Condition for advance of a threading dislocation

suppose that the same advance of the threading dislocation is accomplished in a different way. At some distance ahead of the threading dislocation that is very large compared to hf, a slab of material of unit thickness is imagined to the removed from the system by making cuts on two parallel planes which are perpendicular to the z—axis and which are separated by a unit distance. Tractions are maintained on the cut surfaces so that the two-dimensional state of deformation is maintained. The gap 

An immediate consequence of this important result is that the critical thickness condition based on an energy comparison obtained in Section 6.2 is identical to that based on consideration of configurational forces acting on the threading dislocation, so that (6.16) results in either case (Freund 1987). 

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