Degraded axial buckling strain of multiwalled carbon nanotubes due to interlayer slips

A multiple-shell model is presented for infinitesimal axially compressed buckling of a multiwalled carbon nanotube embedded within an elastic matrix. In contrast to an existing single-shell model which treats the entire multiwalled nanotube as a singlelayer elastic shell, the present model assumes that each of the nested concentric tubes is an individual elastic shell and the deflections of all shells are coupled through the van der Waals interaction between adjacent nanotubes. By examining a doublewalled carbon nanotube, it is found that the change in interlayer spacing has a negligible effect on the axial buckling strain provided that the innermost radius is at least a few nanometers. Under this condition, a single equation is derived which determines the deflection of the multiwalled carbon nanotube, and it is shown that infinitesimal axial buckling of a N-walled carbon nanotubes is equivalent to that of a single layer elastic shell whose bending stiffness is approximately N times the effective bending stiffness of a single walled carbon nanotube. As a result, the axial buckling strain of a N-walled carbon nanotube is about 5 N times lower than that predicted by the existing single-shell model. The degraded axial buckling strain is attributed to the interlayer slips between adjacent nanotubes, which represents an essential feature of mechanical behavior of multiwalled carbon nanotubes.