Using Tolerance Bounds for Estimation of Characteristic Fatigue Curves for Composites with Confidence

Abstract

Fatigue S–N curves provide the number of stress cycles that result in fatigue failure at stress range S and need to be measured for new engineering materials where data are not as readily available as they are for well-characterized and widely used metals. A simple statistical method for the estimation of characteristic fatigue curves defined in terms of lower-tail quantiles in probability distributions of dependent variables is presented. The method allows for the estimation of such quantiles with a specified confidence level, taking account of the statistical uncertainty caused by a limited number of experimental test results available for the estimation. The traditional general approach for estimating characteristic S–N curves by tolerance bounds is complicated and is not much used by engineers. The presented approach allows for calculating the curves with a simple spreadsheet. The only requirement is that the experimental log S data for the S–N curve are fairly uniformly distributed over a finite logS interval, where S denotes the stress range. Experimental fatigue test programs are often designed such that test data fulfil this assumption. Although developed with fatigue of composite laminates in mind, the presented statistical procedure and the presented associated charts are valid for fatigue curve estimation for any material.