Mechanical properties characterization of 2D materials via pressure bulge testing

Pressure bulge testing is one of the standard techniques for characterizing the mechanical properties of thin films, whereas it is far less often used to characterize the mechanical properties of 2D materials. In the present work, the effectiveness of bulge testing on determining the mechanical properties of 2D materials is systematically investigated using numerical analysis. After assuming 2D materials as continuum thin films, we start by simulating the relationship between the pressure difference across the suspended film and the film deflection, and then fit the results with analytical models to extract the elastic modulus of the film. It should be noted that the clamped, pre-stretched film widely assumed in the existing analytical model is not appropriate for atomically thin materials; instead, freestanding 2D materials are actually slack in bulge testing due to the delamination of their adhesive boundary condition. Therefore, the initially unstressed flat films, pre-stretched films and slack films are investigated in the present work, and the Poisson's ratio effect is considered to investigate the effectiveness of bulge testing for most 2D materials. It is found that bulge testing can be an effective approach to characterize the mechanical properties of 2D materials.