Skip to main content Accessibility help

Anomalous size effects in nanoporous materials induced by high surface energies

  • Justin W. Wilkerson (a1)


Several experiments and molecular dynamics calculations have reported anomalous mechanical behaviors of nanoporous materials that may be attributed to capillary effects. For example, nanoporous gold exhibits a tension–compression asymmetry in yield strength with the material being stronger in compression than tension. In addition, some molecular dynamics calculations have reported a spontaneous collapse of pores in nanoporous gold with nanometer-sized ligaments. Despite these perplexing observations, there are few theoretical models capable of shedding light on such capillary phenomena, particularly under general stress states. Here, we utilize a physics-based model to explore the implications of high surface energies on the mechanical response of dislocation-starved nanoporous materials subject to general stress states. For low stress triaxialities, we report an anomalous size effect and an anomalous temperature-dependence of dislocation-starved nanoporous materials with sufficiently large surface energies. Additionally, we provide an analytic criterion for spontaneous pore collapse in nanoporous materials with nanometer-sized ligaments.


Corresponding author

a)Address all correspondence to this author. e-mail:


Hide All
1.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, 23792382 (2006).
2.Volkert, C.A. and Lilleodden, E.T.: Size effects in the deformation of sub-micron au columns. Philos. Mag. 86, 55675579 (2006).
3.Hodge, A., Biener, J., Hayes, J., Bythrow, P., Volkert, C., and Hamza, A.: Scaling equation for yield strength of nanoporous open-cell foams. Acta Mater. 55, 13431349 (2007).
4.Ashby, M.F. and Gibson, L.J.: Cellular Solids: Structure and Properties (Press Syndicate of the University of Cambridge, Cambridge, U.K., 1997); p. 183e231.
5.Volkert, C., Lilleodden, E., Kramer, D., and Weissmüller, J.: Approaching the theoretical strength in nanoporous au. Appl. Phys. Lett. 89, 061920 (2006).
6.Briot, N.J., Kennerknecht, T., Eberl, C., and Balk, T.J.: Mechanical properties of bulk single crystalline nanoporous gold investigated by millimetre-scale tension and compression testing. Philos. Mag. 94, 847866 (2014).
7.Dou, R. and Derby, B.: Deformation mechanisms in gold nanowires and nanoporous gold. Philos. Mag. 91, 10701083 (2011).
8.Dou, R. and Derby, B.: A universal scaling law for the strength of metal micropillars and nanowires. Scr. Mater. 61, 524527 (2009).
9.El-Awady, J.A.: Unravelling the physics of size-dependent dislocation-mediated plasticity. Nat. Commun. 6, 5926 (2015).
10.McCue, I., Benn, E., Gaskey, B., and Erlebacher, J.: Dealloying and dealloyed materials. Annu. Rev. Mater. Res. 46, 263286 (2016).
11.Jin, H-J., Kurmanaeva, L., Schmauch, J., Rösner, H., Ivanisenko, Y., and Weissmüller, J.: Deforming nanoporous metal: Role of lattice coherency. Acta Mater. 57, 26652672 (2009).
12.Liu, R. and Antoniou, A.: A relationship between the geometrical structure of a nanoporous metal foam and its modulus. Acta Mater. 61, 23902402 (2013).
13.Wang, K., Hartig, C., Blankenburg, M., Müller, M., Günther, R., and Weissmüller, J.: Local flow stresses in interpenetrating-phase composites based on nanoporous gold—In situ diffraction. Scr. Mater. 127, 151155 (2017).
14.Jin, H-J., Weissmüller, J., and Farkas, D.: Mechanical response of nanoporous metals: A story of size, surface stress, and severed struts. MRS Bull. 43, 3542 (2018).
15.Huber, N., Viswanath, R., Mameka, N., Markmann, J., and Weißmüller, J.: Scaling laws of nanoporous metals under uniaxial compression. Acta Mater. 67, 252265 (2014).
16.Briot, N.J. and Balk, T.J.: Developing scaling relations for the yield strength of nanoporous gold. Philos. Mag. 95, 29552973 (2015).
17.Mangipudi, K., Epler, E., and Volkert, C.: Topology-dependent scaling laws for the stiffness and strength of nanoporous gold. Acta Mater. 119, 115122 (2016).
18.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, 5571 (2016).
19.Reina, C., Marian, J., and Ortiz, M.: Nanovoid nucleation by vacancy aggregation and vacancy-cluster coarsening in high-purity metallic single crystals. Phys. Rev. B 84, 104117 (2011).
20.Wilkerson, J.: On the micromechanics of void dynamics at extreme rates. Int. J. Plast. 95, 2142 (2017).
21.Lubarda, V., Schneider, M., Kalantar, D., Remington, B., and Meyers, M.: Void growth by dislocation emission. Acta Mater. 52, 13971408 (2004).
22.Belak, J.: On the nucleation and growth of voids at high strain-rates. J. Comput.-Aided Mater. Des. 5, 193206 (1998).
23.Rudd, R.E. and Belak, J.F.: Void nucleation and associated plasticity in dynamic fracture of polycrystalline copper: An atomistic simulation. Comput. Mater. Sci. 24, 148153 (2002).
24.Seppälä, E., Belak, J., and Rudd, R.: Effect of stress triaxiality on void growth in dynamic fracture of metals: A molecular dynamics study. Phys. Rev. B 69, 134101 (2004).
25.Traiviratana, S., Bringa, E.M., Benson, D.J., and Meyers, M.A.: Void growth in metals: Atomistic calculations. Acta Mater. 56, 38743886 (2008).
26.Meyers, M.A., Traiviratana, S., Lubarda, V., Benson, D.J., and Bringa, E.M.: The role of dislocations in the growth of nanosized voids in ductile failure of metals. JOM 61, 3541 (2009).
27.Bringa, E.M., Traiviratana, S., and Meyers, M.A.: Void initiation in fcc metals: Effect of loading orientation and nanocrystalline effects. Acta Mater. 58, 44584477 (2010).
28.Tang, Y., Bringa, E.M., Remington, B.A., and Meyers, M.A.: Growth and collapse of nanovoids in tantalum monocrystals. Acta Mater. 59, 13541372 (2011).
29.Ariza, M., Romero, I., Ponga, M., and Ortiz, M.: HotQC simulation of nanovoid growth under tension in copper. Int. J. Fract. 174, 7585 (2012).
30.Lubarda, V.A.: Emission of dislocations from nanovoids under combined loading. Int. J. Plast. 27, 181200 (2011).
31.Wilkerson, J. and Ramesh, K.: A closed-form criterion for dislocation emission in nano-porous materials under arbitrary thermomechanical loading. J. Mech. Phys. Solids 86, 94116 (2016).
32.Ye, X-L. and Jin, H-J.: Electrochemical control of creep in nanoporous gold. Appl. Phys. Lett. 103, 201912 (2013).
33.Lührs, L., Zandersons, B., Huber, N., and Weissmüller, J.: Plastic Poisson’s ratio of nanoporous metals: A macroscopic signature of tension–compression asymmetry at the nanoscale. Nano Lett. 17, 62586266 (2017).
34.Mameka, N., Markmann, J., and Weissmüller, J.: On the impact of capillarity for strength at the nanoscale. Nat. Commun. 8, 1976 (2017).
35.Farkas, D., Caro, A., Bringa, E., and Crowson, D.: Mechanical response of nanoporous gold. Acta Mater. 61, 32493256 (2013).
36.Crowson, D.A., Farkas, D., and Corcoran, S.G.: Geometric relaxation of nanoporous metals: The role of surface relaxation. Scr. Mater. 56, 919922 (2007).
37.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, 144155 (2015).
38.Weinberger, C.R. and Cai, W.: Plasticity of metal nanowires. J. Mater. Chem. 22, 32773292 (2012).
39.Diao, J., Gall, K., and Dunn, M.L.: Yield strength asymmetry in metal nanowires. Nano Lett. 4, 18631867 (2004).
40.Diao, J., Gall, K., Dunn, M.L., and Zimmerman, J.A.: Atomistic simulations of the yielding of gold nanowires. Acta Mater. 54, 643653 (2006).
41.Peng, J., Jing, F., Li, D., and Wang, L.: Pressure and temperature dependence of shear modulus and yield strength for aluminum, copper, and tungsten under shock compression. J. Appl. Phys. 98, 013508 (2005).
42.Wilkerson, J.: Multiscale mechanics of failure in extreme environments. Ph.D. thesis, Johns Hopkins University, Baltimore, MD, 2014.
43.Vitos, L., Ruban, A., Skriver, H.L., and Kollar, J.: The surface energy of metals. Surf. Sci. 411, 186202 (1998).
44.Zhao, K., Fan, L., and Chen, C.: Multiaxial behavior of nanoporous single crystal copper: A molecular dynamics study. Acta Mech. Solida Sin. 22, 650656 (2009).
45.Iskandarov, A.M., Dmitriev, S.V., and Umeno, Y.: Temperature effect on ideal shear strength of Al and Cu. Phys. Rev. B 84, 224118 (2011).
46.Udin, H., Shaler, A., and Wulff, J.: The surface tension of solid copper. JOM 1, 186190 (1949).
47.Buttner, F., Udin, H., and Wulff, J.: Surface tension of solid gold. JOM 3, 12091211 (1951).
48.Diao, J., Gall, K., and Dunn, M.L.: Surface-stress-induced phase transformation in metal nanowires. Nat. Mater. 2, 656 (2003).
49.Liang, W., Zhou, M., and Ke, F.: Shape memory effect in cu nanowires. Nano Lett. 5, 20392043 (2005).
50.Crowson, D.A., Farkas, D., and Corcoran, S.G.: Mechanical stability of nanoporous metals with small ligament sizes. Scr. Mater. 61, 497499 (2009).
51.Parida, S., Kramer, D., Volkert, C., Rösner, H., Erlebacher, J., and Weissmüller, J.: Volume change during the formation of nanoporous gold by dealloying. Phys. Rev. Lett. 97, 035504 (2006).
52.Rice, J.R. and Thomson, R.: Ductile versus brittle behaviour of crystals. Philos. Mag. 29, 7397 (1974).
53.Dundurs, J. and Mura, T.: Interaction between an edge dislocation and a circular inclusion. J. Mech. Phys. Solids 12, 177189 (1964).
54.Lubarda, V.A.: Image force on a straight dislocation emitted from a cylindrical void. Int. J. Solids Struct. 48, 648660 (2011).


Anomalous size effects in nanoporous materials induced by high surface energies

  • Justin W. Wilkerson (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed