Abstract
Nanoporous Gold (NPG) made by dealloying takes the form of macroscopic millimetre- to centimetresized
porous bodies with a solid fraction around 30%. The material exhibits a uniform, bicontinuous network of
nanoscale pores and solid ligaments. The relationship between the solid fraction and the macroscopic mechanical
behavior is commonly described by the Gibson-Ashby scaling laws for open cell foams. However, one main
observation of various experimental studies is a much lower leading constant, in several cases combined with a higher
exponent within the Gibson-Ashby scaling law for the Young’s modulus.
For deeper understanding of the mechanical behavior and the occurring deformation mechanisms, various modelling
approaches are suggested in literature, which simplify the complex NPG network to unit cell structures such as cubic,
diamond or three point bending beam. This significant simplification and yet lack of satisfactory understanding of the
underlying structure-property relationship brings the risk of losing detailed insight into the real NPG structure, and
thus, possibly important aspects of its mechanical behavior.
Liu et al. (2016) attribute the discrepancy between experiments and the Gibson-Ashby scaling law to a lowered
network connectivity of the NPG structure seen in SEM-images: Some ligaments are dangling ligaments and thus
cannot carry external load. They introduced the “effective relative density” which is much lower than the real relative
density of the examined NPG samples. In the study of Hu et al. (2016) tomographic reconstructions of NPG samples
using a dual-beam FIB and SEM were carried out for the first time. For different samples with varying ligament size, it
was reported that the effective solid fraction is approximately half of the measured solid fraction. The authors likewise
show, that the effective load-bearing ring structure governs the mechanical behavior, rather than the solid volume
fraction.
This paper presents a computational cheap FEM beam model, which is based on skeletonization of such 3D FIB-SEM
tomography data of NPG to bridge computer simulations and experiments. The FEM skeleton beam model is
validated using a FEM solid model generated from the very same 3D tomographic data. Various FEM skeleton beam
models are generated for varying sample sizes out of the 3D FIB-SEM tomography. The resulting macroscopic
properties are analysed in dependence of structural characteristic parameters, such as effective solid fraction and
connectivity, and are compared to results obtained from idealized diamond unit cell structures. The models allow
clarifying the role of dangling ligaments and load bearing rings in terms of the effective relative density. Furthermore,
concerning the diamond structure, the FEM skeleton beam model provides an answer to the question of the
percentage of nodes that are connected with three respectively four ligaments, needed for predicting a macroscopic
response close to the real NPG.
