See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/223600875
Fatigue strength of spring steel under axial and torsional loading in the very
high cycle regime
Article in International Journal of Fatigue · December 2008
DOI: 10.1016/j.ijfatigue.2008.07.004
CITATIONS
READS
73
2,076
5 authors, including:
Yoshiaki Akiniwa
S. Stanzl-Tschegg
Yokohama National University
University of Natural Resources and Life Sciences Vienna
97 PUBLICATIONS 949 CITATIONS
248 PUBLICATIONS 7,560 CITATIONS
SEE PROFILE
Kazuo A Tanaka
Extreme Light Infrastructure - Nuclear Physics
803 PUBLICATIONS 14,593 CITATIONS
SEE PROFILE
Some of the authors of this publication are also working on these related projects:
Cyclic slip activity of persistent slip bands View project
Christian Doppler Laboratory for Fundamentals of Wood Machining View project
All content following this page was uploaded by S. Stanzl-Tschegg on 12 May 2019.
The user has requested enhancement of the downloaded file.
SEE PROFILE
International Journal of Fatigue 30 (2008) 2057–2063
Contents lists available at ScienceDirect
International Journal of Fatigue
journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue strength of spring steel under axial and torsional loading in the very
high cycle regime
Y. Akiniwa a,*, S. Stanzl-Tschegg b, H. Mayer b, M. Wakita c, K. Tanaka d
a
Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Institute of Physics and Materials Science, BOKU, Peter-Jordan-Street 82, A-1190 Vienna, Austria
c
Research and Development Division, Chuo Spring Co. Ltd., 43-1 Miyashita, Fukuta, Miyoshi-cho, Nishikamo-gun, Aichi 470-0225, Japan
d
Department of Mechanical Engineering, Meijyo University, 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan
b
a r t i c l e
i n f o
Article history:
Received 9 January 2008
Received in revised form 7 July 2008
Accepted 8 July 2008
Available online 16 July 2008
Keywords:
Giga cycle fatigue
Axial loading
Torsional loading
Spring steel
Non-damaging defect
a b s t r a c t
The fatigue strength of an oil-tempered Si–Cr steel for valve springs (JIS G3561, SWOSC-V) was investigated. Smooth specimens without residual surface stresses were fatigued with two kinds of ultrasonic
fatigue testing machines to clarify the fatigue properties up to very high numbers of cycles (giga cycle
regime) under axial and torsional loading. The maximum inclusion size in the critical volume of a specimen predicted by the extremal statistics is 7.9 lm. Although scatter is somewhat large, the S–N data
could be approximated by linear lines in double logarithmic plots for both loading conditions up to
the giga cycle regime. The ratio of fatigue strength under torsional and axial loading at the same number
of stress cycles is about 0.68 and is almost constant even in the giga cycle regime. Cracks were initiated
from the specimen surface under tension–compression as well as torsion loading. No specimen showed
crack initiation from the interior. Inclusions and granular facet areas could not be observed. Under torsional loading, cracks initiated either perpendicular or parallel to the longitudinal direction of the specimens. After shear crack propagation to a crack length of about 30 lm, crack branching and mode I
propagation took place. The size of characteristic defects calculated on the basis of the propagation
threshold of long cracks is much larger than the inclusion size calculated by the extremal statistics.
Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction
For structural materials, the fatigue strength is the most important factor to ensure a long-term reliability. In recent years, it is required that materials used in several applications can sustain very
high numbers of load cycles without failure due to the ageing management of engineering plants and high-speed operation of engineering machines. In conventional fatigue design, the fatigue
limit was determined by the strength at a specified number of
stress cycles of 107. High strength steels, however, have shown
anomalous two-step or duplex S–N curves under rotating bending,
and fatigue fracture can take place at numbers of stress cycles beyond 107. In that case, inclusions in components play a significant
role for crack initiation and fatigue life [1–5].
Many components of engineering structures such as axles and
crankshafts are stressed not only with axial tension–compression
loads but also with cyclic torsion loads. So the fatigue strength under torsional loading is also important for the design of such components [6–11]. For coil springs, the loading mode is mostly
torsion, and it is often required that automotive valves operate
without failure in the giga cycle regime [12].
* Corresponding author. Tel.: +81 52 789 4673; fax: +81 52 789 3109.
E-mail address: akiniwa@mech.nagoya-u.ac.jp (Y. Akiniwa).
0142-1123/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijfatigue.2008.07.004
Since long testing times are necessary to investigate the regime
of very long fatigue life by using conventional fatigue testing machines operating with several tens of Hertz, testing machines operating with higher frequency are required. Ultrasonic fatigue testing
machines are very useful for accelerated fatigue testing [13–18].
Fatigue properties under torsional loading in the giga cycle regime
using ultrasonic fatigue testing machines were reported by StanzlTschegg [19], Mayer [20,21] and Bathias [22,23]. However, torsion
fatigue data available until now are not sufficient to understand
the fatigue properties in the giga cycle regime.
In the present study, ultrasonic fatigue tests under axial and
torsional loading were carried out with smooth specimens of a
spring steel (SWOSC-V). The fatigue strength for torsional loading
was compared with that for axial loading. The experimental results, considering the crack initiation site are discussed on the basis
of the size of non-damaging defects.
2. Experimental procedure
2.1. Material and specimen
The material used in this study was an oil-tempered Si–Cr steel
wire used for valve springs (JIS G3561, SWOSC-V). The chemical
composition of the material was as follows (wt%): C0.56, Si1.44,
2058
Y. Akiniwa et al. / International Journal of Fatigue 30 (2008) 2057–2063
Mn0.68, P0.012, S0.005, Cr0.70, Cu0.01. Fig. 1 shows shape and
dimensions of the specimens. The diameter in the center of the
specimens is 3 mm for axial tension–compression fatigue tests,
and 5 mm for torsional loading. The specimens were annealed at
1143 K, oil quenched, tempered at 683 K for 1 h and cooled in N2
gas. After heat treatment, the specimen surface was polished with
emery paper #800. Then a surface layer of 50 lm was removed by
electro-polishing in order to eliminate residual stresses. Finally, the
specimens were polished with alumina powder of 0.3 lm. As a result, the residual stress measured with the X-ray method was
nearly zero. The Vickers hardness after heat treatment is nearly
uniform over the cross-section, and the mean value is 598 HV.
The prior austenitic grain size is 16 lm.
The polished cross-sections of specimens were investigated
with a scanning electron microscope to measure the distribution
of the inclusion size. The inclusions identified by energy dispersive
spectroscopy were Al2O3, SiO2 and TiN. Fig. 2 shows the distribution of the inclusion size plotted in an extreme probability diagram. In a standard inspection area, S0 (0.242 0.182 mm2), the
inclusion of maximum size, (areamax)1/2, was measured and this
procedure was repeated 20 times. The largest inclusion expected
to exist in a critical volume of specimen was estimated with the
statistics of extreme value method [6,24] based on the double
exponential distribution. The standard inspection volume is defined by
a
b
Fig. 1. Shape and dimensions of specimens. (a) Axial loading. (b) Torsional loading.
V 0 ¼ h0 S0
ð1Þ
1/2
where h0 (1.4 lm) is the average value of (areamax) . The critical
volume, V (26.2 mm3) was defined as the region where the stress
is larger than 90% of the maximum stress in specimens used in axial
loading tests, and it was calculated using FEM. The return period
was calculated by
T ¼ V=V 0
ð2Þ
Then the largest inclusion of 7.9 lm could be obtained by the linear
extrapolation as shown in Fig. 2.
2.2. Fatigue test
Fatigue tests were conducted with an ultrasonic fatigue testing
machine under axial tension–compression and torsional loading,
as described in [20]. In these tests, specimens are stimulated to resonance tension–compression or torsion vibrations, respectively,
which causes fatigue loading of the sample. The cycling frequency
used is about 20 kHz and the stress ratio R = 1 in both experiments. Specimens were cooled with compressive air and fatigued
intermittently [17,25]. The operating time was selected to be
100 ms for axial loading and 150 ms for torsional loading. The
pause times were chosen in the range from 300 to 2500 ms
depending on the applied stress. The applied stress amplitudes
were determined from the measured strains using strain gauges attached in the centers of the specimens. For the stress calibration,
the stress amplitude was selected to be between 10% and 50% of
that of the fatigue test. The fatigue tests were stopped when the
endured number of stress cycles exceeded about 109 cycles, or
when a fatigue crack has formed. Initiation of a fatigue crack increases the specimen’s compliance and reduces the resonance frequency, and the experiments were stopped when the resonance
frequency dropped by 115 Hz in axial loading and 35 Hz in torsional loading tests. After the fatigue tests, the fracture surfaces
were investigated in a scanning electron microscope.
Single-edge-notched specimens with a width of 8 mm and a
thickness of 2 mm were fatigued at 30 Hz under axial tension–
compression. The crack propagation behavior was determined
using the load shedding technique. The rate of load shedding with
increasing crack length was set to be 0.08 mm1. The crack opening displacement was measured with an extensometer with a gage
length of 12.5 mm. The crack length was calculated by the unloading elastic compliance method [26] during the fatigue tests.
3. Experimental results and discussion
3.1. S–N curves
The S–N diagram for axial tension–compression is shown in Fig.
3. Open symbols characterize failures and closed symbols with arrows indicate run-outs. The scatter is somewhat large, however, no
duplex S–N curve can be observed. At a stress amplitude of
780 MPa, the shortest fatigue life is 7.0 106 cycles. On the other
hand, another specimen did not break within 1.1 109 cycles.
The fatigue strength at N = 109 cycles is between ra = 650 MPa
and 810 MPa. The regression line shown in Fig. 3 approximates
data of failed specimens assuming power law dependence of tension–compression stress amplitudes, ra, and cycles to failure, Nf,
according to Eq. (3).
ra ¼ 1:21 103 Nf0:027
Fig. 2. Distribution of inclusion size.
ð3Þ
Although the analysis based on the statistics was necessary to estimate the detailed S–N data, the results were simply approximated
by the power function in this study. The broken lines in the figure
show the 90% confidence interval. Although the hardness of all
Y. Akiniwa et al. / International Journal of Fatigue 30 (2008) 2057–2063
Fig. 5. Comparison of axial and torsional data in terms of equivalent stresses.
Fig. 3. S–N curve for axial loading.
specimens was measured again after fatigue tests, the value was
almost constant. The reason why the scatter is so large is not clear.
The results obtained for torsional loading are shown in Fig. 4.
The scatter is larger than that of axial loading. A clear knee point
cannot be seen. The fatigue strength at N = 109 cycles is between
sa = 468 MPa and 520 MPa. These stresses are smaller than those
of axial loading, and the ratio of torsional and axial cyclic strength
is between 0.64 and 0.72. Data of failed specimens are approximated assuming power law dependence of torsion stress amplitudes, sa, and cycles to failure according to Eq. (4).
sa ¼ 7:79 102 N0:024
f
ð4Þ
The mean ratio of torsional, sa and axial stress, ra at the same number of load cycles calculated with the two experimental equations is
about 0.68. The influence of number of stress cycles on the strength
ratio is small. Ratios of sa and ra reported for steel in the literature
vary between 0.58 and 0.72 [6–11]. In ultrasonic tests, ratios of 0.67
for the aluminum alloy 2024-T351 [20] and 0.60 for 0.15%C steel
[21] have been found.
In Fig. 5, the fatigue data measured in both testing series are
presented vs. equivalent stresses. In this work, the equivalent
stress amplitude of the von Mises type was adopted, and calculated
as follows.
req ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r2a þ 3s2a
ð5Þ
The S–N curve obtained for torsional loading is at about 17% higher
equivalent stresses compared with axial loading even in the giga cycle regime. This tendency is quite similar to that for the aluminum
alloy 2024-T351 [20].
3.2. Fracture surfaces
After fatigue testing, cracks with a few millimeters length could
be observed on the surface of failed specimens (indicated with
open symbols in Figs. 3 and 4). On the other hand, no non-propagating cracks could be observed on the surface of run-out specimens (characterized with solid symbols in the S–N diagrams).
Fig. 6a shows the fracture surface of a specimen broken after
Nf = 1.02 105 cycles in a tension–compression test at the stress
amplitude ra = 900 MPa, and Fig. 6b shows a specimen broken at
ra = 650 MPa in the giga cycle regime, at Nf = 1.76 109 cycles.
Although there is a rough region near the surface, the crack origin
was at the specimen surface. It is interesting to note that neither inclusions nor granular facet areas could be observed even in the giga cycle
regime. All specimens broke from the surface, and inclusions do not
influence the crack initiation process. In a bearing steel [27] and a nickel chromium molybdenum steel [28], interior fatigue crack initiation
from both, inclusions and microstructurally weak sites were found. In
those cases, granular facet regions could be observed in the giga cycle
regime, in contrast to the presently investigated material.
In general, a fatigue limit under axial loading can be predicted
from the Vickers hardness with the following equation [29].
rw0 ¼ 1:6 HV
Fig. 4. S–N curve for torsional loading.
2059
ð6Þ
The fatigue limit of the investigated steel calculated according to Eq.
(6) and using the Vickers hardness of 598 is 957 MPa. This value is
much higher than the experimental data as shown in Fig. 3. For high
strength steels, the fatigue limit becomes smaller than the calculated value due to fracture from inclusions [29]. Although the crack
origin is the specimen surface in this material, the fatigue limit is
smaller than the expected value.
Fig. 7a shows the surface of a specimen which broke after
Nf = 6.98 105 cycles at the torsion stress amplitude sa = 577 MPa.
Crack initiation was perpendicular to the longitudinal direction.
After the crack propagated about 28 lm in shear mode, it branched
and propagated in a mode I manner. Fig. 7b shows the fracture surface of this specimen. The fracture surface is smooth by ablation
due to shear motion. In the very high cycle fatigue regime, the
stage I crack was also initiated perpendicular to the longitudinal
direction as shown in Fig. 8a. The specimen broke after
Nf = 1.04 108 cycles at sa = 468 MPa. The length of the shear
2060
Y. Akiniwa et al. / International Journal of Fatigue 30 (2008) 2057–2063
Fig. 6. Fracture surface of specimens broken under axial loading. (a) Nf = 1.02 105,
ra = 900 MPa. (b) Nf = 1.76 109, ra = 650 MPa.
mode crack is 25 lm. Fig. 8b shows the fracture surface. In the
stage I region, the fracture surface is also smooth. On the other
hand, the roughness in the stage II region is larger than that of
the specimen broken at shorter fatigue life (see Fig. 7b), because
the ablation is not so pronounced at the lower stress level. Typical
fracture surfaces of mode I cracks are shown in Fig. 9a (sa = 491 MPa, Nf = 1.65 107 cycles) and Fig. 9b (sa = 468 MPa, Nf = 6.28 107
cycles). The fracture surfaces look similar to that of Fig. 8b. No
inclusions or granular facet areas are visible on the fracture surfaces. No correlation between length of the shear crack and applied
stress or stress intensity range could be detected.
For the spring steel investigated in this study, fatigue fracture
did not occur from internal defects. Namely, inclusions in the
material did not affect the fatigue strength, and the fatigue
strength was determined by the strength of specimen surface up
to the giga cycle regime. The relation between the fatigue strength
and the fatigue life could be estimated by a power law relationship
for both axial and torsional loading. The ratio of torsional and axial
stress at the same number of load cycles is almost constant irrespective of fatigue life. However, it is necessary to note that the fatigue strength for axial tension–compression is much lower than
the value expected from the hardness.
3.3. Non-damaging defect size
As described above, fatigue crack initiation was at the surface in
all specimens fractured in axial and torsion loading tests, and no
Fig. 7. Scanning electron micrographs of a specimen broken after Nf = 6.98 105
under torsional loading at sa = 577 MPa. (a) Specimen surface. (b) Fracture surface.
inclusions were found at the crack initiation sites. When the defect
is less than the critical size, specimens do not break from the internal defect. Then the critical condition of crack propagation is investigated from the viewpoint of non-damaging defect size to explain
why no specimen broke from internal inclusions. The threshold value of the stress intensity factor was determined in crack propagation tests under tension–compression. Fig. 10 shows the relation
between crack propagation rate and maximum stress intensity factor. The triangles indicate the data obtained for a nickel chromium
molybdenum steel (JIS SNCM439) [28]. The resistance against fatigue crack propagation of the spring steel is larger than that of the
nickel chromium molybdenum steel. For the spring steel, the
threshold value of the maximum stress intensity factor, Kmaxth is
4.5 MPa m1/2. Although the threshold value has also a statistical
property as well as fatigue strength, obtained value was used in
this study as a representative value. The fatigue strength calculated
according to Eq. (3) at the number of stress cycles of 109 is
691 MPa. The diameter of the characteristic defect calculated with
these values is 60.9 lm as shown in Fig. 11, where the stress intensity factor for the internal defect was calculated according to the
following equation [29,30]:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffi
K ¼ 0:5r p area
ð7Þ
2061
Y. Akiniwa et al. / International Journal of Fatigue 30 (2008) 2057–2063
Fig. 9. Fracture surface of torsional loading. (a) sa = 491 MPa, Nf = 1.65 107. (b)
sa = 468 MPa, Nf = 6.28 107.
-6
The size of the characteristic defect of high strength steels corresponds to that of a non-damaging defect. The maximum inclusion
size in the critical volume of a specimen is 7.9 lm as shown in
Fig. 2. Thus, the size of the maximum inclusion is much smaller
than the characteristic defect size. On the other hand, for the nickel
chromium molybdenum steel, the fatigue strength at Nf = 109 and
the threshold stress intensity factor are 750 MPa and 2.1 MPa m1/
2
, respectively [28]. In this case, the characteristic defect size is
11.3 lm. The value is close to the inclusion size of about 7–10 lm
observed on the fracture surface.
For the internal fracture, the granular facet size is also important. Fig. 12 shows the change in the facet size with the inclusion
size obtained for several high strength steels [27,31,32], where
the values of (area)1/2 are plotted in the figure. The facet size is
strongly associated with the inclusion size. If the inclusion size in
the critical volume is 7.9 lm, the facet size expected from Fig. 11
will be maximum about 40 lm. The stress intensity factor corresponding to the facet crack at Nf = 109 cycles (rw = 691 MPa) is
3.9 MPa m1/2. This value is smaller than the propagation threshold
of 4.5 MPa m1/2. For the internal cracks, since the crack propagates
without environmental effects of atmospheric air, the threshold
value of long cracks should be larger than 4.5 MPa m1/2 [28]. There-
10
Crack propagation rate. da/dN m/cycle
Fig. 8. Scanning electron micrographs of a specimen broken after Nf = 1.04 108
under torsional loading at sa = 468 MPa. (a) Specimen surface. (b) Fracture surface.
R=-1
SWOSC-V
SNCM439
-7
10
-8
10
-9
10
-10
10
-11
10
2
1
3
4 5 6 78
2
3
10
1/2
Stress intensity factors, Kmax MPam
Fig. 10. Relation between crack propagation rate and stress intensity factor under
axial loading.
fore, no internal crack can propagate at the stress intensity factor of
3.9 MPa m1/2. On the other hand, for the nickel chromium molybdenum steel, the calculated stress intensity factor for the same facet size at Nf = 109 cycles (rw = 750 MPa) is 4.2 MPa m1/2. The value
2062
Y. Akiniwa et al. / International Journal of Fatigue 30 (2008) 2057–2063
regime irrespective of fatigue life. The fatigue strength for axial
tension–compression is much lower than the value expected
from the hardness.
(3) Fatigue cracks were initiated in all specimens at the surface,
and no inclusions or granular facet areas could be detected at
the crack initiation site. Since the resistance against crack propagation from internal inclusions was relatively large, the inclusions did not affect the decrease in fatigue strength up to the
giga cycle regime.
Acknowledgement
The authors are thankful to Miss A. Nakamura of Nagoya University for her help concerning some experiments.
References
Fig. 11. Kitagawa diagram for SWOSC-V and SNCM439.
Fig. 12. Relation between facet size and inclusion size obtained for several high
strength steels.
is twice as large as the measured propagation threshold of
2.1 MPa m1/2, and the specimens thus could fail with cracks initiation in the interior [28]. Strictly speaking, the propagation threshold of small cracks is smaller than that of long cracks. Thus, the
effects of crack size should be investigated to further discuss the
threshold condition.
4. Conclusions
Smooth specimens of a valve spring steel were fatigued up to
the giga cycle regime under axial and torsional loading. Fatigue
strength and fracture morphology were investigated. The results
are summarized as follows:
(1) The fatigue strength of the spring steel was successfully
measured using ultrasonic fatigue testing. Fatigue property of
the spring steel up to the giga cycle regime could be clarified.
Although the scatter is somewhat large, the S–N curves
obtained for both, tension–compression as well as torsion fatigue loading could be approximated by power law functions.
(2) The ratio of the torsional fatigue strength and the axial fatigue strength at comparable number of stress cycles was about
0.68, and the value was almost constant up to the giga cycle
[1] Sakai T, Takeda M, Shiozawa K, Ochi Y, Nakajima M, Nakamura T, et al.
Experimental reconfirmation of characteristic S–N property for high carbon
chromium bearing steel in wide life region in rotating bending. J Soc Mat Sci
Jpn 2000;49(7):779–85.
[2] Murakami Y, Nomoto T, Ueda T, Murakami Y. On the mechanism of fatigue
failure in the superlong life regime (N > 107 cycles). Part 1: influence of
hydrogen trapped by inclusions. Fatigue Fract Eng Mater Struct
2000;23(11):893–902.
[3] Murakami Y, Nomoto T, Ueda T, Murakami Y. On the mechanism of fatigue
failure in the superlong life regime (N > 107 cycles). Part II: influence of
hydrogen trapped by inclusions. Fatigue Fract Eng Mater Struct
2000;23(11):903–10.
[4] Shiozawa K, Lu L. Very high-cycle fatigue behaviour of shot-peened highcarbon chromium bearing steel. Fatigue Fract Eng Mater Struct 2002;25(8/
9):813–22.
[5] Ochi Y, Matsumura T, Masaki K, Yoshida S. High-cycle rotating bending fatigue
property in very long-life regime of high-strength steels. Fatigue Fract Eng
Mater Struct 2002;25(8/9):822–3.
[6] Murakami Y. Metal fatigue: effects of small defects and nonmetallic
inclusions. Elsevier; 2002.
[7] Papadopoulos IV, Davoli P, Gorla C, Filippini M, Bernasconi A. A comparative
study of multiaxial high-cycle fatigue criteria for metals. Int J Fatigue
1997;19(3):219–35.
[8] Davoli P, Bernasconi A, Filippini M, Foletti S, Papadopoulos IV. Independence of
the torsional fatigue limit upon a mean shear stress. Int J Fatigue
2003;25:471–80.
[9] Billaudeau T, Nadot Y, Bezine G. Multiaxial fatigue limit for defective
materials: mechanisms and experiments. Acta Mater 2004;52:3911–20.
[10] Morel F, Flaceliere L. Data scatter in multiaxial fatigue: from the infinite to the
finite fatigue life regime. Int J Fatigue 2005;27:1089–101.
[11] Ninic D. A stress-based multiaxial high-cycle fatigue damage criterion. Int J
Fatigue 2006;28:103–13.
[12] Sonsino CM. Fatigue design of structural ceramic parts by the example of
automotive intake and exhaust valves. Int J Fatigue 2003;25:107–16.
[13] Neppiras EA. Techniques and equipment for fatigue testing at very high
frequencies. In: Proceedings of the 62nd annual meeting of ASTM, vol. 59.
ASTM; 1959. p. 691–710.
[14] Willertz LE. Ultrasonic Fatigue. Int Met Rev 1980;2:65–78.
[15] Stanzl S, Tschegg E. Influence of environment on fatigue crack growth in the
threshold region. Acta Metall 1981;29:21–32.
[16] Roth LR. Ultrasonic fatigue testing. In: Newby JR, Davis JR, Refsnes SK, Dietrich
DA, editors. ASM handbook, vol. 8. Philadelphia: ASTM; 1992. p. 240–58.
[17] Stanzl-Tschegg SE. Ultrasonic fatigue. In: Sixth international fatigue congress,
vol. III. Berlin: Elsevier Science Ltd.; 1996. p. 1887–98.
[18] Mayer H. Fatigue crack growth and threshold measurements at very high
frequencies. Int Mater Rev 1999;44(1):1–36.
[19] Stanzl-Tschegg SE, Mayer H, Tschegg EK. High frequency method for torsion
fatigue testing. Ultrasonic 1993;31(4):275–80.
[20] Mayer H. Ultrasonic torsion and tension–compression fatigue testing:
measuring principles and investigations on 2024-T351 aluminium alloy. Int J
Fatigue 2006;28:1446–55.
[21] Mayer H, Stanzl-Tschegg S. Very high cycle fatigue behavior under cyclic
torsion loading. In: 16th European conference fracture, Alexandroupolis,
Greece, July 3–7, 2006. p. 1123–4.
[22] Xue HQ, Bayraktar E, Marines GI, Bathias C. Torsional fatigue behaviour and
damage mechanism of the perlitic steel(D38MSV5S) in very high cycle regime.
In: Ninth international fatigue congress (Fatigue 2006), Atlanta, USA, May 14–
19. CD-ROM FT98.
[23] Marines-Garcia I, Doucet JP, Bathias C. Development of a new device to
perform torsional ultrasonic fatigue testing. Int J Fatigue 2007;29(911):2094–101.
[24] Murakami Y, Toriyama T, Coudert EM. Instructions for a new method of
inclusion rating and correlations with the fatigue limit. J Test Eval
1994;22(4):318–26.
Y. Akiniwa et al. / International Journal of Fatigue 30 (2008) 2057–2063
[25] Ishii H, Yamanaka K, Tohgo K. Giga cycle fatigue strengths in some high
strength steels by ultrasonic fatigue testing. Mater Sci Res Int
2001;STP1:59–63.
[26] Kikukawa M, Jono M, Tanaka K, Takatani M. Measurement of fatigue crack
propagation and crack closure at low stress intensity level by unloading elastic
compliance method. J Soc Mater Sci Jpn 1976;25(276):899–903.
[27] Akiniwa Y, Miyamoto N, Tsuru H, Tanaka K. Notch effect on fatigue strength
reduction of bearing steel in the very high cycle regime. Int J Fatigue
2006;28:1555–65.
[28] Akiniwa Y, Tanaka K. Evaluation of fatigue strength of high strength steels in
very long life regime. In: Third international conference on very high cycle
fatigue (VHCF-3), Shiga, Japan, September 16–19, 2004. p. 464–71.
View publication stats
2063
[29] Murakami Y. High and ultrahigh cycle fatigue. In: Milne I, Ritchie RO, Karihaloo
B, editors. Comprehensive Structural Integrity. Amsterdam: Elsevier; 2003. p.
1–76.
[30] Murakami Y. Analysis of stress intensity factors of modes I, II and III for
inclined surface cracks of arbitrary shape. Eng Fract Mech 1985;22:101–14.
[31] Miyamoto N, Asai H, Miyakawa S, Akiniwa Y, Tanaka K. Fatigue strength of
martensitic stainless steels in very high cycle regime. In: Third international
conference on very high cycle fatigue (VHCF-3), Shiga, Japan, September 16–
19, 2004. p. 314–21.
[32] Akiniwa Y, Miyamoto N, Tsuru H, Tanaka K. Very high cycle fatigue behavior of
high strength steels. In: 16th European Conference of Fracture,
Alexandroupolis, Greece, July 3–7, 2006. p. 1131–2.