Issue 38

C. Xianmin et alii, Frattura ed Integrità Strutturale, 38 (2016) 319-330; DOI: 10.3221/IGF-ESIS.38.42 322 is a random number obeying the distribution of fatigue life under j th stress level; E(N j ) is the mean value of fatigue life under the j th load level and N f is the random fatigue life under spectrum loading. For the case of constant amplitude loading, the self-consistency of fatigue damage and fatigue life prediction model can be verified by comparing the failure cycles n f obtained from model with the original fatigue life N. However, this rule does not work when it comes to the case of spectrum loading, because the distributions of original fatigue lives are not unique. In order to verify the fatigue damage and fatigue life under spectrum loading predicted by Eq. (6), two engineering assumptions are firstly made on the basis that there are no load sequence effect: 1) the fatigue life distribution under spectrum loading, N f , should be closer to N j with larger damage ratio n j /E(N j ), and the mean value of N f should be in the range of [ E(N j ) min , E(N j ) max ]; 2) the mean value of N f should be very close to the one calculated by Palmgren-Miner’s linear damage accumulation rule. Numerical sampling test and parameter estimation are carried out according to Eq. (6) under two-level spectrum loading. The parameters of fatigue life distribution for each load level are shown in Tab. 1. Four projects with different combinations of load cycles and stress levels are employed in this test and the corresponding simulation results are listed in Tab. 2. The probabilistic density function(PDF) of different fatigue life distributions are compared with each other, as shown in Fig. 1. j α j β j E(N j ) σ exponent a j 1 2.7 1125 1000 400 1.038 2 3.7 11079 10000 3000 1.014 Table 1 : Parameters of fatigue life distribution for each load level. project n 1 n 2 n 1 / E 1 n 2 / E 2 N f  N / N f N  1 200 100 0.2 0.01 1386 1429 0.97 2 400 100 0.4 0.01 1211 1220 0.99 3 100 3000 0.1 0.3 7344 7750 0.95 4 100 5000 0.1 0.5 8278 8500 0.97 Table 2 : Simulation results of 4 projects of two-level spectrum loading. Figure 1 : Comparisons of fatigue life distributions of different projects with the original constant amplitude loading. From Fig. 1, the PDFs of project 1( N f1 ) and project 2( N f2 ), which have larger damage ratios of n 1 / E 1 , are closer to the 1 st level( N 1 ) rather than to the 2 nd level( N 2 ). Furthermore, the PDF of project 2 is closer to the 1 st level than project 1. The PDFs of project 3( N f3 ) and project 4( N f4 ), which have larger damage ratios of n 2 / E 2 , are closer to the 2 nd level( N 2 ) rather than the 1 st level. Furthermore, the PDF of project 4 is closer to the 2 nd level than project 3. The mean values of N f are in the range of [ E(N 1 ) , E(N 2 ) ]. This simulation results verifies the first assumption. In Tab. 2, the mean value of fatigue life