M. S. Bharathi

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.

Dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect: chaos, turbulence, and band propagation.

The analysis of experimental time series, obtained from single and polycrystals subjected to constant strain rate tests, reports 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 the results of an extensive study of all aspects of the Portevin-Le Chatelier (PLC) effect within the context of a recent model that reproduces this crossover. We characterize the dynamics of this crossover by studying the distribution of the Lyapunov exponents as a function of the strain rate, with special attention to system size effects. The distribution of the exponents 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 is similar to the result in a shell model for turbulence, we compare the results of our model with that of the shell model. Interestingly, the null exponents in our model themselves obey a power law. The study is complimented by visualizing the configuration of dislocations 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 pushed to the threshold of unpinning in the scaling regime, thus providing insight into the mechanism of crossover. We also show that this model qualitatively reproduces the different types of deformation bands seen in experiments. At high strain rates, where propagating bands are seen, the model equations can be reduced to the Fisher-Kolmogorov equation for propagative fronts, which in turn shows that the velocity of the propagation of the bands varies linearly with the strain rate and inversely with the dislocation density. These results are consistent with the known experimental results. We also discuss the connection between the nature of band types and the dynamics in the respective regimes. The analysis demonstrates that this simple dynamical model captures the complex spatiotemporal features of the PLC effect.

A dynamical model for the Portevin-Le Chatelier bands

We show that an extension of Ananthakrishnas model to include spatial degrees of freedom produces spatially uncorrelated bands, hopping type and the continuously propagating type with increasing applied strain rate. The velocity of the continuously propagating bands is found to vary linearly with applied strain rate

Chaotic and power law states in the Portevin-Le Chatelier effect

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 experiments and concomitantly, the largest Lyapunov exponent is zero.

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 that 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 an insight into the mechanism of crossover.

Possibility of chaos in internal friction experiments of martensites

Wuttig and Suzukis model on anelastic nonlinearities in solids in the vicinity of martensite transformations is analysed numerically. This model shows chaos even in the absence of applied forcing field as a function of a temperature dependent parameter. Even though the model exhibits sustained oscillations as a function of the amplitude of the forcing term, it does not exactly capture the features of the experimental time series. We have improved the model by adding a symmetry breaking term. The improved model shows period doubling bifurcation as a function of the amplitude of the forcing term. The solutions of our improved model shows good resemblance with the nonsymmetric period four oscillation seen in the experiment.