Stochastic mesoscale mechanical modeling of metallic foams

Abstract

Investigating the mechanical properties of complex, porous microstructures by assessing model representative volumes is an established method of determining materials properties across a range of length scales. An understanding of how behavior evolves with length scale is essential for evaluating the material’s suitability for certain applications where the interaction volume is so small that the mechanical response originates from individual features rather than a set of features. Here, we apply the Kentucky Random Structure Toolkit (KRaSTk) to metallic foams, which are crucial to many emerging applications, among them shielding against hypervelocity impacts caused by micrometeoroids and orbital debris (MMOD). The variability of properties at feature-scale and mesoscale lengths originating from the inherently random microstructure makes developing predictive models challenging. It also hinders the optimization of components fabricated with such foams, an especially serious problem for spacecraft design where the benefit–cost–mass optimization is overshadowed by the catastrophic results of component failure. To address this problem, we compute the critical transition between the feature-scale, where mechanical properties are determined by individual features, and the mesoscale, where behavior is determined by ensembles of features. At the mesoscale, we compute distributions of properties—with respect to both expectation value and standard variability—that are consistent and predictable. A universal transition is found to occur when the side length of a cubic sample volume is ~10× greater than the characteristic length. Comparing KRaSTk-computed converged stiffness distributions with experimental measurements of a commercial metallic foam found an excellent agreement for both expectation value and standard variability at all reduced densities. Lastly, we observe that the diameter of a representative MMOD strike is ~30× shorter than the feature-scale to mesoscale transition for the foam at any reduced density, strongly implying that individual features will determine response to hypervelocity impacts, rather than bulk, or even mesoscale, structure.