Tooth root bending fatigue: An open source framework to model crack’s nucleation and propagation

This work presents a validated modeling approach to predict fatigue failure of gear teeth, both crack nucleation to final propagation, using the Extended Finite Element Method (XFEM) within an open-source framework. Rooted in classical formulations and modern standards, the methodology integrates analytical stress evaluations based on ISO 6336 with advanced numerical simulations, focusing on multiaxial stress states in the critical tooth root region. Through the use of XFEM, the model successfully simulates crack initiation and growth paths under realistic cyclic loading, enabling the reconstruction of the stress-life curve for a tested gear configuration. The framework was validated through comparison with experimental results from controlled fatigue tests conducted under two different load scenarios, complemented by ISO 6336-based theoretical predictions. Although some limitations in experimental data constrained the full quantitative validation, the model demonstrated solid agreement in trend and propagation behavior. The visualization and interpretation of the simulation outputs has been enhanced by specific data processing. The key innovation of this study lies in its combination of analytical theory and enriched finite element techniques in an open-source environment, providing a versatile tool for researchers and engineers. The proposed workflow supports fatigue life estimation with practical relevance for structural health monitoring, and gear design optimization. While currently tailored for spur gears, the methodology can be extended to other gear types and components subjected to cyclic mechanical stress.