Interactions and Images Peach-Koehler Applied

By exercising the instructions dictated by the Peach-Koehler formula using the state of stress given above, the force on dislocation 2 is given by 

If we work in units in which x is measured as a fraction f of d (i.e. x = fd) then the glide force (i.e. the force in the x-direction) may be rewritten in dimensionless form as 

The normalized glide force is plotted in fig. 8.22 where it is seen that there are two equilibrium points for the dislocations one of which is stable and the other of which is unstable. In fact, we have plotted the interaction force for the alternative case in which the dislocations have opposite Burgers vectors as well so as to contrast the resulting solutions. 

Note that we denote the distance of closest approach of the dislocations (i.e. along the Xi-axis) as s. Carrying out the relevant algebra in conjimction with the Peach-Koehler formula leads to the result that 

This result yields the insight that everywhere along the dislocation line the force of interaction is attractive. However, we note that as a function of the perpendicular 

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