Universally scaling Hall-Petch-like relationship in metallic glass matrix composites

Ti-based metallic glass matrix composites (MGMCs) with a composition of TisoZr2oVioCu5Beis (atomic percent, at. %) exhibit excellent tensile ductility and distinct work-hardening capability. A dislocation pile-up model (DPM) has been established to elaborate the dislocation motion near the yield point and to theoretically derive a linear Hall-Petch-like relationship between the yield strength, a, and the inverse square root of the diameter of dendrite arms, d(-1/2). The materials constant, k, in the present Hall-Petch-like relationship can be calculated on the basis of the pileup model, and is very close to the experimental value. The hardness variation in the dendrites and the strengthening effect from unloading-reloading tests prove the reasonability of the DPM during tension. The Hall-Petch-like relationship is verified for a variety of MGMCs, whose plastic deformation is only dominated by dislocation motion. Mean-field theory (MFf) has been first utilized to build a relationship between the critical diameter of dendrites, dc, and the composition in MGMCs with the similar atomic percentages of low solubility elements. By tuning the composition, one can universally scale the Hall-Petch-like relationship, and accurately predict the yield strength of such in-situ MGMCs.