Uncertainty in multi-scale fatigue life modeling and a new approach to estimating frequency of in-service inspection of aging components

Abstract

Uncertainty in modeling the fatigue life of a full-scale component using experimental data at microscopic (Level 1), specimen (Level 2), and full-size (Level 3) scales, is addressed by applying statistical theory of prediction intervals, and that of tolerance intervals based on the concept of coverage, p. Using a nonlinear least squares fit algorithm and the physical assumption that the one-sided Lower Tolerance Limit (LTL), at 95% confidence level, of the fatigue life, i.e., the minimum cycles-to-failure, minNf, of a full-scale component, cannot be negative as the lack or “Failure” of coverage (Fp), defined as 1 − p, approaches zero, we develop a new fatigue life model, where the minimum cycles-to-failure, minNf, at extremely low “Failure” of coverage, Fp, can be estimated. Since the concept of coverage is closely related to that of an inspection strategy, and if one assumes that the predominent cause of failure of a full-size component is due to the “Failure” of inspection or coverage, it is reasonable to equate the quantity, Fp, to a Failure Probability, FP, thereby leading to a new approach of estimating the frequency of in-service inspection of a full-size component. To illustrate this approach, we include a numerical example using the published data of the fatigue of an AISI 4340 steel (N.E. Dowling, Journal of Testing and Evaluation, ASTM, Vol. 1(4) (1973), 271–287) and a linear least squares fit to generate the necessary uncertainties for performing a dynamic risk analysis, where a graphical plot of an estimate of risk with uncertainty vs. a predicted most likely date of a high consequence failure event becomes available. In addition, a nonlinear least squares logistic function fit of the fatigue data yields a prediction of the statistical distribution of both the ultimate strength and the endurance limit.