review of fatigue

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A fracture mechanics approach to interior fatigue crack growth

in the very high cycle regime

Takeshi Ogawa a,1, Stefanie E. Stanzl-Tschegg b,⇑, Bernd M. Schönbauer b,2

a Aoyama Gakuin Univ., Dept. of Mechanical Engineering, Fuchinobe 5-10-1, Chuou-ku, Sagamihara-shi, Kanagawa 252-5258, Japanb University of Natural Resources and Life Sciences (BOKU), Peter Jordan Strasse 82, 1190 Wien, Austria

a r t i c l e i n f o

Article history:

Received 26 February 2013

Received in revised form 18 October 2013

Accepted 2 November 2013

Available online 14 November 2013

Keywords:

Ultrasonic fatigue

Cumulative damage

Repeated two-step tests

Fish-eye fracture

Fatigue crack growth

a b s t r a c t

Growth rates of optically dark areas (ODA) and fish-eyes (FE) were quantified in kHz-

ultrasonic fatigue tests on SUJ2 and 17-4PH steels at constant and repeated two-step

amplitudes. Sizes of ODAs and FEs depended on the stress intensity factor (SIF) range,

and interior fatigue crack growth rates (FCGR) were slower than those of ‘‘long’’ cracks

in air, suggesting vacuum as ODA growth environment. Repeated two-step tests on SUJ2

steel served to form beach marks so that, a quantification of ODA sizes, interior FCGRs

and SIFs became possible. Additional FCGR measurements of long cracks in vacuum and

comparable fracture morphologies allowed estimating the growth rates of ODAs and FEs

in 17-4PH steel.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the demand for longer fatigue lives in technical equipment and constructions, research on fatigue failure has at-

tracted increased attention recently. Responding to this demand, material scientists continually develop new materials with

improved fatigue properties, therefore also relying on exact fatigue failure measurements.

As early as 1978, Schijve emphasized the importance of internally growing cracks in aluminum alloys and showed that the

resulting fatigue lives were determined by such cracks growing in a vacuum under realistic loading conditions [1]. In the

1980s, research on the very high cycle fatigue (VHCF) properties of high-strength steels received a most important input,

namely the detection of failures beyond the traditionally assumed fatigue limit in the regime of 10 6–107 cycles [2,3]. More-

over, under special conditions (i.e. material properties, surface condition, amplitude of loading, number of cycles, etc.) such

VHCF failures were found to originate in the interior of the specimen, whereas fatigue cracks in the regime of up to approx-

imately 107 cycles usually start from some kind of surface imperfections. Since that time, interior fatigue crack initiation has

been discovered in other materials than high-strength steels as well. In addition, cracks were found to originate not only

from inclusions, but also from interior pores or porous areas in cast aluminum alloys [4] or even from internal persistent

slip bands in polycrystalline high purity copper [5].

Numerous investigations were performed to determine how structural features such as grain size, morphology and size of

inclusions, surface treatment and pre-straining influence the fatigue strength and fatigue life of different materials such as

0013-7944/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engfracmech.2013.11.007

⇑ Corresponding author. Tel.: +43 1 47654 5160; fax: +43 1 47654 5159.

E-mail addresses: [email protected] (T. Ogawa), [email protected] (S.E. Stanzl-Tschegg), [email protected]

(B.M. Schönbauer).1 Tel.: +81 42 759 6203; fax: +81 42 759 6502.2 Tel.: +43 1 47654 5169; fax: +43 1 47654 5159.

Engineering Fracture Mechanics 115 (2014) 241–254

Contents lists available at ScienceDirect

Engineering Fracture Mechanics

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c at e / e n g f r a c m e c h

http://dx.doi.org/10.1016/j.engfracmech.2013.11.007mailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.engfracmech.2013.11.007http://www.sciencedirect.com/science/journal/00137944http://www.elsevier.com/locate/engfracmechhttp://www.elsevier.com/locate/engfracmechhttp://www.sciencedirect.com/science/journal/00137944http://dx.doi.org/10.1016/j.engfracmech.2013.11.007mailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.engfracmech.2013.11.007http://-/?-http://-/?-http://-/?-http://-/?-http://crossmark.crossref.org/dialog/?doi=10.1016/j.engfracmech.2013.11.007&domain=pdf


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Austenitic stainless steels [6]. A comprehensive overview of the most important findings by Li [7] was published recently.

The study investigates the effects of hydrogen, vacuum, the boundary segregation of fine grains and carbides. According

to Li, most of the fatigue life is spent on the formation of a characteristic fracture surface morphology. This characteristic

fracture surface is called ODA (optically dark area) [8] because it looks dark when observed with an optical microscope, while

the same region is also called FGA (fine granular area) [9] or GBF (granular bright facet) [10] based on the morphology. Thus,the terms correctly indicate the morphological characteristics and the term ODA is used in this paper, because optical

microscopy was the main means of determining the sizes of the regions.

Detailed fractography and transmission electron micrographs both led to corresponding roughness values of ODAs [9,11]:

compared to the original material microstructure, the grain size of the ODAs’ subsurface structure is extremely reduced [12].

Another remarkable characteristic of ODAs is that a similar morphology can be observed for different material systems, i.e.

high strength steels [13], titanium alloys [14–16] and aluminium alloys [17]. In addition, such a morphology can also be

found on the fracture surface of compact tension (CT) specimens made of these materials for standard FCG tests when tested

in a high vacuum environment [13,14,18,19].

Several theories try to explain the formation of ODAs: Murakami [20] emphasizes the influence of hydrogen, e.g. hydro-

gen assisted fatigue crack growth. Oguma [12] proposes the segregation of extremely fine grains of material as influencing

and accompanying ODA formation and Shiozawa et al. [21] emphasize the importance of the segregation of fine carbides and

subsequent formation and coalescence of microcracks. At variable amplitude loading, beach marks were formed on the frac-

ture surface of the fish-eye region around the ODA. These were used to characterize the ODA’s and fish-eye’s growth rate of an ODA using a fracture mechanics approach [22].

Only very few papers using fracture mechanical methods to quantify the areas of fish-eyes and especially ODAs around

inclusions manage to give quantitative results for fatigue crack propagation rates and stress intensity factors [9,17,23–30]. In

the present study, ultrasonic fatigue tests were performed on high carbon chromium bearing steel, SUJ2, and a precipitation

hardened chromium–nickel–copper steel, 17-4PH, at constant amplitudes. Furthermore, two types of two-step amplitude

stressing tests were conducted on SUJ2 steel in order to investigate the fatigue damage accumulation and the growth behav-

ior of interior cracks. Based on these results together with those from the literature, a formation mechanism of the ODA is

proposed.

2. Material and experimental procedures

The tested materials were SUJ2, a high carbon chromium steel for bearings (Japan industrial standards JIS) and 17-4PH, aprecipitation hardened chromium–nickel–copper steel which is often used for steam turbine blades. Their chemical compo-

sitions and mechanical properties are presented in Tables 1 and 2, respectively. The SUJ2 steel was oil quenched from 850 C

and tempered at 180 C for 120 min. The 17-4PH steel was age hardened at 620 C (condition H1150) and stress relief an-

nealed at 600 C. The specimen shapes for the SUJ2 steel and the 17-4PH steel are shown in Fig. 1(a) and (b), respectively.

The surfaces of the test specimens were polished with abrasive paper in axial direction (final grade 2000 for SUJ2 and 4000

for 17-4PH).

Nomenclature

CT compact tensionda/dN fatigue crack growth rate in mDf cumulative damageN number of cyclesODA optically dark area within fish-eye fracture surface

R stress ratioSEM scanning electron microscopeS –N curve plot of stress versus number of cycles to failureDK stress intensity factor in MPa

p m (defined by tensile component, i.e. amplitude of cyclic stress at R = 1 in

this paper)

Table 1

Chemical composition (mass%) of SUJ2 and 17-4PH steel.

Material C Si Mn P S Ni Cr Mo Cu Nb + Ta O (ppm)

SUJ2 1.00 0.17 0.39 0.017 0.006 0.08 1.40 0.03 – – 5.00

17-4PH 0.033 0.40 0.49 0.027 0.001 4.37 15.57 3.31 0.23

242 T. Ogawa et al./ Engineering Fracture Mechanics 115 (2014) 241–254

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For the ultrasonic fatigue tests on the SUJ2 steel, a machine consisting of an ultrasonic welder (BRANSON Co., CR-20), a

power supply (2000bcd) and software developed at Aoyama Gakuin University (where the experiments were performed)

were used. The cyclic frequency of testing was 20 kHz, and the displacement amplitude at the specimen end lay between

10 and 50lm. Fully reversed loading fatigue tests (R =1) were performed in laboratory air at 24 C with a relative humidityof less than 40%. The Dr values were defined as the tensile component of the stress range for the experiments at R =

1 in

this paper. In order to reduce specimen heating by the high-frequency ultrasonic vibration, compressed cold air was blown

on the specimen surface using a vortex tube, the specimen temperature was monitored with a radiation thermometer and

intermittent loading was employed: typical loading conditions in the constant amplitude test were 120 ms loading with

360–1500 ms pauses. The experiments on the 17-4PH steels were performed at the University of Natural Resources and Life

Sciences in Vienna using closed-loop controlled ultrasonic equipment with vibration gauges serving as feed-back for the

amplitudes [5,17]. The total strain ranges were, in addition, measured with small strain gauges (1 mm gauge length,

2.10 ± 1.0% gauge factor) resulting in a strain measurement accuracy of 2% in all cases. The stress ranges were determinedfrom the strain ranges using Hooke’s law. Intermittent loading with pulse lengths of 2000–10000 cycles and pauses of 500–

1000 ms, depending on the amplitude, served to cool the specimens. The experiments were performed at R = 0.05 by super-

imposing a static tension load with a servo-hydraulic machine. The test temperature was kept constant at 90 C.

Besides constant amplitude loading, two-step and repeated two-step loading tests were performed on the SUJ2 steel. In

the two-step tests (see Fig. 2(a)), the initial stress amplitude Dr1 was 1200 MPa and was applied up to the average number of

cycles to failure determined in the constant amplitude tests (N 1 = 6.85

106). This was followed by a second stress ampli-

tude, Dr2 with values between 1100 and 850 MPa, which was applied either until fracture occurred or until the shut-off

number of cycles, N 1 = 1 1010, was reached (if no fracture occurred).In the repeated two-step tests, a higher stress amplitude DrH = 1200 MPa and lower stress amplitude DrL = 1050 or

850 MPa were repeated alternately until fracture, see Fig. 2(b). Table 3 shows the different testing conditions used in the

repeated two-step tests. Most of the tests began with the application of DrL followed by DrH, which is defined as one block.

The number nH of cycles with DrH, was either nH = 1.0 103 or 1.0 104, and the number nL of cycles with DrL was variedwidely according to the nH/nL values indicated in Table 3. The symbols used to designate the different testing conditions in

the following figures are also listed in Table 3.

The cumulative damage, Df , is defined by Eq. (1), where N Hf and N Lf are the numbers of cycles to failure for DrH and DrL ,

respectively, on the regression line of experimental data (Dr versus N F) as shown in Fig. 3. The cumulative damage forDrH is

defined by Eq. (2).

Df

¼XnH

N Hf þXnL

N Lf ð1

Þ

Table 2

Mechanical properties of SUJ2 and 17-4PH steel.

Material Tensile strength (MPa) Yield strength (MPa) Young’s modulus (GPa) Poisson’s ratio Vickers’ hardness Density (kg/m3)

SUJ2a – – 205 0.28 747 7830

17-4PHb 1030 983 195 – 352 7800

a Quench: 850 C: 50 min., Temper: 180 C: 120 min.b Condition H1150, Stress relieved at 600 C: 60 min.

Fig. 1. Specimen shapes of SUJ2 specimen (a) and 17-4 PH steel (b).

T. Ogawa et al. / Engineering Fracture Mechanics 115 (2014) 241–254 243

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DH ¼X nH

N Hf ð2Þ

3. Results and discussion

3.1. Constant amplitude and two-step amplitude tests

Fig. 3 displays the fatigue life diagram resulting from the constant amplitude and two-step amplitude tests on SUJ2. The

line represents a linear regression of eight fatigue lives under constant amplitude loading. In the two-step amplitude tests,

Fig. 2. Schematic of two-step tests (a) and repeated two-step tests (b).

Table 3

Testing parameters of four kinds of repeated two-step tests with symbols as used in Figs. 7, 9 and 10.

DrL (MPa) DrH (MPa) Starting stress nH (cycles) nH/nL Symbol

1050 1200 DrL 1.0 103 2.0 103 1.0 s1.0 104 5.0 102 2.0 101 4

DrH 1.0 10

3

1.0 101

2.5 101

h

850 DrL 1.0 103 1.0 d

Fig. 3. S–N curve under constant and two-step loading of SUJ2 steel.


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the first-step cyclic stress amplitude, Dr1 = 1200 MPa, was applied for N 1 = 6.85 106, which corresponded to the averagenumber of cycles to failure at this stress range in the constant amplitude tests. In order to avoid confusion, broken specimens

under the first-step amplitude tests were ignored. Then a second-step cyclic stress amplitude was applied until all specimens

which had survived the first step (in Fig. 3, only those specimens are plotted) fractured. Therefore, the cumulative damageDf of these specimens exceeded unity. However, the N f values resulting from the secondary cyclic stress (added to the first step

cyclic stress) were lower than the ones of the constant amplitude test, which suggests that the Df values lay below two.

Fish-eye fractures originated from interior inclusions in all tested specimens. Fig. 4 shows the optical micrographs,

depicting a specimen after the constant amplitude test at Dr = 1200 MPa (a) and after the two-step test at Dr1

= 1200 MPa

followed byDr2 = 900 MPa (b). In both cases, ODAs, are visible, their sizes depending on the test conditions. An inclusion can

be seen at the center of each ODA.

The areas of the inclusion, ODAs and fish-eyes were measured and their square root values,p

area, were used to calculate

the stress intensity factor DK , using the equation for interior cracks [25]:

DK ¼ 0:5 Dr ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffi areap

q ; ð3Þ

Dr being the stress amplitude for R =1 or the stress range for R = 0.05. DK thus always corresponds to the tensile compo-nent of the cyclic stress.

Fig. 5(a) presents the square root of the inclusion sizes,p

areaInc and their stress intensity value,DK Inc, as a function of Dr

for the SUJ2 and the 17-4PH steel: bothp

areaInc and DK Inc were independent of Dr. The DK Inc values varied between 2.3 and

4 MPap

m. Fig. 5(b) shows the square root value of the areas and the stress intensity factors for the ODAs, denoted asp areaODA and DK ODA, respectively. The values of DK ODA were almost constant, ranging from 5 to 5.5 MPa

p m for both steels.

This almost constantDK ODA value implies that this is the border line between the ODA and the fish-eye, i.e. a criterion for thetransition of the crack from an ODA to the neighboring fish-eye area. Equally, the stress intensity values of DK FE for the fish-

eyes in SUJ2 steel (Fig. 6) were approximately constant, ranging from 16 to 21 MPap

m, which agrees with the fracture

toughness measured in a standardized fracture mechanical test with a CT specimen. The asterisks in Fig. 6 mark the cases

in which the fish-eyes joined the specimen surface. In these cases, DK FE was calculated using the following equation [25]:

DK ¼ 0:65 Dr ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffi areap

q ð4Þ

To summarize, the DK Inc and DK ODA values in the threshold regime were rather similar (assuming that only the tensile por-

tion of cyclic loading contributed to the crack propagation) although two different steels were investigated: DK Inc lay be-

tween 2.17 and 3.03 MPap

m and DK ODA was 5.02–5.79 MPap

m (cf. Fig. 5). These similarities were found even though

different testing equipment was used and the R-ratio was different (R = 1 for SUJ2 and R = 0.05 for 17-4PH).

Fig. 4. Optical micrographs of SUJ2 showing ODAs after a constant amplitude loading test at Dr = 1200 MPa (a) and a two-step loading test atDrH = 1200 MPa followed by DrL = 900 MPa (b).


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The run out specimen in Fig. 3 tested at Dr2 = 850 MPa (2nd step) was broken by subsequent fatigue loading at

Dr = 1200 MPa. On the fracture surface, a large ODA with DK ODA = 6.3 MPap

m was observed. This value is apparently larger

than that of the DK ODA demonstrated in Fig. 5(b) suggesting that the ODA grew due to the cyclic stress at Dr = 850 MPa. In

order to confirm this hypothesis, two similar experiments were conducted by applying different run-out numbers of cycles

(N = 2.0 109 and 3.0 1010) at Dr2 = 850 MPa. In both tests, however, the specimens did not break at Dr2 = 850 MPa andwere subsequently broken at Dr = 1200 MPa. The calculated values of DK ODA for these two experiments were 5.3 and

5.1 MPap

m, respectively. These results indicate that in contrast to the above mentioned expectation, there is no growth

of ODA at a cyclic stress of Dr2 = 850 MPa and that in addition, the statistical scatter of DK ODA values and the sizes of the

ODAs is rather large.

Fig. 5. Size and stress intensity factors of SUJ2 for cyclic stress amplitudes at fracture and cyclic stress ranges at fracture of 17-4PH steel for inclusions (a)

and optically dark areas (b).


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The resulting DK Inc and DK ODA values for different sizes of inclusions and ODAs in constant amplitude tests are summa-

rized in Fig. 5(a) and (b) for SUJ2 and 17-4PH steel. Although two different steels were investigated, their DK Inc and DK ODA in

the threshold regime are rather similar – assuming that only the tensile portion of cyclic loading contributes to crack prop-

agation -, with DK inc between 2.17 and 3.03 MPap

m and DK ODA 5.02–5.79 MPap

m, though different testing equipment

was used and the R-ratio was different (R = 1 for SUJ2 and 0.05 for 17-4PH).

3.2. Repeated two-step amplitude tests

Fig. 7 presents the cumulative damage at fracture Df , resulting from the repeated two-step amplitude tests, as a function

of nH/nL . Furthermore, Fig. 7 also shows the value of the damage ratio by higher stress cycles, DH/Df , of the tests with

DrL = 1050 MPa and 850 MPa. In the tests with DrL = 850 MPa (black dots), DH/Df was higher than 0.95 which indicates that

Df was mainly caused by the higher stress cycles. When DrL was chosen to be 1050 MPa (open symbols), the scatter of the Df values was much larger, lying between 0.40 and 14.29, and no correlation with nH/nL was obvious. Since, however, in five of

33 experiments, Df values lower than one resulted, it is assumed that a two-step variation of the stress amplitude increases

the fatigue life when increasing the ratio nL /nH.

Fig. 6. Sizes and stress intensity factors of fish-eyes for stress amplitudes at fracture in SUJ2.

Fig. 7. Relationship between cycle ratios and cumulative damage values (symbols explained in Table 3).


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A fish-eye fracture surface originating from an interior inclusion was observed in all he tested two-step specimens.

Fig. 8(a)–(c) show the optical micrographs of a specimen tested with the starting stress range of DrL = 850 MPa

(nL = 1.0 104, nH = 1.0 103 and N f = 2.87 108) using different magnifications in order to show fish-eye, beach marksand ODA, respectively. ODAs can be seen around the inclusions in all the fractured specimens after two-step tests. Beach

marks were identified in the fish-eye regions but not in the ODAs. The variation of the growth increment of the beach marks

depended on the nH/nL values (see next section), and the relationships revealed that the dark and bright fracture surfaces

corresponded to the crack growth increments caused by DrH and DrL , respectively. Fig. 8(d) presents a scanning electron

microscope (SEM) image of an ODA obtained by backscattering electron imaging; the morphology of the ODA region around

the inclusion is granular. The stress variations were not visible in the high magnification SEM micrograph, which is in agree-

ment with the optical result. The SEM observation indicated that the dark beach mark regions in the fish-eye region were

slightly rougher than the bright one. The number of beach marks in the fish-eye region outside the ODA area indicated that

the number of cycles to form this fracture surface was less than 1% of the total fatigue life, and most of the fatigue cycles

were spent for the formation of the ODA. Therefore, the number of cycles to form an ODA is concluded to be approximately

the same as the total fatigue life.

Fig. 9 shows the relationship betweenp

areaInc and nH/nL , where, as expected, no correlation could be found. This result

and the mentioned tendency of Df to decrease with a decreasing ratio of nH /nL in Fig. 7 provides the relationship between Df and

p areaInc shown in Fig. 10. Ignoring the two exceptions of very small inclusion sizes, Df tended to decrease with an

increasingp

areaInc, and the values were smaller than the one for the three largest inclusions. This result implies that Df de-

pends on the inclusion size at the fracture origin in the repeated two-step tests.

Fig. 11 presents the variations of p

areaODA and DK ODA with nH/nL . Some of the ODAs had different shades of darkness, as

shown in Fig. 12(a). As can be seen, the ODA is the darker interior region, and it is concluded that the widths of outer region

represent different nH/nL conditions: this assumption is based on a comparison of the image with the SEM micrograph shown

in Fig. 12(b). The outer less dark region in Fig. 12(a) grew due to a high stress range, similar to the beach mark region pre-

sented in Fig. 8(b). This fact suggests that the transition from ODA to fish-eye region occurred as soon as the high stress

amplitude was applied, and thusDK ODA should be calculated forDrH = 1200 MPa. When nH/nL was larger than 0.1, the values

of DK ODA were approximately the same as those presented in Fig. 5(b) for constant amplitude and two-step tests. However,

the ODAs tended to increase with decreasing nH/nL , i.e. increasing nL . This means that a high number of lower cyclic stresses

augmented the size of the ODA. Such behavior can be explained by the following: when an ODA reaches the size at which its

DK exceeds the constant value of DK ODA shown in Fig. 5 at DrH = 1200 MPa, a transition of the growth mechanism from the

ODA to the fish-eye region mechanism may occur. If, due to the limited number of cycles, DK at DrL becomes lower than the

critical DK ODA at the cyclic stress of DrL = 850 MPa, the growth mechanism returns to the ODA mechanism. This sequence is

repeated until transition from ODA to fish-eye mechanisms occurs in the following way: when the high cyclic stress is

Fig. 8. Optical and scanning electron micrographs showing a fish-eye (a), beach marks (b), an ODA (c) and an inclusion (d) for DrL = 850 MPa, nH = 1 103

and nL = 1 104. Note that the red and blue arrows in (b) indicate the crack growth increment under high and low stress ranges, respectively.


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reapplied, DK becomes higher thanDK ODA and the crack grows. When the stress is reduced, i.e. at the beginning of low cyclic

stressing at a period of the high cyclic stress, where DK was higher than DK ODA, the crack ceases to grow.

If the value of DK is calculated using the size of the outer contour of the dark area shown in Fig. 12(a) together with DrL, a

value of 8.8 MPap

m results, which exceeds the transition DK ODA by far. Oguma et al. [19] observed an ODA-like fracture sur-

face morphology on fatigue fracture surfaces which had repeated contact in a high vacuum environment. This observation

supports our theory of the ODA growth sequence: fish-eye growth increments change to ODA growth by the repeated surface

contact under DrL conditions. This will be discussed in more detail in 3.4.

3.3. Growth characteristics of interior crack

The beach marks shown in Fig. 8 provide growth rates for the interior crack in the fish-eye region [22]. Fig. 13 represents

the relationships of the crack growth rate, da/dN , and the stress intensity factor range, DK .

The crack growth increments for DrL and DrH are denoted DaL and DaH, respectively. The crack growth rate da/dN was

determined by DaL /nL or DaH/nH; the corresponding DK was obtained from the area inside of the beach mark and the applied

Dr according to Eq. (3). The error bars for DK in Fig. 13 correspond to the widths of beach marks, i.e. DaL or DaH. For com-

parison, Fig. 13 also presents the growth characteristics of a long crack, which grew in a CT specimen in air at a stress ratio of

0.1 in a standard fracture mechanics test [31]: clearly, the interior crack growth rates obtained by the beach marks are lower

than those observed on the CT specimen. A possible reason for this deviation is the environment: while it is assumed that

interior cracks grow in a vacuum (the vacuum quality, however, has not been determined up to now), the crack in the CT

specimen grew in air.

To verify this assumption, crack growth experiments in vacuum are necessary, which, however, could not be performed

with this material. Instead of that, fracture surfaces of crack propagation tests on 12% Cr steel in a vacuum of approx. 103 Pa

Fig. 9. Relationship between cycle ratios and inclusion sizes under repeated two-step amplitude stressing (symbols explained in Table 3).

Fig. 10. Relationship between inclusion sizes and cumulative damage values Df under repeated two-step amplitude stressing (symbols explained in

Table 3).


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Fig. 11. Sizes and stress intensity factors of ODAs under repeated two-step amplitude stressing.

Fig. 12. Micrographs showing a double shaded ODA after tests with DrL = 850 MPa, nH = 1 103 and nL = 1 106 observed with an optical microscope (a)and a scanning electron microscope (b).



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at 19 kHz and very high numbers of cycles are used and compared with the fracture morphology of ODAs [13]. It was con-

cluded that within the ODAs, the growth rates were in the range of approximately 1012 m/cycle. The growth rates in the‘‘smooth’’ area adjacent to the ODAs were found to be below approximately 1011 m/cycle [13]. Based on the similaritiesof the fracture morphologies of fish-eye regions and long-crack fracture surfaces formed in a vacuum, it was further con-

cluded that fracturing occurs according to fracture mechanical laws for long cracks with rates depending on the prevailing

stress intensity factor. As soon as the maximum stress intensity factor exceeds the threshold stress intensity factor for fati-

gue crack propagation of long cracks, higher crack growth rates – ranging from around 109 m/cycle up to about 107 m/cy-cle – will occur outside the fish eye, thus forming the contour of the fish-eye. As stated earlier, the cycle ratio of this fish-eye

growth phase to the total fatigue life is believed to be very small in comparison with the ODA growth and crack initiation

stage. Concerning the environmental question, these studies confirm that vacuum is the crucial environment for fatigue

crack propagation in the ODA, and the authors assume that it is justified to apply this result to the SUJ2 steel.

Concerning fatigue crack growth within the whole fish-eye area (not only ODA), numerous interesting studies are re-ported in the literature. Since this paper, however, is focused on the ODA growth, only few important studies are mentioned.

Petit and Sarrazin-Baudoux [31] developed a model based on plastic deformation accumulation controlling intrinsic crack

propagation in vacuum. They estimated the life of high strength steels with cracks that initiated at a fish-eye and could show

that the portion of life due to crack propagation in vacuum was two to three orders of magnitude greater than in air. This

result confirms the measurements of this study. In [32], ultra-slow fatigue crack propagation at ultrasonic frequency is

treated.

Murakami [20] discovered the influence of hydrogen content trapped around inclusions to play an important role during

internal fatigue crack growth. The extremely low crack growth rates of the ODAs measured in the present study, however,

rather exclude the influence of hydrogen. In a more recent study [33], Murakami pointed out that ‘‘most of life cycles N f are

spent in the ODA area’’. He distinguishes between material containing 0.8 ppm and, respectively, 0.1 ppm hydrogen (Cr–Mo

steel SCM 435 after different heat treatment) and suggested a master curve for the number of cycles to failure N f versus

(p

areaODA/p

areaInclusion). This curve showed material independence at a hydrogen content of 0.2–0.9 ppm. For material con-

taining only 0.2–0.3 ppm hydrogen, a modified model for the fatigue limit was suggested considering that ‘‘the ODA grows asa crack’’. Further work is planned to apply this model to the results of the present study.

The ODA growth rates in the two-step tests of the present study could be estimated making some assumptions, as ex-

plained in the following: in the present study, the first step of Dr1 = 1200 MPa was applied up to a number of cycles that

was somewhat smaller than the number of cycles to failure obtained in the constant amplitude test given in Fig. 3. At this

point, we assumed, an ODA of similar size as those observed in the constant amplitude tests at Dr = 1200 MPa had been

formed. In the subsequent second step, after applying a second defined stress Dr2, this ODA then grew up to the size ob-

served at fracture. In other words, we considered the ODA at Dr1 = 1200 MPa as a pre-crack, which grew at the cyclic stress

amplitude during the second step without any effects of stress history. Fig. 13 shows the da/dN values calculated by the ODA

growth increment divided by the number of cycles to failure during the second step, in which the number of cycles to form a

fish-eye was ignored owing to their much smaller values. The values of DK were determined by the Dr of the second step

together with the initial and final sizes of the ODA, whose corresponding values are characterized by the error bars. As can be

seen, the growth rate of a fish-eye is ten to hundred thousand times larger than that of an ODA. This great difference in the

growth rates seems to be the most probable reason for the apparent change in the fracture surface morphology.

Fig. 13. Relationship between da/dN and DK . Closed symbols: determined from measurements on CT specimens in air. Open symbols with DK in the range

of 7 to 16 MPa: determined from measurements of fish-eye beach marks; open symbols with DK around 5 MPa: determined from radii of ODAs.


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3.4. Mechanism of ODA formation

For further investigation of the mechanism of ODA formation, three-dimensional fracture surface observations were per-

formed using an atomic force microscope (AFM, Keyence Co. VN-8000) for two different conditions of repeated two-step

tests, i.e. nH/nL = 0.20 and 0.02 for nH = 1.0 103. Fig. 14 presents surface roughness profiles resulting from these two differ-ent testing conditions: AFM1 and AFM2 are images of the two opposite fracture surfaces of a specimen after testing with nH/

nL = 0.20(a) and nH/nL = 0.02 (b). The graphs on the right show the sectional appearances along the dashed lines in the photos

on the left, which are considered to be corresponding locations. The sectional appearances revealed that the pair of the ODA

surfaces match nicely, as reported earlier by Shiozawa et al. [9,21].

In the past, significant suggestions for the mechanism of ODA formation were made. Some came from Oguma et al. [12] as

mentioned above, from Furuya et al. [27,28] and Nakajima et al. [29], who studied the development of ODAs, crack initiation

and fatigue limit of SUJ2 steel with two-step loading tests with a rotating bending machine. Other important inputs came

from Murakami et al. [20], Murakami and Matsunaga [33] and Petit and Sarrazin [31,32] as mentioned above.

The present study revealed that the growth of ODAs is ten to hundred thousand times slower than that in the outer fish-

eye regions, though both may be assumed to occur in a vacuum. Also, in the repeated two-step tests, the growth increment

under high stress amplitudes obviously changed to ODA growth, as was concluded from the experiments with higher run-

out numbers of cycles at the ‘‘high’’stress amplitudes (cf. last paragraph of 3.1). This was probably due to the repeated con-

tact under the low stress amplitude. Higher growth rates after the beginning of ODA formation owing to the initial absence of

crack closure effects could not be observed in this study, but cannot be excluded.

The very slow growth of the ODAs may be explained by the following mechanism based on Oguma’s study [19], which

applies to ODA formation: it is assumed that the ODA morphology is formed by repeated fracture surface contact. In a vac-

uum, fracture surface roughness induces local contact, so that such locations may re-bond (cold-weld) because the surface is

active in a vacuum. During the following loading, the welded location may undergo plastic deformation and local cold work

may occur. These considerations are based on numerous pioneer studies on fatigue crack initiation and propagation being

influenced by contact of rough fracture surfaces, rewelding of fresh fracture surfaces and enhanced plasticity thus leading

to longer fatigue lifes [34–37]. If fatigue loading is repeated for a long time, the local cold work may produce fine grains

as observed by Oguma et al. [12] in the TEM. The results strongly suggest that the repeated contact in a vacuum produces

the ODA morphology. Since ODAs grow extremely slowly and discontinuously, the repeated fracture surface contact in a vac-

uum takes place very often, so that a very fine grained microstructure is formed. Thus, the darkness of the ODA seems now to

have the consensus interpretation of being caused by an extreme surface roughness associated with a fine granularity. Fur-

ther investigations, for example, introducing Murakami’s ideas [33] are needed to clarify the mechanisms being relevant for

the ODA formation.

The diffusive nature of the process of small grain formation could be explained as follows: low stress amplitudes, as those

discussed above, lead to shear crack propagation, which produces multiple crack plane deviations. Thus, the local strains at

the asperity interactions and the crack tip are probably very high and would therefore induce very intense point defect cre-

ation. This is one possible cause of a diffusive transformation in the near crack surface grain structure. Another possible cause

can be excluded, namely a significant global temperature rise in the specimen owing to the high frequency of stressing. Such

a global heating was refuted by comprehensive experimental measurements [5]. Very localized temperature increases, how-

ever, cannot be excluded, so that both welding and recrystallization would be possible. An important argument against a

Fig. 14. Surface roughness profile of a fracture surface after repeated two-step amplitude stressing; DrL = 1050 MPa, n H = 1 103

and nL = 5 103

(a),DrL = 1050 MPa, nH = 1 103 and nL = 5 104 (b).


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high-frequency influence is offered by the results of Furuya et al. [27]. They found ODAs at testing frequencies of 100 Hz,

600 Hz and 20 kHz around inclusions of Al2O3 or Al2O3.CaO and, in addition, a frequency independence of the S –N diagrams

for low-temperature-tempered JIS SNCM430 steel. As can be concluded from the above mentioned considerations, ODAs are

probably formed by repeated fracture surface contact in a vacuum without the influence of the original material microstruc-

ture such as grain size. This interpretation also implies that ODA formation is a crack propagation mechanism and cannot be

considered as crack initiation, as assumed by a few authors (e.g. [30]).

After hydrogen and fine carbides were found to affect the growth rates of ODAs [12,20,21]. the finding of the present study

that the ODAs’ morphology was independent of these influences seems interesting. The other characteristic of ODAs – theirpresence in different materials (in high-strength steels [7,9–12,22,27–29], titanium alloys [15,16,18,19], medium strength

alloy steel [13,38,39] and Al alloys [17]) – is corroborated by examples of ODAs in AISI 420 Cr steel, AISI 316L-PM/HIP steel

and spray formed hypereutectic Al–Si alloy in Fig. 15.

4. Conclusion

In the present study, ultrasonic fatigue tests at constant amplitudes were carried out on SUJ2, a high-strength carbon

chromium bearing steel, and 17-4PH, a precipitation hardened chromium-nickel-copper steel at constant amplitudes. In

addition, two-step and repeated two-step amplitude tests were performed on the SUJ2 steel in order to investigate fatigue

damage accumulation and growth behavior of interior cracks. The results obtained are summarized in the following:

(1). In all steels tested in the present study, the fracture origin was from an interior inclusion, around which an optically

dark area (ODA) and fish-eye regions were observed. Their sizes decrease with increasing stress amplitude, whereby

the stress intensity factors (SIF) remain approximately constant.

(2). In the repeated two-step amplitude stress tests, the cumulative damage Df scattered between 0.40 and 14.29. Five of

33 cases of testing conditions resulted in a Df value below unity. It was thus concluded that variations of the stress

amplitude increase the fatigue life. The Df values decrease with increasing inclusion size, while their dependence

on the cycle ratio of high and low stress amplitudes remained unclear.

(3). Fatigue crack growth characteristics expressed by the relationships between the growth rate da/dN and the stress

intensity factor range DK were determined by beach marks in the fish-eye region which resulted from the repeated

two-step tests and the differences in ODA sizes which resulted from the two-step tests. The growth rates of the

fish-eyes were smaller than those for long cracks obtained by fracture mechanics experiments in air, and ten or hun-

dred thousand times higher than those of the ODAs.

(4). It is estimated that the ODA morphology is formed by repeated fracture surface contact in a vacuum, i.e. in the interior

of material, and is not determined by its growing mechanism which, however, causes a disintegration the original

microstructural features.

Acknowledgements

The present research was conducted as a cooperative work of GCF3 committee of The Japan Welding Engineering Society

supported by Kyusyu Electric Power Co., Inc., Hokkaido Electric Power Co. Inc., Tohoku Electric Power Co. Inc., Tokyo Electric

Power Company, Chubu Electric Power Co., Inc., Hokuriku Electric Power Company, The Kansai Electric Power Co., Inc., The

Chugoku Electric Power Co., Inc., Shikoku Electric Power Co. Inc., The Japan Atomic Power Company and Electric Power

Development Co., Ltd. The SUJ2 specimens were provided by Yukio Matsubara of NTN Corporation. The experiments on

the 17-4PH steel were performed within a research project of the Electric Power Research Institute (EPRI), USA, and the Uni-

versity of Natural Resources and Life Sciences, Austria. Language support by Dipl.-Ing Veronika Doblhoff-Dier is gratefully

acknowledged. We also thank two of the reviewers for their constructive criticism, which we implemented in Sections

3.3 and 3.4.

Fig. 15. SEM images of ODAs in AISI 420 Cr-steel (a), in AISI 316L-PM/HP steel (b) and spray formed hypereutectic Al-Si alloy (c).


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