Analytical Description of Brittle-to-Ductile Transition in bcc Metals. Nucleation of dislocation loop at the crack tip

Nucleation of dislocation loop at the crack tip in a material subjected to uniaxial loading is investigated. Analytical expression for the total energy of rectangular dislocation loop at the crack tip is found. Depencence of the nucleation energy barrier on dislocation loop shape and stress intensity factor at the crack tip is determined. It is established that the energetic barrier for nucleation of dislocation loop strongly depends on the stress intensity factor. Nucleation of dislocation loop is very sensitive to stress field modifiers (forest dislocations, precipitates, clusters of point defects, etc.) in the crack tip vicinity.