Stochastic investigation of the facture problem in functionally graded materials with uncertain mechanical properties and an arbitrarily oriented crack

The macro and micro analysis methods of the fracture mechanics are adopted to investigate the fracture mechanics problem of functionally graded materials (FGMs) with uncertain mechanical properties and an arbitrarily oriented crack. In this paper, the piecewise-exponential model and the Mori-Tanaka model are combined to solve the mixed-mode crack problem for every sample analytically. Then according to the probability theory, the mixed-mode SIFs for the samples are obtained. So the probabilistic attributes of the mixed-mode SIFs in FGMs can be obtained. As a result, the probabilistic density function of SIFs can be provided by means of the graphic method. The method based on macro and micro mechanics can be efficiently applied to carry out the related research of the influences of the crack angles and lengths on the stochastic characteristics of the mixed-mode SIFs.