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Indentation response of nanoporous gold from atomistic simulations

Published online by Cambridge University Press:  10 April 2018

Diana Farkas ,
Joshua Stuckner ,
Rachel Umbel ,
Bryan Kuhr  and
Michael J. Demkowicz
Diana Farkas*
Affiliation:
Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA
Joshua Stuckner
Affiliation:
Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA
Rachel Umbel
Affiliation:
Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA
Bryan Kuhr
Affiliation:
Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA
Michael J. Demkowicz
Affiliation:
Department of Materials Science and Engineering, Texas A&M University, College Station, Texas 77843, USA
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

We present classical potential molecular dynamics simulations of nanoporous gold (np-Au) impacted by a spherical indenter. The atomic structure was generated using a phase field model as a template. In agreement with previous experiments, we observe densification in the region under the indenter. The hardness values obtained from our simulations exhibit a transition from an initially perfect-plastic plateau to hardening behavior in the later stages of indentation. This transition occurs when the relative density beneath the indenter exceeds ∼0.9. Hardness values obtained from the nanoindentation simulations reach 0.6 GPa, due to the densification of the material under the indenter. Elevated dislocation densities are observed in the densified region. The mechanism of pore collapse in the densified layer under the indenter is seen to switch from uniaxial to triaxial, consistent with a change in deformation mechanism from one based on shearing of individual ligaments in np-Au to one involving dislocation-mediated plasticity around voids in a Au single crystal undergoing uniaxial compression.

Keywords

foamnanoindentationnanostructure
Type
Article
Information
Journal of Materials Research , Volume 33 , Issue 10 , 28 May 2018 , pp. 1382 - 1390
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Copyright
Copyright © Materials Research Society 2018 

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References

REFERENCES

Biener, J., Hodge, A.M., Hamza, A.V., Hsiung, L.M., and Satcher, J.H.: Nanoporous Au: A high yield strength material. J. Appl. Phys. 97, 4 (2005).CrossRefGoogle Scholar
Weissmuller, J., Newman, R.C., Jin, H.J., Hodge, A.M., and Kysar, J.W.: Nanoporous metals by alloy corrosion: Formation and mechanical properties. MRS Bull. 34, 577 (2009).CrossRefGoogle Scholar
Mameka, N., Markmann, J., and Weissmüller, J.: On the impact of capillarity for strength at the nanoscale. Nat. Commun. 8, 1976 (2017).Google Scholar
Mameka, N., Wang, K., Markmann, J., Lilleodden, E.T., and Weissmüller, J.: Nanoporous gold—Testing macro-scale samples to probe small-scale mechanical behavior. Mater. Res. Lett. 4, 27 (2016).Google Scholar
McCue, I., Ryan, S., Hemker, K., Xu, X.D., Li, N., Chen, M.W., and Erlebacher, J.: Size effects in the mechanical properties of bulk bicontinuous Ta/Cu nanocomposites made by liquid metal dealloying. Adv. Eng. Mater. 18, 46 (2016).Google Scholar
Miyazawa, N., Ishimoto, J., Hakamada, M., and Mabuchi, M.: Mechanical characterization of nanoporous Au modified with self-assembled monolayers. Appl. Phys. Lett. 109, 261905 (2016).Google Scholar
Roschning, B. and Huber, N.: Scaling laws of nanoporous gold under uniaxial compression: Effects of structural disorder on the solid fraction, elastic Poisson’s ratio, Young’s modulus and yield strength. J. Mech. Phys. Solids 92, 55 (2016).Google Scholar
Hodge, A.M., Hayes, J.R., Caro, J.A., Biener, J., and Hamza, A.V.: Characterization and mechanical behavior of nanoporous gold. Adv. Eng. Mater. 8, 853 (2006).Google Scholar
Volkert, C.A. and Lilleodden, E.T.: Size effects in the deformation of sub-micron Au columns. Philos. Mag. 86, 5567 (2006).Google Scholar
Volkert, C.A., Lilleodden, E.T., Kramer, D., and Weissmuller, J.: Approaching the theoretical strength in nanoporous Au. Appl. Phys. Lett. 89, 061920 (2006).Google Scholar
Ruestes, C.J., Farkas, D., Caro, A., and Bringa, E.M.: Hardening under compression in Au foams. Acta Mater. 108, 1 (2016).CrossRefGoogle Scholar
Balk, T.J., Eberl, C., Sun, Y., Hemker, K.J., and Gianola, D.S.: Tensile and compressive microspecimen testing of bulk nanoporous gold. JOM 61, 26 (2009).CrossRefGoogle Scholar
Hakamada, M. and Mabuchi, M.: Mechanical strength of nanoporous gold fabricated by dealloying. Scr. Mater. 56, 1003 (2007).Google Scholar
Hodge, A.M., Biener, J., Hayes, J.R., Bythrow, P.M., Volkert, C.A., and Hamza, A.V.: Scaling equation for yield strength of nanoporous open-cell foams. Acta Mater. 55, 1343 (2007).CrossRefGoogle Scholar
Jin, H.J., Kramer, D., Ivanisenko, Y., and Weissmuller, J.: Macroscopically strong nanoporous Pt prepared by dealloying. Adv. Eng. Mater. 9, 849 (2007).CrossRefGoogle Scholar
Mathur, A. and Erlebacher, J.: Size dependence of effective Young’s modulus of nanoporous gold. Appl. Phys. Lett. 90, 061910 (2007).Google Scholar
Liu, R. and Antoniou, A.: A relationship between the geometrical structure of a nanoporous metal foam and its modulus. Acta Mater. 61, 2390 (2013).CrossRefGoogle Scholar
Sun, X-Y., Xu, G-K., Li, X., Feng, X-Q., and Gao, H.: Mechanical properties and scaling laws of nanoporous gold. J. Appl. Phys. 113, 023505 (2013).Google Scholar
Liu, L.Z., Ye, X.L., and Jin, H.J.: Interpreting anomalous low-strength and low-stiffness of nanoporous gold: Quantification of network connectivity. Acta Mater. 118, 77 (2016).Google Scholar
Liu, R., Gruber, J., Bhattacharyya, D., Tucker, G.J., and Antoniou, A.: Mechanical properties of nanocrystalline nanoporous platinum. Acta Mater. 103, 624 (2016).CrossRefGoogle Scholar
Luhrs, L., Soyarslan, C., Markmann, J., Bargmann, S., and Weissmuller, J.: Elastic and plastic Poisson’s ratios of nanoporous gold. Scr. Mater. 110, 65 (2016).Google Scholar
Mangipudi, K.R., Epler, E., and Volkert, C.A.: Topology-dependent scaling laws for the stiffness and strength of nanoporous gold. Acta Mater. 119, 115 (2016).Google Scholar
Gibson, L.J. and Ashby, M.F.: Cellular Solids: Structure and Properties, 2nd ed. (Cambridge University Press, Cambridge, U.K., 1997).CrossRefGoogle Scholar
Gibson, L.J. and Ashby, M.F.: The mechanics of three-dimensional cellular materials. Proc. R. Soc. London, Ser. A 382, 43 (1982).Google Scholar
Wu, B., Heidelberg, A., and Boland, J.J.: Mechanical properties of ultrahigh-strength gold nanowires. Nat. Mater. 4, 525 (2005).Google Scholar
Weinberger, C.R. and Cai, W.: Plasticity of metal nanowires. J. Mater. Chem. 22, 3277 (2012).Google Scholar
Liang, H., Upmanyu, M., and Huang, H.: Size-dependent elasticity of nanowires: Nonlinear effects. Phys. Rev. B 71, 241403 (2005).CrossRefGoogle Scholar
Dou, R. and Derby, B.: Deformation mechanisms in gold nanowires and nanoporous gold. Philos. Mag. 91, 1070 (2011).Google Scholar
Diao, J.K., Gall, K., Dunn, M.L., and Zimmerman, J.A.: Atomistic simulations of the yielding of gold nanowires. Acta Mater. 54, 643 (2006).Google Scholar
Diao, J.K., Gall, K., and Dunn, M.L.: Atomistic simulation of the structure and elastic properties of gold nanowires. J. Mech. Phys. Solids 52, 1935 (2004).Google Scholar
Hyde, B., Espinosa, H.D., and Farkas, D.: An atomistic investigation of elastic and plastic properties of Au nanowires. JOM 57, 62 (2005).Google Scholar
Rodriguez-Nieva, J.F., Ruestes, C.J., Tang, Y., and Bringa, E.M.: Atomistic simulation of the mechanical properties of nanoporous gold. Acta Mater. 80, 67 (2014).Google Scholar
Crowson, D.A., Farkas, D., and Corcoran, S.G.: Geometric relaxation of nanoporous metals: The role of surface relaxation. Scr. Mater. 56, 919 (2007).CrossRefGoogle Scholar
Crowson, D.A., Farkas, D., and Corcoran, S.G.: Mechanical stability of nanoporous metals with small ligament sizes. Scr. Mater. 61, 497 (2009).Google Scholar
Kolluri, K. and Demkowicz, M.J.: Coarsening by network restructuring in model nanoporous gold. Acta Mater. 59, 7645 (2011).CrossRefGoogle Scholar
Ngo, B.N.D., Roschning, B., Albe, K., Weissmuller, J., and Markmann, J.: On the origin of the anomalous compliance of dealloying-derived nanoporous gold. Scr. Mater. 130, 74 (2017).Google Scholar
Ngô, B-N.D., Stukowski, A., Mameka, N., Markmann, J., Albe, K., and Weissmüller, J.: Anomalous compliance and early yielding of nanoporous gold. Acta Mater. 93, 144 (2015).Google Scholar
Biener, J., Hodge, A.M., Hayes, J.R., Volkert, C.A., Zepeda-Ruiz, L.A., Hamza, A.V., and Abraham, F.F.: Size effects on the mechanical behavior of nanoporous Au. Nano Lett. 6, 2379 (2006).Google Scholar
Farkas, D., Caro, A., Bringa, E., and Crowson, D.: Mechanical response of nanoporous gold. Acta Mater. 61, 3249 (2013).CrossRefGoogle Scholar
Cahn, J.W. and Hilliard, J.E.: Free energy of a nonuniform system. III. Nucleation in a 2-component incompressible fluid. J. Chem. Phys. 31, 688 (1959).Google Scholar
Erlebacher, J., Aziz, M.J., Karma, A., Dimitrov, N., and Sieradzki, K.: Evolution of nanoporosity in dealloying. Nature 410, 450 (2001).Google Scholar
Plimpton, S.: Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117, 1 (1995).Google Scholar
Daw, M.S. and Baskes, M.I.: Embedded-atom method—Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443 (1984).Google Scholar
Foiles, S.M., Baskes, M.I., and Daw, M.S.: Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33, 7983 (1986).Google Scholar
Farkas, D.: Atomistic simulations of metallic microstructures. Curr. Opin. Solid State Mater. Sci. 17, 284 (2013).Google Scholar
Stukowski, A.: Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).CrossRefGoogle Scholar
Stukowski, A. and Albe, K.: Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Modell. Simul. Mater. Sci. Eng. 18, 085001 (2010).CrossRefGoogle Scholar
Kelchner, C.L., Plimpton, S.J., and Hamilton, J.C.: Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, 11085 (1998).Google Scholar
Stuckner, J., Frei, K., McCue, I., Demkowicz, M.J., and Murayama, M.: AQUAMI: An open source Python package and GUI for the automatic quantitative analysis of morphologically complex multiphase materials. Comput. Mater. Sci. 139, 320 (2017).Google Scholar
Badwe, N., Chen, X.Y., and Sieradzki, K.: Mechanical properties of nanoporous gold in tension. Acta Mater. 129, 251 (2017).Google Scholar
Field, J.S. and Swain, M.V.: Determining the mechanical properties of small volumes of material from submicrometer spherical indentations. J. Mater. Res. 10, 101 (1995).Google Scholar
Herbert, E.G., Pharr, G.M., Oliver, W.C., Lucas, B.N., and Hay, J.L.: On the measurement of stress–strain curves by spherical indentation. Thin Solid Films 398–399, 331 (2001).CrossRefGoogle Scholar
Jin, H.J., Kurmanaeva, L., Schmauch, J., Rosner, H., Ivanisenko, Y., and Weissmuller, J.: Deforming nanoporous metal: Role of lattice coherency. Acta Mater. 57, 2665 (2009).Google Scholar
Nix, W.D.: Nanoscale gold pillars strengthened through dislocation starvation. Phys. Rev. B 73, 245410 (2006).Google Scholar
Kocks, U.F. and Mecking, H.: Physics and phenomenology of strain hardening: The FCC case. Prog. Mater. Sci. 48, 171 (2003).Google Scholar
Carroll, M.M. and Holt, A.C.: Static and dynamic pore—Collapse relations for ductile porous materials. J. Appl. Phys. 43, 1626 (1972).Google Scholar
Davila, L.P., Erhart, P., Bringa, E.M., Meyers, M.A., Lubarda, V.A., Schneider, M.S., Becker, R., and Kumar, M.: Atomistic modeling of shock-induced void collapse in copper. Appl. Phys. Lett. 86, 1619021 (2005).Google Scholar
Tang, Y., Bringa, E., Remington, B., and Meyers, M.: Growth and collapse of nanovoids in tantalum monocrystals. Acta Mater. 59, 1354 (2011).Google Scholar
Bulatov, V.V., Wolfer, W.G., and Kumar, M.: Shear impossibility: Comments on “Void growth by dislocation emission” and Void growth in metals: Atomistic calculations. Scr. Mater. 63, 144 (2010).Google Scholar
Torquato, S.: Random Heterogeneous Materials (Springer, New York, NY, 2002).Google Scholar
Schuh, C.A., Hufnagel, T.C., and Ramamurty, U.: Mechanical behavior of amorphous alloys. Acta Mater. 55, 4067 (2007).Google Scholar
Maaß, R. and Löffler, J.F.: Shear-band dynamics in metallic glasses. Adv. Funct. Mater. 25, 2353–2368 (2015).Google Scholar