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

  • John Shimanek (a1), Quentin Rizzardi (a1), Gregory Sparks (a1), Peter M. Derlet (a2) and Robert Maaß (a1)...


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.


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1.Maass, R. and Derlet, P.M.: Micro-plasticity and recent insights from intermittent and small-scale plasticity. Acta Mater. 143, 338 (2018).
2.Vandenbeukel, A.: Theory of effect of dynamic strain aging on mechanical properties. Phys. Status Solidi A 30, 197 (1975).
3.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).
4.Yasuda, H.Y., Shigeno, K., and Nagase, T.: Dynamic strain aging of Al0.3CoCrFeNi high entropy alloy single crystals. Scr. Mater. 108, 80 (2015).
5.Maass, R. and Löffler, J.F.: Shear-band dynamics in metallic glasses. Adv. Funct. Mater. 25, 2353 (2015).
6.Schmid, E. and Valouch, M.A.: About the sudden translation of zinc crystals. Z. Phys. 75, 531 (1932).
7.Becker, R. and Orowan, E.: Sudden expansion of zinc crystals. Z. Phys. 79, 566 (1932).
8.Tinder, R.F. and Trzil, J.P.: Millimicroplastic burst phenomena in zinc monocrystals. Acta Metall. 21, 975 (1973).
9.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).
10.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).
11.Lilleodden, E.T. and Nix, W.D.: Microstructural length-scale effects in the nanoindentation behavior of thin gold films. Acta Mater. 54, 1583 (2006).
12.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).
13.Warren, O.L., Downs, S.A., and Wyrobek, T.J.: Challenges and interesting observations associated with feedback-controlled nanoindentation. Z. Metallkd. 95, 287 (2004).
14.Shim, S., Bei, H., George, E.P., and Pharr, G.M.: A different type of indentation size effect. Scr. Mater. 59, 1095 (2008).
15.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).
16.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).
17.Zhang, L. and Ohmura, T.: Plasticity initiation and evolution during nanoindentation of an iron–3% silicon crystal. Phys. Rev. Lett. 112 (2014).
18.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).
19.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).
20.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).
21.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).
22.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).
23.Dimiduk, D.M., Woodward, C., LeSar, R., and Uchic, M.D.: Scale-free intermittent flow in crystal plasticity. Science 312, 1188 (2006).
24.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).
25.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).
26.Maass, R., Derlet, P.M., and Greer, J.R.: Independence of slip velocities on applied stress in small crystals. Small 11, 341 (2015).
27.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).
28.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).
29.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).
30.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).
31.Sparks, G. and Maass, R.: Shapes and velocity relaxation of dislocation avalanches in Au and Nb microcrystals. Acta Mater. 152, 86 (2018).
32.Sparks, G. and Maass, R.: Nontrivial scaling exponents of dislocation avalanches in microplasticity. Phys. Rev. Mater. 2, 120601 (2018).
33.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).
34.Niiyama, T. and Shimokawa, T.: Atomistic mechanisms of intermittent plasticity in metals: Dislocation avalanches and defect cluster pinning. Phys. Rev. E 91, 022401 (2015).
35.Brown, L.M.: Power laws in dislocation plasticity. Philos. Mag. 96, 2696 (2016).
36.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).
37.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).
38.Alstott, J., Bullmore, E., and Plenz, D.: Powerlaw: A Python package for analysis of heavy-tailed distributions. PLoS One 9, e85777 (2014).
39.Clauset, A., Shalizi, C.R., and Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51, 661 (2009).
40.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).
41.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).
42.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).
43.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).
44.Papanikolaou, S., Cui, Y., Ghoniem, N.: Avalanches and plastic flow in crystal plasticity: An overview. Modell. Simul. Mater. Sci. Eng. 26, 013001 (2018).
45.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).
46.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).
47.Maass, R. and Uchic, M.D.: In situ characterization of the dislocation-structure evolution in Ni micro-pillars. Acta Mater. 60, 1027 (2012).
48.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).
49.Zaafarani, N., Raabe, D., Roters, F., and Zaefferer, S.: On the origin of deformation-induced rotation patterns below nanoindents. Acta Mater. 56, 31 (2008).
50.Metz, F.I.: Electropolishing of metals. Retrospective theses and dissertations, Iowa State University, Paper 2622, 1960.


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

  • John Shimanek (a1), Quentin Rizzardi (a1), Gregory Sparks (a1), Peter M. Derlet (a2) and Robert Maaß (a1)...


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