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The very high strengths that have been reported for nanoporous gold may be related to strain gradients within the deforming porous microstructure. We present a mechanismbased model for the strength of nanoporous foams that is derived from conventional models for the deformation of macroscopic foams and now includes the influence of strain gradients. This model predicts that the strength of the ligaments within the nanoporous gold is proportional to the ligament diameter raised to the power
0.5. We have used the model to analyze experimental data for the strength of nanoporous gold and find excellent agreement with published data. I. INTRODUCTION

Recently, there has been considerable interest in the mechanical properties of nanoporous gold with reported values for the strength of these materials ranging from 1 to 10 GPa.1–6 It is possible to fabricate nanoporous foams with relative density in the range 0.20 to 0.45 by leaching AuxAg1
x alloys (with 0.25 < x < 0.42) in acid. The resulting porous structure has ligament diameters typically in the range of 5 to 50 nm, and this range can be further extended by annealing to diameters close to 1000 nm. The strength of the ligaments within these structures is found to scale with size, and an empirical relation power law has been proposed for this behavior,6 with the plastic flow strength, sY, showing the following scaling with ligament diameter, d: sY ¼ Sd
0:5

;

ð1Þ

where S is an empirical constant. This size-scaled behavior has many similarities with the reported strength of metal micropillars or nanowires tested in compression,7–9 where a similar power-law relation is reported but with the exponent now approximately
0.6. In an earlier paper we compared the strength of nanoporous gold with the strength of gold micropillars tested in compression10 and showed that both these size effects operated in the same region of parameter space. However, the local geometry of deformation is different for these two material classes. With the compression of constant diameter pillars each specimen is loaded uniformly up to yield and subsequent deformation is seen to occur chiefly by dispersed bands of shear, indicating either single slip or multiple slip behavior. This behavior is seen in a number of different metals with a range of pillar orientations.9 In Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0099

http://journals.cambridge.org

II. MECHANICAL PROPERTIES OF HIGHLY POROUS MATERIALS OR FOAMS

In prior work by a number of authors on the mechanical properties of nanoporous metals, the elastic modulus and strength of the ligaments within nanoporous gold have been deduced from its measured bulk mechanical

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nanoporous metals, however, the materials behavior has generally been interpreted using mechanism models originally developed for the deformation of cellular solids or open-cell foams by Gibson and Ashby.11,12 In these materials, deformation is believed to be dominated by bending of the ligaments that make up the