Abstract The significance of the parameters [sgrave]i and k y in Petch's empirical relation [sgrave]y=[sgrave]i+k y d −1/2 between yield stress and grain size is discussed. It is concluded that [sgrave]i is made up of two terms [sgrave]i (L) and [sgrave]i (I). The first, [sgrave]i (L), represents the stress required to propagate a Luders band through a single crystal having no lattice friction stress. It is a function of the stress, [sgrave]d, required to unpin a dislocation from its impurity atmosphere and of the work-hardening properties of the metal. The second, [sgrave]i (I), is a friction stress probably resulting from the presence of impurity atoms. The grain size parameter, k y, measures the extra work-hardening which occurs as a result of forced slip during the propagation of yielding through a polycrystal. It is a function of the work-hardening rate of the metal and of the unpinning stress. A criterion for brittle fracture is derived which is based on the observation that, at and above the ductil...