The Friedel relationship between the effective stress and the average length of dislocation segments agrees with the Fleischer relationship, (Lo/L)2 = (π-θ)/2, in the Lo/L versus φ0 curve within 150° ≤ φ0 ≤ 180°, where Lo was the average spacing of impurities on a slip plane, L was that of impurities along a dislocation and φ0 was the angle at which the dislocation engaged the impurity at a temperature of 0K. Therefore, it was considered that the Friedel relationship was suitable for impurity obstacles that impede the dislocation above a φ0 of about 150° during steady and plastic deformation. In addition, it was confirmed from the value of φ0 that the Friedel relation was appropriate for the interaction between a dislocation and the impurity in alkali halides doped with monovalent impurities. This was based upon data obtained by strain-rate cycling tests associated with ultrasonic oscillation at 80 to 300K.

Bending Angle of Dislocation Pinned by an Obstacle and the Friedel Relation. Y.Kohzuki: Philosophical Magazine, 2010, 90[16], 2273-87