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Scale-dependent pop-ins in nanoindentation and scale-free plastic fluctuations in microcompression

Published online by Cambridge University Press:  10 January 2020

John Shimanek ,
Quentin Rizzardi ,
Gregory Sparks ,
Peter M. Derlet  and
Robert Maaß Open the ORCID record for Robert Maaß [Opens in a new window]
John Shimanek
Affiliation:
Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
Quentin Rizzardi
Affiliation:
Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
Gregory Sparks
Affiliation:
Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
Peter M. Derlet
Affiliation:
Condensed Matter Theory Group, Paul Scherrer Institute, Villigen-PSI 5232, Switzerland
Robert Maaß*
Affiliation:
Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
*
a)Address all correspondence to this author. e-mail: rmaass@illinois.edu
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Abstract

Nanoindentation and microcrystal deformation are two methods that allow probing size effects in crystal plasticity. In many cases of microcrystal deformation, scale-free and potentially universal intermittency of event sizes during plastic flow has been revealed, whereas nanoindentation has been mainly used to assess the stress statistics of the first pop-in. Here, we show that both methods of deformation exhibit fundamentally different event-size statistics obtained from plastic instabilities. Nanoindentation results in scale-dependent intermittent microplasticity best described by Weibull statistics (stress and magnitude of the first pop-in) and lognormal statistics (magnitude of higher-order pop-ins). In contrast, finite-volume microcrystal deformation of the same material exhibits microplastic event-size intermittency of truncated power-law type even when the same plastic volume as in nanoindentation is probed. Furthermore, we successfully test a previously proposed extreme-value statistics model that relates the average first critical stress to the shape and scale parameter of the underlying Weibull distribution.

Keywords

nanoindentationmicrostructurecrystal
Type
Article
Information
Journal of Materials Research , Volume 35 , Issue 2 , 28 January 2020 , pp. 196 - 205
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Copyright
Copyright © Materials Research Society 2020

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References

Maass, R. and Derlet, P.M.: Micro-plasticity and recent insights from intermittent and small-scale plasticity. Acta Mater. 143, 338 (2018).CrossRefGoogle Scholar
Vandenbeukel, A.: Theory of effect of dynamic strain aging on mechanical properties. Phys. Status Solidi A 30, 197 (1975).CrossRefGoogle Scholar
Mulford, R.A. and Kocks, U.F.: New observations on the mechanisms of dynamic strain-aging and of jerky flow. Acta Metall. 27, 1125 (1979).CrossRefGoogle Scholar
Yasuda, H.Y., Shigeno, K., and Nagase, T.: Dynamic strain aging of Al0.3CoCrFeNi high entropy alloy single crystals. Scr. Mater. 108, 80 (2015).CrossRefGoogle Scholar
Maass, R. and Löffler, J.F.: Shear-band dynamics in metallic glasses. Adv. Funct. Mater. 25, 2353 (2015).CrossRefGoogle Scholar
Schmid, E. and Valouch, M.A.: About the sudden translation of zinc crystals. Z. Phys. 75, 531 (1932).CrossRefGoogle Scholar
Becker, R. and Orowan, E.: Sudden expansion of zinc crystals. Z. Phys. 79, 566 (1932).CrossRefGoogle Scholar
Tinder, R.F. and Trzil, J.P.: Millimicroplastic burst phenomena in zinc monocrystals. Acta Metall. 21, 975 (1973).CrossRefGoogle Scholar
Uchic, M.D., Shade, P.A., and Dimiduk, D.M.: Plasticity of micrometer-scale single-crystals in compression. Annu. Rev. Mater. Sci. 39, 361 (2009).CrossRefGoogle Scholar
Sparks, G., Cui, Y., Po, G., Rizzardi, Q., Marian, J., and Maass, R.: Avalanche statistics and the intermittent-to-smooth transition in microplasticity. Phys. Rev. Mater. 3, 080601 (2019).CrossRefGoogle Scholar
Lilleodden, E.T. and Nix, W.D.: Microstructural length-scale effects in the nanoindentation behavior of thin gold films. Acta Mater. 54, 1583 (2006).CrossRefGoogle Scholar
Lorenz, D., Zeckzer, A., Hilpert, U., Grau, P., Johansen, H., and Leipner, H.S.: Pop-in effect as homogeneous nucleation of dislocations during nanoindentation. Phys. Rev. B 67, 172101 (2003).CrossRefGoogle Scholar
Warren, O.L., Downs, S.A., and Wyrobek, T.J.: Challenges and interesting observations associated with feedback-controlled nanoindentation. Z. Metallkd. 95, 287 (2004).CrossRefGoogle Scholar
Shim, S., Bei, H., George, E.P., and Pharr, G.M.: A different type of indentation size effect. Scr. Mater. 59, 1095 (2008).CrossRefGoogle Scholar
Crone, J.C., Munday, L.B., Ramsey, J.J., and Knap, J.: Modeling the effect of dislocation density on the strength statistics in nanoindentation. Modell. Simul. Mater. Sci. Eng. 26, 015009 (2017).CrossRefGoogle Scholar
Barnoush, A., Welsch, M.T., and Vehoff, H.: Correlation between dislocation density and pop-in phenomena in aluminum studied by nanoindentation and electron channeling contrast imaging. Scr. Mater. 63, 465 (2010).CrossRefGoogle Scholar
Zhang, L. and Ohmura, T.: Plasticity initiation and evolution during nanoindentation of an iron–3% silicon crystal. Phys. Rev. Lett. 112 (2014).CrossRefGoogle ScholarPubMed
Sudharshan Phani, P., Johanns, K.E., George, E.P., and Pharr, G.M.: A stochastic model for the size dependence of spherical indentation pop-in. J. Mater. Res. 28, 2728 (2013).CrossRefGoogle Scholar
Schuh, C.A., Mason, J.K., and Lund, A.C.: Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments. Nat. Mater. 4, 617 (2005).CrossRefGoogle ScholarPubMed
Schuh, C.A. and Lund, A.C.: Application of nucleation theory to the rate dependence of incipient plasticity during nanoindentation. J. Mater. Res. 19, 2152 (2004).CrossRefGoogle Scholar
Chiu, Y.L. and Ngan, A.H.W.: Time-dependent characteristics of incipient plasticity in nanoindentation of a Ni3Al single crystal. Acta Mater. 50, 1599 (2002).CrossRefGoogle Scholar
Morris, J.R., Bei, H., Pharr, G.M., and George, E.P.: Size effects and stochastic behavior of nanoindentation pop in. Phys. Rev. Lett. 106, 165502 (2011).CrossRefGoogle ScholarPubMed
Dimiduk, D.M., Woodward, C., LeSar, R., and Uchic, M.D.: Scale-free intermittent flow in crystal plasticity. Science 312, 1188 (2006).CrossRefGoogle ScholarPubMed
Csikor, F.F., Motz, C., Weygand, D., Zaiser, M., and Zapperi, S.: Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science 318, 251 (2007).CrossRefGoogle ScholarPubMed
Zaiser, M., Schwerdtfeger, J., Schneider, A.S., Frick, C.P., Clark, B.G., Gruber, P.A., and Arzt, E.: Strain bursts in plastically deforming molybdenum micro- and nanopillars. Philos. Mag. 88, 3861 (2008).CrossRefGoogle Scholar
Maass, R., Derlet, P.M., and Greer, J.R.: Independence of slip velocities on applied stress in small crystals. Small 11, 341 (2015).CrossRefGoogle ScholarPubMed
Friedman, N., Jennings, A.T., Tsekenis, G., Kim, J-Y., Tao, M., Uhl, J.T., Greer, J.R., and Dahmen, K.A.: Statistics of dislocation slip avalanches in nanosized single crystals show tuned critical behavior predicted by a simple mean field model. Phys. Rev. Lett. 109, 095507 (2012).CrossRefGoogle ScholarPubMed
LeBlanc, M., Angheluta, L., Dahmen, K., and Goldenfeld, N.: Universal fluctuations and extreme statistics of avalanches near the depinning transition. Phys. Rev. E 87, 022126 (2013).CrossRefGoogle ScholarPubMed
Sethna, J.P., Bierbaum, M.K., Dahmen, K.A., Goodrich, C.P., Greer, J.R., Hayden, L.X., Kent-Dobias, J.P., Lee, E.D., Liarte, D.B., Ni, X., Quinn, K.N., Raju, A., Rocklin, D.Z., Shekhawat, A., and Zapperi, S.: Deformation of crystals: Connections with statistical physics. Annu. Rev. Mater. Res. 47, 217 (2017).CrossRefGoogle Scholar
Uhl, J.T., Pathak, S., Schorlemmer, D., Liu, X., Swindeman, R., Brinkman, B.A.W., LeBlanc, M., Tsekenis, G., Friedman, N., Behringer, R., Denisov, D., Schall, P., Gu, X., Wright, W.J., Hufnagel, T., Jennings, A., Greer, J.R., Liaw, P.K., Becker, T., Dresen, G., and Dahmen, K.A.: Universal quake statistics: From compressed nanocrystals to earthquakes. Sci. Rep. 5, 16493 (2015).CrossRefGoogle ScholarPubMed
Sparks, G. and Maass, R.: Shapes and velocity relaxation of dislocation avalanches in Au and Nb microcrystals. Acta Mater. 152, 86 (2018).CrossRefGoogle Scholar
Sparks, G. and Maass, R.: Nontrivial scaling exponents of dislocation avalanches in microplasticity. Phys. Rev. Mater. 2, 120601 (2018).CrossRefGoogle Scholar
Sparks, G. and Maass, R.: Effects of orientation and pre-deformation on velocity profiles of dislocation avalanches in gold microcrystals. Eur. Phys. J. B 92, 15 (2019).CrossRefGoogle Scholar
Niiyama, T. and Shimokawa, T.: Atomistic mechanisms of intermittent plasticity in metals: Dislocation avalanches and defect cluster pinning. Phys. Rev. E 91, 022401 (2015).CrossRefGoogle ScholarPubMed
Brown, L.M.: Power laws in dislocation plasticity. Philos. Mag. 96, 2696 (2016).CrossRefGoogle Scholar
Derlet, P.M. and Maass, R.: The stress statistics of the first pop-in or discrete plastic event in crystal plasticity. J. Appl. Phys. 120, 225101 (2016).CrossRefGoogle Scholar
Maass, R., Wraith, M., Uhl, J.T., Greer, J.R., and Dahmen, K.A.: Slip statistics of dislocation avalanches under different loading modes. Phys. Rev. E 91, 042403 (2015).CrossRefGoogle ScholarPubMed
Alstott, J., Bullmore, E., and Plenz, D.: Powerlaw: A Python package for analysis of heavy-tailed distributions. PLoS One 9, e85777 (2014).CrossRefGoogle ScholarPubMed
Clauset, A., Shalizi, C.R., and Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51, 661 (2009).CrossRefGoogle Scholar
Maass, R., Volkert, C.A., and Derlet, P.M.: Crystal size effect in two dimensions—Influence of size and shape. Scr. Mater. 102, 27 (2015).CrossRefGoogle Scholar
Ispanovity, P.D., Hegyi, A., Groma, I., Gyoergyi, G., Ratter, K., and Weygand, D.: Average yielding and weakest link statistics in micron-scale plasticity. Acta Mater. 61, 6234 (2013).CrossRefGoogle Scholar
Ispánovity, P.D., Tüzes, D., Szabó, P., Zaiser, M., and Groma, I.: Role of weakest links and system-size scaling in multiscale modeling of stochastic plasticity. Phys. Rev. B 95, 054108 (2017).CrossRefGoogle Scholar
Xia, Y., Gao, Y., Pharr, G.M., and Bei, H.: Single versus successive pop-in modes in nanoindentation tests of single crystals. J. Mater. Res. 31, 2065 (2016).CrossRefGoogle Scholar
Papanikolaou, S., Cui, Y., Ghoniem, N.: Avalanches and plastic flow in crystal plasticity: An overview. Modell. Simul. Mater. Sci. Eng. 26, 013001 (2018).CrossRefGoogle Scholar
LeBlanc, M., Nawano, A., Wright, W.J., Gu, X., Uhl, J.T., and Dahmen, K.A.: Avalanche statistics from data with low time resolution. Phys. Rev. E 94, 052135 (2016).CrossRefGoogle ScholarPubMed
Norfleet, D.M., Dimiduk, D.M., Polasik, S.J., Uchic, M.D., and Mills, M.J.: Dislocation structures and their relationship to strength in deformed nickel microcrystals. Acta Mater. 56, 2988 (2008).CrossRefGoogle Scholar
Maass, R. and Uchic, M.D.: In situ characterization of the dislocation-structure evolution in Ni micro-pillars. Acta Mater. 60, 1027 (2012).CrossRefGoogle Scholar
Oh, S.H., Legros, M., Kiener, D., and Dehm, G.: In situ observation of dislocation nucleation and escape in a submicrometre aluminium single crystal. Nat. Mater. 8, 95 (2009).CrossRefGoogle Scholar
Zaafarani, N., Raabe, D., Roters, F., and Zaefferer, S.: On the origin of deformation-induced rotation patterns below nanoindents. Acta Mater. 56, 31 (2008).CrossRefGoogle Scholar
Metz, F.I.: Electropolishing of metals. Retrospective theses and dissertations, Iowa State University, Paper 2622, 1960.Google Scholar