Analysis of CNT reinforced polymer nanocomposite plate in the presence of discontinuities using XFEM

Abstract

In the present study, the effect of holes and inclusions on the stress intensity factor (SIF) in a Carbon NanoTube (CNT) modified polymer nanocomposite (PNC) has been investigated using extended finite element method (XFEM). In order to perform the failure analysis of CNT reinforced nanocomposite two-step procedure is adopted. In the first step, the equivalent properties of the nanocomposites (elastic modulus, fracture energy and fracture toughness) are computed by changing the percentage of weight content of CNTs inside the polymer matrix. Halpin-Tsai equation has been employed to compute the elastic modulus of the material. Whereas, the fracture toughness and fracture energy have been evaluated considering CNT debonding and CNT pull-out as the main toughness criterion. For this purpose, a modified Cottrell-Kelly-Tyson scheme has been chosen in order to account the hollowness of CNTs. In the second step, a thin finite size plate containing an edge crack with multiple holes and inclusions has been taken into consideration. Then, XFEM approach is implemented to perform the failure analysis of cracked nanocomposite plate. The interaction integral approach has been employed to compute the SIF value at the crack tip. The numerical integration has been done using higher order Gaussian quadrature. Few numerical problems have been solved in the presence of discontinuities. It was found that the elastic modulus, fracture toughness and fracture energy improved with increase in weight percent of CNT. The effect of holes was found to be more pronounced than the effect of inclusion on the SIF.