Numerical studies on mixed-mode crack propagation behavior for functionally graded material based on peridynamic theory

Peridynamics (PD) is a new nonlocal theory that unifies the mechanics of discrete particles, continuum, and continuum with discontinuities, and it has inherent advantages in calculating the mixed-mode crack propagating. Functionally graded materials (FGMs) are the advanced composite materials, fracture behavior of which is complicated to be simulated by the traditional continuum mechanics. Hence, a PD model for FGMs is given to investigate the mixed-mode fracture behavior under quasi-static loading. Basic PD equations, damage model, and PD J-integral for FGMs are discussed. A FORTRAN program of PD algorithm is coded to calculate the J-integral and crack propagation of FGMs. The J-integral and the crack paths of the PD model are verified by comparing with the published numerical and experimental results. Effects of the material gradient, the material gradient direction, and the stress load magnitude on the fracture behavior are investigated. It is shown that the PD J-integral and the crack path are strongly affected by the material gradient and the gradient direction under the same stress load. When the gradient of FGMs is linear, the material gradient direction decides whether the mixed-mode crack kinks or not and the magnitude of stress determines the kinking angle.