Probabilistic fracture of isotropic functionally graded materials

This paper presents a new probabilistic method for reliability analysis of cracks in linear-elastic, isotropic, functionally graded media subject to random loads, material and gradation properties, and crack geometry. The method involves an interaction integral for calculating crack-driving forces and a novel function decomposition that facilitates lower-variate approximations of a general multivariate function. The fracture reliability analysis is based on response-surface models of univariate and bivariate approximations and subsequent Monte Carlo simulation. Two numerical examples illustrating both deterministic and stochastic aspects of fracture are presented. The numerical results indicate that the univariate and bivariate response-surface methods provide both accurate and efficient estimates of failure probability of cracks in functionally graded materials.