Comparison Of The Rain Flow Algorithm And The Spectral Method For Fatigue Life Determination Under Uniaxial And Multiaxial Random Loading

This paper presents the strain energy density parameter used for fatigue life calculation under random loading by two methods. The first method is based on schematization of energy parameter histories with the rain flow algorithm. The other one is based on moments of the power spectral density function of the energy parameter. The experimental data of fatigue tests of 10HNAP steel under constant amplitude and random uniaxial loading with non-gaussion probability distribution, zero mean value, and wide-band frequency spectrum used for comparison of the rain flow algorithm and the spectral method gave satisfactory results. Next, histories of the random stress tensor with normal probability distribution, wide-band frequency, and zero mean values corresponding to biaxial tension-compression, combined tension with torsion and triaxial loading with various correlation coefficients were generated, and the lifetime was calculated. It has been observed that both methods of fatigue life determination give almost the same results.

This monograph examines the theoretical foundations of the spectral method for fatigue life determination. The authors discuss a rule of description of random loading states with the matrix of power spectral density functions of the stress/strain tensor components. Some chosen criteria of multiaxial fatigue failure are analyzed. The formula proposed in this book enables readers to determine power spectral density of the equivalent history directly from the components of the power spectral density matrix of the multidimensional stochastic process.

The Rainflow Method in Fatigue: The Tatsuo Endo Memorial Volume documents the proceedings of The International Symposium on Fatigue Damage Measurement and Evaluation Under Complex Loadings held in Fukuoka, Japan, on 25-26 July 1991. The Symposium was held in memory of Professor Tatsuo Endo, inventor of the rainflow method of counting fatigue cycles. His contributions were key to the development of an overall method for evaluating the service life of engineering components subjected to fatigue loading. This volume contains 23 papers organized into four parts. Part I on the cycle counting method includes papers on the historical development of the rainflow cycle counting method, and a fatigue analysis data reduction concept for general multidimensional time series. Part II on ground vehicles includes studies on methods for solving vehicle fatigue problems caused by body resonance, and a synthetic computer system for fatigue damage-based design of weld structure for construction machines. Part III on fatigue testing and analysis includes papers on crack closure load measurements during fatigue crack growth tests on the titanium alloy Ti-6A1-4V, and growing fatigue cracks under varying amplitude loadings. Part IV presents a panel discussion on total system of fatigue damage measurement and evaluation under complex loadings.

This title presents the fundamental elements and theories in fracture and damage analysis, plus the recent research and advances in the development of the analytical and practical approaches required to assess the materials damage and the durability of structures.

In this thesis, fatigue life of a cantilever aluminum plate with a side notch under certain loading conditions is analyzed. Results of experimental stress analysis of the cantilever aluminum plate by using a uniaxial strain gage are presented. The strain gage is glued on a critical point at the specimen where stress concentration exists. Strain measurement is performed on the base-excited cantilever beam under random vibration test in order to examine the life profile simulation. The fatigue analysis of the test specimen is carried out in both time and frequency domains. Rainflow cycle counting in time domain is examined by taking the time history of load as an input. Number of cycles is determined from the time history. In frequency domain analysis, power spectral density function estimates of normal stress are obtained from the acquired strain data sampled at 1000 Hz. The moments of the power spectral density estimates are used to find the probability density function estimate from Dirlik’s empirical expression. After the total number of cycles in both time and frequency domain approaches are found, Palmgren-Miner rule, cumulative damage theory, is used to estimate the fatigue life. Results of fatigue life estimation study in both domains are comparatively evaluated. Frequency domain approach is found to provide a marginally safer prediction tool in this study.

This thesis consists of a fatigue study carried out on an aluminum alloy 2024-T3 in both time domain and frequency domain. Non-zero mean random signals of strain and stress are analyzed in time domain using usual Rainflow method and the damage is accumulated with the Palmgren-Miner rule, according to mean stress equations. The signals are analyzed in frequency domain using the power spectral density and the probability density function. The spectral domain analysis does not consider the negative effect of the mean stress in metal life under fatigue, so the correction factors for mean stresses developed by Goodman, Morrow, and Smith-Watson-Topper are used to change the power spectral density and, thus, the damage calculated by the probability density functions postulated by Dirlik and Tovo and Benasciutti. It is found that both Dirlik and Tovo and Benasciutti are non-conservative for a non-zero mean stress signal when comparing the damage to the one obtained in time domain analysis. When the spectral method is corrected, the results vary from Rainflow 4.9% for wide band and 6.8% for narrow band signals, always in the conservative zone, therefore predicting more damage. Tovo and Benasciutti 2 method is found to be the spectral function with the closest results when compared to the usual Rainflow method in time domain.

By analyzing the material's strain-life data differentially, this paper brings to light the generally overlooked incremental damage concept which underlies the conventional uniaxial rainflow counting algorithm and the strain-based fatigue method. This incremental damage concept not only allows the uniaxial rainflow program to be logically extended to multiaxial problems, it also forms the basis for a new incremental fatigue damage accumulation method. Several simple examples, including a multiaxial rainflow algorithm, are given to illustrate how the new approach can be applied to general multiaxial problems and how it can be formulated so that any chosen uniaxial model using the traditional parametric approach can be closely reproduced.

A fatigue life prediction method suitable for multiaxial stress states and constant amplitude or random loading is developed. In the case of random loading, a suitable counting variable is proposed so that the rainflow counting method can be applied in order to extract cycles. A multiaxial fatigue life criterion is used to define the damage corresponding to each cycle. This criterion is based on the quadratic mean value of a damage indicator over all the planes through the point where the fatigue life calculation is made. The validation of this criterion is made with periodical multiaxial fatigue test results. Miner's rule is used for the cumulation of the damage. The whole fatigue life of the component is evaluated in terms of the number of repetitions of the loading block.