PSI - Issue 22

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

214

4

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

lg pj N

k

j   



(4)



 , , 

j

p v

Under the same condition, the relationship between lg N pj and lg N p ( j +1) is lg N pj < lg N p ( j +1) . Incorporating with Eq.(3) and Eq.(4), the upper bound used to search for the reasonable parameter K is defined as:       1 1 , , j j j j p v K k S S             (5)

According to the upper bound, the decreasing search method about the parameter K can be performed.

2.3. Improved the fitting method for P-S-N curve

As shown in Fig. 1(a), to tackle the so-called transferability, the S-N curve for full-scale components can be estimated by modifying that of small-scale specimens with the four factors. The factors are the type of loading ( C lot ), surface finish ( β ), size ( ε ), and k ( p , γ , v ) . From the graph, it can be seen that the P-S-N curves of full-size structures are parallel to each other. In fact, as the stress level decreases, the STD increases gradually according to formula Eq.(3), so it will inevitably show an open-downward horn shape for small-scale specimens. Considering the influence of STD on P-S-N curve of components corresponding to the different stress levels, the fitting method can be further improved as shown Fig. 1(b) and the steps are as the following:  By combining Eq.(4) and median S-N curve, the fatigue life can be acquired with k ( p , γ , v ) .Then fitting the data with the least square method, the P-S-N curve for small-scaled specimens can be got.  Under the constraints of the confidence level and the error limit, the number should be more than the minimum number corresponding to the CV. When the factor C lot , β and ε are considered, the P-S-N curve of full-scale components is obtained, i.e the (5) curve in Fig. 1(b) . 3. The Fatigue life prediction of axle With the rapid rise of transport speed and capacity, progressive damage remains a concern in modern railway, such as axles. In order to verify the accuracy and reliability of ISIA, this paper combines the proposed method with a five stage load spectrum as shown in Fig. 2 (Wu et al., 2018) and predicts the fatigue life of full-size axles.

Fig. 1. The difference methods for fitting P-S-N curves: (a) the traditional group test method, (b) the ISIA