Analysis of Fracture Probabilities in Nonuniformly Stressed Brittle Materials

The results of theoretical studies on the effect of nonuniform stress fields encountered in prismatic beams under bending on the fracture of brittle materials are described. Derivations were carried out to determine the risk of rupture of bending specimens subjected to a symmetrical four-point load of arbitrary spacing, the symmetric three-point loading and pure bending forming limiting cases of this more general loading. The analysis was based on materials obeying the Weibull distribution function with assumptions for either volumetric or surface flaw dispersion conditions. The predicted strengths of bending and tensile specimens are compared. An analytical method for the determination of the three Weibull parameters from a pure bending test is proposed. This method, based on the best fit of a theoretical curve to the experimental data, was applied successfully to experimental results on Columbia Resin, a brittle amorphous polymer.