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In the paper the spectral analysis of several fatigue criteria under simple and complex states of stress has been done and limitations appearing while formulating new criteria for multiaxial random loadings have been shown. The presented analysis includes determination, with digital simulation, of probability density function and power spectral density function of the equivalent stress according to three special linear criteria of multiaxial random fatigue and six nonlinear criteria. Calculations were carried out for four kinds of random stress state. It has been shown that mathematical models for the criteria of multiaxial random fatigue formulated as nonlinear combinations of stress state components have unfavourable statistical properties, which make their application for fatigue life determination difficult.

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