Fatigue life under variable-amplitude loading according to the cycle-counting and spectral methods
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FATIGUE LIFE UNDER VARIABLE-AMPLITUDE LOADING ACCORDING TO THE CYCLE-COUNTING AND SPECTRAL METHODS E. Macha, T. Łagoda, A. Niesłony, and D. Kardas We compare the values for the fatigue life of 12010.3 steel determined experimentally under variable-amplitude tension–compression and calculated by two methods in time and frequency ranges. The first method is based on the schematization of the loading history and uses the rainflow algorithm. The fatigue life was calculated according to the Serensen–Kogaev linear hypothesis of damage accumulation wit the use of the Manson–Coffin dependence. The second method is based on power spectral density functions. These methods differ in the approaches used for the determination of the probability density of amplitude distribution from the deformation history. It is established that, in the case considered, the values of fatigue life calculated by the cycle-counting method and by the spectral method are close to the values determined experimentally.
Methods for fatigue-life assessment can be divided into two groups. One of them includes algorithms based on numerical methods of cycle counting [1 – 5], and the other group uses the spectral analysis of stochastic processes [4, 6 – 13]. In the first group, the material loading is represented by stress or strain histories, and in the second group it is represented by their frequency characteristics, i.e., power spectral density functions [10]. The paper [9] by Miles belongs to the first papers concerning spectral methods for fatigue-life determination. The author assumes that the probability density of stress peaks is equal to the probability density of amplitudes, which is described by the Rayleigh distribution. This assumption is valid for loading with narrow frequency spectrum and normal probability distribution of instantaneous values of loading course. All parameters occurring in the Miles equation are obtained directly from the power spectral stress density. In literature, we can find many modifications of this equation, including wide frequency spectrum. Kowalewski [14] uses the irregularity coefficient determined on the basis of the power spectral density moments. Bolotin [15] proposes to replace the expected number of peaks in a time unit by the expected number of transitions through the zero level with positive slope. Thus, he obtains a spectral equation for fatigue life that is less sensitive to signal noises. Wirsching and Light [5] propose an empirical coefficient correcting damage including the loading frequency spectrum width. Since the life of damage is directly subjected to correction, the coefficient is determined from the parameters of the fatigue curve and the irregularity coefficient. Dirlik [7] proposes an approximation of amplitude distribution obtained by an empirical equation formulated according to the rainflow algorithm. The equation was obtained during simulation calculations by the Monte Carlo method. There are some proposals concerning the determination of life by spectral methods under non-Gaussian loadi
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