Individual Dislocation Velocities Microscopic Distances

At high velocities (near the velocity of sound), the speed is limited by viscous drag. The conventional wisdom for many years was that the velocity 

An equation that describes the dependence of dislocation velocity, v on the applied shear stress, x is  

For the case of LiF crystals, both the dislocation concentration and the incremental stress caused by plastic deformation are proportional to the amount of deformation. This indicates that the hardening is caused by impediments created by dislocations and dipoles to the motion of subsequent dislocations. 

In metals, the incremental stress of deformation-hardening is often reported to be proportional to the square root of the dislocation density. However, In view of the mechanism of dislocation multiplication, and the subsequent deformation hardening, this is highly unlikely, so this author believes that either the data are faulty, or they are being misinterpreted. 

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