Fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading

Abstract

A B S T R A C T The paper contains a new algorithm for estimation of fatigue life in HCF regime under multiaxial random loading using spectral methods. Loading of Gaussian distribution and narrow-and broad-band frequency spectra were assumed. Various characteristic states of multiaxial loading were considered. The equivalent stress history was determined with use of the failure criteria of multiaxial fatigue based on the critical plane. For determination of the critical plane position, the method of variance was applied. During simulation, the authors compared the results obtained by a spectral method in the frequency domain with those from the rain-flow algorithm in the time domain. The paper also contains the results of fatigue tests for 18G2A structural steel subjected to bending and combined bending with torsion. The tests were performed in order to verify the proposed algorithms for determination of fatigue life. It has been shown that under multiaxial random loading results of fatigue life calculated according to the considered algorithms in frequency and time domains are well correlated with the results of experiments.Keywords critical plane; high cycle fatigue; multiaxial fatigue failure criterion; rainflow algorithm. N O M E N C L A T U R EA = parameter of (σ a − N f ) fatigue relationship a = vector of coefficients dependent on a multiaxial fatigue failure criterion a SK = coefficient enabling to include amplitudes below the fatigue limit b SK = Serensen-Kogayev coefficient CMP1, 2, 3 = blocks for comparison of the cycle counting method with the spectral method E[·] = expected value E = Young's modulus f = frequency FFT = fast Fourier transform IFFT = inverse fast Fourier transform G(f ) = one-side power spectral density function l η , m η and n η = direction cosines of the vectorη normal to the critical plane m = exponent of (σ a − N f ) fatigue relationship m k = k-th moment of power spectral density function N 0 = number of cycles corresponding to fatigue limit n i = number of cycles PSD = power spectral density function p(σ a ) = probability density function of stress amplitude r = correlation coefficientCorrespondence: E. Macha.

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