Evaluating the Effect of Mechanical Loading on the Electrical Percolation Threshold of Carbon Nanotube Reinforced Polymers: A 3D Monte-Carlo Study

Addition of an adequate amount of carbon nanotubes (CNTs) to electrically insulating polymers can make them conductive. The conductivity behavior of such nanocomposites, also known as the percolation behavior, is mainly due to the formation of pathways of touching particles. In this Monte Carlo simulation study, CNTs are modeled as penetrable cylindrical sticks also known as the "soft-core" model which are randomly scattered inside a representative volume element (RVE) of the nanocomposite. As it brings about a new configuration of constituents, the mechanical loading effects on the percolation are investigated assuming simple linear elastic behavior. To evaluate the impact of the mechanical deformation on the percolation, we first propose a two-step homogenization technique aimed at evaluating the effective homogenized stiffness at any configuration is proposed. The displacement field of the RVE is related to the applied stress via this effective stiffness. As the spatial configuration of the composing constituents is altered during the course of stressing the RVE, the effective stiffness and the percolation state change as well. An incremental procedure is therefore proposed for updating the stiffness tensor and for the checking the percolation state. The simulation results indicate that a percolating nanocomposite becomes non-percolating by applying a unidirectional tensile stress. Finally a convincing comparison with several independent experimental results is provided which confirms the results of the proposed methodology.