Mode III Crack Tip Plastic Zone Solution for Work Hardening Solid Using Dislocation Motion

The stress and strain field solutions for the stationary mode III crack in small-scale yielding is obtained from a direct physical picture in which the plastic strain is produced by the motion of infinitesimal dislocations. The analysis is based on a shifting center, cylindrical coordinate system. The nonredundant dislocation density is determined. The ratio of nonredundant to redundant dislocation density within the plastic zone may be a useful measure for placing cracks into a brittle class, a ductile class and semibrittle to semiductile classes.