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 semi-quantitative calculations are made to show how the Paris exponent can be increased by dislocation shielding.