Chaos in the Portevin–Le Châtelier Effect

2008

Phys. Rev. E

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We report a comprehensive investigation of a model for peeling of an adhesive tape along with a nonlinear time series analysis of experimental acoustic emission signals in an effort to understand the origin of intermittent peeling of an adhesive tape and its connection to acoustic emission. The model represents the acoustic energy dissipated in terms of Rayleigh dissipation functional that depends on the local strain rate. We show that the nature of the peel front exhibits rich spatiotemporal patterns ranging from smooth, rugged and stuck-peeled configurations that depend on three parameters, namely, the ratio of inertial time scale of the tape mass to that of the roller, the dissipation coefficient and the pull velocity. The stuck-peeled configurations are reminiscent of fibrillar peel front patterns observed in experiments. We show that while the intermittent peeling is controlled by the peel force function, the model acoustic energy dissipated depends on the nature of the peel front and its dynamical evolution. Even though the acoustic energy is a fully dynamical quantity, it can be quite noisy for a certain set of parameter values suggesting the deterministic origin of acoustic emission in experiments. To verify this suggestion, we have carried out a dynamical analysis of experimental acoustic emission time series for a wide range of traction velocities. Our analysis shows an unambiguous presence of chaotic dynamics within a subinterval of pull speeds within the intermittent regime. Time series analysis of the model acoustic energy signals is also found to be chaotic within a subinterval of pull speeds. Further, the model provides insight into several statistical and dynamical features of the experimental AE signals including the transition from burst type acoustic emission to continuous type with increasing pull velocity and the connection between acoustic emission and stick-slip dynamics. Finally, the model also offers an explanation for the recently observed feature that the duration of the slip phase can be less than that of the stick phase.

“…The method has been used to analyze experimental time series as well (for details, see Ref. [50,51]). …”

Section: Time Series Analysis Of Experimental Ae Signalsmentioning

confidence: 99%

“…Thus, the modification we effect is to allow more number of neighbors so that the noise statistics is sampled properly. (See for details [50,51].) As the sum of the exponents should be negative for a dissipative system, we impose this as a constraint.…”

Section: Time Series Analysis Of Experimental Ae Signalsmentioning

confidence: 99%

Intermittent peel front dynamics and the crackling noise in an adhesive tape

Kumar

2008

Phys. Rev. E

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“…In spite of the idealised nature of the model, it is successful in explaining several generic features of the PLC effect, such as the emergence of the negative SRS [14,21], the existence of critical strain for the onset of the PLC instability, and the existence of a window of strain rates and temperatures for the occurrence of the PLC effect (see [14]). One prediction of the model is that there is a range of strain rates where the PLC effect is chaotic [22], subsequently verified by analysing experimental signals [10,11,12,13]. The model has been studied in detail by our group and others including an extension to the case of fatigue [23,24,25].…”

mentioning

confidence: 91%

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

Bharathi

2002

Europhys. Lett.

PACS. 62.20.Fe -Deformation and plasticity. PACS. 05.65.+b -Self-organized systems. PACS. 05.45.Ac -Low-dimensional chaos.Abstract. -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.The Portevin-Le Chatelier (PLC) effect, discovered at the turn of the last century [1], is a striking example where collective behaviour of defects leads to complex spatio-temporal patterns [2,3,4]. The PLC effect manifests itself as a series of serrations on the stress-strain curves when samples of dilute alloys are deformed under constant strain rate,ǫ a (actually constant pulling speed). The effect is observed only in a window of strain rates and temperatures. Each stress drop is associated with the formation and often the propagation of a dislocation band. In polycrystals, at lowǫ a , the randomly nucleated type C bands with large stress drop amplitudes are seen. At intermediate strain rates, one finds the spatially correlated 'hopping' type B bands moving in a relay race manner with smaller stress drop amplitudes. At high strain rates, propagating type A bands with small amplitudes are observed. (In single crystals such a clear classification does not exist.) These different types of PLC bands are believed to represent distinct correlated states of dislocations in the bands. It is this rich spatio-temporal dynamics that has recently attracted the attention of physicists as well [8,9]. Indeed, the PLC effect is a good example of slow-fast dynamics commonly found in many stick-slip systems such as frictional sliding [5], fault dynamics [6] and peeling of an adhesive tape [7].Recent efforts have shown that surprisingly large body of information about the nature of dynamical correlations is hidden in the stress-strain curves [10,11,12,13]. More recently, an intriguing crossover phenomenon from a chaotic regime occurring at low and medium strain rates to a power law regime at high strain rates has been detected in experiments on the PLC c EDP Sciences

“…The method followed was to analyze the stress-time series [15,16] using dynamical methods [17,18]. Apart from confirming the chaotic nature of stress drops in a window of strain rates, these attempts have shown that a wealth of dynamical information can be extracted from the stress-time series obtained during the PLC effect [15,16]. Indeed, the number of degrees of freedom estimated from the experimental time series turn out to be same as in the model offering justification for ignoring spatial degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Dynamical approach to the spatiotemporal aspects of the Portevin–Le Chatelier effect: Chaos, turbulence, and band propagation

Bharathi

2004

Phys. Rev. E

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The analysis of 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 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 the GOY shell model for turbulence, we compare the results of our model with that of the GOY 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 an 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. Marginal stability analysis shows that the velocity of the propagating 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 spatio-temporal features of the PLC effect.