Ultra-high-cycle fatigue properties and fracture mechanism of modified 2.25Cr–1Mo steel at elevated temperatures

$Page 1: Ultra-high-cycle fatigue properties and fracture mechanism of modified 2.25Cr–1Mo steel at elevated temperatures$
International

International Journal of Fatigue 28 (2006) 1633–1639

JournalofFatigue

www.elsevier.com/locate/ijfatigue

Ultra-high-cycle fatigue properties and fracture mechanism ofmodified 2.25Cr–1Mo steel at elevated temperatures

Hideo Kobayashi a, Akira Todoroki a, Toshikazu Oomura a,Takeru Sano b,*, Tatsumi Takehana b

a Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro, Tokyo 152-8552, Japanb The High Pressure Gas Safety Institute of Japan, 2-16-4, Tadao, Machida, Tokyo 194-0035, Japan

Received 6 December 2004; received in revised form 15 July 2005; accepted 2 August 2005Available online 6 May 2006

Abstract

This paper shows the fatigue properties and fracture mechanism of modified 2.25Cr–1Mo steel. In refineries or chemical plants, mod-ified 2.25Cr–1Mo steel is used in hot and high-pressure environments. Recently, a new fatigue problem concerning these facilities hasbecome important, because number of cycles to failure that should be taken into consideration for maintenance has increased to over107 cycles. For ultra-high-cycle fatigue, interior inclusions in the material are the dominant factor in a fatigue life, but the fracture mech-anism for this has not been clearly elucidated.

The results of ultra-high-cycle fatigue properties at elevated temperatures are presented. Interior fracture takes place at an ultra-high-cycle region, although many cases show no inclusions in the origins of an interior fracture. Crack growth life is predicted using fracturemechanics, so that life prediction for modified 2.25Cr–1Mo steel is possible.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Fatigue; Life prediction; Modified 2.25Cr–1Mo steel; Fatigue properties; Fracture mechanism; Crack growth life

1. Introduction

Recently, consideration of fatigue has become increas-ingly important for maintenance of certain facilities; espe-cially in regard to ultra-high-cycle fatigue from morethan 107 cycles [1–3]. In this region, there is a possibilitythat the material fails from fatigue under a load that is lessthan the accepted fatigue limit. This could be caused by ainclusion in the material or for other reason. Thus, toensure the safety of facilities there is an urgent necessityto clarify the fatigue properties and fracture mechanismin this region.

This paper presents the results of the fatigue propertiesand fracture mechanism of modified 2.25Cr–1Mo steel.

0142-1123/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijfatigue.2005.08.016

* Corresponding author. Tel.: +81 42 789 7221; fax: +81 42 791 1151.E-mail address: [email protected] (Takeru Sano).

Fatigue testing at room temperature (RT) and elevatedtemperatures were carried out. The fracture mechanism isdiscussed by fractographic observation and analysis ofthe fracture surface; and the results of analysis on life pre-diction are shown.

2. Testing method

2.1. Material and specimens

Heat treatment was at 1020 �C for 7 h (water cooling),then at 680 �C for 15 h (air cooling). The type of test spec-imen was a hourglass type with a smallest cross-sectiondiameter of 5 mm. All test specimens were machined in aforging direction that was oriented to the axial directionof the specimens. The chemical composition and mechani-cal properties of the material are shown in Tables 1 and 2.The shape of the test specimen is shown in Fig. 1.

mailto:[email protected]

Table 1Chemical composition of modified 2.25Cr–1Mo steel (mass %)

Element C Si Mn P S Ni Cr Mo V NbComposition 0.15 0.07 0.55 0.006 0.003 0.15 2.47 1.07 0.31 0.034

N Al B Ti Cu Ca As Sb Sn O REM0.0056 0.01 0.0001 0.004 0.05 0.0007 <0.002 0.0006 0.003 0.0011 <0.0001

Table 2Mechanical properties of modified 2.25Cr–1Mo steel

Temperature(�C)

0.2% proofstrength (MPa)

Tensile strength(MPa)

Elongation(%)

Reduction ofarea (%)

Young’s modulus(GPa)

Brinellhardness

RT 597 669 23.7 76.7 210 217400 471 540 20.2 79.8 187 –450 471 540 20.2 79.8 185 –500 451 501 19.7 83.9 185 –

Fig. 1. Specimen for fatigue testing.

Number of cycles to failure, Nf (cycles)

Stre

ss a

mpl

itud

e,

a(M

Pa)

σ

104 105 106 107 108 109200

250

300

350

400

450

500® RT

… 400deg.C

¤ 450deg.C

500 g.C

Modified 2.25Cr-1Mo steel

RT400˚C

400˚C

450˚C

450˚C

500˚C

500˚C


Fig. 2. S–N curves (modified 2.25Cr–1Mo steel).

1634 H. Kobayashi et al. / International Journal of Fatigue 28 (2006) 1633–1639

2.2. Testing machines and conditions

Hydraulic fatigue test machines (capacity: 10 kN) usingservo actuators, and infrared radiation heating instru-ments were used for the fatigue tests. The type of loadingwas axial-load control and the wave shape of the load wasa sine curve. Testing speed was 10–30 Hz. Test tempera-tures were RT (23 �C), 400, 450, and 500 �C. The loadratio (R: rmin./rmax.) was �1. Fractographic observationsof the fracture surfaces and chemical composition analy-ses were carried out by a scanning electron microscope(SEM) and an energy dispersive X-ray analyzer (EDX),respectively.

3. Test results

3.1. Fatigue test results

S–N curves of modified 2.25Cr–1Mo steel are shown inFig. 2. In the case of the fatigue test at RT, all fatiguecracks were initiated from the surface. As the stress ampli-tude became low, the number of cycles to failure increasedand the fatigue limit became clear. But in the high cycleregion at elevated temperatures, the fatigue limit disap-peared and fatigue cracks were often initiated from insidethe material. As the test temperature became higher, fati-gue strength clearly decreased.

3.2. Results of fractography

In the high cycle region at an elevated temperature, afish-eye was observed in several specimens. There weretwo types of fish-eye; one has an inclusion at the centerof the fish-eye (in this paper, called the Fi type), but theother does not have this inclusion (called the Fni type).

Fig. 3. Fractographs (T = 400 �C, ra = 330 MPa, Nf = 1.070 · 106). (a) Macrograph, (b) inclusion.

Fig. 4. Fractographs (T = 450 �C, ra = 320 MPa, Nf = 1.876 · 106). (a) Macrograph, (b) no inclusion.

Fig. 5. Mapping photograph of EDX (T = 400 �C, ra = 330 MPa, Nf = 1.070 · 106).

H. Kobayashi et al. / International Journal of Fatigue 28 (2006) 1633–1639 1635


Additionally, all specimens having fish-eyes had ligamentsbetween the surface and the outer front of the fish-eye.

Typical Fi and Fni types observed at an elevated temper-ature are shown in Figs. 3 and 4, respectively, for compar-ison. The results of chemical composition analysis of theinclusion are shown in Fig. 5. Chemical composition ofthe inclusion is Al, Ca, Mg, S, and it is assumed that theinclusion consisted of an aluminum oxide.

4. Discussion

4.1. Comparisons of surface and interior fractures

For modified 2.25Cr–1Mo steel at 400 �C, the fracturemechanism can be distinguished into surface (initiatedfrom the surface) and interior (initiated from inside) frac-tures by the existence of a fish-eye. A S–N curve is shownin Fig. 6. As the stress amplitude becomes lower, the num-ber of interior fractures tends to increase; but there is nodifference in the fatigue life. Specimen numbers showingthe fracture mechanism are shown in Table 3. In anotherresult, an interior fracture, the only case, is seen at450 �C; it is caused at a medium stress amplitude on theS–N curve. A difference in the fatigue life does not appear.From these results, it can be said that disappearance of thefatigue limit is not caused only by interior fractures. Inte-rior fractures tend to contribute substantially at 400 �C,but in cases of elevated temperatures above 400 �C, the ten-

Number of cycles to failure, Nf (cycles)

Stre

ss a

mpl

itud

e,

a(M

Pa)

σ

104 105 106 107 108 109200

250

300

350

400SurfaceInteriorRun out

400˚C


Fig. 6. S–N curve (T = 400 �C). Surface: fracture from surface. Interior:fracture from inside.

Table 3Number of specimen and fracture mechanism

Material T (�C) Totalnumber

Surface Interior

Inc. Non-inc.

Modified2.25Cr–1Mo

400 23 10 4 9450 20 15 1 4500 23 22 0 1

dency disappears. Research about the contribution of inte-rior fractures at 400 �C or less will be needed. Moreover, asshown in Table 3, there are few Fi but many Fni types. Theelucidation of why fatigue life is different, although eachfracture mechanism differs, is needed; and presents a futuresubject for study.

4.2. Fatigue strength ratio

Generally, the fatigue limit rW shows a strong correla-tion with tensile strength rB, and the relationship of Eq.(1) is known experientially.

rW ¼ 0:5rB ð1ÞIt is assumed that the fatigue limit at elevated tempera-

tures is the fatigue strength at 108 cycles. The relationshipbetween the fatigue strength ratio (rW/rB) and temperature(T) is shown in Fig. 7. The fatigue strength ratio at elevatedtemperatures becomes less than 0.5, and the relationship inEq. (1) cannot stand.

4.3. Quantitative evaluation of fish-eye and ligament

To quantitatively evaluate a fish-eye, the initiation depthfrom the surface and the area of the fish-eye were mea-sured. The definition of the size of the initiation depth fromthe surface (D), ligament (L), and fish-eye area (A) areshown in Fig. 8. The results of the measurement of thefish-eye area are shown in Fig. 9. Although the fish-eyearea takes a range within 0.003–7.1 mm2, it shows a uniquecorrelation with the initiation depth from the surface. Inthis figure, two examples in which the last fracture occurreddirectly from the fish-eye are shown.

When a fish-eye forms at RT, its outer front is in contactwith the surface of the specimen. Conversely, if the interiorcrack grows to the surface, a difference between the

Temperature, T(˚C)RT 400 450 500

0.3

0.4

0.5

0.6

0.7

W =0.5σσ B

WB RT

400˚C450˚C

500˚C


Fat

igue

stre

ngth

rati

oat

N=1

08(σ

/σ)

Fig. 7. Relationship between fatigue strength ratio at 108 cycles andtemperature.

Fig. 8. Definition of size of fish-eye and ligament.

Initiation depth from surface, D(mm)

Fis

h-ey

e ar

ea, A

(mm

2 )

0 1 2 3

5

10

15

® RT

… 400deg.C

¤ 450deg.C

500deg.C

2.25Cr-1Mo-V steelRT400˚C450˚C

500˚C


Fig. 9. Relationship between fish-eye area and initiation depth fromsurface.

Stress intensity range of fish-eye, KFish-eye(MPa m)

Lig

amen

t, L

(mm

)

Δ √0 5 10 15

0.1

0.2

0.3

0.4

0.5400˚C

400˚C

450˚C

450˚C

500˚C

500˚C

400˚C450˚C500˚C

Plane strainPlane stress


Plastic zone size

Fig. 10. Relationship between ligament and DKfish-eye.


environment and the stress intensity factor arises, and theouter front can be discriminated by a sudden change in thecrack growth rate. However, in the case of the elevated tem-peratures used in this research, that a ligament existsbetween the outer front and the surface of the specimen isunexceptional. A ligament is not the final fracture but a fati-gue fracture, and can be quantitatively evaluated as follows.

Stress intensity factor (DKfish-eye) of fish-eye (interiorcrack) is calculated from Eq. (2) using the fish-eye area.

DK fish-eye ¼ MDrffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipafish-eyep ð2Þ

where M is shape factor of a crack, Dr is the stress range,and afish-eye is the crack size of a fish-eye. The value of M is0.5 in the case of an interior crack like a fish-eye. In thiscase, Dr is equal to the stress amplitude (ra), and afish-eye

is defined as the square root of the fish-eye areað ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiareafish-eyep Þ [4]. Then, the size of the crack tip plastic zone

x is calculated using Eqs. (3) and (4).

in the case of plane stress x ¼ 1

pKrY

� �2

ð3Þ

in the case of plane strain x ¼ 2

5:6pKrY

� �2

ð4Þ

where K is the maximum stress intensity factor and rY

the yield stress. In this case, K is DKfish-eye. The relation-ship between the results of measuring the length of theligament, the calculation results of the plastic zone sizeand the stress intensity factor range DKfish-eye are shownin Fig. 10. From these results, the size of the ligament atan elevated temperature is well in agreement with thesize of the crack tip plastic zone of the plane stress. Gen-erally, plane strain occurs on the front of an interiorcrack. But in this research, a ligament will produce afully plastic section on plane stress when the size ofthe ligament decreases with the growth of the interiorcrack and reaches the size of the crack tip plastic zone.A mechanism considered is that the elevated temperatureenvironment flows into the inside of the crack caused bythe local plastic collapse of the ligament. The suddenchange of environment brings about the sudden changein the crack growth rate, and at last the coloring ofthe fracture surface and the outer front can bediscriminated.

4.4. Evaluation of crack growth life of interior fracture

The crack growth life is evaluated against the Fi type ofconfirmed interior fracture. Generally, in the case of aninitial crack size a0, the initial stress intensity factor rangeDK0 is given by Eq. (5), and the relationship between thecrack growth rate da/dN and the stress intensity factorrange DK is given by Eq. (6). The relationship of Eq.(7) can stand between the initial stress intensity factorrange DK0, the crack growth life Nf, and the initial cracksize a0 [5].

Modified 2.25Cr-1Mo steel400˚C

Inclusion- Exp.Inclusion- Cal.

Inclusion- Exp.Inclusion- Cal.

No Inclusion- Exp.

No Inclusion- Exp.

Fig. 12. S–N curves (T = 400 �C).


DK0 ¼ MDrffiffiffiffiffiffiffipa0

p ð5Þda=dN ¼ CDKm ð6Þ

DKm0 N f=a0 ¼

2

ðm� 2ÞC ð7Þ

In the case of an interior crack, the value of M is 0.5,and m and C are defined as material constants. If it isassumed that the stress intensity factor range of inclusionis DKInc. and that the square root of the inclusion area isffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

areaInc:p

; then the material constants (m and C) can be pre-sumed from the condition of DK0 = DKInc., a0 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiareaInc:p

and Nf as the actual measurements of the fatigue life. Inthe case of modified 2.25Cr–1Mo steel at 400 �C, the rela-tion between DKInc. and N f=


is shown in Fig. 11.DKInc. and N f=


reach a straight line relationshipin the double logarithmic plot, so that m = 6.3 andC = 5.2 · 10�13 are obtained. Additionally, the results ofmodified 2.25Cr–1Mo steel at 450 �C are also shown inFig. 11, as reference data. The results are not greatly differ-ent, although quantitative examination was not performedsince as there was only one case. Further, the crack growthlife Nf-Cal. is predicted by


using m, C, and Eq. (7)to evaluate the crack growth life of the Fi type. The resultsare shown in Fig. 12. The results of actual measurements ofthe fatigue life and the results of the prediction of the crackgrowth life are mostly in agreement; while fatigue life canbe predicted by the characteristics of crack growth. How-ever, from Fig. 12, it can be seen that the fatigue life ofthe Fni type is located in a low stress amplitude and onthe low fatigue life side as compared to the Fi type. Gener-ally, when Fi and Fni types have been intermingled, it hasnot been reported, until now, that they are different fromeach other. For the fatigue characteristic of low alloy steelat an elevated temperature, a caution is needed as an inte-

Nf / areaInc. , (cycles / m)μ

Stre

ss in

tens

ity

reng

eof

incl

usio

n,

KIn

c.(M

Pa√

m)

Δ

1010 1011 10120.1

1

10

Ran

ge o

f st

ress

inte

nsit

y fa

ctor

,

400˚C

450˚C


√

m=6.341C=5.227×10-13

m m1

Fig. 11. Relationship between DKInc. and N f=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiareaInc:p

rior fracture of the Fni type may arise at a low stress ampli-tude and with a low fatigue life, compared with an interiorfracture of the Fi type.

5. Conclusions

(1) At elevated temperatures, modified 2.25Cr–1Mo steelshowed interior fractures (fish-eye) that were notshown at RT, and the fatigue limit disappeared. Asthe test temperature became high, fatigue strengthfell. It was predicted that the fatigue strength ratiofell to less than 0.5 at elevated temperatures.

(2) Interior fractures are not the only reason that the fati-gue limit disappears at elevated temperatures. Thecontribution from interior fractures is great at400 �C, but tends to disappear at over 400 �C. More-over, the difference in the fatigue life is not clearbetween surface and interior fractures.

(3) There are two types of fish-eyes at elevated tempera-tures. One has an inclusion at the center of the fish-eye (Fi type), but the other does not (Fni type). Bothare intermingled; contrary to conventional knowl-edge, the Fni type is common.

(4) Ligaments exists in fish-eyes at elevated temperatures;the size equaling the plastic zone size of plane stress atthe outer front of a fish-eye. It is considered that anelevated temperature environment flows into theinside of the crack caused by the local plastic collapseof the ligament.

(5) As crack growth parameters for fish-eye formation ofthe Fi type, m = 6.3 and C = 5.2 · 10�13 wereobtained for modified 2.25Cr–1Mo steel, at 400 �C.Furthermore, as a result of evaluating crack growthlife, it was shown that the fatigue life of the Fi typecan be predicted from the crack growth life. But thisdoes not apply to the Fni type and to surface frac-tures. The elucidation of the mechanism of fracturesremains as a future subject for study.


This research was performed as a national consignmentresearch (commissioned by Ministry of Economy, Tradeand Industry), from the 1998 to the 2002 fiscal years.

References

[1] The Research Subcommittee on high cycle fatigue RC130 researchreport, Japan Society of Mechanical Engineers, Research CooperationCommittee, 1996.

[2] High cycle fatigue evaluation research of the structural materials fornuclear components. The last report in the 2001 fiscal year, JapanWelding Engineering Society, Nuclear Research Committee GCFSubcommittee, 2003.

[3] Ochi Yasuo, Sakai Tatsuo. Fundamentals and recent topics on fatigueIII: fatigue of metallic materials in the very high cycle regime. J SocMater Sci 2003;52(4):433–9.

[4] Murakami Yukitaka. Metal fatigue: effects of small defects andnonmetallic inclusions. Yokendo Ltd.; 1993.

[5] Kobayashi Hideo. Fracture mechanics. Kyoritsu Shuppan Co., Ltd.;1993. p. 143.

Documents

Ultra-high-cycle fatigue properties and fracture mechanism of modified 2.25Cr–1Mo steel at elevated temperatures