Analytical stresses in rough contacts

The pressure distribution generated by rough surfaces contact induces high stresses just beneath the surface. These stresses are at the origin of several failure mechanisms such as wear, crack initiation, etc. Therefore, it is important to be able to predict these stresses.

This article describes an analytical model to evaluate the near surface stresses below a wavy surface. The originality of this work is to combine Herztian stresses in the general case of elliptical contacts and local stresses due to the pressure fluctuations.

Furthermore, in case of wavy surfaces simple analytical solutions permit the calculation of the maximum shear stress and its location. Compared to a fully numerical method, the time of calculation is negligible; moreover, the analytical expressions give one the possibility of a better understanding of the effect of roughness parameters such as the wavelength of the asperities.

Using a Fourier transform the results can be applied to rough surfaces.