A regime beyond the Hall–Petch and inverse-Hall–Petch regimes in ultrafine-grained solids

The strength of polycrystal increases as the grain diameter l decreases, i.e. the Hall–Petch behaviour. This trend reverses at about 3 < l < 15 nm, i.e. the inverse-Hall–Petch behaviour. How the grain size affects material’s strength at l < 3 nm (~12 particles) remains unclear. Here our simulations use mixtures of soft and hard particles so that compression can continuously reduce l to merely a few particles, resulting in ultrafine-grained solids termed as glass-crystal composites. Beyond the conventional Hall–Petch strengthening and inverse-Hall–Petch softening, we observe a power-law strengthening at l < 14 particles as a result of the blockage of shear-banding by crystalline grains. Amorphous and crystalline regions accommodate shear strains via bond-breaking and collective rotation, respectively. Moreover, a polycrystal–glass transition occurs at l = 14 particles featured with peaks of various quantities, which deepens the understanding on softening–strengthening transition.