Cyclic stress-assisted surface diffusion and stress concentration of machined surface topography

•Analytical expressions to describe machined surface diffusion are derived.•The evolution of machined surface topography is characterized by three wavelengths.•A finite element approach is formulated and compared with analytical results. This paper presents an approach that allows modeling and simulating the evolution of machined surface topography under cyclic load as a result of stress-induced surface diffusion. Both elastic strain energy and surface energy are included in the driving force. The analytical expressions of surface morphology and surface stress concentration factor are obtained by decomposing the surface morphology into Fourier series and superposing the evolution of each component. The results suggest that the evolution behavior under cyclic load is characterized by three wavelengths: the critical wavelength for growth, the critical wavelength for cusp, and the fastest growth wavelength. A finite element approach is formulated and implemented, which allows simulating conditions beyond shallow surface waviness. The comparison between analytical and numerical results confirms the applicability of our analytical solution for predicting surface topography as long as the surface waviness is relatively shallow comparing to its wavelength. The analytical form provides a powerful tool to quickly predict the growth of stress concentration factor for estimation of the service life.