular mechanism but are governed by common laws. 2. (ii) The manifestation of a power law in distribution densities, being a sign of self-organization in the dislocation dynamics, depends on the material and on deformation conditions. 3. (iii) In order to draw definite conclusions about the nature of common features of the phenomenon of plastic instability it would be interesting to study simultaneously the macroscopic parameters of deformation curves and “mesoscopic” ones, namely the electric responses to the defect motion. Investigations of the size effect on statistics might also shed light on the problem.

Low-temperature abrupt deformation processes in metals: kinetic and statistical properties observed by means of electronic response

Abstract The properties of abrupt plastic deformation occurring in Nb and Al at low temperature were investigated using electronic response signal measurements. Statistical treatment of the results led to the possible conclusion that a self-organized criticality in the system of plastic carriers leads to the abrupt movement.