Stiffness thresholds of buckypapers under arbitrary loads

Buckypaper, a paper-like carbon nanotube (CNT) network, is an important material structure to utilize the micro-scale excellent properties of CNTs into macro-scale materials. Previous study revealed the existence of stiffness threshold and bending-stretching transitional threshold of CNT networks under uniaxial load. However, the load conditions in practical applications are very complicated. Therefore, the stiffness and thresholds of buckypapers under arbitrary loads are studied by both theoretical analysis and finite element simulations. It is revealed that the thresholds for an arbitrary load are exactly same as those for the uniaxial load, indicating that the stiffness threshold and bending-stretching transitional threshold are both independent of load types. Furthermore, the buckypapers with randomly distributed CNTs are revealed to be well isotropic when the CNT concentration is higher than the bending-stretching transitional threshold. Accordingly, a simple unified piecewise analytical expression is summarized to predict the uniaxial, area/bulk and shear moduli of buckypapers. Besides, it is found that the CNT curliness and paper thickness can influence the thresholds, but the curliness effect can be weakened by hydrostatic loading. This study provides a theoretical guidance to the material structural design of buckypapers, and can be extended to other nanotube and/or nanowire constructed networks as well.