PSI - Issue 4

Pavel Hutař et al. / Procedia Structural Integrity 4 (2017) 42 – 47

47

Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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threshold value in K max expression. In the range of measured data from R = -2 to R = 0.1 the changes of the threshold value are very small and can be neglected, see Fig.5b (Pokorný et al. (2016b)). Then the crack increment  a was evaluated based on Eq. (4). Table 1 shows calculated values of RFL for different considered magnitudes of residual stresses and various initial crack lengths. The estimated RFL of the axle is 97 000 km of train operation in the case of initial crack length a 0 = 2 mm, when no residual stresses are considered. The consideration of lower band of residual stresses (-20 MPa) leads to 6 times longer estimated RFL (628 000 km) in comparison to the case, which does not take into account the existence of residual stresses. If the upper band of residual stress (-60 MPa) is considered the estimated RFL is theoretically infinite. This is evident from Fig. 3b, where maximal stress SIF, K max , is below the threshold value of initial crack ( a 0 = 2 mm). The consideration of residual stress is also important in the case of longer initial cracks. However, the ratio between RFL determined for axle with and without consideration of residual stresses decreases with the crack length increase. It can be concluded, that residual stresses induced during thermo-mechanical treatment play an important role in the RFL of the railway axle and should be included in the procedure of determination of frequency of regular inspections together with a definition of required NDT method. The paper deals with effect of residual stresses induced during manufacturing process of the railway axle on residual fatigue lifetime. The residual stresses reduce the total stress intensity factor of the fatigue crack and contribute to the resistance of the axle surface to fatigue crack propagation. Exclusion of residual stress from RFL estimation leads to the strong underestimation of axle RFL. In the case of initial crack length a 0 = 2 mm the RFL of the axle is about 97 000 km of train operation. The consideration of lower band of residual stresses (-20 MPa) leads to ca 6 times longer RFL (i.e. 628 000 km). For longer initial cracks the influence of residual stresses on RFL decreases, however remains still important. The results obtained show that consideration of residual stresses can explain difference in conservative RFL estimation (without residual stresses) and experimental tests. 3. Conclusions Benyon J.A., Watson A.S., 2001, The use of Monte-Carlo analysis to increase axle inspection interval, In: Procedings of the 13 th international wheelset congress, Rome, Italy, 2001. Beretta S., Carboni M., Regazzi D., 2016. Load interaction effects in propagation lifetime and inspections of railway axles, Int. J. Fatigue 91/2, 423 Luke M., Varfolomeev I., Lütkepohl K., Esderts A., 2010. Fracture mechanics assessment of railway axles: experimental characterization and computation, Eng. Fail. Anal. 17, 617. Luke M., Varfolomeev I., Lütkepohl K., Esderts A., 2011. Fatigue crack growth in railway axles: assessment concept and validation tests, Eng. Fract. Mech. 78, 714. Náhlík L., Pokorný P., Ševčík M., Fajkoš R., Matušek P., P. Hutař , 2017. Fatigue lifetime estimation of railway axles, Eng. Fail. Anal. 73, 139. Pokorny P., Hutar P., Náhlík L., 2016. Residual fatigue lifetime estimation of railway axles for various loading spectra, Theoretical and Applied Fracture Mechanics 82, 25. Pok orný P., Náhlík L., Hutař P., 2016 b. Influence of Variable Stress Ratio During Train Operation on Residual Fatigue Lifetime of Railway Axles, Structural Integrity Procedia 2, 3585 Regazzi D., Beretta S., Carboni M., 2014. An investigation about the influence of deep rolling on fatigue crack growth in railway axles made of a medium strength steel, Eng. Fract. Mech. 138, 587. Smith R.A., 2000. Fatigue of Railway Axles: A Classic Problem Revisited, European Structural Integrity Society 173. Traupe M., Meinen H., Zenner H. 2004. Sichere und wirtschaftliche Auslegung von Eisenbahnfahrwerken. Zerbst U., Mädler K., Hintze H., 2005. Fracture mechanics in railway applications — an overview, Eng. Fract. Mech. 72,163. Zerbst U., Schödel M., Beier H.T., 2011. Parameters affecting the damage tolerance behaviour of railway axles, Eng. Fract. Mech. 78, 793. Zerbst U., Beretta S., Köhler G., Lawton A., Vormwald M., Beier H.T., Klinger C., Černý I., Rudlin J., Heckel T., Klingbeil D ., 2013. Safe life and damage tolerance aspects of railway axles – a review, Eng. Fract. Mech. 98, 214. Zerbst U., Klinger C., Klingbeil D., 2013b. Structural assessment of railway axles - a critical review, Eng. Fail. Anal. 35, 54. Acknowledgements The research infrastructure IPMINFRA supported by the Ministry of Education, Youth and Sports of the Czech Republic through the project No. LM2015069 was used. The co-operation between IPM and Bonatrans Group is realized in the frame of Strategy 21 “Top research in the public interest” of the Czech Academy of Sciences. References