Mechanical properties of crystalline-amorphous composites: generalization of Hall–Petch and inverse Hall–Petch behaviors

The strength, [Formula: see text], of a polycrystal decreases with the mean grain diameter [Formula: see text] for [Formula: see text] atoms (i.e. Hall-Petch behavior) and increases for [Formula: see text] (i.e. inverse Hall-Petch behavior). Our simulations generalize [Formula: see text] to [Formula: see text], where [Formula: see text] is the mean thickness of amorphous grain boundaries of crystalline-amorphous composites. The maximum strength is reached at [Formula: see text] atoms for single-component face-centered-cubic solids and at [Formula: see text] for bidispersed or body-centered-cubic solids because of the different activation stresses of dislocation motions. The results explain recent alloy experiments and provide a way to exceed the maximum strength of polycrystals. Ductility and elastic moduli are also measured in the broad [Formula: see text] space. In regimes without a strength-ductility trade-off, the maximum ductility and ductile-brittle transitions are identified. These results obtained in [Formula: see text] space are important in solid mechanics and can guide the fabrication of crystalline-amorphous composites with outstanding mechanical properties.