Characterization of nanomechanical graphene drum structures is presented in this paper. The structures were fabricated by mechanical exfoliation of graphite onto pre-etched circular trenches in silicon dioxide on a silicon substrate. Drum structures with diameters ranging from 3.8 to 5.7 μm and thicknesses down to 8 nm were achieved. Mechanical characterization of the devices was then carried out by using atomic force microscopy (AFM) to measure their electrostatic deflection. The structures were found to have linear spring constants ranging from 3.24 to 37.4 N m −1 and could be actuated to about 18-34% of their thickness before exhibiting nonlinear deflection. An analytical framework was formulated to model the deflection behaviour which was verified through finite element simulations (FEM). The experimental measurements agree well with analytical and finite element results using Young's modulus of 1 TPa. The resonance characteristics of the structures were derived by both plate theory and FEM simulations. It was found that our drum structures could potentially vibrate at frequencies in excess of 25 MHz. The small size and high operating frequencies of our nanomechanical graphene devices make them very promising for resonant mass sensing applications with 10 −20 g Hz −1 sensitivity, a two order of magnitude improvement over other reported silicon structures.
Considering the SD (strength differential) effect on compressive strength and tensile strength in zirconia ceramic material, a yield criterion with a special parameter is introduced. In addition, by analogy with associated flow rule, the constitutive model of phase transformation ceramic material has been established. Under generalized plane strain condition, the theoretical toughening expressions of mixed-mode I-III stationary cracks and steady-state growing cracks have been developed with the constitutive model. The crack toughening effect has been discussed in detail with the Poisson ratio, parameters k / α (the ratio of nominal yield strength and SD effect factor) and ω (the scale factor of mode I crack and mode III). The integral calculation shows that phase transformation toughening of stationary cracks is negative shielding effect and the toughening effect of the steady-state growing cracks change obviously with the increase of parameter k / α. Comparison between experimental data and theoretical data indicates that the yield criterion is in accord with the actual characteristics of the zirconia ceramic, when the expression of mixed-mode I-III crack is reduced to mode I crack. The results obtained in present paper can provide the useful theoretical reference for the research of phase transformation toughening in ceramic materials.
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