Quantitative explanation of the reported values of the Hall-Petch parameter

TL;DR

This study analyzes the factors influencing the Hall-Petch coefficient in metallic materials, revealing that its variability is largely due to experimental fitting artifacts and underlying physical effects like grain size and elastic anisotropy.

Contribution

It provides a quantitative meta-analysis identifying key factors affecting the Hall-Petch coefficient and challenges the traditional interpretation of its physical significance.

Findings

Weak dependence on composition and bulk strength

Strong dependence on elastic anisotropy and stacking fault energy

No dependence on plastic strain

Abstract

The Hall-Petch effect has been described for the past sixty years as a dependence of the strength of polycrystalline metals on the inverse square-root of grain size d. The value of the coefficient of the dependence has been the subject of discussion throughout. Here, we find what factors in the experiments determine its values. A meta-analysis using maximum-likelihood methods is reported of the literature values of the coefficient in sixty-one datasets. Weak dependence is found on composition and bulk strength. Clear dependence is found on the elastic anisotropy of the different metals and on their stacking fault energies. Surprisingly, no dependence is found on plastic strain, and the strongest dependence is found on the average grain size of each study. Combining these effects accounts for the reported values of about 80% of the sixty-one coefficients. The grain-size dependence and the bulk strength dependence indicate that the Hall-Petch coefficient is an artefact arising from incorrect fitting of the data. Moreover, the grain-size dependence implies a minimum strength described by a simple inverse 1/d or a lnd/d function, which arises theoretically from considerations of dislocation curvature.