Surface stress concentration factor via Fourier representation and its application for machined surfaces

An analytical solution to the stress concentration factors (SCFs) for slightly roughened surfaces is derived and validated by Digital Image Correlation (DIC) experiment as well as finite element analysis. Surface topography is considered as a superposition of numerous cosine waves by means of Fourier transform. The Airy stress function of a semi-infinite half plate with superposed surface topography under tension loading is proposed. It is found that the perturbations of stress concentrations obey the superposition principle under the limitation that the surface topography is shallow. Moreover, the proposed analytical expression is applied to predict the SCFs of real machined surface topographies, and the prediction is validated by finite element analysis. The comparisons show that the proposed analytical expression is feasible in calculating the SCFs of real machined surface topographies. A quantitative relation between the root-mean-square (RMS) value of SCFs and RMS of the surface profile slope is given.