Application of homogenization method on the analysis of micro-stress distribution in non-continuous carbon nanotube reinforced composites

The stress distribution of non-continuous carbon nanotubes (CNTs)/polymer composites was analyzed using the homogenization method with exact periodic boundary conditions, and the numerical calculations for regular and stagger array models were performed by the macro-microscopic finite element method (FEM). In order to utilize the traditional continuous mechanics approaches to determine the mechanical properties of CNTs composites, the carbon nanotubes here were simplified as the effective fiber models which were obtained from the molecular dynamics simulation. The results obtained from regular array model were compared with those from Cox' shear-lag model, Eauke and Fu theories, which show that the stresses transfer in CNTs composites are not only related to the aspect ratio and volume fraction of CNTs as described in the above theories, but also sensitive to CNTs arrays and CNTs' geometrical configuration within the selected representative volume element (RVE). A better stress transfer efficiency is obtained from stagger array, and the distance between two CNTs (2T_f) has a great influence on the stress distribution. The results show that there are some special characteristics for CNTs as the reinforcement phase of composites, and they also prove that the homogenization method with multi-CNTs is efficient to analyze the stress transfer in CNTs composites.