A Theory of the Grain Size Dependence of the Yield Stress in Face-Centered Cubic Alloys

Abstract

The Hall-Petch relation is derived from detailed consideration on the previously proposed mechanism of propagation of slip across a grain boundary, in which the leading dislocation of the pile-up penetrates into the adjacent grain leaving an imperfect dislocation at and a ledge in the grain boundary. In a pure metal the relaxation of local stress at the grain boundary removes the components of the Burgers vector of the imperfect dislocation except for the component normal to the grain boundary and also removes the ledge in the grain boundary simultaneously with the passage of the leading dislocation through the grain boundary. Meanwhile, in an alloy some part of every component of the Burgers vector and of the ledge in the grain boundary must be created as the dislocation passes through the grain boundary, because the grain boundary is pinned by solute atoms. The calculated Petch slope is compared with the experiments on Cu–Al, Cu–Ni and Cu–Zn alloys reported in previous papers.