Issue 38

C. Xianmin et alii, Frattura ed Integrità Strutturale, 38 (2016) 319-330; DOI: 10.3221/IGF-ESIS.38.42

The consistent index b is closely related to statistical parameters α and β of fatigue life distribution and can be solved by Monte Carlo sampling test according to Eq. (2) . When α is assumed as 4, the quantitative relation between index b and scale parameter β can be obtained through large number of sample tests, the results are shown in Tab. 6. Note that the general trend is that b decreases with β and b stay constant in some interval of β instead of changing continuously with β .

β b β b

(8×10 3 ,10 4 ]

(10 4 ,5×10 4 ]

(5×10 4 ,10 5 ]

(10 5 ,10 6 ]

1.011

1.010

1.009

1.008

(5×10 7 ,5×10 8 ]

(5×10 8 ,10 10 ]

(10 6 ,6×10 6 ]

(6×10 6 ,5×10 7 ]

1.007 1.004 Table 6 : Quantitative relation between the consistent index b and scale parameter β(α=4). 1.006 1.005

E XPERIMENTAL VERIFICATION OF THE STATISTICAL FATIGUE DAMAGE MODEL UNDER SPECTRUM LOADING Fatigue tests under spectrum loading he specimens are the same as those used in the fatigue tests under constant amplitude loading [15]. The load spectra and fatigue life results are listed in Tab. 7.

T

spectrum Load order

1

2

3

4

5

Cycles to failure

Sa(MPa)

17.09

27.77

42.73

36.32

21.36

500826 ， 686156 ， 2445490 ， 1201897 ， 2 253944

5-level

cycles

1000

500

200

600

900

Sa(MPa)

27.77

42.73

36.32

\ \

\

371112 ， 522772 ， 670298 ， 507405 ， 426 219 ， 364397

3-level

cycles \ Table 7 : Fatigue test results of straight lugs under spectrum loading. Using the data in Tab. 7, the statistical parameters of fatigue life under spectrum loading can be obtained by BJPM, including ˆ  ,E ， σ , N 95/95 and the interval of 95% fatigue life ( β 1 , β 2 ), ( E 1 , E 2 ) and ( σ 1 , σ 2 ) . Here σ is the standard deviation of the test results, demonstrating the scatter characteristics of fatigue lives. Experimental verification of the fatigue damage model Statistical parameters for each stress level of the multilevel spectrum are obtained via the S-N curves described in section 3, including characteristic life β , the average life E , N 95/95 and the self-consistent index a , listed in Tab. 8. 500 302 600

Sa(MPa)

17.09

27.77

42.73

36.32

21.36

β

158271738 1605853 143457895 1455549

198884 180269

437239 396314 180859

6180778 5602272 2556608

E

N 95/95

65467281

664242

82266

statistical

parameters 1.008 Table 8 : Statistical parameters of fatigue life distributions under constant amplitude loading. self-consistent index a 1.006 1.007 1.008 1.008

Two thousand values of N f

can be acquired using Eq. (6) from 2000 groups of random sampling based on the fatigue life

325