Spectral method for fatigue damage estimation with non-zero mean stress

1. Introduction

The effect of variable loading on materials causing mechanical fatigue is one of the main reasons of failure. The usual technics to estimate fatigue damage are based on signals of strain or stress (KERR et al., [s.d.]) in time domain, followed by a cycle counting and damage estimation. The study in the frequency domain, often called Spectral Fatigue, is a procedure to calculate fatigue damage and life for random vibrations, which are complicated to be analyzed within the time domain, through usual Rainflow.

The Rainflow cycle counting was introduced in 1968 by Matsuishi and Endo (MATSUISHI; ENDO, 1968)

This counting procedure is still used nowadays but it can be dispendious for long time signals because the whole set of data, during the whole test, must be used to compute the damage generated in the material due to the loading. Most of real mechanic behaviors are non-stationary random processes. Nevertheless, as the signal varies slowly or almost constantly, in the majority of cases, the load is considered stationary for any time sample. To analyze the fatigue life and damage, the loading must be considered random, stationary and Gaussian.(BISHOP; SHERRATT, 1989)

The Spectral analysis is carried out in the frequency domain. For this reason, it’s possible to calculate the damage through statistic properties of the Power Spectral Distribution (PSD) of the time signal. These properties are equal for the whole signal as well for smaller samples, due to the ergodic feature of the signal. (NEWLAND; NEWLAND; NEWLAND, 1993)

The Fatigue damage is calculated by the Palmgren-Miner accumulation rule where the number of occurrences is taken from the Power Distribution Function (PDF) of the PSD moments. There are several technics to evaluate the probabilities from the PSD, such as Rayleigh, Dirlik (DIRLIK T., 1985) and Benasciutti-Tovo (TOVO, 2002)

Nonetheless, this method does not include the effects of the mean stress, because the PSD is computed from the Fast Fourier Transform (FFT) of the strain signal in time and a non-zero mean value generates a constant value in the zero frequency. Thus, only the levels of amplitude are considered, (MRŠNIK; SLAVIČ; BOLTEŽAR,