Probabilistic formulation of Miner's rule and application to structural fatigue

The standard stress-based approach to fatigue is based on the use of S-N curves. They are obtained by applying cyclic loading of constant amplitude \(S\) to identical and standardised specimens until they fail. The S-N curves actually depend on a reference probability \(p\): for a given cycle amplit...

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Bibliographic Details
Published in:arXiv.org 2023-03
Main Authors: Francois-Baptiste Cartiaux, Ehrlacher, Alain, Legoll, Frederic, Libal, Alex, Reygner, Julien
Format: Article
Language:English
Subjects:
Amplitudes
Cyclic loads
Fatigue life
Mathematical models
S N diagrams
Size effects
Statistical analysis
Steel beams
Survival
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Summary:The standard stress-based approach to fatigue is based on the use of S-N curves. They are obtained by applying cyclic loading of constant amplitude \(S\) to identical and standardised specimens until they fail. The S-N curves actually depend on a reference probability \(p\): for a given cycle amplitude \(S\), they provide the number of cycles at which a proportion \(p\) of specimens have failed. Based on the S-N curves, Miner's rule is next used to predict the number of cycles to failure of a specimen subjected to cyclic loading with variable amplitude. In this article, we present a probabilistic formulation of Miner's rule, which is based on the introduction of the notion of health of a specimen. We show the consistency of that new formulation with the standard approaches, thereby providing a precise probabilistic interpretation of these. Explicit formulas are derived in the case of the Weibull--Basquin model. We next turn to the case of a complete mechanical structure: taking into account size effects, and using the weakest link principle, we establish formulas for the survival probability of the structure. We illustrate our results by numerical simulations on a I-steel beam, for which we compute survival probabilities and density of failure point. We also show how to efficiently approximate these quantities using the Laplace method.
ISSN:2331-8422