Very high cycle fatigue behavior under constant and variable amplitude loading Academic research paper on "Materials engineering"

Available online at wmv.sciencedirect.com

Structural Integrity

* v^* ■

CrossMark

Procedia Structural Integrity 2 (2016) 034-041

JLI U^LUI Ul <1 PLtyi !l.y

ScienceDirect P rOCed i 0

www.rlsrvirt.cem/lecatr/ptecrdia

21st European Conference on Fracture, ECF21, 20-24 June 2016, Cstsnis, Italy

Very high cycle fatigue behuvior under constant snV variable

amplitude loaVing

Manuels Sander*, Thomas Müller, Carsten Stäcker

Institute of Structural Mechanics, University of Rostock, Albert-Einstein-Str. 2, 18059 Rostock, Germany

Abstract

Components and structures are often exposed a very high number of cycles. The investigations in the field of very high cycle fatigue (VHCF) are mainly eocuted on experiments without mean stresses and with constant amplitude loading. Therefore, within she scope of this paperi sevestigations with coHstFt a^vai'iablm amplitudes with difforent mean stresses will be presented. For studying; variable amplitude loadings in the VHCF regime systematic two-atep block loadino experiments have been performed, in whK;h the maximum load amplitudes ofthe high block and tho number of cycles of the low block with amplitudes below the fatigum strength hane beon varied. Moreover, the standfedized load-time-hiseories Felix/lS and WISPEhh have been used. The influence of different eecanatractions its well as the amount ef the ampiitudes beneath the fatigue strength of the ievestigaUed high strength steel on the initiation the iS-jV curve and the lifetime prediction has been ievestigated. Due to the variable amplitude loadings arrest marks are produced witSen the Sish-eye sslrriistnd]ttg the inclusion. The sizes and the areu, whereaIтeet manfe are ubservable , ae well as the spacings between the anest markf are influenc ed by the different load sequence s. By counting and Measuring the surest miirlcs^n avetage crrrck growa'th rate for the crack propagation within the fish eye can be calculated. Moreover, tSse short chack growth curve is used for calculating lifetimes using fracture mcchanical approaches.

© 2016, PROSTR (Peocedis Structural Integrity) Hosting by Elsevier Ltd. All rights reserved. Peer-review under rtsponsibeity of rhe Sdsntilk Cemmittee oUECF21.

Keywords: VHCF, variable amplitude loading, mean stresses, fatiger

* Corresponding author. Tel.: +49-381-498-9340; fax: +49-381-498-9342. E-mail address: manuela.ssnVer@uni-rostockiVe

2452-3216 © 2016, PROSTR (Procedia Structural Integrity) Hosting by Elsevier Ltd. All rights reserved.

Peer-review under responsibility of the Scientific Committee of ECF21.

10.1016/j.prostr.2016.06.005

1. Introduction

In many applications components and structures, like helicopter rotors, ship propellers, wind turbines or wheelset axles, but also medical products, are commonly exposed to more than 108 cycles. However, due to such a high number of cycles the fatigue strength defined by Wohler is not always given. Moreover, in the very high cycle fatigue (VHCF) regime cracks predominately initiate in the interior of a component with a typical fish-eye formation. The initiation in the interior is influenced by e.g. the size, the position, the shape and the hardness of the inclusion. These investigations are predominately performed with constant amplitude loadings except for few studies, e.g. Mayer et al. (2007, 2009), Fitzka and Mayer (2015), Ogawa et al. (2014) or Meischel et al. (2015). But, during assembly, transport and especially operation machines or means of travel are exposed variable amplitude loadings with different mean stresses. Therefore, the influence of different stress ratios and standardized load spectra in terms of Felix/28 and WISPER on S-N curves in the VHCF regime has been investigated.

2. Experimental setup

For the experimental investigations the ultrasonic testing system (Fig. 1a) developed by the BOKU Vienna (Mayer (2006) or Stanzl-Tschegg (2014)) is used. The testing system was extended with a load frame for the investigations of mean stress effects. Both the ultrasonic testing system and the load frame are computer-controlled. Therefore, the comprehensive software Ultrasonic Fatigue Testing Software for Variable Amplitude Loading (UFaTeSVAL) has been developed (Müller, Sander (2013)). With UFaTeSVAL it is possible to perform automatically VHCF experiments with constant and variable amplitude loadings in terms of block loads as well as different mean stresses. In order to avoid heating due to internal damping, the specimen is cooled by a fan and a pulsed loading is applied. For an optimal pulse-pause-sequence the temperature is measured at the surface of the specimen using an IR sensor and the pulse and pause length are adapted during the experiments. Because the heating of the specimen is significantly influenced by the stress amplitude, the adaptation of the pulse-pause-sequence is even important for variable amplitude loadings in order to reduce testing time. For the realization of experiments with R > -1 the lower end of the specimen is mounted with a counter bearing, which must be situated at a vibration node. The crack length at the surface is measured with an optical microscope, which is mounted on a 360°-ring.

Load frame

Ultrasonic transducer

Amplification-horn

Vibration gauge X/2 rod

digital microsope mounted on a 360°-ring

X/2 rod

Counter specimen bearing

Cooling IR sensor

Fig. 1. a) Experimental setup with the used specimen b) for R > -1 and c) R = -1

The specimens have been made of the quenched and tempered high-strength steel 34CrNiMo6 with an ultimate tensile strength of 1200 MPa and a yield strength of 1000 MPa. The specimen with a minimum diameter of 4 mm are shown in Fig. 1b for experimental investigations of R > -1 and in Fig. 1c for R = -1. The surfaces of the specimens have been emery-polished after machining.

3. Experimental results

For the investigation of the mean stress effect on the fatigue strength at 109 cycles as well as on the S-N curve in the VHCF regime experiments with the R-ratios of -1, 0.8, 0 and 0.5 have been performed. In order to determine the fatigue strength the staircase method has been applied (Sander et al. (2014)). The results have been statistically evaluated with the approach proposed by Huck (1983). The fatigue strengths for probabilities of survival of 10%, 50% and 90% are summarized in a Haigh diagram (Fig. 2) in comparison to the Goodman relation, the Gerber parabola and the (2013).

1000 S 800

■Us 600

Mean stress [MPa]

Fig. 2. Haigh diagram with the experimentally determined fatigue strength in the VHCF regime in comparison to the Goodman relation, the

Gerber parabola and the approach of the FKM-guideline.

The mean stress effect is approximately 0.52 in contrast to the mean stress effect of 0.32 using the conventional fatigue strengths of the material from literature (FKM (2012)). It can be observed that the difference between the fatigue strengths in the VCHF regime and conventionally determined fatigue strengths described by the function of the FKM guideline with M = 0.32 increases with increasing R-ratio, while the fatigue strengths at R = -1 are nearly the same. This can be explained with the number of cycles to failure beyond 108 cycles. Fig. 3a shows that the number of cycles to failure increases with increasing R-ratio. For R > 0, failures occur above 108 cycles, while for R < 0 all failures are below 108 cycles. This means that for R > 0 many experimental data would be assessed in the conventional determination as run-outs in contrast to the results for R < 0 which would be taken into account at the conventionally determined fatigue strength (Sander et al. (2014)). This effect has also been reported by Beck et al. (2013) for a martensitic 12% Cr steel used for low pressure steam turbine blades in power generation. From Fig. 2 also can be observed that neither the Goodman relation nor the Gerber parabola can map the experimental result in the VHCF-regime. However, the relation proposed by the FKM guideline describes the mean stress effect for all R-ratios very well, if the fatigue strengths for R = -1 and R = 0 determined in the VHCF experiments are used.

With some exceptions the cracks mainly initiate at non-metallic inclusions in the interior of the specimens with a typical fish-eye formation both in the HCF and the VHCF regime, which results in continuous S-N curves with a

mean stress relation proposed by the German FKM-guideline "Analytical Strength Assessment"

• Experiments (P = 50%) (Müller (2016))

- Experiments (P = 10%) (Müller (2016))

- Experiments (P = 90%) (Müller (2016)) -FKM guideline (M = 0.32)

-FKM guideline (M = 0.52)

— Goodman relation

— Gerber parabola

200 400

800 1000 1200

large scatter band (Fig. 3a). Fig. 3b shows the results of the modified S-N curves using the approach by Murakami (2002) with

1,56 • (HV +120) (1 - R

(V area )1/6

for internal defects and

1,43 • (HV +120) (1 - R

(Vareay/6 \ 2

for surface defects (SI) in order to account for the different defect sizes in terms of Varea. The exponent a has been calculated from the fatigue strength experiments with 0.5472. It becomes obvious that the scatter is reduced and the S-N curves of all R-ratios fall within one scatter band.

• R = -1 OR = -1 (SI) 700

AR = -0.8 4R = 0 DR = 0.5

AR = -0.8 (SI) OR = 0 (SI) DR = 0.5 (SI)

1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09 1.0E+10 a) Nf(log)

• R = -1

OR = -1 (SI) 2.2

AR = -0.8 R = 0 DR = 0.5

AR = -0.8 (SI) R = 0 (SI) CR = 0.5 (SI)

n-cr • ► ♦

= ° • / ^

. A'A o * * 0

2.0 *1.8 > 1.6 1.4 1.2 1.0

1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09 1.0E+10 b) Nf(log)

Fig. 3. (a) S-N curve and (b) modified S-N curve for different R-ratios (Müller (2016)).

In order to investigate the influence of variable amplitude loadings and especially the loads beneath the fatigue strength on the lifetime, systematic experiments with repeated two-step loadings have been performed. Therefore, the load levels of the high block (Rhl = Uai / öd,vhcf) as well as the cycle number «2 of the low block have been varied, whereby the load level of the low block was 90% of the fatigue strength determined for a limit of 109 cycles (Fig. 4a). The cycle number «1 of the high block is constant 10,000 cycles. The sequence of these two blocks has been repeated until the specimen fails or the limit of 109 cycles has been reached.

■ i 1.2-<td I

1.1-<XD

«!= 10.000

0.9-<7d

I b b"

1.2 1.0 0.8

0.6 0.4 0.2 0.0 0.0E+00

2.0E+06

1.2 1.0 0.8

0.6 0.4 0.2 0.0 0.0E+00

2.0E+05 H

4.0E+05

Fig. 4. Investigated variable amplitude sequences (a) 2-step block loading; (b) Felix (R = -1) and (c) WISPER (R = 0).

For ratios n/n < 10 the number of failure cycles are beneath 107 cycles and are nearly independent of the load level of the high block (Fig. 5a). With an increasing «2/m-ratio the number of failure cycles increases, because the cycle number of the low block increases as well. For the evaluation of the amplitudes beneath the fatigue strength the original and elementary Palmgren-Miner rule as well as the Palmgren-Miner rule modified by Haibach have been applied (Müller, Sander (2013)). These calculations have shown that for Rhl = 12 (CTa1 = 583 MPa) the calculated lifetimes overestimates more or less the failure cycles for the «2/«i-ratios of 1 and 10, but are within the scatter band of the experiments. For n/n = 100 the calculated lifetimes using the original Palmgren-Miner rule matches the experimental lifetimes very well. But, the elementary and modified Palmgren-Miner rules underestimate the failure cycles, which implies that the low amplitudes have only a small amount on the total damage in the experiment.

For Rhl = 13 (CTa2 = 637 MPa) and n/n = 1 again all approaches lead to nearly the same calculated lifetimes, which are in the scatter band of the experimental data. But, the original Palmgren-Miner rule progressively overestimates the lifetime with an increasing ratio of n/n and the calculated values are outside the scatter band, while the elementary and modified approaches overestimate the lifetime as well, but match the lifetime better. This means that the small block loads beneath the fatigue strength contribute to the fatigue damage, if the block loading ratio and the ratio of n/n are high enough. In two-step block loading experiments Mayer et al. (2007) have shown that low amplitudes beneath the fatigue strength contribute significantly to the fatigue damage, if the high loads are more than 15% above the fatigue strength.

a) 1000

■ R_HL = 1.2 ♦RHL = 1.3

♦ ♦♦♦♦ ■ ■

♦ ■ ♦ ♦<

1,0E+05 1,0E+06 1,0E+07 1,0E+08 1,0E+09 1,0E+10 Nf (log)

Fig. 5. Results of two-step block loading experiments (a) failure cycles depending on the n2/n1 and RH (Müller (2016)) and (b) fracture surfaces.

Fig. 5b shows exemplarily two fracture surfaces after block loading experiments. Due to the block loading arrest marks are produced within the fish-eye surrounding the inclusion. This is an indication of interaction effects, which affect the lifetime. Moreover, different colorations with varying spacings are visible, which reveal for the different block loading sequences.

In order to investigate the influence of more complex load sequences on S-N curves, the standardized helicopter load spectrum Felix/28 with 2,276,625 cycles (Fig. 4b) and the standardized wind turbine load spectrum WISPER with 255,128 cycles (Fig. 4c) have been used. Felix has been transformed to a constant R-ratio of -1 and WISPER to 0 using the equations accounting for the mean stress effect with M = 0.52 from VHCF experiments. Because only block loadings with a minimum number of cycles can be applied with the ultrasonic testing system, both spectra have been divided into eight and six classes using the rainflow method, respectively. For the assessment of the class sequences on the lifetime, the classes of Felix have been reconstructed in three different ways. Felix 10 starts with the highest amplitudes and ends with the lowest, Felix 11 was reconstructed with increasing load amplitudes and Felix 12 is randomly mixed. Each spectrum has been repeated until failure occurs or the limit of 109 cycles is reached.

FELIX 10-641 FELIX 11-641 FELIX 12-641 FELIX 10-705 CA (R = -1) 2.4 2.2 jf 2.0 ib" 1.8

♦. v _

ts 1.6

b 1.4 1.2 1.0

1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09 a) fog)

Felix 10

Felix 11

1 Felix 12

FELIX 10-641 «FELIX 11-641 FELIX 12-641 • FELIX 10-705 CA (R = -1) 160 140 _ 120 | 100 ^ 80 is 60

^ 40 20 0

1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09 b) Nf(log)

t \ » '«-

♦ ♦♦ ' * ¿ZU

Fig. 6. (a) Modified S-N curves and (b) the defect size for Felix in comparison to constant amplitude test results with R = -1 (Müller (2016)).

The results of the different experiments with Felix are shown in Fig. 6a in comparison to constant amplitude test results with R = -1 in terms of the modified S-N curve. It becomes obvious that the different reconstructions of the load spectrum have nearly no influence, but the modified S-N curve is shifted to higher lifetimes in comparison to the constant amplitude tests. The inclusion sizes, at which the cracks initiate in constant amplitude tests, lead to higher failure cycles at variable amplitude loading. Moreover, the inclusion sizes decrease with increasing failure cycles. In contrast, the values of Varea are almost independent of Nf for constant amplitude loading. Moreover, due to the variable amplitude loading arrest marks are visible around the inclusion in and outside the fish-eye (Fig. 7). Depending on the reconstruction of the load spectrum the size and the area, where arrest marks are observable, as well as the spacings between the arrest marks are different.

Fig. 7. Fracture surfaces with arrest marks within the fish-eye around non-metallic inclusions from experiments with a) Felix 10, b) Felix 11 and c) Felix 12 (Müller, Sander (2013))

The S-N curve and the modified S-N curve of the experiments with the standardized load sequence WISPER are compared with the results of constant amplitude tests with R = 0 in Fig. 8. While the S-N curve (Fig. 8a) is shifted to higher lifetimes, the modified S-N curves of the constant and variable amplitude loading (Fig. 8b) collapse nearly to one curve.

Under the assumption that an arrest mark occurs, if one sequence ends after 2,276,625 cycles in the case of Felix/28 and another sequence starts, the arrest marks can be counted and related to the loading. For each arrest mark an appropriate cyclic stress intensity factor is calculated using the Varea-approach and an average stress amplitude, which is weighted with the number of cycles of each class. By measuring the arrest marks (Fig. 9b) an average crack growth rate da/dN has been calculated, which is related to an average cyclic stress intensity factor corresponding to two adjacent arrest marks. The results depending on the load sequences are shown in Fig. 9a. It becomes obvious that all determined values are below the long crack growth threshold, but almost all above the short crack growth threshold calculated with the Newman/NASA approach (NASA (2009) and Newman (1999)).

♦ <$ ♦

a) »WISPER O WISPER (SI) • CA (R = 0) 550 _ 500 g 450 « 400 350 ^ 300 250 200

1.0E+05 1.0E+07 1.0E+09 Nf (log)

b) »WISPER O WISPER (SI) A CA (R = 0) 1.8 1.7

ii I te

1.6 1.5 1.4 1.3 1.2 1.1 1

1.0E+05

*—S*

1.0E+07 1.0E+09 Nf (log)

Fig. 8. (a) S-N curve and (b) modified S-N curve for WISPER in comparison to constant amplitude test results with R = 0.

Moreover, the determined crack growth curve can be approximated by a regression line independent of the load sequence. But, the coefficient C and the exponent n of the extended Paris law, which have been calculated from the constant amplitude tests for R = -1 (Sander et al. (2014)) using the approach proposed by Shiozawa et al. (2010) differs.

a) 1.0E-05

] 1.0E-06

JS1.0E-07

te; 53 .s

1.0E-08

: 34 CrNiMo 6 / ?

- R = -1 * ✓ / /

1 1 / / /

! / M ¿f ( ►

- R = - 1 (long crack)

---- short crack (a = 30^m)

--- Shiozawa et al. (2010)

♦ Felix 10-641

■ Felix 11-641

♦ Felix 12-641

• Felix 10-705

Regression line

AK [N/mm3/2]

Fig. 9. (a) Long crack growth curve in comparison to analytically and experimentally determined short crack growth data; (b) Measuring of the

arrest marks.

The power law proposed by Shiozawa et al. (2010) with the corresponding values as well as the regression line determined from the Felix experiments have been used for the calculation of a S-N curve for R = -1. Therefore, the model of an embedded crack in a plate implemented in NASGRO (2009) has been used.

700 650 600 550 500 450 400

-CD2XD-

CD O ~

• -É

• O__O • x. ir «fr

1.0E+05

1.0E+07 Nf (log)

1.0E+09

O Experiments

--Shiozawa et al.

-Regression FELIX

Fig. 10. Experimentally and analytically determined S-N curves.

A comparison of the residual lifetimes starting from the smallest inclusion size of 30 ^m, from which in experiments a crack initiates, is shown in Fig. 10. It becomes obvious that the approach of Shiozawa et al. overestimates the lifetime, but the slope of the experimental S-N curve matches very well, because the parameters have been calculated from the S-N curve. However, the calculations using the regression line of the Felix experiments with the same crack model also overestimate the lifetime, but match the experimental results better. The overestimation using the regression of the Felix experiments can be explained with interaction effects, which are indicated by the arrest marks on the fracture surface, as well as with the crack growth model, which will be investigated both in future.

4. Conclusions

Machines, components and structures are often exposed a very high number of cycles with variable amplitude loadings and different mean stresses. Therefore, experimental investigations for different R-ratios and variable amplitude loadings in terms of the standardized load spectra Felix and WISPER for the high-strength steel 34CrNiMo6 are presented. Due to VHCF testing it could be shown that the mean stress effect is influenced. Moreover, due to variable amplitude loading the S-N curves are shifted to higher lifetimes and arrest marks are produced on the fracture surface surrounding the non-metallic inclusion in the fish-eye. These arrest marks have been used for the calculation of a crack growth curve, with which the lifetimes of the constant amplitude loadings could be reproduced.

Acknowledgements

The authors thank the German Research Foundation (DFG SA 960/2-2) for the financial support. References

Fitzka, M., Mayer, H., 2015. Variable amplitude testing of 2024-T351 aluminum alloy using ultrasonic and servo-hydraulic fatigue testing

equipment. Procedia Engineering 101, 169-176 Forschungskuratorium Maschinenbau, 2013. Analytical Strength Assessment of components: FKM Guideline. VDMA Verlag Hück, M., 1983. Ein verbessertes Verfahren für die Auswertung von Treppenstufenversuchen. Zeitschrift für Werkstofftechnik 14, 406-417 Kovacs, S., Beck, T., Singheiser, L., 2013. Influence of mean stresses on fatigue life and damage of a turbine blade steel in the VHCF-regime.

International Journal of Fatigue 49, 90-99 Mayer, H., 2006. Ultrasonic torsion and tension-compression fatigue testing: Measuring principles and investigations on 2024-T351 aluminium

alloy. International Journal of Fatigue 28, 1446-1455 Mayer, H., Haydn, W., Schuller, R., Issler, S., Bacher-Höchst, M., 2009. Very high cycle fatigue properties of bainitic high carbon-chromium

steel under variable amplitude loading. In: International Journal of Fatigue 31, 1300-1308 Mayer, H., Stochjanovic, S., Ede, C., Zettl, B., 2007. Beitrag niedriger Lastamplituden zur Ermüdungsschädigung von 0,15% C Stahl. Mat.-wiss. u. Werkstofftechnik 38, 581-590

Meischel, M., Stanzl-Tschegg, S.E., Arcani, A., Iyyer, N., Apetre, N., Phan, N., 2015. Constant and variable-amplitude loading of aluminum

alloy 7075 in the VHCF regime. Procedia Engineering 1011, 501-508 Müller, T., 2016. Einfluss variable Amplitudenbelastungen auf die Rissinitiierung und das Risswachstum im Bereich sehr hoher

Lastwechselzahlen. PhD-Thesis, University of Rostock Müller, T., Sander, M., 2013. On the use of ultrasonic fatigue testing technique - Variable amplitude loadings and crack growth monitoring. Ultrasonics 53, 1417-1424

Müller, T., Sander, M., 2013. Experimental and analytical study of the effect of variable amplitude loadings in VHCF regime. ICF 13, Bejing Murakami, Y., 2002. Metal Fatigue: Effects of small defects and non-metallic inclusions. Elsevier, London NASGRO - Fracture Mechanics and Fatigue Crack Growth Analysis Software, Reference manual, Version 6.0, 2009

Newman, J.C. Jr., 1999. Application of small-crack theory to aircraft materials. In: Ravichandran, K. S.; Ritchie, R. O.; Murakami, Y. (eds.):

Small Fatigue Cracks: Mechanics, Mechanisms and Applications, Elsevier Science Ltd., Amsterdam, 431-442 Ogawa, T., Stanzl-Tschegg, S., Schönbauer, B., 2014. A fracture mechanics approach to interior fatigue crack growth in the very high cycle

regime. Engineering Fracture Mechancis 115, 241-254 Sander, M., Müller, T., Lebahn, J., 2014. Influence of mean stress and variable amplitude loading on the fatigue behaviour of a high-strength

steel in VHCF regime. International Journal of Fatigue 62, 10-20 Shiozawa, K., Murai, M., Shimatani, Y., Yoshimoto, T., 2010. Transition of fatigue failure mode of Ni-Cr-Mo low alloy steel in very high cycle

fatigue. International Journal of Fatigue 32, 531-550 Stanzl-Tschegg, S., 2014. Very high cycle fatigue measuring techniques. International Journal of Fatigue 60, 2-17