This paper addresses the usage of inverse power laws in accelerated fatigue testing under wide-band Gaussian random loading. The aim is not at predicting an absolute value of fatigue life but assessing the fatigue damage relative accumulation. The widely accepted inverse power scaling laws in fatigue damage assessment is discussed, reviewing the engineering standards and pointing out their inherent limitations. A physically consistent general scaling law is obtained by rigorous mathematical analysis in the framework of random vibration theory and the rules of safe-life fatigue analysis. Simplifications of the general scaling rule are presented, highlighting conditions under which the current standard practice could provide a correct an acceptable estimation of the relative fatigue damage accumulation
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