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。
It was firstly concluded by Hall and Petch through experimental data that the relationship of exogenous cut stress of polycrystalline materials and the inverse of the square root of grain size is Linear, which is Hall-Perch relationship. But so far, the derivation of this relationship has been cursory, and its applicable range also has been undefined. Then, a reasonable Pileup model of the dislocation is established, with which the relationship of Hall-Perch is theo- retically derived, and its applicable range is analyzed, legitimately getting the upper critical size for dmax and the un- der critical size for drain , so the necessary theoretical data and reference were provided for material synthesis, pro- cessing and its mechanical properties.
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