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Plastic Deformation
Frenkel Model

· An early "atomic" picture of plastic deformation consistent with these observations is due to Frenkel.
· The shear stress required to displace two planes by an amount x is periodic with the period of the lattice in the slip direction, and is assumed to have the form: τ(x) = A sin(2πx/b).
· For small x the response is elastic and A can be evaluated since: τ = Gγ , 
γ =(x/a) so that: A = (Gb/2πa), and: τ(x) = (Gb/2πa)sin(2πx/b).
· At the yield stress, τ(x) will have its maximum value:
τcr = τ(x)max = (Gb/2πa).