An innovative approach to characterize the elastic moduli of 2D materials from the central strain of bulged membrane

Freestanding 2D materials are essentially under the adhesive boundary condition instead of the typically assumed clamped boundary condition, and the membrane deformation in pressure bulge testing is actually similar as that of the slack membrane. A new bulge testing model of freestanding 2D materials is proposed from the central strain of the bulged membrane under a given pressure, based upon which the elastic moduli of 2D materials can be properly characterized by an easy testing approach. In this approach, instead of using a complex pressure loading and measuring system, the 2D materials mounted on the substrate with circular holes are simply placed into the vacuum chamber, and the moduli of materials can be characterized from their central strain measured via Raman spectroscopy. In addition, finite element modeling (FEM) is employed to validate the effectiveness of the model proposed in the present work. The present approach can provide a useful guideline on effectively characterizing the elastic moduli of 2D materials via a very simple approach, based upon which the elastic moduli can be characterized via a new technique, like Raman spectroscopy.