Unified fracture criterion for brittle 2D materials

Abstract Two-dimensional materials (2DMs), possessing atomic-scale thickness, are prone to brittle fracture under loading conditions, which can lead to catastrophic failure. As their structural dimensions approach the nanoscale, conventional linear elastic fracture mechanics (LEFM) based on continuum assumptions is deficient in capturing the underlying failure mechanisms and accurately predicting potential crack instability. This limitation emphasizes the critical need for a new theoretical approach suited to the fracture behavior of 2DM systems. We propose a unified fracture mechanics (UFM) criterion that systematically incorporates two key physical mechanisms governing brittle fracture in 2DMs at the nanoscale, namely nonlinear elasticity and atomic-scale discreteness. By introducing two corrective parameters, for nonlinearity and quantization, the UFM model successfully resolves the limitations of LEFM in predicting failure. This is particularly important in the short crack regime, as small defects are frequent in 2DMs. The theoretical predictions show excellent agreement with molecular dynamics simulations of five different types of 2DMs and accurately capture the fracture strength of both cracked and defect-free structures. In addition, we present an empirical method that allows the fracture behavior of 2DMs to be estimated directly from their intrinsic structural and elastic properties. The unified theoretical framework is applicable not only to the materials simulated in this study but may also be applied to a broader class of atomically thin brittle systems.