Abstract
A three-dimensional (3D) analytical framework was developed to quantify stress concentration factors (SCFs) on engineering surfaces with arbitrary slight undulations, effectively addressing the limitations of existing two-dimensional (2D) models by rigorously integrating the effects of Poisson's ratio (v) and surface texture directionality (θ). Initially, the 3D analytical solutions for single-notched specimens under uniaxial loading, which account for the v effect, were derived and compared with their 2D counterparts. The results demonstrate a clear positive correlation between v and SCFs. Subsequently, the framework was extended to single-layer undulating surfaces, revealing anisotropic stress modulation governed by θ. SCFs increase monotonically with θ, a directional sensitivity that 2D solutions are unable to represent. A parametric analysis of cosine-wave surfaces further identified a nonlinear accuracy dependency on the amplitude-frequency product (Af). Finite element method (FEM) validation showed that the relative errors are less than 5% when Af<0.05, and they rise to 14.8% when Af≈0.1. Furthermore, application to machined surfaces validated the superior accuracy of the 3D solution, achieving approximately 10% improvement compared to 2D methods with errors controlled within 5%. Significantly, the texture direction perpendicular to the loading direction results in notably higher SCFs than the parallel direction, directly correlating texture orientation with stress concentration severity. This study provides a robust theoretical basis for surface topography optimization in engineering applications, with validated reliability across geometric and material parameters.