PSI - Issue 22

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

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

1. Introduce With the speed increasing, the operation conditions of high-speed train continue to deteriorate, so that the incidents caused by defects have increased dramatically. It is well-known that the failures of railway structures (forged axle, welded car body, welded frame, etc.) happen mainly due to the cyclic loading (Wu et al., 2016). In order to ensure the safety, reliability and economy of equipment in service, the P-S-N curve, as a key indicator of the life design, has long been concerned (Hffern, 2002). Owing to the high cost and long test time to obtain the P-S-N curve with the conventional test program (Xie et al., 2014), lots of investigations have been focused on the experiment technique and the statistical methods for the small-sample problem (Zheng and Wei, 2005). For the small sample data, Guida and Penta (2010) presented the Bayes approach for more accurate estimation and less costs, that is obtained by combining the test data with the theoretical studies or previous experimental results. Based on the equivalent fatigue life, Xie et al. (2014) developed the BSIM by defining the relationship between life dispersion and stress levels. Focused on determining the minimum number of tests, Liu et al. (2017) proposed a hierarchical Bayesian model with the prior information incorporating the structural prior and the subjective prior simultaneously. However, for the situation with very finite or small life data, the difficulty still exists to acquire P-S N curve with satisfactory accuracy. In the respective methods, the issues include mathematics complexity, lack of robustness and unreasonable assumption. Based on the BSIM, this paper presents the ISIA to innovate the method estimating the maximum STD of the logarithmic life at the lower stress levels. Moreover, the required number of specimen is also modified with the coefficient of variation (CV). To illustrate the accuracy and reliability, the fatigue life assessment of high-speed railway axles under service load spectrum is carried out. Then the P-S-N curve of key welded structures about the high-speed railway is fitted, such as aluminum alloy body, pantograph and bogie frame.

Nomenclature N ji

fatigue life of the specimen i under the j th stress level F j (lg N ji ) cumulative probability of the fatigue life random variable lg N ji μ j mean of the random variable lg N j σ j STD under stress level S j lg N ji e equivalent life of lg N ji K a negative constant, i.e. the slope of the log-life STD-stress plot p survival rate v degree of freedom k (p, 1- α,v) one-side tolerance factor k slopes of fatigue SN diagram for the finite life regions k′ slopes of fatigue SN diagram for the infinite life region S D stress amplitude for the knee of the S – N diagram N D number of cycle for the knee of the S – N diagram S i stress amplitude for the i th class of the load spectrum D crit Miner index at failure m j sample size associated with cyclic stress S j μ ISIA, σ ISIA, μ BSIM, μ BSIM

value of mean and STD obtained by the ISIM or the BSIM

Stress ratio

R

∆ σ D

characteristic fatigue strength of IIW recommendations

1.1. The backward statistical inference method

In general, the fatigue life follows the lognormal distribution at an arbitrary stress level, i.e lg N ~ N ( μ , σ 2 ), and the consistency of fatigue life sample percentiles can be expressed as: