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

TL;DR

This paper analyzes the stress and dislocation distributions near a crack tip in ductile single crystals using continuum dislocation theory, revealing that stress singularity persists during plastic deformation and dislocation density relates to stress intensity.

Contribution

It provides an asymptotic analytical solution for the crack problem in single crystals with one slip system, including dislocation density distribution and angular distribution.

Findings

Stress singularity remains during plastic deformation.

Dislocation density is proportional to stress intensity factor.

Dislocation density follows a square root distribution from the crack tip.

Abstract

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 as the square root of the distance from the crack tip. The analytical solution for the angular distribution of the dislocation density is found.