4:30 PM - *EQ07.01.08
Poking and Bulging of 2D Crystals
Nanshu Lu1
The University of Texas at Austin1
Show Abstract
Recently, nano-tents and nano-bubbles formed by two-dimensional (2D) materials have seen a surge of interest because they are able to induce in-plane strain as well as strain gradient via out-of-plane deformation.[1] Our previous work has unveiled what sets the in-plane strains in terms of the shape characteristics of nano-tents and nano-bubbles.[2-4] Moreover, out-of-plane poking or bulging, also known as indentation or blister tests, are popular methods for the measurement of in-plane elasticity of thin sheets. For linear elastic sheets, a load-cubic deflection relation has been frequently assumed so that the stiffness of the sheet could be readily extracted. However, we find that recent results of indentation and bulge tests on 2D materials do not follow this relation, which can be attributed to the slippage of atomically smooth 2D materials against their supporting substrates.[5, 6] Besides, the interfacial slippage could cause instabilities in the sheet such as radial wrinkles in suspended region, with finite lengths.[4] To gain a quantitative understanding, we assume constant interfacial shear traction and study the wrinkling extent and the effective stiffness of thin sheets upon poking and bulging. We identify a single dimensionless parameter governing these mechanical responses—the sliding number—defined by comparing the sheet tension (that drives the slippage) with the interfacial traction (that resists the slippage).[7] We discuss several useful asymptotic behaviors emerging at small and large sliding numbers. These understandings are helpful for determining when the effect of the interfacial slippage (as well as other substrate-associated subtleties) can be neglected in these tests. At the end, we propose a simple poking/bulging methodology immune to the complexities caused by the slippage, pretension, Poisson’s ratio, substrate roughness, etc., enabling a robust and accurate measure of 2D material stiffness.
1 Sanchez, D.A., Dai, Z., and Lu, N.: ‘2D Material Bubbles: Fabrication, Characterization, and Applications’, Trends in Chemistry, 2021, 3, (3), pp. 204-217
2 Dai, Z., Hou, Y., Sanchez, D.A., Wang, G., Brennan, C.J., Zhang, Z., Liu, L., and Lu, N.: ‘Interface-Governed Deformation of Nanobubbles and Nanotents Formed by Two-Dimensional Materials’, Physics Review Letters, 2018, 121, (26), pp. 266101
3 Sanchez, D.A., Dai, Z., Wang, P., Cantu-Chavez, A., Brennan, C.J., Huang, R., and Lu, N.: ‘Mechanics of spontaneously formed nanoblisters trapped by transferred 2D crystals’, Proceedings of the National Academy of Sciences, 2018, 115, (31), pp. 7884-7889
4 Dai, Z., Sanchez, D.A., Brennan, C.J., and Lu, N.: ‘Radial Buckle Delamination around 2D Material Tents’, J Mech Phys Solids, 2020, 137, pp. 103843
5 Akinwande, D., Brennan, C.J., Bunch, J.S., Egberts, P., Felts, J.R., Gao, H., Huang, R., Kim, J.-S., Li, T., Li, Y., Liechti, K.M., Lu, N., Park, H.S., Reed, E.J., Wang, P., Yakobson, B.I., Zhang, T., Zhang, Y.-W., Zhou, Y., and Zhu, Y.: ‘A review on mechanics and mechanical properties of 2D materials—Graphene and beyond’, Extreme Mechanics Letters, 2017, 13, pp. 42-77
6 Dai, Z., Lu, N., Liechti, K.M., and Huang, R.: ‘Mechanics at the interfaces of 2D materials: Challenges and opportunities’, Current Opinion in Solid State and Materials Science, 2020, 24, (4), pp. 100837
7 Dai, Z., and Lu, N.: ‘Poking and bulging of suspended thin sheets: Slippage, instabilities, and metrology’, J Mech Phys Solids, 2021, 149, pp. 104320