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

Abstract

Abstract Data of flow stresses σ for pure Cu with ultrafine grains with grain size d ≍ 0:35 μm 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 μm measured by nanoindentation at room temperature. The two sets of data appear to be consistent when σ ≍ H=3. At room temperature the Hall – Petch relation holds, i. e., the flow stress increases monotonically with decreasing grain size by Δ σ ∝ 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.