Uncertainty theory based reliability modeling for fatigue

The study of the fatigue crack growth law is usually carried out by the fatigue crack growth experiments (FCGE), and is expressed by the fatigue crack growth model. Epistemic uncertainties exist in FCGE with small samples. Generally, Bayesian method, interval probability method, and fuzzy probability method are presented to quantify the epistemic uncertainty in the case of small samples. However, the expression of the epistemic uncertainty in most studies is greatly influenced by subjective information, and there are interval expansion problems in the calculation. Therefore, the problem of how to quantify the epistemic uncertainties in FCGE with small samples has not been well solved. Under such circumstance, a novel uncertain measure is used to quantify such epistemic uncertainty in this paper, which is belong to uncertainty theory proposed by Prof. Baoding Liu. Firstly, the fatigue crack growth model proposed by Zhang is introduced as the foundation of modeling. Then, the sources of uncertainties in FCGE are analyzed and the uncertainties are quantified based on the uncertainty theory. Finally, a belief reliability model of fatigue crack growth is proposed, in which the associated reliability function is derived, and the uncertain statistics for the parameter estimations is presented. The case study illustrates the proposed methodology and the corresponding discussions show that the uncertainty theory contributes to more stable reliability evaluation than probability theory when quantifying the epistemic uncertainty, and the influence of the material scatter on fatigue reliability should be emphasized.