High-Fidelity Meshing and Stochastic Simulation for Enhanced Surface Stress Concentration Prediction

The accurate prediction of the Stress Concentration Factor (Kt) induced by surface topography is critical for the fatigue life assessment of engineering components. Existing models, such as the semi-empirical model by Arola-Ramulu, offer methods to estimate Kt, but their accuracy varies with material and roughness characteristics. This study presents a systematic evaluation of these established models using a robust stochastic simulation framework. A computational workflow is developed in Python, integrating a surrogate-based optimization algorithm with the Gmsh library to ensure the generation of high-fidelity Finite Element meshes for 2D dog-bone specimens. A large-scale numerical campaign is conducted on specimens made of aluminum alloy and steel, featuring statistically generated random roughness profiles. The roughness parameters for each specimen were catalogued, and the corresponding Kt is determined via linear elastic Finite Element Analysis (FEA) using Altair OptiStruct.The results from the FEA were directly compared against the predictions from Arola’s rule and Zhang’s Bayesian model. The analysis confirms that while Arola’s rule provides reasonable estimates for low levels of roughness, it significantly underestimates Kt for more severe surface topographies. In contrast, Zhang’s model demonstrated superior predictive accuracy across a wider range of roughness conditions for both materials investigated. The findings highlight that a stochastic FEA approach, underpinned by high-fidelity meshing, is an effective method for validating and comparing surface stress concentration models. The results indicate that Zhang’s model is a more reliable choice for general engineering applications. Future work should extend this framework to include material plasticity, 3D surface topographies, and validation against experimentally measured surface profiles