School of Mechanical Engineering, Iran University of Science and Technology (IUST)
In this paper, a continuum model is proposed so that a Stone-Wales (SW) defected carbon nanotube (CNT) is replaced by an initial circumferential crack in a continuum cylindrical shell. For this purpose, the critical energy release rate and then the fracture toughness of a defected CNT are calculated using the results of an existing atomistic-based continuum finite element simulation. Finally, the equivalent crack length is obtained from the fracture toughness. The proposed model can be applicable tovarious kinds of continuum-based simulations of nano-structures like nano-composites and nano-probes where the fracture resistance studies become important. It is concluded for a case study that the armchair (12, 12) CNT containing a SW defect could be replaced with a continuum cylindrical shell with a circumferential crack length of 0.83 nm. Furthermore, the damage variable is discussed to achieve a method for estimating the effective Young's modulus of defected nanotubes with numerous defects subjected to the progressive damage. This estimation method is evaluated by the atomistic based FE simulation of a double defected CNT.