Chemical aging of large-scale randomly rough frictional contacts

Zhuohan Li, Lars Pastewka, and Izabela Szlufarska

Phys. Rev. E 98, 023001 – Published 2 August 2018

Abstract

It has been shown that contact aging due to chemical reactions in single asperity contacts can have a significant effect on friction. However, it is currently unknown how chemically induced contact aging of friction depends on roughness that is typically encountered in macroscopic rough contacts. Here we develop an approach that brings together a kinetic Monte Carlo model of chemical aging with a contact mechanics model of rough surfaces based on the boundary element method to determine the magnitude of chemical aging in silica-silica contacts with random roughness. Our multiscale model predicts that chemical aging for randomly rough contacts has a logarithmic dependence on time. It also shows that friction aging switches from a linear to a nonlinear dependence on the applied load as the load increase. We discover that surface roughness affects the aging behavior primarily by modifying the real contact area and the local contact pressure, whereas the effect of contact morphology is relatively small. Our results demonstrate how understanding of chemical aging can be translated from studies of single asperity contacts to macroscopic rough contacts.

Received 11 May 2018

DOI:https://doi.org/10.1103/PhysRevE.98.023001

Physics Subject Headings (PhySH)

Friction

Solid-solid interfaces

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhuohan Li¹, Lars Pastewka², and Izabela Szlufarska^1,*

¹Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison 53706-1595, USA
²Department of Microsystems Engineering, University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany

^*szlufarska@wisc.edu

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Vol. 98, Iss. 2 — August 2018

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Images

Figure 1
Surface topography of a self-affine fractal surface with roughness parameters of $h_{rms}^{'} = 0.1$ , $H = 0.8$ , $ζ = 150$ , $η = 3$ .
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Figure 2
Results of kMC simulations for a randomly rough surface shown in Fig. 1. (a) Distribution of energy barriers. Blue dashed, red solid, and green dash-dot curve represents distributions of intrinsic energy barrier to bond formation $E_{b, form, i}$ , initial energy barrier to bond formation $E_{b, form} (t = 0)$ under normal load $F_{N} = 20 μ N$ , and energy barrier to bond breaking $E_{b, break}$ , respectively. All the distributions are scaled so that the maximum is 1 for an easy comparison. (b) Friction drop $Δ F$ , as a function of hold time $t$ for multiple normal loads $F_{N}$ . $Δ F$ can be divided by $〈 f 〉 = 3.0 nN$ in order to convert it to the number of bonds formed across the interface. (c) Load and (d) contact area dependence of $Δ F$ , and $Δ μ$ at different hold times. Fraction of real contact area $A / A_{0}$ is the ratio of the real to the nominal contact area. All results shown in panels (b)–(d) are averaged over 10 different simulations performed for the same conditions (error bars are smaller than the symbol size).
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Figure 3
Results of kMC simulations for surfaces with different roughness parameters at normal load $F_{N} = 20 μ N$ . Red, green, and blue markers represent simulation results for surfaces with $h_{rms}^{'} = 0.05$ , 0.1, and 0.2, respectively. The surface roughness parameters corresponding to each marker are shown in Table 1. Red, green, and blue solid lines are linear fits to the simulation results marked by the open circles (○). (a) The slopes $β$ of the fitted red, green, and blue lines are 0.89, 0.45, and 0.2, respectively. (b) The slopes $β$ of the fitted red, green, and blue lines are 0.98, 0.49, and 0.24, respectively. For simulations shown in the left column (a)–(c), the activation volume $Δ V = 6.4 Å^{3}$ (0.04 eV/GPa) [23, 52]. For simulations shown in the right column (d)–(f), $Δ V = 0.0 Å^{3}$ . (a), (d) Time dependence of $Δ μ$ . $Δ μ$ as a function of the fraction of the real contact area $A / A_{0}$ at hold time $t = 10^{3} s$ [(b) and (e)] and $t = 1 s$ (c, f). All results are averaged over 10 different simulations performed for the same conditions (error bars are smaller than the symbol size.)
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Figure 4
Distributions of (a) local contact pressure $P$ and (b) initial local energy barrier to bond formation $E_{b, form} (t = 0)$ for rough contacts with different values of $h_{rms}^{'}$ and for $H = 0.8$ , $ζ = 150$ , and $η = 3$ [indicated by open circle (○) symbol in Fig. 3] at normal load $F_{N} = 20 μ N$ . Red, green, and blue markers correspond to surfaces with $h_{rms}^{'} = 0.05$ , 0.1, and 0.2, respectively. Effective Young's modulus $E^{*} = 35.3 GPa$ . All the distributions are normalized so that the areas below the distributions are equal to 1.
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Figure 5
Drop in the coefficient of friction $Δ μ$ vs the ratio of circumference to real contact area $C / A$ for the surfaces at hold time $t = 10^{3} s$ . $Δ μ$ is scaled by the fraction of the real contact area $A / A_{0}$ . The same data as shown in Fig. 3 as a function of $A / A_{0}$ . Marker type represents roughness parameters specified in Table 1.
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Figure 6
Time dependence of the drop in the coefficient of friction $Δ μ$ on partially hydroxylated surface ( $ρ_{OH} = 0.5 \times 4.9 OH / n m^{2}$ ) with roughness parameters $h_{rms}^{'} = 0.4$ , $H = 0.8$ , $ζ = 150$ , and $η = 3$ . The values of $Δ μ$ obtained from kMC simulations are multiplied by 0.15 to include the detachment front effect. The results are averaged over 10 different simulations performed for the same conditions.
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