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.
LI Xiaoyang
,
TAO Zhao
,
ZHANG Wei
. Reliability modelling for fatigue based on uncertain differential equation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022
, 43(8)
: 225820
-225820
.
DOI: 10.7527/S1000-6893.2021.25820
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