Probabilistic assessment of VHCF data as pertaining to concurrent populations using a Weibull regression model

The Weibull regression model proposed by Castillo and Canteli to evaluate fatigue results represents a possible and adequate option to be used for the assessment and prediction of very high cycle fatigue (VHCF) lifetimes. Among others, this model provides a probabilistic definition of the S‐N field for determining failure mechanisms, ie, internal and surface ones, based on extreme value distributions of the Weibull family for minima, as well as the existence of an asymptotic fatigue limit and the capability to reduce the S‐N field to a single cumulative distribution function by considering the normalized variable V = (log N‐B) (log Δσ). In this way, both dual fracture mechanisms characterizing the VHCF data can be adequately interpreted and handled as independent distributions in such a particular and complex case of concurrent populations, known statistically as a confounded data problem. Once the model parameters of both normalized cumulative distribution functions are estimated, the probability of failure for any of both failure mechanisms at whatever stress range can be determined by applying a back normalization to the original Wöhler field. Two examples of application are presented, the first one to introduce the proposed methodology by means of an example with simulated data to show the reliability of the proposed approach to fit correctly the model parameters assumed for the simulation, and the second one, using real results from a former external experimental VHCF program. Finally, a test strategy, which optimizes the planning of the fatigue program, is suggested.