Stress intensity factor

The stress intensity factor, ${\displaystyle K}$, is used in fracture mechanics to predict the stress state ("stress intensity") near the tip of a crack caused by a remote load or residual stresses. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of damage tolerance. The concept can also be applied to materials that exhibit small-scale yielding at a crack tip.

The magnitude of ${\displaystyle K}$ depends on sample geometry, the size and location of the crack, and the magnitude and the modal distribution of loads on the material.

Linear elastic theory predicts that the stress distribution (${\displaystyle \sigma _{ij}}$) near the crack tip, in polar coordinates (${\displaystyle r,\theta }$) with origin at the crack tip, has the form

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