Hardening in the Transition to Nanocrystalline State in Pure Metals and Solid Solutions (Ultimate Hardening)

The state of the grain boundaries and the solid solution is analyzed for influence on the yield stress over a wide range of grain sizes for pure metals, low-doped alloys, and multicomponent solid solutions, including high-entropy alloys. A generalized equation is derived using the averaging integrals to describe the yield stress and hardness normalized to Young’s modulus versus the grain size. The potential to reach the maximum hardening for nanostructured materials through the use of grain-boundary engineering is considered. The concept of ‘useful’ impurities intended to bring the strength of such materials to the level comparable with the maximum (theoretically) possible one (E/2π–E/30) is proposed.