Decoding the origins of strength anisotropy in two-dimensional materials

Defects are inevitable in two-dimensional (2D) materials, which is widely recognized to affect the strength of 2D materials. It is known the uniaxial tension strength is significantly different along different directions of defective 2D materials. The defect induced strength anisotropy should have equal importance to defect strength, but unfortunately the mechanism and quantitative description of defect induced anisotropic strength are still unknown. In principle, the atomic origin of materials failure can be attributed to bond fracture, especially for 2D materials comprised of covalent bonds. From the viewpoint of bond fracture, the mystery of anisotropic strength of defective 2D materials is explored, that strength -orientation relations are consisted of complex multi -curves and each curve corresponds to the fracture of same bond. By considering the balance between bond stretch resulting from external loading and bond strength, a strength theory is developed, which can describe the anisotropic strength of graphene and h-BN with vast types of defects, like grain boundary, void, crack. This work deepens the understanding of defect induced anisotropic mechanical properties in 2D materials, which may facilitate defect engineering in 2D materials.