Fracture mechanics is the discipline concerned with analysing the failure of materials containing cracks and flaws. With fracture mechanics we can determine the stress level at which cracks of known size can propagate through the material to give failure.
Cracks in materials under load are stress concentrators. A stress concentrator is any discontinuity that will amplify an applied stress. The stress cannot be transferred through the crack, and therefore stress is concentrated at either side of the crack.
When an increasing stress is applied to a material containing a crack of length a, a stress is reached at which the crack will propagate. Or, for a given applied stress, there is a crack size at which the crack will propagate.