Similarity of internal and external friction: Soft matter frictional instabilities obey mean field dissipation through slip avalanches

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Similarity of internal and external friction: Soft matter frictional instabilities obey mean field dissipation through slip avalanches

S. Zheng, J. M. Urueña, A. C. Dunn, J. T. Uhl, and K. A. Dahmen

Phys. Rev. Research 2, 042016(R) – Published 20 October 2020

Abstract

Resistance to slip across hydrogel surfaces is typically minimal, and sliding is smooth. However, recent surface friction experiments under high applied pressures caused stick-slip behavior between a glass probe and polyacrylamide hydrogel. In this paper we analyze the surface-based interface and its behavior similar to the more internal slip avalanches that occur in plastic deformations of metallic glasses and crystals using statistical descriptions. We find that the stick-slip surface friction satisfies universal power laws and scaling functions predicted by a simple mean field theory (MFT). We provide the rescaled average avalanche slip rate profiles, or average avalanche ‘‘shapes,’’ defined as the average slip rate versus time, averaged over all avalanches with similar durations or sizes. We show that the avalanche shapes obtained in this friction experiment are consistent with MFT. This suggests the similar character of force buildup and release events in internal slip and surface friction for this unique data set, and the suitability of surface microfriction experiments to explore this space.

Received 6 June 2018
Accepted 13 July 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.042016

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Friction

Polymers & Soft MatterStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsInterdisciplinary PhysicsNonlinear Dynamics

Authors & Affiliations

S. Zheng¹, J. M. Urueña², A. C. Dunn³, J. T. Uhl^4,*, and K. A. Dahmen^1,†

¹Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green Street, Urbana, Illinois 61801, USA
²Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA
³Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
⁴Los Angeles, California, USA

^*Retired.
^†dahmen@illinois.edu

Article Text

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Issue

Vol. 2, Iss. 4 — October - December 2020

Subject Areas

Soft Matter

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Images

Figure 1
(a) Schematic of the experimental setup including a smooth glass frictional probe, surface hydrogel, and force measurement mechanism through static flexure deflection. (b) Example force drops versus time for the total sliding motion. The normal force $F_{N}$ in this example is $1876.49 μ N$ . The inset shows a close-up version, which allows us to resolve small force drops.
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Figure 2
Pairs of plots juxtaposing the measured friction force magnitudes $F_{F}$ (gray data) and calculated change in force with time $d F_{F} / d t$ (black data) over the course of 1 s. Plots are organized according to decreasing levels of applied normal force for (a) and (b) $F_{N} = 1876 μ N$ , (c) and (d) $F_{N} = 1265 μ N$ , (e) and (f) $F_{N} = 875 μ N$ , (g) and (h) $F_{N} = 676 μ N$ , (i) and (j) $F_{N} = 482 μ N$ , (k) and (l) $F_{N} = 283 μ N$ , and (m) and (n) $F_{N} = 283 μ N$ . The near periodicity of the large force drops in the data reflects a frictional weakening mechanism, related to static versus dynamic friction, that produces almost-periodic large slips in addition to smaller slips in between [6, 17, 18, 19].
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Figure 3
(a) Cumulative distribution of friction force drops during slip events at interfaces nominally loaded to normal forces between $F_{N} = 127.11$ and 1876.49 μN. The red dashed line has a slope of –1/2, which is predicted by a simple mean field model. Measurements are expected to be valid for force drops $F > 1 μ N$ based on the sensitivity of the data acquisition system. (b) Maximum force drop rate versus force drop size and (c) force drop duration versus force drop size. In both figures, there are 3022 data points in total and the normal forces range from $F_{N} = 127.11$ to 1876.49 μN. The slopes of the red dashed lines again indicate the corresponding scaling exponents predicted by the same mean field model. The slopes of the red lines are 1/2. Data points are split into ten bins, each of which has the same number of data points. Red dots are average values of each bin. At the largest force drop sizes $F > 120 μ N$ , the force drop duration no longer depends on force drop size (i.e., no durations are above $T > 0.02 s$ ).
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Figure 4
Average force drop rate versus time for different force drop sizes F (scaling both axes by a factor of $F^{- 1 / 2}$ ). Profiles are averaged over force drops that have similar force drop sizes. The inset shows the unscaled average force drop rate versus time. The predicted collapse function represented by the red dashed line has the form $A x e^{- B x^{2}}$ , where A and B are nonuniversal constants $A = 2.82 \times 10^{7}$ and $B = 1.54 \times 10^{7}$ . The collapse shows that the model predictions for the scaling exponents and the scaling function are consistent with the experimental data.
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Figure 5
Rescaled force drop rate versus rescaled time (both axes are scaled by their maxima). Profiles are averaged over force drops that have similar durations. The red dashed line shows the model prediction of a parabolic average avalanche shape, which is very similar to the experimental data. The slight asymmetry to the left may reflect frictional delay effects, similar to those in earthquakes [21].
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