Numerical study on crack propagation in functionally graded CNT-reinforced composite plates

This paper presents a numerical method for simulating the crack propagation in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The numerical method is based on 2-D natural element method (NEM) which can overcome the inherent demerits of FEM and conventional meshfree methods. The 3-D displacement field of cracked orthotropic plate is formulated using the (1, 1, 0)* hierarchical model and approximated by 2-D NEM. The thickness-wise mixed-mode stress intensity factors (SIFs) are computed using the modified interaction integral I^(1,2) and the 2-D complex-valued crack-tip singular fields. The crack propagation angle is determined by the modified maximum circumferential stress (MCS) criterion, and the crack trajectories are predicted by an incremental crack propagation simulation scheme. The present numerical method is verified from the comparison of predicted crack trajectories with the published reference solutions. Moreover, using the developed numerical method, the crack trajectory characteristics of FG-CNTRC plates are parametrically investigated with respect to the major parameters. From the parametric investigation, it is found that the crack trajectories of FG-CNTRC are significantly influenced by the material orientation angle and the stiffness ratio. But, the effects of the initial crack angle and the volume fraction and volume fraction pattern of CNTs are not remarkable.