The primary goal of the work in this thesis was to investigate themacroscopic and microscopic nature of dry contact friction at very lowvelocities. Experiments were carried out using a sandpaper and carpet as contacting surfaces. The force required to pull thesandpaper across the carpet was recorded and analyzed on a computer. The very low speed at which the sandpaper was pulled (10-100 micronsper second) gave rise to a so called stick-slip motion. That is, themotion of the sandpaper consists of varying distance and time. The distributions of both jumps and duration times werefound to follow power-laws spanning up to 3 orders ofmagnitude. A scaling relation between event duration time and eventmagnitude has also been found. An analytic relation between the scaling exponents is found, and the experiments are found to follow this relation.The statistical independence of the events is supported by the agreement between theory and the experiment for the time between events of a given magnitude.These properties of the system are often taken as signs of Self-Organized Criticality (SOC), which is a category of non-equilibrium dynamical systems where the complex behavior, both in space and time, can be described statistically with power laws with non trivial exponents.
By varying parameters such as the normal force, sandpaper coarseness andthe elasticity of the system we have investigated how the statistics of the events are affected.However, no (clear) additional scaling laws, such a finite-size scaling, have been observed in the experiments. This raises questions about criticality of the system.
The force released when a single carpet fiber snaps is often too smallfor the resolution in the force measurements, but the sound is easilyheard. Using a microphone and a sound card we are able to resolve these very fine details of the friction process.
We have also found a way of imaging the real contact area betweenthe surfaces: by using an infrared camera and a transparent grid asa surface, we are able to see where the contact occurred because of the heat generated when there is a slip. We have not directly used the information collected using these two methods, butrather showed their potential if they are further developed.
Simulations were carried out to test whether our theories about themicroscopic processes could lead to the macroscopic behavior observedin the experiments. We have come up with a stochastic model where eachcontact point between the surfaces are connected with springs ofindividual strength thresholds. The crucial ingredient in our model compared to other models is that whenever a spring is stretched longer than its threshold allows, the force, or the elastic energy, is spread globally to all other contact points. This can lead to avalanches of breaking springs if sufficiently many springs are close enough to their threshold. We believe this kind of avalanche is what happens during a slip.Results from the simulations show distributions of avalanche size following a power law with exponents close to what we get from experiments. A numerical model for halting events in stick-slip motion is alsopresented. This model describes the halting of events that are relatively short lasting, but where the motion of the slider during a slip is considerable.