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 ofσy(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/Atot is 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.