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Tribology Letters
Erschienen in: Tribology Letters 1/2014

01.10.2014 | Original Paper

The Contact of Elastic Regular Wavy Surfaces Revisited

verfasst von: Vladislav A. Yastrebov, Guillaume Anciaux, Jean-François Molinari

Erschienen in: Tribology Letters | Ausgabe 1/2014

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Abstract

We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we discover previously overlooked transition regimes. These are seen in particular in the evolution with applied load of the contact area and perimeter, the mean pressure and the probability density of contact pressure. These transitions are correlated with the contact area shape, which is affected by long range elastic interactions. Our analysis has implications for general random rough surfaces, as similar local transitions occur continuously at detached areas or coalescing contact zones. We show that the probability density of null contact pressures is nonzero at full contact. This might suggest revisiting the conditions necessary for applying Persson’s model at partial contacts and guide the comparisons with numerical simulations. We also address the evaluation of the contact perimeter for discrete geometries and the applicability of Westergaard’s solution for three-dimensional geometries.
Vorheriger Artikel Effect of Imidazolium Ionic Liquid Additives on Lubrication Performance of Propylene Carbonate under Different Electrical Potentials
Nächster Artikel Erratum to: The Relationship Between Contact Mechanics and Adhesion in Nanoscale Contacts Between Non-Polar Molecular Monolayers

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Fußnoten
1
The original formulation of the FFT algorithm [25] contains some errors. The most relevant is that the solution is shifted in Fourier space by one wave number. For the current and previous studies [30, 31], we use a corrected version of this method, which was validated on many cases.
 
2
The nominal contact area is \(A_0=\lambda ^2\) as we carry out our simulations on a surface \(\lambda \times \lambda \) to make use of periodic boundary conditions. In the following, however, due to symmetry, all results will be shown only on a quarter of the simulation domain.
 
3
This method is quite similar to the one [25] used in this paper, both are based on the Kalker’s variational formulation [15, 16].
 
4
The FFT-based method, which we use, fails to predict accurately the contact area evolution near full contact \(A^{\prime } \gtrapprox 97\,\%\). Thus, to compare with the asymptotic solution near full contact (3), we used a more accurate axisymmetric finite element model with discretization 6,400 points per wavelength (triangles in Fig. 4b).
 
5
One can use Ramanujan’s approximation for the perimeter of an ellipse with semi-axes \(a\) and \(b\), \(S\approx \pi (3(a+b)-\sqrt{(3a+b)(a+3b)})\).
 
6
See also a discussion in [31].
 
7
The term contact perimeter, which is introduced in these references, should not be confused with the contact perimeter employed here. By contact perimeter, the author of [1, 2] understands the number of boundaries between neighboring pixels that form the discrete shape.
 
8
We found the closure compactness close to the percolation limit to be \(c_{\mathrm{closure}}\approx 4.04\). Regardless the fact that for “closing gap” regime, the shape of the contact boundary cannot be approximated by a square, its compactness measurement near the percolation limit can be with a good accuracy approximated by \(c\approx 4\).
 
9
Hereinafter, the PDF of contact pressure is computed only in contact regions; the integral of the PDF over all contact pressures is equal to one.
 
10
We cannot show rigorously that the peak observed in Fig. 10 is a singularity, but we can assume that if at full contact a singularity exists, see Eq. (14), it is probable that it also persists at smaller pressures.
 
11
We recall that in this case, the contact pressure is \(p(r)=p_{\max }\sqrt{1-(r/a)^2}\).
 
12
Differentiation under the integral sign: \(\frac{\hbox {d}}{\hbox {d}x}\!\!\!\int \limits _{a(x)}^{b(x)}\!\!\!\!f(x,t)\hbox {d}t = \!f(x,b(x))\frac{\hbox {d}b(x)}{\hbox {d}x} - f(x,a(x))\frac{\hbox {d}a(x)}{\hbox {d}x} + \!\!\!\int \limits _{a(x)}^{b(x)} \!\!\frac{\hbox {d}f(x,t)}{\hbox {d}x}\hbox {d}t\).
 
Literatur
1.
Bribiesca, E.: Measuring 2-D shape compactness using the contact perimeter. Comput. Math. Appl. 33(11), 1–9 (1997)CrossRef
2.
Bribiesca, E.: An easy measure of compactness for 2D and 3D shapes. Pattern Recognit. 41(2), 543–554 (2008)CrossRef
3.
Bush, A.W., Gibson, R.D., Thomas, T.R.: The elastic contact of a rough surface. Wear 35(1), 87–111 (1975)CrossRef
4.
Carbone, G., Bottiglione, F.: Asperity contact theories: Do they predict linearity between contact area and load? J. Mech. Phys. Solids 56, 2555–2572 (2008)CrossRef
5.
Dapp, W.B., Lücke, A., Persson, B.N.J., Müser, M.H.: Self-affine elastic contacts: percolation and leakage. Phys. Rev. Lett. 108, 244,301 (2012)CrossRef
6.
Dieterich, J.H., Kilgore, B.D.: Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic. Tectonophysics 256(1–4), 219–239 (1996)CrossRef
7.
Dorsey, G., Kuhlmann-Wilsdorf, D.: Metal fiber brushes. In: Slade, P.G. (ed.) Electric Contacts: Principles and Applications, 2nd edn. CRC Press, Boca Raton, FL (2014)
8.
Einzel, D., Panzer, P., Liu, M.: Boundary condition for fluid flow: curved or rough surfaces. Phys. Rev. Lett. 64, 2269–2272 (1990)CrossRef
9.
Gielis, J.: A generic geometric transformation that unifies a wide range of natural and abstract shapes. Am. J. Bot. 90(3), 333–338 (2003)CrossRef
10.
Greenwood, J.A.: A simplified elliptic model of rough surface contact. Wear 261, 191–200 (2006)CrossRef
11.
Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. Lond. A Math. Phys. Sci. 295, 300–319 (1966)CrossRef
12.
Hyun, S., Robbins, M.O.: Elastic contact between rough surfaces: effect of roughness at large and small wavelengths. Tribol. Int. 40, 1413–1422 (2007)CrossRef
13.
Johnson, K., Greenwood, J., Higginson, J.: The contact of elastic regular wavy surfaces. Int. J. Mech. Sci. 27(6), 383–396 (1985)CrossRef
14.
Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1987)
15.
Kalker, J.J.: Variational principles of contact elastostatics. J. Inst. Math. Appl. 20, 199–219 (1977)CrossRef
16.
Kalker, J.J., van Randen, Y.A.: A minimum principle for frictionless elastic contact with application to non Hertzian problems. J. Eng. Math. 6, 193–206 (1972)CrossRef
17.
Krithivasan, V., Jackson, R.L.: An analysis of three-dimensional elasto-plastic sinusoidal contact. Tribol. Lett. 27(1), 31–43 (2007)CrossRef
18.
Manners, W., Greenwood, J.A.: Some observations on Persson’s diffusion theory of elastic contact. Wear 261, 600–610 (2006)CrossRef
19.
McCool, J.I.: Comparison of models for the contact of rough surfaces. Wear 107(1), 37–60 (1986)CrossRef
20.
Nayak, P.R.: Random process model of rough surfaces. J. Lubr. Technol. (ASME) 93, 398–407 (1971)CrossRef
21.
Pastewka, L., Robbins, M.O.: Contact between rough surfaces and a criterion for macroscopic adhesion. Proc. Natl. Acad. Sci. USA 111(9), 3298–3303 (2014)CrossRef
22.
Persson, B.N.J.: Elastoplastic contact between randomly rough surfaces. Phys. Rev. Lett. 87, 116,101 (2001)CrossRef
23.
Persson, B.N.J.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115, 3840–3861 (2001)CrossRef
24.
Persson, B.N.J., Bucher, F., Chiaia, B.: Elastic contact between randomly rough surfaces: comparison of theory with numerical results. Phys. Rev. B 65, 184,106 (2002)CrossRef
25.
Stanley, H.M., Kato, T.: An FFT-based method for rough surface contact. J. Tribol-T ASME 119, 481–485 (1997)CrossRef
26.
Stover, J.C.: Optical Scattering: Measurements and Analysis, 3rd edn. SPIE Press, Bellingham (2012)
27.
Thomas, T.R.: Rough Surfaces, 2nd edn. Imperial College Press, London (1999)
28.
Westergaard, H.M.: Bearing pressures and cracks. J. Appl. Mech. (ASME) 6, 49 (1939)
29.
Yang, C., Persson, B.N.J.: Contact mechanics: contact area and interfacial separation from small contact to full contact. J. Phys.-Condens. Matter 20(21), 215,214+ (2008)CrossRef
30.
Yastrebov, V.A., Anciaux, G., Molinari, J.F.: Contact between representative rough surfaces. Phys. Rev. E 86(3), 035,601(R) (2012)CrossRef
31.
Yastrebov, V.A., Anciaux, G., Molinari, J.F.: From infinitesimal to full contact between rough surfaces: evolution of the contact area (2014) arxiv.​1401.​3800
Metadaten
Titel
The Contact of Elastic Regular Wavy Surfaces Revisited
verfasst von
Vladislav A. Yastrebov
Guillaume Anciaux
Jean-François Molinari
Publikationsdatum
01.10.2014
Verlag
Springer US
Erschienen in
Tribology Letters / Ausgabe 1/2014
Print ISSN: 1023-8883
Elektronische ISSN: 1573-2711
DOI
https://doi.org/10.1007/s11249-014-0395-z

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