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International Journal of Pressure Vessels and Piping 88 (2011) 415e422

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International Journal of Pressure Vessels and Piping

journal homepage: www.elsevier .com/locate/ i jpvp

Effect of vibration loading on the fatigue life of part-through notched pipe

Rahul Mittal a, P.K. Singh b,*, D.M. Pukazhendi c, V. Bhasin b, K.K. Vaze b, A.K. Ghosh b

aNuclear Power Corporation of India Limited, Mumbai, IndiabBhabha Atomic Research Centre, Mumbai, Indiac Structural Engineering research Centre, Chennai, India

a r t i c l e i n f o

Article history:Received 20 May 2010Received in revised form7 July 2011Accepted 8 July 2011

Keywords:Part-through notchFatigue crack initiationFatigue crack growthStress ratioVibration loadingCyclic loading

* Corresponding author. Tel.: þ91 22 25591522.E-mail address: singh_pawank@yahoo.com (P.K. S

0308-0161/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.ijpvp.2011.07.004

a b s t r a c t

A systematic experimental and analytical study has been carried out to investigate the effect of vibrationloading on the fatigue life of the piping components. Three Point bend (TPB) specimens machined fromthe actual pipe have been used for the evaluation of Paris constants by carrying out the experimentsunder vibration þ cyclic and cyclic loading as per the ASTM Standard E647. These constants have beenused for the prediction of the fatigue life of the pipe having part-through notch of a/t ¼ 0.25 and aspectratio (2c/a) of 10. Predicted results have shown the reduction in fatigue life of the notched pipe subjectedto vibration þ cyclic loading by 50% compared to that of cyclic loading. Predicted results have beenvalidated by carrying out the full-scale pipe (with part-through notch) tests. Notched pipes were sub-jected to loading conditions such that the initial stress-intensity factor remains same as that of TPBspecimen. Experimental results of the full-scale pipe tests under vibration þ cyclic loading has shown thereduction in fatigue life by 70% compared to that of cyclic loading. Fractographic examination of thefracture surface of the tested specimens subjected to vibration þ cyclic loading have shown higherpresence of brittle phases such as martensite (in the form of isolated planar facets) and secondary microcracks. This could be the reason for the reduction of fatigue life in pipe subjected to vibration þ cyclicloading.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Piping components are subjected to vibration loading caused byrotary equipments viz. pumps, compressors etc in the pipingsystem. These vibration loadings are of the low amplitudes butextend over the lifetime of plant operation and causes severemechanical damage leading to reduction of the life of the pipingcomponents. Vibration induced fatigue may lead to excessive pipevibration which can cause real problems like loosening of threadedconnections, leakage through flanges, knocking off the pipes fromtheir supports. S.N. Huang [1] brought out the procedure to assessthe fatigue damage of the piping systems and explained the feasi-bility of the estimation of piping responses resulting from pump-induced vibration with the limited test data. ASME O&M designcode [2] calls for qualification of piping system in terms of velocityand deflection of the piping system subjected to the vibrationduring plant operation. These piping components are also sub-jected to higher amplitude cyclic loading due to plant startup andshut down. The effect of simultaneous occurrence of cyclic loading

ingh).

All rights reserved.

along with the vibration loading on piping system has not beendiscussed in ASME.

Fatigue crack initiation has been studied in the past usingnotched small specimens by evaluating local stress or strain at thenotch tip considering the stress or strain concentration, equivalentenergy density method and low cycle fatigue curve [3]. Evaluationof fatigue crack initiation life using fracture mechanics approachhas also been reported.

Austenite to martensite transformation has been observed in300 series stainless steels, which results in a reduced fatigue life [4].The extent of the martensite transformation depends on severalfactors such as the chemical composition of the steel and thetemperature at which the deformation taking place [5,6].Martensite can be induced in an austenitic stainless steel when thematerial is plastically deformed at certain temperature, whichdetermine the stability of the austenite with respect to theformation of alpha martensite [7]. The formation of martensiteduring deformation at the room temperature in austenitic steelsuch as 304L and 304LN steel has been reported [8e11]. Straininduced martensite has a great influence on the mechanical prop-erties of austenitic stainless steels. The presence of the martensitecan produce significant changes in the tensile properties, strainhardening behavior and fracture toughness. There is no literature

Table 2Room temperature tensile properties of pipe material.

Yield strength(MPa)

Ultimate strength(MPa)

Young’s modulus(GPa)

%Elongation

298 620 195 69

Table 3Constants for Cyclic stressestrain and Low cyclic fatigue curve.

k (MPa) n s (MPa) 3 (%) b c E (GPa)

R. Mittal et al. / International Journal of Pressure Vessels and Piping 88 (2011) 415e422416

available showing that the formation of martensite will lead toincrease in crack growth rate.

In view of this, effect of simultaneous occurrence of vibrationand cyclic loading on fatigue life of the piping components isrequired to be investigated for the safe operation of the plant. In thepresent paper, a systematic experimental and analytical study havebeen carried out to investigate the effect of vibration loading alongwith cyclic loading on fatigue life of piping components. The effectof the crack tip radius on the fatigue crack initiation life has alsobeen addressed.

f f

217.36 0.3248 1116.515 33.3 0.1428 �0.5266 195

Fig. 1. Location of the TPB specimen machined from pipe.

2. Experimental details

The piping material under study is austenitic stainless steelSA312Type SS304LN in solution-annealed condition. The chemicalcomposition and the tensile properties are given in Tables 1 and 2.

Cyclic stressestrain and low cycle fatigue properties have beenobtained following ASTM E606 for different strain ranges at roomtemperature and air environment [12,13]. The cyclic stressestrainand the low cycle fatigue curves are given in equations (1) and (2)respectively. The various constants in the equation have beenobtained by fitting the test data points and given in Table 3.

D 3=2 ¼ 100ðDs=2EÞ þ ðDs=2kÞ1=n (1)

D 3=2 ¼ sf =Eð2NiÞbþ 3f ð2NiÞc (2)

where D 3is strain range, Ds is stress range and Ni is the number ofcycles required for failure (complete separation) of the specimen.

Three Point Bend specimens have been machined as per ASTME647 [14] from the pipe of outer diameter 168 mm and thickness14.3 mmwith notch in L-C direction (L refer to load in longitudinaldirection and C refer to notch in circumferential direction). Locationof the specimens and crack plane orientationwith respect to pipe isshown in Fig. 1.The dimensions such as width (W), thickness (B),initial crack length (ao) of TPB specimen are 20 mm, 10 mm and5mm respectively. These specimens were having different crack tipradius as 0.2, 0.3 and 0.5 mm.

Three Point Bend specimens were fatigue tested under constantamplitude sinusoidal vibrationþ cyclic and cyclic loading. The testswere conductedwith load ratio(R) of 0.1. The loading frequencywas20 Hz for vibration loading and 2.5e5 Hz for cyclic loading. Theconstant amplitude load applied during the test was calculatedbased on the fact that the initial stress-intensity factor for the TPBspecimens is same as that of the notched pipe. The details of theload applied during vibration loading and cyclic loading are givenin Table 4.

The full-scale pipes of 168 mm outer diameter and 14.3 mmwallthickness have been used for tests. The pipe specimens were havingsurface notch, machined at the outer surface in the circumferentialdirection. The detail of the notch and pipe test setup has beenshown in Fig. 2. The length (2c) and depth (a) of the crack was36 mm and 3.5 mm respectively. Full-scale pipe tests have beencarried out at room temperature and air environment underconstant amplitude sinusoidal vibrationþ cyclic and cyclic loading.The tests were conducted with stress ratios (R) of 0.1. The loadingfrequencywas 10 Hz for the vibration loading and 0.05e1 Hz for thecyclic loading. The maximum applied loading was such that the

Table 1Chemical composition (in wt %) of pipe material.

C Mn Si P S Mo

0.017 1.76 0.29 0.022 0.0029 0.19

linear elastic condition is maintained. The vibration and cyclicloadings corresponding to 10% and 40% of collapse load respectivelyhas been applied.

3. Experimental results

The fatigue crack initiation life has been evaluated consideringthe effect of notch tip radius for vibrationþ cyclic loading and cyclicloading. The details of the fatigue crack initiation results have beenshown in Table 4 for TPB and pipe test. No crack initiation has beenobserved in TPB specimens during the vibration loading. This wasconfirmed by observing the notch tip of TPB specimen under opticalmicroscope. In case of TPB specimen number of cycles to crackinitiation as given in Table 4 corresponds to the 0.5 mm of crackgrowth. In case of pipe, crack initiation was assumed to occur forthe measured crack growth of 0.1 mm. This is the minimum cracklength, which could be measured using instrument based on theAlternating Current Potential Difference (ACPD) technique.

The fatigue initiation life increases with increase in crack tipradius. During the experiments on the TPB specimen subjected tovibration þ cyclic loading and cyclic loading only, it has been foundthat the fatigue life has been increased by 45%e75% for the crack tipradius variation from 0.2 to 0.5 mm. There is a reduction in thefatigue crack initiation life by 20e35% for specimens subjected tovibration þ cyclic loading in comparison to specimens subjected tocyclic loading only.

During the Fatigue Crack Growth Rate (FCGR) tests, crack lengthand number of cycles have been recorded. The crack length andnumbers of cycles recorded have been shown in Figs. 3 and 4. Thecurves shown in Figs. 3 and 4 for crack growth life includes thenumbers of cycles to crack initiation. The difference in fatigue life isdue to the variation in crack initiation life. The variation of stress-

Cr Ni Ti N Nb Cu

18.9 9.65 0.006 0.08 0.02 0.2

Table 4Experimental results for crack initiation.

Specimen ID. no. Type of loading Tip radius (mm) PL (KN) Maximum applied load(KN)

DK (MPaOm) Cycles (Ni)

Vibration Cyclic Vibration Cyclic

TPB_P3 Vibration þ cyclic 0.2 17.4637 1.7464 7.25 5.99 27.39 5000TPB_R1 Cyclic 0.3 17.4637 1.7464 7.25 5.99 27.39 12000TPB_R2 Vibration þ cyclic 0.3 17.4637 1.7464 7.25 5.99 27.39 9000TPB_R3 Cyclic 0.3 17.4637 1.7464 7.25 5.99 27.39 15000TPB_S1 Vibration þ cyclic 0.5 17.4637 1.7464 7.25 5.99 27.39 20000TPB_S2 Cyclic 0.5 17.4637 1.7464 7.25 5.99 27.39 24750Pipe1 Vibration þ cyclic e 645 55 258 5.99 27.39 1000Pipe2 Cyclic e 645 55 258 5.99 27.39 5000

Vibration þ cyclic means vibration loading followed by cyclic loading, Cyclic means only cyclic loading, Ni is number of cycles to crack initiation, PL is collapse load.

R. Mittal et al. / International Journal of Pressure Vessels and Piping 88 (2011) 415e422 417

intensity range with crack growth rate has been shown in Figs. 5and 6 for vibration þ cyclic and cyclic loading. Figures show therepeatability or scatter in two sets of experiments.

The crack length and number of cycles obtained experimentallyhave been used to calculate the Paris constants following therelationship between the crack growth rate and the stress-intensityfactor range as given in equation (3).

da=dN ¼ cðDKÞm (3)

where, da/dN is fatigue crack growth rate (m/cycle) and DK isStress-intensity factor range (MPaOm). da/dN and correspondingstress-intensity factor ranges (DK) at a point have been evaluatedfor given stress range and crack depth. These data pairs of da/dNand DK have been fitted to obtain Paris Law constants ‘c’ and ‘m’

values. The values of constant c and m obtained for TPB specimenshave been shown in Table 5.

The numbers of cycles and crack length obtained from the full-scale pipe (with surface notch) tests have been shown in Fig. 7 forvibrationþ cyclic and cyclic loading only. The cycles are inclusive ofcrack initiation and growth. The variation in fatigue crack initiationlife with crack tip radius is shown in Fig. 8.

4. Analytical results

Analytical studies have been carried out for fatigue crack initi-ation and fatigue crack growth for TPB specimen and notched pipe.The effect of the initial notch tip radius on the fatigue crack initi-ation life has also been considered during evaluation. The analysisinvolves use of cyclic stressestrain curve to evaluate the strainrange and corresponding number of cycles to crack initiation havebeen evaluated from the low cycle fatigue curve. The cyclicstressestrain curve and the low cycle fatigue curve required foranalysis are given in Section 2. Two approaches have been followedfor evaluation of the strain range (D 3) near the crack tip region. Theyare (1) Estimation by Creager-Neuber’s Rule and (2) Finite ElementAnalysis (FEA).

In Creager-Neuber’s estimation scheme, it is assumed that thestate of stress is plane 2D type. In presence of blunt notch withcrack tip radius ‘r’ and under the action of remote stress range(Dso), the approximate value of maximum pseudo elastic stressrange (Dspe), at any distance ‘d’ from the notch tip can be calculatedby equation (4).

Dspez�DK=

ffiffiffiffiffiffiffiffiffi2pr

p �ð1:0þ r=2rÞ (4)

where, r ¼ dþ r/2. The simplified method for prediction of numberof cycles to crack initiation is approximate. Estimation of elastice-plastic strain range ahead of the crack tip will give more accurate

result. The distance d, at which the representative strain range hasbeen evaluated, is called the characteristic distance. The character-istic distance employed in the French A16 guide [15] is based on thehypothesis that for crack initiation froma blunt notch to occur,finitevolume of the material has to undergo damage. After evaluation ofDspe the corresponding pseudo elastic strain range has been eval-uated by equation (5), which approximately takes into account thestate of tri-axial stress on the pseudo plastic strain range

D 3pe ¼ Dspe=E½2=3ð1þ mÞ� (5)

where m is Poisson’s ratio ¼ 0.3. From the cyclic stressestrain curveand the pseudo elastic strain range, the total strain range has beenevaluated using Neuber’s rule [3]. Knowing the strain range, thenumber of cycles to crack initiation has been evaluated using thelow cycle fatigue life curve.

Non-linear analysis has been carried out on the three-dimensional (3D) solid model of notched pipe specimen. The 20-noded hexahedron elements have been used to discretize thenotched pipe specimen. Only one-fourth symmetric domain hasbeen modeled. Applying normal stress boundary condition at thefree edges simulated the pure bending moment. Finite elementanalysis has been performed to evaluate D 3distribution for theapplied cyclic load. The FE model of pipe specimen has been shownin Fig. 9. The force has been distributed on number of nodes inorder to avoid local yielding at the point of application of load. Ina similar manner, support constraints have been applied ata number of nodes to confirm model requirements.

The equivalent elasticeplastic strain has been evaluated eitherfrom FE analysis or from the Creeger’s hypothesis as mentionedabove at different ‘d’ distance ahead of the notch root. The distance,at which the number of cycles corresponding to effective elas-ticeplastic strain amplitude matches with the experimental value,has been taken as ‘characteristic distance’.

The number of cycles to crack initiation for vibration þ cyclicloading as determined through FEA/creeger’s estimation have beencombined and compared with experimental result using theMiner’s rule to determine the characteristic distance, d. Thecomparison of characteristic distance calculated from FEA andCreager’s estimation scheme (A16) for notched pipe with crack tipradius (r) 0.1 mm has been tabulated in Table 6. The characteristicdistance has been found to vary from 75 to 85 mm forvibration þ cyclic loading and 110e120 mm for cyclic loading. A16gives characteristic distance of 50 microns for austenitic stainlesssteel which is lower than that observed in this paper. This paper hasevaluated the characteristic distance for 304LN steel for cyclic andvibration þ cyclic loading which is 110e120 microns and 75-85microns respectively. This indicates that the characteristic distancedepends on the notch dimensions and the loading conditions.

Fig. 2. Experimental setup for tests on notched pipe with notch detail.

7500 15000 22500 30000 37500 450004

6

8

10

12

14

16

Cra

ck g

row

th in

mm

No of Cycles

TPB_P3 TPB_R2 TPB_S1

Fig. 3. Fatigue Crack growth curve under vibration þ cyclic loading.

00101

1E-7

1E-6

1E-5

Vibration+Cyclic loading

Cyclic loading

da/d

N (

m/c

ycle

)

K, MPa-m1/2

TPB_R1_m=2.965,c=6.722 x10-12TPB_R2_m=3.423,c=1.319 x10-12

Fig. 5. Comparison of fatigue crack growth rate under vibration þ cyclic with cyclicloading.

0010110

-8

10-7

10-6

Vibration+Cyclic loading

cyclic loading

da/d

N (

m/c

ycle

s)

K , MPa-m1/2

TPB_S1_m=3.016,c=7.080 x10-12TPB_S2_m=2.892,c=1.361 x10-11

Fig. 6. Comparison of fatigue crack growth rate under vibration þ cyclic with cyclicloading.

Table 5Paris’s constants for TPB specimens.

SpecimenID no.

Type of loading Crack tipradius(mm)

Paris’s constants

m C (m/cycle)

TPB_P3 Vibration þ cyclic 0.2 2.845 1.099 � 10�11

TPB_R1 Cyclic only 0.3 2.965 6.722 � 10�12

TPB_R2 Vibration þ cyclic 0.3 3.423 1.319 � 10�12

TPB_R3 Cyclic only 0.3 2.967 3.460 � 10�12

TPB_S1 Vibration þ cyclic 0.5 3.016 7.080 � 10�12

R. Mittal et al. / International Journal of Pressure Vessels and Piping 88 (2011) 415e422418

Characteristic distance given by A16 is not unique for the material.Therefore use of 50 microns as given by A16 for austenitic stainlesssteel may lead to conservative results.

The crack growth in notched pipe has been evaluated using Paris-law relationship as given by equation (3). Paris constants obtainedfrom TPB specimens has been used for calculating the crack growthin notched pipe. Analytical results for the crack growth and thenumber of cycles i.e. fatigue crack growth curve for notched pipesubjected to cyclic and vibrationþ cyclic loading have been shown inFigs. 10 and 11.

10000 20000 30000 40000 500004

6

8

10

12

14

Cra

ck G

row

th in

mm

No. of cycles

TPB_R1TPB_S1

Fig. 4. Fatigue Crack growth curve under cyclic loading.

TPB_S2 Cyclic only 0.5 2.892 1.361 � 10�11

0 10000 20000 30000 40000 50000

2

4

6

8

10

12

14

Cra

ck g

row

th (

mm

)

No. of cycles

Pipe under vibration+cyclic loadingPipe under cyclic loading

Fig. 7. Crack initiation and growth curve for notched pipe.

o.2 0.3 0.5

4000

8000

12000

16000

20000

24000N

o. o

f cyc

les

Crack tip radius in mm

under cyclic loading under vibration+cyclic loading

Fig. 8. Effect of crack tip radius on fatigue crack initiation life.

Fig. 9. Finite element model of pipe specimen.

0 15000 30000 45000 60000

4

6

8

10

12

Cra

ck G

row

th in

mm

No. of cycles

ExperimentAnalytical TPB_R3

with m=2.967,c=3.46E-12

Fig. 10. Comparison experimental and predicted of Fatigue crack growth for cyclicloading.

0 15000 30000 45000 600002

4

6

8

10

12

Cra

ck G

row

th in

mm

No. of cycles

Experiment TPB_P3,m=2.845,c=1.099 E-11 TPB_R2,m=3.432,c=1.319 E-12 TPB_S1,m=3.016,c=7.087 E-12 TPB_R3,m=2.967,c=3.460 E-12

Fig. 11. Comparison experimental and predicted of Fatigue crack growth forvibration þ cyclic loading.

R. Mittal et al. / International Journal of Pressure Vessels and Piping 88 (2011) 415e422 419

5. Discussion

Fatigue crack initiation depends on the crack tip radius andcharacteristic distance (d) as per the A16 approach [15] based onfracture mechanics. The variation in equivalent elasticeplasticstrain near the crack tip has been evaluated using FEM for differentcrack tip radius of TPB specimens under cyclic andvibrationþ cyclic loading condition. This has been shown in Fig. 12.Crack initiation in a material involves nucleation and formation offine cracks. The formation of the slip planes coincides with themaximum shear stress, which are the sites for the crack nucleation.Aminimumvalue of the shear stress is required for the formation ofthe slip band, called critical shear stress. However, during thevibration loading the applied stress in global region may not besufficient to form slip band but the state of the stress near the cracktip could be high enough to form slip band, which may lead to

Table 6Comparison of characteristic distance calculated from A16 and FEA.

Specimen ID. no a/t 2c/a Load (KN)

Max.

Pipe1 0.25 10.00 �55 (V)�258 (C)

Pipe2 0.25 10.00 �55 (V)�258 (C)

a Ni is number of cycle for fatigue crack initiation. V-Vibration, C-Cyclic.

formation of crack nucleation sites. The fracture resistance of thematerial reduces if it has been subjected to cyclic loading prior tofracture test. This is due to the hardening taking place in thematerial. Fracture resistance reduction in the material depends onthe product of stress range and number of cycles. If this product ismore fracture resistance reduction is more. Although applied loadamplitude is low but the number of applied cycles during thevibration loading is too large which may be cause for reduction inthe fracture resistance of the material [3]. Reduction in fractureresistance will lead to higher crack growth rate.

The most common approach, based on the stress-intensityfactor range near the crack tip at given characteristic distance hasbeen used for evaluating fatigue crack initiation life in notched pipe[3]. The experimental and analytical results for pipes subjected tovibration þ cyclic loading have been found to be in agreement, for

Nia (experimental) Characteristic

distance d (mm)

Min. A16 FEA

�5.5 1000000 78 6525.8 1000�5.5 1000000 85 7825.8 2000

Fig. 14. Striations away from crack tip.

0.2 0.3 0.4 0.5

0.005

0.010

0.015

0.020

Equi

vale

nt S

train

Crack Tip Radius in mm

Under vibration loading only Under Vibration+cyclic loading

Fig. 12. Variation of Equivalent strain with crack tip radius.

R. Mittal et al. / International Journal of Pressure Vessels and Piping 88 (2011) 415e422420

a characteristic distance ranged from 75 to 85 mm. For 304LNmaterial, characteristic distance is not available in the literature.However a value of 78 mm evaluated using A16 guide [15] and75 mm using FEA produces good comparisonwith the experimentaldata. Use of characteristic distance of 50 mm as given in A16 guidemay lead to conservative prediction of crack initiation life. Foraccurate prediction, characteristic distance for a given material andnotch dimensions required to be evaluated using FEM. As shown inthis paper that evaluation of d using A16 guide and FEA givessimilar value.

The experimental and analytical results for crack growth in thethickness direction have been observed to be in good agreement forthe pipes subjected to cyclic loading. In this case, Paris constantsm ¼ 2.967 and C ¼ 3.460 x10�12 has been used. In case ofvibration þ cyclic loading, Paris constants m ¼ 3.016 andC¼ 7.087� 10�12 has been used. During the fatigue test on the pipeit has been found that the fatigue life (initiation þ growth) of thepipe with vibrationþ cyclic loading reduces in comparison to cyclicloading. The predicted fatigue life of the pipe using Paris constantsobtained from TPB specimen with vibration þ cyclic loading hasbeen observed to be 20,000 cycles (which is 50%) less than thatobtained using Paris constants of TPB with cyclic loading. Thisindicates that vibration loading affects the fatigue life. Paris lawconstants evaluated from virgin pipe will give non-conservativeresults if used, for pipe subjected to vibration þ cyclic loading.Fatigue Crack growth life using Paris constants from TPB specimenssubjected to vibrationþ cyclic loading gives better predictionwhen

Fig. 13. Striations near the crack tip.

the pipe is subjected to both low amplitude vibration loading andhigh amplitude cyclic loading, compared to that of cyclic loading.Use of Paris constants for evaluation of fatigue crack growth life ofthe pipe subjected to vibration loading may be desirable.

The fractographic examination of the fracture surfaces of testedTPB specimens under vibration þ cyclic and cyclic loading, havebeen carried out under Scanning Electron Microscope (SEM).Fracture surface of the tested specimens have not shown regularand clear striations but some patches of striations have beenobserved. Micrographs of the fatigue fracture surface showingpatches of striations near and away from the crack tip have beenshown in Figs. 13 and 14. The striation spacing (measure of crackgrowth per cycle) measured on the fracture surface of the speci-mens tested under cyclic loading has been of the range of1e1.25 mm, which is of the same order as obtained with experi-mental data.

Fracture surface revealed the presence of isolated planar facets(dark patch marks). The typical fractographs of fracture surfaceexhibiting such features in both cases are shown in Figs. 15 and 16.These features basically indicate occurrence of brittle modes offracture at local regions probably originating from presence ofbrittle phases such as martensite in such locations. The fracturesurface examined for both cases i.e. vibration þ cyclic and cyclicloading, indicated that number of these facets were more near the

Fig. 15. Martensite phases for the specimen subjected to vibration þ cyclic loading.

Fig. 16. Martensite phases for the specimen subjected to cyclic loading.Fig. 18. Secondary micro cracks near the crack tip during cyclic loading only.

R. Mittal et al. / International Journal of Pressure Vessels and Piping 88 (2011) 415e422 421

crack tip regionfor specimen subjected to vibration þ cyclic ascompared to the region away from crack tip.

In the quest for explanation of the apparent difference in theFCGR behavior of 304LN stainless steel subjected to vibration þcyclic loading and cyclic loading only, the fracture surfaces near andfar away from the crack tip has been examined. After carefulexamination of the fracture surface, presence of martensitic colo-nies at local regions has been observed. Considering that asreceived microstructure is completely austenitic, this observationsuggests that the martensitic transformation must have occurredduring deformation at the crack tip due to cyclic loading and theformation of martensite is more dominant in the specimen sub-jected to vibration þ cyclic loading.

The fractographic examination also revealed the presence of thesecondary micro cracks along with martensetic planer facets on thefracture surface of the specimens subjected to vibration þ cyclicloading. These secondary micro cracks have been found to be morein the region near to the crack tip for vibrationþ cyclic as comparedto the region away from the crack tip. Representative photographsrevealing such difference in the martensite colonies in both casesi.e. Vibrationþ cyclic loading and cyclic loading have been shown inFigs. 17 and 18. Finally faster crack growth in the specimen

Fig. 17. Secondary micro cracks near the crack tip during vibration þ cyclic loading.

subjected to vibration þ cyclic loading is attributed to themartensite formation and the secondary micro cracks.

6. Conclusions

The study describes the effect of vibration loading on the fatiguelife of the austenitic stainless steel notched pipe and the same issummarized:

1. The fatigue initiation life increases with increase in crack tipradius. During the experiments with TPB specimen subjected tovibration þ cyclic loading and cyclic loading only, it is foundthat fatigue life is increased by 45%e75% if the crack tip radiusvaries from 0.2 to 0.5 mm. There is a reduction in the fatigueinitiation life by 20e35% for specimens subjected tovibration þ cyclic loading as compared to specimens subjectedto cyclic loading only.

2. The analytical and experimental results are found to be in goodagreement for a characteristic distance that varies from 75 mmto 85 mm for pipe subjected to vibration þ cyclic loading.

3. The fatigue life of the notched pipe subjected to vibration þcyclic loading has been found to be 70% lower to that ofnotched pipe subjected to cyclic loading only.

4. The fatigue life of the pipe using Paris constants obtained fromstandard specimen with vibration þ cyclic loading is 20,000cycles, (which is 50%) less than that of using Paris constants ofspecimen with cyclic loading only. Paris law constants evalu-ated from virgin pipe will give non-conservative results if used,for pipe subjected to vibration loading.

5. The fractographic examination confirmed the fatigue crackgrowth observed during test by measuring the striationspacing. Fracture surface examination also revealed that fastcrack growth in the specimen subjected to vibration þ cyclicloading is due to the martensite formation and the secondarymicro cracks.

Acknowledgments

The authors wish to thank Shri Sunil Kumar, PIED, BARC formeasurement of striation spacing by taking the photographs of thefatigue fracture surface under SEM, which helped in comparing themeasured crack growth rate by ACPD.

R. Mittal et al. / International Journal of Pressure Vessels and Piping 88 (2011) 415e422422

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