Design Evaluation Method for Random Fatigue Based on Spectrum Characteristics

This paper shows a new design approach for random fatigue evaluation based on spectral characteristics. Fatigue damage under random loading is usually evaluated by first, decomposing random waves to stress amplitudes using the rainflow-cycle counting (RFC) method; then, evaluating fatigue damage using Palmgren–Miner’s linear summation rule. In the design process, the fluctuation of load is usually characterized through power spectral density (PSD). Therefore, the design process is expected to be generalized, if the fatigue damage is directly evaluated from the PSD together with the S-N diagram of the material. In fact, many properties related to fatigue damage, such as distribution of extreme values, can be derived theoretically from the geometrical properties of PSD. However, it is rather difficult to derive the distribution of stress amplitude counted by RFC theoretically due to its complicated procedure. In this paper, the upper bound of stress amplitude distribution is confirmed for many random waves generated by numerical simulation for many types of PSDs. Expressing the upper-bound distribution by a closed form function using PSD characteristics leads us to the direct evaluation of fatigue damage with a safety margin if the fatigue damage by a particular stress amplitude is approximated using a series expansion form. A simple procedure for approximating high-cycle fatigue damage for austenitic stainless steel and ferritic steel is proposed in this paper. Finally, a design evaluation procedure based on the fatigue-damage evaluation from PSD together with an S-N diagram is summarized.