Stochastic assessment of residual fatigue life of railway axles considering relevant critical factors

Abstract

Statistical distribution of residual fatigue life (RFL) of railway axles under given loading was computed using the Monte Carlo method by considering random variation of the selected input parameters. Experimental data for the EA4T railway axle steel, the loading spectrum, the press fit loading and the residual stress induced by surface hardening were considered in the crack propagation simulations. Usually, the material properties measured by tensile tests are considered to be the most informative source of material data. Under fatigue loading, however, the crack growth rates near the threshold are the most critical data. Two important influencing factors on these crack growth rates are presented: first, the air humidity and, second, the near-surface residual stress. The typical variation of these parameters in operation may change the RFL by one or two orders of magnitude. Experimentally obtained crack growth thresholds and residual stress profiles are highly affected by the used methodology. Therefore, the obtained input data may be located anywhere within a large scatter, while the experimenters are completely unaware of it. This can lead to dangerously non-conservative situations, e.g. when the thresholds are measured in a laboratory under humid air conditions and then applied to predictions of RFLs of axles operated in winter in low air humidity. This is significant for the topic of inspection interval optimisation. The results of experiments done on real 1:1 railway axles were close to the most frequent value found in the histogram of the numerically computed RFLs.

Keywords

Residual fatigue life / Railway axles / Fatigue crack Growth threshold / Air humidity / Monte Carlo method

References

[1] Baig MAA, Khan SA, Baig MAA. High speed trains: a review. IOSR J Mech Civ Eng, 2016, 16: 104-109

[2] Klinger C, Bettge D. Axle fracture of an ICE3 high speed train. Eng Fail Anal, 2013, 35: 66-81

[3] Odanovic Z, Ristivojevic M, Milosevic-Mitic V. Investigation into the causes of fracture in railway freight car axle. Eng Fail Anal, 2015, 55: 169-181

[4] Zerbst U, Beretta S, Köhler Get al.. Safe life and damage tolerance aspects of railway axles–A review. Eng Fract Mech, 2013, 98: 214-271

[5] Smith RA. Fatigue of railway axles: a classic problem revisited. Europ Structur Integr Soc, 2000, 26: 173-181

[6] Zerbst U, Mädler K, Hintze H. Fracture mechanics in railway applications–– an overview. Eng Fract Mech, 2005, 72(2): 163-194

[7] Maierhofer J, Simunek D, Gänser HPet al.. Oxide induced crack closure in the near threshold regime: The effect of oxide debris release. Int J Fatigue, 2018, 117: 21-26

[8] Madia M, Vojtek T, Duarte Let al.. Determination of fatigue crack propagation thresholds for steel in presence of environmental effects. Int J Fatigue, 2021, 153 106449

[9] Newman JC, Yamada Y. Compression precracking methods to generate near-threshold fatigue-crack-growth-rate data. Int J Fatigue, 2010, 32(6): 879-885

[10] Pourheidar A, Patriarca L, Madia Met al.. Progress in the measurement of the cyclic R-curve and its application to fatigue assessment. Eng Fract Mech, 2022, 260 108122

[11] Pokorný P, Vojtek T, Jambor Met al.. Effect of underload cycles on oxide-induced crack closure development in Cr-Mo low-alloy steel. Materials, 2021, 14(10): 2530

[12] Giannella V. Stochastic approach to fatigue crack-growth simulation for a railway axle under input data variability. Int J Fatigue, 2021, 144 106044

[13] Beretta S, Carboni M, Cantini Set al.. Application of fatigue crack growth algorithms to railway axles and comparison of two steel grades. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2004, 2184317-326

[14] Maierhofer J, Gänser H-P, Simunek Det al.. Fatigue crack growth model including load sequence effects–Model development and calibration for railway axle steels. Int J Fatigue, 2020, 132 105377

[15] Dlhý P, Poduška J, Pokorný Pet al.. Methodology for estimation of residual stresses in hardened railway axle. Procedia Struct Integr, 2019, 23: 185-190

[16] Hutař P, Pokorný P, Poduška Jet al.. Effect of residual stresses on the fatigue lifetime of railway axle. Procedia Struct Integr, 2017, 4: 42-47

[17] Náhlík L, Pokorný P, Ševčík Met al.. Fatigue lifetime estimation of railway axles. Eng Fail Anal, 2017, 73: 139-157

[18] Zhang JW, Lu LT, Shiozawa Ket al.. Analysis on fatigue property of microshot peened railway axle steel. Mater Sci Eng A, 2011, 528(3): 1615-1622

[19] Gong H, Wu Y, Feng Xet al.. Analysis of quenching stresses in 35CrMo axle. J Wuhan Univ Technol Mater Sci Ed, 2016, 31(3): 630-635

[20] Isomura S, Yomoda K (1995) Manufacturing history of axles for Shinkansen. In: 11th International Wheelset Congress, Paris. pp 51–54

[21] Wu SC, Xu ZW, Liu YXet al.. On the residual life assessment of high-speed railway axles due to induction hardening. Int J Rail Transp, 2018, 6(4): 218-232

[22] Qin T, Hu F, Xu Pet al.. Gradient residual stress and fatigue life prediction of induction hardened carbon steel S38C axles: Experiment and simulation. Int J Fatigue, 2024, 185 108336

[23] Regazzi D, Beretta S, Carboni M. An investigation about the influence of deep rolling on fatigue crack growth in railway axles made of a medium strength steel. Eng Fract Mech, 2014, 131: 587-601

[24] Hassani-Gangaraj SM, Carboni M, Guagliano M. Finite element approach toward an advanced understanding of deep rolling induced residual stresses, and an application to railway axles. Mater Des, 2015, 83: 689-703

[25] Gänser H-P, Maierhofer J, Tichy Ret al.. Damage tolerance of railway axles–the issue of transferability revisited. Int J Fatigue, 2016, 86: 52-57

[26] Yasniy O, Lapusta Y, Pyndus Yet al.. Assessment of lifetime of railway axle. Int J Fatigue, 2013, 50: 40-46

[27] Madia M, Beretta S, Zerbst U. An investigation on the influence of rotary bending and press fitting on stress intensity factors and fatigue crack growth in railway axles. Eng Fract Mech, 2008, 75: 1906-1920

[28] Luo Y, Li C, Kang Xet al.. Fatigue limit and residual life evaluation of railway EA4T axles with artificial surface impacts. J Mater Eng Perform, 2023, 32(11): 5167-5175

[29] Hu Y, Wu S, Withers PJet al.. Corrosion fatigue lifetime assessment of high-speed railway axle EA4T steel with artificial scratch. Eng Fract Mech, 2021, 245 107588

[30] Zou L, Zeng D, Li Yet al.. Experimental and numerical study on fretting wear and fatigue of full-scale railway axles. Railw Eng Sci, 2020, 28(4): 365-381

[31] Pokorný P, Dlhý P, Poduška Jet al.. Influence of heat treatment-induced residual stress on residual fatigue life of railway axles. Theor Appl Fract Mech, 2020, 109 102732

[32] Anderson TL. Fracture mechanics: fundamentals and applications, 20053Boca Raton, Taylor & Francis

[33] Pokorný P, Hutař P, Náhlík L. Residual fatigue lifetime estimation of railway axles for various loading spectra. Theor Appl Fract Mech, 2016, 82: 25-32

[34] CEN (2021) CSN EN 13260: Railway applications - Wheelsets and bogies - Wheelsets -Product requirements. Brussels

[35] Pokorný P, Vojtek T, Náhlík Let al.. Crack closure in near-threshold fatigue crack propagation in railway axle steel EA4T. Eng Fract Mech, 2017, 185: 2-19

[36] Pokorný P, Náhlík L, Hutař P. Influence of variable stress ratio during train operation on residual fatigue lifetime of railway axles. Procedia Struct Integr, 2016, 2: 3585-3592

[37] Ciavarella M, Paggi M, Carpinteri A. One, no one, and one hundred thousand crack propagation laws: a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth. J Mech Phys Solids, 2008, 56(12): 3416-3432

[38] Schijve J. Fatigue of structures and materials, 2008, New York, Springer

[39] SWRI (2002) NASGRO ® Fracture Mechanics and Fatigue Crack Growth Analysis Software. https://www.swri.org/sites/default/files/industries/nasgro.pdf. Accessed 15 July 2024

[40] Harter JA (1999) AFGROW Users Guide and Technical Manual. http://afgrow.cn/wp-content/uploads/2022/02/AFGROW_Technical_Manual_and_Users_Guide_5-3-5-24.pdf. Accessed 12 July 2024

[41] Klesnil M, Lukáš P. Fatigue of metallic materials, 19922New York, Elsevier

[42] Castillo E, Fernández-Canteli A, Siegele D. Obtaining S–N curves from crack growth curves: an alternative to self-similarity. Int J Fract, 2014, 187(1): 159-172

[43] Fernández-Canteli A, Castillo E, Blasón S. A methodology for phenomenological analysis of cumulative damage processes. Application to fatigue and fracture phenomena. Int J Fatigue, 2021, 150: 106311

[44] Barten AP. The coefficient of determination for regression without a constant term. The Practice of Econometrics, 1987, Dordrecht, Springer181-189

[45] Marsaglia G, Tsang WW, Wang J. Evaluating Kolmogorov’s distribution. J Statistic Software, 2003

[46] Stoica P, Selen Y. Model-order selection: a review of information criterion rules. IEEE Signal Process Mag, 2004, 21(4): 36-47

[47] Neath AA, Cavanaugh JE. The Bayesian information criterion: background, derivation, and applications. Wires Comput Stat, 2012, 4(2): 199-203

[48] Li B, Rosa LG. Prediction models of intrinsic fatigue threshold in metal alloys examined by experimental data. Int J Fatigue, 2016, 82: 616-623

[49] Li B, Rosa LG. Prediction models of intrinsic fatigue threshold in metal alloys examined by experimental data. Int J Fatigue, 2016, 82: 616-623

[50] Hertzberg RW. On the calculation of closure-free fatigue crack propagation data in monolithic metal alloys. Mater Sci Eng A, 1995, 190(1–2): 25-32

[51] Pokluda J, Pippan R, Vojtek Tet al.. Near-threshold behaviour of shear-mode fatigue cracks in metallic materials. Fatigue Fract Eng Mat Struct, 2014, 37(3): 232-254

[52] Vojtek T, Pokorný P, Kuběna Iet al.. Quantitative dependence of oxide-induced crack closure on air humidity for railway axle steel. Int J Fatigue, 2019, 123: 213-224

[53] Maierhofer J, Kolitsch S, Pippan Ret al.. The cyclic R-curve–determination, problems, limitations and application. Eng Fract Mech, 2018, 198: 45-64

Funding

Grantová Agentura České Republiky(22-28283S)

Technologická Agentura České Republiky(CK03000060)

RIGHTS & PERMISSIONS

The Author(s)