A universal scaling relationship between the strength and Young’s modulus of dealloyed porous Fe0.80Cr0.20

Abstract

The fact that ligament strength is strongly affected by size has become an obstacle to understanding the relationship between structural topology and mechanical response of dealloyed nanoporous metals. Herein we studied the mechanical properties of porous Fe0.80Cr0.20 prepared by liquid metal dealloying. The ligament diameters of these samples are stabilized at ∼ 4 µm, so that the ligament strength is constant in all samples. The variation of strength (or flow stress) and Young’s modulus with relative density, on a log–log scale, is nonlinear. Both properties decrease more steeply with decreasing relative density at lower relative density. These results are similar to the observations in nanoporous gold prepared by (electro)chemical dealloying but deviate from Gibson–Ashby (G-A) scaling laws. However, the strength of the porous Fe0.80Cr0.20 plotted against the Young’s modulus on a log–log scale exhibits a linear relation in the full range, with a slope of ∼ 3/4 that matches perfectly with the standard G-A prediction. This confirms the significant role played by “dangling ligaments” in the deformation of dealloyed porous materials: Coarsening-induced pinch-off of some ligaments is responsible for the anomalously low strength and stiffness of dealloyed porous materials; the load-bearing network remains self-similar, and its mechanical response follows the standard G-A scaling laws, despite the fact that the porous material itself may not do so. Our study confirms that, for dealloyed porous materials, the G-A scaling relations are valid if the apparent relative density or, alternatively, genus density-related prefactors are introduced.