Multiscale analysis method and experiments for the fracture toughness optimization analysis of carbon nanotube-epoxy composites

Abstract

To better understand the facture mechanics and optimize the fracture toughness of carbon nanotube (CNT)-epoxy composites, a multiscale analysis method was established in this paper. The multiscale analysis method includes three scales: (1) at the microscale, an interfacial model was established based on the Cauchy-Born rule to deduce the relationship between the interfacial stress tensor and CC bond vector; (2) at the mesoscale, the transition condition of the failure mode from the CNT pullout to CNT fracture was established based on the shear-lag theory. And the relationships between the pulling force and CNT pullout displacement were given corresponding to these two failure modes; (3) at the macroscale, the analytical solution of fracture toughness increment was given to conduct the fracture toughness optimization analysis. By validating this method by the experiment, we found that the optimal CC bonds volume density and interfacial length are reached under the transition condition of the failure mode from the CNT pullout to CNT fracture. At last, we proposed a method to approximately estimate the optimal CC bonds volume density and CNT length.