Generalization of the Hall-Petch and inverse Hall-Petch behaviors by tuning amorphous regions in 2D solids

The strength σy(D) of a polycrystal can decrease or increase with the grain diameter D, i.e., the famous Hall-Petch(HP) and inverse-Hall-Petch(IHP) behaviors, respectively. However, σy(D) under thick grain boundaries(GBs)(i.e., GB thickness l > 1 particle) and σy(l) have rarely been explored. Here we measure them by systematically varying D and l of two-dimensional glass-crystal composites in simulations. We demonstrate that increasing l and decreasing D have similar effects on reducing dislocation motions and promoting GB deformations. Consequently, the classical HP-IHP behaviors of σy(D, l = 1) and our generalized HP-IHP behaviors of σy(D, l) share similar mechanisms and can be unified as σy(AGB/Atot),where AGB/Atotis the fraction of the amorphous region. The results reveal a way to exceed the maximum strength of normal polycrystals. The generalized HP-IHP behaviors of σy(D, l) should be similar in 2D and 3D, except that the HP effect in 3D is stronger.