A shear-lag model for carbon nanotube-reinforced polymer composites

A shear-lag model is developed for carbon nanotube-reinforced polymer composites using a multiscale approach. The main morphological features of the nanocomposites are captured by utilizing a composite cylinder embedded with a capped nanotube as the representative volume element. The molecular structural mechanics is employed to determine the effective Young's modulus of the capped carbon nanotube based on its atomistic structure. The capped nanotube is equivalently represented by an effective (solid) fiber having the same diameter and length but different Young's modulus, which is determined from that of the nanotube under an isostrain condition. The shear-lag analysis is performed in the context of linear elasticity for axisymmetric problems, and the resulting formulas are derived in closed forms. To demonstrate applications of the newly developed model, parametric studies of sample cases are conducted. The numerical results reveal that the nanotube aspect ratio is a critical controlling parameter for nanotube-reinforced composites. The predictions by the current analytical model compare favorably with the existing computational and experimental data.