Phase-field modeling of fatigue crack growth rates considering crack closure effect

This paper presents a novel phase-field model for forecasting crack propagation behavior during the stable crack propagation stage in metallic materials, emphasizing the importance of crack closure on fatigue crack growth rates. This model uses a unified and phenomenological fracture closure factor U , as well as the maximum stress σ_max, to change the effective energy in response to cumulative fatigue damage. This formulation develops a unique phase-field framework appropriate for various stress ratios (R = 0.5, 0.06, and −1) and materials. By comparing the fatigue crack growth test data of 7075-T6 aluminum alloy and TA15 titanium alloy MT specimens, the model shows exceptional ability in predicting the stable crack propagation behavior of diverse materials across different stress ratios. Furthermore, both the experimental and numerical fatigue crack growth rate results exhibit high concordance with the Paris formula, indicating the effect of varying crack closure factors on fatigue crack growth rates of materials at the same stress amplitude. In addition, the model’s validity and robustness were assessed using a comparative study of important parameters. Finally, to address typical computational efficiency and numerical stability issues in high-cycle fatigue, an adaptive switching strategy is used between the full Newton-Raphson and modified Newton-Raphson techniques.