A refined model for the effective tensile stiffness of Carbon NanoTube fibers

The paper presents a solid-mechanics based method for the determination of the macroscopic tensile properties of fibers composed of monodispersed Carbon NanoTubes (CNTs), whose length is much lower than the fiber length, arranged in a cross-sectional square lattice. In the longitudinal direction, each CNT is offset, with respect to the neighboring ones, of a given quantity. The interaction between the CNTs caps is negligible, while the model takes into account the coupling occurring on their lateral surfaces, thanks to van der Waals forces and cross-links, modeled as distributed springs. One of the main improvements with respect to previous studies is that the CNTs are here modeled as deformable elastic bars, with given axial stiffness. Under the assumption that, due to the periodicity of the CNTs arrangement, each CNT is subjected to the same loading state, it is demonstrated that the axial strain/stress fields are governed by a delayed-advanced differential equation, that is here solved by means of finite difference technique. This allows to evaluate the total axial force on the fiber, and, consequently, its effective tensile stiffness, strongly dependent on the length of the constituent CNTs, their offset and their axial compliance. Comparisons with literature data confirm the accuracy of the proposed approach.