Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression

International Journal of Plasticity

Volumn 26, Issue 2, 2010, Pages 239-257

  Akarapu, S ^a   Zbib, H M ^a   Bahr, D F ^a  

^a Washington State University   (United States)

Author keywords

Dislocation dynamics; micro3d; Micropillars; Size effect

Indexed keywords

CRITICAL STRESS; DEFORMATION BAND; DEFORMATION FIELD; DISCRETE DISLOCATION DYNAMICS; DISCRETE DISLOCATIONS; DISLOCATION CONFIGURATIONS; DISLOCATION DENSITIES; DISLOCATION DYNAMICS; ELASTO-VISCOPLASTIC; EXPERIMENTAL OBSERVATION; HETEROGENEOUS DEFORMATION; INTERMITTENT OPERATION; MACROSCOPIC STRAINS; MICRO-SCALES; MICRO3D; MICROPILLARS; MULTISCALES; PINNING SITES; SIMULATION MODEL; SIZE DEPENDENT; SIZE EFFECT; STRESS-STRAIN BEHAVIORS; UNI-AXIAL COMPRESSION;

COMPUTER SOFTWARE; DEFORMATION; DYNAMICS; SIMULATORS; SINGLE CRYSTALS; STRESS CONCENTRATION;

DISLOCATIONS (CRYSTALS);

EID: 70350724571     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2009.06.005     Document Type: Article

References (75)

1. Abu Al-Rub R.K., and Voyiadjis G.Z. Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments. Int. J. Plasticity 20 (2004) 1139-1182
2. Acharaya A., and Bassani J.L. Lattice incompatibility and a gradient theory of crystal plasticity. J. Mech. Phys. Solids 48 (2000) 1565-1595
3. Aifantis E.C. On the microstructural origin of certain inelastic models. ASME J. Eng. Mat. Tech. 106 (1984) 326-330
4. Akarapu S., Zbib H.M., and Hirth J.P. Modeling and analysis of disconnections in tilt walls. Scr. Mater. 59 (2008) 265-267
5. Akarapu S., and Zbib H.M. Dislocations interaction with tilt walls. Int. J. Mech. Mater. Des. 4 33 (2008) 339-406
6. Akarapu, S., Zbib, H.M., 2009. Line-integral solution for the stresses and displacement fields of an arbitrary dislocation segment in isotropic bi-materials in 3D space, Phil. Mag, in press.
7. Akasheh, F., Zbib, H.M., Akarupa, S., Overman, C., Bahr, D., 2009. Multiscale modeling of dislocation mechanisms in nanoscale multilayered composites. In: Proceeding of Mater. Res. Soc. Sympoisum, vol. 1130, W13-01.
8. Arsenlis A., and Parks D.M. Crystallographic aspects of geometrically necessary and statistically-stored dislocation density. Acta Metal. 47 (1999) 1597-1611
9. Ashby M.F. The Deformation of Plastically Non-homogeneous Alloys (1971), Amsterdam, Elsevier
10. Bahr D.F., and Gerberich W.W. Pile up and plastic zone size around indentations. Met. Mater. Trans. 27A (1996) 3793-3800
11. Bahr D.F., Kramer D.E., and Gerberich W.W. Non-linear deformation mechanisms during nanoindentation. Acta Mater. 46 (1998) 176-182
12. Bammann D.J. An internal variable model of viscoplasticity. Int. J. Eng. Sci. 8-10 (1984) 1041
13. Bammann, D.J., Aifantis, E.C., 1981. On the perfect lattice-dislocated state interaction. in: International Symposium on Mechanical Behavior of Structured Media, Amsterdam-Oxford-New York, Elsevier Scientific Publishing.
14. Benzerga, A.A., Shaver, N.F., 2006. Size dependence of mechanical properties of single crystals under uniform deformation. Scripts Mater. 54, 1937.
15. Clayton J.D., McDowell D.L., and Bammann D.J. Modeling dislocations and disclinations with finite micropolar elastoplasticity. Int. J. Plasticity 22 (2006) 210-256
16. Clemens B.M., Kung H., and Barnett S.A. Structure and strength of multilayers. MRS Bull. 24 2 (1999) 20-26
17. Demir I., and Zbib H.M. A mesoscopic model for inelastic deformation and damage. Int. J. Eng. Sci. 39 (2001) 1597-1615
18. Deshpande V.S., Needleman A., and der Giessen Van E. Plasticity size effects in tension and compression of single crystals. J. Mech. Phys. Solids 53 (2005) 2661
19. Dewald D.K., Lee T.C., Robertson I.M., and Birnbaum H.K. Dislocation structures ahead of advancing cracks. Scr. Metall. 23 (1989) 1307
20. Dillon O.W., and Kratochvil J. A Strain gradient theory of plasticity. Int. J. Solids Struct. 6 (1970) 1513-1533
21. Dimiduk D.M., Uchic M.D., and Parthasarathy T.A. Size-affected single slip behavior of pure nickel microcrystals. Acta Mater. 53 (2005) 4065
22. Espinosa H.D., Panico M., Berbenni S.M., and Schwartz K.W. Discrete dislocation dynamics to interpret size and grain boundary effects in free-standing FCC thin films. Int J. Plasticity 22 (2006) 22-2091
23. Fivel M.C., Roberston C.F., Canova G., and Bonlanger L. Three-dimensional modeling of indent-induced plastic zone at a mesoscale. Acta Mater. 46 17 (1998) 6183-6194
24. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42 (1994) 475-487
25. Foreman A.J.E. The bowing of a dislocation segment. Phil. Mag. 15 (1967) 1011
26. Frick C.P., Clark B.G., Orso S., Schneider A.S., and Artz E. Size effect on strength and strain hardening of small-scale [1 1 1] nickel compression pillars. Mater. Sci. Eng. A. 489 (2008) 319-329
27. Greer J.R., and Nix W.D. Size dependence of mechanical properties of gold at the sub-micron scale. Appl. Phys. A 80 (2005) 1625-1629
28. Greer J.R., and Nix W.D. Nanoscale gold pillars strengthened through dislocation starvation. Phys. Rev. B 73 (2006) 245210
29. Groh S., Marin E.B., Horstemeyer M.F., and Zbib H.M. Multiscale modeling of plasticity in an aluminum single crystal. Int. J. Plasticity 25 (2009) 1456-1473
30. Gurber P.A., Bohm J., Onuseit F., Wanner A., Spolenak R., and Arzt E. Size effects on yield strength and strain hardening for ultra-thin Cu films with and without passivation: A study by synchrotron and bulge test techniques. Acta Mater. 56 (2008) 2318-2335
31. Hirth J.P., Zbib H.M., and Lothe J. Forces on high velocity dislocations. Model. Simul. Mater. Sci. Eng. 6 (1998) 165-169
32. Horstemeyer M.F., Baskes M.I., and Plimpton S.J. Size scale and strain rate effects on yield and plasticity of metals. Acta Mater. 49 (2001) 4363
33. Khan S., Zbib H.M., and Hughes D. Modeling planar dislocation boundaries using a multi-scale approach. Int. J. Plasticity 20 (2004) 1059-1092
34. Khraishi T.A., Khaleel M., and Zbib H.M. A parametric study of void growth in superplastic deformation. In. J. Plasticity 17 3 (2001) 297-315
35. Kiener D., Grosinger W., Dehm G., and Pippan R. A further step towards an understanding of size-dependent crystal plasticity: in situ tension experiments of miniaturized single-crystal copper samples. Acta Mater. 56 (2008) 580
36. Koehler J.S. Attempt to design a strong solid. Phys. Rev. B 2 2 (1970) 547-551
37. Kubin L., Canova G., Condat M., Devincre B., Pontikis V., and Brechet Y. Dislocation structures and plastic flow: a 3d simulation. Solid State Phenom. 23-24 (1992) 455-472
38. Maaß R., Grolimund D., Van Petegem S., Willimann M., Jensen M., Van Swygenhoven H., Lehnert T., Gijs M., Volkert C.A., Lilleodden E.T., and Schwaiger R. Defect structure in micropillars using X-ray microdiffraction. Appl. Phys. Lett. 89 (2006) 151905
39. Maaß R., Van Petegem S., Grolimund V.S.H., Kiener D., and Dehm G. Crystal rotation in Cu single crystal micropillars: in situ Laue and electron backscatter diffraction. Appl. Phys. Lett. V 92 (2008) 071905
40. Mesarovic S. Energy, configurational forces and characteristic lengths associated with the continuum description of geometrically necessary dislocations. Int. J. Plasticity 21 (2005) 1855-1889
41. Mindlin R.D. Micro-structure in linear elasticity. Arch. Rat. Mech. Anal. 16 (1964) 51-78
42. Misra A., Hirth J.P., Hoagland R.G., Embury D.J., and Kung H. Dislocation mechanisms and symmetric slip in rolled nano-scaled metallic multilayers. Acta Mater. 52 (2004) 2387-2394
43. Misra A., and Kung H. Deformation behavior of nanostructured metallic multilayers. Adv. Eng. Mater. 3 4 (2001)
44. Misra A., Kung H., Hammon D., Hoagland R.G., and Nastasi M. Damage mechanisms in nanolayered metallic composites. Int. J. Damage Mech. 12 (2003) 365
45. Misra A., Verdier M., Lu Y.C., Kung H., Mitchell T.E., Nastasi M., and Embury D.J. Structure and mechanical properties of Cu-X (X = Nb, Cr, Ni) nanolayered composites. Scr. Mater. 39 4/5 (1998) 555-560
46. Mughrabi H. Dislocation walls and cell structures and long range internal stresses in deformed metal crystals. Acta Mater. 31 (1983) 1367
47. Needleman A. Computational mechanics at the mesoscale. Acta Mater. 48 (2000) 105-124
48. Nibur K.A., Akasheh F., and Bahr D.F. Analysis of dislocation mechanisms around indentations through slip step observations. J. Mater. Res. 42 (2007) 889-900
49. Nibur K.A., and Bahr D.F. Identifying slip systems around indentations in FCC metals. Scripts Mater. 49 (2003) 1055-1060
50. Nix W.D. Mechanical properties of thin films. Metall. Trans. A 20A (1989) 2217-2245
51. Nye J.F. Some geometrical relations in dislocated crystals. Acta Metal. 1 (1953) 153-162
52. Oberle R.R., and Cammarata R.C. Dependence of hardness on modulation amplitude in electrodeposited Cu-Ni compositionally modulated thin films. Scr. Metall. Mater. 32 4 (1995) 583-588
53. Ohashi T. "Finite-element analysis of plastic slip and evolution of geometrically necessary dislocations in fcc crystals. Phil. Mag. Lett. 75 2 (1994) 51
54. Rhee M., Hirth J.P., and Zbib H.M. A superdislocation model for the strengthening of metal composites and the initiation and propagation of shear bands. Acta Metall. Mater. 42 8 (1994) 2645-2655
55. Rhee M., Zbib H.M., Hirth J.P., Huang H., and Diaz de la Rubia T. Models for long-/short-range interaction and cross slip in 3D dislocation simulation of BCC single crystals. Modell. Sim. Mater. Sci. 6 (1998) 467-492
56. Sansour C., and Saktulla S. A strain gradient generalised continuum approach for modelling elastic scale-effects. Comput. Methods Appl. Mech. Eng. 198 (2009) 1401-1412
57. Shan Z.N., Mishra R.K., Syed-Asif S.A., Warren O.L., and Minor A.M. Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals. Nature 7 (2008) 115
58. Shizawa K., and Zbib H.M. Thermodynamical theory of strain gradient elastoplasticity with dislocation density: Part I - fundamentals. Int. J. Plasticity 15 (1999) 899-938
59. Stolken J., and Evans A.G. A microbend test method for measuring the plasticity length scale. Acta Mater. 46 (1998) 5109-5115
60. Stoudt M.R., Ricker R.E., and Cammarata R.C. The influence of a multilayered metallic coating on fatigue crack nucleation. Int. J. Fatigue 23 (2001) 215-223
61. Tang H., Schwarz K.W., and Espinosa H.D. Dislocation escape related size effects in single-crystal micropillars under uniaxial compression. Acta Mater. 55 (2007) 1607
62. Tang H., Schwartz K.W., and Espinosa H.D. Dislocation-source shutdown and the plastic behavior of single-crystal micropillars. Phys. Rev. Lett. 100 (2008) 185503
63. Van der Giessen E., and Needleman A. Discrete dislocation plasticity: a simple planar model. Mater. Sci. Eng. 3 (1995) 689-735
64. Volkert C.A., and Lilleodden E.T. Size effects in the deformation of sub-micron Au columns. Phil. Mag. 86 (2006) 5567-5579
65. Wang Y.C., Misra A., and Hoaglan R.G. Fatigue properties of nanoscale Cu/Nb multilayers. Scr. Mater. 54 9 (2006) 1593-1598
66. Was G.S., and Foecke T. Deformation and fracture in microlaminates. Thin Solid Films 286 (1996) 1-31
67. Watanabe O., Zbib H.M., and Takenouchi E. Crystal plasticity: micro-shear banding in polycrystals using Voroni tessellation. Int. J. Plasticity 14 8 (1998) 7710788
68. Yasin H., Zbib H.M., and Khaleel M.A. Size and boundary effects in discrete dislocation dynamics: coupling with continuum finite element. Mater. Sci. Eng. A309-310 (2001) 294-299
69. Zbib H.M., and Aifantis E.C. A gradient-dependent flow theory of plasticity: application to metal and soil instabilities. ASME J. Appl. Mech. Rev. 42 (1989) 295-304 (No. 11, Part 2)
70. Zbib H.M., and Diaz de la Rubia T. A multiscale model of plasticity. Int. J. Plasticity 18 9 (2002) 1133-1163
71. Zbib H.M., de la Rubia Diaz T., and Bulatov V.A. A multiscale model of plasticity based on discrete dislocation dynamics. ASME J. Eng. Mater. Tech. 124 (2002) 78-87
72. Zbib H.M., and Jubran J.S. Dynamic shear banding - A 3-dimensional analysis. Int. J. Plasticity 8 6 (1992) 619-641
73. Zbib H.M., Rhee M., and Hirth J.P. 3D simulation of curved dislocations: discretization and long range interactions. In: Abe T., and Tsuta T. (Eds). Advances in Engineering Plasticity and its Applications (1996), Pergamon, NY 15-20
74. Zbib H.M., Rhee M., and Hirth J.P. On plastic deformation and the dynamics of 3D dislocations. Int. J. Mech. Sci. 40 (1998) 113-127
75. Zhang G.P., Volkert C.A., Schwaiger R., Arzt E., and Kraft O. Damage behavior of 200-nm thin copper films under cyclic loading. J. Mater. Res. 20 1 (2005) 201-207