Bi-conditional probabilistic fatigue stress-based curve definition and comparison with other models

Abstract

The definition of the relationship between probability, fatigue stress and cycles to failure is of great importance, especially in applications which requires very low probability of failure (e.g. Pf=0.1%). In this paper a new formulation is presented, which allows to separately consider the probability of the endurance and the probability of existence of the initiating defect. This approach is then compared to a number of known models. For this purpose, the proprietary results of 8 fatigue test sets, each with at least 24 data points, have been analyzed. A ranking of goodness-of-fit based on the Relative Likelihood can be used to choose the best distribution within each model, but unfortunately cannot be used to compare different models. The conclusions were: 1- the better description of the HCF strength, in terms of performance and robustness, were obtained by the 2-p Weibull distribution; 2- the choice of the model has a great influence in the estimate of the low probability quantiles, but it still subjective and a definitive answer cannot be given after this benchmark; 3- the strength of the proposed model is its flexibility.