Continuous strain bursts in crystalline and amorphous metals during plastic deformation by nanoindentation


Using depth-sensing indentation with sub-nanometer displacement resolution, the plastic deformation of a range of materials, including a metallic glass, amorphous selenium, Ni3Al, pure Nb, Al, Cu, and Zn metals, and an Al-Mg alloy, has been investigated at room temperature. In amorphous selenium, even the sub-nanometer displacement resolution of the nanoindentation technique cannot reveal any strain burst during deformation at room temperature. In all other metals studied, what may appear to be smooth load-displacement curves at macroscopic scale during indentation deformation in fact turn out to consist of a continuous series of random bursts of the nanometer scale. The occurrence probability of the bursts is found to decrease at increasing burst size. In all of the crystalline metals and alloys studied, the size distribution of the strain bursts seems to follow an exponential law with a characteristic length scale. The absence of the self-organized critical behavior is likely a result of the small size of the strained volume in the nanoindentation situation, which gives rise to a constraint of a characteristic strain. In the metallic glass sample, due to the limited range of the burst sizes encountered, whether the deformation bursts follow an exponential or a power-law behavior corresponding to self-organized criticality is inconclusive. From a theoretical viewpoint based on the Shannon entropy, the exponential distribution is the most likely distribution at a given mean burst size, and this is thought to be the reason for its occurrence in different materials.

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


  1. 1.

    P. Bak, C. Tang and K. Wiesenfeld: Self-organized criticality: An explanation of 1/f noise. Phys. Rev. Lett. 59, 381 (1987).

    CAS  Article  Google Scholar 

  2. 2.

    P. Bak: How Nature Works (Springer-Verlag, Berlin, Germany, 1996).

    Google Scholar 

  3. 3.

    De J.T. Hosson.M., G. Boom, U. Schlagowski and O. Kanert: Solution hardening in Al-Zn alloys. Acta Metall. 34, 1571 (1986).

    Article  Google Scholar 

  4. 4.

    M.-C. Miguel, A. Vespingnani, S. Zapperi, J. Weiss and J.-R. Grasso: Intermittent dislocation flow in viscoplastic deformation. Nature 410, 667 (2001).

    CAS  Article  Google Scholar 

  5. 5.

    P. Häfner, K. Bay and M. Zaiser: Fractal dislocation patterning during plastic deformation. Phys. Rev. Lett. 81, 2470 (1998).

    Article  Google Scholar 

  6. 6.

    M. Zaiser, K. Bay and P. Häfner: Fractal analysis of deformation-induced dislocation patterns. Acta Mater. 47, 2463 (1999).

    CAS  Article  Google Scholar 

  7. 7.

    A.H.W. Ngan: Dislocation patterning—A statistical mechanics perspective. Scripta Mate. 52, 1005 (2005).

    CAS  Article  Google Scholar 

  8. 8.

    Y. Golovin.I., V.I. Ivolgin, V.A. Khonik, K. Kitagawa and A.I. Tyurin: Serrated plastic flow during nanoindentation of a bulk metallic glass. Scripta Mater. 45, 947 (2001).

    Article  Google Scholar 

  9. 9.

    T.G. Nieh, C. Schuh, J. Wadsworth and Y. Li: Strain rate-dependent deformation in bulk metallic glasses. Intermetallics 10, 1177 (2002).

    CAS  Article  Google Scholar 

  10. 10.

    C.A. Schuh, T.G. Nieh and Y. Kawamura: Rate dependence of serrated flow during nanoindentation of a bulk metallic glass. J. Mater. Res. 17, 1651 (2002).

    CAS  Article  Google Scholar 

  11. 11.

    C.A. Schuh, A.S. Argon, T.G. Nieh and J. Wadsworth: The transition from localized to homogeneous plasticity during nanoindentation of an amorphous metal. Philos. Mag. 83, 2585 (2003).

    CAS  Article  Google Scholar 

  12. 12.

    C.A. Schuh and T.G. Nieh: A nanoindentation study of serrated flow in bulk metallic glasses. Acta Mater. 51, 87 (2003).

    CAS  Article  Google Scholar 

  13. 13.

    A. Savitzky and M.J.E. Golay: Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627 (1964).

    CAS  Article  Google Scholar 

  14. 14.

    A.F. Bower, N.A. Fleck, A. Needleman and N. Ogbonna: Indentation of a power law creeping solid. Proc. R. Soc. London, Ser. A 441, 97 (1993).

    Article  Google Scholar 

  15. 15.

    B. Tang and A.H.W. Ngan Measurement of viscoelastic properties of amorphous selenium using depth-sensing indentation. To appear in Soft Mater. 2, 125 (2005).

    Article  Google Scholar 

  16. 16.

    Y.I. Golovin, V.I. Ivolgin and M.A. Lebedkin: Unstable plastic flow in the Al-3%Mg alloy in the process of continuous nanoindentation. Phys. Solid State 44, 1310 (2002).

    CAS  Article  Google Scholar 

  17. 17.

    G. Bérces, J. Lendvai, A. Juhász and N.Q. Chinh: Dynamic characterization of Portevin-Le Châtelier instabilities occurring in depth-sensing microhardness tests. J. Mater. Res. 18, 2874 (2003).

    Article  Google Scholar 

  18. 18.

    W.A. Soer, De J.T. Hosson.M., A.M. Minor, J.W. Morris Jr. and E.A. Stach: Effects of solute Mg on grain boundary and dislocation dynamics during nanoindentation of Al-Mg thin films. Acta Mater. 52, 5783 (2004).

    CAS  Article  Google Scholar 

  19. 19.

    N.Q. Chinh, J. Gubicza, Z. Kovács. and J. Lendvai: Depth-sensing indentation tests in studying plastic instabilities. J. Mater. Res. 19, 31 (2004).

    CAS  Article  Google Scholar 

  20. 20.

    Z. Kovács., N.Q. Chinh, J. Lendvai and G. Vörös: Portevin–Le Châtelier type plastic instabilities in depth sensing macro-indentation. Mater. Sci. Eng. A325, 255 (2002).

    Article  Google Scholar 

  21. 21.

    P.B. Hirsch: A model of the anomalous yield stress for (111) slip in L12 alloys. Prog. Mater. Sci. 36, 63 (1992).

    CAS  Article  Google Scholar 

  22. 22.

    A.H.W. Ngan, M. Wen and C.H. Woo: Atomistic simulations of Paidar–Pope–Vitek lock formation in Ni3Al. Comput. Mater. Sci. 29, 259 (2004).

    CAS  Article  Google Scholar 

  23. 23.

    A.H.W. Ngan and M. Wen: Dislocation kink-pair energetics and pencil glide in body-centered-cubic crystals. Phys. Rev. Lett. 87, 075505 (2001).

    CAS  Article  Google Scholar 

  24. 24.

    D. Caillard and A. Couret: Dislocation movements controlled by friction forces and local pinning in metals and alloys. Mater. Sci. Eng. A322, 108 (2002).

    CAS  Article  Google Scholar 

  25. 25.

    G. Molenat and D. Caillard: Dislocation mechanisms in Ni3Al at room-temperature—In situ straining experiments in TEM. Philos. Mag. A 64, 1291 (1991).

    CAS  Article  Google Scholar 

  26. 26.

    C.E. Shannon: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379 623–656(1948).

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to A. H. W. Ngan.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Li, H., Ngan, A.H.W. & Wang, M.G. Continuous strain bursts in crystalline and amorphous metals during plastic deformation by nanoindentation. Journal of Materials Research 20, 3072–3081 (2005).

Download citation