Two-dimensional (2D) tungsten disulfide (WS$_2$), tungsten diselenide (WSe$_2$), and tungsten ditelluride (WTe$_2$) draw increasing attention due to their attractive properties deriving from the heavy tungsten and chalcogenide atoms, but their mechanical properties are still mostly unknown. Here, we determine the intrinsic and air-aged mechanical properties of mono-, bi-, and trilayer (1-3L) WS$_2$, WSe$_2$ and WTe$_2$ using a complementary suite of experiments and theoretical calculations. High-quality 1L WS$_2$ has the highest Youngs modulus (302.4+-24.1 GPa) and strength (47.0+-8.6 GPa) of the entire family, overpassing those of 1L WSe$_2$ (258.6+-38.3 and 38.0+-6.0 GPa, respectively) and WTe$_2$ (149.1+-9.4 and 6.4+-3.3 GPa, respectively). However, the elasticity and strength of WS$_2$ decrease most dramatically with increased thickness among the three materials. We interpret the phenomenon by the different tendencies for interlayer sliding in equilibrium state and under in-plane strain and out-of-plane compression conditions in the indentation process, revealed by finite element method (FEM) and density functional theory (DFT) calculations including van der Waals (vdW) interactions. We also demonstrate that the mechanical properties of the high-quality 1-3L WS$_2$ and WSe$_2$ are largely stable in the air for up to 20 weeks. Intriguingly, the 1-3L WSe$_2$ shows increased modulus and strength values with aging in the air. This is ascribed to oxygen doping, which reinforces the structure. The present study will facilitate the design and use of 2D tungsten dichalcogenides in applications, such as strain engineering and flexible field-effect transistors (FETs).
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