PSI - Issue 22

S.C. Wu et al. / Procedia Structural Integrity 22 (2019) 211–218 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

213

3

lg

lg

N

N



j 



g 

ji

gi



(1)





j

g

The equivalent process can be expressed as:

 





g

e

lg

lg N N 





j 

g 

(2)

ji

ji

j

Note that the mean life at all stress levels is acquired from the median S-N curve and the STD is determined as follows. 1.2. Determination of the standard deviation As is known to all, the STD represents the scattering of fatigue life for various materials. It is also believed that the stress level is a major influence factor on the STD (Zhai and Li, 2012). At present, many researchers presume that for the majority of metallic materials, there exists approximately linear relationship between the STD and stress levels (Duquesnay and Underhill, 2010). The relationship can be expressed as:   = i k k i K S S     (3) 2. An improved statistical inference approach As we all know, the sample size at each stress level is rarely large enough, e.i.15 or more (Xie et al., 2014). Therefore, it is hardly probable to acquire the ( X-x-x-x ) type test program and deal with the data easily. At the same time, the P-S-N curve obtained by the traditional group test method can ′ t reflect the different dispersion of fatigue life at various stress levels. For overcoming these shortcomings, this paper proposes the ISIA to calculate the P-S-N curve which is consistent with the actual changing trend. 2.1. Improved the number of experiments Obviously, the required amounts of test data under a certain stress level for the traditional group test method is hard to reach in engineering practice. In the meanwhile, it is impossible to judge the accuracy and reliability of STD just by the number of tests. Hence the ISIA sets the parameter to decide the rational number of tests. In accordance with HB/Z 112-86, the minimum number of test specimens required is 6. Influenced by the confidence level γ and the error limit δ max , the CV, that is the ratio of the STD and the average, should also be taken into account. For example, when γ is 90%, δ max is 5% and CV ∈ (0.0746, 0.0806), the required number is 9. Altogether, the accuracy of STD is guaranteed by the following two conditions:  The number of test data at each group should be more than 6.  Under the constraints of the confidence level and the error limit, the number should be more than the minimum number corresponding to the CV. 2.2. The improved search method of parameter K For the decreasing search method, the maximum value of the K in a certain range is determined. From Eq.(3), it can be seen that the STD for the stress level below the base-line stress level gets the maximum value. The method for determining the upper limit for K values is described below. Considering the effect of reliability level ( k ( p , γ , v ) ), the fatigue life lg N pj for the j th stress level can be calculated with the equation as: