Rough viscoelastic sliding contact: Theory and experiments

In this paper, we show how the numerical theory introduced by the authors [Carbone and Putignano, J. Mech. Phys. Solids 61, 1822 (2013)] can be effectively employed to study the contact between viscoelastic rough solids. The huge numerical complexity is successfully faced up by employing the adaptive nonuniform mesh developed by the authors in Putignano et al. [J. Mech. Phys. Solids 60, 973 (2012)]. Results mark the importance of accounting for viscoelastic effects to correctly simulate the sliding rough contact. In detail, attention is, first, paid to evaluate the viscoelastic dissipation, i.e., the viscoelastic friction. Fixed the sliding speed and the normal load, friction is completely determined. Furthermore, since the methodology employed in the work allows to study contact between real materials, a comparison between experimental outcomes and numerical prediction in terms of viscoelastic friction is shown. The good agreement seems to validate—at least partially—the presented methodology. Finally, it is shown that viscoelasticity entails not only the dissipative effects previously outlined, but is also strictly related to the anisotropy of the contact solution. Indeed, a marked anisotropy is present in the contact region, which results stretched in the direction perpendicular to the sliding speed. In the paper, the anisotropy of the deformed surface and of the contact area is investigated and quantified.

Figure 1

The viscoelastic friction coefficient as a function of the dimensionless sliding speed $\xi$ for a constant normal load $P=0.30$ N.

Figure 2

The real part $E_1=Re\left[E\left(\omega \right)\right]$ (red line) and the imaginary part $E_2=Im$ (green line) of the viscoelastic modulus $E\left(\omega \right)$ of the SBR rubber samples at a room temperature of 12${}^{\circ }$C. Squares represent the measured values, and the solid lines denote the fit obtained according to the generalized viscoelastic models [28].

Figure 3

The test bench (schematic) used to measure the sliding friction of rubber. The sliding speed is controlled by pulling the sample with a weight (tangential load in the figure).

Figure 4

Rough contact surface obtained by use of the confocal microscope in the wave vector range $4.46\times {10}^3$ ${\mathrm{m}}^{-1}\le q\le 7.94\times {10}^5$ m${}^{-1}$ (top) and by use of the atomic force microscope in the range $1.26\times {10}^5$ ${\mathrm{m}}^{-1}\le q\le 3.16\times {10}^7$ m${}^{-1}$ (bottom).

Figure 5

Power spectral density $C\left(\mathbf{q}\right)$ of the rough surface. Red dots refer to confocal measures, blue crosses to AFM measures, and yellow dots to the numerically generated surface employed for the theoretical predictions.

Figure 6

The viscoelastic friction ${\mu }_V$ for different sliding speeds $v$, given a normal constant pressure $p_0=94$ KPa. The numerical calculated values (blue rhomboids) are compared to the measured ones (red squares). Red lines are referred to the standard deviation of the experimental outcomes. Notice that the $x$ axis is in a logarithmic scale.

Figure 7

Dimensionless contact area $A/A_{v_0}$ as a function of the dimensionless sliding speed $\xi$ for a constant normal load $P=0.30$ N.

Figure 8

Real contact area for $\xi =0$ (left) and $\xi =4.5\times {10}^{-3}$ (right), given a constant normal load $P=0.30$ N. The same region is extracted to enlighten anisotropic effects.

Figure 9

Polar plots of $m_2\left(\theta \right)$ for $\xi =0$ and $\xi =1.17\times {10}^{-2}$ given a constant normal load $P=0.30$ N.

Figure 10

Contours of $C\left(\mathbf{q}\right)$ for stationaty conditions (left) and for a dimensionless speed $\xi =1.17\times {10}^{-2}$ (right). Red dots refers to punctual values of $C\left(\mathbf{q}\right)$; black lines are elliptical fits.