A three-phase cylindrical shear-lag model for carbon nanotube composites

In this article the viscoelastic behavior of carbon nanotubes (CNTs) reinforced composites is investigated theoretically by using the three-phase concentric cylindrical shell model along with shear-lag arguments. The parameters which influence the fiber stress, the matrix stress and the interfacial stress have been revealed. The aspect ratio of CNTs βt, the cross-sectional area ratio of CNTs βA, the matrix-to-fiber modulus ratio λm and the interphase-to-fiber modulus ratio λn are common influencing parameters of both the stresses in nanocomposites and the composite modulus. In addition, the effective composite modulus has three other influencing parameters of its own, i.e., the fiber volume fraction vf, the interphase volume fraction vn and the RVE-to-fiber length ratio η, whereas the stresses have their own influencing parameters of the RVE-to-fiber diameter ratio βR and the interphase-to-fiber diameter ratio βb. The modulus of CNTs composites depends strongly upon the modulus and thickness of the interphase. Carbon nanotube fibers improve the viscoelastic stiffness in the whole time period. However, the magnitude of modulus improvement does not vary monotonically with time.