Experimental lower bounds on geometrically necessary dislocation density

International Journal of Plasticity

Volumn 26, Issue 8, 2010, Pages 1097-1123

  Kysar, J W ^a   Saito, Y ^a   Oztop, M S ^a   Lee, D ^b   Huh, W T ^c  

^a Columbia University ^*  (United States)

^b Pusan National University   (South Korea)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Electron Backscatter Diffraction (EBSD); Geometrically Necessary Dislocation (GND) density; Lattice rotation; Orientation Imaging Microscopy (OIM); Single crystal

Indexed keywords

ELECTRON BACK SCATTER DIFFRACTION; GEOMETRICALLY NECESSARY DISLOCATIONS; LATTICE ROTATIONS; ORIENTATION IMAGING MICROSCOPY; ORIENTATION IMAGING MICROSCOPY (OIM);

BACKSCATTERING; CRYSTAL LATTICES; DISLOCATIONS (CRYSTALS); ELECTRON DIFFRACTION; NICKEL ALLOYS; ROTATION; SINGLE CRYSTALS; VICKERS HARDNESS TESTING;

CRYSTAL ORIENTATION;

EID: 77955515119     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2010.03.009     Document Type: Article

References (86)

1. R.K. Abu Al-Rub, G.Z. Voyiadjis, and D.J. Bammann A thermodynamic based higher-order gradient theory for size dependent plasticity International Journal of Solids and Structures 44 9 2007 2888 2923
2. A. Acharya, and J.L. Bassani Lattice incompatibility and a gradient theory of crystal plasticity Journal of the Mechanics and Physics of Solids 48 8 2000 1565 1595
3. A. Acharya, A. Beaudoin, and R. Miller New perspectives in plasticity theory: dislocation nucleation, waves, and partial continuity of plastic strain rate Mathematics and Mechanics of Solids 13 3-4 2008 292 315
4. A. Acharya, and A. Roy Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of mesoscopic field dislocation mechanics: Part I Journal of the Mechanics and Physics of Solids 54 8 2006 1687 1710 (Pubitemid 43776865)
5. B.L. Adams Orientation imaging microscopy: emerging and future applications Ultramicroscopy 67 1-4 1997 11 17
6. E.C. Aifantis The physics of plastic-deformation International Journal of Plasticity 3 3 1987 211 247
7. L. Anand, M.E. Gurtin, S.P. Lele, and C. Gething A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results Journal of the Mechanics and Physics of Solids 53 8 2005 1789 1826
8. A. Arsenlis, and D.M. Parks Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density Acta Materialia 47 5 1999 1597 1611
9. A. Arsenlis, D.M. Parks, R. Becker, and V.V. Bulatov On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals Journal of the Mechanics and Physics of Solids 52 6 2004 1213 1246
10. M.F. Ashby Deformation of plastically non-homogeneous materials Philosophical Magazine 21 170 1970 399 424
11. D.S. Balint, V.S. Deshpande, A. Needleman, and E. Van der Giessen Discrete dislocation plasticity analysis of the wedge indentation of films Journal of the Mechanics and Physics of Solids 54 11 2006 2281 2303
12. J.L. Bassani, and T.Y. Wu Latent hardening in single crystal II: analytical characterization and predictions Proceedings of the Royal Society of London Series A 435 1893 1991 21 41
13. A.F. Bastawros, and K.S. Kim Experimental analysis of near-crack-tip plastic flow and deformation characteristics (I): polycrystalline aluminum Journal of the Mechanics and Physics of Solids 48 1 2000 67 98
14. C.J. Bayley, W.A.M. Brekelmans, and M.G.D. Geers A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity International Journal of Solids and Structures 43 24 2006 7268 7286
15. B.A. Bilby, R. Bullough, and E. Smith Continuous distributions of dislocations - a new application of the methods of non-Riemannian geometry Proceedings of the Royal Society of London Series A 231 1185 1955 263 273
16. E. Bittencourt, A. Needleman, M.E. Gurtin, and E. Van der Giessen A comparison of nonlocal continuum and discrete dislocation plasticity predictions Journal of the Mechanics and Physics of Solids 51 2 2003 281 310 (Pubitemid 35412415)
17. U. Borg Strain gradient crystal plasticity effects on flow localization International Journal of Plasticity 23 8 2007 1400 1416
18. S. Bouvier, and A. Needleman Effect of the number and orientation of active slip systems on plane strain single crystal indentation Modelling and Simulation in Materials Science and Engineering 14 7 2006 1105 1125
19. P. Cermelli, and M.E. Gurtin On the characterization of geometrically necessary dislocations in finite plasticity Journal of the Mechanics and Physics of Solids 49 7 2001 1539 1568
20. J.D. Clayton, D.L. McDowell, and D.J. Bammann A multiscale gradient theory for single crystalline elastoviscoplasticity International Journal of Engineering Science 42 5-6 2004 427 457
21. W.C. Crone, and T.W. Shield Experimental study of the deformation near a notch tip in copper and copper-beryllium single crystals Journal of the Mechanics and Physics of Solids 49 12 2001 2819 2838
22. W.C. Crone, and T.W. Shield An experimental study of the effect of hardening on plastic deformation at notch tips in metallic single crystals Journal of the Mechanics and Physics of Solids 51 8 2003 1623 1647
23. W.C. Crone, T.W. Shield, A. Creuziger, and B. Henneman Orientation dependence of the plastic slip near notches in ductile FCC single crystals Journal of the Mechanics and Physics of Solids 52 1 2004 85 112
24. E. Demir, D. Raabe, N. Zaafarani, and S. Zaefferer Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography Acta Materialia 57 2 2009 559 569
25. W.J. Drugan, and J.R. Rice Restrictions on quasi-statically moving surfaces of strong discontinuity in elastic-plastic solids G.J. Dvorak, R.T. Sheild, Mechanics of Material Behavior (The D.C. Drucker Anniversary Volume) 1984 Elsevier 59 73
26. W.J. Drugan, J.R. Rice, and T.-L. Sham Asymptotic analysis of growing plane strain tensile cracks in elastic-ideally plastic solids Journal of the Mechanics and Physics of Solids 30 6 1982 447 473
27. W.J. Drugan, J.R. Rice, and T.-L. Sham Erratum for "Asymptotic analysis of growing plane strain tensile cracks in elastic-ideally plastic solids" Journal of the Mechanics and Physics of Solids 31 2 1983 191-191
28. B.S. El-Dasher, B.L. Adams, and A.D. Rollett Viewpoint: experimental recovery of geometrically necessary dislocation density in polycrystals Scripta Materialia 48 2 2003 141 145
29. J.D. Eshelby The continuum theory of lattice defects Solid State Physics 3 1956 79 144
30. L.P. Evers, W.A.M. Brekelmans, and M.G.D. Geers Non-local crystal plasticity model with intrinsic SSD and GND effects Journal of the Mechanics and Physics of Solids 52 10 2004 2379 2401
31. G. Feng, A.S. Budiman, W.D. Nix, N. Tamura, and J.R. Patel Indentation size effects in single crystal copper as revealed by synchrotron X-ray microdiffraction Journal of Applied Physics 104 4 2008 043501
32. D.P. Field, P.B. Trivedi, S.I. Wright, and M. Kumar Analysis of local orientation gradients in deformed single crystals Ultramicroscopy 103 1 2005 33 39
33. N.A. Fleck, and J.W. Hutchinson A reformulation of strain gradient plasticity Journal of the Mechanics and Physics of Solids 49 10 2001 2245 2271
34. N.A. Fleck, G.M. Muller, M.F. Ashby, and J.W. Hutchinson Strain gradient plasticity - theory and experiment Acta Metallurgica et Materialia 42 2 1994 475 487
35. N.A. Fleck, and J.R. Willis A mathematical basis for strain-gradient plasticity theory - Part I: Scalar plastic multiplier Journal of the Mechanics and Physics of Solids 57 1 2009 161 177
36. N.A. Fleck, and J.R. Willis A mathematical basis for strain-gradient plasticity theory. Part II: Tensorial plastic multiplier Journal of the Mechanics and Physics of Solids 57 7 2009 1045 1057
37. N. Fox A continuum theory of dislocations for single crystals IMA Journal of Applied Mathematics 2 4 1966 285 298
38. P. Franciosi, and A. Zaoui Multislip in f.c.c. crystals a theoretical approach compared with experimental data Acta Metallurgica 30 8 1982 1627 1637
39. Y.X. Gan, J.W. Kysar, and T.L. Morse Cylindrical void in a rigid-ideally plastic single crystal II: experiments and simulations International Journal of Plasticity 22 1 2005 39 72
40. H. Gao, Y. Huang, W.D. Nix, and J.W. Hutchinson Mechanism-based strain gradient plasticity I. Theory Journal of the Mechanics and Physics of Solids 47 6 1999 1239 1263
41. P. Gudmundson A unified treatment of strain gradient plasticity Journal of the Mechanics and Physics of Solids 52 6 2004 1379 1406
42. M.E. Gurtin A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations Journal of the Mechanics and Physics of Solids 50 1 2002 5 32
43. M.E. Gurtin A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations International Journal of Plasticity 24 4 2008 702 725
44. M.E. Gurtin, L. Anand, and S.P. Lele Gradient single-crystal plasticity with free energy dependent on dislocation densities Journal of the Mechanics and Physics of Solids 55 9 2007 1853 1878
45. C.S. Han, H. Gao, Y. Huang, and W.D. Nix Mechanism-based strain gradient crystal plasticity - I. Theory Journal of the Mechanics and Physics of Solids 53 5 2005 1188 1203 (Pubitemid 40303117)
46. J.P. Hirth, and J. Lothe Theory of Dislocations 1992 Krieger Publishing Company Malabar, Florida
47. Huang, Y., 1991. A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program: Mech. Report 178. Technical Report, Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts.
48. J. Kacher, C. Landon, B.L. Adams, and D. Fullwood Bragg's law diffraction simulations for electron backscatter diffraction analysis Ultramicroscopy 109 9 2009 1148 1156
49. D. Kiener, R. Pippan, C. Motz, and H. Kreuzer Microstructural evolution of the deformed volume beneath microindents in tungsten and copper Acta Materialia 54 10 2006 2801 2811
50. K. Kondo On the analytical and physical foundations of the theory of dislocations and yielding by the differential geometry of continua International Journal of Engineering Science 2 3 1964 219 251
51. E. Kröner Allgemeine kontinuumstheorie der versetzungen und eigenspannungen Archive for Rational Mechanics and Analysis 4 1 1959 273 334
52. M. Kuroda, and V. Tvergaard A finite deformation theory of higher-order gradient crystal plasticity Journal of the Mechanics and Physics of Solids 56 8 2008 2573 2584
53. Kysar, J.W., 1997. Addendum to a user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program: Mech. Report 178. Technical Report, Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts.
54. J.W. Kysar Continuum simulations of directional dependence of crack growth along a copper/sapphire bicrystal interface: Part I: Experiments and crystal plasticity background Journal of the Mechanics and Physics of Solids 49 5 2001 1099 1128
55. J.W. Kysar, and C.L. Briant Crack tip deformation fields in ductile single crystals Acta Materialia 50 9 2002 2367 2380
56. J.W. Kysar, Y.X. Gan, and G. Mendez-Arzuza Cylindrical void in a rigid-ideally plastic single crystal I: anisotropic slip line theory solution for face-centered cubic crystals International Journal of Plasticity 21 8 2005 1481 1520
57. J.W. Kysar, Y.X. Gan, T.L. Morse, X. Chen, and M.E. Jones High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: geometrically necessary dislocation densities Journal of the Mechanics and Physics of Solids 55 7 2007 1554 1573
58. B.C. Larson, W. Yang, J.Z. Tischler, G.E. Ice, J.D. Budai, W. Liu, and H. Weiland Micron-resolution 3-D measurement of local orientations near a grain-boundary in plane-strained aluminum using X-ray microbeams International Journal of Plasticity 20 3 2004 543 560
59. X.M. Li, F.P. Chiang, J. Wu, and M. Dudley Experimental-measurement of the crack tip strain field in a single-crystal Engineering Fracture Mechanics 43 2 1992 171 184
60. Q. Ma, and D.R. Clarke Size-dependent hardness of silver single-crystals Journal of Materials Research 10 4 1995 853 863
61. K.K. McLaughlin, and W.J. Clegg Deformation underneath low-load indentations in copper Journal of Physics D 41 7 2008 074007
62. S.Dj. Mesarovic Energy, configurational forces and characteristic lengths associated with the continuum description of geometrically necessary dislocations International Journal of Plasticity 21 10 2005 1855 1889
63. M. Montagnat, P. Duval, P. Bastie, and B. Hamelin Strain gradients and geometrically necessary dislocations in deformed ice single crystals Scripta Materialia 49 5 2003 411 415
64. H.L. Mughrabi, and B. Obst Misorientations and geometrically necessary dislocations in deformed copper crystals: a microstructural analysis of X-ray rocking curves Zeitschrift für Metallkunde 96 7 2005 688 697
65. C.F. Niordson On higher-order boundary conditions at elastic-plastic boundaries in strain-gradient plasticity Philosophical Magazine 88 30-32 2008 3731 3745
66. C.F. Niordson, and J.W. Hutchinson On lower order strain gradient plasticity theories European Journal of Mechanics A-Solids 22 6 2003 771 778
67. J.F. Nye Some geometrical relations in dislocation solids Acta Metallurgica 1 2 1953 153 162
68. T. Ohashi Crystal plasticity analysis of dislocation emission from micro voids International Journal of Plasticity 21 11 2005 2071 2088
69. T. Ohashi, R.I. Barabash, J.W.L. Pang, G.E. Ice, and O.M. Barabash X-ray microdiffraction and strain gradient crystal plasticity studies of geometrically necessary dislocations near a Ni bicrystal grain boundary International Journal of Plasticity 25 5 2009 920 941
70. T. Ohashi, M. Kawamukai, and H. Zbib A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals International Journal of Plasticity 23 5 2007 897 914
71. W. Pantleon Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction Scripta Materialia 58 11 2008 994 997
72. D. Peirce, R.J. Asaro, and A. Needleman Material rate dependence and localised deformation in crystalline solids Acta Metallurgica 31 12 1983 1951 1976
73. M. Rester, C. Motz, and R. Pippan Microstructural investigation of the volume beneath nanoindentations in copper Acta Materialia 55 19 2007 6427 6435
74. M. Rester, C. Motz, and R. Pippan The deformation-induced zone below large and shallow nanoindentations: a comparative study using EBSD and TEM Philosophical Magazine Letters 88 12 2008 879 887
75. J.R. Rice Tensile crack tip fields in elastic-ideally plastic crystals Mechanics of Materials 6 4 1987 317 335
76. A. Roy, and A. Acharya Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of mesoscopic field dislocation mechanics: Part II Journal of the Mechanics and Physics of Solids 54 8 2006 1711 1743 (Pubitemid 44218853)
77. T.W. Shield An experimental study of the plastic strain fields near a notch tip in a copper single crystal during loading Acta Materialia 44 4 1996 1547 1561
78. T.W. Shield, and K.S. Kim Experimental measurement of the near-tip strain field in an iron silicon single-crystal Journal of the Mechanics and Physics of Solids 42 5 1994 845 873
79. J.S. Stölken, and A.G. Evans A microbend test method for measuring the plasticity length scale Acta Materialia 46 14 1998 5109 5115
80. G. Strang Introduction to Linear Algebra 2009 Wellesley-Cambridge Press Wellesley, Massachusetts
81. S. Sun, B.L. Adams, and W.E. King Observations of lattice curvature near the interface of a deformed aluminium bicrystal Philosophical Magazine A 80 1 2000 9 25
82. M.D. Uchic, D.M. Dimiduk, J.N. Florando, and W.D. Nix Sample dimensions influence strength and crystal plasticity Science 305 5686 2004 986 989
83. J. Wheeler, E. Mariani, S. Piazolo, D.J. Prior, P. Trimby, and M.R. Drury The weighted Burgers vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials Journal of Microscopy 233 3 2009 482 494
84. S. Yefimov, I. Groma, and E. Van der Giessen A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations Journal of the Mechanics and Physics of Solids 52 2 2004 279 300
85. N. Zaafarani, D. Raabe, F. Roters, and S. Zaefferer On the origin of deformation-induced rotation patterns below nanoindents Acta Materialia 56 1 2008 31 42
86. N. Zaafarani, D. Raabe, R.N. Singh, F. Roters, and S. Zaefferer Three-dimensional investigation of the texture and microstructure below a nanoindent in a Cu single crystal using 3D EBSD and crystal plasticity finite element simulations Acta Materialia 54 7 2006 1863 1876