PSI - Issue 38

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

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3.1. Basquin model

Basquin's model is perhaps the most used model by the scientific community because of its simplicity of analysis and modelling [3]. Indeed, it is represented by a line in a logarithmic space in the field of limited endurance and allows a simple and fast reading of the overall performances in fatigue without graphical representation. It is worded as follows: = ↔ = − (1) Or in linear formulation [8] log( ) = log( ) − log( ) ↔ ln( ) = ln( ) − ln( ) (2) The simplest methodology for estimating the tw parameters of this model (C and m) is the least squares. This method, effectively easy to use and which does not need complex resolution algorithm, is, however, limited because it does not allow considering censored data. According to the experimental results, this neglect can be very conservative. Authors such as E. Castillo and A. F. Canteli [6] have written an iterative approach to least squares to integrate censored data into the estimation of parameters, but this method is nevertheless limited to least squares and therefore to models whose formulation is linear [6]. As presented in the Figure 2, an analysis without censored data is very conservative estimating endurance limit at 10 million cycles.

Figure 2: Basquin model

3.2. Stromeyer model Stromeyer proposed in 1914 [4], based on Basquin's model, a formulation to consider the fatigue limit in the modelling of the S-N curve and thus obtain a curve of asymptotic behaviour. It is worded as follows: = ( − ) (3) Or in linear formulation [8] log( ) = log( ) − log( − ) ↔ ln( ) = ln( ) − ln( − ) (4) This model has 3 parameters, a simple regression is not suitable. An assumption about parameter C can nevertheless be made to facilitate the modelling of the curve by making it equal to the unit. This strong hypothesis may be useful, but it is sometimes not adapted according to experimental data as shown in Figure 3. This parameter has an influence on the general level of inflection of the curve.