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