Shear Controls Frictional Aging by Erasing Memory

We simultaneously measure the static friction and the real area of contact between two solid bodies. These quantities are traditionally considered equivalent, and under static conditions both increase logarithmically in time, a phenomenon coined aging. Here we show that the frictional aging rate is determined by the combination of the aging rate of the real area of contact and two memory-erasure effects that occur when shear is changed (e.g., to measure static friction.) The application of a static shear load accelerates frictional aging while the aging rate of the real area of contact is unaffected. Moreover, a negative static shear—pulling instead of pushing—slows frictional aging, but similarly does not affect the aging of contacts. The origin of this shear effect on aging is geometrical. When shear load is increased, minute relative tilts between the two blocks prematurely erase interfacial memory prior to sliding, negating the effect of aging. Modifying the loading point of the interface eliminates these tilts and as a result frictional aging rate becomes insensitive to shear. We also identify a secondary memory-erasure effect that remains even when all tilts are eliminated and show that this effect can be leveraged to accelerate aging by cycling between two static shear loads.

Figure 1

Slide-hold-slide experiments. (a) Schematic of the biaxial compression and translation stage. Experiments are conducted using one of two shear application points, as shown by the horizontal arrows. (b) Typical experimental slide-hold-slide protocol for measuring static friction. $A_R$ is measured during the hold period, as indicated. Inset: typical example of static frictional peak. (c) ${\mu }_S$ vs $t_H$ for $S_0=\{-30,-20,-10,0,10,20,30\}\text{N}$. Color represents $S_0$ value. In this experiment, shear is applied at the level of the interface [yellow arrow in (a)]. (d) ${\beta }^{\mu }(S_0)/{\beta }_0^{\mu }$ vs $S_0$. Colors correspond to shear application points in (a), shapes correspond to sample pairs, and both are consistent in Figs. 1 and 2. Triangles indicate data taken with a load cell attached directly to the bottom sample as described in the text. This allows for positive and negative shear. Dashed lines correspond to ${\epsilon }^{\mu }\sim 0.017{\text{N}}^{-1}$ and $0{\text{N}}^{-1}$, and are repeated in (f). Inset: ${\beta }^{\mu }$ vs $S_0$. (e) Area of contact $A_R$ in arbitrary units [19] vs $t_H$ for the same experiment as (c). (f) ${\beta }^A(S_0)/{\beta }^A(S_0=0)$ as a function of $S_0$, for the same experiments as (d). Inset: ${\beta }^A$ as a function of $S_0$.

Figure 2

Contact redistribution drives shear-accelerated aging. (a) Typical images of the interfacial contact plane after background subtraction, binned for visual clarity. Images are taken at static shear load $S=0$ and $S=40\text{N}$, respectively, applied at the level of the interface. Scale bars are 2 mm. (b) Subtraction of interfacial images at $S=0$ and $40\text{N}$ for shear load applied at the interface (yellow) and 3 cm below the interface (green). Red indicates positive change, blue negative. Center of mass $(\overline{x},\overline{y})$ for the two subtracted images are superimposed as hollow black circles. (c) $\overline{x}$ vs $S_0$. Shapes correspond to samples, colors to shear application position, as in Figs. 1 and (d). (d) ${\beta }^{\mu }/{\beta }_0^{\mu }$ vs $\overline{x}$ for four sample pairs and approximately 4000 total experiments.

Figure 3

A change in shear erases interfacial memory in two ways. (a) A typical two-step protocol in shear with constant normal load, $t_H=60s$ and $S/N=0$ to $S/N=1/2$. (b) Mean values of $\mathrm{\Delta }A\equiv A-A(T_W)$ for five distinct two-step shear protocols with constant normal load. Lines are fits to Eq. (5). Colors and shapes are consistent in (b) and (c), and the legend indicates values of $S/N$. (c) $\varphi$ for eight distinct two-step protocols in shear plotted vs absolute change in shear. Black hollow symbols represent $\varphi$ measured only from regions of the interface with less than 5% change in total contact when the shear load is changed. Lines are guides for the eye. (d) ${\beta }^{\mu }$ and ${\beta }^A$ for two standard slide-hold-slide experiments at $S_0=0$ and $40\text{N}$, and one experiment (in the middle) wherein $S$ was cycled between $0\text{N}$ and $40\text{N}$ every 8 sec, as shown for a typical example in the inset.