Fig. 1: Three regimes of flow stress σf(l).
From: A regime beyond the Hall–Petch and inverse-Hall–Petch regimes in ultrafine-grained solids
As grain diameter l decreases, σf exhibits the Hall–Petch relationship (green curve) and the inverse Hall–Petch softening (grey line) in polycrystal regime1,2,3,4,5,6,10, and a power-law strengthening (magenta curve) in the glass-crystal composite (GCC) regime. Symbols refer to the measured results at mixing ratio x = 0.5. The fitted lc = 1.89 ± 0.01. The boundary (dashed line) between the inverse Hall–Petch softening and power-law strengthening coincides with the polycrystal–glass transition (see Supplementary Note 1 for the details). The mechanisms of the three regimes: dislocation motion, grain boundary (GB) sliding, and grain blocked shear transformation zone (STZ) are shown in the bottom.
