assesment of interaction effect between two aligned surface cracks in elbows subjected to internal...

7/29/2019 Assesment of Interaction Effect Between Two Aligned Surface Cracks in Elbows Subjected to Internal Pressure

1/6

1 Copyright 2010 by ASME

Proceedings of the ASME 2010 Pressure Vessels & Piping Divis ion / K-PVP ConferencePVP2010

July 18-22, 2010, Bellevue, Washington, USA

PVP2010-25604

ASSESMENT OF INTERACTION EFFECT BETWEEN TWO ALIGNED SURFACECRACKS IN ELBOWS SUBJECTED TO INTERNAL PRESSURE

Han-Beom Seo, Jae-Boong Choi and Young-Jin K imSchool of Mechanical Engineering, Sungkyunkwan University

300 Chunchun-dong, J angan-gu, Suwon, Kyonggi-do 440-746, Republic of Korea

Yoon-Suk ChangDepartment of Nuclear Engineering, Kyung Hee University

1 Seochen-dong, Giheung-gu, Yongin, Kyonggi-do 446-701, Republic of Korea

Hyun-Su KimKorea Power Engineering Company, Inc.

360-9 Mabuk-dong, Giheung-gu, Yongin, Kyonggi-do 449-713, Republic of Korea

ABSTRACT

Adjacent multiple cracks can be found in power plant

components such as pressure vessel, piping and so forth. Ifmultiple cracks are detected, it can be affected significant effect

to structure integrity due to high interaction effect of the

multiple cracks. Therefore general fitness-for-service (FFS)

codes and standards propose assessment method for the

multiple cracks. The Section XI of ASME Code suggests crack

coalescence method for multiple cracks. It employs the

approach combining neighbored cracks as single crack if the

distance between them is close. In some cases, since this

combined rule can be considered as a conservative approach,

more accurate investigation of the interaction effect between

multiple cracks is needed. In this study, the interaction effect

between two aligned coplanar circumferential surface cracks in

elbows subjected to internal pressure was investigated. Sincemost previous studies dealt with only plates or straight pipes,

the present research was centered on cracked elbow. FE (Finite

element) limit analyses were carried out by changing elbow

geometries and crack shapes. Also, applicability of the current

criterion for the multiple cracks was discussed.

INTRODUCTION

During in-service inspection (ISI), several adjacent flaws

are frequently detected in power plant components. If theses

adjacent flaws are located nearly, they can have a significant

effect on structure integrity due to interference of stress field

around crack tip. Accordingly, the adjacent multiple cracks

should be treated in fitness-for-service (FFS) to evaluate

precise structure integrity. Generally, various FFS codes and

standards such as Section XI of ASME Code[1], JSMECode[2], API 579[3] proposed assessment approach for the

adjacent multiple cracks.

The Section XI of ASME Code recommends the crack

coalescence model to estimate structure integrity of multiple

cracks. If the distance between the adjacent cracks is equal to

or less than specific criterion which depends on the crack

depth, they are substituted as a single crack. However, this

coalesced rule is regarded as conservative manner in some

cases. It means that the interaction effect of adjacent cracks is

highly estimated. Several researches are performed to examine

the interaction effect between the adjacent cracks and its

conservatism[4,5]. To evaluate the interaction effect around

adjacent cracks, fracture mechanics assessment methods wereutilized such as linear elastic fracture mechanics, elastic plastic

fracture mechanics and limit load analysis.

In this study, detailed parametric 3-dimensional plastic

limit analyses for two aligned surface cracks in elbows are

carried out. Conservatism of coalesced criterion in the Section

XI of ASME is reviewed and assessment of interaction effect

between multiple coplanar surface cracks in elbow is

investigated.

CONSERVATISM OF COALESCED CRITERION INASME SECTION XI

ownloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 07/22/2013 Terms of Use: http://asme.org/terms


2/6


In accordance with the Section XI of ASME, when thedistance of adjacent multiple cracks is too close, they are

substituted as equivalent single cracks. To determine the

combined condition, the standard of distance between adjacentcracks (S) and offset distance (H) are defined as follows;

H 13mm (1)S 0.5 max (a1, a2)

where l is the crack length and a is the crack depth as

demonstrated in figure 1. In case of aligned coplanar flaws, theoffset distance is ignored. Only the distance between adjacentcracksis solely remained to determine the combined condition.The size of equivalent single crack was determined as follows;

l = l1+l2+S (2)a = max (a1, a2)

Furthermore, the limit load solution for the elbow with asingle crack (PL) subjected to internal pressure was proposedby Kim et al.[6] as follows;

l1 S l2

a1

a2a

Coalesced

single crack

Fig. 1 Combined rule of the adjacent multiple cracks in ASME

SECTION XI

0.0 0.2 0.4 0.6 0.8 1.00.2

0.4

0.6

0.8

1.0

1.2

Maximum

difference : 37%

Rm/t= 5 , = 0.5

Eq. (3)

FE results (Dual crack)

PL

/PO

a/t

Fig. 2 Comparison of normalized FE limit pressure betweenmultiple cracks and coalesced single crack

min 1.0, 3.9 1.5 1.5L

o

P a

P t

(3)

2

2

3 (1 exp( ( / ))o o

B m

tP

r A B R t R

(4)

0.09

1.19 1 1

0.0013 0.307

rA

t

rB

t

where PO is the un-cracked limit load subjected to internalpressure. The plastic limit pressure with cracked elbow is

normalized to the limit load pressure of un-cracked.Some limitations of the ASME coalesced criterion were

confirmed throughout the preliminary FE analyses. Figure 2shows comparison of the normalized limit loads between dual

cracks by FE results and coalesced single crack by Kimssolution[6]. The single crack was combined by ASMEcriterion. As shown in Fig. 2, when a/tis smaller than 0.5, thedifference between them was approximately 7%. It means thatthe coalesced criterion is useful in given condition. However,

as the increase of the a/t value, the difference increased morethan 37%. It means that the coalesced criterion is tooconservative as crack depth is deeper.

DETAILED FE ANALYSESThe FE limit load analyses were carried to evaluate

interaction effect of multiple cracks. Detailed procedure was

described in the following sub-sections.

Geometry

Figure 3 demonstrates the geometry condition of elbow inthe present work. The piping system was conducted as

attaching the two straight pipes at the end of 90 elbow. Notethat the length of straight pipe is three times of outer radius ofpipe. Herein, RB is the bend radius andL is the length ofstraight pipes. Several variables are chosen to perform the FEanalyses for multiple cracks and coalesced single crack. Figure

4 demonstrates the shapes of crack were employed in thepresent work. Multiple crack depth, angle and length aredenoted as a, , and l. Also, single crack angle and length aredenoted as S andlS. The relevant range of these variables wasconsidered. Values ofRm/t as 5 and 10, four values of a/t

ranging from 0.25 to 1, three values of / from 0.167 to 0.5and two values ofRB/Rm as 2 and 4 are selected. Furthermore,both of coplanar cracks which have identical geometry wereconsidered. The distance between multiple cracks is taken into

account as a1/2 preferentially in the present work.



3/6


RB

Extrados

Intrados

Crack

L

Fig. 3 Schematic illustration of 90elbow with a crack

a a

S

t

Rm Ro

l l

as

ls=l+S+ls

t

Rm Ro

(a) (b)Fig. 4 Geometry and dimensions for (a) circumferential

coplanar aligned surface cracks and (b) circumferentialcoalesced single surface crack

Analysis Method

Figure 5 shows typical FE models used in this study. Sincethe geometry of cracked elbows has a symmetric characteristic,

a half model was generated. To avoid incompressibilityproblem, iso-parametric reduced twenty-node quadratic brick

element (C3D20R in ABAQUS element library) wasutilized[7]. Approximately 11,000 nodes and 48,000 elementswere used to build the model. To verify the model, the FE

results of single crack and Eq. (3) was compared in figure 6.Note the geometry and dimension of adjacent dual cracks andcoalesced single crack in figure 4. As a result, the maximumdifference was less than 7% as depicted in the figure. It shows

that applicability of the employed FE model. Internal pressurewas applied to inner surface of elbow and crack face. Also,

(a) Elbow with single surface crack

(b)Elbow with multiple surface cracksFig. 5 Typical FE models employed in the present study

tension load is added at the end of attached straight pipe forconsidering end effect[8]. Material was assumed to obeyelastic-perfectly plastic approximation in the FE analyses.

Material properties is defined; Youngs modulus as 182.7GPa,Poissons ratio as 0.3 and yield strength as 194MPa,respectively. ABAQUS RIKS option was utilized to obtainreliable estimate for the load carry capacity of structure innonlinear analysis.



4/6


0.0 0.2 0.4 0.6 0.8 1.00.6

0.7

0.8

0.9

1.0

1.1

1.2R

m/t= 5, = 0.167

Eq. (3)

FE results (Single crack)

PL

/PO

a/t

Fig. 6 Verification of solution for single surface cracked elbow

Analysis Results

In the preliminary study, the conservatism of coalesced

criterion of ASME code was confirmed in figure 2. To verifymore precisely this conservatism, limit pressure betweenmultiple cracks and coalesced single crack is compared in

figure 7. Here, limit pressure of multiple cracks by FEA(PLM) isnormalized to that of single crack by Kims solution(PLS)[6].

This figure shows that most of PLM/PLS values are higher than1. and increasingly higher as crack depth and length are deeperand longer. It represents that ASME criterion for multiple

cracks is too conservative.To investigate detailed interaction effect of limit pressure

for multiple cracks, the variation of normalized FE limitpressures for adjacent surface crack with a/tand/ is shown

in Fig. 8 and Fig. 9, respectively. Also, limit pressure ofcracked elbow is normalized to that of un-cracked elbow. WhenS=a/2, effects of geometric variables on interaction effect formultiple cracks were exposed;

0.0 0.2 0.4 0.6 0.8 1.00.8

1.0

1.2

1.4

1.6

1.8

2.0

= 0.167,Rm/t

= 0.167,Rm/t

= 0.333,Rm/t

= 0.333,Rm/t

= 0.5,Rm/t

= 0.5,Rm/t

PLM

/PLS

a/t Fig. 7 Comparison of limit pressure between multiple cracks

and coalesced single crack

0.0 0.2 0.4 0.6 0.8 1.00.2

0.4

0.6

0.8

1.0

1.2

Eq. (3) = 0.167

Rm/tR

B/R

m

Rm/t=5R

B/R

m

Rm/t=10R

B/R

m

Rm/t=10R

B/R

m

PL

/PO

a/t

t

Rm

(a)/= 0.167

t

Rm

0.0 0.2 0.4 0.6 0.8 1.00.2

0.4

0.6

0.8

1.0

1.2

Eq. (3) = 0.333

Rm/tR

B/R

m

Rm/t=5R

B/R

m

Rm/t=10R

B/R

m

Rm/t=10R

B/R

m

PL

/PO

a/t (b)/= 0.333

0.0 0.2 0.4 0.6 0.8 1.00.2

0.4

0.6

0.8

1.0

1.2

= 0.5Eq. (3)R

m/tR

B/R

O

Rm/t=5R

B/R

O

Rm/t=10R

B/R

O

Rm/t=10R

B/R

O

PL

/

P

O

a/t

t

Rm

(c) /= 0.5

Fig. 8 Variation of normalized limit pressures with different a/t

for adjacent multiple surface cracks in elbow



5/6


(i) Normalized limit pressure for adjacent multiple crackswas almost unaffected byRB/Rm. In all cases, the differences of

limit pressure between RB/Rm=2 andRB/Rm=4 was below 3%

regardless of anther variables.(ii) In the case of part through-wall cracks, the normalized

limit pressure for multiple cracks had no change aroundPL/PO=1 even though crack length and depth have somewhathigh value. In the Fig. 8, the normalized limit pressure forcoalesced single crack linearly decreased if the crack depth andcrack length have high value. However, FE results weremaintained constant aroundPL/PO=1 to a/t=0.85. Also, in the

Fig. 9 (a) and Fig. 9 (b), FE results were maintained constantaround PL/PO=1 to /=0.5. It demonstrated that combinedcriterion highly estimate the interaction effect of the adjacentcracks. Only in the case of a/t, / is sufficiently small, a/t issmaller than 0.5 or/ is smaller than 0.167, FE results and the

normalized limit pressure for coalesced single crack had a goodagreement with Eq. (3) and ASME coalesced criterion isproper. At this time, these differences are less than 8%.

(iii) In the case of through-wall crack, the interaction effectfor adjacent multiple cracks is affected by Rm/t. Note that a/t=1

indicates the trough-wall crack. In case of part through-wallcrack (a/t


6/6


0.0 0.2 0.4 0.6 0.8 1.00.2

0.4

0.6

0.8

1.0

1.2R

m/t= 5 ,R

B/R

m= 2

Eq. (5)

/

/

/

PL

/PO

a/t

Increasing,

/= 0.167,0.333,0.5

(a) R

m

/t=5

Increasing,

/= 0.167,0.333,0.5

0.0 0.2 0.4 0.6 0.8 1.00.2

0.4

0.6

0.8

1.0

1.2R

m/t= 10 ,R

B/R

m= 2

Eq. (5)

/

/

/

PL

/PO

a/t (b)Rm/t=10

Fig. 10 Comparison of FE limit pressure with Eq.(5) for surface

crack

CONCLUDING REMARKSIn this paper, through the FE limit analysis, the

conservatism of coalesced rule recommended by the Section XI

of ASME was investigated in some geometric shape. DetailedFE analyses were performed to evaluate interaction effectincluding multiple cracks in elbow by evaluating thenormalized failure pressure. The conservatism of Section XI ofASME criterion for adjacent multiple cracks was investigatedand prediction of limit pressure for multiple cracks was

proposed. However, since the research only focused on theS=a/2 case, it has still some remained weakness. Thus, theadditional research which is related with variable S will benecessary as well as that effect of crack size should beconsidered.

0.0 0.1 0.2 0.3 0.4 0.50.2

0.4

0.6

0.8

1.0

1.2

Eq. (5)

Rm/t= 5

Rm/t= 10

a/t= 1 , RB

/Rm= 2

PL

/PO

Increasing,

Rm/t = 5, 10

Fig. 11 Comparison of FE limit pressure with Eq.(5) forthrough-wall crack

REFERENCES[1] ASME, 2004, "Rules for In-Service Inspection of Nuclear

Power Plant Components, ASME Sec. XI, Division 1,

IWA-3000.[2] JSME, 2004, "Rules on Fitness-for-Service for Nuclear

Power Plants, S NA1-2004.[3] American Petroleum Institute, 2007, "Fitness-for-Service,

API 579-1/ASME FFS-1.

[4] Park Y-W, Song M-H, Lee J-H, Moon S-I and Kim Y-J,2002, "Investigation on the interaction effect of twoparallel axial through-wall cracks existing in steamgenerator tube, Nuclear Engineering and Design, Vol.214,pp. 13-23.

[5] Hasegawa, K., Saito, K., Iwamatsu, F.and Miyazaki, K.,2007, "Prediction of fully plastic failure stresses for pipeswith multiple circumferential flaws, PVP2007-26011, SanAntonio, Texas.

[6] Hong S-P, Kim J-H and Kim Y-J, 2009, "Limit pressures of

90elbows with circumferential surface cracks,Engineering Fracture Mechanics, Vol. 76, pp. 2202-2216.

[7]. ABAQUS version 6.7, 2008, " User`s Manual, Inc. andDassault Systems.

[8] Yahiori, K., Moffat D-M and Moreton, D-M, 2000, "Pipingelbows with cracks Part 1 : a parametric study of theinfluence of crack size on limit loads due to pressure and

opening bending, J. Strain Analysis, Vol. 35(1), pp. 35-46.

assesment of interaction effect between two aligned surface cracks in elbows subjected to internal...

Documents