Stress transfer in multi-walled carbon nanotubes

The interaction and load transfer between the multiple shells of a multi-walled carbon nanotube (MWNT) are the subject of intense research by both analysts and experimentalists. Observations of both lubricated sliding and adhesion between individual shells in MWNT have been observed. While the atomic interactions due to simple separation have been successfully modeled by the Lennard-Jones interaction potential for graphene structures, modeling of the shearing deformation mode has been problematic. In the present work, the authors utilize two approaches in continuum mechanics to examine the shearing transfer between shells in a MWNT subjected to extensional and torsional loading wherein the load is transferred through the outermost shell to interior shells. The first approach follows the earlier developments of the authors wherein imperfect bonding between the shells is governed by a shearing transfer efficiency that varies between perfect bonding and zero shearing traction. The second approach utilizes a classical shear lag model to study the shearing transfer between the shells. A comparison between the shear lag and shear transfer models shows the equivalence of the two approaches for two-shell MWNT and numerical solutions are presented for the shear lag model for multiple layers beyond two. Agreement between the two models for multi-shells is demonstrated by varying an adjustable parameter that depends solely on the MWNT geometry. The simplicity of the shear transfer model as compared to the shear lag model constitutes an important advantage. The fundamental discrepancy between the two models lies in the fact that length dependence is inherent to the shear lag analysis, while according to the shear transfer model, stress transfer does not depend explicitly on length.