Stress triaxiality

In continuum mechanics, stress triaxiality is relative degree of hydrostatic stress in a given stress state. It is commonly used as a triaxiality factor, T.F, which is the ratio of the hydrostatic stress, formula_1, to the Von Mises equivalent stress, formula_2.
formula_3
Stress triaxiality has important applications in fracture mechanics and can often be used to predict the type of fracture (i.e. ductile or brittle) within the region defined by that stress state. A higher stress triaxiality corresponds to a stress state which is primarily hydrostatic rather than deviatoric. High stress triaxility (> 2-3) promotes brittle cleavage fracture as well as dimple formation within an otherwise ductile fracture. Low stress triaxiality corresponds with shear slip and therefore larger ductility, as well as typically resulting in greater toughness. Ductile crack propagation is also influenced by stress triaxiality, with lower values producing steeper crack resistance curves. Several failure models such as the Johnson-Cook (J-C) fracture criterion (often used for high strain rate behavior), Rice-Tracey model, and J-Q large scale yielding model incorporate stress triaxiality.