Topology-dependent scaling laws for the stiffness and strength of nanoporous gold

Abstract

Nanoporous gold (np-Au) differs from its macroporous counterparts through its ligament and pore length scales, its high relative density, and its very distinct mesoscale cellular architecture. When reexamining the applicability of conventional macroporous foam scaling laws to np-Au, difficulties persist not only in determining the solid properties of nanoscale ligaments, but also because np-Au structure is not self-similar as the relative density changes. Thus, a clear distinction of the effects of relative density and structure is required. This paper aims to capture the role of topology and morphology into the scaling laws by comparing the overall mechanical response of real np-Au structures with the behavior of spinodal and gyroid structures. Quantitative morphological and topological characterization of these structures has been carried out and their role on the macroscopic elastoplastic response of np-Au has been studied using finite element (FE) simulations. The predicted elastic modulus of real np-Au structures from FE simulations is in remarkable agreement with the nanoindentation measurements, and validates the numerical simulations. Quantitative structural analysis reveals that np-Au and spinodal structures are topologically very distinct, but similar in their morphology. On the other hand, gyroids are both morphologically and topologically very distinct from np-Au. The results suggest that the macroscopic stiffness and strength are highly sensitive to the topology, while being relatively much less sensitive to the morphology. The effects of structural topology are captured into modified scaling laws where the geometric pre-factors for the stiffness and strength are found to vary linearly with the scaled genus.