This paper presents observation of mechanical effects of a graphene monolayer deposited on a quartz substrate designed to operate as an extremely low-loss acoustic cavity standard at liquid-helium temperature. Resonances of this state-of-the-art cavity are used to probe the mechanical loss of the graphene film, assessed to be about $80 : 10^{-4}$ at 4K. Significant frequency shifts of positive and negative sign have been observed for many overtones of three modes of vibration. These shifts cannot be predicted by the mass-loading model widely used in the Quartz Microbalance community. Although thermo-mechanical stresses are expected in such a graphene-on-quartz composite device at low temperature due to a mismatch of expansion coefficients of both materials, it cannot fully recover the mismatch of the mass loading effect. Based on a force-frequency theory applied to the three thickness modes, to reconcile the experimental results, the mean stresses in the graphene monolayer should be of the order of 140 GPa, likely close to its tensile strength.
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