PSI - Issue 19

Zhu Li et al. / Procedia Structural Integrity 19 (2019) 528–537

533

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 4. Schematic representation to determine associated stress amplitudes and cycles from each narrowband PSD segment.

2.4. Fatigue Damage Summation If stress amplitudes and cycles are obtained, the fatigue damage can be predicted by the fatigue stress-life curve of the given material on the basis of damage accumulation [25,26,27,28,29,30]. In order to calculate fatigue damage for each of the v PSD segments, k number of different applied stresses and associated stress cycles were calculated for each PSD segment by discretizing the corresponding Rayleigh distribution. A number of cycles, n and applied stresses, S k , provides the necessary information to compute fatigue damages for each narrowband PSD segment; the number of cycles to failure, N for each narrowband PSD segment can be calculated from the traditional S-N curve in Eq. (5) and (6) as shown in Fig. 4. N j,k = − , (5) Where , is the number of cycles to failure, , is the stress amplitude, b is the slope of the S-N curve, and C is a constant corresponding to the material constant. Additionally, k = 1…5 and j = 1… v (the number of PSD segments): Different stress regions in the PDF of Rayleigh distribution have different probabilities, as indicated in Figs. 4 and 5. Applied stress cycles for each of the v PSD segments can be obtained by Eq. (6). n , = , (6) Where is the central frequency of j-th response PSD band, T the time duration, and , represents the probability of the Rayleigh stress distributions for the v-th PSD segments. According to the cumulative damage rule i.e. Miner’s rule , fatigue damage for all PSD segments can be calculated by summing up the fatigue damages of each PSD segment as expressed in Eq. (7): d = ∑∑ , N j,k 5 =1 =1 (7) Where, v is the number of the PSD segments. Additionally, d is considered as damage per a PSD position. Since d is damage per a single discrete PSD position, after considering u number of discrete PSD positions, n , ,