Dislocation crack tip shielding and the Paris exponent

In a previous paper we considered how the crack blunting dislocation emission mechanism likely leads to a Paris fatigue crack growth rate law exponent n=2 if dislocation shielding is not important and showed how dislocation crack tip shielding can cause a reduction in the fatigue crack growth rate and showed qualitatively how it might lead to an increase in the Paris exponent n. In this paper semiquantitative calculations are made to show how the Paris exponent can be increased by dislocation shielding.