Fatigue crack growth in full-scale railway axles – Influence of secondary stresses and load sequence effects

Journal Pre-proofs Fatigue Crack Growth in Full-Scale Railway Axles - Influence of Secondary Stresses and Load Sequence Effects Martin Rieger, Christian Moser, Peter Brunnhofer, David Simunek, FranzJosef Weber, Andreas Deisl, Hans-Peter Gänser, Reinhard Pippan, Norbert Enzinger PII: DOI: Reference:

S0142-1123(19)30464-5 https://doi.org/10.1016/j.ijfatigue.2019.105360 JIJF 105360

To appear in:

International Journal of Fatigue

Received Date: Revised Date: Accepted Date:

23 October 2019 29 October 2019 31 October 2019

Please cite this article as: Rieger, M., Moser, C., Brunnhofer, P., Simunek, D., Weber, F-J., Deisl, A., Gänser, HP., Pippan, R., Enzinger, N., Fatigue Crack Growth in Full-Scale Railway Axles - Influence of Secondary Stresses and Load Sequence Effects, International Journal of Fatigue (2019), doi: https://doi.org/10.1016/ j.ijfatigue.2019.105360

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© 2019 Published by Elsevier Ltd.

Fatigue Crack Growth in Full-Scale Railway Axles - Influence of Secondary Stresses and Load Sequence Effects Martin Riegera,∗ , Christian Mosera , Peter Brunnhofera , David Simunekc , Franz-Josef Weberc , Andreas Deislc , Hans-Peter Gänserd , Reinhard Pippane and Norbert Enzingerb a Graz University of Technology, Institute of Thermal Turbomachinery and Machine Dynamics, Area of Structural Durability and Railway Vehicles, Inffeldgasse 25/D, 8010 Graz, Austria b Graz University of Technology, Institute of Materials Science, Joining and Forming, Kopernikusgasse 24, 8010 Graz, Austria c Siemens Mobility GmbH, Eggenberger Strasse 31, 8020 Graz, Austria d Materials Center Leoben Forschung GmbH, Roseggerstrasse 12, 8700 Leoben, Austria e Erich Schmid Institute of Material Science, Jahnstrasse 12, 8700 Leoben, Austria

ARTICLE INFO

ABSTRACT

Keywords: Railway axle Crack propagation 1:1 scale tests Optical crack measurement Residual stresses

A wheel-set axle is located in the unsprung part of a rail vehicle and takes a supporting role in the running gear. If the wheel-set axle fails, the train will inevitably derail. Depending on the time of failure, this can lead to catastrophic consequences. For this reason, a wheel-set axle is a highly safety-critical component of railway vehicles. Detailed knowledge of crack propagation in wheel-set axles is therefore of great importance for a modern safety concept. To analyse the material behaviour under external loads approximated from operating conditions, experimental investigations were carried out on 1:1 specimens. This article presents the results of these experimental investigations carried out within the framework of the research project "Eisenbahnfahrwerke 3 (EBFW 3)" - "Probabilistic Fracture Mechanical Concept for the Assessment of Railway Wheel-sets".

1. Introduction Wheel-set axles are highly safety-critical railway components [1, 2]. Therefore, the fatigue behaviour and crack propagation in the mentioned components are very important. A fitting safety concept has to be chosen and continuously developed [3, 4, 5, 6], and all the influencing parameters must be thoughtfully investigated [7, 8]. Experimental investigations with rotating bending test benches on railway axles in original size are of great importance to understand the fatigue behaviour and the effects of cracks in wheelset axles [9, 10, 11, 12]. Within this work, 35 full-scale axles were tested, in total. The findings from a predecessor project "Eisenbahnfahrwerke 2" (EBFW2) - "Safe and economical operation of undercarriages" [4, 13, 14, 15], were incorporated into the tests. This article describes the experiments carried out and discusses the points that have been encountered in the course of the project. Crack propagation tests on full-scale railway axles are time-consuming. Therefore, the output of such tests should be as high and accurate as possible. The existing measurement and testing methods for railway applications were insufficient in terms of accuracy and reliability. For this reason, a new measuring principle for crack monitoring in real-time, proposed in [16], was pursued. This method for real-time measurement during crack propagation tests was further developed and implemented for the requirements given in the project. Thus, crack propagation could be monitored for different load situations without interrupting the test. ∗ Corresponding

author. [email protected], +43 664 608731383 (M. Rieger) orcid(s): 0000-0002-0802-9487 (M. Rieger); 0000-0001-8392-4943 (H. Gänser); 0000-0003-4723-3170 (R. Pippan); 0000-0003-0051-9518 (N. Enzinger)

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Full-Scale Tests on Railway Axles

Furthermore, two test benches were optimized, and a method for estimating residual stresses at the crack tip during testing was applied.

Nomenclature a a0 A5 c C, m CA D E da/dN KC Kmax p, q R R2 Rm Rp0,2 s s0 VA X1 X2 X3 σres σa ∆K ∆Kth

Depth of semi-elliptical starter notch and fatigue crack Depth of semi-elliptical starter notch Percentage elongation after fracture Semi major axis of starter notch and fatigue crack Material constant Constant Amplitude Diameter of specimen or axle Young’s modulus Crack growth rate in depth Critical stress intensity factor Maximum stress intensity factor Material constant Load ratio Coefficient of determination Tensile strength Yield strength Half surface length of starter notch and fatigue crack Half surface length of starter notch Variable Amplitude Distance from the wheel seat edge to the observed crack level Distance from the wheel seat edge to the additional measurement level Distance from the wheel seat edge to the control level Mean estimate of residual stress Stress amplitude Stress intensity factor range Threshold stress intensity factor range

mm mm % mm

mm N/mm2 µm/cycle √ MPa·√m MPa· m

N/mm2 N/mm2 mm mm mm mm mm MPa MPa √ MPa·√m MPa· m

2. Experimental investigation In the course of this experimental investigations, crack propagation tests were carried out. The used variable amplitude load sequences consist of individual blocks with a certain number of cycles that correspond to different load situations during service. In the used load sequence, the number of cycles within one block varies from only 200 to 4000. Especially those with about 200 load cycles are very challenging for a resonance test rig. For this reasons, the rig was optimized concerning a high test frequency and fast block jumps, in advance to the construction. Electric engines were decoupled from the imbalanced exciter, fixed to the outside, and coupled via a clutch. A new foundation with approximately 145 t was developed, to isolate experiments from the environment. Furthermore, a method for optical crack growth measurement was developed [16]. With this monitoring system, it was possible to observe the crack propagation during the whole tests in real-time.

2.1. Specimen Testing a full-scale specimen (see Figure 1) under realistic loading conditions is important for fracture mechanic research to determine the behaviour of a crack containing railway axle. For a meaningful outcome it is important that the production of these specimens were analogously to real applications. For this reason, the axles and clamping plates were forged at Bahntechnik Brand-Erbisdorf GmbH from single batches Martin Rieger: Preprint submitted to Elsevier

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Full-Scale Tests on Railway Axles

of EA1N and EA4T pre-material [17], respectively, and machined at Gutehoffnungshütte Radsatz GmbH according to the standards [17, 18]. In each axle, three semi-elliptical starter notches, with a semi-axis ratio a0 /c0 = 0.8, a depth of a0 = 1 mm and a surface length 2s0 ≈ 2c0 = 2.5 mm were introduced by means of electrical discharge machining at TU Clausthal.

2c 2s

Control plane C

Ø180

C

a

x3

A

x2

Measurement plane

x1

Crack plane

(a)

(b)

Figure 1: (a) Geometry of the used full-scale specimen with marked strain gauge plane X1 = 32 mm, X2 = 100 mm, X3 = 332 mm; (b) schematic sketch of a notch.

In overall, 14 strain gauges were applied on each specimen. Eight strain gauges in the control level, four in a separate measurement level and two additionally in the cross-section of the introduced cracks (Fig. 1a and 2). 225° 240° CH4_1

270°

CH3_1

45°

0°

315° CH2_1

CH1_1

CH4_2

90° CH3_2

120° 135° CH2_2

180° CH1_2

Control plane 10cm

X3 = 332 mm

4|3|2|1

CH7

CH10

CH9

CH8

CH8 E_1B

CH7 E_1A

X1 = 32 mm

X2 = 100 mm

Measurement plane

Crack plane SN2

SN3

SN1 CH5

0°

CH6

Wheel-seat edge

SN…Starting notch CH…Channel

Figure 2: Applied strain gauges and their positions on the specimen.

The starting notch position were calculated prior the testing with finite element calculations and was set to the highest stress level (including press-fit stresses) at X1 = 32 mm [19]. An idealised geometry after initiation of a fatigue crack at one starting notch is shown in Figure 1b. The surface length 2s as well as the semi-axes a and c evolve out of the starting notch. Compared to a diameter of 180 mm in relation to the Martin Rieger: Preprint submitted to Elsevier

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Full-Scale Tests on Railway Axles

crack length examined, the error caused by the surface curvature can be neglected. It follows that 2s ≈ 2c. More detailed informations about the measurement precision are included in section 2.3.

2.2. Test rigs The main components of the test rigs are the control system, the imbalanced exciter, the flexible clutch, as well as, the electrical engine and the foundation with an integrated clamping plate (Fig. 3, 4). To control the test, eight strain gauges (each 45 degrees) applied in a pre-defined cross-section were connected to four half bridges which measure the applied bending moment evenly. These strain gauges are mounted at a distance of X3 = 332 mm from the wheel seat edge. All applied strain gauges with there position are shown in Fig. 2.

Electric engine

Drive Rotational speed signal

Clutch Monitor

Imbalanced exciter

Computer

Specimen Control level

Strain gauges

8

4 2

Measurement level Crack level

Bridge-adapter

Clamping set

Measurement and control system Iengine

U

Converter

Foundation Figure 3: Principle sketch of the test rig with marked signal flow. By applying strain gauges at a pre-defined level the control is done.

(a)

(b)

(c)

Figure 4: (a) Applied strain gauges; (b) Calibration rig for obtaining the transfer function from the control to the crack level; (c) Used test rigs.

Prior the actual test procedure all strain gauges were calibrated. For this purpose a calibration rig was designed. This rig uses the equal fixture of the resonance test rig and doesn’t have to be opened during the Martin Rieger: Preprint submitted to Elsevier

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Full-Scale Tests on Railway Axles

entire process. For a full calibration, all eight strain gauges, each 45 degrees must be aligned once with the test cylinder and loaded with a defined force on tension and compression. For this four different positions the servo-hydraulic cylinder with its calibrated load cell is rotated around the specimen.

2.3. Optical real-time crack length measurement system Figure 5 shows a schematic diagram of the measurement setup which was applied for three cameras at one test rig, each observed one starter notch at the specimen. The system consists of a high resolution CCD cameras with a telecentric lens. An illumination by means of high power led flashes were realized from above and below of the optics. Due to the low depth of field with the telecentric objective, the cameras were mounted on a micrometer table. This enables precise focusing. The camera as well as the lighting are triggered, at the highest tensile load of the respective crack. This guarantees the greatest possible opening of the observed crack and therefore the highest accuracy. Data processing is done in a PXIe chassis from National Instruments. In this used real-time system, image acquisition, crack detection, data storage, shutdown triggered of a defined crack length, are performed. A host PC connected to the system was used for operation, visualization, parametrization and storage. Camera System

GigE Vision

Data Processing System PXIe-Chassis PXIe Core i7Quad Real Time Controller

Camera Trigger LED Trigger

FPGA with I/O

Load Signal Halt Signal

Host PC • • • •

Image Acquisition Crack Detection & Crack Growth Measurement Trigger Unit: Camera & LED Illumination Signals from/to Test Rig – Control (Trigger & Halt)

• • • •

User Interface Parameterization Visualization Storage

Figure 5: Real-time crack length measurement system for crack monitoring.

An example image of a preserved crack pattern is shown in Figure 6. With the hardware used, which covers an image width of 35.9 mm, a theoretical resolution of 8.5 µm for one pixel is achieved (pixel size on the camera sensor 3.1 µm multiplied by magnification 2.74). However, this resolution was not always achieved during the tests as it cannot always be guaranteed that the crack tip will be detected. Experience has shown that reliable detection of the crack tip of fewer than 5 pixels can be assumed. This corresponds to a resolution smaller than 42.5 µm. The data processing and storage of the camera system for a fully evaluated crack length is approximately 4 s. Assuming a test frequency of 30 Hz, this results in a measured crack length every 120 load cycles. Since the system is also used for the shutdown of the test bench, it must be expected that approximately 120 cycles were still tested when the shutdown criterion was reached. However, the accuracy of the optical measuring system used is not only due to the resolution and detection probability of the crack tip. The deviation due to the curvature of the surface also matters. With a diameter of D = 180 mm, which corresponds to the test specimens used, and a maximum crack length of 2c = 35.9 mm (maximum image width), a crack length of 2s = 36.14 mm results in a deviation of 240 µm. In the case of longer cracks, the curvature must therefore be taken into account and corrected afterwards.

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Full-Scale Tests on Railway Axles

2c = 18.19 mm 2c0 = 2.5 mm

Figure 6: Sample image from the real-time crack length measuring system.

2.4. Load sequence

150

Stress amplitude σ a in MPa

Stress amplitude σ a in MPa

The load sequences used were derived from test runs and adapted to the test bench boundary conditions. The derivation was done from a dataset provided by Stadler Rail AG. The measurement data used include 1800 km with full load and 1800 km without additional load. The test drives were carried out in Germany. The route was defined as a circuit from Bielefeld via Dortmund, Cologne, Frankfurt and back to Bielefeld. Fig. 7a shows the derived load sequence for the material EA4T and Fig. 7b the load sequence for EA4T with omission of the lowest three load levels. The omission was carried out by cutting-out the load cycles to be omitted with subsequent pushing together and connecting the remaining blocks. One can see that the used load sequence includes a lot of block jumps with very little load cycles each. As described in [8], tensile overloads may have a retarding effect on crack propagation and compressive overloads may cause acceleration of crack growth. Therefore, when deriving the load sequence, care was taken to ensure that the load sequences from the measurement data were adhered to as far as possible.

100

50

150

100

50 0

50

100 150 103 load cycles (a)

200

250

0

10

20 30 103 load cycles

40

50

(b)

Figure 7: (a) Load sequence for EA4T (without omission) - VA 0; (b) Load sequence for EA4T with omission of the lowest three load levels - VA 1. The omission was carried out by cutting out the load cycles to be omitted with subsequent pushing together and connecting the remaining blocks.

Load sequence VA 0 (Fig. 7a) serves as base for all other load sequences and Table 1 shows all deviations from this base. A comparison of the nominal signals with the measured ones has shown that with a defined tolerance field of 5 MPa, the measurement signal lies outside this field in 3.7 % of the time (Fig. 8). The load sequence VA 5 was only tested in the range of 2c = 30 mm and 2c = 35 mm and is therefore not considered in detail.

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140

Stress (crack plane) in MPa

Stress (crack plane) in MPa

Full-Scale Tests on Railway Axles

120 100 80 Measured signal Nominal signal

60 0

10

20 30 103 Load cycles

40

(a)

50

140 120 100 80 60

Measured collective Nominal collective 103

104

105

106

Cumulative frequency (log) (b)

Figure 8: (a) Load sequence VA 1, comparing nominal and measured signal; (b) Comparing the nominal and measured collective of VA 1. Table 1 Overview of the different experimental setups. No.

Name

Explanation

1 2 3 4 5

VA VA VA VA VA

6

VA 5

Base variable amplitude load sequence without omission. Variable amplitude load with omission of the lowest three load levels (compared to VA 0). Load increased by 10 %, with omission of the lowest three load levels (compared to VA 0). Load increased by 10 %, with omission of the lowest two load levels (compared to VA 0). Load decreased (reduction-factor 1.084 with respect to VA 0) with omission of the lowest three load levels. Load decreased (reduction-factor 1.084 with respect to VA 0) without omission.

0 1 2 3 4

2.5. Tests performed For the performed experiments, the first specimen was used to configure both test benches. The next two specimens were used to investigate crack growth with a starter notch in the shaft, which was used to investigate the transferability of crack propagation parameters from small-scale specimens up to real-scale components [20]. The rest of 35 specimens have been tested with crack starter notches at the fillet [21]. In this article results of 22 performed tests with variable amplitude loading are included (see Table 2). The testing procedure consists of a crack initiation procedure and a crack propagation test itself [21]. The crack initiation procedure consists of a phase in which the load amplitude is increased as long as a fatigue crack propagation of ∆2c = 0.4 mm in at least one of the starting notches was observed. Followed by a second phase in which the crack was grown to a minimum surface length 2c = 5 mm while reducing the stress amplitude each ∆2c = 0.2 mm until σa = 100 MPa. This load was used on the one hand to prevent influences from the introduction of starting notches, and on the other hand, to reduce plasticity induced-zones at the crack tip caused by the high load for crack initiation. With the load sequence VA 0, the first two specimens (TM5362 and TM5357) were tested. These tests lasted approximately six months until the defined test termination at a crack length of 35 mm was reached (Fig. 9b). Although the lifetimes of these two axles are quite similar, the specimen TM5362 exhibited two periods of retarded crack growth at surface crack lengths of approximately 2c ≈ 8 mm and 2c ≈ 12 mm, respectively (Fig. 9b). They were caused by two accidental overloads due to faults in the controller circuit. In order to reduce the testing time from about six months, the remaining experiments were conducted Martin Rieger: Preprint submitted to Elsevier

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Full-Scale Tests on Railway Axles Table 2 Overview of the conducted experiments. Load sequence

No. of experiments

Explanation

VA VA VA VA VA VA

2 9 3 2 6 0

Test duration of approximately six months. 7 experiments with EA4T and 2 with EA1N. 3 experiments with EA4T. 2 experiments with EA4T. 6 esperiments with EA1N Experiment only from 2c = 30 mm to 2c = 35 mm.

0 1 2 3 4 5

"with omission", i.e., by omission of stress levels √ with stress intensity factor ranges√∆K below the fatigue crack growth thresholds ∆Kth,EA4T = 7.35 MPa · m and ∆Kth,EA1N = 7.38 MPa · m. In Table 2 a list of all load sequences, the number of experiments and a short explanation is provided. For investigating the effects caused by omitting the load levels each crack propagation test is divided into two stages: • Phase 1: conducted with the different load sequences included in Table 1 until a crack length 2c = 30 mm (or, in some cases, 2c = 10 mm) • Phase 2: up to the final crack length of 2c ≈ 35 mm without omission (VA0, VA5), i.e., including also those load levels which have been omitted. The change of the load sequences always refers to the fastest grown crack of a specimen.

3. Results The obtained results showed a large scatter-band in the residual lifetime (Figs. 9, 10). The test duration regarding the same material and load sequence at the same test bench with same conditions, varied from 6 months to 3 days. Therefore, the results achieved were broken down into two essential quantities. Firstly, the results from crack propagation measurements at different load sequences assigned to the materials and secondly the results regarding residual stresses.

3.1. Crack growth fatigue tests Figure 9 shows all tests performed with EA4T material and variable amplitude load. The results executed with omission (Fig. 9a) were separated from those without omission (Fig. 9b). The break point which is visible within all curves in Fig. 9a is the switching of load sequence from with omission (phase 1) to without omission (phase 2). This point shows a retardation of crack growth rate in all cases. Two curves in Fig. 9a show an additional buckling point at approximately 15 mm. This point formed after an overload due to a defect on the test bench. The scatter-bands of the test results are very large for all load sequences. One test specimen has grown disproportionately fast until the termination criteria (approximately 1 million load cycles) for each of the sequence in Fig. 9a. Nevertheless, a tendency of sequences VA 2 and VA 3, which had a 10 % higher load compared to VA 1, towards faster crack growth on average can be detected. However, this is not clearly visible due to the large scatter. Since not every crack was tested up to the termination criteria, an even greater scatter of the results must therefore be considered. Figure 9b show results with a load sequence without omission (VA 0). The very long remaining service life of these tests in comparison with the tests with omission can be seen at first glance.

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Full-Scale Tests on Railway Axles

40

40 EA4T

Crack length 2c in mm

Crack length 2c in mm

EA4T

Phase 2 Phase 1

30

TM17678

20

Phase 1: VA 1; Phase 2: VA 0 Phase 1: VA 2; Phase 2: VA 0

10

30

20 TM5357

10

TM5362

Phase 1: VA 3; Phase 2: VA 0

0

10

20 30 40 50 6 10 load cycles (as tested)

60

70

0

50

VA 0

100 150 200 250 10 load cycles (as tested)

300

6

(a)

(b)

Figure 9: Results from the conducted crack tests on the material EA4T with different variable amplitude loadings; (a) Results of propagating cracks in relation to the applied load sequences (VA 0 - VA 3); (b) Result of the fastest propagating cracks tested with a load sequence without omission - VA 0.

The results relating to EA1N are shown in Figure 10. Similar to EA4T, there are significant variations in the results. Contrary to expectations, the tendency of the tests with a higher load (VA 1) is towards longer residual lifetime than with lower loads (VA 4). The difference between load sequence VA 1 and VA 4 is 8.4 %. Unfortunately, no residual stress measurements were carried out in the tests with the load sequence VA 1, so that the influence of residual stresses could not be further investigated in these results.

40

40 EA1N

Crack length 2c in mm

Crack length 2c in mm

EA1N

Phase 2 Phase 1

30

TM15824

20

Phase 1: VA 1; Phase 2: VA 0

10

Phase 1: VA 4; Phase 2: VA 5

30

20

Phase 2 Phase 1

10

Phase 1: VA 4; Phase 2: VA 5

0

2

4 6 8 106 load cycles (as tested) (a)

10

0

10 20 30 106 load cycles (as tested)

40

(b)

Figure 10: Results from the conducted crack tests on the material EA1N with different variable amplitude loadings; (a) Results of propagating cracks in relation to the applied load sequences (VA 1, VA 4 and VA 5); (b) Results of propagating cracks in relation to the applied load sequences VA 4 and VA 5.

In a comparison of the results (Fig. 11) with correction of the omitted load cycles, both EA4T and EA1N show on average that the crack growth is overestimated by the subsequent omission correction of the results. This in turn suggests that load cycles which do not contribute to crack growth cause a retardation effect. Martin Rieger: Preprint submitted to Elsevier

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Full-Scale Tests on Railway Axles

40

40 EA1N

Crack length 2c in mm

Crack length 2c in mm

EA4T

30

20 VA 0 Phase 1: VA 1; Phase 2: VA 0

10

30

20

Phase 1: VA 1; Phase 2: VA 0

10

Phase 1: VA 2; Phase 2: VA 0

Phase 1: VA 4; Phase 2: VA 5 (30 mm)

Phase 1: VA 3; Phase 2: VA 0

0

50 100 150 200 250 106 load cycle with omitted load cycles (a)

Phase 1: VA 4; Phase 2: VA 5 (10 mm)

300

0

10 20 30 40 106 load cycles with omitted load cycles

50

(b)

Figure 11: Results with omission adjusted load cycle. The cycles which have been omitted are added to this result; (a) EA4T; (b) EA1N.

3.2. Secondary Stress State There are several other impacts on crack growth in addition to external loading. Two essential influencing factors are stresses from joining the wheel to the axle and residual stresses in the axle, which are introduced during production. To investigate the influence of these stress states, they were examined more closely. During the joining of the press-fit, the stresses at the investigated cross-section were measured by strain gauges. The residual stresses from heat treatment and manufacturing are best determined experimentally. The stress values are averaged over a more or less extended volume, depending on the measurement method [22]. During the measurements, a very large inhomogeneity of residual stresses in the circumferential direction and axially were detected. As the fatigue crack grows, the residual stresses in the region of a propagating crack are redistributed. Taking into account this spatial inhomogeneity of the residual stresses, an exact determination of the residual stresses after the crack propagation tests is impossible. Therefore, a new method for estimating the residual stresses during the tests is suggested.

3.2.1. Press fit stresses Press fit stresses depend mainly on the diameter pairing of axle and clamping plate, besides the elastic constant. They can be estimated computationally using the finite element method (FEM) on one hand [19]; on the other hand, the press fit strains can be measured locally by strain gauges and converted to local stress estimates. In the performed strain gauge measurements at an axial coordinate position of X1 = 32 mm from the wheel seat edge into the fillet, the surface stress range in axial direction (crack opening) from 25 to 31 MPa was obtained. This gives a mean value of approximately 28 MPa with a scatter-band of ±3 MPa [23]. A Shapiro-Wilk test does not reject the null hypothesis of a normal distribution (p = 0.60).

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Full-Scale Tests on Railway Axles

3.2.2. Crack tip strain gauge measurements By applying strain gauges near the crack flanks it has been shown that an estimation of the crack opening and closure stresses can be evaluated [24, 25]. Such strain gauges have been applied to selected axles. 5 mm

5 mm

Strain gauge #2

2 mm

Strain gauge #1

2c

Figure 12: Example picture of a propagated crack, out of a starter notch, with applied crack tip strain gauges and their positions regarding the middle of the starter notch.

Figure 12 shows an example image of a recorded crack and the positions of the attached crack tip strain gauges at a distance of 5 mm radial from the center of notch and 2 mm in axial direction from the crack plane.

40 c = 2.7 mm c = 5.0 mm

100 Load F in kN

Stress in MPa

c = 8.3 mm

20

0 c = 2.7 mm c = 5.0 mm

c = 12.0 mm

0

−20

c = 8.3 mm

−100

c = 12.0 mm

0

10

20

30 40 Time in ms

50

60

70

−40 −150

−100

(a)

0

−50

50

100

150

Stress in MPa (b)

Figure 13: Evaluation of the measured signals; (a) Measured stresses in MPa applied over time in milliseconds; (b) Crack opening and crack closure curve.

After a defined period, discontinuously measurements of the applied strain gauges were carried out. From these measurements, two load cycles at the same load level were cut out for subsequent evaluation. Figure 13a shows these measurements in milliseconds at four different crack lenghts. In Figure 13b, the applied load and the measured stresses at the crack tip were correlated. With this correlation the subsequent evaluation of the crack opening and closure stress were carried out: • Firstly (c = 2.7 mm): The crack opening and closing does not affect the measured strain signal (Calculated to stress by using E = 210 000 N/mm2 ). The strain gauge is to far away from the crack tip to see the stress fields of the crack. • Secondly (c = 5.0 mm): Still no affect on the measured strain. • Thirdly (c = 8.3 mm): A buckling point begins to form which allows at a certain crack length to estimate the crack opening and crack closing load. The goal of this measurements are the determination Martin Rieger: Preprint submitted to Elsevier

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Full-Scale Tests on Railway Axles

of the contact of the whole crack flanks and not the detail of the near crack tip closure phenomena, which results in a small deviation from lineare load vs. stress curves. • Last crack length (c = 12.0 mm): At a certain crack length, the crack is large enough so that no additional strain at the strain gauge can be measured at a certain load. At this stage, the crack opening and closure stress can be evaluated from the buckling points. The strain gauge is now in the wake of the crack tip. In the absence of residual stresses, crack opening starts at load stresses of a few MPa in tension. Compressive residual stresses will lead to additional tensile stresses of the same value becoming necessary for crack opening, whereas tensile residual stresses will shift the crack opening stresses to smaller values or even into compression. The shown example in Figure 13 is not included in Table 3, as this specimen was a different experiment. However, this measurement is intended to explain the procedure for the measurements carried out in more detail. The points at which the buckling points are formed, represent the limits for the estimated secondary stresses (Table 3). As a rough estimate for the residual stresses near the crack, also the arithmetic mean of these bounds have been calculated σres . In order to derermine the residual stresses in axles where no crack tip strain measurements had been performed the following estimation hav been applied. Table 3 Bounds for average residual stresses (crack opening and crack closure stresses) near the fastest growing crack of selected test axles, estimated from the evaluation of crack tip strain gauge measurements and correlated with the obtained test duration (tested load cycles without adding the omitted load cycles) until a crack length 2c = 30 mm. Specimen

TM15820 TM15824 TM15818 TM17679 TM17678 TM17684

Material Lower limit of Upper limit of Mean estimate of Tested load cycles Load sequence residual stress residual stress residual stress from 5 to 30 mm in MPa in MPa σres in MPa in millions EA1N EA1N EA1N EA4T EA4T EA4T

29.5 22.6 8.5 -14.6 -35.5 -54.2

49.6 48.6 29.6 4.0 -16.6 -16.8

39.6 35.6 19.1 -5.3 -26.1 -35.5

1.63 1.59 2.84 5.13 15.13 16.71

VA VA VA VA VA VA

4 4 4 2 3 2

A combination of the residual stresses from press-fit plus residual stresses from heat treatment and manufacturing are measured. If the mean estimated residual stress σres is correlated with the crack growth rate, a clear correlation between these two values is obtained (Fig. 14). In the calculation of da/dN it was assumed that the crack grew with an average ratio a/c = 0.8 to a crack length of 30 mm. With these experimental results, a logarithmic fit for EA1N with a coefficient of determination R2 = 0.9511, as well as, for EA4T (R2 = 0.9466) could be obtained (Equation 1 and 2).

EA1N,VA4 σres,i = 32.313 · ln

3

dai dNi

4

+ 201.74

(1)

EA4T,VA2 = 22.956 · ln σres,i

3

dai dNi

4

+ 138.27

(2)

The calculated fitting curve was done respective to the material and can be seen in Fig. 14. All tests calculating the curve for EA1N were tested with the same load sequence. For EA4T, only 2 tests with crack Martin Rieger: Preprint submitted to Elsevier

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40 20

Mean residual stress σ res in MPa

Mean residual stress σ res in MPa

Full-Scale Tests on Railway Axles

TM15820 TM15824 TM15818

0

−20 −40 10−4

10−3 Crack growth rate da/dN in ţm/cycle (a)

10−2

40 20

TM17679 TM17678 TM17684

0

−20 −40 10−4

10−3 Crack growth rate da/dN in ţm/cycle

10−2

(b)

Figure 14: Correlation of the mean estimated residual stress σres applied over the averaged crack growth rate da/dN between 2c = 5 mm and 2c = 30 mm; (a) EA1N; (b) EA4T.

tip strain gauges were performed at the same load sequence. However, an axle was measured at the same load sequence with a slightly modified omission (one load block less omitted). The results of TM17678 were subsequently mathematically adapted by excluding the load cycles of the not omitted load block.

4. Crack Growth Assessment Base of the calculation model is the original NASGRO fatigue crack growth model according to Forman and Mettu [26] used in the precursor project Eisenbahnfahrwerke 2 [14] (Equ. 3):

da =C dN

53

1−γ 1−R

4

∆K

6m

4p ∆Kth 1− ∆K 3 4q Kmax 1− Kc

3

(3)

With the material parameters C, m, p, q, Kc , the function γ(R) and the threshold Kth a crack propagation curve can be described [27]. This model was significantly enhanced [28], as briefly summarized in what follows. Details about the model are explained in [28, 29]. For long crack threshold, Newmans’s closure model [30] as in the original NASGRO equation [26] was used. For the fatigue crack growth threshold of short cracks, with increasing crack extension, the model described in [27] was used. A cyclic crack resistance curve was used and approximated by an analytical description [27]. Plasticity-induced load sequence effects were modeled using a modified Willenborg-Gallagher model. Despite the limitations of this model described in [31, 32], the Willenborg-Gallagher model as described in [32] was used as a starting point for a further development to describe the experiments for reasons of computational efficiency. Oxide-induced closure buildup was modeled using a phenomenological approach based on load level and number of cycles [28]. All developed models were implemented in a software tool called INARA (INtegrity Assessment of Railway Axles). With this software tool all calculations have been performed. Two tests were selected for recalculation and comparison. These tests are listed in Table 4. Martin Rieger: Preprint submitted to Elsevier

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Full-Scale Tests on Railway Axles Table 4 With INARA calculated specimens. No.

Specimen

Material

load sequence

1 2

TM17678 TM15824

EA4T EA1N

Phase 1: VA 3; Phase 2: VA 0 Phase 1: VA 4; Phase 2: VA 5

4.1. Definition of the Input Parameter For the calculations carried out, properties related to the respective material, residual stresses determined from the interference fit and heat treatment as well as the external load were applied.

4.1.1. Secondary Stresses The local load stresses across the cracked cross-section were calculated by multiplying the nominal stress from the given load sequence by the normalized stress distribution obtained from finite element simulation [33]. The press fit stress was obtained by scaling the normalized press fit stress profile from [19], by the measured press fit stress at the surface. The total secondary stresses were finally obtained by superposition of the press fit and residual stresses. If the secondary stresses were estimated from crack tip strain gauge measurements, no depth profile was available, and a constant secondary stress over the complete cross-section was assumed for simplicity.

4.1.2. Material Properties In Table 5 the mechanical properties are listed. All material data and parameters used for the crack propagation calculations can be found in [28]. Table 5 Mechanical properties from tensile testing [28]. Material

Rp0,2 in MPa

Rm in MPa

A5 in %

Z in %

EA4T EA1N

541 411

690 605

20.5 26

65 63

5. Comparison In order to demonstrate the quality of the developed prediction procedure a comparison of the predicted and measured crack propagation behaviour of an axle produced out of EA1N and EA4T is presented in the following. Figure 15 shows the calculation results with the upper and lower limit of residual stresses from crack tip measurement in comparison with the conducted experiment. The behaviour of this EA1N test axle (TM15824) is well in the range of the results estimated with minimum and maximum residual stresses (Calculation number 2). The upper stress bound estimates the service life from the beginning until the end conservatively. The lower limit in turn overestimates the residual lifetime at the beginning. Even if the curves at 2c = 30 mm do not meet yet, the crack growth da/dN is, in the second half, faster than in the experiment. This can be described as a conservative calculation. In general also the test result for the EA4T test axle TM17678 (Fig. 16) is most of the time within the predicted residual lifetime. However, the wide bounds of the crack tip strain gauge residual stress estimate lead to extremely wide bounds for the crack growth behaviour. In view of this strong influence on the residual lifetime, the knowledge of residual stresses within railway axles are from great interest and are needed for an appropriate prediction (Calculation number 1). For this EA4T test axle, the lower stress bound of the calculation overpredicts residual lifetime at the beginning. After the first half of the calculation, which overestimates the service life, the crack growth rate accelerates and the calculated residual life after 2c = 30 mm Martin Rieger: Preprint submitted to Elsevier

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Full-Scale Tests on Railway Axles 40 Experiment Calculation (residual stress 22.6 MPa)

Crack length 2c in mm

35

Calculation (residual stress 48.6 MPa)

30 25 20 15 10 5 0

0.2

0.4

0.6

0.8 1 1.2 106 load cycles (as tested)

1.4

1.6

1.8

2

Figure 15: Test axle TM15824 (EA1N) in comparison of experimental crack growth with calculation results using the residual stress limits of 22.6 MPa and 48.6 MPa from crack tip measurements.

is estimated conservatively. The upper stress bound estimates the service life from the beginning of the calculation until the end as conservative. 40 Experiment Calculation (residual stress −16.6 MPa)

Crack length 2c in mm

35

Calculation (residual stress −35.5 MPa)

30 25 20 15 10 5 0

2

4

6 8 10 106 load cycles (as tested)

12

14

16

Figure 16: Test axle TM17678 (EA4T) in comparison of experimental crack growth with calculation results using the residual stress limits of −35.5 MPa and −16.6 MPa from crack tip measurements.

The deviation may also be due to a different predicted a/c - ratio as in the actual specimen. Therefore, the cracked areas of the different test specimens have to be investigated with respect to a/c ratios.

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Full-Scale Tests on Railway Axles

6. Summary & Conclusion With the experiments carried out, it can be stated that a way for obtaining more accurate crack propagation data for verification and development of new designs on full-scale railway axle tests have been found. With the development of an optical crack detection system for crack propagation tests on wheel-set axles, the quality of tests for this purpose could be increased. A correlation of crack growth and residual stress state have been taken into account in the results, by measuring residual stresses throughout the experiments. At the same external load, tensile residual stresses lead to an increase of the fatigue crack growth rate. By showing that the fatigue crack growth rates correlate with residual stress estimation, the dependence of fatigue crack growth on the load ratio R was corroborated. The residual stress state near an individual crack cannot be determined with sufficient precision. However, rough bounds for the residual stresses have been established via crack tip strain gauges. From this, the following conclusion can be derived: • To estimate an actual crack growth (2c vs. N ) curve the residual stress state is an essential influence parameter. • To assess the residual lifetime of a cracked axle the residual stress state must be considered. • To estimate the lifetime for a batch of axles, the scatter-band of residual stresses must be known. Therefore, a sufficient number of measurements are required. • This distribution of residual stresses(mean value and standard deviation) has to be taken into account in the damage tolerance concept for crack growth and residual lifetime estimates. • By changing the load sequence and omitting load blocks below a certain level a retardation effect for fatigue crack growth was observed. This means that the usual laboratory tests with load omission as they are currently used for validation of the damage tolerance calculations - are conservative with respect to the residual lifetime.

Acknowledgement This work has been performed jointly with the industry partners Alstom Transport Deutschland GmbH, Bochumer Verein Verkehrstechnik GmbH, Gutehoffnungshütte Radsatz GmbH, Siemens AG Österreich, Stadler Pankow GmbH, Voith Turbo GmbH, and the scientific partners Erich Schmid Institute for Materials Science (Austrian Academy of Sciences), Fraunhofer Institute for Mechanics of Materials in Freiburg, Materials Center Leoben, Virtual Vehicle Research Center Graz, TU Clausthal (Institute of Plant Engineering and Fatigue Analysis), TU Graz (Institute for Lightweight Design), University of Leoben (Institute of Mechanical Engineering). Financial support by the Austrian Federal Government (in particular from Bundesministerium für Verkehr, Innovation und Technologie and Bundesministerium für Wissenschaft, Forschung und Wirtschaft) represented by Österreichische Forschungsförderungsgesellschaft mbH and the Styrian and the Tyrolean Provincial Government, represented by Steirische Wirtschaftsförderungsgesellschaft mbH and Standortagentur Tirol, within the framework of the COMET Funding Programme is gratefully acknowledged.

References [1] Klinger, C. ; Bettge, D.: Axle fracture of an ICE3 hight speed train. In: Engineering Failure Analysis, 35:66-81 (2012) [2] Gürer, G. ; Gur, C.H.: Failure analysis of fretting fatigue initiation and growth on railway axle press-fits. In: Engineering Failure Analysis, 84:151-66 (2017) [3] Zerbst, U. et al.: Fracture mechanics in railway applications - an overview. In: Engineering Fracture Mechanics 72, 163-194 (2005) [4] Luke, M. et al.: Fatigue crack growth in railway axles: Assessment concept and validation tests. In: Engineering Fracture Mechanics 78, 714 - 730 (2011) [5] Wu, S.C. ; Zu, Z.W. ; G.Z., Kang ; He, W.F.: Probabilistic fatigue assessment for high-speed railway axles due to foreign object damages. In: International Journal of Fatigue, 117:90-100 (2018)

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Full-Scale Tests on Railway Axles [6] Xu, Z.W. ; Wu, S.C. ; Wang, X.S.: Fatigue eveluation for high-speed train. In: International Journal of Fatigue, 123:79-86 (2019) [7] Zerbst, U. et al.: Parameters affecting the damage tolerance behaviour of railway axles. In: Engineering Fracture Mechanics 78, 793-809 (2011) [8] Zerbst, U. et al.: Safe life damage tolerance aspects of railway axles - A review. In: Engineering Fracture Mechanics 98, 214-271 (2013) [9] Yamamoto, M. ; Makino, K. ; Ishiduka, H.: Experimental validation of railway axle fatigue crack growth using operational loading. In: Engineering Fracture Mechanics, 142-52 (2019) [10] Yamamoto, M. ; Makino, K. ; Ishiduka, H.: Comparison of crack growth behaviour between full-scale railway axle and scaled specimen. In: International Journal of Fatigue 92, 159-165 (2016) [11] Cervello, S. et al.: Fatigue properties of railway axles: new results of full-scale specimens from EURAXLES project. In: International Journal of Fatigue 86, 2-12 (2016) [12] Beretta, S. ; Regazzi, D.: Probabilistic fatigue assessment for railway axles and derivation of a simple format for damage calculations. In: International Journal of Fatigue 86, 13-23 (2016) [13] Lütkepohl, K. et al.: Sicherer und wirtschaftlicher Betrieb von Eisenbahnfahrwerken, vol. 1-3. Clausthal. (2009) [14] Lütkepohl, K. ; Esderts, A. ; Luke, M. ; Varfolomeev, I.: Sicherer und wirtschaftlicher Betrieb von Eisenbahnfahrwerken / TU Clausthal und IWM. 2009. – Forschungsbericht [15] Luke, M. et al.: Fracture mechanics assessment of railway axles: Experimental characterization and computation. In: Engineering Fractuer Analysis 17, 617-623 (2010) [16] Thurner, T.: Real-Time Detection and Measurement of Cracks in Fatigue Test Applicaitons. In: AMA Conferences 2015 (2015) [17] EN13261, DIN: Bahnanwendungen - Radsätze und Drehgestelle - Radsatzwellen - Produktanforderungen; Deutsche Fassung EN 13261:2003. (2006) [18] EN13260, DIN: Bahnanwendungen - Radsätze und Drehgestelle - Radsätze - Produktanforderungen; Deutsche Fassung EN 13260:2009+A1:2010. (2010) [19] Wächter, M. et al.: Bruchmechanische Berechnungen zur Festlegung der Position der Starterkerbe und zum Vergleich möglicher Prüfkollektive / Institut für Maschinelle Anlagentechnik und Betriebsfestigkeit, TU Clausthal. 2014. – Forschungsbericht [20] Simunek, D. ; Leitner, M. ; Rieger, M. ; Pippan, R. ; Gänser, H.-P. ; Weber, F.-J.: Fatigue Crack Growth in Railway Axle Specimens - Transferability and Model Validation. In: Submitted in International Journal of Fatigue 2019. (2019) [21] Wächter, M. ; Schröder, V.: Specification for crack propagation tests. / Institut für Maschinelle Anlagentechnik und Betriebsfestigkeit, TU Clausthal. 2016. – Forschungsbericht [22] Gänser, H.-P. ; Maierhofer, J.: Entwicklung einer Methode zur Bestimmung von Eigenspannungen in Radsatzwellen mit Hilfe des Cut-Compliance-Verfahrens / Materials Center Leoben. 2015. – Forschungsbericht [23] Wächter, M. ; Schröder, V.: Eisenbahnfahrwerke 3: Ergebnisse des Fügens der Radsätze vom 17.05.2017 (Presentation slides for project meeting Oberhausen 30.05.2017). / Institut für Maschinelle Anlagentechnik und Betriebsfestigkeit, TU Clausthal. 2017. – Forschungsbericht [24] Pippan, R.: The sensitivity to measure crack closure with strain gauges near the crack tip. In: Engineering Fracture Mechanics 31 (1988) [25] Pippan, R. ; Haas, G. ; Stüwe, H.-P.: Comparison of two methods to measure crack closure in ultra-high-vacuum. In: Engineering Fracture Mechanics 34 (1989) [26] Forman, RG. ; Mettu, SR.: Behavior of Surface and Corner Cracks Subjected to Tensile Bending Loads in Ti-6A1-4V Alloy. In: ASTM STP 1131, Philadelphia, 519-546 (1992) [27] Maierhofer, J. ; Pippan, R. ; Gänser, H.-P.: Modified NASGRO equation for physically short cracks. In: International Journal of Fatigue (2014) [28] Maierhofer, J. et al.: Extended NASGRO equation including load sequence effects. In: Submitted in International Journal of Fatigue 2019. (2019) [29] Gänser, H.-P. et al.: The EBFW3 probabilistic fatigue crack growth assessment method for railway axles. In: Submitted in International Journal of Fatigue 2019. (2019) [30] Newman, J.C.: A crack opening stress equation for fatigue crack growth. In: Int. J. Fracture 24, R131-R135 (1984) [31] Sander, M ; Richard, H.A.: Fatigue crack growth under variable amplitude loading. Part II: analytical and numerical investigations. In: Fatigue Fract. Engng Mater Struct 29, 303-319 (2006) [32] Meggiolaro, M.A. ; Castro, J.T. Pinho d.: Comparing overload-induced retardation models on fatigue crack propagation. In: Proc. 56ř Congresso Annual da ABM, 16.-19.07.2001, Belo Horizonte, pp. 1719-1729 (2001) [33] Fasswald, J.: Personal communication / Kompetenzzentrum - Das vurtuelle Fahrzeug Forschungsgesellschaft mbH. 2014. – Forschungsbericht

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Declaration of interests ‫ ܈‬The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: