Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties

Carbone, Giuseppe; Lorenz, B.; Persson, B. N. J.; Wohlers, Alexander

doi:10.1140/epje/i2009-10484-8

Cited by 153 publications

(122 citation statements)

References 14 publications

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“…Of course this is not unexpected since the C σ (q) and C u (q) are related each-other through C σ (q) = 1 4 E * 2 q 2 C u (q) [15], [16]. Using that C u (q) ≈ q −(2+H) , and assuming the adhesion interaction is not important (which occurs in the mid range of wavevectors q), one obtains, C σ (q) ≈ q −H .…”

Section: Resultsmentioning

confidence: 93%

“…We observe that the original version of Persson's theory [10], [11] was conceived to deal with isotropic surfaces, but in our case the surfaces is strongly anisotropic, being rough only in one direction. Therefore, in order to compare theoretical and numerically calculated data we have employed an extended version of Persson's theory [16], which is able to handle anisotropic surfaces as in the case of 1D rough surfaces. There are mainly two reasons for studying a 1D rough surface: (i) first of all one should consider that surface roughness is characterized by a large number of length scales, which can cover 3-4 decades and even more.…”

Section: Introductionmentioning

confidence: 99%

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Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

2009

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The authors have employed a numerical procedure to analyze the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution of the problem, which belongs to the class of the free boundary problems, is obtained by calculating the Green's function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel, and the boundaries of the contact area are calculated by requiring that the energy of the system is stationary. The methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the prediction of an extended version of the Persson's contact mechanics theory, able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson's theory underestimates the contact area of about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than what is found for 2D rough surfaces in case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson's theory is a mean field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe, that the predicted value of separation is in very good agreement with our numerical results as well as the exponent of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson's theory captures almost exactly the main qualitative behavior of the rough contact phenomena.

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Section: Resultsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

2009

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“…The contact mechanics theory of Persson [6,[41][42][43][44][45][46][47] can be used to calculate (approximately) the stress distribution at the interface, the area of real contact and the interfacial separation between the solid walls [41,42]. In this theory the interface is studied at different magnifications ζ = L/λ, where L is the linear size of the system and λ the resolution.…”

Section: Jkr-limitmentioning

confidence: 99%

Theory of adhesion: Role of surface roughness

Persson¹,

Scaraggi

2014

The Journal of Chemical Physics

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We discuss how surface roughness influence the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length scales. We consider two limiting cases relevant for (a) elastically hard solids with weak adhesive interaction (DMT-limit) and (b) elastically soft solids or strong adhesive interaction (JKR-limit). For the former cases we study the nature of the adhesion using different adhesive force laws (F ∼ u −n , n = 1.5 − 4, where u is the wall-wall separation). In general, adhesion may switch from DMT-like at short length scales to JKR-like at large (macroscopic) length scale. We compare the theory predictions to the results of exact numerical simulations and find good agreement between theory and the simulation results.

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“…7 for isotropic roughness, and in Ref. 39 for the general case of anisotropic roughness. In the absence of viscoelastic effects, the average shear stress at the solid-solid contact is assumed to be:…”

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confidence: 97%

Lubrication in soft rough contacts: A novel homogenized approach. Part I - Theory

et al. 2011

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We study the lubricated steady sliding contact between rough surfaces of (elastically) soft solids. A novel mean field theory of mixed lubrication is presented, which takes into account the coupled effect of asperity-asperity and asperity-fluid interactions. We calculate the fluid flow factors, and discuss the nature of the transition from the boundary lubrication regime, where the normal load is supported by the asperity-asperity interactions (sometimes mediated by boundary films), to the hydrodynamic regime, where a thin fluid film prevents direct contact between the mating surfaces.

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Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties

Cited by 153 publications

References 14 publications

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

Theory of adhesion: Role of surface roughness

Lubrication in soft rough contacts: A novel homogenized approach. Part I - Theory

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