Frictional weakening of slip interfaces

Abstract

When two objects are in contact, the force necessary to overcome friction is larger than the force necessary to keep sliding motion going. This difference between static and dynamic friction is usually attributed to the growth of the area of real contact between rough surfaces in time when the system is at rest. We directly measure the area of real contact and show that it actually increases during macroscopic slip, despite the fact that dynamic friction is smaller than static friction. This signals a decrease in the interfacial shear strength, the friction per unit contact area, which is due to a mechanical weakening of the asperities. This provides a novel explanation for stick-slip phenomena in, e.g., earthquakes.

Fig. 1. Time evolution of the friction force and the area of real contact.

(A) Original friction curves and inverted fluorescence images (75 μm by 75 μm) of the real contact area taken before the first and the last friction test. Fluorescence images of the contact were recorded seconds before the friction measurement was started. (B) Real contact area A (red squares) measured before the onset of sliding, arbitrarily scaled total fluorescence intensity I (red circles) and static (blue triangles pointing up) or dynamic (blue triangles pointing right) friction force F as a function of the time elapsed since the contact was initially formed [same data as (A)]. The background fluorescence is measured and subtracted from the intensity values reported in (B). The friction/microscopy setup is schematically shown in the inset in (B). The distance between the sphere center and the rotation axis of the rheometer is more than two orders of magnitude larger than the size of the contact or the sliding distance for a single friction test. Contacts were immersed in formamide to avoid strong light scattering at the interface. Dry experiments, or experiments on glass without rigidochromic molecules, reveal identical frictional behavior (fig. S5). a.u., arbitrary units.

Fig. 2. The area of real contact.

(A) Half of the fluorescence image (left) and the mirrored elastoplastic contact calculation (right) of the rough PS on smooth glass contact at a normal force of 392 mN. The plasticity is modeled by increasing the gap at which contact is defined in the purely elastic calculation from 0.1 to 170 nm: This is the only adjustable parameter, and the plain strain modulus is independently measured (18): E* = 3.7 GPa. (B) The AFM topograph of the PS sphere before (left) and after (right; mirrored, areas outside AFM range shown in green) contact with glass shows plastic deformation of the same order. Before the contact experiment, the root mean square roughness of the sphere is 650 nm, and that of the substrate is 2 nm (fig. S4). (C) Calculated contact area as a function of the full width half maximum of the Gaussian PSF with which the contact area is convolved. The AFM and contact calculations both have a pixel size of 32 nm, roughly an order of magnitude lower than the microscopy PSF. The sphere curvature was subtracted from the AFM topographs shown in (B) to highlight the surface roughness. To define the experimental or calculated and convolved area of real contact, we set an intensity threshold (38) and simply multiply the pixel area with the total number of pixels with intensities above the threshold (fig. S1); for all experiments and calculations, the pixel size is smaller than the PSF.

Fig. 3. Contact area growth in time.

(A) Contact area as a function of the time the sphere has spent in contact with the glass at N ≈ 400 mN (black circles). The contact area growth is accelerated when slip is imposed right after each contact area measurement (red triangles, time measured relative to the moment of contact formation, not to the end of each slip event) but saturates at the same logarithmic growth rate after the first few slip events (black solid lines). Inset images show contact areas (black areas) corresponding to the first data points. (B) Difference images highlighting contact area growth (left) after 50 min of contact (without macroscopic slip) and (right) after the first slip event.

Fig. 4. The stick-slip transition.

Normalized contact area (A), total fluorescence intensity (I), contact displacement (D), and friction force (F) measured during the 78-s slip event also shown in Fig. 1. The arrows and numbers indicate which data points were used for the difference images in Fig. 5. Contact displacement is measured by optimally overlapping subsequent fluorescence images to the first fluorescence image in the series. Inset shows shear stress σ—defined as the ratio of friction force to real contact area—corresponding to the data in the main figure.

Fig. 5. Difference images corresponding to Fig. 4.

Top: Newly formed contacts are shown in blue, and broken contacts are shown in red. Bottom: Fluorescence intensity changes. Before sliding starts (2-1), existing contacts shrink under the influence of the tangential force (contact edges turn red), while a slight rolling motion of the sphere causes trailing edge contacts (left) to break and leading edge contacts (right) to form. During macroscopic slip (3-2), leading edge contacts continue to grow, while trailing edge contacts disappear. As sliding stops and the tangential force is removed from the contact (4-3), contacts grow again at the asperity level (contact edges turn blue), while the sphere rotates back to restore the trailing edge contacts that were broken and to remove the leading edge contacts that were formed.

Fig. 6. Contact breaking.

The change in fluorescence intensity (ΔI) observed at various distances from the contact center (a) during the buildup of the static friction force. Inset shows friction force as a function of time, with arrows indicating the moments at which the intensity distributions were recorded. The fluorescence intensity is radially averaged around the center of the contact. As the friction force approaches its static value, a front of increased fluorescence intensity moves from the perimeter of the contact area toward the center at a speed of approximately 10 μm/s.