Fatigue life of a design subject to wide-band random loading

Metal fatigue is one of the most important failure modes to be considered in mechanical and structural design. The only satisfactory way to prevent fatigue failures in the service life span is by proper design; i.e., being able to predict the fatigue lifetime of a particular design through design analysis or testing. For engineering applications, designers need a simple and reasonably accurate design code to predict the reliability or fatigue lifetime of a design for a specified application. This paper will provide a methodology in frequency domain to determine the reliability (high-cycle fatigue life) under wide-band Gaussian random loading. For the wide-band variable-amplitude stress, stress cycles and cycle counts are not obvious. A cycle-counting method is proposed for the wide-band random stress in this paper. After deriving the distributions of both the amplitude and the mean value of the stress cycles according to the proposed cycle-counting method, the fatigue lifetime distribution can be obtained directly from knowledge of the power spectral density (PSD) of the hot-spot stress and the statistical expression of fatigue strength (i.e., P-S-N curves). The effect of a non-zero mean of stress process is also easily taken into account in this approach. The derived formula has been verified with several random fatigue tests and can be used at the engineering design stage where the hot-spot stress history is actually not available.