Abstract
Structural hierarchies are universal design paradigms of biological materials, e.g., several materials in nature used for carrying mechanical load or impact protection such as bone, nacre, dentin show structural design at multiple length scales from the nanoscale to the macroscale. Another example is the case of diatoms, microscopic mineralized algae with intricately patterned silica-based exoskeletons, with substructure from the nanometer to micrometer length scale. Previous studies on silica nano-honeycomb structures inspired from these diatom substructures at the nanoscale have shown a great improvement in plasticity, ductility and toughness through these designs over macroscopic silica, though along with a substantial reduction in stiffness. Here, we extend the study of these structural designs to the micron length scale by introducing additional hierarchy levels to implement a multilevel composite design. To facilitate our computational experiments we first develop a mesoscale particle-spring model description of the mechanics of bulk silica/nano-honeycomb silica composites. Our mesoscale description is directly derived from constitutive material behavior found through atomistic simulations at the nanoscale with the first principles-based ReaxFF force field, but is capable of describing deformation and failure of silica materials at tens of micrometer length scales. We create several models of randomly-dispersed fiber-composite materials with a small volume fraction of the nano-honeycomb phase, and analyze the fracture mechanics using J-integral and R-curve studies. Our simulations show a dominance of quasi-brittle fracture behavior in all cases considered. For particular materials with a small volume fraction of the nano-honeycomb phase dispersed as fibers within a bulk silica matrix, we find a large improvement (≈4.4 times) in toughness over bulk silica, while retaining the high stiffness (to 70%) of the material. The increase in toughness is observed to arise primarily from crack path deflection and crack bridging by the nano-honeycomb fibers. The first structural hierarchy at the nanometer scale (nano-honeycomb silica) provides large improvements in ductility and toughness at the cost of a large reduction in stiffness. The second structural hierarchy at the micron length scale (bulk silica/nano-honeycomb composite) recovers the stiffness of bulk silica while substantially improving its toughness. The results reported here provide direct evidence that structural hierarchies present a powerful design paradigm to obtain heightened levels of stiffness and toughness from multiscale engineering a single brittle — and by itself a functionally inferior material — without the need to introduce organic (e.g., protein) phases. Our model sets the stage for the direct simulation of multiple hierarchical levels to describe deformation and failure of complex biological composites.
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