Size Effects During Nanoindentation: Molecular Dynamics Simulation

  • George Z. VoyiadjisEmail author
  • Mohammadreza Yaghoobi
Reference work entry


In this chapter, the molecular dynamics (MD) simulation of nanoindentation experiment is revisited. The MD simulation provides valuable insight into the atomistic process occurring during nanoindentation. First, the simulation details and methodology for MD analysis of nanoindentation are presented. The effects of boundary conditions on the nanoindentation response are studied in more detail. The dislocation evolution patterns are then studied using the information provided by atomistic simulation. Different characteristics of metallic sample during nanoindentation experiment, which have been predicted by theoretical models, are investigated. Next, the nature of size effects in samples with small length scales are studied during nanoindentation. The results indicate that the size effects at small indentation depths cannot be modeled using the forest hardening model, and the source exhaustion mechanism controls the size effects at the initial stages of nanoindentation. The total dislocation length increases by increasing the dislocation density which reduces the material strength according to the exhaustion hardening mechanisms. The dislocation interactions with each other become important as the dislocation content increases. Finally, the effects of grain boundary (GB) on the controlling mechanisms of size effects are studied using molecular dynamics.


Nanoindentation Molecular dynamics Size effects Dislocation Grain boundary 


  1. A.H. Almasri, G.Z. Voyiadjis, Nano-indentation in FCC metals: experimental study. Acta Mech. 209, 1–9 (2010)CrossRefGoogle Scholar
  2. R.K.A. Al-Rub, G.Z. Voyiadjis, Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro-and nano-indentation experiments. Int. J. Plast. 20, 1139–1182 (2004)CrossRefGoogle Scholar
  3. M.I. Baskes, Modified embedded-atom potentials for cubic materials and impurities. Phys. Rev. B 46, 2727 (1992)CrossRefGoogle Scholar
  4. S.G. Corcoran, R.J. Colton, E.T. Lilleodden, W.W. Gerberich, Anomalous plastic deformation at surfaces: nanoindentation of gold single crystals. Phys. Rev. B 55, 16057–16060 (1997)CrossRefGoogle Scholar
  5. C.F.O. Dahlberg, Y. Saito, M.S. Öztop, J.W. Kysar, Geometrically necessary dislocation density measurements associated with different angles of indentations. Int. J. Plast. 54, 81–95 (2014)CrossRefGoogle Scholar
  6. M.S. Daw, M.I. Baskes, Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443–6453 (1984)CrossRefGoogle Scholar
  7. E. Demir, D. Raabe, N. Zaafarani, 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 Mater. 57, 559–569 (2009)CrossRefGoogle Scholar
  8. E. Demir, D. Raabe, F. Roters, The mechanical size effect as a mean-field breakdown phenomenon: example of microscale single crystal beam bending. Acta Mater. 58, 1876–1886 (2010)CrossRefGoogle Scholar
  9. K. Durst, B. Backes, M. Göken, Indentation size effect in metallic materials: correcting for the size of the plastic zone. Scr. Mater. 52, 1093–1097 (2005)CrossRefGoogle Scholar
  10. J.A. El-Awady, Unravelling the physics of size-dependent dislocation-mediated plasticity. Nat. Commun. 6, 5926 (2015)CrossRefGoogle Scholar
  11. J.A. El-Awady, M. Wen, N.M. Ghoniem, The role of the weakest-link mechanism in controlling the plasticity of micropillars. J. Mech. Phys. Solids 57, 32–50 (2009)CrossRefGoogle Scholar
  12. D. Faken, H. Jonsson, Systematic analysis of local atomic structure combined with 3D computer graphics. Comput. Mater. Sci. 2, 279–286 (1994)CrossRefGoogle Scholar
  13. J.R. Greer, Nano and Cell Mechanics: Fundamentals and Frontiers. Wiley, Chichester, pp 163–190 (2013)CrossRefGoogle Scholar
  14. A. Hasnaoui, P.M. Derlet, H. Van Swygenhoven, Interaction between dislocations and grain boundaries under an indenter – a molecular dynamics simulation. Acta Mater. 52, 2251–2258 (2004)CrossRefGoogle Scholar
  15. H. Jang, D. Farkas, Interaction of lattice dislocations with a grain boundary during nanoindentation simulation. Mater. Lett. 61, 868–871 (2007)CrossRefGoogle Scholar
  16. C.L. Kelchner, S.J. Plimpton, J.C. Hamilton, Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, 11085–11088 (1998)CrossRefGoogle Scholar
  17. C.C. Koch, I.A. Ovid’ko, S. Seal, S. Veprek, Structural Nanocrystalline Materials: Fundamentals and Applications (Cambridge University Press, Cambridge, 2007)CrossRefGoogle Scholar
  18. M. de Koning, R.J. Kurtz, V.V. Bulatov, C.H. Henager, R.G. Hoagland, W. Cai, M. Nomura, Modeling of dislocation–grain boundary interactions in FCC metals. J. Nucl. Mater. 323, 281–289 (2003)CrossRefGoogle Scholar
  19. O. Kraft, P. Gruber, R. Mönig, D. Weygand, Plasticity in confined dimensions. Annu. Rev. Mater. Res. 40, 293–317 (2010)CrossRefGoogle Scholar
  20. Y. Kulkarni, R.J. Asaroa, D. Farkas, Are nanotwinned structures in fcc metals optimal for strength, ductility and grain stability? Scr. Mater. 60, 532–535 (2009)CrossRefGoogle Scholar
  21. J.W. Kysar, C.L. Briant, Crack tip deformation fields in ductile single crystals. Acta Mater. 50, 2367–2380 (2002)CrossRefGoogle Scholar
  22. J.W. Kysar, Y.X. Gan, T.L. Morse, X. Chen, M.E. Jones, High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: geometrically necessary dislocation densities. J. Mech. Phys. Solids 55, 1554–1573 (2007)CrossRefGoogle Scholar
  23. Y. Lee, J.Y. Park, S.Y. Kim, S. Jun, Atomistic simulations of incipient plasticity under Al (111) nanoindentation. Mech. Mater. 37, 1035–1048 (2005)CrossRefGoogle Scholar
  24. J. Li, K.J. Van Vliet, T. Zhu, S. Yip, S. Suresh, Atomistic mechanisms governing elastic limit and incipient plasticity in crystals. Nature 418, 307–310 (2002)CrossRefGoogle Scholar
  25. S.N. Medyanik, S. Shao, Strengthening effects of coherent interfaces in nanoscale metallic bilayers. Comput. Mater. Sci. 45, 1129–1133 (2009)CrossRefGoogle Scholar
  26. M.A. Meyers, A. Mishra, D.J. Benson, Mechanical properties of nanocrystalline materials. Prog. Mater. Sci. 51, 427–556 (2006)CrossRefGoogle Scholar
  27. Y. Mishin, D. Farkas, M.J. Mehl, D.A. Papaconstantopoulos, Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Phys. Rev. B 59, 3393–3407 (1999)CrossRefGoogle Scholar
  28. A.K. Nair, E. Parker, P. Gaudreau, D. Farkas, R.D. Kriz, Size effects in indentation response of thin films at the nanoscale: a molecular dynamics study. Int. J. Plast. 24, 2016–2031 (2008)CrossRefGoogle Scholar
  29. W.D. Nix, H.J. Gao, Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411–425 (1998)CrossRefGoogle Scholar
  30. D.M. Norfleet, D.M. Dimiduk, S.J. Polasik, M.D. Uchic, M.J. Mills, Dislocation structures and their relationship to strength in deformed nickel microcrystals. Acta Mater. 56, 2988–3001 (2008)CrossRefGoogle Scholar
  31. T.A. Parthasarathy, S.I. Rao, D.M. Dimiduk, M.D. Uchic, D.R. Trinkle, Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples. Scr. Mater. 56, 313–316 (2007)CrossRefGoogle Scholar
  32. P. Peng, G. Liao, T. Shi, Z. Tang, Y. Gao, Molecular dynamic simulations of nanoindentation in aluminum thin film on silicon substrate. Appl. Surf. Sci. 256, 6284–6290 (2010)CrossRefGoogle Scholar
  33. S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)CrossRefGoogle Scholar
  34. N.M. Pugno, A general shape/size-effect law for nanoindentation. Acta Mater. 55, 1947–1953 (2007)CrossRefGoogle Scholar
  35. S.I. Rao, D.M. Dimiduk, M. Tang, T.A. Parthasarathy, M.D. Uchic, C. Woodward, Estimating the strength of single-ended dislocation sources in micron-sized single crystals. Philos. Mag. 87, 4777–4794 (2007)CrossRefGoogle Scholar
  36. S.I. Rao, D.M. Dimiduk, T.A. Parthasarathy, M.D. Uchic, M. Tang, C. Woodward, Athermal mechanisms of size-dependent crystal flow gleaned from three-dimensional discrete dislocation simulations. Acta Mater. 56, 3245–3259 (2008)CrossRefGoogle Scholar
  37. M.D. Sangid, T. Ezaz, H. Sehitoglu, I.M. Robertson, Energy of slip transmission and nucleation at grain boundaries. Acta Mater. 59, 283–296 (2011)CrossRefGoogle Scholar
  38. S. Shao, S.N. Medyanik, Dislocation–interface interaction in nanoscale fcc metallic bilayers. Mech. Res. Commun. 37, 315–319 (2010)CrossRefGoogle Scholar
  39. W.A. Soer, J.T.M. De Hosson, Detection of grain-boundary resistance to slip transfer using nanoindentation. Mater. Lett. 59, 3192–3195 (2005)CrossRefGoogle Scholar
  40. A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials. Model. Simul. Mater. Sci. Eng. 20, 045021 (2012)CrossRefGoogle Scholar
  41. A. Stukowski, Computational analysis methods in atomistic modeling of crystals. JOM 66, 399–407 (2014)CrossRefGoogle Scholar
  42. A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Model. Simul. Mater. Sci. Eng. 18, 085001 (2010)CrossRefGoogle Scholar
  43. A. Stukowski, K. Albe, D. Farkas, Nanotwinned fcc metals: strengthening versus softening mechanisms. Phys. Rev. B 82, 224103 (2010)CrossRefGoogle Scholar
  44. A. Stukowski, V.V. Bulatov, A. Arsenlis, Automated identification and indexing of dislocations in crystal interfaces. Model. Simul. Mater. Sci. Eng. 20, 085007 (2012)CrossRefGoogle Scholar
  45. S. Suresh, T.G. Nieh, B.W. Choi, Nanoindentation of copper thin films on silicon substrates. Scr. Mater. 41, 951–957 (1999)CrossRefGoogle Scholar
  46. J.G. Swadener, E.P. George, G.M. Pharr, The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50, 681–694 (2002)CrossRefGoogle Scholar
  47. J. Tersoff, New empirical approach for the structure and energy of covalent systems. Phys. Rev. B 37, 6991–7000 (1988)CrossRefGoogle Scholar
  48. T. Tsuru, Y. Kaji, D. Matsunaka, Y. Shibutani, Incipient plasticity of twin and stable/unstable grain boundaries during nanoindentation in copper. Phys. Rev. B 82, 024101 (2010)CrossRefGoogle Scholar
  49. M.D. Uchic, P.A. Shade, D.M. Dimiduk, Plasticity of micrometer-scale single crystals in compression. Annu. Rev. Mater. Res. 39, 361–386 (2009)CrossRefGoogle Scholar
  50. G.Z. Voyiadjis, R.K.A. Al-Rub, Gradient plasticity theory with a variable length scale parameter. Int. J. Solids Struct. 42, 3998–4029 (2005)CrossRefGoogle Scholar
  51. G.Z. Voyiadjis, M. Yaghoobi, Large scale atomistic simulation of size effects during nanoindentation: dislocation length and hardness. Mater. Sci. Eng. A 634, 20–31 (2015)CrossRefGoogle Scholar
  52. G.Z. Voyiadjis, M. Yaghoobi, Role of grain boundary on the sources of size effects. Comput. Mater. Sci. 117, 315–329 (2016)CrossRefGoogle Scholar
  53. G.Z. Voyiadjis, M. Yaghoobi, Size and strain rate effects in metallic samples of confined volumes: dislocation length distribution. Scr. Mater. 130, 182–186 (2017)CrossRefGoogle Scholar
  54. M. Yaghoobi, G.Z. Voyiadjis, Effect of boundary conditions on the MD simulation of nanoindentation. Comput. Mater. Sci. 95, 626–636 (2014)CrossRefGoogle Scholar
  55. M. Yaghoobi, G.Z. Voyiadjis, Atomistic simulation of size effects in single-crystalline metals of confined volumes during nanoindentation. Comput. Mater. Sci. 111, 64–73 (2016a)CrossRefGoogle Scholar
  56. M. Yaghoobi, G.Z. Voyiadjis, Size effects in fcc crystals during the high rate compression test. Acta Mater. 121, 190–201 (2016b)CrossRefGoogle Scholar
  57. M. Yaghoobi, G.Z. Voyiadjis, Microstructural investigation of the hardening mechanism in fcc crystals during high rate deformations. Comp. Mater. Sci. 138, 10–15 (2017)CrossRefGoogle Scholar
  58. N. Zaafarani, D. Raabe, F. Roters, S. Zaefferer, On the origin of deformation-induced rotation patterns below nanoindents. Acta Mater. 56, 31–42 (2008)CrossRefGoogle Scholar
  59. T.T. Zhu, A.J. Bushby, D.J. Dunstan, Materials mechanical size effects: a review. Mater. Technol. 23, 193–209 (2008)CrossRefGoogle Scholar
  60. J.A. Zimmerman, C.L. Kelchner, P.A. Klein, J.C. Hamilton, S.M. Foiles, Surface step effects on nanoindentation. Phys. Rev. Lett. 87, 165507 (2001)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringLouisiana State UniversityBaton RougeUSA

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