Issue 38

C. Xianmin et alii, Frattura ed Integrità Strutturale, 38 (2016) 319-330; DOI: 10.3221/IGF-ESIS.38.42 328 The predicted PDFs of fatigue life by the modified model considering load sequence effect are compared with the test results under spectrum loading, as shown in Fig. 5. The original test data is also marked in the curve and the fatigue life with 95% intervals are denoted by the vertical lines. It can be found that the test data all fall into the 95% interval of life distributions based on the modified fatigue damage accumulation model under the spectrum loading. The average life and the standard deviation based on the modified model both fall into the 95% interval estimation of test data, and the ratio of model to test is close to 1. The shape parameter obtained by the modified model is closer to 4 indicating that the modified model is more coincident with the fatigue test than the original model. In addition, as shown in Fig.5, the schematic PDFs of predicted fatigue life N f and the test results are quite close. Therefore, it can be concluded that the modified model can precisely predict the fatigue damage and fatigue life under spectrum loading, and at the same time, properly reflect the stochastic nature and load sequence effects on fatigue behavior. a) fatigue life distributions under 5-level spectrum loading. b) fatigue life distributions under 3-level spectrum loading. Figure 5 : Fatigue life distributions under spectrum loading. Moreover, the mean fatigue lives E and N 95/95 are also calculated by Palmgren-Miner’s linear damage summation rule and are compared with those based on test data, as listed in Tab. 11. Load level E (×10 6 ) R E N 95/95 (×10 5 ) R N 95,95 E fall into the ( E 1 , E 2 ) interval 5 1.0209 0.5914 4.6588 0.5820 no 3 0.39686 0.8551 1.8111 0.8415 yes Table 11 : Comparisons of parameters based on Palmgren-Miner’s linear damage summation rule with those of fatigue tests. The results illustrate that the fatigue lives calculated by Palmgren-Miner’s linear damage summation rule are too conservative, especially for the 5-level spectrum loading. The modified model is more accurate and reasonable than the Palmgren-Miner’s rule in engineering applications, and can be easily expanded to the application of other metal materials. The fatigue damage calculation steps are summarized as follows. 1) Conduct the fatigue test under constant amplitude loading with 3 stress levels. At each stress level, the number of test specimens is not less than 6. According to the test data, the p-S-N curve is fitted. 2) The fatigue life distribution is assumed to obey the Weibull distribution, and the parameters are obtained based on the p-S-N curve. 3) Get the consistent index b corresponding to different stress levels through the large number of Monte Carlo sampling using Eq. (2). 4) Calculate the fatigue damage under spectrum loading using Eq. (10). As for the application of the statistical fatigue damage accumulation model, two aspects should be noted. Firstly, the shape parameter of Al-alloy is different in the data processing. For the experiments, it is assumed to be 4 for both constant and variable amplitude loading conditions; however, for the model simulation, it is estimated by the maximum likelihood method based on the large number of Monte Carlo sampling (not equal to 4, as shown in Tab. 9 and Tab. 10. Secondly, the stress ratio R may be different for each load level in variable spectrum loading. The method based on p-S-N curve and constant life diagram could be applied [20]. The stress level at arbitrary R can be converted to the stress level at