On the probability density function of rainflow stress range for stationary Gaussian processes

Abstract

The prediction of fatigue damage under random loading is usually based on Miner's rule combined with the rainflow cycle counting method. However, the process of counting cycles is extremely time consuming and requires a reasonably long time history to be analysed for the results to be reliable. This paper describes a model for the probability distribution of the rainflow stress range based on a mixed-distribution Weibull model whose parameters can be evaluated from only two spectral properties, namely the irregularity factor I and a bandwidth parameter β 0.75. Comparison of the probability distribution function (PDF) of the stress range based on the model with results from simulation and rainflow counting shows very good agreement over a wide range of stress spectra. In addition, comparisons have been made in terms of the damage correction factor. These show that the model gives a better assessment of damage than any previous model within the practical range of the Paris' parameter m for steel. This model may therefore be used in place of rainflow counting and hence provides an efficient and accurate tool for the prediction of fatigue under random loading.