PSI - Issue 4

Shun-Peng Zhu et al. / Procedia Structural Integrity 4 (2017) 3–10

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S.P. Zhu et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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damage accumulation is treated as a random variable which follows a lognormal distribution, its mean and variance are dependent on the usage life given by Eq. (4) and Eq. (12). For a given critical threshold damage, failure occurs when the random cumulative damage D is larger than C D . The limit state function   G n is     C G n D D n   (15) where   0 G n  is the boundary between the safe domain (defined by   0 G n  ) and the failure domain (defined by   0 G n  ). Following the lognormal assumption of cumulative fatigue damage   D n , fatigue reliability can be calculated through the strength-damage interference       Pr[ 0]= R n G n     (16) where the safety margin is Combining Eq. (5) and Eq. (14), fatigue reliability can be estimated by considering continuous degradation phenomenon of the railway axles with usage cycles using Eq. (16). 3. Experimental validation with two material databases In this section, the prediction results using the proposed method are compared with experimental data available in [7]. The variability of threshold damage at fatigue failure life is calculated by   = ln ln C f D N f a N n   . The damage exponent a and S - N curve parameters are experimentally fitted from experimental data . Using Eq. (16), fatigue reliability of 45 steel and LZ50 steel under different stress levels is plotted in Fig. 4. It shows that the trend of reliability loss with increase in time or loading cycles under constant amplitude loading. Moreover, initially the reliability is relatively high and later decreases with usage cycles. 2     C D D   D D 2 C   (17)

(a) (b) Fig. 4 Fatigue reliability prediction under constant amplitude loading (a) 45 steel and (b) LZ50 steel

Moreover, to assess and predict the reliability of railway axles subjected to VAL, the variability of the threshold damage is firstly estimated based on experimental descriptions [7]. After estimating the variability at threshold damage and variability at any given usage cycles, the reliability of 45 steel subjected to a given amplitude loading can be calculated using Eq. (16). The variation of predicted reliability is compared with those from experimental data. The comparisons are given in Fig. 5.