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

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 70, Issue 2 2, 2004, Pages

  Ananthakrishna, G ^a   Bharathi, M S ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; DIFFUSION; DISLOCATIONS (CRYSTALS); MATHEMATICAL MODELS; STRAIN RATE; STRESSES; TEMPERATURE; TIME SERIES ANALYSIS; TURBULENCE;

BAND PROPAGATION; LE CHATELIER EFFECT; LYAPUNOV EXPONENTS; SPATIOTEMPORAL ASPECTS;

POLYCRYSTALLINE MATERIALS;

EID: 42749101771     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.026111     Document Type: Article

References (74)

1. L. P. Kubin, C. Fressengeas, and G. Ananthakrishna, in Collective Behaviour of Dislocations, edited by F. R.N. Nabarro and M. S. Deusbery (North-Holland, Amsterdam, 2002), Vol. 11, p. 101.
2. A detailed study of this effect may be found in F. Le Chatelier, Rev. de Métal. 6, 914 (1909). However, the phenomenon was first observed by F. Savart [Ann. Chim. Phys., Second series, 65, 337 (1937)].
3. A detailed study of this effect may be found in F. Le Chatelier, Rev. de Métal. 6, 914 (1909). However, the phenomenon was first observed by F. Savart [Ann. Chim. Phys., Second series, 65, 337 (1937)].
4. M. Zaiser and P. Hähner, Phys. Status Solidi B 199, 267 (1997).
5. A. H. Cottrell, Dislocations and Plastic Flow in Crystals (Clarendon, Oxford, 1953).
6. A. Van den Beukel, Phys. Status Solidi A 30, 197 (1975).
7. L. P. Kubin and Y. Estrin, Acta Metall. 33, 397 (1985).
8. P. Penning, Acta Metall. 20, 1169 (1972).
9. J. Weertman, Can. J. Phys. 45, 797 (1967).
10. B. N. J. Persson and E. Tosatti, Physics of Sliding Friction (Kluwer, Dordrecht, 1996).
11. J. M. Carlson and J. S. Langer, Phys. Rev. Lett. 62, 2632 (1989); Phys. Rev. A 40, 6470 (1989).
12. J. M. Carlson and J. S. Langer, Phys. Rev. Lett. 62, 2632 (1989); Phys. Rev. A 40, 6470 (1989).
13. D. Maugis and M. Barquins, Adhesion, edited by K. W. Allen (Elsevier, London, 1988), Vol. 12.
14. J. Dumas and D. Feinberg, Europhys. Lett. 2, 555 (1986).
15. G. Ananthakrishna and M. C. Valsakumar, J. Phys. D 15, L171 (1982). The basic model was actually introduced in G. Ananthakrishna and D. Sahoo, J. Phys. D 14, 2081 (1981).
16. G. Ananthakrishna and M. C. Valsakumar, J. Phys. D 15, L171 (1982). The basic model was actually introduced in G. Ananthakrishna and D. Sahoo, J. Phys. D 14, 2081 (1981).
17. S. Rajesh and G. Ananthakrishna, Phys. Rev. E 61, 3664 (2000).
18. G. Ananthakrishna and M. C. Valsakumar, Phys. Lett. 95, 69 (1983).
19. G. Ananthakrishna et al., Scr. Metall. Mater. 32, 1731 (1995).
20. S. J. Noronha et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 2577 (1997).
21. A. J. Lichtenberg and M. A. Libermann, Regular and Chaotic Dyanmics (Springer-Verlag, New York, 1991).
22. H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, New York, 1996).
23. G. Ananthakrishna et al., Phys. Rev. E 60, 5455 (1999).
24. M. S. Bharathi et al., Phys. Rev. Lett. 87, 165508 (2001).
25. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988).
26. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988).
27. P. Bak, How Nature Works (Springer-Verlag, New York, 1996).
28. H. J. Jensen, Self-Organized Criticality (Cambridge University Press, Cambridge, 1998).
29. G. D'Anna and F. Non, Phys. Rev. Lett. 85, 4096 (2000); S. V. Franklin, F. Martens, and M. Marder, Phys. Rev. E 62, 8195 (2000); Phys. Rev. Lett. 78, 4502 (1997).
30. G. D'Anna and F. Non, Phys. Rev. Lett. 85, 4096 (2000); S. V. Franklin, F. Martens, and M. Marder, Phys. Rev. E 62, 8195 (2000); Phys. Rev. Lett. 78, 4502 (1997).
31. G. D'Anna and F. Non, Phys. Rev. Lett. 85, 4096 (2000); S. V. Franklin, F. Martens, and M. Marder, Phys. Rev. E 62, 8195 (2000); Phys. Rev. Lett. 78, 4502 (1997).
32. See, for instance, F. Heslot, B. Castaing, and A. Libchaber, Phys. Rev. A 36, 5870 (1987).
33. T. Bohr, M. H. Jensen, G. Paladin, and A. Vulpiani, Dynamical Systems Approach to Turbulence (Cambridge University Press, Cambridge, England, 1997).
34. M. Yamada and K. Ohkitani, J. Phys. Soc. Jpn. 56, 4210 (1987); M. Yamada and K. Ohkitani, Phys. Rev. Lett. 60, 983 (1988); Prog. Theor. Phys. 79, 1265 (1988); A. Cristani et al., Physica D 76, 239 (1994), and the references therein.
35. M. Yamada and K. Ohkitani, J. Phys. Soc. Jpn. 56, 4210 (1987); M. Yamada and K. Ohkitani, Phys. Rev. Lett. 60, 983 (1988); Prog. Theor. Phys. 79, 1265 (1988); A. Cristani et al., Physica D 76, 239 (1994), and the references therein.
36. M. Yamada and K. Ohkitani, J. Phys. Soc. Jpn. 56, 4210 (1987); M. Yamada and K. Ohkitani, Phys. Rev. Lett. 60, 983 (1988); Prog. Theor. Phys. 79, 1265 (1988); A. Cristani et al., Physica D 76, 239 (1994), and the references therein.
37. M. Yamada and K. Ohkitani, J. Phys. Soc. Jpn. 56, 4210 (1987); M. Yamada and K. Ohkitani, Phys. Rev. Lett. 60, 983 (1988); Prog. Theor. Phys. 79, 1265 (1988); A. Cristani et al., Physica D 76, 239 (1994), and the references therein.
38. B. Gutenberg and C. F. Richter, Ann. Geofis. 9, 1 (1956).
39. X. Che and H. Suhl, Phys. Rev. Lett. 64, 1670 (1990); K. L. Babcock and R. M. Westervelt, ibid. 64, 2168 (1990).
40. X. Che and H. Suhl, Phys. Rev. Lett. 64, 1670 (1990); K. L. Babcock and R. M. Westervelt, ibid. 64, 2168 (1990).
41. M. S. Bharathi and G. Ananthakrishna, Europhys. Lett. 48, 1355 (2002).
42. M. S. Bharathi and G. Ananthakrishna, Phys. Rev. E 67, 065104(R) (2003).
43. M. Bekele and G. Ananthakrishna, Phys. Rev. E 56, 6917 (1997).
44. S. Rajesh and G. Ananthakrishna, Physica D 140, 193 (2000).
45. M. V. Glazov et al., Appl. Phys. A: Mater. Sci. Process. 64, 373 (1997).
46. M. Zaiser et al., Comput. Mater. Sci. 5, 35 (1999).
47. m, but an essential one for analytical work (see, for instance, [14,33,34]). It is also possible to introduce additional variables, for instance, the density of solute atoms stored in the Cottrell-type of dislocations. However, these additional terms tend only to obscure the physics of the PLC effect. In this sense, the model should be regraded as some kind of minimal model.
48. A. Milik et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 505 (1998).
49. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. 45, 712 (1980).
50. P. Grassberger and I. Procaccia, Physica D 9, 189 (1983).
51. M. Ding, C. Grebogi, E. Ott, T. Sauer, and J. A Yorke, Phys. Rev. Lett. 70, 3872 (1993).
52. D. Broomhead and G. King, Physica D 20, 217 (1987).
53. G. Benettin, L. Galgani, A. Giorgilli, and J. M. Strelcyn, Mechanica 15, 9 (1980).
54. D. Ruelle, Commun. Math. Phys. 87, 287 (1982).
55. M. S. Bharathi, S. Rajesh, and G. Ananthakrishna, Scr. Mater. 48, 1355 (2003).
56. G. Dee and J. S. Langer, Phys. Rev. Lett. 50, 383 (1983).
57. W. van Saarloos, Phys. Rev. A 37, 211 (1988).
58. P. Hähner, A. Ziegenbein, E. Rizzi, and H. Neuhäuser, Phys. Rev. B 65, 134109 (2002).
59. A. Korbel, J. Zasadzinski, and Z. Siekluka, Acta Metall. 24, 921 (1976).
60. A. Erzan and S. Sinha, Phys. Rev. Lett. 66, 2750 (1991).
61. M. de Sousa Vieira and A. J. Lichtenberg, Phys. Rev. E 53, 1441 (1996).
62. B. Cessac, Ph. Blanchard, and T. Kruger, Phys. Rev. E 64, 016133 (2001).
63. P. G. McCormick and C. P. Ling, Acta Metall. Mater. 43, 1069 (1995).
64. S. Zhang, P. G. McCormick, and Y. Estrin, Acta Mater. 49, 1087 (2001).
65. M. Lebyodkin, L. Dunin-Barkowskii, Y. Bréhet, Y. Estrin, and L. P. Kubin, Acta Mater. 48, 2529 (2000), and the references therein.
66. S. Kok, M. S. Bharathi, A. J. Beaudoin, C. Fressengeas, G. Ananthakrishna, L. P. Kubin, and M. Lybyodkin, Acta Mater. 51, 3651 (2003).
67. H. Chate and P. Manneville, Physica D 32, 409 (1988); S. Sinha and D. Biswas, Phys. Rev. Lett. 71, 2010 (1993); S. Sinha, Int. J. Mod. Phys. B 9, 875 (1994); T. Bohr et al., Phys. Rev. Lett. 86, 5482 (2001).
68. H. Chate and P. Manneville, Physica D 32, 409 (1988); S. Sinha and D. Biswas, Phys. Rev. Lett. 71, 2010 (1993); S. Sinha, Int. J. Mod. Phys. B 9, 875 (1994); T. Bohr et al., Phys. Rev. Lett. 86, 5482 (2001).
69. H. Chate and P. Manneville, Physica D 32, 409 (1988); S. Sinha and D. Biswas, Phys. Rev. Lett. 71, 2010 (1993); S. Sinha, Int. J. Mod. Phys. B 9, 875 (1994); T. Bohr et al., Phys. Rev. Lett. 86, 5482 (2001).
70. H. Chate and P. Manneville, Physica D 32, 409 (1988); S. Sinha and D. Biswas, Phys. Rev. Lett. 71, 2010 (1993); S. Sinha, Int. J. Mod. Phys. B 9, 875 (1994); T. Bohr et al., Phys. Rev. Lett. 86, 5482 (2001).
71. J. Dumas, C. Schlenker, J. Marcus, and R. Buder, Phys. Rev. Lett. 50, 757 (1983); J. Dumas and C. Schlenker, Lect. Notes Phys. 217, 439 (1985).
72. J. Dumas, C. Schlenker, J. Marcus, and R. Buder, Phys. Rev. Lett. 50, 757 (1983); J. Dumas and C. Schlenker, Lect. Notes Phys. 217, 439 (1985).
73. P. A. Lee and T. M. Rice, Phys. Rev. B 19, 3970 (1979).
74. G. Ananthakrishna, J. Indian Inst. 78, 165 (1998).