Resistance to motion of dislocations
In pure materials the main source of resistance to the motion of dislocations other than the lattice resistance is from other dislocations that intersect the glide plane (picturesquely known as forest dislocations).
If a glide dislocation has its path blocked by forest dislocations that are separated by an average distance λ, then the dislocation must bow between these pinning points. The stress required to do this is given by
τ = Gb/ λ
If the dislocation density, ρ, is known, then the flow stress can be estimated, since ρ is related to λ by
ρ = 1/λ2
The difference in dislocation density between annealed and work-hardened crystals can be as much as 105 m-2, meaning that the difference in stress required to move the dislocation can vary by a factor of 300.
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