Bi-level Hybrid Uncertainty Quantification in Fatigue Analysis: S-N Curve Approach

Due to its physical complexity, fatigue phenomenon inherently presents a significant number of uncertain parameters to be predicted. In uncertainty quantification (UQ), research has demonstrated that even a small variation in uncertain input quantities (UIQs) may lead to a wide dispersion in the system response quantities (SRQs). In this paper, a bi-level hybrid UQ analysis of a fatigue problem is presented based on the S-N curve approach. The uncertain fatigue analysis presented is able to deal simultaneously with aleatory- and epistemic-type uncertainties in two levels (a SRQ in the first level is a UIQ in the second level). To this end, the proposed scheme is tested for an AISI 4130 clamped beam subjected to a concentrated load, which material information comes from experiments reported in the literature. The UIQs are geometrical parameters, material properties, loading magnitude, and stress, while the SRQs are the stress (which is also a UIQ for fatigue life) and fatigue life. The results evidenced that the uncertain fatigue analysis, instead of providing a unique value for a SRQ, now produces a possible range of values. Therefore, depending on the risk an engineer can take on a design, there will be a corresponding level of optimization achieved.