Hall和Petch首先通过试验数据归纳出多晶材料的外加切应力与晶粒直径平方根的倒数呈线性关系,即Hall-Petch关系。但至今此关系的推导仍很粗略,也没有明确的适用范围。建立合理的位错塞积模型,从理论上推导出Hall-Petch关系,并讨论它的适用范围,得到适用的上临界尺度dmax和下临界尺度dmin,为材料的力学性能分析,及材料的合成与加工提供必要的理论数据和参考依据。 Hall and Petch first concluded from the experimental data that the applied shear stress of the polycrystalline material is linear with the reciprocal of the square root of the grain diameter, ie, the Hall-Petch relationship. But so far the derivation of this relationship is still very crude, there is no clear scope of application. A reasonable model of dislocation plugging is established. The Hall-Petch relationship is deduced theoretically and its applicable scope is discussed. The upper and lower critical scales dmax and dmin are obtained, which are the mechanical properties of materials and the synthesis of materials With the processing to provide the necessary theoretical data and reference.