Length Scale Effect in Frictional Aging of Silica Contacts

Friction between two solid surfaces often exhibits strong rate and slip-history dependence, which critically determines the dynamic stability of frictional sliding. Empirically, such an evolutional effect has been captured by the rate-and-state friction (RSF) law based on laboratory-scale experiments; but its applicability for generic sliding interfaces under different length scales remains unclear. In this Letter, frictional aging, the key manifestation of the evolutional behavior, of silica-silica contacts is studied via slide-hold-slide tests with apparent contact size spanning across 3 orders of magnitude. The experimental results demonstrate a clear and strong length scale dependency in frictional aging characteristics. Assisted by a multiasperity RSF model, we attribute the length scale effect to roughness-dependent true contact area evolution as well as scale-dependent friction stress due to nonconcurrent slip.

Figure 1

(a) A schematic showing the experimental setup of SHS tests: Probes at three different size scales, i.e., thermally oxidized AFM tip, silica microsphere, and silica ball (left panel); lateral force and velocity profiles during SHS tests (right panel). Typical friction evolution curves for (b) nanometer-scale, (c) micrometer-scale, and (d) macroscale tests. The friction curve is locally magnified in the inset in (d) for the macroscale test. The fitted parameter $D_c$ and fitted curves (represented by the dashed lines) are shown in (b)–(d). Results in (b)–(d) were obtained in the following conditions: hold time $t_h=100\mathrm{s}$, sliding velocity $V_s=3\text{μ}\mathrm{m}/\mathrm{s}$, and $\mathrm{RH}=40\%$. The external applied loads for the nanometer-scale, micrometer-scale, and millimeter-scale experiments were 11.32 nN, 293.66 nN, and 20 mN, respectively, and the resultant apparent contact radii were 6.2 nm, 46.3 nm, and $7.38\text{μ}\mathrm{m}$, respectively (see Supplemental Material, Sec. III [26]).

Figure 2

Variations of frictional aging coefficient with hold time measured in nanometer-, micrometer-, and macroscale experiments. Each data point is an average of five repeated tests. The experimental conditions remain the same as those for Fig. 1.

Figure 3

(a) $b$ and $\tilde{b}$ extracted from the SHS experiments in Fig. 2 at three length scales. (b) A schematic showing that the friction coefficient can depend on friction shear stress and true contact area-load relation, both of which can be scale dependent.

Figure 4

(a) A schematic showing the multiasperity RSF model. (b) Frictional aging behavior of different simulation systems: single asperity, 367 asperities ($\tilde{R}=100$), and 5815 asperities ($\tilde{R}=400$). (c) Variations of friction aging coefficient with hold time for different systems. The dashed lines are log-linear fits for calculating parameter $b$. (d) Distribution of the normalized lateral force $\tilde{f}=f/(E{r}^2)$ at the moment of peak global friction for the interface with $\tilde{R}=400$. The parameters of the specific model are given in Supplemental Material, Sec. VI [26].