Weibull Distribution in a Multi-Axial Stress Field

3 Weibull Distribution in a Multi-Axial Stress Field 

Multi-axial stress states can be taken into account by replacing the stress a in the above considerations by an equivalent stress a  

The equivalent (uniaxial) stress is the uniaxial tensile stress which would have the same damaging action as an applied multi-axial stress state. The proper definition of the equivalent stress depends on the type of the fracture causing flaws, and how such flaws act as cracks (though this remains a matter of some debate). The definition also depends on the fracture criterion for multi-axial stress states, and this should also take into account the action of compressive stresses. Precise information on real flaw distributions and multi-axial strength data are rarely available, and the large scatter of strength values makes unambiguous interpretation of these data difficult. 

Although, many different proposals to define equivalent stress in ceramics have been made [ 3,4,78-81 ], there is not yet a consensus on the best choice. For small data sets, of the type most commonly tested, the scatter obscures any differences between reasonable alternative fracture criteria. The most frequently used criteria are described below. 

The first-principle stress (FPS) criterion simply assumes that only the first-principle stress 0/ is taken into account. The FPS criterion [3, 4] reads  

---