Hall-Petch Description of the Necking Point Stress

We posited that the grain size dependence of the tensile necking stress, as determined by the Considere criterion for plastic instability, is a more meaningful characteristic of the Hall-Petch (H-P) effect than that of the yield stress or the 0.2% proof stress. An inverse square-root dependence of the necking stress on the grain size was derived from a dislocation dynamics-based constitutive model. In this model, the grain size effect enters the stress indirectly via the evolution of the dislocation density. Model predictions were confirmed by the experimental data for nickel and titanium.