Probabilistic modeling of S–N curves

•We model fatigue life using mixture of propagation and initiation.•We give an algorithm to find the model’s parameters.•We apply this algorithm on an Inconel718 database.

S–N curve is the main tool to analyze and predict fatigue lifetime of a metallic material, component or structure. But, standard models based on mechanic of rupture theory or standard probabilistic models for analyzing S–N curves could not fit S–N curve on the whole range of cycles without microstructure information. This information is obtained from costly fractography investigation rarely available in the framework of industrial production. On the other hand, statistical models for fatigue lifetime do not need microstructure information but they could not be used to service life predictions because they have no material interpretation. Moreover, fatigue test results are widely scattered, especially for High Cycle Fatigue region where split S–N curves appear. This is the motivation to propose a new probabilistic model. This model is a specific mixture model based on a fracture mechanic approach, and does not require microstructure information. It makes use of the fact that the fatigue lifetime can be regarded as the sum of the crack initiation and propagation lifes. The model parameters are estimated with an EM algorithm for which the Maximisation step combines Newton–Raphson optimization method and Monte Carlo integrations. The resulting model provides a parsimonious representation of S–N curves with parameters easily interpreted by mechanic or material engineers. This model has been applied to simulated and real fatigue test data sets. These numerical experiments highlight its ability to produce a good fit of the S–N   curves on the whole range of cycles. We must also notice that this model is proposed for large database (>50>50 data).