Analysis of localized failure of single-wall carbon nanotubes

A method is developed to determine the conditions for the onset of localized failure of carbon nanotubes. Examples of failure modes include ductile necking under tension or localized crushing under compression. A nanoscale continuum theory for carbon nanotube is adapted. The onset of localized failure is identified by the singularity point of the acoustic tensor derived from continuum energy function based on Tersoff-Brenner potential. The analysis predicts 35-44% of breaking strains for tension and 18-25% compressive strain for plastic collapse. The results are in agreement with molecular dynamics simulations and experimental estimations reported in the literature.