Theoretical mechanical properties of strands and cables made of wound carbon nanotube fibers

Thanks to their very high strength-to-weight ratio, Carbon-NanoTube Fibers (CNTFs) hold great promise for challenging structural applications, such as super-long suspension bridges or power lines. Here we present a theoretical model, propaedeutic for an experimental campaign, to describe the mechanical response of stretched and twisted strands/cables made of wound CNTFs. The fibers, to the touch, have a consistency similar to a cotton thread, with dominant axial stiffness over bending stiffness, as confirmed by microstructurally-motivated models and experiments. Therefore, instead of using the classical Kirchhoff-Love rod model, as usually done for the helical wires in steel cables/strands, the problem is defined in a variational form susceptible to coherent simplifications to obtain closed-form expressions. First, we consider the manufacturing of a strand/cable starting from fibers with a pre-twist, which can be naturally converted in the tortuosity of a helical shape, as done for hemp ropes. From this reference configuration, we define the tensional and torsional response of N-wire strands, with N = 2, 3, 4, 7, and of cables made of several concentric layers of helical fibers. In a parametric analysis, the mechanical (stiffness parameters, Poisson's ratio) and geometric (helical pitch) properties of the CNTFs are varied. Expressions are presented for the internal forces associated with the radial interaction among adjacent layers of fibers, which may affect the strength of the fibers and the resilience of the cable. Such forces show a variation with the helical pitch which is opposite to that of the cable axial stiffness, suggesting by insight the existence of an optimal compromise between strength and stiffness, yet to be experimentally verified.