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D. A. Hills et aliii, Frattura ed Integrità Strutturale, 25 (2013) 27-35 ; DOI: 10.3221/IGF-ESIS.25.05 27 Special Issue: Characterization of Crack Tip Stress Field Sharp contact corners, fretting and cracks D. A. Hills, R. C. Flicek Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK D. Dini Department of Mechanical Engineering, Imperial College London, South Kensington Campus, Exhibition Road, London, SW7 2AZ, UK A BSTRACT . 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. K EYWORDS . asymptotic approaches; complete contacts; fretting fatigue; mode mixity; sharp notches; small scale yielding; Williams solution I NTRODUCTION ur aim is to provide a framework for the understanding of fretting fatigue for complete contacts, when the geometry of the contact itself and both the type and history of loading are completely general. We do this by studying only the extreme corners of the contact, and which we assume, for now, are both closed and adhered. The form of the contact and the loading then enter the solution only through the generalised stress intensity factors, I K , II K , defining the loading on a monolithic semi-infinite wedge. So, we begin by stating Williams' solution [2] for the stress at the tip of a semi-infinite sharp notch, of included angle in the solid of 2  , which shows that the state of stress may be written in the form       1  1  , I II I II ij I ij II ij r K r f K r f           , (1) where   , , i j r   , and, assuming plane strain, O