On the Hall-Petch relation between flow stress and grain size

Data of flow stresses a for pure Cu with ultrafine grains with grain size d approximate to 0.35 mu m produced by severe plastic deformation and grains of conventional size obtained in the range of homologous temperatures T-hom from 0.22 (room temperature) to 0.33 are compared to data for hardnesses H for Cu of various grain structures from single crystalline to d = 0.01 mu m measured by nanoindentation at room temperature. The two sets of data appear to be consistent when sigma approximate to H/3. At room temperature the Hall-Petch relation holds, i.e., the flow stress increases monotonically with decreasing grain size by Delta sigma alpha d(-0.5). At elevated T-hom the saturated flow stress decreases when the grains become ultrafine. The transition from hardening to softening by grain boundaries in the saturation stage is discussed on the basis of a simple statistical dislocation model considering the influence of grain boundaries on the balance between generation and annihilation of dislocations.