Issue 38

C. Xianmin et alii, Frattura ed Integrità Strutturale, 38 (2016) 319-330; DOI: 10.3221/IGF-ESIS.38.42 326 distributions under constant amplitude loading, as shown in Tab. 8. The steps of random sampling are as follows: 1) For the j th stress level, do n j times of sampling according to the probabilistic distribution of fatigue life N ji using parameters in Tab. 8. The damage caused by the j th level of stress( D Bj ) is obtained through Eq. (6). 2) The whole fatigue damage D B in one loading block can be obtained by summing up D Bj from the 1 st level to the m th level. 3) Fatigue life( N f ) under spectrum loading is calculated using the second formula of Eq. (6). 4) Repeating steps 1), 2)and 3) for 2000 times. Based on 2000 values of N f , the statistical parameters of fatigue lives, including ˆ  (shape parameter), ˆ  , E, σ and N 95/95 , are estimated by the method of maximum likelihood. The ratios of parameters between model and test data are indicated by R E , R σ and R N 95 respectively. The results are listed in Tab. 9. N 1 is the number of test data outside the 95% confidence interval of the model’s probability distribution, which reflects the rationality of the model. Whether E and σ from test data, respectively, fall into the interval ( E 1 , E 2 ) and ( σ 1 , σ 2 ) from the model also indicates the validity of the prediction, as listed in the last 2 columns of Tab. 9. load level ˆ  ˆ  (×10 6 ) E (×10 5 ) R E  (×10 5 ) R  N 95/95 (×10 5 ) R N 95 N 1 Fall into ( E 1 , E 2 ) Fall into (  1 ,  2 ) 5 5.833 1.035 9.585 0.555 1.906 0.394 6.180 0.772 2 no no 3 5.283 0.404 3.717 0.801 0.810 0.622 2.284 1.061 2 no no Table 9 : Comparisons of parameters based on the statistical fatigue damage model with those from fatigue tests. The predicted PDFs of fatigue life under spectrum loading are compared with the test results, as shown in Fig. 4. The comparisons indicate that significant discrepancy exists in the mean values, standard deviation and lateral deviations, especially for the 5-level spectrum loading. In addition, as shown in Fig.4, the schematic PDFs of predicted fatigue life N f and the test results are quite different. Load sequence effect is believed to be the main reason for the difference between prediction and tests [16]. Therefore, improvements have to be brought to this model since interactions among variable stress levels should be considered. a) fatigue life distributions under 5-level spectrum loading. b) fatigue life distributions under 3-level spectrum loading. Figure 4 : Fatigue life distributions under spectrum loading. A MODIFIED FATIGUE DAMAGE ACCUMULATION MODEL UNDER SPECTRUM LOADING CONSIDERING LOAD SEQUENCE EFFECT he difference between the model and the tests under spectrum loading is mainly attributed to the load sequence effects, i.e. the acceleration effect and the retardation effect, as demonstrated by many researches in various fatigue tests [17, 18]. This direct effect of loading sequence plays an important role in the process of damage T