Analytical prediction of the fatigue limit for axisymmetric round bars with rough surface morphology

Abstract

Analytical approaches to calculating stress distribution in machined round bars with slightly axisymmetric surface topography were derived. Surface morphologies of machined round bars were simplified as axisymmetric geometries and simulated in the form of Fourier representation. According to the point method of the theory of critical distance (TCD), an analytical expression for predicting the fatigue notch factor (FNF) of rough round specimens was proposed as well. The effectiveness of the proposed analytical expression was well verified by finite element method (FEM), with relative errors of less than 15%. Besides, the definition of the upper cut‐off frequency for estimating the fatigue limit of rough round bars was discussed comprehensively. Results showed that stress concentration factor (SCF) was sensitive to the upper cut‐off frequency and unable to be convergent, while FNF tended to be convergent and was mainly determined by low frequencies of surface topography. It explained why the height parameters of surface morphologies are the most significant characteristic parameters in determining fatigue behaviors.

Finite-element method for the analysis of surface stress concentration factor and relative stress gradient for machined surfaces

“…Cheng et al (2017Cheng et al ( , 2020 derived analytical solutions for the stress concentration of slightly undulating twodimensional (2D) and 3D surfaces using the first-order perturbation method. Cheng et al (2022) derived an analytical approach to calculate the stress distribution in machined round bars with a slightly axisymmetric surface topography. Perez et al (2020) proposed an analytical method for calculating the SCF of a 3D surface topography in different loading directions.…”