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

Friction, Sep 2017

In this study, models are proposed to analyze the combined effect of surface microgeometry and adhesion on the load–distance dependence and energy dissipation in an approach–separation cycle, as well as on the formation and rupture of adhesive bridges during friction. The models are based on the Maugis–Dugdale approximation in normal and frictional (sliding and rolling) contacts of elastic bodies with regular surface relief. For the normal adhesive contact of surfaces with regular relief, an analytical solution, which takes into account the mutual effect of asperities, is presented. The contribution of adhesive hysteresis into the sliding and rolling friction forces is calculated for various values of nominal pressure, parameters of microgeometry, and adhesion.

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

Friction 2223-7690 Combined effect of surface microgeometry and adhesion in normal and sliding contacts of elastic bodies In this study, models are proposed to analyze the combined effect of surface microgeometry and adhesion on the load-distance dependence and energy dissipation in an approach-separation cycle, as well as on the formation and rupture of adhesive bridges during friction. The models are based on the Maugis-Dugdale approximation in normal and frictional (sliding and rolling) contacts of elastic bodies with regular surface relief. For the normal adhesive contact of surfaces with regular relief, an analytical solution, which takes into account the mutual effect of asperities, is presented. The contribution of adhesive hysteresis into the sliding and rolling friction forces is calculated for various values of nominal pressure, parameters of microgeometry, and adhesion. adhesion; roughness; discrete contact; rolling friction; sliding friction - Irina GORYACHEVA*, Yulia MAKHOVSKAYA Institute for Problems in Mechanics of the Russian Academy of Sciences, Pr. Vernadskogo 101-1, Moscow 119526, Russia Received: 28 April 2017 / Revised: 06 June 2017 / Accepted: 19 June 2017 © The author(s) 2017. This article is published with open access at Springerlink.com Adhesive interactions play a very important role in surface friction, particularly at micro and nanoscale levels [ 1, 2 ]. It was established experimentally and theoretically that at these scale levels, the contact characteristics and friction forces depend on the mechanical properties of the interacting bodies, their surface energy, and surface microgeometry. Theoretical models that have been developed to analyze the adhesion during contact of deformable bodies differ in constitutive equations for solids, models of adhesive interaction, and description of the geometry of contacting surfaces. The commonly used models of adhesive interaction include the classical JKR [ 3 ] and DMT [ 4 ] theories, Maugis–Dugdale model [ 5 ], exact form of the Lennard–Jones potential [ 6 ] as well as its approximations by various analytical functions [ 7 ], double-Hertz approximation [ 8 ], and piecewise-constant approximation [ 9 ]. The geometry of interacting surfaces can be described as a set of asperities of determined configuration, or it can be modeled by statistical or fractal approaches. All these models and approaches being combined in the formulation of a contact problem have generated a large number of theoretical works, each having a specific limit and applicability area. The normal adhesive contact between rough elastic bodies was first studied by Johnson [ 10 ] and Fuller and Tabor [ 11 ], who employed exponential and Gaussian distributions of heights of asperities, respectively, and the JKR model of adhesion. It was shown that large diversity of heights of asperities leads to low adhesion between the surfaces, because high asperities coming into contact can cause elastic forces of repulsion between the surfaces. The DMT model of adhesion was generalized for the case of a rough surface with a specified distribution of heights in Ref. [ 12 ]. The method suggested by Fuller and Tabor [ 11 ] was applied in Ref. [ 13 ] to describe a rough contact with the use of the Maugis–Dugdale model. The adhesion of rough elastic bodies with arbitrary nominal geometry at macrolevel was modeled in Ref. [ 14 ] by applying a statistical description of roughness at microlevel and the JKR and DMT models of adhesion. The models of adhesive contact developed by Rumpf [ 15 ] and Rabinovich et al. [ 16 ] consider rigid rough surfaces having hemispherical asperities, whose centers lie on the surfaces (small asperities superimposed on large asperities), and both models use the Derjaguin approximation for adhesive interaction [ 17 ] (see the discussion on Derjaguin approximation in Ref. [ 18 ]). There were several studies that considered normal contact between rough surfaces with adhesion by using a fractal approach. Following are several examples. A contact problem between self-affine fractal surfaces was studied using a method of dimensionality reduction in Ref. [ 19 ]. 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. A model for adhesion between self-affine rough surfaces based on the JKR theory was suggested by Ciavarella [ 24 ] for a contact close to saturation. A numerical simulation of adhesion for self-affine rough surfaces was carried out in Ref. [ 25 ]. The results of this simulation and the applicability area of the DMT approximation in rough adhesive contacts were discussed in Refs. [ 26, 27 ]. A simplified model for adhesion between elastic rough solids with Gaussian multiple scales of roughness was suggested (...truncated)


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Irina Goryacheva, Yulia Makhovskaya. Combined effect of surface microgeometry and adhesion in normal and sliding contacts of elastic bodies, Friction, 2017, pp. 339-350, Volume 5, Issue 3, DOI: 10.1007/s40544-017-0179-1