Indentation tests investigation of mechanical behavior of two-dimensional materials

Fully understanding the mechanical properties of two-dimensional (2D) materials is highly important for developing applications based on 2D-materials. Free-standing indentation (FSI) is currently the most common method to measure the mechanical properties of 2D-materials. The present work reviewed the state-of-the-art FSI investigations of 2D-mateirals, the issues to be considered, and some future works in this area. In FSI tests, 2D-materials are firstly transferred on the top of the substrate with cylindrical holes to create beam/drum-type samples, and atomic force microscopy (AFM) is then used to measure the indentation load-displacement relationship of these samples. Finally, the mechanical properties, including the elastic modulus and intrinsic strength, can be determined by fitting the experimental results as the indentation analysis model is developed on the basis of the continuum thin film. However, since the thickness of 2D-materials is far less than that of the continuum thin film, the van der Waals (vdW) adhesion interactions from the AFM-tip and the side-wall of substrate hole have a strong influence on the indentation response, which leads to measurement inaccuracy of the elastic modulus of 2D-materials from FSI tests. In addition, the nonlinear response of 2D-materials under large deformation as well as the stress concentration created by defects cannot be effectively described by the conventional indentation analysis model, and thus, the intrinsic stress of 2D-materials cannot be accurately determined, especially for the poly-crystalline 2D-materials. Therefore, we should correctly understand the present experimental results from FSI tests, and in the meantime, it is very necessary to further improve the FSI technique for measuring the mechanical properties of 2D-materials.