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Available online at www.sciencedirect.com

Nuclear Engineering and Design 238 (2008) 801–813

Fatigue studies on carbon steel piping materialsand components: Indian PHWRs

P.K. Singh a,∗, V. Bhasin a, K.K. Vaze a, A.K. Ghosh a, H.S. Kushwaha a,D.S.R. Murthy b, P. Gandhi b, S. Sivaprasad c

a Health Safety & Environmental Group, Bhabha Atomic Research Centre, Mumbai 400085, Indiab Structural Engineering Research Centre, Chennai 600113, Indiac National Metallurgical Laboratory, Jamshedpur 831007, India

Received 2 May 2007; received in revised form 11 September 2007; accepted 17 September 2007

bstract

This paper describes the results of fatigue studies on carbon steel piping materials and components of Indian Pressurized Heavy Water ReactorsPHWRs). The piping components include pipes and elbows, of outer diameter 219 mm, 324 mm and 406 mm, made of carbon steel (SA333 Gr.6rade) material. Tests on actual pipes and elbows with part through notch were carried out to study the behaviour of crack growth under cyclicoading for different pipe sizes, notch aspect ratios, stress ratios, etc. During the tests, numbers of cycles for crack initiation from blunt notch wereecorded with an accuracy of 0.1 mm. In conjunction with component tests, the experimental studies were also conducted on standard specimens

o understand the effect of different variables such as size (thickness), type of specimen and components (elbow and pipe), welding, stress ratio,otch orientation on fatigue crack growth rate. The fatigue crack growth curve (da/dN versus �K) obtained from three-point bend specimen andipe was compared with that given in ASME Section XI. The comparison shows that da/dN versus �K curves obtained from the specimen and pipeests are nearly same. The analytical predictions for crack initiation and crack growth for the tested components were compared with experimentalesults. Such comparisons validate the modeling procedure for crack initiation and growth.

1st

bp1acbtfr

2007 Elsevier B.V. All rights reserved.

. Introduction

Fatigue is one of the mechanisms, considered active in theiping system, which may lead to crack initiation from either theighly stressed regions or the undetected flaws. It is desirableo confirm that crack initiation, due to cyclic loading in serviceeriod of the reactor, will not occur. Behaviour of initiated cracksnder cyclic loading is also of concern for safe operations of theeactor. In addition to this safety considerations also call for sat-sfaction of leak-before-break (LBB) criteria by demonstratinghat the flaw at the end of life will not propagate through wallNUREG 1061, 1980). Usually fatigue crack initiation has beentudied in the past using notched small specimens by evaluat-

ng local stress or strain at the notch tip considering the stress ortrain concentration, equivalent energy density method and low-ycle fatigue (LCF) curve (ASME Section II, 1992; Kassir et al.,

∗ Corresponding author. Tel.: +91 22 25591522; fax: +91 22 25505151.E-mail address: pksingh@barc.gov.in (P.K. Singh).

fdfwstS

029-5493/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2007.09.002

993; Costa and Ferreira, 1993; Ellyn, 1997). In this paper localtress and strain at the notch tip have been evaluated consideringhe stress intensity factor and cyclic stress–strain curve.

Fatigue crack growth rate (FCGR) based on the Paris law haseen studied extensively using compact tension (CT) or three-oint bend (TPB) specimens following ASTM E647 (E647,995). The ASME Boiler and Pressure Vessel Code Section XIlso give the FCGR curve for air and water environments forarbon and low-alloy ferritic steels (ASME Section XI, 1989)ased on small specimens. In this paper the curve correspondingo air environment has been referred to for comparison purposesor the material (SA333 Gr.6) under study. The effects of stressatio on the fatigue crack growth behaviour are widely availableor standard specimens (Ellyn and Li, 1984). These crack growthata obtained from CT or TPB specimens are used convenientlyor prediction of crack growth in surface flawed components

ith assumptions such as surface flaw assumes semi-elliptical

hape during growth, crack growth rate is independent of direc-ion and stress state, etc. Few researchers (Shibata et al., 1994;himakawa et al., 1993; Yoo and Kotoji, 1999; Dover et al.,

802 P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813

Table 1aWelding parameters

C -heat8 ◦C

1pff

ttoTscbTi(dstt

AaaTd

2

pTcI

sibmwhwi

o

(o

nu

2

sg

i(tlmn

Tlt

((

(

(

(

(

2

TC

M

BW

urrent (A) Voltage (V) Rod/electrode diameter (mm) Pre0–130 10–14 2.4/3.15–4 120

980) have carried out fatigue crack growth studies on full scaleiping components. Shimakawa et al. performed studies on sur-ace cracked pipes to establish a method based on non-linearracture mechanics.

Conventional approach for prediction of fatigue crack ini-iation and growth is based on LCF and FCGR properties ofhe specimens. In order to validate this approach large numberf fatigue tests on component and specimen were conducted.he tests were planned to account for parameters such as pipeize, thickness, notch orientation/location, manufacturing pro-ess, base/weld metal, etc. Further, the aim was to understand theehaviour of crack growth under predominant bending moment.his aspect is important for Level-2 LBB requirements, where it

s desirable to prove that the crack grows more rapidly in depththickness) direction as compared to surface (circumferential)irection. The data of the actual piping component tests andtandard specimens will also be useful in the accurate predic-ion of the remaining life of the component which is of concerno most of the older Nuclear Power Plants.

As a part of component integrity test program at Bhabhatomic Research Centre, 17 fatigue tests on carbon steel pipes

nd elbows were conducted. In addition, fatigue tests werelso conducted on the standard specimens such as CT andPB specimens. In this paper the outcome of this program isiscussed.

. Experimental program

Studies were carried out on seamless pipes of SA333 Gr.6 andipe elbows of SA420 WPL6 material used in Indian PHWRs.he pipes and elbows were in the normalized and temperedondition and conform to the specifications of ASME SectionsI and III.

Welding of pipes was carried out as per the guidelines given inection XI of the ASME code. The welding parameter is shownn Table 1a. The gas tungsten arc welding (GTAW) process haseen followed for root pass and the second pass and shieldedetal arc welding (SMAW) for the remaining passes. ER-70S-2elding rod has been used for GTAW and E-7018-1 electrodeas been used for SMAW. After completion of welding, post-

eld heat treatment has been carried out to relieve the stresses

ntroduced during welding.The measured chemical composition and tensile properties

f the pipe and pipe weld material are shown in Tables 1b and 2

et

able 1bhemical composition (in wt%) of pipe material

aterial C Mn Si P S A

ase 0.14 0.9 0.25 0.016 0.018 <eld 0.27 1.2 0.43 0.21 0.017 <

temperature Interpass temperature Post-weld heat treatment120–150 ◦C 620 ◦C with 66 min hold time

Singh et al., 1998). The values for elbow material are of similarrder.

The fatigue tests were conducted on specimens and compo-ents (pipes and elbows). The brief summary of tests conductednder this program is discussed below.

.1. Specimen testing

Specimen testing was conducted to determine the basic cyclictress–strain curve, low-cycle fatigue (LCF) and fatigue crackrowth rate (FCGR) properties.

The LCF tests were conducted on standard uniaxial spec-mens under strain-controlled condition in which strain range�ε) was varied from 0.4 to 3.0 %. In all 40 specimens wereested. The outcome of these tests was cyclic stress–strain andow-cycle fatigue curve. These properties are required for assess-

ent of number of cycles to crack initiation ahead of a bluntotch.

The FCGR tests were conducted on CT and TPB specimens.he outcome of these tests was the material constants of FCGR

aw, i.e., Paris law. About 50 specimens were tested to understandhe effect of different conditions:

a) Specimen type: CT and TPB.b) Stress ratio (R = minimum load/maximum load): 0.1, 0.3 and

0.5.c) Base and weld: specimens were machined from pipe base

and pipe weld.d) Thickness of specimen: specimens were machined from dif-

ferent sizes of pipe, i.e., 10 mm, 15 mm and 20 mm from219 mm, 324 mm and 406 mm outer diameter, respectively.

e) Product form: specimens were machined from seamless pipeand pipe bend (elbow).

f) Notch orientation: specimens were machined in two ori-entations namely LC and CL. The notch is in longitudinaldirection with respect to the pipe in CL orientation, whereasit is in circumferential direction in LC orientation.

.2. Component testing

The fatigue crack growth studies were conducted on pipes andlbows with pre-machined notch. In all 17 tests were conductedo cover the effect of the following variables:

l Cr Ni V N Fe

0.1 0.08 0.05 <0.01 0.01 Balance0.1 0.04 0.013 <0.01 <0.001 Balance

P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813 803

Table 2Room temperature tensile properties of pipe material

Material Yield strength, σy (MPa) Ultimate tensile strength, σu (MPa) % elongation % reduction in area

BW

(

((

(

(

3

taaswti

atwtd

Aiaa

rltk

4

a1furTilsb

TD

T

PPPPPPPPPPPPP

O

ase 302 450eld 325 466

a) Component type and size: component type is pipe and elbow.Three pipe sizes tested were of outer diameters, 219 mm,324 mm, and 406 mm, which are designated in this paper as200NB, 300NB and 400NB, respectively. The correspond-ing thickness is listed in Table 3a. Elbow size tested was 90◦short radius of 219 mm outer diameter and 15.1 mm nominalwall thickness.

b) Stress ratio (R = minimum load/maximum load): 0.1and 0.5.c) Pipe and pipe weld: tests were conducted on seamless pipes

with initial notch in pipe base, and girth welded pipe withnotch at weld location.

d) Notch size or notch aspect ratio: notch length (2C), notchdepth (a) and aspect ratio. Actual size of notch and aspectratios are listed in Table 3a.

e) Notch location: in elbow tests the notch was machined atcrown and intrados (Table 3b).

. Typical experimental procedure for component tests

Schematic loading condition and actual test set up for pipeests are shown in Figs. 1b and 2. Actual test set up consists of

servo hydraulic loading system, a support for the specimennd various instruments for measurement of data. The supportystem for pipe test consists of two pedestals with two rollers,hich provides four-point bending. This type of loading ensures

hat the mid-section of the specimen, where the notch is located,s subjected to pure bending.

The support system for the elbow consists of two hingest either ends, one fixed to the test floor and other connected

o the actuator. The hinge support connected to the actuatoras loaded with in plane bending condition. In order to cap-

ure crack growth profile, the crack depth was measured at fewiscrete locations along the crack length during the fatigue test.

T

t

able 3aetails of the carbon steel pipe/pipe welds and initial notch dimension

est no. Notch location OD (mm) t (mm) Outer span (mm

BSC8-1 Base 219 15.58 2500BSC8-2 Base 219 15.38 2500BSC8-3 Base 219 15.12 2500BSC8-4 Base 219 15.38 2500BSC8-5 Base 219 15.17 2500BSC8-6 Base 219 15.13 2500BSC12-1 Base 324 21.5 5000BSC12-2 Base 324 21.5 5000BSC12-4 Base 324 21.5 5000BSC12-6 Weld 324 21.5 5000BSC16-1 Base 406 26.5 6500WSC16-4 Weld 406 26.5 6500WSC16-5 Weld 406 26.5 6500

D: outer diameter; 2C: crack length; a: crack depth; t: thickness.

36.7 72.9618.7 –

lternating current potential difference (ACPD) principle-basednstrument was used for the crack growth measurement. The loadnd number of cycles corresponding to each crack depth werelso recorded.

Tests were carried out at room temperature and air envi-onment under load control mode using sinusoidal waveformoading with constant amplitude. The tests were conducted forwo different stress ratios (R), viz. 0.1, 0.5 and frequency wasept in the range of 0.5–1.0 Hz.

. Low-cycle fatigue (LCF) test results

Cyclic stress–strain and LCF properties were evaluatedccording to the procedure given in ASTM E606 standard (E606,995). The LCF specimens (diameter 4.5 mm) were machinedrom the 400 mm outer diameter pipes. Tests were conductednder fully reversible condition for different strain ranges atoom and operating (288 ◦C) temperature in air environment.he LCF curves for room and operating temperature are given

n Fig. 3. Based on the LCF test data cyclic stress–strain andow-cycle fatigue curve constants were obtained. The cyclictress–strain curve can be represented by Eq. (1) and LCF curvey Eq. (2).

Δε

2= 100

E×

(Δσ

2

)+

(Δσ

2k

)1/n

(1)

Δε

2= σ′

f

E(2N)b + ε′

f(2N)c (2)

Values of constants in above Eqs. (1) and (2) are given inable 4.

In the above equations, �ε is in (%), �σ in (MPa), N ishe number of cycles required for failure (complete separation)

) Inner span (mm) 2C (mm) a (mm) 2C/a a/t

880 114.3 2.01 57 0.13880 113.4 1.97 57 0.13880 110 3.0 36 0.2880 113 3.5 32 0.23880 113.8 5.98 19 0.4880 113.2 5.5 20 0.36

1480 100 5.0 20 0.231480 61 5.2 11 0.241300 60.2 5.0 12 0.231300 61.2 5.1 12 0.241600 133 6.5 20 0.241600 131 6 21 0.231600 66 6 11 0.23

804 P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813

Table 3bDetails of the loading and initial notch dimensions for the elbow tests

Test no. Notch location OD (mm) t (mm) Moment arm length (mm) Bend radius (mm) 2C (mm) a (mm) 2C/a a/t

ESCBC8-1 Both crown 219 15.58 485 219 80 2.0 40 0.13EWC8-2 No notch 219 15.38 485 219 – – – –ESCC8-3 One crown 219 15.12 485 219 87 2.0 43 0.13ESCI8-4 Intrados 219 15.38 485 219 106 4.0 26 0.26

OD: outer diameter; 2C: crack length; a: crack depth; t: thickness.

Fig. 1. (a) Schematic of the location of specimen machined form the pipe and pipe weld. (b) Schematic sketch showing loading condition for pipe and elbow test.

Fig. 2. Actual tests set up for fatigue test on pipe and elbow.

P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813 805

Table 4The values of fatigue curve constants and cyclic stress–strain curve constants

Strain ratio Temperature (◦C) σ′f ε′

f b c n K

0 RT 91207 47.97 −0.1283 −0.5551 349.9 0.1766− .06 −0.0757 −0.4814 354.27 0.1523

.15 −0.0454 −1.004 360.46 0.04865− −0.0049 −0.7150 358.27 −0.00575

ouoswTitdAfnATfI

5

tPcpdsTd

Fa

Ff

5

rumTfrom 400 mm outer diameter pipe. Figures indicate that, for a

1 RT 58606 240 288 50727 211 288 966240 127

f the specimen, E is the Young’s Modulus in (MPa). Materialndergoes cyclic strain hardening which is more pronounced atperating temperature. LCF properties have been observed to beuperior at room temperature than at 288 ◦C for low-strain rangehereas properties are almost identical at higher strain range.his is consistent with the fact that serrations were observed,

n hysteresis loop, for the strain amplitude above ±0.5% andemperature 288 ◦C showing that the material is susceptible toynamic strain aging (DSA). LCF curve was also compared withSME Section II of Boiler and Pressure Vessel code design

atigue curve. In order to do so, a factor 2 on stress and 20 onumber of cycles was used on experimental data points becauseSME design fatigue curve takes into account these factors.he comparison is shown in Fig. 4. It is observed that material

atigue curve compares well with that given by ASME SectionI of Boiler and Pressure Vessel code for C–Mn steel.

. Fatigue crack growth rate specimen tests results

The FCGR tests on specimens were conducted to determinehe crack growth rate constants. FCGR is modeled using thearis law given as: da/dN = C(�K)m, where C and m are FCGRonstants. The specimens used for testing were machined out ofipes and elbows. As mentioned earlier, several tests were con-ucted to understand the effect of different parameters such as

tress ratio, source of specimens, thickness of specimen, etc.he experimentally observed effects of these parameters areiscussed in following paragraphs.

ig. 3. Comparison fatigue life vs. total strain amplitude for different strain rationd temperature.

gea

Fs

ig. 4. Comparison of LCF curve of SA333 Gr.6 from experiment and ASMEor C–Mn steel.

.1. Effect of stress ratio

The fatigue crack growth rate curves were generated for stressatios 0.1, 0.3, 0.5 as per the ASTM standard E647 (E647, 1995)sing TPB and CT specimens machined from the same pipeaterial. The effect of R is shown in Figs. 5 and 6 for CT andPB specimens, respectively. These specimens were machined

iven �K, da/dN increases with increase in stress ratio. Thisffect is relatively more significant at lower R-values. This vari-tion is mainly because of the crack closure effect, which gets

ig. 5. Comparison of FCGR curves at different stress ratio, obtained using CTpecimen.

806 P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813

Fs

rvt

5

omTsfp

smF

Fm

Fa

5e

pottdn

5

pt406 outer diameters are compared and shown in Fig. 10. FCGR

ig. 6. Comparison of FCGR curves at different stress ratio obtained using TPBpecimen.

educed as stress ratio increases. It is also observed that da/dNersus �K behaviour is nearly the same in CT and TPB specimenests.

.2. Effect of thickness and product form

TPB specimens were machined from all the sizes of pipef diameter such as 219 mm, 324 mm and 406 mm. The speci-ens from different pipe sizes differed with respect to thickness.he aim of this study was to see the effect of thickness ofpecimen on FCGR. The results are shown in Fig. 7. It wasound out that there is no significant difference in the FCGRroperty.

Specimens machined from pipes and elbows also exhibit the

ame FCGR behaviour, as shown in Fig. 8. This indicates thatanufacturing process of the piping components does not affectCGR curve significantly, for this grade of steel.

ig. 7. Comparison of FCGR curves for specimens of different thicknessachined from various sizes of pipe.

cds

Fo

ig. 8. Comparison of FCGR curves for TPB specimens machined from pipend elbow.

.3. Effect of notch orientation with respect to pipextrusion axis

CT specimens machined from the 400 mm outer diameteripe were tested in two orientations, namely LC and CL. In CLrientation the notch is in longitudinal direction with respect tohe pipe, whereas in LC orientation it is in circumferential direc-ion. The test results in Fig. 9 show that there is no significantifference in FCGR behaviour with respect to orientation of theotch with respect to pipe axis.

.4. Effect of base and welds

TPB specimens were prepared from the different sizes ofipe and pipe weld, and FCGR studies were carried out. Theest results for CT specimens from pipe (base) and pipe weld of

urves obtained for TPB specimens from pipe welds of outeriameters 219 mm, 324 mm and 406 mm are also compared andhown in Fig. 11. Comparison of FCGR curves for base and

ig. 9. Comparison of FCGR curves for specimens with notch in differentrientation with respect to pipe axis.

P.K. Singh et al. / Nuclear Engineering

Fp

wFb

5

tTao

6

(

Fo

rwftunwa

aTltiuetccases crack initiation could only be detected after a crackgrowth of 0.5 mm. The experimental findings and relatednumber of cycles to crack initiation, fatigue crack growth andtheir analytical modeling are discussed in following paragraphs.

ig. 10. Comparison of FCGR curve for specimens machined from pipe andipe weld.

eld obtained using TPB specimens are shown in Fig. 12a.igs. 10 and 12 indicate that there is no significant differenceetween base and welds of different sizes of pipe.

.5. Summary of the specimen testing

The above results show that, for the present grade of material,he FCGR is not significantly affected by specimen type (CT andPB), specimen thickness, product form (specimen from elbownd pipe), base and weld metal and notch orientation. The effectsf stress ratio are mildly significant at lower R-values.

. Component test results

The basic aim of carrying out the fatigue tests on componentsi.e., pipe and elbow) was to compare the fatigue crack growth

ig. 11. Comparison of FCGR curves for TPB specimens from different sizesf pipe weld.

F(

and Design 238 (2008) 801–813 807

ate determined using specimens (CT or TPB) and that of pipehich is under more realistic stress field. A brief detail of the

atigue tests on pipes and elbows was described (given) in Sec-ions 2.2 and 3. In all the 17 tests the initial notch was machinedsing a milling cutter. This machining process induced the bluntotch having tip radius of approximately 0.1 mm. This valueas assumed based on milling cutter tip radius and, hence, it is

pproximate.The details regarding range of cyclic moment/stress

pplied, R-ratio, etc., for each test are listed inables 5a (pipes) and 5b (elbows). The initial cycles of

oading produce sharpening of machined blunt notch. Oncehe crack tip is sharpened, then each loading cycle producesncremental crack growth. The initiation of crack was detectedsing instrument based on alternating potential current differ-nce (ACPD) technique. The instrument used had a detectionhreshold of 0.1 mm. This in turn implies that crack initiationan only be detected after a crack growth of 0.1 mm. In few

ig. 12. (a) Comparison of FCGR curves of base and weld using TPB specimen.b) Comparison of experimental and analytical results for crack initiation.

808 P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813

Table 5aDetails of the fatigue test results on carbon steel pipe and pipe welds with crack

Test no. Control Load (KN) Stress range(MPa)

Number of cycles (×103) 2C/a at throughwall

Total cyclesa

(×103)Max Min Initiation at

depthInitiation atsurface

Through wall

PBSC8-1 Load 200 20 158 53(0.1) – 273 7.3 273PBSC8-2 Load 250 125/75 110/66 320(0.1) – 869 7.3 869PBSC8-3 Load 200 100 87.5 235(0.1) – 572 7.3 572PBSC8-4 Load 160 16 126 6(0.1) – 104 7.3 104PBSC8-5 Load 200 100 87.5 45(0.1) – 252 7.3 252PBSC8-6 Load 160 0.1 126 3(0.1) – 53 for a/t = 0.8 7.3 –PBSC12-1 Load 308 50 156 2.5 (0.1) 55 55 4.65 72PBSC12-2 Load 313 50 159 1 (0.4) 33 77 3.2 118PBSC12-4 Load 313 157 100 7 (0.2) 40.85 494 3.8 526PBSC12-6 Load 320 32 183 10(0.2) 3.1 76 3.6 97.93PBSC16-1 Load 500 50 196 0.5 (0.1) 1.2 24 5.13 32.9PBSC16-4 Load 500 50 196 0.4 (0.1) 1 32.35 5.3 38.17PBSC16-5 Load 500 50 196 4.5(0.5) 45 54.9 2.86 91.7

For PBSC8-2 specimen, initial 0.4 million cycles were applied with R = 0.5 and remaining cycle with R = 0.3.a In certain cases the fatigue test was continued even after formation of through wall crack.

Table 5bDetails of the fatigue test results on carbon steel elbow with crack

Test no. Control Load (KN) Type of moment Number of cycles (×103)

Max Min Initiation at depth Through wall

ESCBC8-1 Load −150 −15 Closing 27(0.1) 97EWC8-2 Load −120 −12 Closing 249(0.1) 400EE

6

stg

6

mmf

aATtrib

TC

T

PPPPPPPPPEEE

SCC8-3 Load −150 −15SCI8-4 Load +80 8

.1. Fatigue crack initiation in components

The observed numbers of cycles to detect crack initiation forelected pipe tests are listed in Table 6. This table lists only thoseests in which initiation could be detected at instant when crackrowth is around 0.1 mm.

.1.1. Analytical estimation

In order to predict the number of cycles to crack initiation a

odel was used in which the elastic–plastic strain range is esti-ated based on K-fields (where K is linear elastic crack driving

orce parameter) combined with Neuber’s rule. The crack tip tri-

tt�

t

able 6omparison of experimental and analytical results for crack initiation

est no. Component Stress ratio

BSC8-1 Pipe 0.1BSC8-2 Pipe 0.5BSC8-3 Pipe 0.5BSC8-4 Pipe 0.1BSC8-5 Pipe 0.5BSC8-6 Pipe 0.1BSC12-1 Pipe 0.1BSC16-1 Pipe 0.1BSC16-4 Pipe 0.1WC8-2 Elbow 0.1SCC8-3 Elbow 0.1SCI8-4 Elbow 0.1

Closing 2(0.1) 64.1Opening 8(0.1) 147

xiality was accounted for by using a correction term based on-16, Appendix of RCC-MR code (Creager and Paris, 1967).hese calculations are based on cyclic stress–strain curve of

his material given in Section 4. Once the elastic–plastic strainange is known then the number of cycles to crack initiations determined from LCF curve. The model is briefly discussedelow.

It is assumed that the state of stress is plane 2D type. For

he notch having tip radius ρ and the remote stress range �σ0,he approximate value of maximum pseudo elastic stress rangeσpe, at distance, d (known as characteristic distance), from

he notch tip can be evaluated by Creager formula (Creager and

Experimental (for crack to grow by 0.1 mm) Analytical

53,000 89,646320,000 344,275235,000 250,3298000 600045,000 35,8353000 40982500 1550500 278400 270249,000 240,1802000 25568000 136,29

ering

P

Δ

((tt

tedideTA

sts

Δ

w

sbociwg

traiianadptdyoa

(credmT

smpc

crfdfi

6

cteteg

6T

lSrtmacsfison of the crack growth curve indicates that for all �K the crackgrowth rate given by ASME is higher. It can be inferred that useof the crack growth rate given in ASME will give conservativeprediction of life.

P.K. Singh et al. / Nuclear Engine

aris, 1967):

σpe = {ΔK/

√(2πr)

} ×(

1.0 + ρ

2r

)(3)

where, r = d + ρ/2 (ρ = 100 �m based on cutter radius). �Kstress intensity factor range) = �σ0√(πa) × FG; a = depth ofhe notch, FG = Geometry factor (A16, 1995) (depends on theype of notch, shape of the component and type of load).

The simplified method for prediction of number of cycleso crack initiation is approximate. It involves estimation oflastic–plastic strain range ahead of the crack tip. The distance, at which the representative strain range has been evaluated,s called the characteristic distance. It has been found that pre-iction of cycles to crack initiation gives good matching withxperimental results for d = 70 �m for the present material.his procedure is similar to as recommended by French A-16,ppendix of RCC-MR code (A16, 1995).After evaluation of �σpe, the corresponding pseudo elastic

train range has been evaluated by Eq. (4), which approximatelyakes into account the state of tri-axial stress on the pseudo plastictrain range:

εpe =(

Δσpe

E

)×

[2(1 + μ)

3

](4)

here μ is the Poisson’s ratio = 0.3.From the cyclic stress–strain Eq. (1) and the pseudo elastic

train range, the total strain range was evaluated using Neu-er’s rule (A16, 1995). Knowing the strain range, the numberf cycles to crack initiation was evaluated using the fatigue lifeurve Eq. (2). Predicted number of cycles required for cracknitiation are given in Table 6 for the pipes and elbows forhich crack initiation could be detected at 0.1 mm of crackrowth.

The comparisons of experimental and analytical crack initia-ion results, given in Table 6 and Fig. 12b, show that agreement iseasonable for many cases. Differences in the experimental andnalytical results may be due to the various assumptions maden the model of fatigue crack initiation. Initiation of the cracks strongly dependent on the material condition, state of stresshead of the crack tip, and characteristic distance (d) ahead ofotch tip. In reality characteristic distance varies with grain sizend inclusion content of the material and hence it is difficult toetermine an exact value. The state of stress is assumed to belane 2D and the triaxiality effect is accounted approximately inhe present model. However, in real case the triaxiality may beifferent and has to be evaluated based on 3D finite element anal-sis. Above all initiation of crack growth significantly dependsn the notch tip radius, which may not be exactly the same forll cases.

Observation shows that pipes tested with higher stress ratiolower stress range with higher mean stress) require moreycles for initiation compared to pipes tested with lower stressatio (higher stress range and lower mean stress). This can be

xplained by the fact that the mechanism of initiation requiresevelopment of slip planes in the material, which coincide withaximum shear stress, and becomes sites for crack initiation.his development of slip bands depends on the magnitude of

and Design 238 (2008) 801–813 809

tress range at the notch tip. The slip plane formation in theaterial may take place irrespective of the nature of the stress

rovided that the magnitude of the stress range applied is suffi-ient for creation of a slip band.

For a given stress range, the number of cycles required forrack initiation depends on the initial notch depth. Local stressange ahead of the crack tip will be higher for a deeper crack thanor shallow crack because the stress intensity factor is higher foreeper crack. This explains why the number of cycles requiredor initiation of crack in pipes having a deep notch would be lessn comparison to the pipe having a shallow notch.

.2. Fatigue crack growth in component tests

The fatigue crack growth tests on pipes and elbows wereonducted to determine the crack growth rate constants. As men-ioned earlier, several tests were conducted to understand theffect of different variables such as stress ratio, notch orienta-ion, pipe size, pipe and pipe weld. The experimentally observedffects of these variables are discussed in the following para-raphs.

.2.1. Comparison between pipes and specimen (CT orPB)

FCGR curves were determined for pipes from the crackength versus number of cycles record obtained during the tests.tress intensity factor range was evaluated based on the stressange (given in Tables 5a and 5b), instantaneous crack length andhe geometry factor (Andersson et al., 1996). FCGR curve deter-

ined for 219 mm, 324 mm and 406 mm outer diameter pipesre shown in Figs. 13–16. The comparison of crack growth rateurves of pipes with TPB specimens and the ASME curve [7] arehown in Figs. 13, 15 and 16. The Paris law constants evaluatedrom pipe and TPB specimens are given in Table 7. The compar-

Fig. 13. Comparison of FCGR curve of pipe and TPB specimen.

810 P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813

Fig. 14. Comparison of FCGR curve of pipe for different stress ratio.

F

tntc

TP

S

123456

Fig. 16. (a) Comparison of FCGR curve of pipe (406 mm outer diameter) andTs

6

oI

ig. 15. Comparison of FCGR curve of pipe 324 mm outer diameter and TPB.

From the component tests results it can be concluded thathe FCGR curve for the pipes and TPB specimens are not sig-

ificantly different. Experimental FCGR curve for pipes lies onhe lower side of ASME Section XI curve. This observation isonsistent with the specimen test results, too.

able 7aris law constants evaluated form pipe and TPB specimen

l No. Specimen ID Paris law constants

C m

Pipe 324 mm OD Pipe 2.262e-08 2.6287TPB 2.143e-09 3.21

Pipe 406 mm OD Pipe 8.2e-08 2.279TPB 8.87e-10 3.8

Pipe weld 406 mm OD Pipe Weld 9.4e-08 2.151TPB 6.98e-10 3.65

cFcs

6

alriorat

PB for base and weld. (b) Effect of stress ratio on FCGR in pipe and CTpecimen.

.2.2. Effect of stress ratio on FCGR in pipesIn Section 5.1, effect of stress ratio on FCGR has been brought

ut based on the results of the tests on CT or TPB specimen.nvestigations on the stress ratio effect on FCGR have been alsoarried out for pipes and is shown in Fig. 14. Fig. 14 indicates thatCGR is mildly affected by stress ratio in Paris region, which isonsistent with observation of specimen test results. This is alsohown in Fig. 16a.

.2.3. Aspect ratio evaluation with crack growthDuring the pipe test, crack length (circumferential direction)

nd crack depth (thickness direction) were measured at differentoading cycles. Based on these data, variation of crack aspectatio (2C/a) with crack growth in thickness direction is shownn Figs. 17 and 18 for 300NB and 400NB pipes, respectively. It is

bserved that aspect ratio decreases and becomes constant in theange of 4–5 at the time of through wall. Nature of 2C/a versus/t behaviour, as shown in Figs. 17 and 18, clearly highlightshat crack grows more rapidly in depth direction than in surface

P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813 811

Fig. 17. Variation in aspect ratio with crack growth for 324 mm outer diameterpipe.

Fp

dv

AsF

6

tcFT

P

Δ

Δ

E

wfs1lLi are outer and inner span of the four-point bend loadingcondition.

Analytical and experimental plot of maximum crack depthversus number of cycles are shown in Figs. 21–24 for pipes

ig. 18. Variation in aspect ratio with crack growth for 406 mm outer diameteripe.

irection. Such a behaviour is very important from the point ofiew of Level 2 LBB requirements.

Crack depth were measured along the crack length usingCPD instrument for all the cases. Typical crack shape as mea-

ured using ACPD and on the fracture surface is shown inigs. 19 and 20 respectively.

Fig. 19. Crack shape measured using ACPD-based instrument.Fd

Fig. 20. Typical fatigue fracture surface of pipe (1 × 1).

.2.4. Analytical estimationIn order to predict the number of cycles required for a crack

o grow through thickness after crack initiation, analytical cal-ulations were carried out based on the Paris law. In this analysisCGR constants obtained from the TPB specimen were used.he details of the analysis are given below.

Stress intensity factor range can be calculated from

ipe : ΔK = Δσ0√(πa) × FG (5)

σ0 = ΔM/Z (5a)

M = ΔP/4 (Lo − Li) and Z = π/32do × (d4o − d4

i ) (5b)

lbow : ΔK = (ΔσmMm + ΔσbMb)√

(πa) (6)

here �σm is the membrane stress range, Mm the correctionactor for membrane stress (ASME, 1989), �σb the bendingtress, Mb the correction factor for bending stress (ASME,989), �M the range of applied moment, �P–range of appliedoad, do the outer diameter and di the inner diameter, Lo and

ig. 21. Maximum crack depth vs. number of cycles for different initial crackepth (ai) and R = 0.1.

812 P.K. Singh et al. / Nuclear Engineering and Design 238 (2008) 801–813

Fig. 22. Maximum crack depth vs. number of cycles for different initial crackdepth (ai) and R = 0.5.

Fig. 23. Comparison of experimental and analytical results for 324 mm outerdiameter pipe.

Fig. 24. Comparison of experimental and analytical results for 406 mm outerdiameter pipe.

Fc

aa

tfcg

7

mcR

(

(

(

(

(

ig. 25. Comparison of experimental and analytical crack growth for crownrack elbow.

nd Fig. 25 for elbow. The analysis has been performed up to/t = 0.8.

Experimental and analytical results for crack growth in thehickness direction have been observed to be in good agreementor the pipes till a/t = 0.8. The overall comparison of analyti-al and experimental observation proves that the fatigue crackrowth model, employed in this paper, yields satisfactory results.

. Conclusions

The study describes the fatigue behaviour of the carbon steelaterial and piping components used in Indian PHWR. It also

ompares the fatigue behaviour of pipe welds with base material.esults of the study can be summarized as follows:

1) Low-cycle fatigue properties are higher (better) at room tem-perature compared to 288 ◦C for low-strain range, whereasat higher strain range properties are almost identical. Fatiguestrength (life) curve of SA333 Gr.6 compares well with thatgiven by ASME Section II of Boiler and Pressure Vesselcode for C–Mn steel.

2) FCGR does not depend on the notch orientation, pipe size,manufacturing process. FCGR in case of base and weld arealso the same. There is a mild dependence on stress ratio atlower values of R.

3) FCGR Paris law constants obtained for the pipe and standardspecimen, prepared from the tested pipe, are approximatelythe same for all the pipes. Slope of Paris curve, i.e., m, ismarginally higher for TPB compared to that of pipe.

4) Number of cycles to crack initiation can be predicted rela-tively well by a model based on evaluation of local stressbased on a fracture mechanics approach.

5) The use of the fatigue crack growth curve given in ASMESection XI will predict conservative results.

ering

(

(

R

A

A

A

A

C

C

D

E

E

E

E

K

N

S

S

S1998. Tensile and fracture properties evaluation of PHT system piping mate-

P.K. Singh et al. / Nuclear Engine

6) The experimental results also confirm that significant mar-gin is available against Level 2 LBB requirements. Thenumber of cycles required to produce through wall pene-tration is considerably higher than that anticipated in IndianPHWRs.

7) The crack growth in depth (thickness) direction is signifi-cantly more rapid than in length (circumferential) direction.This is desirable for application of LBB.

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