How does a crack concentrate stress in a solid material?

In materials testing, a crack concentrates stress because it acts as a geometric discontinuity that disrupts the uniform distribution of force within a solid.

When a material is subjected to tension, stress flows around openings or defects. Research by Gury Vasilyevich Kolosov and Charles Edward Inglis demonstrated that the concentration of stress at the boundary of an elliptical hole increases significantly as the radius of curvature at the tip of the opening becomes small relative to its overall length.1

In the limit where the hole becomes extremely thin, it defines a crack. At the crack tip, the stress becomes highly localized, creating a singularity in the linear elastic stress field. This phenomenon is quantified in engineering practice by the stress intensity factor, which characterizes the intensity of the stress field near the crack tip. Because these sharp tips create localized stress levels far exceeding the nominal stress applied to the structure, they serve as critical sites for crack nucleation and propagation, which can lead to structural failure.1