Friction and fracture

Consider a block placed on a table and pushed sideways until it begins to s lide. Amontons and Coulomb found that the force required to initiate slidin g is proportional to the weight of the block (the constant of proportionali ty being the static coefficient of friction), but independent of the area o f contact(1). This is commonly explained by asserting that, owing to the pr esence of asperities on the two surfaces, the actual area in physical conta ct is much smaller than it seems, and grows in proportion to the applied co mpressive force(1). Here we present an alternative picture of the static fr iction coefficient, which starts with an atomic description of surfaces in contact and then employs a multiscale analysis technique to describe how sl iding occurs for large objects. We demonstrate the existence of self-healin g cracks(2-4) that have been postulated to solve geophysical paradoxes abou t heat generated by earthquakes(5-11,25-27), and we show that, when such cr acks are present at the atomic scale, they result in solids that slip in ac cord with Coulomb's law of friction. We expect that this mechanism for fric tion will be found to operate at many length scales, and that our approach for connecting atomic and continuum descriptions will enable more realistic first-principles calculations of friction coefficients.