Dynamical Analysis of the Portevin - Le Châtelier Effect

Quaouire, L.; Fressengeas, Claude

doi:10.4028/www.scientific.net/ssp.42-43.293

Cited by 4 publications

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“…The methodology used was the simplest algorithm for implementation, due to Grassberger and Procaccia (GP) [1983]. Recently, there has been three more attempts [Quaouire & Fressengeas, 1995;Ananthakrishna & Noronha, 1995;Venkadesan et al, 1995Venkadesan et al, , 1996, of which [Quaouire & Fressengeas, 1995;Ananthakrishna & Noronha, 1995] are on the same data. In these two studies, use was made of more sophisticated methods such as the Singular Value Decomposition (SVD) method coupled to the GP algorithm and the calculation of the positive Lyapunov exponent.…”

Section: Introductionmentioning

confidence: 99%

Chaos in the Portevin–Le Châtelier Effect

Noronha

Ananthakrishna

Quaouire

et al. 1997

Int. J. Bifurcation Chaos

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We report the verification of the prediction of chaos in the Portevin-Le Châtelier 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 Châtelier 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.

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Section: Introductionmentioning

confidence: 99%

Chaos in the Portevin–Le Châtelier Effect

Noronha

Ananthakrishna

Quaouire

et al. 1997

Int. J. Bifurcation Chaos

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“…This offers justification for the use of only a few degrees of freedom for the description of the temporal aspect, eventhough the system is spatially extended. Ananthakrishna & Noronha, 1995;Quaouire & Fressengeas, 1995;Venkadesan et al 1995;Noronha et al 1996Noronha et al & 1997. (Note that a spatially extended system implies infinite degrees of freedom.)…”

Section: Introductionmentioning

confidence: 99%

Numerical Continuation at Double Bifurcation Points of a Reaction–Diffusion Problem

Chien

Mei

Shen

1998

Int. J. Bifurcation Chaos

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We consider a model proposed earlier by us for describing a form of plastic instability found in creep experiments . The model consists of three types of dislocations and some transformations between them. The model is known to reproduce a number of experimentally observed features. The mechanism for the phenomenon has been shown to be Hopf bifurcation with respect to physically relevant drive parameters.Here, we present a mathematical analysis of adiabatically eliminating the fast mode and obtaining a Ginzburg-Landau equation for the slow modes associated with the steps on creep curve. The transition to the instability region is found to be one of subcritical bifurcation over most of the interval of one of the parameters while supercritical bifurcation is found in a narrow mid-range of the parameter. This result is consistent with experiments. The dependence of the amplitude and the period of strain jumps on stress and temperature derived from the Ginzburg-Landau equation are also consistent with experiments. On the basis of detailed numerical solution via power series expansion, we show that high order nonlinearities control a large portion of the subcritical domain.

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From mesoscopic heterogeneity of slip to macroscopic fluctuations of stress and strain

Ha¨hner

Zaiser

1997

Acta Materialia

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Dynamical Analysis of the Portevin - Le Châtelier Effect

Cited by 4 publications

References 0 publications

Chaos in the Portevin–Le Châtelier Effect

Chaos in the Portevin–Le Châtelier Effect

Numerical Continuation at Double Bifurcation Points of a Reaction–Diffusion Problem

From mesoscopic heterogeneity of slip to macroscopic fluctuations of stress and strain

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