Probabilistic mechanical properties and reliability of carbon nanotubes

Carbon nanotubes (CNTs) and their products such as polymer nanocomposite (PNC) are an undeniable part of future materials. To use such future materials, it is necessary to have an accurate evaluation of their properties. Several uncertainties such as structural defects and their distributions cause change in the properties of CNTs that could be considered probabilistic variables. A novel procedure is presented for evaluating CNTs' probabilistic fracture properties and structural reliability using stochastic finite element methods. By employing two dimensionless parameters, both types of Stone-Wales 5-7-7-5 defects are randomly applied to CNTs. Section defect density and critical section defect density are defined and used to manage the distribution and geometrical configuration of CNTs' structural defects. A probabilistic method is used to evaluate the effect of defects' distribution on Young's modulus, ultimate strain, and ultimate stress. It has been observed that normal and Weibull distribution functions are suitable for describing Young's modulus distribution and ultimate stress distribution, respectively. Defect density ratio is defined and, using this parameter, the effect of aggregated defects on mechanical properties is evaluated. It is demonstrated that the defects out of critical section have an unavoidable effect on Young's modulus and ultimate strain; but they have an insignificant effect on ultimate stress. A reliability analysis is performed on armchair (15,15) CNTs and it is investigated that the reliability of CNTs depends on critical defect density significantly. In addition, the reliability is equal to one for the stress of less than 50 GPa and this value is equal to zero for the stress of higher than 100 GPa, independent from the changes of critical defect density. Eventually, a procedure is described to estimate the reliability of armchair CNTs using critical defect density and the results' accuracy is discussed and evaluated.