Probabilistic treatment of fracture using two failure models

A probabilistic methodology for brittle fracture based on two local failure models is presented. Probabilistic fracture parameters are obtained using a weakest link and a chain-of-bundles formulation. Both models define limiting distributions for the fracture stress described by a two-parameter Weibull distribution. Numerical procedures employing measured toughness data and finite element solutions are also described to calibrate the Weibull parameters. An application of the methodology then follows to predict geometry and stable crack growth effects on the distribution of macroscopic fracture toughness (Jc) for a high-strength steel. Measured fracture toughness values for a high-constraint geometry that exhibit no prior ductile tearing are effectively `transferredʹ to a different geometry having much lower constraint and in which tearing precedes cleavage. The inherent difficulty in predicting the scatter of experimental fracture toughness, as well as constraint and ductile tearing effects, within the scope of conventional procedures appears greatly reduced in the framework presented in this work.