A Statistical Theory for the Fracture of Brittle Structures Subjected to Nonuniform Polyaxial Stresses

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Abstract
A weakest link theory for macroscopically homogeneous isotropic materials containing randomly oriented microcracks uniformly distributed in location is developed under the assumption that fracture depends only on the macroscopic stress normal to a crack plane. The function representing the number of cracks per unit volume failing at each value of normal stress is expanded as a Taylor series with coefficients determined from tensile test data. This function is used without additional assumptions to determine the probability of fracture under arbitrary (but not predominantly compressive) stress conditions. The results can be readily incorporated into a finite-element code to predict the failure probability of any structure to which the code applies.