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
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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)