Failure theories

Failure theories are used if an experiment is unable to analyse all possible states of stress in a component.

Components are normally subject to multiaxial stresses that induce a two-dimensional or three-dimensional state of stress. Up to three normal stresses and three shear stresses (components of a stress matrix) can occur simultaneously in a component.

Failure theories are used to calculate an equivalent stress from the stress components and this is compared with uniaxial Strength values. The condition ${{\sigma }_{current}}\ge {{\sigma }_{permissible}}$ needs to be met to prove the durability of a component or structure.

Various failure theories are used depending on the Material and Failure mode. They include:

• principal Normal stress theory, which is used to evaluate failure due to the rupture of brittle materials
• distortion energy theory, which calculates the flow-related failure of tough, ductile materials
• principal Shear stress theory, which illustrates the pressure-related failure of brittle materials with a pronounced yield point.

Equivalent stress theories are only suitable for isotropic materials. They do not Work with anisotropic materials such as fibre composites and Wood derivatives.