The distribution of dislocations in the vicinity of a mode-I crack tip was formulated on the basis of transmission electron microscopic observations of a monocrystal. Closed-form expressions were derived for the dislocation density function and for the dislocation-free zone condition of a mode-I crack. The relationship between the size of the crack, the dislocation-free zone and the plastic zone was predicted as a function of the applied stress.

The Dislocation-Free Zone at a Mode I Crack Tip. J.Chen, S.Takezono: Engineering Fracture Mechanics, 1995, 50[2], 165-73