EXTREME-VALUE PROBABILISTIC THEORY FOR MIXED-MODE BRITTLE-FRACTURE

In this investigation, extreme value probabilistic methods are combine d With Sih's mixed-mode fracture model to furnish strength distributio ns in plates of brittle materials with random cracks. The crack length s are described by a two-parameter probability density function, their orientations follow a uniform distribution and the crack number follo ws a binomial distribution. Materials of interest are assumed to be is otropic and statistically homogeneous. A ''weakest link'' model, thoug ht to be appropriate for brittle materials, is used in which catastrop hic failure occurs if the dominant crack attains a critical condition. Extreme value distributions for strength of the plates are derived as a function of the size (crack number) of the plates, the parameters o f the fracture model and the parameters of the crack length distributi on. Numerical results are presented showing the effect of the normaliz ed variance of the crack length distribution on the scale dependence o f the mean and variance of the plate strength distribution. (C) 1997 E lsevier Science Ltd.