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ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 2022, Vol. 43 ›› Issue (8): 225820.doi: 10.7527/S1000-6893.2021.25820

• Solid Mechanics and Vehicle Conceptual Design • Previous Articles     Next Articles

Reliability modelling for fatigue based on uncertain differential equation

LI Xiaoyang1,2, TAO Zhao1,2, ZHANG Wei1,2   

  1. 1. School of Reliability and Systems Engineering, Beihang University, Beijing 100083, China;
    2. Science and Technology on Reliability and Environmental Engineering Laboratory, Beihang University, Beijing 100083, China
  • Received:2021-05-17 Revised:2021-08-18 Online:2022-08-15 Published:2021-08-17
  • Supported by:
    National Natural Science Foundation of China (51775020,51875019);Science Challenge Project (TZ2018007);Fundamental Research Funds for the Central Universities (YWF-21-BJ-J-515)

Abstract: To quantify the dynamic characteristic of uncertainty in the fatigue crack growth process in the time dimension, the uncertain differential equation of uncertainty theory is introduced to describe the dynamic characteristic of uncertainty from a small time scale (i.e., smaller time unit macroscopically). Specifically, for the crack growth process considering the crack closure and the retardation effect caused by overloads, the dynamic characteristic of the uncertainty in the time dimension and the static characteristic of the uncertainties in the physical properties, the external load and the crack threshold are considered and quantified in the framework of uncertainty theory. A fatigue crack growth model based on the uncertain differential equation is built from the small time scale. The margin equation is constructed regarding the crack length as the performance parameter, and the reliability function is deduced for the fatigue reliability modelling. The proposed model is applied to a case of fatigue crack growth experiment, and the reliability evaluation and the prediction of crack growth are obtained. The discussion and analysis of the proposed model shows that the modelling of fatigue crack growth from the small time scale and the careful classification and scientific quantification of the uncertainties are significant.

Key words: fatigue crack growth, uncertainty, dynamic change, small time scale, uncertain differential equation, reliability

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