The Hall-Petch effect as a manifestation of the general size effect
The experimental evidence for the Hall-Petch dependence of strength on the inverse square-root of grain size is reviewed critically. Both the classic data and more recent results are considered. While the data can be fitted to the inverse square-root dependence excellently (but using two free fitting parameters for each dataset), it is also consistent with a dependence on the simple inverse of grain size (with one free fitting parameter for each dataset). There have been difficulties, recognised for half-a-century, in explaining the inverse square-root expression. A Bayesian analysis shows that the data strongly supports the simple inverse expression proposed. Since this expression derives from underlying theory, it is also more readily explicable. It is concluded that the Hall-Petch effect is not to be explained by the variety of theories found in the literature, but is a manifestation of, or underlain by, the general size effect observed throughout micromechanics, due to the inverse relationship between the stress required and the space available for dislocation sources to operate.