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

摘要

A weakest link theory for macroscopically homogeneous isotropic materials containing uniformly distributed, randomly oriented cracks is developed under the assumption that fracture depends only on the stress normal to a crack plane. The function representing the number of cracks 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 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. (Author)