Constitutive modeling of size-dependent deformation behavior in nano-dual-phase glass-crystal alloys

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.