Contacts with sharp edges subject to oscillatory loading are likely to nucleate cracks from the corners, if the loading is sufficiently severe. To a first approximation, the corners behave like notches, where the local elastic behaviour is relieved by plasticity, and which in turn causes irreversibilities that give rise to crack nucleation, but also by frictional slip. One question we aim to answer here is; when is the frictional slip enveloped by plastic slip, so that the corner is effectively a notch in a monolithic material? We do this by employing the classical Williams asymptotic solution to model the contact corner, and, in doing so, we render the solution completely general in the sense that it is independent of the overall geometry of the components. We then re-define the independent parameters describing the properties of the Williams solution by using the inherent length scale, a procedure that was described at the first IJFatigue and FFEMS joint workshop [1]. By proceeding in this way, we can provide a self-contained solution that can be ‘pasted in’ to any complete contact problem, and hence the likelihood of crack nucleation, and the circumstances under which it might occur, can be classified. Further, this reformulation of Williams' solution provides a clear means of obtaining the strength (defined by crack nucleation conditions) of a material pair with a particular contact angle. This means that the results from a test carried out using a laboratory specimen may easily be carried over to any complicated contact problem found in engineering practice, and a mechanical test of the prototypical geometry, which may often be quite difficult, is avoided.