Scaling Behaviour and Complexity of the Portevin-Le Chatelier Effect

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 effect was studied using two complementary scaling analysis 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. Moreover, the multiscale entropy analysis is carried out on the stress time series data observed during the PLC effect 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.Comment: 35 pages, 6 figure

Measuring the equation of state of a hard-disc fluid

We use video microscopy to study a two-dimensional (2D) model fluid of charged colloidal particles suspended in water and compute the pressure from the measured particle configurations. Direct experimental control over the particle density by means of optical tweezers allows the precise measurement of pressure as a function of density. We compare our data with theoretical predictions for the equation of state, the pair-correlation function and the compressibility of a hard-disc fluid and find good agreement, both for the fluid and the solid phase. In particular the location of the transition point agrees well with results from Monte Carlo simulations.Comment: 7 pages, to appear in EPL, slightly corrected versio

Dynamics of stick-slip in peeling of an adhesive tape

We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. We derive the equations of motion for the angular speed of the roller tape, the peel angle and the pull force used in earlier investigations using a Lagrangian. Due to the constraint between the pull force, peel angle and the peel force, it falls into the category of differential-algebraic equations requiring an appropriate algorithm for its numerical solution. Using such a scheme, we show that stick-slip jumps emerge in a purely dynamical manner. Our detailed numerical study shows that these set of equations exhibit rich dynamics hitherto not reported. In particular, our analysis shows that inertia has considerable influence on the nature of the dynamics. Following studies in the Portevin-Le Chatelier effect, we suggest a phenomenological peel force function which includes the influence of the pull speed. This reproduces the decreasing nature of the rupture force with the pull speed observed in experiments. This rich dynamics is made transparent by using a set of approximations valid in different regimes of the parameter space. The approximate solutions capture major features of the exact numerical solutions and also produce reasonably accurate values for the various quantities of interest.Comment: 12 pages, 9 figures. Minor modifications as suggested by refere

Geometry-dependent electrostatics near contact lines

Long-ranged electrostatic interactions in electrolytes modify their contact angles on charged substrates in a scale and geometry dependent manner. For angles measured at scales smaller than the typical Debye screening length, the wetting geometry near the contact line must be explicitly considered. Using variational and asymptotic methods, we derive new transcendental equations for the contact angle that depend on the electrostatic potential only at the three phase contact line. Analytic expressions are found in certain limits and compared with predictions for contact angles measured with lower resolution. An estimate for electrostatic contributions to {\it line} tension is also given.Comment: 3 .eps figures, 5p

Effective dimensionality of the Portevin - Le Chatelier effect

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.Comment: 12 pages, 5 figure

Dynamics of Crossover from a Chaotic to a Power Law State in Jerky Flow

We study the dynamics of an intriguing crossover from a chaotic to a power law state as a function of strain rate within the context of a recently introduced model which reproduces the crossover. While the chaotic regime has a small set of positive Lyapunov exponents, interestingly, the scaling regime has a power law distribution of null exponents which also exhibits a power law. The slow manifold analysis of the model shows that while a large proportion of dislocations are pinned in the chaotic regime, most of them are pushed to the threshold of unpinning in the scaling regime, thus providing insight into the mechanism of crossover.Comment: 5 pages, 3 figures. In print in Phy. Rev. E Rapid Communication

A dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect: Chaos,turbulence and band propagation

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 set of null exponents in the scaling regime. As the latter feature is similar to the GOY shell model for turbulence, we compare our results with the GOY model. Interestingly, the null exponents in our model themselves obey a power law. The configuration of dislocations is visualized through the slow manifold analysis. This shows that while a large proportion of dislocations are in the pinned state in the chaotic regime, most of them are at the threshold of unpinning in the scaling regime. The model qualitatively reproduces the different types of deformation bands seen in experiments. At high strain rates where propagating bands are seen, the model equations are reduced to the Fisher-Kolmogorov equation for propagative fronts. This shows that the velocity of the bands varies linearly with the strain rate and inversely with the dislocation density, consistent with the known experimental results. Thus, this simple dynamical model captures the complex spatio-temporal features of the PLC effect.Comment: 17 pages, 18 figure

Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect

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 strain rate sensitivity of the flow stress. We attempt to understand the above issues by analyzing the geometry of the slow manifold underlying the relaxational oscillations in the model. We show that the nature of the relaxational oscillations is a result of the atypical bent geometry of the slow manifold. The analysis of the slow manifold structure helps us to understand the time scales operating in different regions of the slow manifold. Using this information we are able to establish connection with the strain rate sensitivity of the flow stress. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity.Comment: 7 figures, To appear in Phys. Rev.

New apparatus for DTA at 2000 bar: thermodynamic studies on Au, Ag, Al and HTSC oxides

A new DTA (Differential Thermal Analysis) device was designed and installed in a Hot Isostatic Pressure (HIP) furnace in order to perform high-pressure thermodynamic investigations up to 2 kbar and 1200C. Thermal analysis can be carried out in inert or oxidising atmosphere up to p(O2) = 400 bar. The calibration of the DTA apparatus under pressure was successfully performed using the melting temperature (Tm) of pure metals (Au, Ag and Al) as standard calibration references. The thermal properties of these metals have been studied under pressure. The values of DV (volume variation between liquid and solid at Tm), ROsm (density of the solid at Tm) and ALPHAm (linear thermal expansion coefficient at Tm) have been extracted. A very good agreement was found with the existing literature and new data were added. This HP-DTA apparatus is very useful for studying the thermodynamics of those systems where one or more volatile elements are present, such as high TC superconducting oxides. DTA measurements have been performed on Bi,Pb(2223) tapes up to 2 kbar under reduced oxygen partial pressure (p(O2) = 0.07 bar). The reaction leading to the formation of the 2223 phase was found to occur at higher temperatures when applying pressure: the reaction DTA peak shifted by 49C at 2 kbar compared to the reaction at 1 bar. This temperature shift is due to the higher stability of the Pb-rich precursor phases under pressure, as the high isostatic pressure prevents Pb from evaporating.Comment: 6 figures, 3 tables, Thermodynamics, Thermal property, Bi-2223, fundamental valu

Human and preclinical studies of the host-gut microbiome co-metabolite hippurate as a marker and mediator of metabolic health.

OBJECTIVE: Gut microbial products are involved in regulation of host metabolism. In human and experimental studies, we explored the potential role of hippurate, a hepatic phase 2 conjugation product of microbial benzoate, as a marker and mediator of metabolic health. DESIGN: In 271 middle-aged non-diabetic Danish individuals, who were stratified on habitual dietary intake, we applied 1H-nuclear magnetic resonance (NMR) spectroscopy of urine samples and shotgun-sequencing-based metagenomics of the gut microbiome to explore links between the urine level of hippurate, measures of the gut microbiome, dietary fat and markers of metabolic health. In mechanistic experiments with chronic subcutaneous infusion of hippurate to high-fat-diet-fed obese mice, we tested for causality between hippurate and metabolic phenotypes. RESULTS: In the human study, we showed that urine hippurate positively associates with microbial gene richness and functional modules for microbial benzoate biosynthetic pathways, one of which is less prevalent in the Bacteroides 2 enterotype compared with Ruminococcaceae or Prevotella enterotypes. Through dietary stratification, we identify a subset of study participants consuming a diet rich in saturated fat in which urine hippurate concentration, independently of gene richness, accounts for links with metabolic health. In the high-fat-fed mice experiments, we demonstrate causality through chronic infusion of hippurate (20 nmol/day) resulting in improved glucose tolerance and enhanced insulin secretion. CONCLUSION: Our human and experimental studies show that a high urine hippurate concentration is a general marker of metabolic health, and in the context of obesity induced by high-fat diets, hippurate contributes to metabolic improvements, highlighting its potential as a mediator of metabolic health