Crack Growth Analysis of CNT Reinforced Polymer Nanocomposite using XFEM

Abstract

In the present work, the crack growth analysis of carbon nanotube (CNT) reinforced polymer nanocomposite has been executed using extended finite element method (XFEM). The equivalent properties such as elastic modulus, Poisson’s ratio, fracture energy and fracture toughness of the polymer nanocomposites have been evaluated by varying the percentage of CNT in terms of weight (both single walled CNT and multi walled CNT) in the polymer matrix. The elastic modulus of the polymer nanocomposite has been evaluated using modified Halpin- Tsai equation. The fracture energy of the polymer nanocomposite has been computed considering CNT pull-out and CNT debonding as the main toughening criterion. In XFEM, the crack faces are modelled by discontinuous Heaviside jump functions, whereas the singularity in the stress field at the crack tip is modelled by crack tip enrichment functions. The value of stress intensity factor (SIF) is evaluated using domain form of interaction integral. The level set method has been used to track the crack growth. To obtain the crack growth direction, maximum principal stress criterion has been used in which the crack growth occurs in the direction perpendicular to the maximum principal stress. The numerical integration has been performed using Gaussian quadrature. In order to achieve higher accuracy in approximation of displacement and stress fields near the crack, sub-triangulation has been used in split and tip elements for the numerical integration. The numerical examples with an edge and a centre crack in the polymer nanocomposite are analysed and the influence of various parameters such as percentage of CNT and the aspect ratio on SIF are observed.