The Portevin-Le Chatelier(PLC) effect has been investigated by deforming Al-2.5%Mg alloy in the strain rate regime where simultaneously two types (type B and type A) of serrations appear in the stress strain curve. Our analysis reveal that in this strain rate regime the entire PLC dynamics for a particular strain rate experiment is governed by a single band which changes its character during the deformation.
Tensile tests have been carried out by deforming polycrystalline samples of substitutional Al-2.5%Mg alloy at room temperature at a range of strain rates. The Portevin - Le Chatelier (PLC) effect was observed. From an analysis of the experimental stress versus time series data we have inferred that the dynamics of the PLC effect in a local finite time is controlled by a finite number of degrees of freedom and this effective dimension becomes reduced with increasing strain.
Recent studies on the Portevin - Le Chatelier effect report an intriguing crossover phenomenon from a low dimensional chaotic to an infinite dimensional scale invariant power law regime in experiments on CuAl single crystals and AlMg polycrystals, as a function of strain rate. We devise a fully dynamical model which reproduces these results. At low and medium strain rates, the model is chaotic with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, power law statistics for the magnitudes and durations of the stress drops emerge as in exper…
We present a continuous time random walk model for the Portevin-Le Chatelier (PLC) effect. From our result it is shown that the dynamics of the PLC band can be explained in terms of the Levy Walk.
Tensile tests were carried out by deforming polycrystalline samples of Al-2.5%Mg alloy at four different temperatures in an intermediate strain rate regime of 2x10-4s-1 to 2x10-3s-1. The Portevin-Le Chatelier (PLC) effect was observed throughout the strain rate and temperature region. The mean cumulative stress drop magnitude and the mean reloading time exhibit an increasing trend with temperature which is attributed to the enhanced solute diffusion at higher temperature. The observed stress-time series data were analyzed using the nonlinear dynamical methods. From the analyses, we could estab…
The Portevin-Le Chatelier (PLC) effect is a kind of plastic instability observed in many dilute alloys when deformed at certain ranges of strain rate and temperature. In this letter we establish that the dynamical process responsible for the PLC effect is Poisson in nature by applying statistical analysis to the observed experimental data obtained during the PLC effect in a substitutional alloy, Al-2.5%Mg and in an interstitial alloy, low carbon steel subjected to uniaxial tensile test at constant imposed strain rate.
The scaling behavior of the Portevin-Le Chatelier (PLC) effect was studied by deforming Al-2.5%Mg alloy for a wide range of strain rates. To reveal the exact scaling nature, the time series data of true stress vs. time, obtained during deformation, were analyzed by two complementary methods: the finite variance scaling method and the diffusion entropy analysis. From these analyses we could establish that in the entire span of strain rates, PLC effect showed Levy walk property.
Tensile tests were carried out by deforming polycrystalline samples of Al-2.5%Mg alloy at room temperature in a wide range of strain rates where the Portevin-Le Chatelier (PLC) effect was observed. The experimental stress-time series data have been analyzed using the recurrence analysis technique based on the Recurrence Plot (RP) and the Recurrence Quantification Analysis (RQA) to study the change in the dynamical behavior of the PLC effect with the imposed strain rate. Our study revealed that the RQA is able to detect the unique crossover phenomenon in the PLC dynamics.
The complexity of the Portevin-Le Chatelier effect in Al-2.5%Mg polycrystalline samples subjected to uniaxial tensile tests is quantified. Multiscale entropy analysis is carried out on the stress time series data observed during jerky flow to quantify the complexity of the distinct spatiotemporal dynamical regimes. It is shown that for the static type C band, the entropy is very low for all the scales compared to the hopping type B and the propagating type A bands. The results are interpreted considering the time and length scales relevant to the effect.
Tensile tests were carried out by deforming polycrystalline samples of an interstitial alloy, low carbon steel at room temperature in a wide range of strain rates where the Portevin-Le Chatelier (PLC) effect was observed. The observed stress time series data were analyzed using the nonlinear dynamical methods. From the analyses, we could establish the presence of marginal deterministic chaos in the PLC effect of the low carbon steel. Moreover, we made a comparative study of the PLC effect of this interstitial alloy with the substitutional Al-Mg alloy which shows that the dynamics of the PLC ef…
We investigate the Portevin-Le Chatelier effect (PLC), by compressing Al-Mg alloys in a very large deformation range, and interpret the results from the viewpoint of phase transitions and critical phenomena. The system undergoes two dynamical phase transitions between intermittent (or "jerky") and "laminar" plastic dynamic phases. Near these two dynamic critical points, the order parameter 1/τof the PLC effect exhibits large fluctuations, and "critical slowing down" (i.e., the number $τ$ of bursts, or plastic instabilities, per unit time slows down considerably).
The scaling behavior of the Portevin-Le Chatelier (PLC) effect is studied by deforming a substitutional alloy, Al-2.5%Mg and an interstitial alloy, low carbon steel (0.15%C, 0.33%Mn, 0.04%P, 0.05%S, 0.15%Si and rest Iron) at room temperature for a wide range of strain rates. To reveal the exact scaling nature, the time series data of true stress vs. time, obtained during the tensile deformation (corrected for drift due to strain hardening by polynomial fitting method), are analyzed by two complementary methods: the standard deviation analysis and the diffusion entropy analysis. From these anal…
The chapter presents the problem of the complexity of plastic flow in alloys, which is manifested by serrated deformation curves and transient plastic strain localizations. This phenomenon uncovers an inherently collective nature of the dynamics of crystal defects. The chapter discusses the state-of-the art of this research under the angle of distinct regimes of collective dislocation dynamics found in conventional, basically binary alloys, e.g., self-organized criticality, deterministic chaos, or synchronization. It concludes with the formulation of diverse open questions, notably concerning …
The plastic deformation of dilute alloys is often accompanied by plastic instabilities due to dynamic strain aging and dislocation interaction. The repeated breakaway of dislocations from and their recapture by solute atoms leads to stress serrations and localized strain in the strain controlled tensile tests, known as the Portevin-Le Chatelier (PLC) effect. In this present work, we analyse the stress time series data of the observed PLC effect in the constant strain rate tensile tests on Al-2.5%Mg alloy for a wide range of strain rates at room temperature. The scaling behaviour of the PLC eff…
A characteristic feature of the Portevin - Le Chatelier effect or the jerky flow is the stick-slip nature of stress-strain curves which is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to result from the competition of a few relevant time scales controlling the dynamics of jerky flow. We address the issue of time scales and its connection to the negative strain rate sensitivity of the flow stress within the framework of a model for the jerky flow which is known to reproduce several experimentally observed features including the negative s…
Experimental time series obtained from single and poly-crystals subjected to a constant strain rate tests report an intriguing dynamical crossover from a low dimensional chaotic state at medium strain rates to an infinite dimensional power law state of stress drops at high strain rates. We present results of an extensive study of all aspects of the PLC effect within the context a model that reproduces this crossover. A study of the distribution of the Lyapunov exponents as a function of strain rate shows that it changes from a small set of positive exponents in the chaotic regime to a dense se…
Scale invariant power law distributions for acoustic emission signals are ubiquitous to several plastically deforming materials. However, power law distributions for the acoustic emission energies are reported in distinctly different plastically deforming situations such as in hcp and, fcc single and polycrystalline samples exhibiting smooth stress-strain curves, and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there has been no models that predict the power…
Tensile tests were carried out by deforming polycrystalline samples of substitutional Al-2.5%Mg alloy at room temperature for a range of strain rates. The Portevin-Le Chatelier (PLC) effect was observed throughout the strain rate regime. The deformation bands in this region are found to be of type A in nature. From the analysis of the experimental stress time series data we could infer that the dynamics of type A dislocation band propagation is a Markov process.
Despite the long history, so far there is no general theoretical framework for calculating the acoustic emission spectrum accompanying any plastic deformation. We set up a discrete wave equation with plastic strain rate as a source term and include the Rayleigh-dissipation function to represent dissipation accompanying acoustic emission. We devise a method of bridging the widely separated time scales of plastic deformation and elastic degrees of freedom. The efficacy of the framework is illustrated by considering three distinct cases of plastic deformation. The first one is the acoustic emissi…
Matallic alloys, such as Al or Cu, or mild steel, display plastic instabilities in a well defined range of temperatures and deformation rates, a phenomenon known as the Portevin-Le Chatelelier (PLC) effect. The stick-slip behavior, or serration, typical of this effect is due to the discontinuous motion of dislocations as they interact with solute atoms. Here we study a simple model of interacting dislocations and show how the classical Einstein fluctuation-dissipation relation can be used to define the temperature in a range of model parameters and to construct a phase diagram of serration tha…
Metals are important structural materials for transport and the built environment. Low carbon steels can fail through strain localisation due to the role of interstitial solute atoms (such as carbon and nitrogen) interacting with mobile dislocations, and this gives rise to the Portevin-Le Chatelier effect and the formation of Luders bands. In this work, we use in-situ tensile testing and observation with High Angular Resolution Electron Back Scatter Diffraction (HR-EBSD) to explore deformation patterning in two Interstitial Free (IF) steel samples. One of these steels was heat treated to trigg…
The plastic deformation of metal alloys localizes in the Portevin--Le Chatelier effect in bands of different types, including propagating, or type 'A' bands, usually characterised by their width and a typical propagation velocity. This plastic instability arises from collective dynamics of dislocations interacting with mobile solute atoms but the resulting sensitivity to the strain-rate lacks fundamental understanding. Here we show, by employing high-resolution imaging in tensile deformation experiments of an aluminum alloy, that the band velocities exhibit large fluctuations. Each band produc…
Jerky flow in solids results from collective dynamics of dislocations which gives rise to serrated deformation curves and a complex evolution of the strain heterogeneity. A rich example of this phenomenon is the Portevin-Le Chatelier effect in alloys. The corresponding spatiotemporal patterns showed some universal features which provided a basis for a well-known phenomenological classification. Recent studies revealed peculiar features in both the stress serration sequences and the kinematics of deformation bands in Al-based alloys containing fine microstructure elements, such as nanosize prec…
