Fracture mechanisms in multilayer phosphorene assemblies: from brittle to ductile.

The outstanding mechanical performance of nacre has stimulated numerous studies on the design of artificial nacres. Phosphorene, a new two-dimensional (2D) material, has a crystalline in-plane structure and non-bonded interaction between adjacent flakes. Therefore, multi-layer phosphorene assemblies (MLPs), in which phosphorene flakes are piled up in a staggered manner, may exhibit outstanding mechanical performance, especially exceptional toughness. Therefore, molecular dynamics simulations are performed to study the dependence of the mechanical properties on the overlap distance between adjacent phosphorene layers and the number of phosphorene flakes per layer. The results indicate that when the flake number is equal to 1, a transition of fracture patterns is observed by increasing the overlap distance, from a ductile failure controlled by interfacial friction to a brittle failure dominated by the breakage of covalent bonds inside phosphorene flakes. Moreover, the failure pattern can be tuned by changing the number of flakes in each phosphorene layer. The results imply that the ultimate strength follows a power law with the exponent -0.5 in terms of the flake number, which is in good agreement with our analytical model. Furthermore, the flake number in each phosphorene layer is optimized as 2 when the temperature is 1 K in order to potentially achieve both high toughness and strength. Moreover, our results regarding the relations between mechanical performance and overlap distance can be explained well using a shear-lag model. However, it should be pointed out that increasing the temperature of MLPs could cause the transition of fracture patterns from ductile to brittle. Therefore, the optimal flake number depends heavily on temperature to achieve both its outstanding strength and toughness. Overall, our findings unveil the fundamental mechanism at the nanoscale for MLPs as well as provide a method to design phosphorene-based structures with targeted properties via tunable overlap distance and flake number in phosphorene layers.