We review some of the factors that influence the hardness of polycrystalline materials with grain sizes less than 1 µm. The fundamental physical mechanisms that govern the hardness of nanocrystalline materials are discussed. The recently proposed dislocation curvature model for grain size-dependent strengthening and the 60-year-old Hall–Petch relationship are compared. For grains less than 30 nm in size, there is evidence for a transition from dislocation-based plasticity to grain boundary sliding, rotation, or diffusion as the main mechanism responsible for hardness. The evidence surrounding the inverse Hall–Petch phenomenon is found to be inconclusive due to processing artefacts, grain growth effects, and errors associated with the conversion of hardness to yield strength in nanocrystalline materials.

中文翻译：

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霍尔-佩奇和逆霍尔-佩奇关系以及纳米晶金属的硬度

我们回顾了影响晶粒尺寸小于 1 µm 的多晶材料硬度的一些因素。讨论了控制纳米晶材料硬度的基本物理机制。比较最近提出的晶粒尺寸相关强化的位错曲率模型和 60 年前的 Hall-Petch 关系。对于尺寸小于 30 nm 的晶粒，有证据表明从基于位错的塑性到晶界滑动、旋转或扩散的转变是导致硬度的主要机制。由于加工人工制品、晶粒生长效应以及与纳米晶材料中硬度向屈服强度转换相关的错误，围绕逆霍尔-佩奇现象的证据被发现是不确定的。