Fracture mechanics at the nanoscale level is a very complex phenomenon, whereas the macroscale fracture mechanics approach can be employed for nanoscale to simulate the effect of fracture in single-walled carbon nanotubes (SWCNTs). In this study, an extended finite element method is used to simulate crack propagation in carbon nanotubes. The concept of the model is based on the assumption that carbon nanotubes, when loaded, behave like space frame structures. The nanostructure is analyzed using the finite element method, and the modified Morse interatomic potential is used to simulate the nonlinear force field of the C–C bonds. The model has been applied to single-walled zigzag, armchair, and chiral nanotubes subjected to axial tension. The contour integral method is used for the calculation of the J-integral and stress intensity factors (SIFs) at various crack locations and dimensions of nanotubes under tensile loading. A comparative study of results shows the behavior of cracks in carbon nanotubes. It is observed that for the smaller length of nanotube, as the diameter increased, the stress intensity factor is linearly varied while for the longer nanotube, the variation in stress intensity factor is nonlinear. It is also observed that as the crack is oriented closer to the loading end, the stress intensity factor shows higher sensitivity to smaller lengths, which indicates more chances for crack propagation and carbon nanotube breakage. The SIF is found to vary nonlinearly with the diameter of the SWCNT. Also, it is found that the predicted crack evolution, failure stresses, and failure strains of the nanotubes correlate very well with molecular mechanics simulations from literature.
Stress intensity factor for an eccentric circular inner crack in a round bar subjected to tensile loading
