Hall–Petch Description of the Necking Point Stress

Alexey Vinogradov, Yuri Estrin

Research output: Contribution to journalArticlepeer-review


We posited that the grain size dependence of the tensile necking stress, as determined by the Considère 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.

Original languageEnglish
Article number690
Number of pages13
Issue number4
Publication statusPublished - Apr 2023


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