Abstract Nano-dual-phase glass-crystal (NDPGC) metallic materials as the novel nanostructured materials have been proved experimentally to possess excellent mechanical properties, e.g. the nearly ideal strength. The present work is concerned with the constitutive analysis of size-dependent deformation behaviors in micropillars of a NDPGC alloy based on the micromechanics approach. The mechanism-based constitutive models are developed to explore the sample-size dependent mechanical behaviors of NDPGC pillars. An energy-based criterion for shear-band nucleation is employed to predict the diameter-dependent number of shear bands in large micropillars subjected to compression. The flow activation in metallic glass, grain reorganization, and grain refinement are involved in the proposed constitutive model for small micropillars. Numerical results demonstrate that the proposed theoretical model can describe the constitutive behaviors of the Mg-based NDPGC alloy. Good agreements between the theoretical and experimental results are achieved for the stress-strain relations and the diameter-dependent number of shear bands in large micropillars. It is found that the critical pillar diameter for generating shear bands increases with grain size and that the yield strength of NDPGC micropillars increases with the reduction in grain size (from 50 to 10 nm) without causing the inverse Hall-Petch effect. Therefore, a good combination of high yield strength and excellent plasticity can be achieved with small micropillars under compression. These findings show that the proposed model can be applied to optimize the mechanical performance of NDPGC alloys by controlling the microstructural size and sample (or feature) size.

中文翻译：

---

纳米双相玻璃晶体合金尺寸相关变形行为的本构建模

摘要 纳米双相玻璃晶体(NDPGC)金属材料作为新型纳米结构材料已被实验证明具有优异的机械性能，如近乎理想的强度。目前的工作涉及基于微观力学方法的 NDPGC 合金微柱中尺寸相关变形行为的本构分析。开发了基于机制的本构模型来探索 NDPGC 支柱的样本大小相关的机械行为。采用基于能量的剪切带成核标准来预测受压缩的大型微柱中剪切带的直径相关数量。金属玻璃中的流动活化、晶粒重组和晶粒细化都参与了所提出的小微柱本构模型。数值结果表明，所提出的理论模型可以描述镁基 NDPGC 合金的本构行为。对于应力-应变关系和大微柱中剪切带的直径相关数量，理论和实验结果之间取得了良好的一致性。发现用于产生剪切带的临界柱直径随着晶粒尺寸而增加，并且 NDPGC 微柱的屈服强度随着晶粒尺寸的减小（从 50 到 10 nm）而增加，而不会引起反向霍尔-佩奇效应。因此，压缩下的小微柱可以实现高屈服强度和优异塑性的良好结合。