For components with different defects, selecting a proper criterion to predict their failure is very important, but sometimes this brings confusion to engineers. In this paper, we explore to establish a unified failure criterion for defects with various geometries. First, a fundamental and universal law on failure that all criteria should follow, so-called the zeroth law of failure, is introduced, and the failure is completely governed by the local status of failure determining zone (FDZ), such as the stress distribution, material properties, and geometrical features. Failure criteria lacking a local dimension parameter within FDZ may have limited applicability, such as the traditional strength and fracture criteria. We choose the blunt V-notch as an example to demonstrate how to establish a unified failure criterion for quasi-brittle materials, and a series of experiments are carried out to verify its applicability. The proposed unified failure criterion and some existing failure criteria are also discussed and compared. The failure criteria that only include a single critical constant are incapable of reflecting the whole stress field information and local geometrical features of the FDZ. Our proposed unified failure criterion is expressed with a two-parameter function and has a wider applicability.
The Invariant Two-Parameter Function of Algebras ψ
