Stress Intensity Factor

The stress intensity factor, 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 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 near the crack tip, in polar coordinates with origin at the crack tip, has the form

where is the stress intensity factor (with units of stress length1/2) and is a dimensionless quantity that depends on the load and geometry. This relation breaks down very close to the tip (small ) because as goes to 0, the stress goes to . Plastic distortion typically occurs at high stresses and the linear elastic solution is no longer applicable close to the crack tip. However, if the crack-tip plastic zone is small, it can be assumed that the stress distribution near the crack is still given by the above relation.