Interfacial Stress Transfer in Carbon Nanotube Systems

ABSTRACT: Stress transfer is of paramount importance in composite materials, since load must be transferred from the matrix to the reinforcement element as efficiently as possible in order to fully realize the potential of the latter. In addition, the benefits obtained from a given reinforcement are conventionally measured in terms of its volume fraction, so efficient usage of the occupied volume places another requirement on a successful reinforcement. Understanding load transfer is key in Multiwalled carbon nanotubes, for which it is known that the intershell interactions are orders of magnitude weaker than those along the principal axis. Traditionally stress transfer in composites has been analyzed through shear lag load models, which prescribe an interfacial shear stress as a function of the local deformation. The present work assumes the validity of continuum mechanics at the scales of interest and introduces a different concept called shear transfer efficiency that quantifies the ability of a given interface to withstand the shear stress necessary to transfer load. The two approaches are demonstrated to be equal for a two-shell structure and for larger structures the much simpler shear transfer model is able to reproduce numerical solutions of the shear lag model, with reasonable accuracy. The length dependence of the effective elastic properties typical of shear lag models is not present in the corresponding shear transfer model. The models developed based on the shear transfer efficiency are capable of capturing the experimentally observed decrease in stiffness as the size of the carbon nanotube structure is increased, under a variety of deformation modes. Interestingly, experiments performed independently by two research groups are brought into agreement without adjustment of parameters.