Chapter EightRandom Multiaxial Fatigue Loading

A new spectral method of fatigue-life calculation under random multiaxial loading has been shown. The method consists in extension of the known formulae of Miles, Kowalewski, Rajcher, Bolotin and Wirsching and Light, based on the power-spectral density function (PSDF) of stresses under uniaxial random loading. PSDF of the equivalent stress, determined according to linear failure criteria of multiaxial random fatigue, was introduced to the method. It has been shown that while reducing the multiaxial state of stress to the uniaxial one with linear failure criteria, the frequency bands of stress-state components are transformed to the frequency band of equivalent stress without increase of its width. Such a favorable result cannot be obtained if the equivalent stress is calculated according to the nonlinear multiaxial-fatigue-failure criteria. The chapter contains an approach for estimation of fatigue life in the HCF regime. Loading of Gaussian distribution and narrow- and broadband frequency spectra were assumed. Various characteristic states of multiaxial loading were considered. The reduced stress history was determined with use of failure criteria of multiaxial fatigue based on the critical plane. For determination of the criticalplane position, the methods of variance and damage accumulation were applied. During simulation, the authors compared the results obtained by the spectral method in the frequency domain with those from the rain-flow algorithm in the time domain. The chapter also contains the results of fatigue tests for 18G2A structural steel subjected to 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