Stress intensity factor

Summary

The stress intensity factor measures the strength of the stress singularity at the tip of a crack in a linear elastic body. Near the tip the stresses grow like $K / \sqrt{2 \pi r}$, where $r$ is the distance to the tip and $K$ is the stress intensity factor. There is one factor $K_I$, $K_{II}$, $K_{III}$ for each of the modes of fracture. These numbers carry all the dependence on the size of the body, the crack length and the loads. The angular shape of the field is universal. Comparing $K_I$ with the fracture toughness of the material decides whether the crack grows.