Stochastic Fracture Analysis of Three-Dimensional Functionally Graded Materials Employing Concurrent Multiscale Model

This article presents a stochastic multiscale fracture analysis of three-dimensional functionally graded, particle-matrix composites with random microstructures employing a moment-modified polynomial dimensional decomposition method. The stochastic model is based on a level-cut, inhomogeneous, filtered Poisson random field for representing spatially-varying random microstructures and a moment-modified polynomial dimensional decomposition for calculating the probabilistic characteristics of crack-driving forces. The decomposition involves Fourier-polynomial expansions of component functions by orthonormal polynomial bases, an additive control variate in conjunction with Monte Carlo simulation for calculating the expansion coefficients, and a moment-modified random output to account for the effects of particle locations and geometry. A numerical problem involving a horizontally placed, planar edge-crack in a three-dimensional functionally graded specimen under a mixed-mode deformation was efficiently calculated by the univariate dimensional decomposition to calculate the statistical moments and distribution functions of crack-driving forces and the conditional probability of fracture initiation. The fracture results show significant variation of the stress intensity factors and fracture initiation probability along the crack front of the fracture specimen.