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

Abstract

The strength $ σ_{y}(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, $ σ_{y}(D)$ under thick grain boundaries (GBs) (i.e., GB thickness $l>1$ particle) and $ σ_{y}(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 $ σ_{y}(D,l=1)$ and our generalized HP-IHP behaviors of $ σ_{y}(D,l)$ share similar mechanisms and can be unified as $ σ_{y}$ ($A_\textrm{GB}/A_\textrm{tot}$), where $A_\textrm{GB}/A_\textrm{tot}$ 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 $ σ_{y}(D,l)$ should be similar in 2D and 3D, except that the HP effect in 3D is stronger.

Keywords

• polycrystal
• amorphous solid
• crystal-glass crossover
• Hall-Petch strengthening
• inverse Hall-Petch weakening