PSI - Issue 12

Guido Violano et al. / Procedia Structural Integrity 12 (2018) 58–70

66

G. Violano et al. / Structural Integrity Procedia 00 (2018) 000–000

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Fig. 3. The relative contact area A / A 0 as a function of the applied load F / ( A 0 E ∗ h rms ). ICHA model results are plotted with red markers, the Persson’s theory ones with blue solid line, the GW-M model ones with black dashed line. Calculations are performed in presence ( ∆ γ = 0 . 2 J / m 2 ) and absence ( ∆ γ = 0) of adhesion on a surface with N = 32 and H = 0 . 8.

Calculations with the GW-M model are instead performed by considering a Gaussian height distribution of circular asperities with radius equal to the average curvature radius ¯ R = 2 / h rms of the generated fractal surfaces (where h rms = ∇ 2 h 2 1 / 2 ), and standard deviation equal to the root mean square (rms) roughness amplitude h rms . In all simulations, we have assumed E ∗ = 1 . 33 · 10 12 Pa and ∆ γ = 0 . 2 J / m 2 . The attractive range of adhesive interactions ε has been fixed to 1 nm. Fig. 3 shows the area-load relation in presence and absence of adhesion. Calculations have been performed on a surface with H = 0 . 8 and N = 32. The curves predicted by the GW-M model (black dashed line) significantly deviate from the ICHA model (red line with circular markers) and Persson’s theory (blue line), which instead are in very good agreement. In absence of adhesion, as expected, in the range of small contact areas the area-load relation is linear. However, in such case, the ICHA model correctly predicts the coe ffi cient of proportionality κ ( κ ∼ 2), while the Persson’s theory slightly overestimate it ( κ ≈ 2 . 15). On the contrary, at high loads, close to complete contact, the Persson’s theory is expected works well. Figs. 4 and 5 investigate the e ff ect of fractal dimension D = 3 − H and number of scales on the contact behavior. Specifically, in Fig. 4 calculations are performed on surfaces with N = 64 and H = 0 . 4 , 0 . 6 , 0 . 8, while in fig. 5 on surfaces with H = 0 . 8 and N = 16 , 32 , 64. At fixed load, the contact area increases with the Hurst exponent H , as the size of the contact spots reduces because of the shrinking of the asperities radii of curvature. The e ff ect of increasing N is instead opposite, with the relative area which reduces when the number of scales grows. In such case, indeed, the contact is splitted in several microspots and the resulting contact area is smaller. In the DMT limit, adhesive hysteresis is neglected and this is e ff ectively observed when we deal with hard solids and low surface energy (see Pastewka & Robbins (2014), Medina & Dini (2014)). The pull-o ff force can be hence assumed equal to the maximum tensile load reached during the loading phase. Fig. ?? shows the normalized pull-o ff force as a function of the Fuller & Tabor (FT) adhesive parameter θ FT = E ∗ h 3 / 2 rms ¯ R 1 / 2 / ∆ γ ¯ R . The parameter θ FT represents the ratio between the compressive repulsive force and the tensile adhesive one. When θ FT increases a reduction of the detachment force is then expected. Results in fig. ?? are obtained at di ff erent values of the number of scales ( N = 16 , 32 , 64) and Hurst exponent ( H = 0 . 4 , 0 . 6 , 0 . 8). The symbols size decreases at higher values of N , while the shape of the symbols depends on the value of H , as specified in the figure