A general model for fatigue damage due to any stress history

The aim of this paper is to give a general model for predicting fatigue behavior for any stress level and range based on laboratory tests. More precisely, an existing Weibull model is generalized and adapted to this type of predictions via compatibility and functional equations techniques. A wide family of models is obtained, for which inference, testing hypotheses, model choice and model validation problems are dealt with. Laboratory testing strategies adequate to the estimation process are also briefly discussed. The relevant result is that testing four groups of specimens at four different stress levels is sufficient to estimate the parameters of the model and consequently, to give the Wöhler fields for any stress level. Together the proposed model and laboratory tests allow any fatigue analysis to be performed. This includes a possible solution of the fatigue damage accumulation problem. One example of application is given to illustrate the proposed methods.