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Bridging the Scales from the Atomistic to the Continuum

  • Mohammed CherkaouiEmail author
  • Laurent Capolungo
Chapter
  • 904 Downloads
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 112)

Although some understanding seems to be emerging on the influence of grain size on the strength of nanocrystalline (NC) materials, it is not presently possible to accurately model or predict their deformation, fracture, and fatigue behavior as well as the relative tradeoffs of these responses with changes in microstructure. Even empirical models predicting deformation behavior do not exist due to lack of reliable data. Also, atomistic modeling has been of limited utility in understanding behavior over a wide range of grain sizes ranging from a few nanometers (~5 nm) to hundreds of nanometers due to inherent limitations on computation time step, leading to unrealistic applied stresses or strain rates, and scale of calculations. Moreover, the sole modeling of the microstructures is hindered by the need to characterize defect densities and understand their impact on strength and ductility. For example, nanocrystalline materials processed by ball milling of powders or extensive shear deformation (e.g., equal channel angular extrusion [ECAE]) can have high defect densities, such as voids, and considerable lattice curvature. Accordingly, NC materials are often highly metastable and are subject to coarsening. Recently, processing techniques such as electrodeposition have advanced to the point to allow the production of fully dense, homogeneous, and low defect material that can be used to measure properties reliably and reduce uncertainty in modeling associated with initial defect densities [53].

Keywords

Triple Junction Partial Dislocation Coincident Site Lattice Equal Channel Angular Extrusion Dislocation Nucleation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Aifantis, E.C., The physics of plastic deformation. International Journal of Plasticity 3, 211–247, (1987)CrossRefGoogle Scholar
  2. 2.
    Asaro, R.J. and S. Suresh, Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano-scale twins. Acta Materialia 53(12), 3369–3382, (2005)Google Scholar
  3. 3.
    Ashby, M.F., The deformation of plastically non homogeneous materials. Philosophical Magazine 21, 399–424, (1970)CrossRefGoogle Scholar
  4. 4.
    Ashby, M.F., A first report on deformation-mechanism maps. Acta Metallurgica (pre 1990), 20, 887, (1972)Google Scholar
  5. 5.
    Bachurin, D.V., R.T. Murzaev, et al., Atomistic computer and disclination simula-tion of [001] tilt boundaries in nickel and copper. Fizika Metallov i Metallovedenie 96(6), 11–17, (2003)Google Scholar
  6. 6.
    Benkassem, S., L. Capolungo, M. Cherkaoui, Mechanical properties and multi-scale modeling of nanocrystalline materials. Acta Materialia 55(10), 3563–3572, (2007)Google Scholar
  7. 7.
    Berbenni, S., Favier, V. et al., Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels having different microstructures. Materials Science and Engineering A, 372(1–2), 128–136, (2004)Google Scholar
  8. 8.
    Cai, B., Q.P. Kong, et al., Creep behav-ior of cold-rolled nanocrystalline pure cop-per. Scripta Materialia 45(12), 1407–1413, (2001)CrossRefGoogle Scholar
  9. 9.
    Cai, B., Q.P. Kong, et al., Low tempera-ture creep of nanocrystalline pure copper. Materials Science and Engineering A 286(1), 188–192, (2000)CrossRefGoogle Scholar
  10. 10.
    Capolungo, L., M. Cherkaoui, et al., A self consistent model for the inelastic de-formation of nanocrystalline materials. Journal of engineering materials and tech-nology 127, 400–407, (2005)CrossRefGoogle Scholar
  11. 11.
    Capolungo, L., M. Cherkaoui, et al., On the elastic-viscoplastic behavior of nanocrystalline materials. International Journal of Plasticity 23(4), 561–591, (2007)Google Scholar
  12. 12.
    Capolungo, L., C. Jochum, et al., Ho-mogenization method for strength and ine-lastic behavior of nanocrystalline materials. International Journal of Plasticity 21, 67–82, (2005)CrossRefGoogle Scholar
  13. 13.
    Capolungo, L., D.E. Spearot, et al., Dis-location nucleation from bicrystal interfaces and grain boundary ledges: Relationship to nanocrystalline deformation. Journal of the Mechanics and Physics of Solids, 55(11), November, 2007, 2300–2327, (2007)CrossRefGoogle Scholar
  14. 14.
    Coble, R.L., A Model for Boundary Diffusion Controlled Creep in Polycrystal-line Materials. Journal of Applied Physics 34(6): 1679–1682, (1963)CrossRefGoogle Scholar
  15. 15.
    Dai, H. and D.M. Parks, Geometrically-necessary dislocation density and scale-dependent crystal plasticity. In A. S. Khan (ed.), Proceedings of Plasticity ’97: The Fifth International Sym-posium on Plasticity and its Current Applications, 17–18, Juneau, Alaska. Neat Press, (1997)Google Scholar
  16. 16.
    Dai, H., Geometrically-necessary dislocation density in continuum plasticity theory, FEM implementation and applications. Ph.D. thesis, Massachusetts Institute of Technology, Department of Mechanical En-gineering, (1997)Google Scholar
  17. 17.
    Derlet, P.M. and H. Van Swygenhoven, Length scale effects in the simulation of de-formation properties of nanocrystalline met-als. Scripta Materialia 47(11), 719–724, (2002)CrossRefGoogle Scholar
  18. 18.
    Douglas, E.S., I.J. Karl, and D.L. McDowell, Nucleation of dislocations from [0 0 1] bicrystal interfaces in aluminum. Acta Materialia 53(13), 3579–3589, (2005)Google Scholar
  19. 19.
    Eshelby, J.D., The determination of an ellispoidal inclusion and related problems. Proceedings of the Royal Society of London A241, 376–396, (1957)Google Scholar
  20. 20.
    Eshelby, J.D. Elastic inclusions and inhomogeneities. North Hol-land, (1961)Google Scholar
  21. 21.
    Fleck, N.A., G.M. Muller, M.F. Ashby, and J.W. Hutchinson, Strain gradient plastic-ity: theory and experiment. Acta metallur-gica et Materialia 42, 475–487, (1994)CrossRefGoogle Scholar
  22. 22.
    Fleck, N.A. and J.W. Hutchinson, Strain gradient plasticity. Advances in Ap-plied Mechanics, 33, 295–361, (1997)CrossRefGoogle Scholar
  23. 23.
    Friedel, J., Physics of Strength and Plasticity, MIT Press, Boston, (1969)Google Scholar
  24. 24.
    Froseth, A., H. Van Swygenhoven, et al., The influence of twins on the mechani-cal properties of nc-Al. Acta Materialia 52, 2259–2268, (2004)CrossRefGoogle Scholar
  25. 25.
    Froseth, A.G., P.M. Derlet, et al., Dis-locations emitted from nanocrystalline grain boundaries: Nucleation and splitting dis-tance. Acta Materialia 52(20), 5863–5870, (2004)CrossRefGoogle Scholar
  26. 26.
    Gao, H., Y. Huang, W.D. Nix, and J.W. Hutchinson, Mechanism-based strain gradi-ent plasticity–I. Theory. Journal of the Mechanics and Physics of Solids 47, 1239–1263, (1999)CrossRefGoogle Scholar
  27. 27.
    Ghoniem, N.M., E. Busso, et al., Mul-tiscale modelling of nanomechanics and mi-cromechanics: an overview. Philosophical Magazine 83, 3475–3528, (2003)CrossRefGoogle Scholar
  28. 28.
    Granato, A.V., K. Lucke, et al., Journal of Applied Physics 35, 2732, (1964)CrossRefGoogle Scholar
  29. 29.
    Gutkin, M.Y., I.A. Ovid'Ko, et al., Transformation of grain boundaries due to disclination motion and emission of dislocations pairs. Materials Science and Engineering A339, 73–80, (2003)Google Scholar
  30. 30.
    Hall, E.O., The deformation and aging of mild steel. Proceedings of the Physical Society of London B64, 747, (1951)Google Scholar
  31. 31.
    Hoover, W.G. (Ed.), Proceedings of the the international school of physics - Enrico Fermi- Molecular Dynamics Simulations of Statistical Mechanical Systems. North Holland, Amsterdam, (1985)Google Scholar
  32. 32.
    Hosford, W.F., The Mechanics of Crystals and Textured Polycrys-tals. New York, Oxford University Press, (1993)Google Scholar
  33. 33.
    Jiang, B. and G.J. Weng, A generalized self consistent polycrystal model for the yield strength of nanocrystalline materials. Journal of the Mechanics and Physics of Solids, 52, 1125–1149, (2004)CrossRefGoogle Scholar
  34. 34.
    Jin, Z.H., P. Gumbsch, et al., The inter-action mechanism of screw dislocations with coherent twin boundaries in different face-centred cubic metals. Scripta Materialia 54(6), 1163–1168, (2006)CrossRefGoogle Scholar
  35. 35.
    Ke, M., S.A. Hackney, et al., Observa-tions and measurement of grain rotation and plastic strain in nanostructured metal thin films. Nanostructured Materials 5, 689–697, (1995)CrossRefGoogle Scholar
  36. 36.
    Kim, B.-N., K. Hiraga, et al., Viscous grain-boundary sliding and grain rotation accommodated by grain-boundary diffusion. Acta Materialia 53(6), 1791–1798, (2005)CrossRefGoogle Scholar
  37. 37.
    Kim, H.S. and Y. Estrin, Phase mixture modeling of the strain rate dependent me-chanical behavior of nanostructured materi-als. Acta Materialia 53, 765–772, (2005)CrossRefGoogle Scholar
  38. 38.
    Kim, H.S., Y. Estrin, et al., Plastic de-formation behaviour of fine grained materi-als. Acta Materialia 48, 493–504, (2000)CrossRefGoogle Scholar
  39. 39.
    Kocks, U.F., Laws for work hardening and low temperature creep. Journal of Engineering Materials and Technology Transactions of ASME 98(1), 76–85, (1976)Google Scholar
  40. 40.
    Kocks, U.F. and H. Mecking, Physics and phenomenology of strain hardening. Progress in Materials Science 48, 171–273, (2003)CrossRefGoogle Scholar
  41. 41.
    Konstantinidis, D.A. and E.C. Aifantis, On the “anomalous” hard-ness of nanocrystalline materials. Nanos-tructured Materials 10, 1111–1118, (1998)CrossRefGoogle Scholar
  42. 42.
    Kumar, K.S., S. Suresh, et al., Defor-mation of electrodeposited nanocrystalline nickel. Acta Materialia 51, 387–405, (2003)CrossRefGoogle Scholar
  43. 43.
    Kunin, I.A., Elastic media with microstructure II: Three dimensional mod-els. Springer-Verlag, Berlin, (1983)CrossRefGoogle Scholar
  44. 44.
    Li, J.C.M., Petch relation and grain boundary sources. Transactions of the Met-allurgical Society of AIME 227, 239, (1963)Google Scholar
  45. 45.
    Li, Y.J., W. Blum, et al., Does nanocrystalline Cu deform by Coble creep near room temperature? Materials Science and Engineering A 387–389, 585–589, (2004)CrossRefGoogle Scholar
  46. 46.
    Markmann, J., P. Bunzel, et al., Micro-structure evolution during rolling of inert-gas condensed palladium. Scripta Materialia 49(7), 637–644, (2003)CrossRefGoogle Scholar
  47. 47.
    Mishin, Y., D. Farkas, et al., Intera-tomic potentials for monoatomic metals from experimental data and ab initio calcula-tions. Physical Review B 59, 3393–3407, (1999)CrossRefGoogle Scholar
  48. 48.
    Muller, P. and A. Saul, Elastic effects on surface physics. Surface Science Reports 54(5–8), 157, (2004)CrossRefGoogle Scholar
  49. 49.
    Mura, T., Micromechanics of defects in solids. Kluwer Academic Publisher, Dordrecht, (1993)Google Scholar
  50. 50.
    Murr, L.E., Strain induced dislocation emission from grain boundaries in stainless steel. Materials Science and Engineering 51, 71–79, (1981)CrossRefGoogle Scholar
  51. 51.
    Murr, L.E. and E. Venkatesh, Contrast phenomena and identification of grain boundary ledges. Metallography 11, 61–79, (1978)CrossRefGoogle Scholar
  52. 52.
    Nes, E., Modelling of work hardening and stress saturation in FCC metals. Pro-gress in Materials Science 41, 129–193, (1997)CrossRefGoogle Scholar
  53. 53.
    Nieh, T.G. and J.G. Wang, Hall Petch relationship in nanocrystalline Ni and Be-B alloys. Intermetallics 13, 377–385, (2005)CrossRefGoogle Scholar
  54. 54.
    Nose, S., A molecular dynamics method for simulations in the canonical ensemble. Molecular physics 52, 255–268, (1984)Google Scholar
  55. 55.
    Nozieres, P. and D.E. Wolf, Interfacial properties of elastically strained materials. I. Thermodynamics of a planar interface. Zeitschrift fur Physik B (Condensed Matter) 70(3), 399, (1988)CrossRefGoogle Scholar
  56. 56.
    Nye, J.F., Some geometric relations in dislocated crystals. Acta Metallurgica 1: 153–162, (1953)CrossRefGoogle Scholar
  57. 57.
    Petch, N.J., The cleavage strength of polycrystals. Journal of Iron Steel Institute, 174, 25–28, (1953)Google Scholar
  58. 58.
    Qin, W., Z. Chen, et al., Dislocation pileups in nanocrystalline materials. Journal of Alloys and Compounds 289, 285–288, (1999)CrossRefGoogle Scholar
  59. 59.
    Qin, W., Z.H. Chen, et al., Crystal lat-tice expansion of nanocrystalline materials. Journal of Alloys and Compounds 292, 230–232, (1999)CrossRefGoogle Scholar
  60. 60.
    Qin, W., Y.W. Du, et al. Dislocation stability and configuration in the crystallites of nanocrystalline materials. Journal of Al-loys and Compounds 337, 168–171, (2002)CrossRefGoogle Scholar
  61. 61.
    Qu, J., The effect of slightly weakened interfaces on the overall elastic properties of composite materials. Mechanics of Materials 14(4), 269–281, (1993)CrossRefGoogle Scholar
  62. 62.
    Rittner, J.D. and D.N. Seidman, <110> symmetric tilt grain-boundary structures in FCC metals with low stacking-fault ener-gies. Physical Review B: Condensed Matter 54(10), 6999, (1996)CrossRefGoogle Scholar
  63. 63.
    Romanov, A.E., Mechanics and physics of disclinations in solids. European Journal of Mechanics – A/Solids 22(5), 727–741, (2003)CrossRefGoogle Scholar
  64. 64.
    Sanders, P.G., M. Rittner, et al., Creep of nanocrystalline Cu, Pd, and Al-Zr. Nanostructured Materials 9(1–8), 433–440, (1997)CrossRefGoogle Scholar
  65. 65.
    Sansoz, F. and J.F. Molinari, Mechani-cal behavior of Sigma tilt grain boundaries in nanoscale Cu and Al: a quasicontinuum study. Acta Materialia 53, 1931–1944, (2005)CrossRefGoogle Scholar
  66. 66.
    Shi, M.X., Y. Huang, and K.C. Hwang, Plastic flow localization in mechanism-based strain gradient plasticity. International Journal of Mechanical Sciences 42, 2115–2131, (2000)CrossRefGoogle Scholar
  67. 67.
    Shu, J.Y. and N.A. Fleck, Strain gradi-ent crystal plasticity: size-dependent defor-mation of bicrystals. Journal of the Mechan-ics and Physics of Solids 47, 297–324, (1999)CrossRefGoogle Scholar
  68. 68.
    Spearot, D.E., Atomistic Calculations of Nanoscale Interface Behavior in FCC metals. Woodruff School of Mechanical En-gineering. Georgia Institute of Technology, Atlanta, 276, (2005)Google Scholar
  69. 69.
    Spearot, D.E., K.I. Jacob, et al., Nuclea-tion of dislocations from [001] bicrystal in-terfaces in aluminum. Acta Materialia 53, 3579–3589, (2005)CrossRefGoogle Scholar
  70. 70.
    Spearot, D.E., K.I. Jacob, et al., Dislo-cation nucleation from bicrystal interfaces with dissociated structure. International Journal of Plasticity 23(1), 143–160, (2007)Google Scholar
  71. 71.
    Sutton, A.P. and V. Vitek, On the struc-ture of tilt grain boundaries in cubic metals. I. Symmetrical tilt boundaries. Philosophical Transactions of the Royal Society of London A 309(1506), 1–36, (1983)CrossRefGoogle Scholar
  72. 72.
    Van Petegem, S., F. Dalla Torre, et al., Free volume in nanostructured Ni. Scripta Materialia 48, 17–22, (2003)Google Scholar
  73. 73.
    Van Swygenhoven, H. and A. Caro, Plastic behavior of nanophase Ni: a molecu-lar dynamics computer simulation. Applied Physics Letters 71(12), 1652, (1997)CrossRefGoogle Scholar
  74. 74.
    Van Swygenhoven, H., A. Caro, et al., Grain boundary structure and its influence on plastic deformation of polycrystalline FCC metals at the nanoscale: a molecular dynamics study. Scripta Materialia 44, 1513–1516, (2001)CrossRefGoogle Scholar
  75. 75.
    Van Swygenhoven, H., P.M. Derlet, et al., Stacking fault energies and slip in nanocrystalline metals. Nature Materials 3, 399–403, (2004)CrossRefGoogle Scholar
  76. 76.
    Van Swygenhoven, H., M. Spaczer, et al., Microscopic descritpion of plasticity in computer generated metallic nanophase samples: a comparison betwwen Cu and Ni. Acta Metallurgica 47, 3117–3126, (1999)Google Scholar
  77. 77.
    Venkatesh, E.S. and L.E. Murr, The in-fluence of grain boundary ledge density on the flow stress in Nickel. Materials Science and Engineering 33, 69–80, (1978)CrossRefGoogle Scholar
  78. 78.
    Volterra, V., Ann. Ecole Normale Supérieure de Paris 24, 401, (1907)Google Scholar
  79. 79.
    Wang, Y.M., A.V. Hamza, et al., Acti-vation volume and density of mobile dislo-cations in plastically deforming nanocrystal-line Ni. Applied Physics Letters 86(24), 241917, (2005)Google Scholar
  80. 80.
    Warner, D.H., F. Sansoz, et al., Atom-istic based continuum investigation of plas-tic deformation in nanocrystalline copper. International Journal of Plasticity 22(4), 754, (2006)CrossRefGoogle Scholar
  81. 81.
    Wei, Y.J. and L. Anand, Grain-boundary sliding and separation in polycrys-talline metals: application to nanocrystalline fcc metals. Journal of the Mechanics and Physics of Solids 52(11), 2587, (2004)CrossRefGoogle Scholar
  82. 82.
    Wolf, D., Structure-energy correlation for grain boundaries in F.C.C. metals-III. Symmetrical tilt boundaries. Acta Metallurgica et Materialia 338(5), 781–790, (1990)Google Scholar
  83. 83.
    Wolf, D., V. Yamakov, et al., Deforma-tion of nanocrystalline materials by molecu-lar dynamics simulation: relationship to ex-periments? Acta Materialia 53, 1–40, (2005)CrossRefGoogle Scholar
  84. 84.
    Wolf, D.E. and P. Nozieres, Interfacial properties of elastically strained materials. II. Mechanical and melting equilibrium of a curved interface. Zeitschrift fur Physik B (Condensed Matter) 70(4), 507, (1988)CrossRefGoogle Scholar
  85. 85.
    Yamakov, V., D. Wolf, et al., Deforma-tion twinning in nanocrystalline Al by mo-lecular dynamics simulation. Acta Materi-alia 50, 5005–5020, (2002)CrossRefGoogle Scholar
  86. 86.
    Yamakov, V., D. Wolf, et al., Length-scale effects in the nucleation of extended dislocations in nanocrystalline Al by mo-lecular-dynamics simulation. Acta Materi-alia 49(14), 2713–2722, (2001)CrossRefGoogle Scholar
  87. 87.
    Yin, W.M., S.H. Whang, et al., Creep behavior of nanocrystalline nickel at 290 and 373 K. Materials Science and Engineer-ing A 301(1), 18–22, (2001)CrossRefGoogle Scholar
  88. 88.
    Zhu, B., R.J. Asaro, et al., Effects of grain size distribution on the mechanical re-sponse of nanocrystalline metals: Part II. Acta Materialia 54(12), 3307–3320, (2006)CrossRefGoogle Scholar
  89. 89.
    Zhu, Y.T. and T.G. Langdon, Influence of grain size on deformation mechanisms: An extension to nanocrystalline materials. Materials Science and Engineering: A 409(1–2), 234–242, (2005)CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Georgia Institute of TechnologyAtlantaUSA
  2. 2.Los Alamos National LaboratoryLos AlamosUSA

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