Characterising the notch root radii and analyses of stress concentration factors near the dominant valleys of rough surface profiles

Surface roughness is one of the key surface integrity factors affecting the strength and fatigue life of components. Stress concentrations occur due to the randomness of the surface profiles. The presence of a dominant valley, a complex geometry and interacting effects exasperate the severity of the stress concentrations. To estimate the theoretical stress concentration factor (SCF) at the valley, the notch root radius should be estimated carefully. We propose an effective method for estimating the root radius of the deepest valley using numerical derivative techniques. The surface roughness of a carefully sanded Alumec 89 block was measured using SJ-400 tester. The 1-D roughness data was used first to evaluate the root radius of the deepest valleys and then, estimate the SCF using analytical and computational methods. We used 2-D finite element (FE) models under uniaxial tension for the computational analyses. The validity of our method is based on determining the SCF using different theoretical methods and comparing the results to the FE calculations. The theoeritical estimations are made using the Neuber, Inglis and Arola-Ramulu approaches, whereas COMSOL Multiphysics is used for the FE analyses. Comparing the theoeritical methods with the FE calculations, the Arola-Ramulu approach was better, with a maximum of  error. The minimum deviations can be explained by the model containing parameters such as , and  which are inherent to the roughness profile of the material.