Nonmonotonic Aging and Memory in a Frictional Interface

We measure the static frictional resistance and the real area of contact between two solid blocks subjected to a normal load. We show that following a two-step change in the normal load the system exhibits nonmonotonic aging and memory effects, two hallmarks of glassy dynamics. These dynamics are strongly influenced by the discrete geometry of the frictional interface, characterized by the attachment and detachment of unique microcontacts. The results are in good agreement with a theoretical model we propose that incorporates this geometry into the framework recently used to describe Kovacs-like relaxation in glasses as well as thermal disordered systems. These results indicate that a frictional interface is a glassy system and strengthen the notion that nonmonotonic relaxation behavior is generic in such systems.

Figure 1

Experimental setup. (a) Schematic of the biaxial compression or translation stage (top) with integrated optical measurement apparatus (bottom). (b) ${\mu }_S$ versus experiment number for a typical PMMA-PMMA interface before (top) and after (bottom) trend removal described in text. (c) $I(F_N)$ (blue circles) and $g(F_N)$ (black line) measured in arbitrary units versus $F_N$ for a typical loading cycle. Inset: A typical snapshot of an interface illuminated with TIR at $F_N=100\mathrm{N}$ after background subtraction. Scale bar is 1 mm.

Figure 2

Glassy dynamics in the real area of contact (a) $A_R$ and $F_N$ versus time for a typical two-step protocol with $F_1=100\mathrm{N}$, $T_W=1000\mathrm{s}$, $F_2=25\mathrm{N}$. (b) Evolution of $A_R$ as a function of time shifted by $T_W$ following a step down in force with $F_1=100\mathrm{N}$ and $F_2=25\mathrm{N}$. Fits (black lines) use Eq. (2). (c) $T_{\min }^A$ as a function of $T_W$. $F_2=25\mathrm{N}$. (d) $\{{\beta }_1,{\beta }_{\mathrm{\Delta }},{\beta }_2\}$ as a function of $\{F_1,F_{\mathrm{\Delta }},F_2\}$, respectively. Gray line is a linear fit to ${\beta }_1(F_1)$ and ${\beta }_2(F_2)$. Note the deviation of deaging rate (${\beta }_{\mathrm{\Delta }}$, $F<0$) from the linear trend.

Figure 3

Memory in static friction (a) ${\mu }_S$ versus time for $F_1=90\mathrm{N}$, $F_2=25\mathrm{N}$. Line is a guide for the eye to highlight nonmonotonicity. (b) Evolution of $A_R$ and ${\mu }_S$ as a function of time shifted by $T_W$ following a step down in force with $F_1=90\mathrm{N}$, $T_W=60\mathrm{s}$, $F_2=40\mathrm{N}$. (c) Local $T_{\min }^A$ for the experiment shown in (b). Notice that local $T_{\min }^A$ corresponds to $T_{\min }^{\mu }$, $\sim 8\mathrm{s}$, only over a portion of the interface.

Figure 4

A phenomenological model for aging of a frictional interface. (a) Graphical representation of the ensemble of springlike modes which compose the interface in the model. A rigid line at global height $H(F_N)$ compresses all springs in contact. Probability of a spring height $P(h)$ is shown on the right. (b) Simulated ${\beta }_{\mathrm{\Delta }}$ versus $\mathrm{\Delta }F$ for $F_1=100\mathrm{N}$ and a Gaussian distribution of heights $P(h)$. (c) Measured ${\beta }_{\mathrm{\Delta }}$ versus simulated ${\beta }_{\mathrm{\Delta }}$ for five values of $\alpha$. A perfect correspondence would lie on the black, $x=y$, line. Darker and brighter shades correspond to exponential and Gaussian distributions of $P(h)$, respectively. (d) Local $T_{\min }^A$ versus $T_W$ for $F_1=100\mathrm{N}$, $F_2=25\mathrm{N}$. The seven locations are indicated in the inset with corresponding colors. Scale bar is 1 mm.