A Hall-Petch-like relationship linking nanoscale heterogeneity to yield stress of heterogeneous metallic glasses

Abstract

Metallic glasses (MGs) undergo plastic deformation through shear transformation zones (STZs) at small deformations and shear banding at large deformations. The STZ mechanism is linked to microstructural heterogeneities, including nano-heterogeneities associated with atom clustering and their spatial distribution. Shear banding occurs due to the coalescence of STZs. In this study, we investigate the yielding behavior of heterogeneous MGs by varying the spatial correlation and standard deviation of local shear moduli associated with clustering atoms on the nanoscale. Using a mesoscale shear transformation zone (STZ) dynamics model, we compute the yielding strength and observe deformation behaviors associated with the formation and propagation of STZs. We propose a Hall-Petch-like relationship where the yield stress of the MG scales inversely with the square root of the spatial correlation length. Our results show that the yielding of MGs corresponds to the percolation of STZs from soft to hard regions. Prior to macroscopic yielding, the activated STZs tend to accumulate inside soft regions, forming a Super-STZ array, which is similar to the formation of dislocation pile-up at grain boundaries. We derive the stress concentration in the front of the Super-STZ using the Eshelby inclusion model and formulate a Hall-Petch-like equation to quantify the yield of MGs with the spatial correlation length and standard deviation of the nanoscale heterogeneity. Our results provide insights into the structure-property relationship of MGs and have important implications for the design of nanoscale MGs with tunable properties.