G. Ananthakrishna

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.

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.

Repeated yield drop phenomenon: a temporal dissipative structure

Based on well known mechanisms, the authors set up a system of coupled nonlinear rate equations for the densities of three types of dislocations, namely, the mobile, the immobile and those with clouds of solute atoms, and for the load sensed by the load cell. For a range of values of the parameters, these equations admit periodic solutions called limit cycles, leading to repeated yield drops. The model exhibits many experimentally observed features. The new temporal order is an example of a dissipative structure.

Chapter 57 Collective behaviour of dislocations in plasticity

Publisher Summary This chapter discusses the collective dislocation behavior in cyclic deformation. During plastic flow, the spatial arrangement of the dislocation structure essentially derives from a competition between two factors. When it exists, the interaction of dislocations with strong and dense localized obstacles other than dislocations (small clusters and precipitates, lattice friction and Peierls forces) tends to induce rather uniform dislocation distributions. In such conditions, the plastic flow properties of the bulk material may simply reflect the behavior of isolated mobile dislocations. In contrast, the mutual interactions of dislocations, both local and long ranged, become all the more important as dislocations multiply. Thus, the contribution of dislocation interactions to the flow stress increases during plastic flow. At a certain stage that is characterized by a critical stress, strain, or dislocation density, the collective dislocation behavior sets in which is characterized by the emergence of dislocation-rich and dislocation-poor regions. This is usually referred to as dislocation patterning.

A model based on nonlinear oscillations to explain jumps on creep curves

A dislocation transformation model with three types of dislocations-namely the mobile, the immobile and those with clouds of solute atoms-is considered. Some physically reasonably reactions are postulated, leading to a coupled set of nonlinear differential equations for the rate of change of their densities. The basic idea of Cottrells mechanism has been incorporated. It is shown that these equations admit a class of periodic solutions called limit cycles which are typical of nonlinear systems, suggesting that nonlinearity plays a fundamental role in the model. The rate equations are solved on a computer to obtain the oscillatory behaviour of the densities and hence leading to steps on the creep curve. The theory predicts that there is a range of temperature over which the phenomenon can occur, in agreement with the experiment of L.N. Zagorukuyko et al. (1977). The theory also reproduces other normal forms of creep curves.

Hidden order in serrated flow of metallic glasses

We report results of statistical and dynamic analysis of the serrated stress-time curves obtained from compressive constant strain-rate tests on two metallic glass samples with different ductility levels in an effort to extract hidden information in the seemingly irregular serrations. Two distinct types of dynamics are detected in these two alloy samples. The stress-strain curve corresponding to the less ductile Zr65Cu15Ni10Al10 alloy is shown to exhibit a finite correlation dimension and a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. In contrast, for the more ductile Cu47.5Zr47.5Al5 alloy, the distributions of stress drop magnitudes and their time durations obey a power-law scaling reminiscent of a self-organized critical state. The exponents also satisfy the scaling relation compatible with self-organized criticality. Possible physical mechanisms contributing to the two distinct dynamic regimes are discussed by drawing on the analogy with the serrated yielding of crystalline samples. The analysis, together with some physical reasoning, suggests that plasticity in the less ductile sample can be attributed to stick-slip of a single shear band, while that of the more ductile sample could be attributed to the simultaneous nucleation of a large number of shear bands and their mutual interactions

Chaotic flow in a model for repeated yielding

Chaos exhibited by a model introduced in the context of repeated yielding is studied. The model shows an infinite sequence of period-doubling bifurcations with an exponent δ = 4.67 ± 0.1. The associated one-dimensional map and the projection of the strange attractor are also studied.

Chaos in the Portevin-Le Chatelier effect

We report the verification of the prediction of chaos in the Portevin-Le Chatelier effect or the jerky flow by analyzing the stress signals obtained from samples of polycrystalline Al-Mg alloys subjected to a constant strain rate test. Particular care is taken to obtain reasonably long and accurate stress signals. The analysis of these signals is carried out by using several complementary methods such as calculation of correlation dimension, singular value decomposition and the spectrum of Lyapunov exponents. The analysis shows the existence of a finite correlation dimension and a positive Lyapunov exponent. Using the existence of a positive Lyapunov exponent and finite correlation dimension as a discriminator, we also carry out a surrogate analysis of the time series to ascertain that the signals are not from a power law stochastic process. The analysis provides an unambiguous support for the existence of chaos in Portevin-Le Chatelier effect thus verifying the prediction of the model. Further, from the analysis we find that the minimum number of variables required for a dynamical description of the jerky flow appears to be four or five consistent with the model.

Critical behavior of electrical resistivity in polar + nonpolar binary liquid systems

The behavior of electrical resistivity in the critical region of three polar + nonpolar binary liquid systems CS2 +(CH3CO)2O, C6H12+(CH3CO)2O, and n‐C7H16+(CH3CO)2O is studied. For the mixtures with critical composition, the two phase region shows a conductivity behavior with σ1−σ2∼ (−e)β with β?0.35. In the one phase region d R/d T has a singularity e−b with b?0.35. A possible theory of the impurity conduction is given, which broadly explains these results. The possibility of d R/d T being positive or negative is also discussed.