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Journal Club Theme of December 2011: Mechanics of Porous Materials

john.balk's picture

Porous materials can be created by a variety of methods and exhibit properties that are advantageous in certain applications, e.g. insulation, energy absorption, and core materials in sandwich panels. As the length scale of the pores/ligaments is reduced below one micron, size effects arise and cause changes in the deformation mechanisms that operate in the ligament material. The mechanical properties can change dramatically, especially for so-called “nanoporous metals”, which have pores and ligaments as small as a few nanometers.

The mechanical properties of nanoporous gold (np-Au) have been studied more than any other dealloyed nanoporous material, due to its ease of fabrication. Np-Au is often created by dealloying, which involves the selective dissolution of a sacrificial element (e.g. silver) from a precursor alloy, followed by surface diffusion and the formation of nanoscale Au ligaments. Most of the mechanical testing results in the literature have been obtained using nanoindentation [1, 2], and these results suggest that the ligaments may approach the theoretical strength level before yielding. Recent results have also been obtained using small-scale bulk test methods [3, 4], but those results indicate that the yield strength of np-Au ligaments is much lower than that measured by nanoindentation. Thus, there is not yet a consensus about the mechanical behavior of nanoporous metals.

Mechanical properties of porous/cellular materials are often interpreted with the help of scaling equations, which relate the measured porous properties (e.g. modulus or strength) to equivalent bulk values that would be expected if the ligament material were used to create a fully dense material. Both open-cell np-Au [1] and a fully compacted material that formed nanocrystalline Au [2] were tested by one research group, using nanoindentation, and both yielded very high hardness values. A compressive yield strength of 145 MPa was measured for the ligaments within np-Au [1], much higher than would be expected from scaling laws for cellular solids based on bulk mechanical properties. The authors interpreted their results by invoking a Gibson-Ashby equation as the scaling law, which is the best framework currently available for understanding porous material mechanical behavior [5]:

σ*/σs ≈ 0.3(ρ*/ρs)1.5             (Eq. 1)

where σ* is the strength of the porous material, σs the strength of the corresponding bulk material, ρ* the density of the porous material, and ρs the density of the bulk material. The ratio (ρ*/ρs) is also called the relative density of the porous material. For np-Au, the relative density is equal to the atomic percentage of Au in the Au-Ag precursor alloy, due to the equal lattice parameters of Au and Ag. However, volume contraction during dealloying can be significant, up to 30% depending on alloy composition [6], so the relative density itself can change significantly as the nanoporous structure evolves. This of course changes the scaling relationship between σ* and σs in the Gibson-Ashby relation (Eq. 1) above.

Microstructural studies of nanoporous metals and alloys have revealed new aspects of the mechanical behavior of these materials. As was recently presented at meetings of the Materials Research Society, Cynthia Volkert’s work on mechanical deformation of np-Au indicates that dislocations are not active in nanoscale ligaments or wires. Instead, twins were observed in the deformation microstructure, a surprising result given the well-established ductility of Au. This agrees with studies of Au nanowires [7]. However, this contrasts with observations of significant dislocation activity in ligaments during in situ nanoindentation of np-Au in the TEM [8]. This may be due to details of sample preparation or testing, but illustrates the unexpected behavior exhibited by nanoporous metals.

One of the interesting properties of np-Au is its macroscale brittleness. Gold is a highly ductile material, but np-Au fails in a brittle manner. Recently, tension and compression testing was performed on small-scale bulk np-Au specimens [4]. This was the first time that np-Au had been successfully tested in uniaxial tension. The compressive yield strengths matched the tensile yield/fracture strengths very well, indicating that permanent deformation begins at a stress of ~15 MPa for polycrystalline np-Au. This is one order of magnitude lower than the strengths reported from nanoindentation studies of np-Au. This difference also affects the equivalent bulk strength values that would be calculated with the Gibson-Ashby scaling equation above. The small-scale tension tests of np-Au also allowed the estimation of fracture toughness for np-Au, in this case 0.17 MPa•√m. This low value is more typical of a weak glass than a ductile metal, despite the fact that ligament deformation in np-Au is accompanied by the nucleation and motion of dislocations [8].

There are some unresolved questions concerning the mechanical behavior of nanoscale porous materials. One reason is the difficulty of directly observing deformation mechanisms during in situ testing, and another is the complex loading structure that distributes applied loads throughout the ligament structure.

The summary above is meant to provide a quick introduction to nanoporous materials, but does not cover all of the novel and interesting results obtained by researchers around the world. Please comment on this field of research and join the discussion about mechanical behavior of nanoscale porous materials.



1.   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, p. 024301 (2005).

2.   Hodge, A.M., Biener, J., Hsiung, L.L., Wang, Y.M., Hamza, A.V. and Satcher, J.H., Monolithic nanocrystalline Au fabricated by the compaction of nanoscale foam, Journal of Materials Research 20, p. 554 (2005).

3.   Jin, H.J., Kurmanaeva, L., Schmauch, J., Rosner, H., Ivanisenko, Y. and Weissmuller, J., Deforming nanoporous metal: Role of lattice coherency, Acta Materialia 57, p. 2665 (2009).

4.   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, p. 26 (2009).

5.   Gibson, L.J. and Ashby, M.F., Cellular Solids - Structure and Properties (Cambridge University Press) 1997.

6.   Parida, S., Kramer, D., Volkert, C.A., Rosner, H., Erlebacher, J. and Weissmuller, J., Volume change during the formation of nanoporous gold by dealloying, Physical Review Letters 97, p. 035504 (2006).

7.   Richter, G., Hillerich, K., Gianola, D.S., Monig, R., Kraft, O. and Volkert, C.A., Ultrahigh Strength Single Crystalline Nanowhiskers Grown by Physical Vapor Deposition, Nano Letters 9, p. 3048 (2009).

8.   Sun, Y., Ye, J., Minor, A.M. and Balk, T.J., In Situ Indentation of Nanoporous Gold Thin Films in the Transmission Electron Microscope, Microscopy Research and Technique 72, p. 232 (2009).




Lifeng Wang's picture

In addition to porous metal materials, porous polymers, especially periodic structured polymers at various length scales, have attracted great interest in material science. Potentially, these materials can also provide a good combination of stiffness, strength, impact resistance, toughness, and energy dissipation, as well as multifunctional applications. 

I am listing several such papers.  

Jang, J. H., Ullal, C. K., Choi, T. Y., Lemieux, M. C., Tsukruk, V. V., Thomas, E. L., "3D polymer microframes that exploit length-scale-dependent mechanical behavior", Advanced Materials, 18, 2123, (2006).

L. F. Wang, M. C. Boyce, C. Y. Wen, and E. L. Thomas, “Plastic Dissipation Mechanisms in Periodic Microframe-Structured Polymers”, Advanced Functional Materials 19, 1343-1350 (2009).

J. H. Lee, L. F. Wang, S. Kooi, M. C. Boyce and E. L. Thomas, “Enhanced Energy Dissipation in Periodic Epoxy Nanoframes”, Nano Letters 10, 2592-2597 (2010).

L. F. Wang, J. Lau, E. L. Thomas, and M. C. Boyce, “Co-Continuous Composite Materials for Stiffness, Strength and Energy Dissipation”, Advanced Materials 23, 1524-1529 (2011).

john.balk's picture

Thanks very much for your post, Lifeng.  Porous polymers are definitely an interesting class of materials, and they also allow additional processing methods when compared to (nano-)porous metals.  Your comments remind me of some other recent reports on structured porous polymers, produced by interference patterns of incident beams.  A group at the Karlsruhe Institute of Technology developed a method for creating small-scale ordered networks of polymers.  The issue of energy dissipation is very interesting and it will be useful for the metals and polymers people to learn from each other here.  I see that there is also a new book called Porous Polymers, by Silverstein, Cameron and Hillmyer.

Thanks, John, for an interesting post. I've recently been interested in understanding the limits of stability of nanoporous materials. In fact, a former postdoc of mine and I recently published a paper that suggests that below a certain ligament dimension, these materials become unstable with respect to plastic flow, leading to spontaneous coarsening. See Acta Mater. 59, 7645 (2011). I'd be interested in hearing people's comments on how these materials might be engineered to be more stable.


Xiaodong Li's picture

Thanks John for posting this topic. I think that Mother Nature has been using porous materials for various functions. It may has multi-functionalities. May you or someone please list some of the papers on this? Thanks

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