RESUMO
Three types of uncertainties exist in the estimation of the minimum fracture strength of a full-scale component or structure size. The first, to be called the "model selection uncertainty," is in selecting a statistical distribution that best fits the laboratory test data. The second, to be called the "laboratory-scale strength uncertainty," is in estimating model parameters of a specific distribution from which the minimum failure strength of a material at a certain confidence level is estimated using the laboratory test data. To extrapolate the laboratory-scale strength prediction to that of a full-scale component, a third uncertainty exists that can be called the "full-scale strength uncertainty." In this paper, we develop a three-step approach to estimating the minimum strength of a full-scale component using two metrics: One metric is based on six goodness-of-fit and parameter-estimation-method criteria, and the second metric is based on the uncertainty quantification of the so-called A-basis design allowable (99 % coverage at 95 % level of confidence) of the full-scale component. The three steps of our approach are: (1) Find the "best" model for the sample data from a list of five candidates, namely, normal, two-parameter Weibull, three-parameter Weibull, two-parameter lognormal, and three-parameter lognormal. (2) For each model, estimate (2a) the parameters of that model with uncertainty using the sample data, and (2b) the minimum strength at the laboratory scale at 95 % level of confidence. (3) Introduce the concept of "coverage" and estimate the fullscale allowable minimum strength of the component at 95 % level of confidence for two types of coverages commonly used in the aerospace industry, namely, 99 % (A-basis for critical parts) and 90 % (B-basis for less critical parts). This uncertainty-based approach is novel in all three steps: In step-1 we use a composite goodness-of-fit metric to rank and select the "best" distribution, in step-2 we introduce uncertainty quantification in estimating the parameters of each distribution, and in step-3 we introduce the concept of an uncertainty metric based on the estimates of the upper and lower tolerance limits of the so-called A-basis design allowable minimum strength. To illustrate the applicability of this uncertainty-based approach to a diverse group of data, we present results of our analysis for six sets of laboratory failure strength data from four engineering materials. A discussion of the significance and limitations of this approach and some concluding remarks are included.
RESUMO
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.