Journal Club Theme of December 2011: Mechanics of Porous Materials
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  and a fully compacted material that formed nanocrystalline Au  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 , 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 :
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 , 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 . However, this contrasts with observations of significant dislocation activity in ligaments during in situ nanoindentation of np-Au in the TEM . 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 . 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 .
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.
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).
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).