A Fractal Analysis of Adhesion at the Contact between Rough Solids

Abstract

Analyses of adhesion between rough solids hitherto relied on a random rough surface model which is appropriate for engineering surfaces. Adhesion occurs at the peaks of the asperities and is pronounced when the surface roughness effect is small, down to the nanometre level. It therefore follows that while the microscopic roughness would inhibit the two surfaces to come to close separation, adhesive bonds may still form at the peaks of the small-scale asperities. In order to account for the effect of asperities ranging from the nanometre to the micrometre level, it is necessary to introduce a scale-independent model. A fractal approach essentially gives this. The paper describes analysis of adhesion between rough solids using a fractal model and the results are compared with those using the conventional approach and experimental results. Some of the existing experimental observations such as adhesion-induced plasticity have been confirmed. The present analysis also gives a generalized solution and, depending on the values of fractal parameters D, the dimension, and G, the roughness parameter, specific solutions may be obtained. The solution obtained using the conventional stochastic model is thus a specific case in the generalized fractal solution.

A fractal analysis of normal impact between rough surfaces in presence of adhesion

“…Since Mandelbrot [17] first conceived and developed the fractal geometry, the concept has been discussed in various depths and used successfully in different fields of science and technology by different authors [18][19][20][21][22][23][24]. Basically, a number of objects or phenomena in nature exhibit disorder that cannot be characterized by Euclidian geometry, and fractional dimensions are required to describe them.…”

“…The equation may be solved to give the non-dimensional apparent critical contact areaā c1 and this can be related to the nondimensional real critical areaā c as [18] (ā c ) 1−D/2 = (ā c1 ) 1…”

“…Possibilities of both the separation modes for elastically and plastically deformed asperities have been discussed at length [32] and the unloading force functions in fractal mode have been derived [18]. Asperities may separate in a ductile manner, irrespective of their mode of loading [11] and load on an asperity during ductile extension is simply (aH).…”

Combined effect of surface microgeometry and adhesion in normal and sliding contacts of elastic bodies

“…The fractal approach was also employed in Ref. [20] for studying adhesive contact between rough surfaces. An approach similar to fractal surface roughness description was used by Persson and Tossati with the JKR [21,22] and DMT [23] models of adhesion.…”

An adhesive wear model of fractal surfaces in normal contact

“…To overcome shortcomings with scale-dependent statistical surface parameters (Greenwood and Williamson, 1966) and random process theory (Nayak, 1973) commonly used in contact mechanics, the surface topography in contemporary contact analyses was described by fractal geometry Bhushan, 1990, 1991;Komvopoulos, 1994a,b, 1995;Sahoo and Roy Chowdhury, 1996;Komvopoulos and Yan, 1998;Borri-Brunetto et al, 1999;Ciavarella et al, 2000;Komvopoulos and Ye, 2001;Persson et al, 2002;Yang and Komvopoulos, 2005;Gong and Komvopoulos, 2005a,b;Komvopoulos and Yang, 2006;Komvopoulos and Gong, 2007;Komvopoulos, 2008). Because fractal geometry is characterized by the properties of continuity, nondifferentiability, scale invariance, and self-affinity (Mandelbrot, 1983), it has been used in various fields of science and engineering to describe disordered phenomena, including changes in surface topography due to wear and fracture processes.…”