The yield strength of nanocrystalline metals is an emphasis for designing and fabricating more reliable and cost-effective devices for application in aircraft and renewable energy systems. Grain size is a major influence factor affecting the variation of yield strength. Both Hall-Petch strengthening and inverse Hall-Petch softening, which focus on the variation of grain size, have always been the main areas of interest. Determining the critical grain size between Hall-Petch strengthening and inverse Hall-Petch softening is a challenge. In this study, a yield criterion for nanocrystalline metals is proposed by considering the dominant mechanism of plasticity yielding, which encompasses both Hall-Petch strengthening and inverse Hall-Petch softening. Subsequently, a new theoretical model for the grain size effect on yield strength is established based on the proposed criterion, which considers the grain size effect on Young's modulus, grain interior energy, and grain boundary energy. Further, taking the grain boundary migration into account to modify the established inverse Hall-Petch model. The established model accurately captures the quantitative relationships between elastic deformation energy and the dominant yielding mechanism, leading to the precise determination of the yield strength of three exemplary metals (bcc, fcc, hcp) across a wide range of grain sizes. In addition, the critical grain size between Hall-Petch strengthening and inverse Hall-Petch softening can be effectively predicted by the established model. By incorporating more detailed considerations and introducing a reference point to effectively capture experimental errors, this work achieves higher prediction accuracy compared to other existing theoretical models. In light of the established model, the analysis of influencing factors is conducted, indicating that the effect of grain boundary migration energy is greater than that of grain boundary energy. This work contributes to a deeper understanding of the plastic deformation mechanism of nanocrystalline metals and provides a new avenue and theoretical guidance for designing more high-strength systems.

中文翻译：

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模拟纳米晶金属的屈服强度


纳米晶金属的屈服强度是设计和制造用于飞机和可再生能源系统的更可靠和更具成本效益的设备的重点。晶粒尺寸是影响屈服强度变化的主要影响因素。 Hall-Petch 强化和逆 Hall-Petch 软化都关注晶粒尺寸的变化，一直是人们感兴趣的主要领域。确定霍尔-佩奇强化和逆霍尔-佩奇软化之间的临界晶粒尺寸是一个挑战。在这项研究中，通过考虑塑性屈服的主要机制，提出了纳米晶金属的屈服准则，其中包括霍尔-佩奇强化和逆霍尔-佩奇软化。随后，基于所提出的准则，建立了晶粒尺寸对屈服强度影响的新理论模型，该模型考虑了晶粒尺寸对杨氏模量、晶粒内能和晶界能的影响。进一步，考虑晶界迁移，对建立的逆Hall-Petch模型进行修正。建立的模型准确地捕捉了弹性变形能和主要屈服机制之间的定量关系，从而可以精确确定三种示例性金属（bcc、fcc、hcp）在各种晶粒尺寸上的屈服强度。此外，所建立的模型还可以有效预测Hall-Petch强化和逆Hall-Petch软化之间的临界晶粒尺寸。通过纳入更详细的考虑因素并引入参考点来有效捕捉实验误差，与其他现有理论模型相比，这项工作实现了更高的预测精度。 根据建立的模型，对影响因素进行分析，表明晶界迁移能的影响大于晶界能的影响。这项工作有助于更深入地理解纳米晶金属的塑性变形机制，并为设计更高强度的系统提供新的途径和理论指导。