Abstract
Different empirical models have been proposed in the literature to determine the fatigue strength as a function of lifetime, according to linear, parabolic, hyperbolic, exponential, and other shaped solutions. However, most of them imply a deterministic definition of the S-N field, despite the inherent scatter exhibited by the fatigue results issuing from experimental campaigns. In this work, the Bayesian theory is presented as a suitable way not only to convert deterministic into probabilistic models, but to enhance probabilistic fatigue models with the statistical distribution of the percentile curves of failure probability interpreted as their confidence bands. After a short introduction about the application of the Bayesian methodology, its advantageous implementation on an OpenSource software named OpenBUGS is presented. As a practical example, this methodology has been applied to the statistical analysis of the Maennig fatigue S-N field data using the Weibull regression model proposed by Castillo and Canteli, which allows the confidence bands of the S-N field to be determined as a function of the already available test results. Finally, a question of general interest is discussed as that concerned to the recommendable number of tests to carry out in an experimental S-N fatigue program for achieving “reliable or confident” results to be subsequently used in component design, which, generally, is not adequately and practically addressed by researchers.
Highlights
Repeated application of variable loads over time may lead to fatigue failure of real structures and components
There is an extensive list of models devoted to the study of material fatigue strength, which are focused on predicting the service life (N) in terms of a particular generalized parameter (GP), such as the equivalent range of stresses (∆σ), strains (∆ε) or combinations of both (Smith–Watson–Topper, etc.)
Once the model has been implemented into the program, it is necessary to define the initial values of the variables (Equation (14)) and the experimental data of the fatigue life that to be fitted by the model, giving rise to the posterior distributions (Figure 5)
Summary
Repeated application of variable loads over time may lead to fatigue failure of real structures and components. This type of failure occurs often unexpectedly because the magnitude of the stresses acting on these components usually remains far below the static material strength. Accurate estimation of the fatigue strength of materials is crucial to ensure safe design and maintenance of structures and components. There is an extensive list of models devoted to the study of material fatigue strength, which are focused on predicting the service life (N) in terms of a particular generalized parameter (GP), such as the equivalent range of stresses (∆σ), strains (∆ε) or combinations of both (Smith–Watson–Topper, etc.). There are different standards and guidelines, such as ISO [1], Materials 2019, 12, 3239; doi:10.3390/ma12193239 www.mdpi.com/journal/materials
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