Analysis of Constant and Variable Amplitude Strain-Life Data Using a Novel Probabilistic Weibull Regression Model

The relation between the total strain amplitude and the fatigue life measured in cycles is usually given as strain-life curves based on the former proposals of Basquin, for the elastic strain-life, and Coffin–Manson, for the plastic strain-life. In this paper, a novel Weibull regression model, based on an existing well established Weibull model for the statistical assessment of stress-life fatigue data, is proposed for the probabilistic definition of the strain-life field. This approach arises from sound statistical and physical assumptions and not from an empirical proposal insufficiently supported. It provides an analytical probabilistic definition of the whole strain-life field as quantile curves, both in the low-cycle and high-cycle fatigue regions. The proposed model deals directly with the total strain, without the need of separating its elastic and plastic strain components, permit dealing with run-outs, and can be applied for probabilistic lifetime prediction using damage accumulation. The parameters of the model can be estimated using different well established methods proposed in the fatigue literature, in particular, the maximum likelihood and the two-stage methods. In this work, the proposed model is applied to analyze fatigue data, available for a pressure vessel material—the P355NL1 steel—consisting of constant amplitude, block, and spectrum loading, applied to smooth specimens, previously obtained and published by authors. A new scheme to deal with variable amplitude loading in the background of the proposed regression strain-life Weibull model is described. The possibility to identify the model constants using both constant amplitude and two-block loading data is discussed. It is demonstrated that the proposed probabilistic model is able to correlate the constant amplitude strain-life data. Furthermore, it can be used to correlate the variable amplitude fatigue data if the model constants are derived from two-block loading data. The proposed probabilistic regression model is suitable for reliability analysis of notched details in the framework of the local approaches.