Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation

Nature Materials volume 3, pages 43–47 (2004)Cite this article

Abstract

Molecular-dynamics simulations have recently been used to elucidate the transition with decreasing grain size from a dislocation-based to a grain-boundary-based deformation mechanism in nanocrystalline f.c.c. metals. This transition in the deformation mechanism results in a maximum yield strength at a grain size (the 'strongest size') that depends strongly on the stacking-fault energy, the elastic properties of the metal, and the magnitude of the applied stress. Here, by exploring the role of the stacking-fault energy in this crossover, we elucidate how the size of the extended dislocations nucleated from the grain boundaries affects the mechanical behaviour. Building on the fundamental physics of deformation as exposed by these simulations, we propose a two-dimensional stress-grain size deformation-mechanism map for the mechanical behaviour of nanocrystalline f.c.c. metals at low temperature. The map captures this transition in both the deformation mechanism and the related mechanical behaviour with decreasing grain size, as well as its dependence on the stacking-fault energy, the elastic properties of the material, and the applied stress level.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Comparison of two snapshots taken after 1% plastic straining of two identical microstructures of (a) a high- and (b) a low-SFE material with a grain size of 24 nm.
Figure 2: Comparison of the plastic strain versus time behaviour of a high- and low-SFE material for a grain size of 24 nm.
Figure 3: Proposed deformation-mechanism map incorporating the role of the stacking-fault energy in the deformation behaviour.

Similar content being viewed by others

References

  1. Weertman, J. & Weertman, J.R. in Physical Metallurgy (ed. Cahn, J. W.) 921–1010 (North-Holland, Amsterdam, 1965).

    Google Scholar 

  2. Mukherjee, A.K., Bird, J.E. & Dorn, J.F. Experimental correlations for high-temperature creep. Trans. Am. Soc. Metals 62, 155–179 (1969).

    CAS  Google Scholar 

  3. Ashby, M.F. A first report on deformation-mechanism maps. Acta Metall. 20, 887–897 (1972).

    Article  CAS  Google Scholar 

  4. Frost, H.J. & Ashby, M.F. Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics (Pergamon, Oxford, 1982).

    Google Scholar 

  5. Mukherjee, A.K. An examination of the constitutive equation for elevated temperature plasticity. Mat. Sci. Eng. A 322, 1–22 (2002).

    Article  Google Scholar 

  6. McFadden, S.X., Mishra, R.S., Valiev, R.Z., Zhilyaev, A.P. & Mukherjee, A.K. Low-temperature superplasticity in nanostructured nickel and metal alloys. Nature 398, 684–686 (1999).

    Article  CAS  Google Scholar 

  7. Mukherjee, A.K., Mishra, R.S. & Bieler, T.R. Some critical aspects of high strain rate superplasticity. Mater. Sci. Forum 233–234, 217–234 (1997).

    Google Scholar 

  8. Higashi, K. & Mabuchi, M. Recent works in high strain rate superplasticity. Mater. Sci. Forum 233–234, 155 (1997).

    Google Scholar 

  9. Mishra, R.S., Valiev, R.Z., McFadden, S.X. & Mukherjee, A.K. Tensile superplasticity in a nanocrystalline nickel aluminide. Mater. Sci. Eng. 252, 174–178 (1998).

    Article  Google Scholar 

  10. Mishra, R.S., McFadden, S.X., Valiev, R.Z. & Mukherjee, A.K. Deformation mechanisms and tensile superplasticity in nanocrystalline materials. J. Mater. Min. Soc. 51, 37–40 (1999).

    Article  CAS  Google Scholar 

  11. Koch, C.C. & Suryanarayana, C. in Microstructure and Properties of Materials Vol. 2 (ed. Li, J.C.M.) 380–385 (World Scientific, Singapore, 2000).

    Google Scholar 

  12. Karch, J., Birringer, R. & Gleiter, H. Ceramics ductile at low-temperature. Nature 330, 556–558 (1987).

    Article  CAS  Google Scholar 

  13. McFadden, S.X., Mishra, R.S., Valiev, R.Z., Zhilyaev, A.P. & Mukherjee, A.K. Low-temperature superplasticity in nanostructured nickel and metal alloys. Nature 398, 684–686 (1999).

    Article  CAS  Google Scholar 

  14. Lu, L., Sui, M.L. & Lu, K. Superplastic extensibility of nanocrystalline copper at room temperature. Science 287, 1463–1466 (2000).

    Article  CAS  Google Scholar 

  15. Kim, B.N., Hiraga, K., Morita, K. & Sakka, Y. A high-strain-rate superplastic ceramic. Nature 413, 288–291 (2001).

    Article  CAS  Google Scholar 

  16. Nieh, T.G. & Wadsworth, J. Hall-Petch relation in nanocrystalline solids. Scripta Met. Mater. 25, 955–958 (1991).

    Article  CAS  Google Scholar 

  17. Siegel, R.W. Mechanical properties of nanophase materials. Mater. Sci. Forum 235–238, 851–860 (1997).

    Google Scholar 

  18. Morris, D.G. & Morris, M.A. Hardness, strength, ductility and toughness of nanocrystalline materials. Mater. Sci. Forum 235–238, 861–872 (1997).

    Google Scholar 

  19. Yip, S. Nanocrystals — the strongest size. Nature 391, 532–533 (1998).

    Article  CAS  Google Scholar 

  20. Yamakov, V., Wolf, D., Phillpot, S.R., Mukherjee, A.K. & Gleiter, H. Crossover in Hall–Petch behaviour in nanocrystalline materials by molecular-dynamics simulation. Phil. Mag. Lett. 83, 385–393 (2003).

    Article  CAS  Google Scholar 

  21. Schiotz, J., DiTolla, F.D. & Jacobsen, K.W. Softening of nanocrystalline metals at very small grain sizes. Nature 391, 561–563 (1998).

    Article  Google Scholar 

  22. Swygenhoven, H.V., Spaczer, M., Caro, A. & Farkas, D. Competing plastic deformation mechanisms in nanophase metals. Phys. Rev. B 60, 22–25 (1999).

    Article  Google Scholar 

  23. Swygenhoven, H.V., Derlet, P.M. & Hasnaoui, A. Atomic mechanism for dislocation emission from nanosized grain boundaries. Phys. Rev. B 66, 024101 (2002).

    Article  Google Scholar 

  24. Hirth, J.P. & Lothe, J. Theory of Dislocations 1st edn 306–353 (Wiley, New York, 1982).

    Google Scholar 

  25. Yamakov, V., Wolf, D., Phillpot S.R. & Gleiter, H. Grain-boundary diffusion creep in nanocrystalline palladium by molecular-dynamics simulation. Acta Mater. 50, 61–73 (2002).

    Article  CAS  Google Scholar 

  26. Yamakov, V., Wolf, D., Salazar, M., Phillpot S.R. & Gleiter, H. Length-scale effects in the nucleation of extended lattice dislocations in nanocrystalline Al by molecular-dynamics simulation. Acta Mater. 49, 2713–2722 (2001).

    Article  CAS  Google Scholar 

  27. Yamakov V., Wolf D., Phillpot S.R., Mukherjee A.K. & Gleiter H. Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation. Nature Mater. 1, 45–48 (2002).

    Article  CAS  Google Scholar 

  28. Cheng, S., Spencer, J.A. & Milligan, W.W. Strength and tension/compression asymmetry in nanocrystalline and ultrafine-grain metals. Acta Mater. 51, 4505–4518 (2003).

    Article  CAS  Google Scholar 

  29. Li, J.C.M. Petch relation and grain boundary sources. Trans. Metall. Soc. AIME 227, 239–247 (1963).

    CAS  Google Scholar 

  30. Ercolessi, F. & Adams J.B. Interatomic potentials from 1st-principle calculations — the force-matching method. Europhys. Lett. 26, 583–588 (1994).

    Article  CAS  Google Scholar 

  31. Bulatov, V.V., Richmond, O. & Glazo, M.V. An atomistic dislocation mechanism of pressure-dependent plastic flow in aluminum. Acta Mater. 47, 3507–3514 (1999).

    Article  CAS  Google Scholar 

  32. Mukai, T. & Higashi, K. Ductility enhancement of ultra fine-grained aluminium under dynamic loading. Scripta Mater 44, 1493–1496 (2001).

    Article  CAS  Google Scholar 

  33. Ogata, S., Li, J. & Yip, S. Ideal pure shear strength of aluminum and copper. Science 298, 807–811 (2002).

    Article  CAS  Google Scholar 

  34. Wolf, D., Yamakov, V., Phillpot, S.R. & Mukherjee A.K. Deformation mechanism and inverse Hall-Petch behaviour in nanocrystalline materials. Z. Metallkd 94, 1091–1097 (2003).

    Article  CAS  Google Scholar 

  35. Liao, X.Z. et al. A new deformation mechanism in nanocrystalline Al: partial dislocation slip. Appl. Phys. Lett. 83, 632–634 (2003).

    Article  CAS  Google Scholar 

  36. Coble, R.L. A model for boundary diffusion controlled creep in polycrystalline materials. J. Appl. Phys. 34, 1679–1682 (1963).

    Article  Google Scholar 

  37. Foiles, S.M. & Adams, J.B. Thermodynamic properties of fcc transition metals as calculated with the embedded-atom method. Phys. Rev. B 40, 5909–5915 (1989).

    Article  CAS  Google Scholar 

  38. Dillamore, I.L. & Smallman, R.E. The stacking-fault energy of f.c.c. metals. Phil. Mag. 12, 191–193 (1965).

    Article  CAS  Google Scholar 

  39. Parrinello, M. & Rahman, A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 52, 7182–7190 (1981).

    Article  CAS  Google Scholar 

  40. Melchionna, S., Ciccotti, G. & Holian, B.L. Hoover NPT dynamics for systems varying in shape and size. Mol. Phys. 78, 533–544 (1993).

    Article  CAS  Google Scholar 

  41. Clarke, A.S. & Jonsson, H. Structural changes accompanying densification of random hard-sphere packings. Phys. Rev. E 47, 3975–3984 (1993).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

V.Y., D.W. and S.R.P. are supported by the US Department of Energy, BES-Materials Science under contract W-31-109-Eng-38. V.Y. is also grateful for support from the DOE/BES Computational Materials Science Network (CMSN). A.K.M. acknowledges support from NSF-DMR. We are grateful for grants of computer time on the Cray-T3E at the John-von-Neumann-Institute for Computing in Jülich, Germany, and on the Chiba City Linux cluster at Argonne National Laboratory.

Author information

Author notes

  1. V. Yamakov

    Present address: National Institute of Aerospace, Hampton, Virginia, 23666, USA

  2. S. R. Phillpot

    Present address: Department of Materials Science and Engineering, University of Florida, Gainesville, Florida, 32611, USA

Authors and Affiliations

  1. Materials Science Division, Argonne National Laboratory, Argonne, 60439, Illinois, USA

    V. Yamakov, D. Wolf & S. R. Phillpot

  2. Division of Materials Science & Engineering, Department of Chemical Engineering and Materials Science, University of California, Davis, 95616, California, USA

    A. K. Mukherjee

  3. Institut für Nanotechnologie, Forschungszentrum Karlsruhe, Karlsruhe, 76021, Germany

    H. Gleiter

Authors
  1. V. Yamakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Wolf
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. R. Phillpot
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. K. Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H. Gleiter
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Wolf.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yamakov, V., Wolf, D., Phillpot, S. et al. Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation. Nature Mater 3, 43–47 (2004). https://doi.org/10.1038/nmat1035

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat1035

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing