Breaking down the exceptional size-dependent toughness of nanocellular foams

Natural materials commonly exhibit cellular architectures that demonstrate remarkable toughness, even when made of intrinsically brittle constituents. Understanding this unique behavior requires investigating the origins of toughness across the length scales that cellular solids occupy. In this work, we produce microcellular and nanocellular polyetherimide (PEI) foams via a solid-state foaming process using carbon dioxide as the blowing agent at saturation pressures of $1\text{MPa}$ and $5\text{MPa}$, respectively. Foaming temperatures were tuned to achieve corresponding cell sizes ranging from 3 µm to 5 µm and 15 nm to 40 nm, with relative densities ranging from 42%–80%. Tensile and fracture tests coupled with digital image correlation (DIC) revealed that nanocellular foams exhibit a pronounced increase in fracture toughness compared to equivalently dense microcellular foams. Notably, the highest-density nanofoams dissipated more fracture energy per unit weight than even fully-dense PEI. This defies conventional foam fracture scaling laws that predict reduced toughness at smaller cell sizes. We performed a detailed size-effect analysis on the extent of damage and plasticity in the micro- and nanofoams to understand this unexpected behavior. Higher-density nanocellular foams are found to have a significantly larger plastic zone size ($rp$) than comparable microfoams, which extends their stable crack growth behavior. Finite element analysis with crack band fracture modeling was performed to isolate fracture mechanisms, revealing that the main contributor to improved toughness in nanocellular foams is increased plastic energy dissipation. We posit that size-enhanced ductility in the nanoscale ligaments is the origin of the disrupted cell size vs. toughness scaling relationship. These findings demonstrate a new paradigm wherein nanostructured design can be used to create novel materials with superior fracture toughness-to-weight ratios.