Physical mechanism interpretation of polycrystalline metals’ yield strength via a data-driven method: A novel Hall–Petch relationship

The Hall–Petch relationship σ y = σ 0 + k y d − 0.5 is widely used to describe the relationship between yield strength and grain size of polycrystalline metals, and the material constants σ ₀ and k _y fitted by experimental data are interpreted as lattice friction resistance and coefficient of grain boundary resistance, respectively. The frequent deviations from the Hall–Petch relationship between σ _y and d in coarser or finer grains, as well as the physical essence of σ ₀ and k _y, have always been the focus of material scientists. In this study, intrinsic factors of the fitted constants σ ₀ and k _y in the traditional Hall–Petch relationship are mined via a data-driven machine learning method, which reveals that the key physical quantities affecting σ ₀ are valence electron distance ( S ), cohesive energy ( W), and coefficient of linear thermal expansion ( l_t); meanwhile, the key physical quantities affecting k _y are grain boundary interface energy ( γ ), Young`s modulus ( E) and coefficient of linear thermal expansion ( l_t). Then, a novel Hall–Petch model σ y = 79 W / ( S 3 l t ) + 1.2 γ E / l t d − 0.5 with satisfying prediction accuracy is constructed by symbolic regression methods. There is no experimental fitting constant term in the novel model, which can directly predict the yield strength of polycrystalline metals by key physical quantities. The novel Hall–Petch model has an excellent generalization ability and can be extended to the correlation calculation between the composition, grain structure and mechanical properties of single-phase alloys, which provides a theoretical method for the trans-scale calculation of metallic materials.