Stress and dislocation distributions near a crack tip in ductile single crystals

Within the continuum dislocation theory the asymptotic analysis of the plane strain crack problem for a single crystal having only one active slip system on each half-plane is provided. The results of this asymptotic analysis show that the square root stress singularity remains valid during the plastic deformation, while the dislocation density is proportional to the stress intensity factor and distributed inside the crystal as the square root of the distance from the crack tip. The analytical solution for the angular distribution of the dislocation density is found.