Fracture Mechanics implications for apparent static friction coefficient in contact problems involving slip-weakening laws

摘要

We consider the effect of differing coefficients of static and dynamicfriction coefficients on the behaviour of contacts involving microslip. Theclassic solutions of Cattaneo and Mindlin are unchanged if the transition incoefficients is abrupt, but if it occurs over some small slip distance, thesolution has some mathematical similarities with those governing the normaltractions in adhesive contact problems. In particular, if the transition todynamic slip occurs over a sufficiently small area, we can identify a `JKR'approximation, where the transition region is condensed to a line. A localsingularity in shear traction is then predicted, with a stress-intensity factorthat is proportional to the the square root of the local contact pressure andto a certain integral of the friction coefficient-slip distance relation. Wecan also define an equivalent of the `small-scale yielding' criterion, whichenables us to assess when the singular solution provides a good approximation.One consequence of the results is that the static coefficient of frictiondetermined from force measurements in experiments is significantly smaller thanthe value that holds at the microscale.