On stress concentration on nearly flat contacts

Fretting fatigue can severely damage components subjected to oscillatory tangential loads, leading to a dramatic reduction in fatigue life and causing catastrophic ruptures. A conservative approach that can be used when considering the effect of stress concentration induced by fretting is to ensure that the peak stress is smaller than the fatigue limit of the material. However, this depends on details of the geometry as well as loading conditions. In the present work, the contact problem of a flat rounded punch in contact with a half-plane is considered, where a dovetail joint contact geometry is approximated and the classical Hertzian contact is retrieved in the limit. Developing the analytical results given by Ciavarella, Hills and Monno, an approximate Hertzian equivalent solution using Cattaneo superposition is obtained, leading to a simple formula to estimate the maximum tangential stress as a function of the load parameter Q/(f P) and geometric parameter a/b. The accuracy of the formula is checked numerically. The proposed formula gives a maximum error as low as 4 per cent in the case of zero bulk loads. For non-zero bulk loads an analytical solution is possible for the Hertzian case for moderate bulk. This leads to a second general formula containing the three dependencies (geometry, tangential load and bulk stress), which also gives a very good approximation for rounded flat and larger bulk loads, the error being generally well below 10 per cent.