The stability of critical distance theory model for high cycle fatigue limit prediction of foreign object damaged blade samples

Fan and compressor blades are the critical components of aircraft engine. During flight operations, aircraft engines are inherently susceptible to ingesting debris, resulting in foreign object damage (FOD) that compromises structural integrity of fan and compressor blade assemblies. Accurately evaluating blades high cycle fatigue (HCF) strength after external damage is of great scientific significance and engineering value for the maintenance free/scrapping of blades in service. Among all the available prediction models, the theory of critical distances (TCD) model shows excellent potential due to its higher accuracy and simplicity. However, the model stability is a key factor for constraining its application. In the present work, the TCD model for fatigue strength prediction of FOD specimen was further investigated, and the model stability was in-depth discussed. The fatigue limit of 3 × 10⁷ cycles for titanium aerofoil specimens after FOD was evaluated using the TCD model. A total of 18 specimens after FOD were tested under first-order bending vibration fatigue conditions. Finite element analysis was employed to investigate the first-order bending vibration modes of notched samples featuring various semi-elliptical notch geometries, allowing the determination of the critical distance through a combination of experimental data and numerical simulations. Additionally, 9 further aerofoil specimens underwent both FOD and HCF testing, with fatigue limit predictions derived from the Peterson and Neuber formula as well as the TCD approach. The results indicate that TCD model provides significantly greater predictive accuracy compared to the conventional Peterson and Neuber models. The correction factor η has little influence on the model accuracy, indicating that an arbitrary value of η can be used for model prediction as long as its geometric features and surface roughness are identical. The distribution of weight function has little influence on the model accuracy, and the constant distribution f(r) = 1 is accurate enough for the model prediction. The TCD model built in the present work demonstrates excellent stability and provides significant convenience for engineering application.