Skip to main content

Size Effects During Nanoindentation: Molecular Dynamics Simulation

  • Living reference work entry
  • First Online:
Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • A.H. Almasri, G.Z. Voyiadjis, Nano-indentation in FCC metals: experimental study. Acta Mech. 209, 1–9 (2010)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • M.I. Baskes, Modified embedded-atom potentials for cubic materials and impurities. Phys. Rev. B 46, 2727 (1992)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • J.A. El-Awady, Unravelling the physics of size-dependent dislocation-mediated plasticity. Nat. Commun. 6, 5926 (2015)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • D. Faken, H. Jonsson, Systematic analysis of local atomic structure combined with 3D computer graphics. Comput. Mater. Sci. 2, 279–286 (1994)

    Article  Google Scholar 

  • J.R. Greer, Nano and Cell Mechanics: Fundamentals and Frontiers. Wiley, Chichester, pp 163–190 (2013)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • H. Jang, D. Farkas, Interaction of lattice dislocations with a grain boundary during nanoindentation simulation. Mater. Lett. 61, 868–871 (2007)

    Article  Google Scholar 

  • C.L. Kelchner, S.J. Plimpton, J.C. Hamilton, Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, 11085–11088 (1998)

    Article  Google Scholar 

  • C.C. Koch, I.A. Ovid’ko, S. Seal, S. Veprek, Structural Nanocrystalline Materials: Fundamentals and Applications (Cambridge University Press, Cambridge, 2007)

    Book  Google Scholar 

  • 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)

    Article  Google Scholar 

  • O. Kraft, P. Gruber, R. Mönig, D. Weygand, Plasticity in confined dimensions. Annu. Rev. Mater. Res. 40, 293–317 (2010)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • J.W. Kysar, C.L. Briant, Crack tip deformation fields in ductile single crystals. Acta Mater. 50, 2367–2380 (2002)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • S.N. Medyanik, S. Shao, Strengthening effects of coherent interfaces in nanoscale metallic bilayers. Comput. Mater. Sci. 45, 1129–1133 (2009)

    Article  Google Scholar 

  • M.A. Meyers, A. Mishra, D.J. Benson, Mechanical properties of nanocrystalline materials. Prog. Mater. Sci. 51, 427–556 (2006)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

    Article  MATH  Google Scholar 

  • N.M. Pugno, A general shape/size-effect law for nanoindentation. Acta Mater. 55, 1947–1953 (2007)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • S. Shao, S.N. Medyanik, Dislocation–interface interaction in nanoscale fcc metallic bilayers. Mech. Res. Commun. 37, 315–319 (2010)

    Article  MATH  Google Scholar 

  • W.A. Soer, J.T.M. De Hosson, Detection of grain-boundary resistance to slip transfer using nanoindentation. Mater. Lett. 59, 3192–3195 (2005)

    Article  Google Scholar 

  • A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials. Model. Simul. Mater. Sci. Eng. 20, 045021 (2012)

    Article  Google Scholar 

  • A. Stukowski, Computational analysis methods in atomistic modeling of crystals. JOM 66, 399–407 (2014)

    Article  Google Scholar 

  • A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Model. Simul. Mater. Sci. Eng. 18, 085001 (2010)

    Article  Google Scholar 

  • A. Stukowski, K. Albe, D. Farkas, Nanotwinned fcc metals: strengthening versus softening mechanisms. Phys. Rev. B 82, 224103 (2010)

    Article  Google Scholar 

  • A. Stukowski, V.V. Bulatov, A. Arsenlis, Automated identification and indexing of dislocations in crystal interfaces. Model. Simul. Mater. Sci. Eng. 20, 085007 (2012)

    Article  Google Scholar 

  • S. Suresh, T.G. Nieh, B.W. Choi, Nanoindentation of copper thin films on silicon substrates. Scr. Mater. 41, 951–957 (1999)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • J. Tersoff, New empirical approach for the structure and energy of covalent systems. Phys. Rev. B 37, 6991–7000 (1988)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • G.Z. Voyiadjis, M. Yaghoobi, Role of grain boundary on the sources of size effects. Comput. Mater. Sci. 117, 315–329 (2016)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • M. Yaghoobi, G.Z. Voyiadjis, Effect of boundary conditions on the MD simulation of nanoindentation. Comput. Mater. Sci. 95, 626–636 (2014)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • M. Yaghoobi, G.Z. Voyiadjis, Size effects in fcc crystals during the high rate compression test. Acta Mater. 121, 190–201 (2016b)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • N. Zaafarani, D. Raabe, F. Roters, S. Zaefferer, On the origin of deformation-induced rotation patterns below nanoindents. Acta Mater. 56, 31–42 (2008)

    Article  Google Scholar 

  • T.T. Zhu, A.J. Bushby, D.J. Dunstan, Materials mechanical size effects: a review. Mater. Technol. 23, 193–209 (2008)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to George Z. Voyiadjis .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this entry

Cite this entry

Voyiadjis, G.Z., Yaghoobi, M. (2016). Size Effects During Nanoindentation: Molecular Dynamics Simulation. In: Voyiadjis, G. (eds) Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-22977-5_41-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22977-5_41-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22977-5

  • Online ISBN: 978-3-319-22977-5

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics