Scaling equation for yield strength of nanoporous open-cell foams

Abstract

A comprehensive study on the relationship between yield strength, relative density and ligament sizes is presented for nanoporous Au foams. Depth-sensing nanoindentation tests were performed on nanoporous foams ranging from 20 to 42% relative density with ligament sizes ranging from 10 to 900 nm. The Gibson and Ashby yield strength equation for open-cell macro-cellular foams is modified in order to incorporate ligament size effects. This study demonstrates that at the nanoscale, foam strength is governed by ligament size, in addition to relative density. Furthermore, we present the ligament length scale as a new parameter to tailor foam properties and achieve high strength at low densities.

Grain size dependence of the strength of metals: The Hall–Petch effect does not scale as the inverse square root of grain size

“…Bushby and Dunstan, 2011), micropillars in compression (see Korte and Clegg, 2010, for a compilation of much data), in foams (e.g. Hodge et al, 2007)) and in other geometries such as indentation hardness testing (e.g. Bushby & Dunstan, 2004).…”

Scaling laws and deformation mechanisms of nanoporous copper under adiabatic uniaxial strain compression

“…Recent experiments have shown that the fitted exponent coefficients are 2 and 1.5 for modulus and yield strength, respectively, for low density open-cell foam materials, 6,8,12,15 which is similar from the Gibson-Ashby's scaling law. However, when the relative density is high, they have the following relations based on GibsonAshby's scaling law:…”

“…As indicated, the current results have shown that the mechanical properties with the high relative density under adiabatic uniaxial strain compression show a strong dependence on the void diameter d, expressed by exponential relations with decay coefficients much higher than the experimental determined value for nanoindentation tests on the low relative density nanoporous foams (-1/2). 15 Combining Eqs. (4) and (6) and Eqs.…”

“…15 Such distinct size effect can be understood from the size dependent strength of single crystalline nanowires or nano-pillars, which often exhibits a similar exponential relation. 42,43 When considering the effect of void diameter on mechanical properties under adiabatic uniaxial strain compression, the similar exponential relations are also indicated by our simulation results, but with much higher decay coefficients: Where C 6 ,C 7 ,C 8 are fitting constants.…”

“…[4][5][6] Extensive experimental, theoretical and MD efforts have been devoted to investigate the mechanical properties of nanoporous metals under moderate conditions. [6][7][8][9][10][11][12][13][14][15][16][17][18] These studies have shown that the mechanical properties of nanoporous metals, such as the effective elastic modulus and the yield strength, are closely related to the relative density and the ligament size. A number of models 15,18,19 have been proposed to capture the scaling laws and the deformation mechanisms at the nanoscale due to the large surface-to-volume ratio for nanoporous metals, while the Gibson-Ashby model 7 has been widely used for porous metals with microstructural sizes on the order of micrometers and above.…”