Plastic Deformation

· Frank-Reed sources may be deactivated under the sum of the internal (pile-up) and external stresses and the work hardening will then increase.
· For n dislocations in a planar pileup, the leading dislocation sees a stress,
τ = n τ₀ , due to the other dislocations. The i^th dislocation in the pile-up is at the position: x_i = (πGb/16nτ₀){i - 1}².
· The "back stress" on the Frank-Reed source is: τ_Β = (G b n)/πL , where L is the length of the pileup
· Shutoff of the Frank-Reed source occurs when τ_Β = τ_cr .