Plastic deformations in crystal, polycrystal, and glass in binary mixtures under shear: Collective yielding

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

Volumn 81, Issue 5, 2010, Pages

  Shiba, Hayato ^a,b   Onuki, Akira ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FIXED SIZE; HEXAGONAL ORDER; LARGE PARTICLES; LENNARD-JONES BINARY MIXTURE; MOLECULAR DYNAMICS SIMULATIONS; MOVING BOUNDARIES; ORIENTATION ANGLES; SCALE YIELDING; TIME-SCALES; TWO-DIMENSION; WALL STRESS;

DISLOCATIONS (CRYSTALS); GLASS; GRAIN BOUNDARIES; GRAIN BOUNDARY SLIDING; MOLECULAR DYNAMICS; PLASTICS; POLYCRYSTALS;

BINARY MIXTURES;

EID: 77952066135     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.051501     Document Type: Article

References (110)

1. A. S. Argon, in Physical Metallurgy, edited by, R. W. Cahn, and, P. Haasen, (North-Holland, Amsterdam, 1996), p. 1878
2. P. Haasen, Physical Metallurgy, (North-Holland, Amsterdam, 1996), p. 2010
3. J. L. Strudel, ibid., Physical Metallurgy (North-Holland, Amsterdam, 1996), p. 2106.
4. F. Spaepen, in Physics of Defects, edited by, R. Balian, M. Kléman, and, J-P. Poirier, 1981 Les Houches Lectures (North-Holland, Amsterdam, 1981), p. 133.
5. J. Friedel, Dislocations (Pergamon, New York, 1954).
6. M.-C. Miguel, A. Vespignani, S. Zapperi, J. Weiss, and Jean-Robert Grassok, Nature 410, 667 (2001) 10.1038/35070524
7. T. Richeton, J. Weiss, and F. Louchet, Nat. Mater. 4, 465 (2005) 10.1038/nmat1393
8. M. Zaiser, Adv. Phys. 55, 185 (2006). 10.1080/00018730600583514
9. D. M. Dimiduk, C. Woodward, R. LeSar, and M. D. Uchic, Science 312, 1188 (2006). 10.1126/science.1123889
10. B. Devincre and L. P. Kubin, Mater. Sci. Eng., A 234-236, 8 (1997) 10.1016/S0921-5093(97)00146-9
11. V. Bulatov, F. F. Abraham, L. Kubin, B. Devincre, and S. Yip, Nature (London) 391, 669 (1998). 10.1038/35577
12. T. M. Pollock and A. S. Argon, Acta Mater. 40, 1 (1992). 10.1016/0956-7151(92)90195-K
13. A. Minami and A. Onuki, Phys. Rev. B 70, 184114 (2004) 10.1103/PhysRevB.70.184114
14. A. Minami and A. Onuki, Acta Mater. 55, 2375 (2007). 10.1016/j.actamat. 2006.11.030
15. H. Hahn, P. Mondal, and K. A. Padmanabhan, Nanostruct. Mater. 9, 603 (1997). 10.1016/S0965-9773(97)00135-9
16. J. Schiotz, F. D. Di Tolla, and K. W. Jacobsen, Nature (London) 391, 561 (1998). 10.1038/35328
17. A. Hasnaoui, H. Van Swygenhoven, and P. M. Derlet, Phys. Rev. B 66, 184112 (2002). 10.1103/PhysRevB.66.184112
18. S. Yip, Nat. Mater. 3, 11 (2004). 10.1038/nmat1053
19. V. Yamakov, D. Wolf, S. R. Phillpot, A. K. Mukherjee, and H. Gleiter, Nat. Mater. 3, 43 (2004). 10.1038/nmat1035
20. T. Hamanaka, H. Shiba, and A. Onuki, Phys. Rev. E 77, 042501 (2008). 10.1103/PhysRevE.77.042501
21. H. Zhang, D. J. Srolovitz, J. F. Douglas, and J. A. Warren, Phys. Rev. B 74, 115404 (2006) 10.1103/PhysRevB.74.115404
22. H. Zhang, D. J. Srolovitz, J. F. Douglas, and J. A. Warren, Proc. Natl. Acad. Sci. U.S.A. 106, 7735 (2009). 10.1073/pnas.0900227106
23. J. H. Simmons, R. K. Mohr, and C. J. Montrose, J. Appl. Phys. 53, 4075 (1982) 10.1063/1.331272
24. R. Yamamoto and A. Onuki, EPL 40, 61 (1997) 10.1209/epl/i1997-00419-1
25. R. Yamamoto and A. Onuki, Phys. Rev. E 58, 3515 (1998) 10.1103/PhysRevE.58.3515
26. R. Yamamoto and A. Onuki, J. Phys.: Condens. Matter 12, 6323 (2000). 10.1088/0953-8984/12/29/304
27. L. Angelani, G. Ruocco, F. Sciortino, P. Tartaglia, and F. Zamponi, Phys. Rev. E 66, 061505 (2002). 10.1103/PhysRevE.66.061505
28. M. Fuchs and M. E. Cates, Phys. Rev. Lett. 89, 248304 (2002) 10.1103/PhysRevLett.89.248304
29. K. Miyazaki, D. R. Reichman, Phys. Rev. E 66, 050501 (R) (2002). 10.1103/PhysRevE.66.050501
30. F. Varnik, L. Bocquet, J.-L. Barrat, and L. Berthier, Phys. Rev. Lett. 90, 095702 (2003). 10.1103/PhysRevLett.90.095702
31. L. Berthier, J. Phys.: Condens. Matter 15, S933 (2003). 10.1088/0953-8984/15/11/317
32. D. J. Lacks and M. J. Osborne, Phys. Rev. Lett. 93, 255501 (2004). 10.1103/PhysRevLett.93.255501
33. A. Tanguy, F. Leonforte, and J.-L. Barrat, Eur. Phys. J. E 20, 355 (2006). 10.1140/epje/i2006-10024-2
34. C. E. Maloney and A. Lemaitre, Phys. Rev. E 74, 016118 (2006) 10.1103/PhysRevE.74.016118
35. A. Lemaitre and C. Caroli, Phys. Rev. E 76, 036104 (2007). 10.1103/PhysRevE.76.036104
36. Y. Shi, M. B. Katz, H. Li, and M. L. Falk, Phys. Rev. Lett. 98, 185505 (2007). 10.1103/PhysRevLett.98.185505
37. T. Gibaud, C. Barentin, and S. Manneville, Phys. Rev. Lett. 101, 258302 (2008). 10.1103/PhysRevLett.101.258302
38. A. Furukawa, K. Kim, S. Saito, and H. Tanaka, Phys. Rev. Lett. 102, 016001 (2009). 10.1103/PhysRevLett.102.016001
39. N. P. Bailey, J. Schiøtz, A. Lemaitre, and K. W. Jacobsen, Phys. Rev. Lett. 98, 095501 (2007) 10.1103/PhysRevLett.98.095501
40. A. Lemaitre and C. Caroli, Phys. Rev. Lett. 103, 065501 (2009) 10.1103/PhysRevLett.103.065501
41. H. G. E. Hentschel, S. Karmakar, E. Lerner, and I. Procaccia, Phys. Rev. Lett. 104, 025501 (2010). 10.1103/PhysRevLett.104.025501
42. T. Okuzono and K. Kawasaki, Phys. Rev. E 51, 1246 (1995). 10.1103/PhysRevE.51.1246
43. D. J. Durian, Phys. Rev. E 55, 1739 (1997) 10.1103/PhysRevE.55.1739
44. S. A. Langer and A. J. Liu, J. Phys. Chem. B 101, 8667 (1997). 10.1021/jp971265b
45. P. Hébraud, F. Lequeux, J. P. Munch, and D. J. Pine, Phys. Rev. Lett. 78, 4657 (1997). 10.1103/PhysRevLett.78.4657
46. R. Besseling, E. R. Weeks, A. B. Schofield, and W. C. K. Poon, Phys. Rev. Lett. 99, 028301 (2007). 10.1103/PhysRevLett.99.028301
47. P. Schall, D. A. Weitz, and F. Spaepen, Science 318, 1895 (2007). 10.1126/science.1149308
48. J. Desrues, J. Lanier, and P. Stutz, Eng. Fract. Mech. 21, 909 (1985) 10.1016/0013-7944(85)90097-9
49. J. Desrues and R. Chambon, Int. J. Solids Struct. 39, 3757 (2002). 10.1016/S0020-7683(02)00177-4
50. B. Miller, C. O'Hern, and R. P. Behringer, Phys. Rev. Lett. 77, 3110 (1996). 10.1103/PhysRevLett.77.3110
51. O. J. Schwarz, Y. Horie, and M. Shearer, Phys. Rev. E 57, 2053 (1998). 10.1103/PhysRevE.57.2053
52. O. Dauchot, G. Marty, and G. Biroli, Phys. Rev. Lett. 95, 265701 (2005). 10.1103/PhysRevLett.95.265701
53. A. Fall, F. Bertrand, G. Ovarlez, and D. Bonn, Phys. Rev. Lett. 103, 178301 (2009). 10.1103/PhysRevLett.103.178301
54. P. Olsson and S. Teitel, Phys. Rev. Lett. 99, 178001 (2007) 10.1103/PhysRevLett.99.178001
55. T. Hatano, Phys. Rev. E 79, 050301 (R) (2009). 10.1103/PhysRevE.79.050301
56. K. Binder and W. Kob, Glassy Materials and Disordered Solids (World Scientific, Singapore, 2005).
57. F. Spaepen, Acta Metall. 25, 407 (1977). 10.1016/0001-6160(77)90232-2
58. A. S. Argon, Acta Metall. 27, 47 (1979). 10.1016/0001-6160(79)90055-5
59. M. L. Manning, J. S. Langer, and J. M. Carlson, Phys. Rev. E 76, 056106 (2007). 10.1103/PhysRevE.76.056106
60. C. A. Schuh, T. C. Hufnagel, and U. Ramamurty, Acta Mater. 55, 4067 (2007). 10.1016/j.actamat.2007.01.052
61. H. S. Chen and M. Goldstein, J. Appl. Phys. 43, 1642 (1972). 10.1063/1.1661374
62. D. Srolovitz, V. Vitek, and T. Egami, Acta Metall. 31, 335 (1983). 10.1016/0001-6160(83)90110-4
63. M. Zink, K. Samwer, W. L. Johnson, and S. G. Mayr, Phys. Rev. B 73, 172203 (2006). 10.1103/PhysRevB.73.172203
64. K. Maeda and S. Takeuchi, Phys. Status Solidi 49, 685 (1978) 10.1002/pssa.2210490233
65. S. Kobayashi, K. K. Maeda, and S. Takeuchi, Acta Metall. 28, 1641 (1980). 10.1016/0001-6160(80)90017-6
66. T. Muranaka and Y. Hiwatari, Phys. Rev. E 51, R2735 (1995). 10.1103/PhysRevE.51.R2735
67. M. M. Hurley and P. Harrowell, Phys. Rev. E 52, 1694 (1995) 10.1103/PhysRevE.52.1694
68. D. N. Perera and P. Harrowell, Phys. Rev. E 54, 1652 (1996). 10.1103/PhysRevE.54.1652
69. R. Yamamoto and A. Onuki, J. Phys. Soc. Jpn. 66, 2545 (1997). 10.1143/JPSJ.66.2545
70. W. Kob, C. Donati, S. J. Plimpton, P. H. Poole, and S. C. Glotzer, Phys. Rev. Lett. 79, 2827 (1997). 10.1103/PhysRevLett.79.2827
71. C. Donati, J. F. Douglas, W. Kob, S. J. Plimpton, P. H. Poole, and S. C. Glotzer, Phys. Rev. Lett. 80, 2338 (1998). 10.1103/PhysRevLett.80.2338
72. N. Lačević, F. W. Starr, T. B. Schroder, and S. C. Glotzer, J. Chem. Phys. 119, 7372 (2003). 10.1063/1.1605094
73. B. Doliwa and A. Heuer, J. Non-Cryst. Solids 307-310, 32 (2002). 10.1016/S0022-3093(02)01437-0
74. G. Biroli, J.-P. Bouchaud, K. Miyazaki, and D. R. Reichman, Phys. Rev. Lett. 97, 195701 (2006). 10.1103/PhysRevLett.97.195701
75. A. Widmer-Cooper and P. Harrowell, Phys. Rev. Lett. 96, 185701 (2006). 10.1103/PhysRevLett.96.185701
76. T. Hamanaka and A. Onuki, Phys. Rev. E 74, 011506 (2006) 10.1103/PhysRevE.74.011506
77. T. Hamanaka and A. Onuki, Phys. Rev. E 75, 041503 (2007). 10.1103/PhysRevE.75.041503
78. T. Kawasaki, T. Araki, and H. Tanaka, Phys. Rev. Lett. 99, 215701 (2007). 10.1103/PhysRevLett.99.215701
79. K. Yoshimoto, T. S. Jain, K. Van Workum, P. F. Nealey, and J. J. de Pablo, Phys. Rev. Lett. 93, 175501 (2004). 10.1103/PhysRevLett.93.175501
80. M. Tsamados, A. Tanguy, C. Goldenberg, and J.-L. Barrat, Phys. Rev. E 80, 026112 (2009). 10.1103/PhysRevE.80.026112
81. In this paper, we do not consider fracture or brittle behavior. We use the term "shear band" widely to represent quasilinear (in two dimensions) mesoscopic objects where shear strains are localized.
82. Jing Li, F. Spaepen, and T. C. Hufnagel, Philos. Mag. A 10.1080/01418610208240056 82, 2623 (2002).
83. Q. Wei, D. Jia, K. T. Ramesh, and E. Ma, Appl. Phys. Lett. 81, 1240 (2002). 10.1063/1.1501158
84. D. Deng, A. S. Argon, and S. Yip, Philos. Trans. R. Soc. London, Ser. A 329, 613 (1989). 10.1098/rsta.1989.0092
85. Y. Shi and M. L. Falk, Phys. Rev. B 73, 214201 (2006). 10.1103/PhysRevB.73.214201
86. C. E. Maloney and M. O. Robbins, J. Phys.: Condens. Matter 20, 244128 (2008). 10.1088/0953-8984/20/24/244128
87. N. P. Bailey, J. Schiøtz, and K. W. Jacobsen, Phys. Rev. B 73, 064108 (2006). 10.1103/PhysRevB.73.064108
88. V. V. Bulatov and A. S. Argon, Modell. Simul. Mater. Sci. Eng. 2, 167 (1994) 10.1088/0965-0393/2/2/001
89. A. S. Argon, V. V. Bulatov, P. H. Mott, and U. W. Suter, J. Rheol. 39, 377 (1995). 10.1122/1.550728
90. A. Onuki, Phys. Rev. E 68, 061502 (2003) 10.1103/PhysRevE.68.061502
91. A. Onuki, A. Furukawa, and A. Minami, Pramana 64, 661 (2005). 10.1007/BF02704575
92. H. Shiba and A. Onuki, Prog. Theor. Phys. Suppl., e-print arXiv:1004.0866
93. / 3 π / 4 ≅ 0.9895 is close to unity.
94. S. Nosè, Mol. Phys. 52, 255 (1984). 10.1080/00268978400101201
95. W. G. Hoover, Computational Statistical Mechanics (Elsevier, Amsterdam, 1991).
96. - 3.
97. H. Shiba, A. Onuki, and T. Araki, EPL 86, 66004 (2009). 10.1209/0295-5075/86/66004
98. B. I. Halperin and D. R. Nelson, Phys. Rev. Lett. 41, 121 (1978). 10.1103/PhysRevLett.41.121
99. A. Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, England, 2002). 10.1017/CBO9780511534874
100. R. Zwanzig and R. D. Mountain, J. Chem. Phys. 43, 4464 (1965). 10.1063/1.1696718
101. - 2 ∫ d r 1 ∫ d r 2 □ δ Π x y (r 1, t) δ Π x y (r 2, t) □ for the x y component of the stress tensor Π x y (r, t) (Ref.).
102. Y. Estrin and L. P. Kubin, Mater. Sci. Eng., A 137, 125 (1991) 10.1016/0921-5093(91)90326-I
103. G. D'Anna and F. Nori, Phys. Rev. Lett. 85, 4096 (2000) 10.1103/PhysRevLett.85.4096
104. P. Barat, A. Sarkar, P. Mukherjee, and S. K. Bandyopadhyay, Phys. Rev. Lett. 94, 055502 (2005). 10.1103/PhysRevLett.94.055502
105. T. Shikata, H. Niwa, and Y. Morishima, J. Rheol. 42, 765 (1998). 10.1122/1.550911
106. Dislocation gliding involves motions of a relatively small number of particles, while the other form of dislocation motions, climbing, requires motions of many particles and is not easily induced (Ref.).
107. A. S. Argon and H. Y. Kuo, Mater. Sci. Eng. 39, 101 (1979). 10.1016/0025-5416(79)90174-5
108. R. Peierls, Proc. Phys. Soc. 52, 34 (1940) 10.1088/0959-5309/52/1/305
109. F. R. N. Nabarro, Proc. Phys. Soc. 59, 256 (1947). 10.1088/0959-5309/59/ 2/309
110. M. Peach and J. S. Koehler, Phys. Rev. 80, 436 (1950). 10.1103/PhysRev.80.436