Combining phase field method and critical distance theory for predicting fatigue life of notched specimens

Notch features, widely used in engineering components, have negative effect on the fatigue life of structural parts due to the stress concentration caused by their geometry. This highlights the importance of numerical methods to help assessing the adverse effect of geometrical discontinuities like notch on the fatigue properties of structural components. In this study, a new phase field fatigue formulation was proposed to predict the fatigue behavior of metallic notched specimens, suggesting a dimensionless parameter based on the critical distance theory to capture the notch effect. The slope of S-N curve was regarded as a function of the effective stress ratio obtained from different critical distances, and the fatigue damage threshold was varied with the slope of the S-N curve. Two S-N curves of smooth and notched specimens were used to calibrate the fatigue model parameters for each material. Numerical examples validated by experimental data of various configurations in terms of geometry, stress ratio and loading mode indicated the validity of the proposed model and its ability to accurately predict the fatigue life of notched specimens with different notch geometries and materials, as the predicted fatigue lives mostly fell within the +/- 2 scatter band. The results indicated that compared with the traditional TCD method the proposed model eliminates the requirement to recalculate the critical distance at different fatigue lives, and the stress ratio effect can be naturally captured without recalibrating the critical distance.