Consider how dislocation intersections affect the stress necessary to continue slip. Let the density of screw dislocations be ρ (meters of dislocations/m3) and for simplicity assume that these dislocations are equally divided into three sets of dislocations, each set being parallel to one of the three orthogonal axes.
A. Assume each set of dislocations is arranged in a square pattern. Express the distance between the dislocations in a set in terms of ρ.
B. Now, consider the jogs formed as a screw dislocation moves. What will be the distance between jogs?
C. Assume the energy of forming a row of interstitials is so high that the jogs essentially pin the dislocation. Express the shear stress necessary to continue the motion in terms of G, b, and ρ.
D. Now assume that the dislocation density is proportional to √ε. What would this model predict as the value of n in σ = Kεn?