Conventional Theory of Critical Distances (TCD) often struggles to predict fatigue life across varying geometric scales because the critical distance (L) is treated as a material constant or a simple life-dependent parameter, ignoring the “geometrical size effect.” To address this limitation, this work proposes a refined notch fatigue life prediction model that couples the stress concentration factor ( \(K_{t}\) ranging from 1.39 to 7.27) and the relative stress gradient (RSG) to dynamically calibrate the critical distance. Physically, the proposed formulation captures two distinct drivers: \(K_{t}\) governs the peak stress amplification for crack nucleation, while RSG characterizes the spatial stress decay that determines the “support effect” and the effective damage process volume. Validated by high-temperature (650 °C) fatigue experiments on GH4169 superalloy with six distinct notch configurations, the model demonstrates superior robustness compared to traditional methods. Fractographic analysis confirms that the transition from single- to multi-source crack initiation correlates strongly with the gradient-controlled stress field. Quantitative analysis shows that the proposed model significantly improves the prediction accuracy compared with the Susmel and Taylor model, with most results falling within the ± 2 scatter bands. The results establish that explicitly incorporating stress-gradient-induced size effects is essential for accurate life assessment of critical aero-engine components.
