Predicting fatigue life with the IMWCW under complex loading

The Integration Modified Wöhler Curve Method (IMWCW), a novel approach for predicting fatigue life under complex strain-based non-proportional loading paths is introduced in this research. This method integrates concepts from the Modified Wöhler Curve Method (MWCW) with the principle of damage incremental integration to provide a more nuanced prediction of material fatigue. Besides two established E-N curves (strain-number of cycles) for uniaxial tension and torsion, a new fundamental E-N curve that characterizes the strain-life relationship under complete non-proportional loading paths is introduced. A novel strain path decomposition technique is presented, which dissects an infinite number of instantaneous micro-elements along any loading path into components parallel and perpendicular to the proportional loading direction. It is assumed that each instant will cause fatigue damage to the material. A concurrent model for the incremental integration of damage is formulated, allowing for the calculation of cumulative damage. The model is further expanded to provide analytical expressions for proportional loading and non-proportional loading, linking them to three fundamental E-N curve, so as to calibrate the parameters required for the integration model. The empirical validity of the model is confirmed through experimental testing on 7 different metallic materials under 20 loading conditions, with 391 data points analyzed. The results demonstrate that 91% of the model's predictions fall within a scatter band of 2, confirming its robustness and reliability in forecasting fatigue life in complex, real-world scenarios.