Modelling the onset of dynamic friction : A study of rupture velocities

The onset of dynamic dry friction between two blocks of PMMA has recently been studied experimentally. Technological advances enable the study of the onset of sliding at high temporal resolutions, resulting in new insights regarding how slip occurs at a local scale along the interface. In this thesis, spring-block models are used to study the onset of dynamic dry friction. These models have been used to study earthquakes for a long time, and have later been adopted to study friction on a laboratory scale. The agreement with the mentioned experimental results has, however, up until now been rather poor. In these models, which are fully resolved in time, the local friction law has to be imposed. Using a local Amontons--Coulomb friction law, the one-dimensional model shows qualitative agreement with the experimental results. A quantitative comparison, however, reveals serious discrepancies. Studies reveal the importance of dimensionality to the kinetics, i.e. the states where slip nucleates and arrests, of the system. An example is the length of precursors as a function of the applied tangential load, which appears to be improved by including two-dimensional effects in the one-dimensional model. Both dimensionality and the local friction law are seen to be crucial for the dynamics of the system, e.g. micro-slip front propagation. In the one-dimensional model, a specific relationship between the rupture velocity, the initial shear to normal stress ratio and the local friction coefficients is derived. This reveals the importance of the interfacial strength to the rupture velocities in addition to the stress ratio which has been suggested in the experimental papers. A (2 + 0)D model, where both horizontal dimensions of the system are included, is also studied. It is shown that details of how the driving force is applied are crucial. As an illustration, a precursor has in a (2 + 0)D system both a length and a size. The development of these two quantities as a function of the applied tangential load can significantly deviate from each other depending on how the driving force is applied. The lack of experimental results studying these effects, however, makes the analysis difficult