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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.

international journal of materials research

On the Hall–Petch relation between flow stress and grain size: Dedicated to Professor Eckard Macherauch on the occasion of the 80th anniversary of his birth