2023/03/25 by Francois-Baptiste Cartiaux, Cartiaux, Francois-Baptiste, Alain Ehrlacher +7
Decision Sciences · Engineering · #Computational Engineering #FOS: Computer and information sciences #Fatigue and fracture mechanics #Finance #Probabilistic and Robust Engineering Design #Structural Health Monitoring Techniques #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2303.14504
openalex publication_date 2023/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The standard stress-based approach to fatigue is based on the use of S-N\ncurves. They are obtained by applying cyclic loading of constant amplitude S\nto identical and standardised specimens until they fail. The S-N curves\nactually depend on a reference probability p: for a given cycle amplitude\nS, they provide the number of cycles at which a proportion p of specimens\nhave failed. Based on the S-N curves, Miner's rule is next used to predict the\nnumber of cycles to failure of a specimen subjected to cyclic loading with\nvariable amplitude. In this article, we present a probabilistic formulation of\nMiner's rule, which is based on the introduction of the notion of health of a\nspecimen. We show the consistency of that new formulation with the standard\napproaches, thereby providing a precise probabilistic interpretation of these.\nExplicit formulas are derived in the case of the Weibull--Basquin model. We\nnext turn to the case of a complete mechanical structure: taking into account\nsize effects, and using the weakest link principle, we establish formulas for\nthe survival probability of the structure. We illustrate our results by\nnumerical simulations on a I-steel beam, for which we compute survival\nprobabilities and density of failure point. We also show how to efficiently\napproximate these quantities using the Laplace method.\n