Estimation of a Minimum Allowable Structural Strength based on Uncertainty in Material Test Data

Abstract

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 full-scale 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.