  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.
