Review of the development of the probabilistic damage tolerance assessment of life-limited parts in compliance with the airworthiness regulations

Probabilistic damage tolerance is a critical method to understand and communicate risk and safety. This paper reviews recent research on the probabilistic damage tolerance design for life-limited parts. The vision of the probabilistic damage tolerance assessment is provided. Five core parts of the probabilistic damage tolerance method are introduced separately, including the anomaly distribution, stress processing and zone definition, fatigue and fracture calculation method, probability of failure (POF) calculation method, and the combination with residual stress induced by the manufacturing process. The above currently-available risk assessment methods provide practical tools for failure risk predictions and are applied by the airworthiness regulations. However, new problems are exposed with the development of the aero-engines. The time-consuming anomaly distribution derivation process restricts the development of the anomaly distribution, especially for the developing aviation industries with little empirical data. Additionally, the strong transient characteristic is prominent because of the significant temperature differences during the take-off and climbing periods. The complex loads then challenge the fatigue and fracture calculation model. Besides, high computational efficiency is required because various variables are considered to calculate the POF. Therefore, new technologies for the probabilistic damage tolerance assessment are provided, including the efficient anomaly distribution acquisition method based on small samples, the zone definition method considering transient process, and stress intensity factor (SIF) solutions under arbitrary stress distributions combined with the machine learning method. Then, an efficient numerical integration method for calculating failure risk based on the probability density evolution theory is proposed. Meanwhile, the influence of the manufacturing process on residual stress and the failure risk of the rotors is explored. The development of the probabilistic damage tolerance method can meet the requirement of the published airworthiness regulation Federal Aviation Regulation (FAR) 33.70 and guide the modification or amendment of new regulations to ensure the safety of the high-energy rotors.