Weakest Link Theory Reformulated for Arbitrary Fracture Criterion

TLDR

The study aims to predict failure probability under arbitrary stress states using known failure statistics from a specific stress state, such as simple tension. The authors derive a Weibull-based rule assuming only the normal stress component drives fracture, and evaluate four shear-sensitive failure criteria against experimental data. The rule is proven valid for shear‑insensitive cracks, and the comparison of four shear‑sensitive criteria with test data demonstrates their relative performance.

Abstract

A primary objective of statistical fracture theory is to predict the probability of failure for an arbitrary stress state when the failure statistics are known for a particular stress state, e.g. simple tension. It is proved that a rule for accomplishing this (given without proof by Weibull) is valid for shear‐insensitive cracks, i.e. on the assumption that only the component of stress normal to a crack plane contributes to its fracture. Four failure criteria for shear‐sensitive cracks are considered and the results are compared with test data.