Modeling the yield strength of nanocrystalline metals

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.