The mechanical characterization of stacked, multilayer graphene cantilevers and plates
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The mechanical characterization of stacked, multilayer graphene cantilevers and plates Emil J. Sandoz-Rosado1 , Joshua T. Smith2, Satoshi Oida2, Jingwei Bai2, Eric D. Wetzel1 1 U.S. Army Research Laboratory, Materials and Manufacturing Sciences Division, APG, MD, 21005, U.S.A. 2 IBM Watson Research Center, 1101 Kitchawan Rd., Yorktown Heights, NY 10598, U.S.A. ABSTRACT The mechanical properties of stacked graphene sheets with varying number of layers are examined. The stacked sheets are assembled by manually combining single layer CVD-grown graphene monolayers, resulting in a turbostratic multilayer graphene with irregular layer spacings greater than crystalline graphite. Due to the presence of multiple layers, the material is analyzed as a plate rather than a membrane. Bending stiffness is determined via the deflection of micron-scale cantilevers, prepared using focused ion beam milling, while in-plane tensile stiffness is characterized through center-loading of edge-supported circular specimens. Computational modeling and established analytical solutions are used to extract material and structural property information, and benchmark measured properties relative to complementary results from indentation tests. Stacked, few-layer CVD-grown graphene retains an in-plane elastic modulus of 350N/m/layer (corresponding to 1.04 TPa for an inter-layer spacing of 0.335nm), suggesting good load-sharing between stacked layers. Width-normalized bending stiffness was unmeasurable for cantilevers of 1 and 3 layers, while cantilevers of 5 and 10 layers had values of 11,100nN·nm and 1.3×106nN·nm respectively. INTRODUCTION The in-plane tensile elastic modulus of graphene, reported at 1 TPa for both CVD-grown granular graphene1 and exfoliated graphene2, makes graphene one of the stiffest materials known to exist. The intrinsic strength of graphene is estimated to be much greater than most engineering polymers, metals, and composites, making it a potentially ideal structural material. However, the scaling of graphene’s mechanical properties with increased number of layers has yet to be fully explored. A common approach for quantifying monolayer and few-layer graphene is to center-load an edge-supported circular graphene membrane. The primitive load-deflection data is then analyzed using a semi-empirical membrane model in order to extract an in-plane elastic modulus value2. This approach assumes that the few-layer graphene stack behaves as a pure membrane, without bending stiffness. However, as the graphene stack reaches 3 or 4 layers, the bending stiffness cannot be neglected and a plate model is needed3, 4. A plate model assuming infinitely small beam bending rotations has been implemented for experimental characterization of a graphene flake 69 layers thick, although this approach is not applicable to few-layer graphene for which significant rotations during loading are expected5. An appropriate analysis approach for a thin plate with finite bending rotations, such as for a few-layer graphene stack, is a von Karman plate model6. Th
