A generic Hall-Petch relationship in metallic materials with varied grain morphology

Abstract

The Hall-Petch relationship relates the yield strength (YS) of metallic materials to grain diameter (d), but for alloys with dendritic grains, secondary dendritic arm spacing (λ2) provides a better fit. This manuscript underscores the significance of considering a perimeter-associated parameter (p'), rather than relying solely on d or λ2, to account for strength contribution from morphological changes in various alloys. We propose a generic Hall-Petch relation expressed as σ = σ<inf>o</inf> + k'ʹ/√pʹ, where p' is the area per unit perimeter which can be accurately measured using digital imaging tools and k'ʹ is the Hall-Petch constant. To validate this approach, controlled solidification experiments were conducted on Al-Si and Al-Ce alloys across cooling rates from 0.000167 °C/s to 0.34 °C/s. The degree of primary α-Al grain complexity was manipulated through solute additions (Si or Ce), revealing a nonlinear relationship between λ2 and p', both experimentally and theoretically. This underscores the critical importance of incorporating the perimeter-associated parameter p' as a fundamental strength metric in the Hall-Petch relation. Hardness changes were analysed alongside evolving grain morphologies. Experimental data from various morphologies (facetted, rosette, dendritic) fit more effectively with the proposed generic Hall-Petch relationship than conventional models.