The role of vacancy defects and holes in the fracture of carbon nanotubes

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Modulus, Fracture Strength, and Brittle vs. Plastic Response of the Outer Shell of Arc-grown Multi-walled Carbon Nanotubes (2007, background): “For example, computational modeling shows that one- and two-atom vacancy defects reduce the failure stresses of pristine tubes by as much as 26% and the failure strains by as much as a factor of two [30].”
Electrochemomechanical degradation of high-capacity battery electrode materials (2017, background): “Given that the Young’s modulus of graphene is approximately 1TPa, the 6% hoop strain corresponds to 60 GPa hoop stress [157,158].”
A bridging domain and strain computation method for coupled atomistic–continuum modelling of solids (2007, background): “Fracture of small nanotubes containing such a defect has also been studied quantum mechanically [27].”
Quantized fracture mechanics (2004, methodology): “Applying QFM and its stress and strain analogs and using the value of a ffiffiffi 3 p r0 previously deduced yields the results reported in Table 3; there is close agreement with the MM calculations on nanotubes by Mielke et al. (2004).”