Chaos in the Portevin-Le Châtelier effect

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 11, 1997, Pages 2577-2586

  Noronha, S J ^a   Ananthakrishna, G ^a   Quaouire, L ^b   Fressengeas, C ^b   Kubin, L P ^c  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b UNIVERSITÉ DE LORRAINE   (France)

^c CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031278987     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497001734     Document Type: Article

References (29)

1. Albano, A. M., Muench, J., Schwartz, C., Mees, A. I. & Rapp, P. E. [1988] "Singular-value decomposition and the Grassberger-Proccacia algorithm," Phys. Rev. A38, 3017-3026.
2. Ananthakrishna, G. [1993] "Formation and propagation of bands, and chaos in jerky flow," Scipta Metall. et Mater. 29, 1183-1188.
3. Ananthakrishna, G. & John, T. M. [1990] "Instabilities and chaos in plastic flow," in Directions in Chaos, ed. Hao, B.-L. (World Scientific, Singapore), pp. 133-148.
4. Ananthakrishna, G. & Valsakumar, M. C. [1982] "Repeated yield drop phenomena; a temporal dissipative structure," J. Phys. D15, L171-L175.
5. Ananthakrishna, G. & Valsakumar, M. C. [1983] "Chaotic flow in a model for repeated yielding," Phys. Lett. A95, 69-71.
6. Ananthakrishna, G., Fressengeas, C., Grosbras, M., Vergnol, J., Engelke, C., Plessing, J., Neuhäuser, H., Bouchaud, E., Planès, J. & Kubin, L. P. [1995] "On the existence of chaos in jerky flow," Scipta Metall. et Mater. 32, 1731-1737.
7. Ananthakrishna, G. & Noronha, S. J. [1995] "Chaos in jerky flow: Theory and Experiment," in Nonlinear Phenomena in Materials Science III, eds. Ananthakrishna, G., Kubin, L. P. & Martin, G. (Scitec Publications, Switzerland), pp. 277-286.
8. Cottrell, A. H. [1953] Dislocations and Plastic Flow in Crystals (Clarendon Press, Oxford).
9. Ding, M., Grebogi, C., Ott, E., Sauer, T. & Yorke, J. A. [1993] "Plateau onset for correlation dimension: When does it occur," Phys. Rev. Lett. 70, 3872-3875.
10. Eckmann, J. P., Kamphorst, S. O., Ruelle D. & Ciliberto, S. [1986] "Lyapunov exponents from time series," Phys. Rev. A34, 4971-4979.
11. Estrin Y. & Kubin, L. P. [1989] "Collective dislocation behaviour in dilute alloys," J. Mech. Behavior Materials 2, 255-292.
12. Grassberger, P. & Procaccia, I. [1983] "Measuring the strangeness of attractors," Physica D9, 189-208.
13. Jeanclaude, V., Fressengeas, C. & Kubin, L. P. [1992] "The propagation of the Portevin-Le Châtelier deformation bands," in Nonlinear Phenomena in Materials Science II, eds. Kubin, L. P. & Martin, G. (Trans Tech, Switzerland), pp. 385-402.
14. Karantonis, A. & Pagitsas, M. [1996] "Comparative study for the calculation of the Lyapunov spectrum from nonlinear experimental signals," Phys. Rev. E53, 5428-5444.
15. Kubin, L. P. & Estrin, Y. [1985] "The Portevin-Le Châtlier effect in deformation with constant stress rate," Acta Metall. 33, 397-407.
16. Kubin, L. P. & Estrin, Y. (organizers) [1993] "Viewpoint set no. 21: Propagative instabilities," Scripta Metall. et Mater. 29, 1147-1188.
17. Le Châtelier, F. [1909] "Influence du temps et de la temperature sur les essais au choc," Rev. de Métallurgie 6, 914-917.
18. Osborne, A. R. & Provenzale A. [1989] "Finite correlation dimension for stochastic systems with power-law spectra," Physica D35, 357-381.
19. Penning, P. [1972] "Mathematics of the Portevin-Le Châtlier effect," Acta Metall. 20, 1169-1175.
20. Provenzale. A., Smith, L. A., Vio, R. & Murante, G. [1992] "Distinguishing between low-dimensional dynamics and randomness in measured time series," Physica D58, 31-49.
21. Quaouire L. & Fressengeas, C. [1995] "Dynamical analysis of the Portevin-Le Châtelier effect," in Nonlinear Phenomena in Materials Science III, eds. Ananthakrishna, G., Kubin, L. P. and Martin, G. (Scitec Publications, Switzerland), pp. 293-302.
22. Sano, M. & Sawada, Y. [1985] "Measurement of the Lyapunov spectrum from a chaotic time series," Phys. Rev. Lett. 55, 1082-1085.
23. Theiler, J. [1986] "Spurious dimension from algorithms applied to limited time series data," Phys. Rev. A34, 2427-2432.
24. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. & Farmer, J. D. [1992] "Testing for non-linearity in time series: The method of surrogate data," Physica D58, 77-94.
25. van den Beukel, A. [1975] "Theory of the effect of dynamic strain ageing on mechanical properties," Phys. Stat. Sol. (a) 30, 197-206.
26. Venkadesan, S., Murthy, K. P. N. & Valsakumar, M. C. [1995] "Chaotic flow in Al-Mg alloy," in Nonlinear Phenomena in Materials Science III, eds. Ananthakrishna, G., Kubin, L. P. & Martin, G. (Scitec Publications, Switzerland), pp. 287-292.
27. Venkadesan, S., Valsakumar, M. C., Murthy, K. P. N. & Rajasekar, S. [1996] "Evidence for chaos in an experimental time series from serrated plastic flow," Phys. Rev. E54, 611-616.
28. Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. [1985] "Determining Lyapunov exponents from a time series," Physica D16, 285-317.
29. Zeng, X., Eykholt, R. & Pielke, R. A. [1991] "Estimating the Lyapunov-exponent spectrum from short time series of low precision," Phys. Rev. Lett. 66, 3229-3232.