Scaling laws of nanoporous metals under uniaxial compression

N. Huber, R.N. Viswanath, N. Mameka, J. Markmann, J. Weißmüller
2014 Acta Materialia  
This study is motivated by discrepancies between recent experimental compression test data of nanoporus gold and the scaling laws for the strength and elasticity by Gibson and Ashby. We present a systematic theoretical investigation of the relationship between microstructure and macroscopic behaviour of nanoporous metals. The microstructure is modelled by four-coordinated spherical nodes interconnected by cylindrical struts. The node positions are randomly displaced from the lattice points of a
more » ... lattice points of a diamond lattice. We report scaling laws for Young's modulus and yield strength, which depend on the extension of nodal connections between the ligaments and the solid fraction. A comparison with the scaling laws of Gibson and Ashby revealed a significant deviation for the yield stress. The model was applied for identifying a continuum constitutive law for the solid fraction. Matching the model's predicted macroscopic stress-strain behaviour to experimental data for the flow stress at large compression strain requires the incorporation of work hardening in the constitutive law. Furthermore, the amount of disorder of the node positions is decisive in matching the * Corresponding Author: 2 model results to the experimental observations of an anomalously low stiffness and an almost complete lack of transverse plastic strain. Keywords Nanoporous; Structure-property relationship; Plastic deformation; Compression test; Finiteelement simulation Introduction Nanoporous metal made by dealloying takes the form of macroscopic (mm-or cm-sized) porous bodies with a solid fraction around 30% [1-3]. The material exhibits a network structure of 'ligaments' with a uniform characteristic ligament diameter that can be adjusted between 5 and 500 nm. Current research explores the use of nanoporous metal, and specifically of nanoporous gold, made by dealloying as functional material with attention to catalysis [4] [5] [6] [7] , actuation [8-10], and sensing [11] . Mechanical performance is of relevance for each of these fields. It is therefore noteworthy that the strength of nanoscale objects -such as the ligaments in nanoporous gold -increases systematically with decreasing size. Nanoporous network structures made by dealloying offer themselves as suitable model systems for i) exploring this phenomenon in experiment and ii) implementing the high strength of individual nano-objects into a materials design strategy that yields macroscopic functional and/or structural materials which exploit the strength of nanoscale objects. The first experimental studies of the mechanical behaviour of nanoporous gold used nanoindentation or micropillar compression. Their results, as summarized in references [3, [12] [13] , were found to agree with the Gibson-Ashby foam scaling equations [14] for the variation of strength with solid fraction and with the power-law relation between strength and structure size [15] [16] [17] . More recently, two studies using atomistic simulation have confirmed the
doi:10.1016/j.actamat.2013.12.003 fatcat:cacagnm22fbyhobhvst77smw2q