PSI - Issue 38

Robin Hauteville et al. / Procedia Structural Integrity 38 (2022) 507–518 Robin Hauteville, Xavier Hermite, Fabien Lefebvre / Structural Integrity Procedia 00 (2021) 000 – 000

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with mathematical consideration for the more complex expressions (typically the asymptotic models) and for the consideration of censored data. CETIM proposes a generic method to deal with the model expressions and the censored (or not) data and creates its own software algorithm to analyse fatigue experiments results. This method is a combination of the least square regression method, the probabilistic regression known as the maximum likelihood estimates, and a numerical iterative process such as Newton – Raphson or Generalized Reduced Gradient to estimate model parameters, fatigue strength standard deviation, and correction factor K C used to estimate the design curves associated with a probability of failure, a confidence level, and a sample size. 2. Nomenclature A Stromeyer and Bastenaire parameter Distribution parameter B Bastenaire parameter Distribution parameter C Basquin, Stromeyer and Bastenaire parameter The logarithm of the likelihood E Stromeyer and Bastenaire parameter f The probability density of the distribution law F The standard normal distribution function L The likelihood m Basquin parameter (slope) n Number of experimental data (failure) Stress l og Standard deviation associated with lifetimes l og Standard deviation associated with stresses N Lifetime or number of cycles Degree of freedom ̂ Estimation of the x variable ̅ Mean of the x variable 3. Fatigue models As said before, there is a multitude of mathematical models allowing the fitting of the Wöhler curve whether in the oligocyclic domain and limited or unlimited endurance domain (Figure 1). The examples of models that will be discussed in this document are mainly adapted to the field of limited endurance: Basquin, Stromeyer, Bastenaire models. However, the tool and methodology used can be adapted according to the field studied.

Figure 1: Main field of the Wöhler curve [2]