The ductile—brittle transition in body-centred cubic transition metals

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 ductile-brittle transition temperature, a growing microcrack is unable to penetrate the region of forced slip near the boundary of the grain in which it is nucleated. This criterion is used to calculate values of γ_e, the effective surface energy for fracture, for a number of b.c.c. transition metals. The interpretation of these values of γ_e is discussed and it is suggested that for a metal to be brittle it must have both strongly locked dislocations and a high work-hardening rate. A new interpretation of existing experimental results on the hardening and embrittlement of mild steel and molybdenum by neutron irradiation is developed. The deviation from Petch's relation shown by irradiated molybdenum is shown to result from the combination of a particularly high unpinning stress and a high work-hardening rate.