Fatigue notch factors prediction of rough specimen by the theory of critical distance

Analytical solutions to predict the fatigue notch factors (FNFs) of rough specimen are derived. Surface topography is reconstructed by superposing numerous cosine waves by means of Fourier transform analysis. The first-order boundary perturbation approach is used to derive the stress distribution of machined surface topography for the cases of plane stress and plane strain. The point method (PM) and line method (LM) of the theory of critical distance (TCD) are employed to derive analytical expressions to predict the fatigue notch factors (FNFs) of rough specimen. Based on the PM of TCD, the high frequency cut-off of machined surface topography is defined, which is related to a material parameter a₀. Besides, the proposed analytical expressions are applied to predict the stress concentration factors (SCFs) and FNFs of three machined specimens with varying degree of surface roughness. The prediction is also validated by finite element analysis (FEA). Predictions for the highest 10 values of SCFs using the analytical solutions are within 10% of that by FEA. The errors between FNFs based on LM in notches with highest 10 values of SCFs from the analytical solution and that by FEA are within 10%, while the errors between FNFs based on PM in these notches from the analytical solution and that by FEA are within 15%.