Optimal length scales emerging from shear load transfer in natural materials: Application to carbon-based nanocomposite design

Numerous theoretical and experimental studies on various species of natural composites, such as nacre in abalone shells, collagen fibrils in tendon, and spider silk fibers, have been pursued to provide insight into the synthesis of novel bioinspired high-performance composites. However, a direct link between the mechanical properties of the constituents and the various geometric features and hierarchies remains to be fully established. In this paper, we explore a common denominator leading to the outstanding balance between strength and toughness in natural composite materials. We present an analytical model to link the mechanical properties of constituents, their geometric arrangement, and the chemistries used in their lateral interactions. Key critical overlap length scales between adjacent reinforcement constituents, which directly control strength and toughness of composite materials, emerge from the analysis. When these length scales are computed for three natural materials-nacre, collagen molecules, and spider silk fibers-very good agreement is found as compared with experimental measurements. The model was then used to interpret load transfer capabilities in synthetic carbon-based materials through parametrization of in situ SEM shear experiments on overlapping multiwall carbon nanotubes.