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An effect of strength of railway axle steels on fatigue resistance under press fit
Engineering Fracture Mechanics 78 (2011) 731–741
Contents lists available at ScienceDirect
Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
An effect of strength of railway axle steels on fatigue resistance under press fit V. Linhart, I. Cˇerny´ ⇑ SVÚM a.s., Podnikatelská 565, CZ-19011 Praha 9, Beˇchovice, Czech Republic
a r t i c l e
i n f o
Article history: Available online 5 December 2010 Keywords: High-cycle fatigue Rotating bending Press fit Fretting fatigue Fatigue crack growth Railway axle steels
a b s t r a c t High-cycle fatigue tests with an evaluation of fatigue limit were carried out on large model components of bars with press fitted hubs of diameter 63/59 mm. Bars were made of three railway axle steels EA1N, EA4T and 34CrNiMo6 with considerable different strength from 586 MPa to 1041 MPa, respectively. Detection and measurement of crack growth under hubs by ultrasonic method was performed during the tests. In spite of the differences in strength and alloying of tested bars, differences in mean value of fatigue limit were not significant. This result was connected with specific damage mechanism and microcracks initiation under hubs with fretting effects. Short fatigue crack growth under hubs occurred at stress intensity factor range DK considerably bellow threshold value DKth of long cracks. Simultaneous growth of main cracks from more than one point of surface circumferential area under hub was quite frequently observed. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Press fit technology is commonly used for an attachment of components of railway wheel sets, i.e. axles, wheels and traction gears. As a result of cyclic loading in operation, cracks can be initiated under hubs of these parts. The cracks are further developed by fatigue process and so determine total life of axles and wheel sets. These problems represent a current issue to be solved to fulfil safety an reliability requirements, particularly important in connection with increasing transport speeds [1]. Besides design of axles and press fitted joints including optimum dimensions, material selection and surface treatment are important issues. According to EN 13261, steels EA1N and EA4T are mentioned as standard materials, first of them being a low strength carbon steel with 0.4% C. EA4T is a low alloyed steel of fairly high strength. As regards especially locomotive axles or high speed train axles, numerous producers have recently used other steels with a higher content of alloying elements, e.g. 30CrNiMoV12 or 34CrNiMo6 steels, sometimes characteristic by a significantly higher strength, about 1000 MPa [2]. In general, high strength steels enable to use advanced design approaches to reduce total unsprung axle mass and consequently dynamic forces on track and ground borne vibrations being particularly important with high speed trains [3,4]. Fatigue resistance of components with smooth surface without defects are usually positively affected by material strength. On the other hand, not very significant effect of material strength on fatigue strength of axles under hubs was already indicated by Horger in the past [5]. An important question therefore is, whether and how the use of higher strength steels, usually with an increased amount of alloying elements, can contribute to an increase of fatigue strength and life at critical axle ⇑ Corresponding author. Address: SVÚM a.s., Strength Department, Podnikatelská 565, 19011 Praha 9, Czech Republic. Tel.: +420 222724098; fax: +420 222724509. ˇ erny´). E-mail address: [email protected] (I. C 0013-7944/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2010.11.023
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positions under press fitted hubs. An experimental programme was carried out with the aim to contribute to the clarification of problems in this field. Results of the investigation are presented and discussed in this paper. 2. Experiments Besides standard EA1N and EA4T steels, a 34CrNiMo6 steel according to DIN with a considerably higher strength, being often used for manufacture of axles, has been investigated. Chemical composition and mechanical properties of the steels are in Tables 1 and 2. The investigated steels are characteristic by graded strength levels in the range typical for real manufacture conditions, namely Rm = 586 MPa, 789 MPa and 1041 MPa. Experimental programme was performed using model test bars of diameters 63 mm and 59 mm in press fitted head and central part, respectively – Fig. 1. Model hubs of diameters 220/135 mm were press fitted on both the test bar heads – Fig. 2. The contact surfaces of specimen heads and hubs were lubricated with Molykote G-n-plus before press fitting. The hubs and specimen heads were manufactured with interference values between 1.2‰ and 2.0‰ which correspond exactly to actual full-scale components. Due to linearity in the elastic area of stresses in the material, the same relative interference values used in case of reduced models namely result in equivalent radial and tangential stresses at the contact area, if mutual dimensional proportions in the model, both hub and axle head, are retained. Concerning quantitative description of the stresses coming from the press fitting, for the interference Dr/r = 0.002, both radial and tangential stresses are considerable lower than yield stress, even in case of the A1N steel with lowest strength. Fatigue tests were carried out on a Wöhler type rotating bending machine – SCHENCK UMBI 750. Test frequency was 1500 rpm, maximum target number of cycles 2 107 or alternatively 5 107, if damage did not occur earlier. An initiation and growth of cracks under hubs was periodically checked and monitored using ultrasonic device Krautkramer USK 7 with an inclined 45° transducer. In order to crack initiation and growth measurement, fatigue tests were periodically interrupted and detailed ultrasonic measurement all along the circumference was performed at defined and marked positions of the press fit. The ultrasonic method was calibrated before its use on the basis of measurement performed using model steel bars of the same dimensions with artificial circumferential narrow notches with different depths simulating cracks. On the basis of the calibration, it was also determined that minimum threshold crack depth being able reliably detected was approximately 0.15 mm in this specific experimental arrangement. It should be however pointed out that during actual fretting fatigue tests, accuracy of measurement of rather deep cracks of more than 2 mm depth could be affected by a presence of corrosion oxide debris.
Table 1 Chemical composition of steels. Steel
C (wt.%)
Si (wt.%)
Mn (wt.%)
Cr (wt.%)
Ni (wt.%)
Mo (wt.%)
P (wt.%)
S (wt.%)
EA1N EA4T 34CrNiMo6
0.40 0.26 0.352
0.24 0.29 0.228
0.95 0.70 0.61
– 1.0 1.37
– – 1.32
– 0.20 0.19
0.0027 0.020 0.015
0.017 0.007 0.026
Rm (MPa)
A (%)
Z (%)
586 789 1041
29.4 18.5 16
58 – 53.8
Table 2 Mechanical properties. Steel
ReH (Rp
EA1N EA4T 34CrNiMo6
364 (ReH) 631 849
0.2)
(MPa)
Fig. 1. Model fatigue test specimen.
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Fig. 2. Model hub for fatigue testing.
3. Experimental results Results of individual fatigue test series are presented in Figs. 3–5, they are summarised in Fig. 6. Regression lines were calculated considering failure cases and occurrence of fairly significant cracks deeper than 0.9 mm, respectively. It means that very short cracks of the length less than 0.5 mm, which were arrested, were not considered for the regression analysis. Fatigue dependencies have a Wöhler curve character usually up to 5 107 cycles. Fatigue limit was usually evaluated on the basis of tests to 5 107 cycles. In this work, fatigue limit was defined by two conditions that on the basis of 5 107 cycles (i) no failure occurred or (ii) depth of fretting corrosion cracks, if initiated, was considerably less than 1 mm (roughly about 0.5 mm). Though the target number of cycles to confirm fatigue limit was mostly 5 107, several results of tests performed up to number of cycles between 1 and 2 107 without damage were considered as fatigue limit, too. The mentioned definition of failure case should be commented, too. In some cases, tests could not be performed to final cracking, because the testing machine started to strongly vibrate, when the crack approximately 2 mm deep arose. Critical crack depth causing vibrations significantly depended on the crack circumferential asymmetry. The machine vibrations started as a result of progressively growing asymmetrical crack were considered as failure case, too. Results are characteristic by fairly high scatter, typical for this type of rather complicated tests. The scatter, larger than usual scatter of standard fatigue tests, can be considered as a consequence of the complexity of fretting fatigue crack initiation mechanisms. All the test pieces were namely press fitted at identical conditions and so any effect of press fitting procedure on the scatter is unlikely. Due to the scatter, fatigue limit only could be evaluated with a precision of cca ± 10% or cca ± 5% in case of the 34CrNiMo6 steel, respectively. Under these circumstances, fatigue limit of EA1N and EA4T steel bars evaluated from Figs. 3 and 4 is in the range between 100 and 120 MPa and between 85 and 105 MPa, respectively. Fatigue limit of 34CrNiMo6 steel bars, with the highest strength Rm = 1041 MPa, corresponds to 95–105 MPa (Fig. 5). It follows from Fig. 6, where fatigue curves of separate steels are compared, that considering the scatter, there are no significant differences between the series of materials of different strength. The only small difference of somewhat steeper slope of the EA4T fatigue regression line is caused by the two points indicated as ‘‘retarded failure’’, which correspond to quite a high number of cycles at relatively high stress amplitude.
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Fig. 3. Fatigue tests results of EA1N steel specimen (Rm = 586 MPa) with press fit.
Fig. 4. Fatigue tests results of EA4T steel specimen (Rm = 789 MPa) with press fit.
Fig. 5. Fatigue tests results of 34CrNiMo6 steel specimen (Rm = 1041 MPa) with press fit.
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Fig. 6. Comparison of fatigue tests results on model steel specimens with press fit.
Fig. 7. Measurement of crack development under press fit, EA1N steel specimen (No. 1.16).
The non-destructive measurement under the hubs by the ultrasonic method enabled not only to detect crack initiation, but also to monitor their gradual development. Fretting fatigue cracks were initiated under press fit at the distance between 7 and 8 mm from the hub edge. In case of heat treated bars, further additional cracks sometimes arose outside this area. Examples are shown in Figs. 7 and 8, representing bar No. 1.16 of EA1N steel and bar No. 4.33 of EA4T steel, respectively. In the former case, cracks were initiated by fretting fatigue process at several circumferential sites (Figs. 9 and 10), whilst just a single crack was initiated in the later case. This crack was then developed from this site till failure. Single or multiple crack initiation was not connected with a specific material, both mechanisms were observed with all three steels.
4. Discussion 4.1. Fatigue resistance Comparing results of fatigue tests of the quite large model components with press fitted hubs tested under rotating bending with a considerably high number of cycles to 5 107 (Fig. 6), it is evident that the substantial differences in strength of the material between 586 MPa and 1041 MPa did not result in any fairly distinct changes of fatigue strength. Fatigue limit of the model bars made of 34CrNiMo6 alloyed steel of strength Rm = 1041 MPa with press fitted hubs, namely 95 MPa, is not
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Fig. 8. Measurement of crack development under press fit, EA4T steel specimen (No. 4.33).
Fig. 9. Fretting cracks initiation at several circumferential sites.
Fig. 10. Coalescence of initial fretting circumferential cracks.
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higher in comparison with bars made of carbon EA1N steel of strength Rm = 590 MPa, as well as in comparison with bars of EA4T steel of strength 790 MPa. If the mentioned increased scatter of results characteristic for fatigue tests at the complicated conditions is considered, then differences in fatigue strength in the area of limited life are not significant either. Ultrasonic measurement made possible to detect crack initiation and approximately determine the area of crack initiation under hub in the fatigue diagrams. It follows from the measurement that first small cracks were detected even with fatigue loading of the amplitude zone between 50 and 100 MPa – Figs. 3 and 4. According to the obtained results, such cracks were retarded with no further development even after high number of cycles 107 or more. 4.2. Crack initiation and growth under press fitted hub Crack growth measurement under press fitted hub demonstrated that at the test stress amplitudes, they are initiated in all three steels regardless of their significant differences in strength. This is determined by specific conditions and damage mechanisms during interaction cyclic fretting effects at critical sites of the press fitted joints. For linear elastic fracture mechanics approach (LEFM) used bellow, in connection with physically short fatigue cracks, information on some microstructural characteristics, particularly grain size, is usually considered as important. Grain size (ferrite), however, only could be evaluated in case of the A1N steel with ferritic–pearlitic microstructure. The grain size was very fine, nine according to EN ISO 634. Microstructure of the heat-treated steels is formed by transformed constituents of quenched structure. These constituents are very fine and so, grain size evaluation is problematic. Size of original austenitic grain is not suitable characteristics either, because its effect on mechanical properties is indistinct. Repeated cyclic plastic deformation in the surface contact layer of test bars occurring due to vibration fretting effects and high pressure loading under press fit results in substantial changes in microstructure of the layer and degradation of properties. Finally, first isolated microcracks are initiated in the affected layer. Under rotating bending characteristic by cyclic loading over the whole perimeter, cracks are often initiated at multiple circumferential sites as shown in Fig. 7 or Figs. 9 and 10. The initiation mechanism is significantly different from common fatigue conditions, when initiation of first microcracks and fatigue strength are strongly affected by material strength. Therefore, short fretting fatigue cracks can only be retarded or even arrested using additional surface treatment technologies introducing axial surface compression residual stresses [6]. Ultrasonic monitoring of crack growth as a dependence of number of cycles enabled to evaluate growth rate of these cracks in terms of increasing depth. The evaluation was carried out for the circumferential sites where the crack started to grow most rapidly leading to final failure. An exact calculation of stress intensity factor for the complicated circumferential crack shape is not simple, but quite an exact estimation can be made using the formula for a semi-elliptical surface crack in shaft under bending according to Murakami and Tsuru [7]:
K ¼ ro
pffiffi ðpbÞF;
ro ¼ 32M=ðpd3 Þ
where a is circumferential crack length, b is crack depth and d is bar diameter, M is bending moment, F is K-calibration factor depending on specimen dimensions. For the estimation, values of the factor F (b/a, b/d) were taken for a fixed value b/a = 0.1, which was decided to be the best approximation considering the typical crack shape, when crack depth was considerably lower in comparison with surface length. This estimation can be considered as sufficiently exact, because factor F values for b/a = 0.0 (infinite surface crack length), which could be assumed as a possible alternative for the actual experimental cases, differ from those for b/a = 0.1 by no more than 3%. It should be mentioned that the use of the LEFM approach for the evaluation of growth of very short fatigue cracks of the depth less than 0.5 mm is problematic and may not be correct, because the near surface layer was affected by the cyclic plastic deformation process. However, for deeper cracks with crack front outside the affected surface layer, the LEFM approach can be assumed as a suitable tool to compare different growth kinetics of these short cracks with standard long fatigue cracks. An additional measurement of growth rates of physically long fatigue cracks in the base material EA1N and EA4T was carried out to obtain data for a comparison with the short crack growth under hubs. Measurement of long cracks was performed on three-point-bend specimens (SEN(B3)), of 25 mm width and 5 mm thickness, 120 mm test span, load asymmetry R = 0.1. The specimens were manufactured of the exactly identical material, which was namely taken from central parts of heads of selected bars used for previous fretting fatigue tests. It should be pointed out that such the material could not be affected by previous fatigue loading at all, because fatigue loading in the centre of the heads was negligible. Results of fatigue crack growth (FCG) rate measurements of long cracks are shown in Fig. 11. The curves are fitted using regression analysis according to Ohta et al. [8] with a modification of Paris equation suitable for stable and near-threshold regions according to Klesnil and Lukáš [9]:
da=dN ¼ CðDK m DK m th Þ; which enables to extrapolate also threshold values from near-threshold data. The diagram contains also FCG data for EA4T steel according to Varfolomeev and Moroz [10], where crack growth rates in the near-threshold region are lower by more
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Fig. 11. FCG rates of long fatigue cracks measured on laboratory specimens.
than 3-times in spite of that the measurement in [10] was performed on M(T) specimens with constraint conditions resulting typically in highest FCG values [11]. Therefore, the differences in FCG rates can only be explained by actual material variability when made by different manufacturers. It confirms that FCG and threshold data of these steels should be experimentally verified for any specific purposes, even though the material is of a standard type. A comparison of short crack growth rates under hubs with long FCG is in Fig. 12 representing FCG dependence on amplitude of stress intensity factor (K-factor) and on crack depth, respectively (inserted diagram in Fig. 12). For the evaluation of K-factor of the short cracks in bars under hub loaded by rotating bending, i.e. with R = 1, bending stress amplitude instead of stress range was considered in order that the values can be compared with the long FCG values measured at R = 0.1, due to reasons discussed bellow. Strong differences between behaviour of short and long cracks are evident. Short fatigue cracks grow at K-factor amplitudes significantly lower than threshold values for long cracks. In addition, short crack growth rates in EA1N and EA4T are almost identical and have a very similar character. There is an initial growth rate increase, followed by a retardation after approximately 1.5 mm depth. After reaching approximately 2.5 mm depth, further acceleration is indicated. The short crack behaviour under hubs demonstrates that growing mechanisms differ from those of long fatigue cracks, evoking growth character of physically short fatigue cracks on free material surface. The early growth period is certainly controlled by fretting fatigue mechanism, an interaction with physically short FCG mechanisms in further growth stage is likely. Comparing growth of cracks under hubs after reaching 2.5 mm in EA4T steel with FCG measured on SEN(B3) specimens (Fig. 12), growth rates of cracks under hubs are considerably lower, almost by one order. This phenomenon can be explained considering compression axial stresses occurring under press fit, which typically reach values up to –40 MPa in relevant areas [12,13]. In case of rotating bending stress amplitude of 134 MPa and 130 MPa used in this work for the tests of model
Fig. 12. Growth of cracks under hubs in comparison with FCG of long crack in laboratory specimens.
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bars of EA4T and EA1N, respectively, the original load asymmetry of external rotating bend loading R = 1 is then shifted to R = 1.85 and R = 1.89, respectively, simply by superposition of bending fatigue stresses with the 40 MPa static compression stress due to the press fit As an example, in the former case under the press fit, the values of rmax and rmin after the superposition correspond to rmax = 134–40 = 94 MPa and rmin = 134–40 = –174 MPa. Therefore, R = rmin/rmax = 174/ 94 = 1.85. It is known that if cyclic loading contains tension and compression parts, predominantly positive part of the load cycle determines FCG, compression part having just a minor effect of several percent contribution [14–16]. Moreover, the contribution of compression stress is stronger in low strength steels than in heat-treated steels of medium or high strength. Considering this phenomenon, K-factor values of cracks under hubs were re-calculated in terms of effective stress range, i.e. just 70% (EA4T) and 69% (EA1N), respectively, of rotating bending stress amplitude (i.e. 35% of rotating bending stress range) was considered. Then, fatigue growth rates of cracks under hubs longer than 2.5 mm are quite comparable with FCG rates of long cracks – Fig. 13. Character of the main crack and growth conditions are affected by a number of points with simultaneous long crack development, located circumferentially under the press fit. Long crack growth from a single point is the simplest case, e.g. Fig. 8. K-factor then can be calculated for example according to [7] or [17]. However, multiple crack growth from more
Fig. 13. Growth rates of cracks under hubs considering positive effective part of load cycle with FCG in laboratory specimens.
Fig. 14. Fatigue fracture of specimen with several initial cracks.
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than one circumferential points is quite a frequent case, as shown in Figs. 7, 9 and 10, resulting in a kind of fracture character documented in Fig. 14. In such cases, FCG is determined by more complicated interaction conditions, which cannot be described by simple formulas. 5. Conclusions Rotating bending fatigue tests up to 2–5 107 cycles with evaluation of fatigue limit were carried out on large model bars with press fitted hubs of diameter 63/59 mm made of three railway axle steels EA1N, EA4T and 34CrNiMo6 with considerable different strength from 586 MPa to 1041 MPa, respectively. Detection and measurement of crack growth under hubs by ultrasonic method was performed during the tests. The most important results can be summarised as follows: In spite of considerable differences in strength and alloying of tested bars, differences in mean value of fatigue limit are not significant, being in the interval between 95 and 110 MPa or 85 and 120 MPa considering the scatter, respectively. Higher fatigue limit values are not connected with bars of higher strength. Therefore, no increase of fatigue strength under press fit can be expected using a higher strength steel. In comparison with the EA1N steel with the lowest strength, fatigue life of bars of EA4T steel with the medium strength is somewhat higher at higher load amplitudes of S–N curve (overloading range with finite life), but not nearby fatigue limit, the S–N curve slope being generally somewhat steeper. This effect may be connected with lower FCG rates at high K-factor range as compared to EA1N steel, but higher rates in near-threshold region. Crack detection and measurement under press fitted hubs demonstrated an occurrence of numerous microcracks at loading band between 50 and 90 MPa. They were, however, retarded and arrested, with no further development even after long-time high-cycle fatigue testing. The unexpected result of fatigue tests with no significant effect of strength and alloying of base material is connected with specific damage mechanisms and microcracks initiation under hubs as a result of fretting effects. Repeated cyclic plastic deformation in the surface layer of test bars under hubs occurring due to vibration fretting effects and pressure loading results in changes of microstructure of the layer and degradation of properties. Fretting fatigue microcracks are then initiated in the affected layer. Specific mechanisms of short crack growth under hubs also were indicated after evaluation and comparison of their rate with FCG rates and threshold values of physically long cracks measured in laboratory specimens made of the entirely identical material. Short fatigue cracks under hubs grow at K-factor range significantly bellow threshold range DKth of standard long fatigue cracks. Acceleration and retardation periods in the interval up to 2.5 mm are rather typical for short crack behaviour. Growth rate of cracks of depth more than 2.5 mm are comparable with FCG of long cracks, if axial compression stresses and effective parts of loading cycles are considered. Whilst short crack initiation under press fit is determined by cyclic fretting mechanisms, the development after their coalescence is mostly affected by usual FCG mechanisms. Simultaneous growth from more than one point of surface circumferential area is quite frequent.
Acknowledgement The work was carried out within the Project supported by the Czech Ministry of Education, Youth and Sport under Grant MSM 2579700001. References [1] Linhart V, Aurˇedník A, Furbacher I, Cˇerny´ I, Zima R, Matušek P, Novosad M. Experimental modelling and evaluation of fatigue strength and damage mechanisms of railway axles and wheels. In: Smith RA, editor. Proc int seminar on railway axles, 25–26 September 2003. Imperial College London, UK. [2] Beretta S, Ghidini A, Lombardo F. Fracture mechanics and scale effects in the fatigue of railway axles. Engng Fract Mech 2005;72:195–208. [3] Guidelines for the specification, design and data analysis of footprint measuring systems to characterize the environmental footprint of vehicles. Mayer RM, Poulikakos L, Partl M, editors. Eureka R! 2486 footprint project, EMPA Dübendorf; October 2007. ˇ erny´ I. Evaluation of dynamic characteristics of different types of railway springs using laboratory quarter-chassis test rig. EUREKA E! 2486 logchain [4] C footprint final workshop, EMPA Zürich; 26 November 2008. [5] Horger OJ. Fatigue characteristics of large sections. In: Dolan TJ, Lazan BJ, Horger OJ, editors. Fatigue. Cleveland: ASM; 1953. p. 77–118. [6] Linhart V, Hampl V, Chvojan J. Increase of axle fatigue resistance in pressed on place by surface hardening. In: Proc 18th int conf current problems in rail vehicles PRORAIL, University of Zˇilina, Slovakia; 2007. p. 1–10 [in Czech]. [7] Murakami Y, Tsuru H. Stress-intensity factor equations for a semi-elliptical surface crack in a shaft under bending. In: Stress intensity factor handbook. Japan: Soc. Mater. Sci.; 1986, p. 657–8. [8] Ohta A, Soya I, Nishijima S, Kosuge M. Statistical evaluation of fatigue crack propagation properties including threshold stress intensity factor. Engng Fract Mech 1986;24:789–802. [9] Klesnil M, Lukáš P. Effect of stress cycle asymmetry on fatigue crack growth. Mater Sci Engng 1972;9:231–40. [10] Varfolomeev I, Moroz S. Numerical investigation of constraint effects on fatigue crack propagation. In: Atzori B, Carpinteri A, Lazzarin P, Pook LP, editors. Proc int conf crack paths (CP 2009), Vicenza, Italy; 23–25 September 2009. [11] Hutarˇ P, Seitl S, Knésl Z. Quantification of the effect of specimen geometry on the fatigue crack growth response by two-parameter fracture mechanics. Mater Sci Eng A 2004;387–389:491–4. [12] Zerbst U, Schödel M, Beier HTh. Parameters affecting the damage tolerance behaviour of railway axles. Engng Fract Mech 2011;78:793–809.
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[13] 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. Engng Fract Mech 2008;75:1906–20. [14] Linhart V. Crack propagation – an important stage of fatigue damage. In: Proc seminar on recent knowledge about fatigue strength of structural materials and machinery components, SVÚM Praha; 6 September 1971. p. 3–24 [in Czech]. [15] Luke M, Varfolomeev I, Lütkepohl K, Esderts A. Fracture mechanics assessment of railway axles: experimental characterization and computation. Engng Failure Anal 2010;17:617–23. [16] Luke M, Varfolomeev I. Fracture mechanics assessment of crack propagation behaviour in railway axles. In: Proc 8th int conf on contact mechanics and wear of rail/wheel systems (CM2009), Firenze, Italy, September 15–18; 2009. [17] Beretta S, Carboni M. Experiments and stochastic model for propagation lifetime of railway axles. Engng Fract Mech 2008;73:2627–41.
Contents lists available at ScienceDirect
Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
An effect of strength of railway axle steels on fatigue resistance under press fit V. Linhart, I. Cˇerny´ ⇑ SVÚM a.s., Podnikatelská 565, CZ-19011 Praha 9, Beˇchovice, Czech Republic
a r t i c l e
i n f o
Article history: Available online 5 December 2010 Keywords: High-cycle fatigue Rotating bending Press fit Fretting fatigue Fatigue crack growth Railway axle steels
a b s t r a c t High-cycle fatigue tests with an evaluation of fatigue limit were carried out on large model components of bars with press fitted hubs of diameter 63/59 mm. Bars were made of three railway axle steels EA1N, EA4T and 34CrNiMo6 with considerable different strength from 586 MPa to 1041 MPa, respectively. Detection and measurement of crack growth under hubs by ultrasonic method was performed during the tests. In spite of the differences in strength and alloying of tested bars, differences in mean value of fatigue limit were not significant. This result was connected with specific damage mechanism and microcracks initiation under hubs with fretting effects. Short fatigue crack growth under hubs occurred at stress intensity factor range DK considerably bellow threshold value DKth of long cracks. Simultaneous growth of main cracks from more than one point of surface circumferential area under hub was quite frequently observed. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Press fit technology is commonly used for an attachment of components of railway wheel sets, i.e. axles, wheels and traction gears. As a result of cyclic loading in operation, cracks can be initiated under hubs of these parts. The cracks are further developed by fatigue process and so determine total life of axles and wheel sets. These problems represent a current issue to be solved to fulfil safety an reliability requirements, particularly important in connection with increasing transport speeds [1]. Besides design of axles and press fitted joints including optimum dimensions, material selection and surface treatment are important issues. According to EN 13261, steels EA1N and EA4T are mentioned as standard materials, first of them being a low strength carbon steel with 0.4% C. EA4T is a low alloyed steel of fairly high strength. As regards especially locomotive axles or high speed train axles, numerous producers have recently used other steels with a higher content of alloying elements, e.g. 30CrNiMoV12 or 34CrNiMo6 steels, sometimes characteristic by a significantly higher strength, about 1000 MPa [2]. In general, high strength steels enable to use advanced design approaches to reduce total unsprung axle mass and consequently dynamic forces on track and ground borne vibrations being particularly important with high speed trains [3,4]. Fatigue resistance of components with smooth surface without defects are usually positively affected by material strength. On the other hand, not very significant effect of material strength on fatigue strength of axles under hubs was already indicated by Horger in the past [5]. An important question therefore is, whether and how the use of higher strength steels, usually with an increased amount of alloying elements, can contribute to an increase of fatigue strength and life at critical axle ⇑ Corresponding author. Address: SVÚM a.s., Strength Department, Podnikatelská 565, 19011 Praha 9, Czech Republic. Tel.: +420 222724098; fax: +420 222724509. ˇ erny´). E-mail address: [email protected] (I. C 0013-7944/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2010.11.023
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positions under press fitted hubs. An experimental programme was carried out with the aim to contribute to the clarification of problems in this field. Results of the investigation are presented and discussed in this paper. 2. Experiments Besides standard EA1N and EA4T steels, a 34CrNiMo6 steel according to DIN with a considerably higher strength, being often used for manufacture of axles, has been investigated. Chemical composition and mechanical properties of the steels are in Tables 1 and 2. The investigated steels are characteristic by graded strength levels in the range typical for real manufacture conditions, namely Rm = 586 MPa, 789 MPa and 1041 MPa. Experimental programme was performed using model test bars of diameters 63 mm and 59 mm in press fitted head and central part, respectively – Fig. 1. Model hubs of diameters 220/135 mm were press fitted on both the test bar heads – Fig. 2. The contact surfaces of specimen heads and hubs were lubricated with Molykote G-n-plus before press fitting. The hubs and specimen heads were manufactured with interference values between 1.2‰ and 2.0‰ which correspond exactly to actual full-scale components. Due to linearity in the elastic area of stresses in the material, the same relative interference values used in case of reduced models namely result in equivalent radial and tangential stresses at the contact area, if mutual dimensional proportions in the model, both hub and axle head, are retained. Concerning quantitative description of the stresses coming from the press fitting, for the interference Dr/r = 0.002, both radial and tangential stresses are considerable lower than yield stress, even in case of the A1N steel with lowest strength. Fatigue tests were carried out on a Wöhler type rotating bending machine – SCHENCK UMBI 750. Test frequency was 1500 rpm, maximum target number of cycles 2 107 or alternatively 5 107, if damage did not occur earlier. An initiation and growth of cracks under hubs was periodically checked and monitored using ultrasonic device Krautkramer USK 7 with an inclined 45° transducer. In order to crack initiation and growth measurement, fatigue tests were periodically interrupted and detailed ultrasonic measurement all along the circumference was performed at defined and marked positions of the press fit. The ultrasonic method was calibrated before its use on the basis of measurement performed using model steel bars of the same dimensions with artificial circumferential narrow notches with different depths simulating cracks. On the basis of the calibration, it was also determined that minimum threshold crack depth being able reliably detected was approximately 0.15 mm in this specific experimental arrangement. It should be however pointed out that during actual fretting fatigue tests, accuracy of measurement of rather deep cracks of more than 2 mm depth could be affected by a presence of corrosion oxide debris.
Table 1 Chemical composition of steels. Steel
C (wt.%)
Si (wt.%)
Mn (wt.%)
Cr (wt.%)
Ni (wt.%)
Mo (wt.%)
P (wt.%)
S (wt.%)
EA1N EA4T 34CrNiMo6
0.40 0.26 0.352
0.24 0.29 0.228
0.95 0.70 0.61
– 1.0 1.37
– – 1.32
– 0.20 0.19
0.0027 0.020 0.015
0.017 0.007 0.026
Rm (MPa)
A (%)
Z (%)
586 789 1041
29.4 18.5 16
58 – 53.8
Table 2 Mechanical properties. Steel
ReH (Rp
EA1N EA4T 34CrNiMo6
364 (ReH) 631 849
0.2)
(MPa)
Fig. 1. Model fatigue test specimen.
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Fig. 2. Model hub for fatigue testing.
3. Experimental results Results of individual fatigue test series are presented in Figs. 3–5, they are summarised in Fig. 6. Regression lines were calculated considering failure cases and occurrence of fairly significant cracks deeper than 0.9 mm, respectively. It means that very short cracks of the length less than 0.5 mm, which were arrested, were not considered for the regression analysis. Fatigue dependencies have a Wöhler curve character usually up to 5 107 cycles. Fatigue limit was usually evaluated on the basis of tests to 5 107 cycles. In this work, fatigue limit was defined by two conditions that on the basis of 5 107 cycles (i) no failure occurred or (ii) depth of fretting corrosion cracks, if initiated, was considerably less than 1 mm (roughly about 0.5 mm). Though the target number of cycles to confirm fatigue limit was mostly 5 107, several results of tests performed up to number of cycles between 1 and 2 107 without damage were considered as fatigue limit, too. The mentioned definition of failure case should be commented, too. In some cases, tests could not be performed to final cracking, because the testing machine started to strongly vibrate, when the crack approximately 2 mm deep arose. Critical crack depth causing vibrations significantly depended on the crack circumferential asymmetry. The machine vibrations started as a result of progressively growing asymmetrical crack were considered as failure case, too. Results are characteristic by fairly high scatter, typical for this type of rather complicated tests. The scatter, larger than usual scatter of standard fatigue tests, can be considered as a consequence of the complexity of fretting fatigue crack initiation mechanisms. All the test pieces were namely press fitted at identical conditions and so any effect of press fitting procedure on the scatter is unlikely. Due to the scatter, fatigue limit only could be evaluated with a precision of cca ± 10% or cca ± 5% in case of the 34CrNiMo6 steel, respectively. Under these circumstances, fatigue limit of EA1N and EA4T steel bars evaluated from Figs. 3 and 4 is in the range between 100 and 120 MPa and between 85 and 105 MPa, respectively. Fatigue limit of 34CrNiMo6 steel bars, with the highest strength Rm = 1041 MPa, corresponds to 95–105 MPa (Fig. 5). It follows from Fig. 6, where fatigue curves of separate steels are compared, that considering the scatter, there are no significant differences between the series of materials of different strength. The only small difference of somewhat steeper slope of the EA4T fatigue regression line is caused by the two points indicated as ‘‘retarded failure’’, which correspond to quite a high number of cycles at relatively high stress amplitude.
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Fig. 3. Fatigue tests results of EA1N steel specimen (Rm = 586 MPa) with press fit.
Fig. 4. Fatigue tests results of EA4T steel specimen (Rm = 789 MPa) with press fit.
Fig. 5. Fatigue tests results of 34CrNiMo6 steel specimen (Rm = 1041 MPa) with press fit.
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Fig. 6. Comparison of fatigue tests results on model steel specimens with press fit.
Fig. 7. Measurement of crack development under press fit, EA1N steel specimen (No. 1.16).
The non-destructive measurement under the hubs by the ultrasonic method enabled not only to detect crack initiation, but also to monitor their gradual development. Fretting fatigue cracks were initiated under press fit at the distance between 7 and 8 mm from the hub edge. In case of heat treated bars, further additional cracks sometimes arose outside this area. Examples are shown in Figs. 7 and 8, representing bar No. 1.16 of EA1N steel and bar No. 4.33 of EA4T steel, respectively. In the former case, cracks were initiated by fretting fatigue process at several circumferential sites (Figs. 9 and 10), whilst just a single crack was initiated in the later case. This crack was then developed from this site till failure. Single or multiple crack initiation was not connected with a specific material, both mechanisms were observed with all three steels.
4. Discussion 4.1. Fatigue resistance Comparing results of fatigue tests of the quite large model components with press fitted hubs tested under rotating bending with a considerably high number of cycles to 5 107 (Fig. 6), it is evident that the substantial differences in strength of the material between 586 MPa and 1041 MPa did not result in any fairly distinct changes of fatigue strength. Fatigue limit of the model bars made of 34CrNiMo6 alloyed steel of strength Rm = 1041 MPa with press fitted hubs, namely 95 MPa, is not
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Fig. 8. Measurement of crack development under press fit, EA4T steel specimen (No. 4.33).
Fig. 9. Fretting cracks initiation at several circumferential sites.
Fig. 10. Coalescence of initial fretting circumferential cracks.
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higher in comparison with bars made of carbon EA1N steel of strength Rm = 590 MPa, as well as in comparison with bars of EA4T steel of strength 790 MPa. If the mentioned increased scatter of results characteristic for fatigue tests at the complicated conditions is considered, then differences in fatigue strength in the area of limited life are not significant either. Ultrasonic measurement made possible to detect crack initiation and approximately determine the area of crack initiation under hub in the fatigue diagrams. It follows from the measurement that first small cracks were detected even with fatigue loading of the amplitude zone between 50 and 100 MPa – Figs. 3 and 4. According to the obtained results, such cracks were retarded with no further development even after high number of cycles 107 or more. 4.2. Crack initiation and growth under press fitted hub Crack growth measurement under press fitted hub demonstrated that at the test stress amplitudes, they are initiated in all three steels regardless of their significant differences in strength. This is determined by specific conditions and damage mechanisms during interaction cyclic fretting effects at critical sites of the press fitted joints. For linear elastic fracture mechanics approach (LEFM) used bellow, in connection with physically short fatigue cracks, information on some microstructural characteristics, particularly grain size, is usually considered as important. Grain size (ferrite), however, only could be evaluated in case of the A1N steel with ferritic–pearlitic microstructure. The grain size was very fine, nine according to EN ISO 634. Microstructure of the heat-treated steels is formed by transformed constituents of quenched structure. These constituents are very fine and so, grain size evaluation is problematic. Size of original austenitic grain is not suitable characteristics either, because its effect on mechanical properties is indistinct. Repeated cyclic plastic deformation in the surface contact layer of test bars occurring due to vibration fretting effects and high pressure loading under press fit results in substantial changes in microstructure of the layer and degradation of properties. Finally, first isolated microcracks are initiated in the affected layer. Under rotating bending characteristic by cyclic loading over the whole perimeter, cracks are often initiated at multiple circumferential sites as shown in Fig. 7 or Figs. 9 and 10. The initiation mechanism is significantly different from common fatigue conditions, when initiation of first microcracks and fatigue strength are strongly affected by material strength. Therefore, short fretting fatigue cracks can only be retarded or even arrested using additional surface treatment technologies introducing axial surface compression residual stresses [6]. Ultrasonic monitoring of crack growth as a dependence of number of cycles enabled to evaluate growth rate of these cracks in terms of increasing depth. The evaluation was carried out for the circumferential sites where the crack started to grow most rapidly leading to final failure. An exact calculation of stress intensity factor for the complicated circumferential crack shape is not simple, but quite an exact estimation can be made using the formula for a semi-elliptical surface crack in shaft under bending according to Murakami and Tsuru [7]:
K ¼ ro
pffiffi ðpbÞF;
ro ¼ 32M=ðpd3 Þ
where a is circumferential crack length, b is crack depth and d is bar diameter, M is bending moment, F is K-calibration factor depending on specimen dimensions. For the estimation, values of the factor F (b/a, b/d) were taken for a fixed value b/a = 0.1, which was decided to be the best approximation considering the typical crack shape, when crack depth was considerably lower in comparison with surface length. This estimation can be considered as sufficiently exact, because factor F values for b/a = 0.0 (infinite surface crack length), which could be assumed as a possible alternative for the actual experimental cases, differ from those for b/a = 0.1 by no more than 3%. It should be mentioned that the use of the LEFM approach for the evaluation of growth of very short fatigue cracks of the depth less than 0.5 mm is problematic and may not be correct, because the near surface layer was affected by the cyclic plastic deformation process. However, for deeper cracks with crack front outside the affected surface layer, the LEFM approach can be assumed as a suitable tool to compare different growth kinetics of these short cracks with standard long fatigue cracks. An additional measurement of growth rates of physically long fatigue cracks in the base material EA1N and EA4T was carried out to obtain data for a comparison with the short crack growth under hubs. Measurement of long cracks was performed on three-point-bend specimens (SEN(B3)), of 25 mm width and 5 mm thickness, 120 mm test span, load asymmetry R = 0.1. The specimens were manufactured of the exactly identical material, which was namely taken from central parts of heads of selected bars used for previous fretting fatigue tests. It should be pointed out that such the material could not be affected by previous fatigue loading at all, because fatigue loading in the centre of the heads was negligible. Results of fatigue crack growth (FCG) rate measurements of long cracks are shown in Fig. 11. The curves are fitted using regression analysis according to Ohta et al. [8] with a modification of Paris equation suitable for stable and near-threshold regions according to Klesnil and Lukáš [9]:
da=dN ¼ CðDK m DK m th Þ; which enables to extrapolate also threshold values from near-threshold data. The diagram contains also FCG data for EA4T steel according to Varfolomeev and Moroz [10], where crack growth rates in the near-threshold region are lower by more
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Fig. 11. FCG rates of long fatigue cracks measured on laboratory specimens.
than 3-times in spite of that the measurement in [10] was performed on M(T) specimens with constraint conditions resulting typically in highest FCG values [11]. Therefore, the differences in FCG rates can only be explained by actual material variability when made by different manufacturers. It confirms that FCG and threshold data of these steels should be experimentally verified for any specific purposes, even though the material is of a standard type. A comparison of short crack growth rates under hubs with long FCG is in Fig. 12 representing FCG dependence on amplitude of stress intensity factor (K-factor) and on crack depth, respectively (inserted diagram in Fig. 12). For the evaluation of K-factor of the short cracks in bars under hub loaded by rotating bending, i.e. with R = 1, bending stress amplitude instead of stress range was considered in order that the values can be compared with the long FCG values measured at R = 0.1, due to reasons discussed bellow. Strong differences between behaviour of short and long cracks are evident. Short fatigue cracks grow at K-factor amplitudes significantly lower than threshold values for long cracks. In addition, short crack growth rates in EA1N and EA4T are almost identical and have a very similar character. There is an initial growth rate increase, followed by a retardation after approximately 1.5 mm depth. After reaching approximately 2.5 mm depth, further acceleration is indicated. The short crack behaviour under hubs demonstrates that growing mechanisms differ from those of long fatigue cracks, evoking growth character of physically short fatigue cracks on free material surface. The early growth period is certainly controlled by fretting fatigue mechanism, an interaction with physically short FCG mechanisms in further growth stage is likely. Comparing growth of cracks under hubs after reaching 2.5 mm in EA4T steel with FCG measured on SEN(B3) specimens (Fig. 12), growth rates of cracks under hubs are considerably lower, almost by one order. This phenomenon can be explained considering compression axial stresses occurring under press fit, which typically reach values up to –40 MPa in relevant areas [12,13]. In case of rotating bending stress amplitude of 134 MPa and 130 MPa used in this work for the tests of model
Fig. 12. Growth of cracks under hubs in comparison with FCG of long crack in laboratory specimens.
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bars of EA4T and EA1N, respectively, the original load asymmetry of external rotating bend loading R = 1 is then shifted to R = 1.85 and R = 1.89, respectively, simply by superposition of bending fatigue stresses with the 40 MPa static compression stress due to the press fit As an example, in the former case under the press fit, the values of rmax and rmin after the superposition correspond to rmax = 134–40 = 94 MPa and rmin = 134–40 = –174 MPa. Therefore, R = rmin/rmax = 174/ 94 = 1.85. It is known that if cyclic loading contains tension and compression parts, predominantly positive part of the load cycle determines FCG, compression part having just a minor effect of several percent contribution [14–16]. Moreover, the contribution of compression stress is stronger in low strength steels than in heat-treated steels of medium or high strength. Considering this phenomenon, K-factor values of cracks under hubs were re-calculated in terms of effective stress range, i.e. just 70% (EA4T) and 69% (EA1N), respectively, of rotating bending stress amplitude (i.e. 35% of rotating bending stress range) was considered. Then, fatigue growth rates of cracks under hubs longer than 2.5 mm are quite comparable with FCG rates of long cracks – Fig. 13. Character of the main crack and growth conditions are affected by a number of points with simultaneous long crack development, located circumferentially under the press fit. Long crack growth from a single point is the simplest case, e.g. Fig. 8. K-factor then can be calculated for example according to [7] or [17]. However, multiple crack growth from more
Fig. 13. Growth rates of cracks under hubs considering positive effective part of load cycle with FCG in laboratory specimens.
Fig. 14. Fatigue fracture of specimen with several initial cracks.
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than one circumferential points is quite a frequent case, as shown in Figs. 7, 9 and 10, resulting in a kind of fracture character documented in Fig. 14. In such cases, FCG is determined by more complicated interaction conditions, which cannot be described by simple formulas. 5. Conclusions Rotating bending fatigue tests up to 2–5 107 cycles with evaluation of fatigue limit were carried out on large model bars with press fitted hubs of diameter 63/59 mm made of three railway axle steels EA1N, EA4T and 34CrNiMo6 with considerable different strength from 586 MPa to 1041 MPa, respectively. Detection and measurement of crack growth under hubs by ultrasonic method was performed during the tests. The most important results can be summarised as follows: In spite of considerable differences in strength and alloying of tested bars, differences in mean value of fatigue limit are not significant, being in the interval between 95 and 110 MPa or 85 and 120 MPa considering the scatter, respectively. Higher fatigue limit values are not connected with bars of higher strength. Therefore, no increase of fatigue strength under press fit can be expected using a higher strength steel. In comparison with the EA1N steel with the lowest strength, fatigue life of bars of EA4T steel with the medium strength is somewhat higher at higher load amplitudes of S–N curve (overloading range with finite life), but not nearby fatigue limit, the S–N curve slope being generally somewhat steeper. This effect may be connected with lower FCG rates at high K-factor range as compared to EA1N steel, but higher rates in near-threshold region. Crack detection and measurement under press fitted hubs demonstrated an occurrence of numerous microcracks at loading band between 50 and 90 MPa. They were, however, retarded and arrested, with no further development even after long-time high-cycle fatigue testing. The unexpected result of fatigue tests with no significant effect of strength and alloying of base material is connected with specific damage mechanisms and microcracks initiation under hubs as a result of fretting effects. Repeated cyclic plastic deformation in the surface layer of test bars under hubs occurring due to vibration fretting effects and pressure loading results in changes of microstructure of the layer and degradation of properties. Fretting fatigue microcracks are then initiated in the affected layer. Specific mechanisms of short crack growth under hubs also were indicated after evaluation and comparison of their rate with FCG rates and threshold values of physically long cracks measured in laboratory specimens made of the entirely identical material. Short fatigue cracks under hubs grow at K-factor range significantly bellow threshold range DKth of standard long fatigue cracks. Acceleration and retardation periods in the interval up to 2.5 mm are rather typical for short crack behaviour. Growth rate of cracks of depth more than 2.5 mm are comparable with FCG of long cracks, if axial compression stresses and effective parts of loading cycles are considered. Whilst short crack initiation under press fit is determined by cyclic fretting mechanisms, the development after their coalescence is mostly affected by usual FCG mechanisms. Simultaneous growth from more than one point of surface circumferential area is quite frequent.
Acknowledgement The work was carried out within the Project supported by the Czech Ministry of Education, Youth and Sport under Grant MSM 2579700001. References [1] Linhart V, Aurˇedník A, Furbacher I, Cˇerny´ I, Zima R, Matušek P, Novosad M. Experimental modelling and evaluation of fatigue strength and damage mechanisms of railway axles and wheels. In: Smith RA, editor. Proc int seminar on railway axles, 25–26 September 2003. Imperial College London, UK. [2] Beretta S, Ghidini A, Lombardo F. Fracture mechanics and scale effects in the fatigue of railway axles. Engng Fract Mech 2005;72:195–208. [3] Guidelines for the specification, design and data analysis of footprint measuring systems to characterize the environmental footprint of vehicles. Mayer RM, Poulikakos L, Partl M, editors. Eureka R! 2486 footprint project, EMPA Dübendorf; October 2007. ˇ erny´ I. Evaluation of dynamic characteristics of different types of railway springs using laboratory quarter-chassis test rig. EUREKA E! 2486 logchain [4] C footprint final workshop, EMPA Zürich; 26 November 2008. [5] Horger OJ. Fatigue characteristics of large sections. In: Dolan TJ, Lazan BJ, Horger OJ, editors. Fatigue. Cleveland: ASM; 1953. p. 77–118. [6] Linhart V, Hampl V, Chvojan J. Increase of axle fatigue resistance in pressed on place by surface hardening. In: Proc 18th int conf current problems in rail vehicles PRORAIL, University of Zˇilina, Slovakia; 2007. p. 1–10 [in Czech]. [7] Murakami Y, Tsuru H. Stress-intensity factor equations for a semi-elliptical surface crack in a shaft under bending. In: Stress intensity factor handbook. Japan: Soc. Mater. Sci.; 1986, p. 657–8. [8] Ohta A, Soya I, Nishijima S, Kosuge M. Statistical evaluation of fatigue crack propagation properties including threshold stress intensity factor. Engng Fract Mech 1986;24:789–802. [9] Klesnil M, Lukáš P. Effect of stress cycle asymmetry on fatigue crack growth. Mater Sci Engng 1972;9:231–40. [10] Varfolomeev I, Moroz S. Numerical investigation of constraint effects on fatigue crack propagation. In: Atzori B, Carpinteri A, Lazzarin P, Pook LP, editors. Proc int conf crack paths (CP 2009), Vicenza, Italy; 23–25 September 2009. [11] Hutarˇ P, Seitl S, Knésl Z. Quantification of the effect of specimen geometry on the fatigue crack growth response by two-parameter fracture mechanics. Mater Sci Eng A 2004;387–389:491–4. [12] Zerbst U, Schödel M, Beier HTh. Parameters affecting the damage tolerance behaviour of railway axles. Engng Fract Mech 2011;78:793–809.
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