Randomness and slip avalanches in gradient plasticity

International Journal of Plasticity

Volumn 22, Issue 8, 2006, Pages 1432-1455

  Zaiser, Michael ^a   Aifantis, Elias C ^b,c  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

^c MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

Author keywords

Avalanches; Gradient plasticity; Material instabilities; Slip localization

Indexed keywords

CRYSTALLINE MATERIALS; DEFORMATION; GRAPH THEORY; MORPHOLOGY; STRESS ANALYSIS;

AVALANCHES; GRADIENT PLASTICITY; MATERIAL INSTABILITIES; SLIP LOCALIZATION;

PLASTICITY;

EID: 33645364141     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2005.07.010     Document Type: Article

References (72)

1. E.C. Aifantis On the microstructural origin of certain inelastic models J. Eng. Mater. Technol. 106 1984 326 330
2. E.C. Aifantis The physics of plastic deformation Int. J. Plasticity 3 1987 211 247
3. E.C. Aifantis On the role of gradients in the localization of deformation and fracture Int. J. Eng. Sci. 30 1992 1279 1299
4. E.C. Aifantis Pattern formation in plasticity Int. J. Eng. Sci. 33 1995 2161 2178
5. E.C. Aifantis Non-linearity, periodicity and patterning in plasticity and fracture Int. J. Non-linear Mech. 31 1996 797 809
6. E.C. Aifantis Gradient deformation models at nano, micro and macro scales J. Eng. Mater. Technol. 121 1999 189 202
7. E.C. Aifantis Gradient plasticity J. Lemaitre Handbook of Mechanical Behavior Models 2001 Academic Press New York 291 307
8. E.C. Aifantis Update on a class of gradient theories Mech. Mater. 35 2003 259 280
9. Aifantis, K.E., Willis, J.R., 2004. Interfacial jump conditions in strain-gradient plasticity and relations of Hall-Petch type. In: Kounadis, A., Providakis, C., Exadaktylos, G. (Eds.), Proceedings of the Seventh National Congress on Mechanics, vol. II, Chania, Greece, June 24-26, 2004, pp. 372-377.
10. K.E. Aifantis, and J.R. Willis The role of interfaces in enhancing the yield strength of composites and polycrystals J. Mech. Phys. Sol. 53 2005 1047 1070
11. J.-C. Baret, D. Vandembroucq, and S. Roux An extremal model for amorphous media plasticity Phys. Rev. Lett. 89 2002 195506
12. N. Charalambakis, and E.G. Aifantis Thermoviscoplastic shear instability and higher order strain gradients Int. J. Eng. Sci. 29 1991 1639 1650
13. K. Chen, P. Bak, and S.P. Obukhov Self-organized criticality in a crack-propagation model of earthquakes Phys. Rev. A 43 1991 625 630
14. D.S. Fisher Collective transport in random media: From superconductors to earthquakes Phys. Rep. 301 1998 113 150
15. N.A. Fleck, and J.W. Hutchinson A phenomenological theory for strain gradient effects in plasticity J. Mech. Phys. Solids 41 1993 1825 1857
16. N.A. Fleck, and J.W. Hutchinson Strain gradient plasticity J.W. Hutchinson T.W. Wu Advances in Applied Mechanics 1997 Academic Press New York 295 361
17. N. Fleck, and J.W. Hutchinson A reformulation of strain gradient plasticity J. Mech. Phys. Solids 49 2001 2245 2271
18. N. Fleck, and J.R. Willis Bounds and estimates for the effect of strain gradients upon the effective plastic properties of an isotropic two-phase composite J. Mech. Phys. Solids 52 2004 1855 1888
19. N.A. Fleck, G.M. Muller, M.F. Ashby, and J.W. Hutchinson Strain gradient plasticity: theory and experiment Acta Metall. Mater. 42 1994 475 487
20. G. Frantziskonis, and E.G. Aifantis On the stochastic interpretation of gradient-dependent constitutive equations Eur. J. Mech. A 21 2002 589 596
21. H. Gao, Y. Huang, W.D. Nix, and J.W. Hutchinson Mechanism-based strain gradient plasticity-I. Theory J. Mech. Phys. Solids 47 1999 1239 1263
22. I. Groma, and B. Bako Probability distribution of internal stresses in parallel straight dislocation systems Phys. Rev. B 58 1998 2969 2974
23. I. Groma, F. Csikor, and M. Zaiser Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics Acta Mater. 51 2003 1271 1281
24. P. Gudmundson A unified treatment of strain gradient plasticity J. Mech. Phys. Solids 52 2004 1379 1406
25. M.E. Gurtin On the plasticity of single crystals: free energy, micro-forces, plastic strain gradients J. Mech. Phys. Solids 48 2000 989 1036
26. M.E. Gurtin A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations J. Mech. Phys. Solids 50 2002 5 32
27. Y. Huang, H. Gao, W.D. Nix, and J.W. Hutchinson Mechanism-based strain gradient plasticity-II. Analysis J. Mech. Phys. Solids 48 2000 99 128
28. T. Kleiser, and M. Bocek The fractal nature of slip in crystals Z. Metallkde. 77 1986 582 587
29. A. Konstantinidis, and E.G. Aifantis Recent developments in gradient plasticity - part II: plastic heterogeneity and wavelets J. Eng. Mater. Technol. 124 2002 358 364
30. L.P. Kubin, Y. Estrin, and E.G. Aifantis Viewpoint set on propagative plastic instabilities Scripta Metall. Mater. 29 1993 1147 1150
31. L.P. Kubin, and J. Lepinoux The dynamic organization of dislocation structures P.O. Kettunen Strength of Metal and Alloys (ICSMA 8) 1 1988 Pergamon Press Oxford 35 59
32. G.A. Maugin, and W. Muschik Themodynamics with internal variables J. Non-Equil. Thermodyn. 19 1994 217 249 250-289
33. O. Meissner, J. Schreiber, and A. Schwab Formation of mesostructures at the surface of ferritic steel and a nickel monocrystal under increasing load - An in situ AFM experiment Appl. Phys. A 66 1998 S1113 S1116
34. A. Menzel, and P. Steinmann On the continuum formulation of higher gradient plasticity for single and polycrystals J. Mech. Phys. Solids 48 2000 1777 1796
35. M.C. Miguel, A. Vespignani, S. Zapperi, J. Weiss, and J.-R. Grasso Intermittent dislocation flow in viscoplastic deformation Nature 410 2001 667 671
36. Moretti, P., Zaiser, M., Aifantis, E.G., forthcoming. Avalanche phenomena and deformation patterns in plasticity.
37. [see also: Zaiser, M., Aifantis, E.C., forthcoming. Random effects and instabilities in gradient plasticity.]
38. H.B. Muhlhaus, and E.G. Aifantis A variational principle for gradient plasticity Int. J. Solids Struct. 28 1991 845 857
39. H. Neuhäuser Slip-line formation and collective dislocation motion F.R.N. Nabarro Dislocations in Solids vol. 4 1984 North-Holland Amsterdam 319 440
40. F. Oka, A. Yashima, T. Adachi, and E.G. Aifantis Instability of gradient-dependent viscoplastic model for clay saturated with water and FEM analysis Appl. Mech. Rev. 45 1992 140 148
41. F. Oka, A. Yashima, K. Sawada, and E.G. Aifantis Instability of gradient-dependent elastoplastic model for clay and strain localization Comput. Meth. Appl. Mech. Eng. 183 2000 67 86
42. C. Polizzotto, and G. Borino A thermodynamics-based formulation of gradient-dependent plasticity Eur. J. Mech. A 17 1998 741 761
43. J. Pontes, D. Walgraef, and E.C. Aifantis On dislocation patterning: Multiple slip effects in the rate equation approach Int. J. Plast. 2006
44. C. di Prisco, S. Impomisato, and E.G. Aifantis A viscoplastic constitutive model for granular soils modified according to nonlocal and gradient approaches Int. J. Numer. Anal. Meth. Geomech. 26 2002 121 138
45. N. Triantafyllidis, and E.G. Aifantis A gradient approach to localization of deformation - I. Hyperelastic materials J. Elasticity 16 1986 225 238
46. K.C. Valanis A gradient theory of internal variables Acta Mech. 116 1996 1 14
47. K.C. Valanis A gradient thermodynamic theory of self-organization Acta Mech. 127 1998 1 23
48. K.C. Valanis Diffusion potential and well-posedness in non-associative plasticity Int. J. Solids Struct. 35 1998 5173 5188
49. K.C. Valanis Gradient field theory of material instabilities Arch. Mech. 52 2000 817 838
50. I. Vardoulakis, and E.G. Aifantis A gradient flow theory of plasticity for granular materials Acta Mech. 87 1991 197 217
51. G.Z. Voyiadjis, B. Deliktas, and E.G. Aifantis Multi-scale analysis of multiple damage mechanisms coupled with inelastic behavior of composite materials J. Eng. Mech. 127 2001 636 645
52. D. Walgraef, and E.C. Aifantis Dislocation patterning in fatigued metals as a result of dynamical instabilities J. Appl. Phys. 58 1985 688 691
53. D. Walgraef, and E.C. Aifantis On the formation and stability of dislocation patterns - Parts I-III Int. J. Eng. Sci. 23 1985 1351 1358 1359-1364; 1365-1372
54. J. Weiss, and J.-R. Grasso Acoustic emission in single crystals of ice J. Phys. Chem. B 32 1997 6113 6117
55. J. Weiss, and D. Marsan Three-dimensional mapping of dislocation avalanches: clustering and space/time coupling Science 299 2003 89 92
56. S. Yefimov, I. Groma, and E. Van der Giessen A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations J. Mech. Phys. Solids 52 2004 279 300
57. S. Yefimov, I. Groma, and E. Van der Giessen Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations Modelling Simul. Mater. Sci. Eng. 12 2004 1069 1086
58. M. Zaiser Statistical modelling of dislocation systems Mater. Sci. Eng. A 309/310 2001 304 315
59. M. Zaiser, and E.C. Aifantis On the dynamic interaction between moving dislocations Appl. Phys. A 66 1998 393 397
60. M. Zaiser, and E.C. Aifantis Materials instabilities and deformation patterning in plasticity Recent Res. Devel. Metall. Mater. Sci., Research Signpost 3 1999 79 103
61. M. Zaiser, and E.G. Aifantis Geometrically necessary dislocations and strain gradient plasticity - a dislocation dynamics point of view Scripta Mater. 48 2003 133 139
62. M. Zaiser, and E.C. Aifantis Avalanches and slip patterning in plastic deformation J. Mech. Behavior Mater. 14 2003 255 270
63. M. Zaiser, and P. Hähner Random aspects of macroscopic plastic deformation Philos. Mag. Lett. 73 1996 369 375
64. M. Zaiser, and A. Seeger Long-range internal stresses, dislocation patterning and work hardening in crystal plasticity F.R.N. Nabarro M.S. Duesbery Dislocations in Solids vol. 11 2002 North-Holland Amsterdam 1 100
65. M. Zaiser, S.I. Marras, E. Nadgorni, H.P. Stunk, and E.C. Aifantis Fractal dislocation patterning in plastically deformed NaCl polycrystals Phys. Status Solidi A 185 2001 R4 R5
66. M. Zaiser, M.-C Miguel, and I. Groma Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations Phys. Rev. B 64 2001 224102
67. M. Zaiser, F. Madani, V. Koutsos, and E.C. Aifantis Self-affine surface morphology of plastically deformed metals Phys. Rev. Lett. 93 2004 195507
68. S. Zapperi, P. Cizeau, G. Durin, and H.E. Stanley Dynamics of a ferromagnetic domain wall - avalanches, depinning and the barkhausen effect Phys. Rev. B 58 1998 6353 6366
69. H.M. Zbib, and E.C. Aifantis On the localization and postlocalization behavior of plastic deformation - I/II/III Res. Mech. 23 1988 261 305
70. H.M. Zbib, and E.C. Aifantis A gradient-dependent flow theory of plasticity: application to metal and soil instabilities Appl. Mech. Rev. 42 1989 295 304
71. H.M. Zbib, and E.C. Aifantis On the gradient-dependent theory of plasticity and shear banding Acta Mech. 92 1992 209 225
72. H.M. Zbib, and E.C. Aifantis Size effects and length scales in gradient plasticity and dislocation dynamics Scripta Mater. 48 2003 155 160