Fatigue life prediction under random vibrations: An acceleration framework combining scale factor analysis and critical distance theory

In response to the practical need for efficient vibration fatigue testing of aircraft aluminum alloy components, this work proposes a novel random vibration fatigue acceleration factor model that integrates the concept of scale factors with the Theory of Critical Distances (TCD). Unlike conventional approaches, the proposed model accounts for the unique features of random vibration fatigue loads, particularly the presence of numerous small load cycles and the probabilistic nature of stress amplitudes. The fatigue behavior of the material is described by an S–N curve characterized by three parameters, while the influence of load amplitude distribution is captured through a general probabilistic stress amplitude model. To address stress concentration effects in notched components, the point method of TCD is used to identify the critical distance, where the response stress spectrum is evaluated using the von Mises equivalent stress. A scale factor is then computed at this location and used to derive the acceleration factor. The model is experimentally validated through random vibration fatigue tests on notched aluminum alloy specimens involving three materials and multiple notch configurations. The predicted acceleration factors show good agreement with the experimental data, confirming the model’s accuracy and practical applicability in aerospace engineering design.