A parametric study on probabilistic fracture of functionally graded composites by a concurrent multiscale method

This article reports the results of a parametric study on the fracture behavior of a crack in functionally graded materials. The study involves stochastic descriptions of particle and void numbers; location, size, and orientation characteristics; and constituent elastic properties; a concurrent multiscale model for calculating crack-driving forces; and Monte Carlo simulation for fracture reliability analysis. A level-cut, inhomogeneous, filtered Poisson field describes the statistically inhomogeneous microstructures of graded composites. Numerical results for an edge-cracked, graded specimen show that the particle shape and orientation for the same phase volume fractions have negligible effects on fracture reliability, even for graded materials with a high modular ratio. However, voids and the particle gradation parameter, if they exist or increase, can significantly raise the probability of fracture initiation. Limited crack-propagation simulations in graded composites containing brittle particles reveal that the fracture toughness of the matrix material can significantly influence the likelihood or the extent of crack growth.