Using Multiple Regression Models and Methods to Estimate Fatigue‐Life Distributions and Construct Constant‐Life Diagrams

ABSTRACT Fatigue is the most common reliability failure mechanism and has been studied widely since the 19th century. Material specimens are used in laboratory experiments to obtain fatigue test data. An S‐N curve is used to depict the relationship between the stress (or strain) and the number of cycles to failure . Statistical methods are used to fit an S‐N relationship that can be used further to estimate properties of fatigue‐life and fatigue‐strength distributions. In particular, one can obtain estimates and confidence intervals for distribution quantiles and failure probabilities. Likelihood‐based and Bayesian inference methods are the foundational methods for statistical estimation and quantification of statistical uncertainty. Improvements in computing technology (hardware, software, and computational methods) have made it practicable to use these methods for important applications. This paper uses these foundational methods to model fatigue life and fatigue strength as a function of the experimental variables stress amplitude, mean stress, and stress ratio, extending and importantly improving methods currently used for such applications. We illustrate the methods with two different data sets. The first example is based on S‐N test data of a composite material widely used to manufacture wind turbine blades, where the fatigue‐life model is specified, and the fatigue‐strength is induced. The second example is based on S‐N test data of an aluminum alloy commonly used in aerospace applications. Because of the complicated features of the fatigue life data for this example, we use a specified fatigue‐strength model and show how it can be used to make inferences about the corresponding fatigue‐life model. Finally, we show how to use these multiple regression models to obtain constant‐life diagrams (CLDs), an engineering tool that provides a visual representation of the quantiles of a fatigue‐life distribution as a function of stress amplitude and mean stress. We compare CLDs based on multiple regression models with CLDs obtained by using separate simple regression models for each level of stress ratio.