BARCM994/EJOU

I1tn

STABILITY ANALYSIS OF THROUGH WALL CRACKEDPRIMARY HEAT TRANSPORT PIPE

OF 500 MWe PHWR - PART I

byS. Visuanaiha. I). K. Muhaniy and H. S. Kushwaha

Reactor Ensiincerinsr Division

1994

BARC/199*/E/0Il

o

^ GOVERNMENT OF INDIA& ATOMIC ENERGY COMMISSION

I<

STABILITY ANALYSIS OF THROUGH WALL CRACKED

PRIMARY HEAT TRANSPORT PIPE

OF 500 MWe PHWR - PART 1

by

N. Viswanatha, D.K. Mahanty and H.S. KushwahaReactor Engineering Division

BHABHA ATOMIC RESEARCH CENTREBOMBAY, INDIA

1994

BARC/1994/E/O11

BIBLIOGRAPHY DESCRIPTION SHEET FOR TECHNICAL REPORT

(as per IS i 940O - 1980)

01 Security classification t

02 Distribution :

03 Report status s

04 Series i

Unclassified

05 Report type z

06 Report No. :

07 Part No. or Volume No. t

08 Contract No. t

10 Title and subtitle x

External

New

BARC External

Technical Report

BARC/1994/E/011

Stability analysis of through wallcracked primary heat transport pipeof 500 MWe PHWR-Part 1

11 Collation t

13 Project No.

82 p., figs., 19 tabs.

20 Personal author Cs> z N. Viswanatha; D.K. Mahanty;H.S. Kushwaha

21 Affiliation of author (s) i Reactor Engineering Division, BhabhaAtomic Research Centre, Bombay

22 Corporate author(s) c

23 Originating unit t

Bhabha Atomic Research Centre,Bombay-400 085

Reactor Engineering Division, BARC,Bombay

24 Sponsor<s) Name

Type *

30 Date of submission s

31 Publication/Issue date

Department of Atomic Energy

Government

May 1994

June 1994

contd...<ii)

(ii)

40 Publisher/Distributor i Head, Library and Information Division,Bhabha Atomic Research Centre, Bombay

42 Form of distribution t Hard copy

90 Language of text t English

91 Languigr of summary i English

92 No. of references * 29 refs.

93 Gives data on i

60 Abstract tThe Advent of Leak-Before-Break (LBB) concept isprogressively replacing the traditional design basis event of DoubleEnded Guillotine Break (DEGB) in the design of high energy fluidpiping system. The stability analysis of the through-wall crackedprimary heat transport pipe of 9OO MWe PHWR is carried out byJ-integral <J) and Tearing modulus <T> concept. The flaws are assumedin circumferential and longitudinal directions. The loadingsconsidered are bending moment due to Safe Shutdown Earthquake <SSE>and axial force due to the pressure of the coolant. The critical sizeof the circumferential flaw which leads to catastrophic failure isdetermined under the assumed loading conditions. The leak rate isdetermined based on LEFM with Irwin's plastic correction. The leakagesize crack is determined by applying margin of 1O on detectable leakrate. The crack stability is checked for leakage size crack undernormal plus seismic stresses.

Keywords/Descriptors i PHWR TYPE REACTORS; PRIMARY COOLANT CIRCUITS}PIPESf CRACKS; CRACK PROPAGATION; DEFECTS; DYNAMIC LOADS; STRESSES}FRACTURE MECHANICS; LEAKS; FINITE ELEMENT METHOD; BENDING; FAILURES;STABILITY; POWER RANGE 1OO-1OOO MW; DESIGN

71 Class No. i INIS Subject Category x E34OO

99 Supplementary elements z

STABILITY ANALYSIS OF THROUGH WALL CRACKED PRIMARY HEAT

TRANSPORT PIPE OF 500 MWe PHWR

PART I

H. Viswanatha, D.K. Hahanty and H.S. Kushwaha

ABSTRACT

The advent of Leak-Before-Break(LBB) concept is progresively

replacing the traditional design basis event of Doable Ended

Guillotine Break (DEGB) In the design of high energy fluid piping

system. The LBB approach alas in the application of fracture

mechanics studies to demonstrate that piping is unlikely to

experience DEGB under all loading conditions. The Elasto Plastic

Fracture Mechanics (KPFM) methods employ techniques ranging fro*

detailed finite element analysis to simple estimation schemes for

given geometries and loading conditions. Detailed EPIftf studies

based on estimation schemes is applied to straight section of

primary heat transport pipe connecting steam generator and

primary heat transport pump of 500 MWe PHWR.

The stability analysis of the through-wall cracked pipes is

carried out by J-integral (J) and Tearing modulus (T) concept. The

flaws are assumed in circumferential and longitudinal directions.

The loadings considered are bending moment due to Safe Shutdown

Earthquake (SSE) and axial force due to the pressure of the

coolant. The critical size of the circumferential flaw which leads

to catastrophic failure is determined under the assumed loading

conditions. The leak rate is determined based on LEFH with Irwin's

plastic correction. The leakage size crack is determined by

applying margin of 10 on detectable leak rate. The crack

stability is checked for leakage size crack under normal plus

seismic stresses.

CHAPTER I

INTRODUCTION

Doublet Ended Guillotine Break (DEOB) was introduoad in order

to design both containment and Emergency Core Coo11ns System

(ECCS) from a thermohydraulic stand point. However, the above

hypothecis was considered as design basis accident due to lack of

advanced reliability knowledge of pipe fracture behaviour. This

has led to installation of a large number of pipe whip restraints

and jet impingement barriers which are hinderance to piping

inspection. This also increases the doses to workers during plant

outages to remove restraints and barriers for accessibility.

Therefore, there was a need for a sore realistic, yet

conservative definition of the Design Basle Accident (DBA). After

extensive analytical and experimental studies, Leak-Before-Break

(LBB) based design criteria was finally Introduced. The approach

to LBB is to demonstrate that even though a crack either exists

or is generated in a pipe during service, it will not grow during

plant design life to break the pipe. A crack is postulated and

assumed to grow stably by some mechanics to a sise at which it

penetrates the ligament of wall of the component resulting In the

leakage of the pressurised fluid. When the crack growth continues

and reaches a sise at which leakage is deemed to be detectable,

an assessment is done to show the margin against unstable

failure. The margin can be expressed aa a factor of safety on the

time available to effect a safe shutdown of the nuclear reactor

before the crack grows to a critical sise.

Currently about 65X of the Pressurised Water Reactors (FWR)

in the tt.S. have obatined the approval of the application of LBB

1

in the primary coolant loop. There are four PWBs which have LBS

approval for their auxiliary lines. One of the four plant* also

has approval for the safety injection lines and reactor coolant

bypass lines. However, the application of LBB has not been

permitted as yet for Boiling Hater Reactors. Perclusion of double

ended circumferential rupture of main coolant line is achieved by

demonstrating three levels of confidence. These three levels of

confidence say be stated as defence in depth strategy. Level 1

confidence is inherent in the design philosophy of ASMS Sec. Ill

£1], which designs the piping with a factor of safety. ASMS

criteria provides margins against failure under static loads

encountered in normal service and dynamic loads such as

earthquake. The load produces the stresses which are categorised

as either primary or secondary. The primary loads satisfy

eqilllbrium between internal and external forces and moments.

Secondary stress is the stress developed by the self-constraint

of a structure and is self limiting as local yielding deformation

will reduce or eliminate the stress. The primary stress limits in

ASME Sec.Ill are specified to protect against failure by plastic

collapse. The primary plus secondary stress limits ensure

shakedown to elastic behaviour and thus protect against potential

failure due to ratcheting. Limits on peak stress levels are

specified to protect against fatigue failure. However, it does

not consider the presence of any flaw in the pipe. But certain

flaw size which can be accepted after Non Destructive

Examinations (NDK) criteria are taken care by ASMI in the design.

Level 2 consists of postulating a part-through crack at the

inside surface of the Primary Heat Transport fPHT) piping and

then to demonstrate that it will not grow through wall during the

interval of inservice inspection/ repair or if possible, during*

the entire life period of the reactor. Level 3 postulates the

Initial part-through flan to grow through-wall due to SOBS

unforeseen events. Once the flaw penetrates through the

thickness, it Kill lead to leakage of high pressure liquid and

the flaw will continue to grow along its length causing gradual

increase in leak flow rate. At sone point, the leakage will be

detected by the plant leakage Monitoring system. Level 3

postulates through nail crack that will ensure detectable leakage

and then demonstrate that the flaw will not grow further or even

if it grows, it will grow stable and hence slowly giving

sufficient tine to take remedial actions.

Therefore, by using tough Materials, with conservative

loading and with high level of non-destructive examinations. high

quality of fabrication (welding) and appropriate leakage

•onitorlng system, the spontaneous failure need not be postulated

m.

LIMITATIONS OF THE LBB CONCEPT s

While the concept of LBB is universally accepted in

designing high energy fluid piping in nuclear power plants, the

concept with its present status has some limitations. These are

as follows,

(a) For specifying design criteria for emergency core coolant

systems, containments and other engineered safety features,

loss of coolant shall be assumed in accordance with exlsitlng

regulations.

(b) The LBB approach should not be considered applicable to high

3

energy fluid syetea pipine, where the operating experience has

indicated particular sussceptibility to failure fro* the

effects of corrosion, stress corrosion cracking, erosion,

ageing* vibration, fretting and water baaaer. Most of

potential failure aechanisas could be avoided by proper

design, fabrication, installation and operating controls

Implemented in nuclear power station. However, erosloa with

corrosion is an important failure mechanisa for carbon steel

piping. Presently, water chensitry control, oxygen control and

P™ control are judged to be sufficient to avoid degradation in

piping sirs tea.

(«j) The LBB approach should not be considered applicable if

there is a high probability of degradation or failure of the

piping froa sore indirect causes such as fires, aissiles and

damage froa equipment failure (e.g. crane faxlure) and failure

of systems or components in close proxlalty.

(d) The LBB approach as described here is Halted in application

to piping systems where the material is not sussceptible to

clevage type fracture over the full range of system

operating temperature where pipe rupture could have

significant adverse consequences.

The only failure mechanism to be considered is fatigue,

although even fatigue failure is protected against design. USB

assumes that fatigue cracks propagate more quickly in the through

thickness direction of the pipe than in circumferential or axial

directionsC3,41.

APPLICATION OF FRACTURE MECHANICS :

The nuclear piping for which LBB is generally applied le

made of ductile Materials. Linear Elastic Fracture Heachanios

(LEFM) method would be unable to account for nonlinear phenomena,

such as crack growth initiation and stable crack growth involve in

LBB analysis. Ductile fracture mechanics Methods employ analytical

techniques ranging fro* elaborate Finite Element modeling to

sinpllfied Fracture Mechanics (FH) Methods for a systematic

evaluation of large range of pipe geometries and loading

conditions. Since, Finite Element analysis requires high cost and

time, a simplified estimation scheme based on closed fora solution

of cracked pipe is often preferred. Although all fracture concepts

are based on fracture mechanics theory, it is necessary to include

certain idealising assumptions related to crack shapes, consistent

geometry and crack behaviour, if the crack initiates and grows as

a result of increased accidental loads. The estimation scheaes are

based on far-field moment, far-field rotation relation. In

addition to this, there are a number of factors such as ovallaation,

wall thinlng near crack, material property discontinuities, crack

instabilitltes, dynamic strain ageing and growth of craok in

different directions which can not be accounted for. Therefore,

somewhat eaperical but conservative estimation procedures were

adopted. Several J-estlmation techniques can be used to give

conservative but reasonably accurate predictions of load versus

displacement relationship.

The first step in LBB is to screen the candidate systems for

Bussceptibility to the known degradation aechanisa including

generic and system specific phenomena. These include creep*

fatigue. Inter Granular Stress Corrosion Cracking (IGSOC). erosion.

themal agoing. In addition the failure from indirect CMMMMW suck

as fire, missiles and equlpaent failure* 1* another •creeainc

consideration.

The second step is to select the highest stress point* and

determine the load for each pipe sixes for which candidate system

through the piping stress analysis. The pressure, thermal

expansion stresses, stresses due to Safe Shutdown Earthquake CS6C)

and Seismic Anchor Moment (SAB) shall be determined from piping

analysis. The highest piping stresses produced by a combination of

noraal operation loads plus SSE are considered.

The third step is to determine material properties of

stress-strain and JR curve. The material testing consist of true

stress-trus stain and Jx testing for Base metal, weldment and Beat

Affected Zone (HAZ).

The fourth step is to determine the lowest detectable leakage

inside the containment. The leakage detection system are designed

with a detectable leakage of better than 63 cms/sec (0.05 Kg/see).

This value was adjusted by a factor of 10 to apply a margin termed

as "Adjusted leakrate margin" to compensate for uncertainties

related to analytical uncertalnities in the calculation of leakage

flow through cracked pipe configurations.

The fifth step is to calculate leakage size oraok which

yields 630 C B /sec(0.5 Kg/sec) leakage in normal operating

conditions. The use of a lower bound material properties result In

smaller predicted crack size which is not conservative.

The final step is to evaluate the crack stability of the

piping eyateio. To assess crack stability, two steps are involved.

One is to assess stability with a crack length equal to twice the

leakage size crack under normal plus SSE loads. The other la to

6

assess stability with a crack length equal to the leakage sise

crack under V2 times normal plus BSE loads. The former and the

latter are called a flair size margin and load margin respectively*

When each margin is greater than or equal to unity, this

demonstrate acceptable stability. The governing cause for crack

stability Has always found to be crack size Margin.

i

PRESSURISED HEAVY WATER REACTOR s

Reactor of 500 HWe pressurised heavy water cooled, heavy

water moderated and natural Uranium fuelled nuclear power plants

at Tarapur is under planning stage. The heart of the reactor is

the cylindrical horizontal, single walled stainless steel vessel

called the calandria. The calandria tubes contains and support

the fuel channels in the core portion and isolate the pressure

tubes from direct contact with the heavy water moderator.

This feature of the PHWR design, with entirely separate

moderator and heat transport systems, allows a low pressure cover

gas pressure, low temperature heavy water moderator system. Since

moderator and heat transport system are separate, tight chemistry

control is achievable at all the tides in the heat transport

system. Oxygen levels are maintained at low level {0.05 ppa) and

P levels have been set at 10.5 to minimize corrosion. This

precludes the need for cladding. The heat transport system

operates at a relatively low outlet pressure of 10 MPa (at*) and

at a outlet temperature of 300°C.

The heat transport system circulate pressurised heavy

water through the reactor fuel channels. The main heat transport

circuit consists of two loops each containing two pumps, two

steam generators, two reactor inlet headers, two outlet headers.

7

and one inlet feeder and one outlet feeder for each of the 392

reactor fuel channels. Each loop reaovee the heat fro* half of the

core. The two BOIn circuits provide bi-directional flow through

the core such that flow in individual feeder pipe sine are

selected and channel flow is trlaaed to give the same exit quality

froa all outlet feeders at full reactor power. Heavy water i«

punped through the large dlaaeter heat transport puap discharge

lines to the reactor inlet header (RIH) and fro* there fed to each

of the fuel channel through individual inlet feeder pipes and froa

each fuel channel through individual outlet feeder pipes to the

horizontal reactor outlet headers (ROB).

Froa the reactor outlet headers, the coolant flows

through the two 5S9 aa lines to the steaa generator where the

heat is transferred to the the secondary side. Each steaa

generator ie connected to the suction of one heat transport puap

by one 610 na line. Each heat transport puap delivers heavy water

to one reactor inlet header through two 408 aa lines. It is

possible to assess the stability of PHT carbon steel piping and

demonstrate that it will not break catastrophioally; at worst it

would leak at detectable rate and corrective action would be

taken well before catastrophic rupture could occur. The carbon

steel material SA 333 Grade 6 is being used in the 500 Mile heat

transport piping system. The piping is seaaless. designed and

constructed to ASKE CIOBO 1 and all the welds are radiographed

and 100% voluoetrlc exaainatlon is performed. The operating

procedure of reactor requires ianediate shutdown at confined

leakage rates of 0.5 Kg/sec froa the heat transport system. The

fatigue crack growth analysis of the largest creditable Inaugural

flaw (1/4 T) [51 ensured, that it will not grow through the pipe

8

wall during the design service life of the piping. In this report

the stability of suction .line connecting steam generator and pump

againat sudden catastrophic break is demonstrated. It has been

assumed that material properties of Held, HAZ and based metal is

nearly same.

In general, guillotine rupture at girth butt welds and

longitudinal ruptures at the sides of those elbows which exceeds

the stress related criterion are to be postulated. The stress

related criterion requires postulating break at those locations

where stress levels exceeds 2/3 of the allowable stress at normal

operating conditon. The geometry related criterion requires for

postulating guillotine ruptures at piping anchors, nozzles and

also requires postulated longitudinal ruptures at the notch of the

branch tee connection.

ELASTO PLASTIC FRACTURE CRITERIA :

Linear Elastic Fracture Mechanics assume linear elastic

•aterlal behaviour which ignore crack tip plasticity. Its

prediction nay be very much misleading for the estimation of

load-carrying capacity of the structure. In turn, this can lead

to premature plant shutdowns and unwarranted repairs that could

actually increase the risk of failure. For the propagating crack

the extent of the stable growth depends on loading system and

material properties. The fracture criteria examined initially

included all possibilities shown in table 1 15}, but concentrated

on J-integral(J), and the local and average crack opening angles.

J-integral under certain conditions is identical to potential

energy release rate, when crack grows. It represents a localised

measure of the driving force and is a vector quantity. It is

9

based on deformation plasticity and ie universally accepted for

the initltation of growth. Its -validity ceases after some amount

of crack growth, which say be quite United for certain flaw

structure geometries. Crack Tip Oening angle (CTOA) may be

prefered for simulation of large amount of crack growth. CTOA

becomes constant with increasing crack growth. CTOA reflects the

actual slope of the crack faces during fracture process. It is

well known that the amount of triaxiallty ie a strong factor in a

material crack resistance. Thus, if two materials are cracking

with the same JR, are not necessarily equivalent. Tearing modulus

(T) is a dimensionless parameter which represents the resistance

of the structure to unstable crack extension. Fracture toughness

associated with crack initiation is measured by J and the

material resistance to crack growth by T which are analogousmat

to material characterisation of yield stress and ultimate stress.

In faulted condition, a small amount of crack initiation by

ductile tearing is nllowed. Tearing modulus is proportional to

rate of variation of J with respect to crack growth. The amount

of stable crack growth decreases with increasing compliance. The

values of J, T and applied load at Initiation also depend on

compliance of the loading system. In J-T aproach the slope of JM

curve is used explicitly, which can vary with crack extension,

strain hardening properties of the material and system compliance

are accounted for in the driving force. In J/T approach it should

be recognised that not only must the JR curve be a lower bound,

its slope nust also be a minimum value. Extent of stable crack

growth prior to instability, load carrying capacity of configura-

tion at various etagea of growth are explicitly given. Stable

crack growth must also be J-contolled,

10

I.e. w >> (b/J) (dJ/da).

where, b = uncracked ligament.

a = crack length

dJ/da = slope of JR curve

There are indications by Shin et.al f6] that « is on order of

40, which will restrict the amount of crack growth to only a few

percent of the remaining ligament. Experiments and analytical

study Bust satisfy this condition. Detailed evaluation using J/T

approach provides a more precise estimate of the margins against

unstable crack extension.

OBJECTIVE OF STUDY :

The objective of this report is to evaluate the failure

load of straight section of the primary heat transport carbon

steel pipe containing circumferential flaw. In this report,

efforts are made to determine the maximum unstable load by J/T

approach. Instability condition has been found by plotting J as a

function of both the applied loads and flaw size, and material

flaw extension resistance. The crack initiated at the surface has

propagated by fatigue over the period of time during the service

and a through wall crack {TWO is finally resulted. The

orientation of the crack is assumed to be (a) circumferntial. the

one which may be created during welding (girth welding) and (b)

longitudinal. When a defect is postulated, it is more likely to be

found In girth weld than in base metal, accordingly the weld is

the location of flaw. The initial else of circuferential flaw can

be taken from Non-destructive examination carried out during

acceptance test and in-service inspection. However, this could be

11

used for crack growth study. For stability purpose one mm use

crack else equal to leakage aise crack. In noraal and upset

condition, J calculated fro* the prlaary plus secondary stress

ran&e i.e. (P +P.4Q) is leas than the fracture touchnees J__,m D zc

therefore* the crack Initiation is prevented. The internal

pressure and axial loads acting in the pipe nail thickness are

taken into consideration for determining the critical crack slse.

Bending aoaenta that act on the pipe is due to Safe Shutdown

Earthquake (SSK). The crack detected following the leakage

•eaaureaent can withstand such unexpected loading before It is

repaired.

12

CHAPTER II

METHODS OF ANALYSIS

Various methods of analysis to predict the load/ moment

bearing capacity of a pipe containing Through-Hall Crack (TffC) are

available. Other than analytical methods, experimental and

numerical procedures are also adopted for the purpose of

Validating analytical predictions.

2.1. Experimental Hethod :

Sharp artificial circumferential crack is introduced on

the pipe by electro-erosion and then extended by fatigue for

conducting experiments. The experiments are carried out for

bending load [7] and also with /without Internal pressure.

The guidelines consist of flaw growth analysis to

determine the maximum size of the flaw at the end of the test. The

aim is to demonstrate that the crack growth is stable for the

given flaw with adequate margins for different loading conditions,

such as axial, bending, internal pressure loadings.

ASMS Section XI uses net section collapse analysis for

the evaluation of circumferentially and axially cracked carbon

steel pipes. This methods assume the gross yielding of the net

section (remaining ligament) prior to failure. It is based on

limit load analysis technique. The net section collapse stress is

then multiplied by a correction factor known as Z-factor (Z) to

predict the failure stress. The Z-factor comes from an analysis

using the GE/EPRI J-estiuation scheme and the factor varies with

pipe diameter, toughness and crack length. However, effect of

13

crack length is very small and th«r«£or« haa hmmn natflaotod. To

separate the cases in which net section collapse conditions are

met (fully plastic) from those in which they are not (contained

plasticity), a screening criterion based on plastic zone ahead of

crack tip has been developed. When plastic zone becomes equal to

the tensile ligament (i.e. distance from crack tip to the neutral

axis), it is assumed that fully plastic conditions have reached.

However, J-integral is more suitable parameter since it can be

applied to high tough and also to low tough pipe materials and

complex structures.

Hilkowski and Scott [83 have given a simple engineering

approach to evaluate surface flaws in Carbon steel and Stainless

steel piping and their weldments which is based on statistical

data from a large number of pipe fracture experiments. To ensure

a resonably conservative approach, a 95% confidence level was

established. Toughness and pipe size effects are accounted for in

one correction factor, while ovalizatlon and flow stress effects

are accounted for in two other factors. The limitations and

possible improvement to such an approach are also discussed.

2.2 numerical Methods !

The finite element method is one of the powerful

technique for carrying out the stress analysis of structures. It

has been used very exhaustively for carrying out stress analysis

of components with or without crack to a fairly high degree of

accuracy. The crack postulated surrounded by finer mesh around the

crack tip is used for the modelling of the pipe with crack. The

available packages [91 are capable of analysing the non-linear

14

behaviour of the material. The main draw back of this method is

computation time for evaluation.

J-integral is one of the most potential fracture criterion

and is used to a great extent for both crack Initiation and

growth.

J-integral is defined as

J = / p ( Wdy - T 6u/<5x ds)

where W : strain energy density

r : closed contour surrounding an area in a

stressed solid.

T : Tension vector perpendicular to r

in the outside direction,

a.. = stress tensor and n. direction cosine

u : Displacement in x-direction

ds : is an element of r

The integral can be evaluated using a standard line

integral in finite element method. However. ABAQDS uses a virtual

crack extension method to evaluate J-integral. It is calculated

for number of separate contours around the crack tip. The level of

path independence in the J-integral for these different contour is

measure of the adequacy of mesh refinement and convergence of

equillibrium flO].

2.3 Et-6 Procedure :

R-6 curve is a generalisation of both the plastic limit

load concept and linear elastic fracture mechanics. It allows to

interpolate between linear elastic fracture mechanics and rigid

15

plastic behaviour and additionally provide a aeans of taking the

hardening effects into account la these oases where an extensive

elasto-plastic analysis is not performed. The failure assessment

dlagraa is contsructed in the K -S plane wherer T

2.3.1 >

where, &c :plastic collapse stress

K, :Fracture toughnessJO

S_ and K are proportional to the applied load through ther r

paraaeter o and K . The failure assessaent curve is shown in

Vis,2.1 is the loci of points (K )-, (S )_. Three options BTB

available in this procedure depending upon the non-linear

treatnent of natetrial. However, option 2 [11] is aost preferred.

The Unit aoaent predicted for a given crack angle is. then

determined froa.

K _ f -—r*f~ + r~J- ( 2 . 3 . 2 )r - ' . L e y 2 K e - J

f

for L < Lr

r y

K =3 0 f o r L > Lr r max

with e . = a t/E + (& Jet )n

Cf . - L cttat r y

where H . is appllied uoment and M, i s Halt aoaent which

i s determined froa,

ML = 2 Ru * f̂ C 2 COB<e/4> ~ oin(©/2)] (2.3.3)

where o-f : flow stress

16

© : Half crack angle

RM t nean radius of pipe and

t : thickness of pipe

The reference strain e is the true strain obtainedref

fron the uniaxial tensile stress-strain equation at the true

stress L a , and E is Young's modulus.

Failure associated with any combination of loadina and

crack size giving rise to a point { K ,S (or L )} falling on or

outside of this curve, and conversly, the combination Hill be

safe if the point lies inside the curve. Since K and S (L ) are

proportional to the applied load, the distance from origin to the

point (K ,S ) is also proportional to load. For a crack of fixed

length, changing the applied load causes the point <Kr,Sp) to be

displaced along the origin. The safety factor is the ratio of the

distance froa the origin to the point of intersection of this ray

and the failure assessnent curve and the distance between the

origin and the (Kr,Sr). For a prescribed load intensity the loci

of points (K ,S ) for different crack lengths is referred to as

the path to failure. Once a path to failure has been established

for one intensity of load, other paths can be constructed for

other intensities by simple proportionality.

2.4. Analytical Estimation Methods :

One of the important issue in the application of LBB concept

in nuclear piping is the development of simplified methods for a

systematic evaluation of a large range of pipe geometries and

loading conditions. Simplified methods should be loir coat and

efficient. Host of the engineering methods (simplified methods)

17

are based on J-integral approach. The J-integral is expressed in

terms of functions, limit load solution, component geometry and

constant used in power law for describing stress-strain behaviour

of material. It is therefore. Important to discuss the J-integral

estimation schemes in detail.

2.4.1. J -Integral Technique :

J-Integral is defined as the loss in potential energy

per unit crack extension. The mathematical definition of J is

given earlier in 2.2. J is a generalised relation for the energy

release due to crack propagation, which is also valid if there Is

appreciable crack-tip plasticity. J-R curve can be evaluated by

plotting the load/moment versus displacement/rotation diagram for

pipe having flaw. The load-displacement diagram may have

non-linearity as a result of plasticity. This is shown in fig 2.2.

The area between two load displacement curves for 'a' and

'a+Aa' proportional to JAa. One can measure load-displacement

curves on a pipe by successively increasing the crack sise, and

the area between the curves for two cracks of slightly different

sixe can be graphically determined.

0J = / 6M/6A 60

J = A- E^Hx A0.A A . «• vi

where M = bending moment

0 = bending angle

The sum in the above equation simply represents the area bounded

by two load displacements curves of two specimens that have "a'

and 'a+Aa' crack length.

The values of J so obtained can be plotted as a function of

18

"a' or displacement. This gives both initiation fracture

toughness (<?.„) and crack growth fracture toughness (T . ) . T

which is non-dimensionalised by multiplying K/c* where, a Is -the

flow stress {&t - (o^ )/21.

The J-integral can also be expressed as

J* = J*i* JPi (2.4.1)

for linear elastic material loss In potential energy

per unit crack extension is called 6 or J ,. J , is plastic

component of JR. In general J#l can be written as

J , s 7i ftza £ ael

where ft : dimensionless factor known as geometry factor

o and £ i remote stress and strain and

'a' is crack size. Similarly the J t can be expressed ae

J . = Ho-n**a/F = H & £ ,a ( 2.4.2 )pi pi

where H is a geometry factor

F = Plastic Modulus

n : hardening parameter.

The value for n and F can be easily obtained from

stress-strain curve of material since total strain can be

expressed as

lot ~ el pi

a c/E -f crn/V ( 2.4.3 )

The geometry factor H(a,n) were developed [16,17] for a

number of structural geometries and n-values after conducting a

series of elasto-plastic finite element analysis. The equation

for J , is suggested aspi

where P : load

Pb : collapse load

19

c : unbroken ligament

hA : geometry factor

It is to be noted that tbe collapse strength does not

•ake J , dependent upon the sane. It merely amounts to multiplying

numerator and denominator by tbe same number, which does not

change tbe basic equation. Collapse does not enter in LKFH

eaations. nor does it enter EPFH equations in their present form.

An artificial introduction does not chance this fact (121.

Researchers have expressed great concern about the

large variability of J and consequently JR. The reason for the

large variability la obvious, since it depends upon stress to the

nth power. Therefore, a slight difference of 5 percent in the

stress with n=9 leads to a difference of (1.05) =1.63 or a

difference of 63 percent in J . This may be seen bothereone but

it is of little practical importance. The value of JR is of no

interest as long as the predicted fracture stress is reasonably

accurate. In fracture mechanics the situation is reversed i.e. *

difference of 63 percent in J with n=9 will lead to only

difference of 5 percent in predicted fraoture stress.

[(1.63)°'*=1.05], On the similar argument, a difference in J by a

factor of 2 and for n=7, the predicted fracture stress would

differ only by 9 percent. In general, the stress in a structure

will not be known with better accuracy. Therefore, it would be

satisfactory from an engineering point of view.

For the estimation of J-integral values, five different

procedures are available for assessing ductile fracture mechanics

of THC pipes subjected to axial and bending loads. The date

obtained through various J-estimatlon schemes are compared, to

20

predict the maxima, failure loads/moment.

2.5 Tearing Instability Theory :

For evaluation of crack stability. J-integral/tearing

modulus (J/T) is most, widely accepted. J/T approaoh is sore

prominent in nonlinear fracture mechanics applications, since it

incorporates a rational crack tip parameter. In addition to this

it can discriminate between Material of different toughness and

tensile properties. It can also acconodate various boundary

conditions such as load versus displacement and pipe system

characterstics [131.

Tearing Modulus concept is based on the fact that

fracture instability can occur after soae amount of stable crack

growth in tough and ductile materials with an attendant. higher

applied load level at fracture. To take account of such a process.

the reistance (material) curve concept is useful. This is a

function of material properties which depend upon the thickness.

The condition for fracture of a cracked body is obviously not

synonymous with the conditions for achieving crack initiation. The

fracture point is instead determined through a stability analysis.

This focuses on the point in the stable crack growth process at

which the rate of change of the crack driving force exceeds the

rate of change of the material's resistance to continued crack

growth. Thus, fracture instability occurs when dJ/da exceeds

dJR/da. Paris £163 formalised this concept which has already been

defined earlier as

dJT = —* ^ ( 2.5.1)

21

dJ.

The critical value TR= TR(Aa), also known as T . taken

to be the Material property. The instability is determined via the

J/T diagram ehown in Pig.2.3.

There is substantial load carrying capacity comparing

with that associated with the crack initiation before the crack

becomes unstable. The Incentive for the use of the tearing Modulus

approach is that it offers a convenient way to calculate the load

carrying capacity srhen small amounts of crack growth are permitted

in ductile Materials.

2.6.0. Estimation Schemes *

analysis of the EPFH parameters require a exclusive

numerical calculations. Therefore, developments of a simple

engineering method is necessary to apply the elastic plastic

fracture mechanics. Kunar et. al [141 proposed a simple

J-estimation formulae combining elastic and fully plastic

solutions. Later on, several other estimation techniques are also

proposed. The estimation schemes described in DSNRC [13] for

through-wall cracked (THC) pipes are used to evaluate the

stability of suction pipe of 500 MWe PHWB. The crack geometry and

loading is shown in Fig. 2.4-2.5.

22

(A) CIRCUFERENTIALLY ORIENTED CRACKS I

2.6.1 General glectrlc-gleetric Power Research Institute Method

(GE-HPBI) [151 {

This aethod is based on a compilation of numerical

solution which are obtained through thin shell Finite Element

analysis for THC in pipes subjected to bending and combined

tension and bending loads. The numerical solutions for various

geometric and Material parameters encompassing the typical range

of in service nuclear piping are done. For pure bending In pipes

containing TWC, J -applied is calculated as

J = Je 4 Jp (2.6.1.1)

where J - elastic portion of J

J - plastic portion of J

2.6.1.1 Estimation technique for Pipes subjected to pure bending?

The elastic and plastic J for pipes subjected to pure

bending is calculated based on the following equations

J = f,(a ,R /t)Ba/B and (2.6.1.2)

J B <*&oeo (b-a)(a/b) h1(a/b.B.B^/t)(H/llL)n*A.. (2.6.1.3)

where

R - mean radius of pipe

t - thickness of pipe

M - applied bending moment

E - Young's modulus

a - half crack length at mean radius = B &

t± - elastic function

h< - plastic function

a - plastic zone sise correction to half cracke

length

M, - the limit moment for a cracked pipe under

pure bending

f, - elastic f-function23

b - Bm*n

a,a , * ,n - parameters In Ramberg-Oegoodo o

stress-strain relationsflthl ~ tabulated from finite element calculations.

2.6:1.2 Combined Axial and Bending load;

In this case the total J will have contribution from both

axial force *P' and moment 'M'. The functions derived fro* detailed

finite element analysis for combined loadings.

J = f. pV4Bt 4 f. M*/R t2E (2.8.1.4)

f.and f. are geometry factors taking plastic aone correction

on the initial crack length.

The effective crack angle is given by

d^= © Cl+lCn-lM^^F^/WCn+DaJfl^CP/P^'l'lH —{2.6.1.6)

where <*. «= P/2"R t, is applied tensile stress andt vn

^t, is applied bendimr stress

Po is the liait load for given crack length in tension for

coablned axial and bending load,

P a 0.5 (-XP^B /M +*(-^P2R /M >%4P ^* * (2.6.1.6)o o m o o m o ,owhere X = M/P R

P is the plastic liait load in tensionoM is the plastic Unit noaent

Plastic portion J calculation :p

2.6.1.7)

Where. H is now function of (a/b.n,H /t) in addition to X. This

results are compiled for various a/b,n,X values in Ref.C171» The

results available for R /t= 10.

This aethod has a trend of over estimating J due to the use

of shell elements for pipes with large Rm/T. TLese eleaento are

etiffer than 3D eleaents. The limitation to the accuracy of this

schene is. Ranberg-Oagood representaion does not always fit very

well the erees-strain. relationship.

2.6.2 PARIS - TADA METHOD T16] *

The J esinatlon in this scheae is based on

•oment-rotaion (M-0) carves. The elastic-plastic loading regiae

eetlnation is based on interpolation between the linear elastic

solution and fully plastic Halt solution. The procedure utilises

the technique developed for a planar fracture specimens

appropriately adopted for TWC pipe.

2.6.2.1 Linear Elastic solution:

The energy release rate for a circuaferentially cracked

pipe applied to bending is given by

G = « /

G = &llfi+Unc)/6K = <50c/*A ( 2.6.2.1 )

where, G - energy release rateT0 - total internal energy

U n o - strain energy which would exist in the pipe

if there were no crack present

0° - <0T- Dnc) additional strain energy due to

presence of a crack.

A - pipe crack area = 2nB&

RM= mean radius of pipe and

& - half crack angle

Dc s o/A G dA = ^ ( K ^ / E ) dA

25

Kt - stress Intensity factor

For linear elastic body subjected to bendinc

leiads,

arid for combined axial and bending loading

(V nRw » ) Ft(e) (2.6.2.2)

&.,&, are applied bending and tensile stress respectively. F.,F.

are geometric factors calculated using Sander's function fl71.

F. (©) s 1 + 1 (©/« ) ̂ 2 + B. (© /n ) ' •D D D

F4.(o) = 1 • a, (©/* )"'* + B. (© /n ) 3'* • I

By Castlgliano's theorem it can be written elastic load

point rotation of both ends of pipe

0 C = <5OC/«5M = — S & (K* /K)dA ( 2.6.2.3 )e <5M ° *

suiDstituting for K± we get,

0 c = 1/8 {<?. I. (•)• </ I (9} }e o t i t t

where, Ib(0> s 4 / © Fb(©)*d©

It(©) = 4 / © Ft(©)*d»

knowing the stress intensity factor for given

and axial load , elastic J is given by

Fully Plastic Solution1

IFor a rigid plastic behaviour of the material model limit moment

is given by

H = 4<y Hat (COB (i - 0.5sin©) (2.6.2.5)p o m

where ft = angle between crack tip to neutral axis

26

J s a R t F.(e) 0 (2.6.2.6)rp o )

F ( e ) = Bin/? ••• COB©

2.6.2.2 Blastic-Plastic Estimation {

When an uncracked body is subjected to applied load, the load

displacement relation is linear upto the load level which is large

enough to cause yielding at certain parts fo the body. There la a

distinct point on load displacement diagram where the deviation

from linerity occurs. On the other hand, the load displacement

relation for a cracked body, rigorously speaking does not have

linear portion because of stress singularity at crack tip. The

localised yielding begins with load application and causes

deviation from purely elastic solution.

The plastic zone correction method is employed to account for

the effect of local yielding. This method was developed for

evaluating material fracture toughness in small scale yielding and

crack tip is well contained with in surrounding elastic field.

In analysis & is correction factor on initial crack length

e and effective crack length & ,. is used for calculating elasticO Oil

solution.

&^ _. ( 2.6.2.7 )

ft n Rm <<*y>2

where, K* = J B

& - yield strength of material

ft is geometric factor, which is 2 for plane stress and 6 for

plane strain depending on constraining conditions near crack tip.

Substituting for KJL we get ,

27

© - l(&./& ) ( B{E. (0)+cr /& (F. (©))!• J /ft —-(2.6.2.8)y by b l o b

G (e) = efFre)**/*. (P. (e)»* (2.6.2.9)o l o o

G {©) = [ © „ - e ] ft/Sz with 6 = c/b (2.6.2.10)

Two equations(2.6.2.9 and 2.6.2.10) are solved lteratlvely till

convergence 1B achieved.

G(€>ef_) has no solution for '8' beyond aomo value.

Vasquez [18] defined this as 'plastic sone size instability*. At

S=S, , the plastic zone sores in an unstable fashion such thattan

the couplet© cross section becones plastically deforoed that is

the elastic field around the crack tip can not Maintain the

plastic zone near the tip. The total load point rotation for the

given nonent is

0 = 1/K <*fe I b(^ f f) + ax ̂ (0^) > (2.6.2.11)

Calculation of Plastic J:

For given load, total rotation is given by

0 = 0 + 0 (2.6.2.12)P e

0 = 0-0p «i

0

J = s p C^H/dA)d0 (2.6.2.13)P °

It can be shown that F4](2.6.2.14)M ()/A| 0 M()/M

Substituting (2.6.2.14) in to (2.6.2.13) one gets

28

Mp

p d0 (2.6.2.15)p

where , F (©) = ain/J + coa&

M = 4 & R t Ccoa(/?) - 0 .5 e i n ( e ) ]p y m

<y = flow stressy

from the moment-rotation relations the curve Jia numerically

integrated. The complete solution is given by

J = J e + J p

This gives the complete solution for elastic plastic regime.

All the other estimation schemes are based on similar calculations

except for the calculation of & and hence J .p p

This estimation scheme is essentially based on LEFH. The

elastic solution for two different crack lengths is calculated.

The material is assumed to be rigid plastic. The elastic-plastic

solution is obtained by interpolating between elastic and rigid

plastic solutions. The material stain hardening parameter is not

taken into consideration in this method.

2.6.3 LBB.HRC Method [19] :

The NRC procedure is similar to Paris-Tada method, except for

calculation of & , i.e. plastic part of load point rotation. Inp

Parls-Tada scheme O is obtained based on essentially LEFM methods

by taking the plastic zone correction. In reality the carbon

steels will show considerable plastic region around the crack tip.

The NBC estimation gives only engineering attempt to estimate

piastic rotation based on smooth bar tensile specimen.

Ramberg-Osgood equation based on deformation theory of plasticity

can be written for applied stress & as

e/e = a/a +a (a/a ) n

o o o29

By changing the reference stress fnw et %o &t

e s a/B +« (&t/K) (o-/o'0)n"*(o'/^f)

n (2.6.3.1)

e - *# Cl + «<Sb+St)n"']

where a' = a {ot/a )n"* (2.6.3.2)

The elastic and plastic component of strain is increased

based on current applied stress level. By asssualnc the relation

for load point rotation proportional to strain it can be written

as 0/0#= * / V (2.6.3.3)

This Is obtained through engineering Judgeeent, the

theoretical basis of these equation is not clear and plastic

rotation Is obtained by this Judgement as

0e = 0e ( %tty ( 2.6.3.5)

a and n are material parameters

The stain hardening Is accounted for by using Ramberg-Osgood

stress-strain law, instead of perfectly plastic behaviour as in

Paris-Tada estimation. Though the load point displacements in case

of planar specimens are proportional to strain, the assumption of

the load point rotation following this proportionality (2.6.3.4)

is not having theoretical basis.

2.6.4 LBB.BCL1 Method f20]:

There are a number of simplifying assumptions involved

with all J-estimation analysis techniques. Wor GE-EPRI method, the

assumptions are those used for the numerical analysis approach.

Paris-Tada and LBB.NRC assumptions include (1) using an artificially

larger crack size in the elastic solution to estimate the plastic

30

zone and (11) approximating the partial derivatives of the moment

with respect to the crack angle. The first assumption ie an

inconsistency with deformation theory of plasticity. Following

relation based on deformation theory of plasticity assuming that

the material follows Ramberg-Osgcod relation, the load line

displacement and load point rotation are given by

.n& - K

and O - K a.(ct/a )n

(2.6.4.1)

(2.6.4.2)

K and K are known functions of spatial

position. For plastic part of load point rotation it can be written

as

0p = K' O.

K must be determined by numerical method. GS-EPRI hand book

gives the following relation for load point rotation for the

clrcumferentially cracked pipe subjected to pure bending. The

expression is based on finite element analysis.

= f (M/E) +c*£ h (M/M )4 o 4 p

ho 4

(2.6.4.3)

where M = 4 0.5 sin(e)]

f. = 4aRn

a _ 4aRw wI vz

0 =

whereK =

4aRm

Kn h.

4* V

V, !$

4 V"

2.6.4.4

i

n4 (coa(e/2) - 0.5 sine)

0 ( 2.6.4.5)

31

This scheae is applicable only for pure bending case aa V2

and h4 values are available for this particular case only.

The J and J are calculated in siailar ways as

described by the LBB.NRC and Faris-Tada estimation scheaes.

The scheae is the hybrid of Paris-Tada scheae for calculation

of J based on H-0 relation and GK-IPRI echeae of setting load

point rotation based on nuaerical aethod. For snail crack ancles*

load point rotation due to crack Bay becoae negative as per

nuaerical calculations. This elves physically unrealistic results

for V3 and \ fl5].

2.6.5 LBB.BCL2 Method [201:

In this aethod the actual circumferential TWC pipe is

replaced by a pipe with reduced thickness extending for a

distance at the center of the pipe. The reduced thickness section

vhich actually results in a naterial discontinuity, is an atteapt

to siaulate the reduced ayatea conpliance due to the presence of

the crack. It is assuned that deforaation theory of plasticity

controls the stress-strain response and that beaa theory

assuaptions hold.

From Raaberg-Oegood equation, neglecting saall elastic

strains, plastic strain can be written as

e •=. c* e {&/& )

a s (/ )

Force acting on infinitesimal element taken at an angle <=» at aean

radius is given by

dF = c R d&.t, and moaent is given by

dM = o R d&.t.R sin© (2.6.5.1)m rn

strain at any section distance e is given by

32

e = R sin© / Rm e

where R is radius cf curvature of the beam. By Integratingc

equation (2.6.5.1) from Units 0 to n/2 we get

n

) ( 2.6.5.2 )d2y 1 H n

dx2 R M.m K

M. = 4 K I K ( 2.6.5.3)

where,

M. = .K nR

n

K = J j f , — ( 2.6.5.4)

m

V 7T r (1 + l/2n)K = ~2 r(3/2 + l/2n) ~"7 ( 2.6.5.5 )

Gamma function is approxinately calculated using solution

given by Sterlings formula [201. The curvature equation solved by

enforcing suitable boundary conditions and compatibility

conditions to get slope of the equation in the equivalent

thickness region. The slope is given by

t ""* n n

°P = ( T > ( T T ~ ) a (~^~) 0P ~ ( 2-6-5«>

\ - t [cos(e) - 0.5 sin(©)] for © > 60° ( 2.6.5.7 )

t = (4/ff)t [ cos(e) - 0.6 sin(e)] for © <45° —(2.6.5.8)

for angles between 45 and 60 degrees t le Interpolated.

After calculating the plastic rotation the U-& curve is

integrated as in previous nethods to find the plastic J.

This method does not require any computation as In GE-EPRI,

LBB.BCL1 estinatlon scheme where geometry factors obtained. Is

based on finite element method. The strain hardening of the

material is accounted as the method is based on Ramberg-Oegood

33

equation.

LONGITUDINALLY ORIENTED CRACKS s

In the analysis of the longitudinally oriented cracks It Is

regarded that the bending moment and axial force on the pipe

section are non-contributory loadings for crack extension. The

hoop etre8B acting in the circumferential direction of the pipe is

assumed as critical loading direction for the crack extension.

For the pipe with mean radius B and thickness T is subjected

to internal pressure 'P '. The crack length is assumed to be 2c. The

estimation of J is given by [21]

J = C8c o-/nrR] In C«ee {Wto/2ff)]

where c = PR /2 T ; E - Youngs*s Modulus

o>t = flow stress

M r f 1+1.287X* -0.026905X4 +5.3649x l(f\a i°S

X = c/R Tm

The applicability of this scheme is for 0<X<5 and &<o/H

C O LEAK RATE CALCULATION :

For the application of the LBB concept to high energy piping

system design the leak rate from the system Is one of the factors

of high concern. The leak detection system capabilities and

demonstration of leak rate detected should not threaten the pipe

work structural integrity is more important than the fracture of

the pipe. Leak rate calculations are made based on models given by

researchers. The leak area and leckage rates are verified by

experiments. The load consists of internal pressure together with

bending moment. Leak rate studies In connection with LBB

considerations are performed especially in DSA, Canada. Japan.

34

France and Germany. The cracks were either artificially produced

or grown by fatigue notches. The leak rate experiments were also

carried out at water temperature of 300°c with internal pressure

(10 HPa) and a step change in bending moment at HDB,Germany. Host

of the investigators performed calculations of the two phase

mixture (water/steam) streaming through a crack. Computer programs

require crack geometry, thermal hydraulic conditions and crack

roughness. Large deviation between calculation and measured data

were noted.

Faris-Tada estimation:

The leak rate calculations are based on LEFM, taking into

account Irwins's small scale plastic correction.

a = a n B2 I(e) /Bm

where e = &o + K*/(CM?RM©'2 )

K ie the* stress intensity factor and I(e) is the geometry

factor as explained earlier. After getting the leak area the leak

rate constant for the particular geometry, operating conditions

will give the leak rate.

35

CHAPTER III

RESULTS AND DISCUSSIONS

The estimation techniques are applied to the two

numerical examples for the validation of the code developed.

Problem 1: [22]

Pipe material - Austentic Steel

Mean Diameter of Pipe - 9 inch

Thickness of pipe - 0.75 inch

Reference stress (c -o ) - 0.23E+5 PSI

Modulus of Elasticity (B) - 0.26B+8 PSI

Flow Stress (<rf) - 0.435E+6 PSI

Alpha (a) - 3.0

n - 5.0

Half crack angle - 42.96° to 63°

Problem 2 :[23]

Mean Diameter of Pipe - 52.87 mm

Thickness of pipe - 8.56 mm

Reference stress (c = c ) - 200 MPao y

Modulus of Elasticity (B) - 175760 MPa

Flow Stress <cf) - 303.3

Alpha (a) - 9.42

n - 3.826

Half Crack angle(e) - 69.5°

The J- estimation schemes can be used to give

conservative predictions of the bending moments that can initiate

the crack propagation in circumferentially THC pipes.

Comparisions are made for various sizes of crack under different

36

moments. For the known geometric details of the pipe the tonelie

stress-strain properties and J-resistance curve of the pipe

material are required. These parameters completely define the

input required for J-estimation analysis.

The problem with Raaberg-Osgood fit is that one may

only fit Ramberg-Osgood constants over certain range of strain

that is, either for low strains or high strains. The constants in

Ramberg-Osgood equation is obtained from the ref.[24].

Table 1 gives the comparision between [22] and GE-EPRI

estimation technique for the first problem. The J calculated by

GE-EPRI estimation scheme for crack angles of 42.96, 45, 43.71

54.43 and 63 degrees, for the applied moment varied between 1000

kips-in to 3500 kips-in. The values of J calculated by authors are

compared with ref [22] and it is found that percentage variation

in calculated value of J is 8.9 %. The slope of J-R curve is

calculated by fitting the curve using second order polynomial. The

slope is converted into crack growth toughness which is commonly

known as Tearing Modulus. The percentage variation in Tearing

modulus calculated by authors compared with ref [221. The

percentage variation was found to be - 15 % .

The table 2 gives the comparision of values of J estimation

schemes with the J value given for the problem 2. The J estimated

in [23] is based on 6CL2 estimation. The maximum variation in the

J value compared to BCL2 scheme is 7.41%. The variation is due to

linear interpolation scheme followed in numerical integration.

The estimation schemes are then applied to PHT piping of 500

MWe PHWEL The dimensions and material details are as given below

[24].

pipe outer diameter - 610 vna

37

thickness of tha pipe - SO tm

pipe material - ASTM A333 Grade 6

yield stress (o) - 24.57 Kg/mm2

flow stress (o-f) - 35.09 Kg/art9

ultimate streBB(c ) - 40.837 Kg/u

Youngs Modulue E - 18318 K«/v»2

Alpha (<*) •• 8.656

n 4.16

reference strain (*o) ~ 0.0010

The orientation of the crack is asBiuaed to be circumferential

THC. The initial crack length assumed to vary froa 6X to 50 % of

the circuaference. The loading considered is bending aoaent due to

thermal expansion, Safe Shutdown Earthquake and axial force due to

the internal pressure.

Table 3 shows the Halt moment calculated for

different postulated crack angles considered. The screening

criteria for Unit nonent application,

EJ /2^.2(rl)> {n-e)R /2 (r2)

where, <?{ - flow stress; E = Elastic Modulus

0 = Half crack angle; Jic= naterial crack initiation parameter

The plastic zone at the crack initiation with the distance between

the crack tip and neutral axis is given in the table 3. This shows

that a detailed Elasto Plastic Fracture Mecahnios is to be carried

out for the pipe material.

The figs 3.1-3.8 are graphical representation of variation of

J for various applied Moment keeping axial force zero. The bending

Bonent considered varies fros 30 T-M (SSE aonent) to 100 T-M,

which is the load to be (considered) for the design as per

ASMS,Sec.III,KB [i.e. a factor of safety of 1.5 times the faulted

38

load plus the thermal expansion moment!. The J calculated by

different estimation schemes are plotted against the crack angle

for given moment. The GE-EPRI scheme estimate the higher value of

J when crack angles are less than 25% of the circumference. The

percentage difference between the upper and lower bound values

calculated is within Zb% . The estimation schemes are compared by

percentage difference in the upper and lower bound values

calculated. The percentage difference is given by

X dlff={upper bound value - lower bound valuel/upper bound value

The percentage difference between the upper and lower bound

values of the J calculated hy different estimation schemes for the

crack lengths more than 25% of the circumference tend to increase.

The LBB.NRC and Paris-Tada schemes gives the lower bound value.

This deviation is due to under estimation of the plastic rotation

in Paris-Tada estimation scheme which is based on the Irwin's

plastic zone correction. The LBB.NRC scheme assumes that the ratio

of 0 /& varies linearly with the ratio of strains & /£. . Thisp e p o

assumption following the tests on planar specimens, where load

point deflection is linearly varying with the strains. But in the

case of pipe specimens even though the load point rotations are

proportional to strains the assumption of linearity may lead to

erraneouB eetimate. The J estimated by GB-SPRI and BCL1 are based

on geometric factors which are estimated through finite element

calculations, varies marginally.

The figs. 3.9-3.14 shows the J value estimated by different

schemes for the applied moment considered as earlier in addition

to the axial force. The axial force taken is equal to the force

acting in the axial direction due to internal pressure in the

pipe. The operating pressure being 10 MPa, which results in 260 T

39

axial force. In this case also the NBC scheme fives the lower bound

values when the applied stresses are high. The GE-EPRI ecbe»e

which is based on geometric functions gives higher bound values

when applied load is large. The value of J estimated by different

estimation schemes for crack lengths of 25% of the circumference

is deviating by 22% beween lower and upper bound value. For

larger crack angles the difference in upper and lower bound

values varies drastically as seen in the case of pure bending

loading. Apart from the reasons nentioned earlier, the one core

contributory factor is that the geometric functions used in

GE-EPRI estimation schemeare available only for the B/T ratio of

10. The geometric functions for this can be generated using the

non-linear finite element analysis.

Tables 4-8 give the values of J calculated by different

estimation schemes such as GE-EPRI. PARIS-TADA, LBB.NBC, LBB.BCL1

and LBB.3CL2 for pure bending moment. Tables 9-11 give the value

of J for combined loading of axial force and bending moment.

The J values estimated is the controlling parameter to

predict the crack initiation using the material parameter J. . For

the material of interest, the reported value of the J at

operating temperature of 230 C is 5.1 Kg/mm £7]. The applied

value of J exceeding this limit will characterise the onset of

crack growth. The crack size, for the applied moment of 30 T-m to

100 T-m which gives onset of crack propagation as estimated

by different estimation schemes are tabulated in table 12-13.

Tables 13-14 shows the crack initiation based on the J

recommended by ASME. The value prescribed is 30.25 Kg/mm.

From table 13-14 it is Been that the crack length at the

initiation predicted by the different methods, varies from 3.9 %

40

to 16.5% with respect to lower and upper bound. The GE-EPRI and

BCL methods predict smaller crack angles compared to Parie-Tada and

LBB.NRC estination. All the methods are based on LEFH for

calculating the elastic portion of J. Hence when there is snail

scale yielding near the crack tip, all the methods evaluate the J

value accurately. The plastic J contribution will be very less as

the moment-rotation relation follows nearly linear relation before

the initiation.

The stability of this propagating cracks is established by

using J-T concept. This involves calculation of Tearing modulus at

the applied J value. If at any instant T > T , the crack• app mat

propagation will be in a unstable fashion which means that the

energy supplied is more than the energy required for creation of

new surfaces. This type of crack propagation will lead to

catastrophic failure of the piping system. The material JR curve

[24] for the carbon steel material is used to establish the J '.root

v* T , curve. Since, the material curve is available in limitedmat

range, this has been extrapolated In this study.

The fig. 3.15-3.22 shows the intersection of material J-T

curve and the applied J-T curve for pure bending loads with

corresponding J-© curves. The instability region is given by the

intersection point of these two curves. The critical value of J is

read from this curve. From the J-& curve the values higher than

this J critical value shows instability of the crack. The

instability sets in for different crack sizes as predicted by

different estimation schemes under the operating loading

conditions. Fig.'3.23-3.28 shows the intersection of material J-T

curve and the applied J-T curve for the combined loading with

corresponding J-& curves. Table 16-17 gives the unstable crack

41

size predicted-by the estimation schemes. Without axial force at a

nonent of 80 T-M the crack size of 50% of the circumference will

not propagate in a unstable fashion. Whereas, when the axial force

is acting, a nonent of around 35 T-M is sufficient to lead to a

catastrophic failure of the pipe having crack size higher than 50%

of the circunference, This shows the stringent safety measures to

be taken when the plant is in operating condition. The axial load

on the pipe due to the coolant pressure will bring down load

carrying capacity by half as predicted under pure bending load.

The crack initiation nonent predicted by different estimation

schemes, with and without axial force varies narginally, whereas

the naxinun load capacity predicted by different estimation

schenes varies considerably. The Paris-Tada and LBB.NRC estination

schenes overpredict the load carrying capacity of the piping

compared to other estimation schemes.

For predicting the flaw sizes acceptable by ASMS code the

Isak rates are calculated for the crack angles ranging from 10° to

30°. ASME Code gives guidelines for acceptable flaw size leading

to ten tines the leak rate that can be detected by the leak

detecting system. The leak rate of 0.05 Kg/sec can be detected by

leak detecting system. The leak rate constant is taken as

0.0245Kg/sec/mm as reported [25]. The leak rate has been

calculated and plotted against the total crack angle (26). Fig.

3.29-3.30 gives leak rate vs crack length without and with axial

force respectively. The leak rate of 0.5 Kg/sec is detected at a

moment of 30 t-m and axial forco of 260 T when circumferential

crack reaches a size of 38 . It can also be seen that there is no

initiation of crack corresponding to this crack size, with applied

moment of 80 T-m and axial force of 250 T. Hence the leakage flaw

42

size will be detected by the leakage detecting system. This flaw

will not grow. It may be possible to Identify it and repair in

next outage. The minimum crack size is around 73 that can be

initiated at a moment of 80 T-M with axial load of 260 T. This

would give us a margin of 2 on initiation size crack to leakage

size crack.

In the analysis of through walled axial cracks the crack

lengths upto 1000 mm has been considered. The fig.3.31 shows the

variation of J with increase In crack length when the pipe is

carrying the coolant at operating pressure of 10 MPa. The hoop

stress will lead to the node 1 failure. The J estimated reaches a

value of around 5Kg/mm due to hoop stess when the crack length is

about three times the mean radius of the pipe. The applicability

of the estimation scheme has the limitation. However, the crack

initiation Is not observed under operating conditions due to

internal pressure.

There is a dramatic reduction in J and tearing modulus from

20°C to 300°C. This unexpected five to six fold reduction is

probably attributed to dynamic strain ageing phenomena occurs at

288°C. There appears to be three mechanism that contribute to the

drop in fracture toughness with Increased temperature. The first

mechanism is a drop in the JR curve properties because of a drop

in the tensile properties of the material. The second mechanism is

a drop in toughness caused by static strain ageing. This causes

reloading peaks in the load displacement curve. The third

mechanism in dynamic strain ageing which occur during the loading

of the specimen. It appears that dynamic strain ageing mechanism

was active in non-post-weld heat treated welds at 280°C in SA

106 carbon steel. Therefore, all welds in PHT system of

43

Darlington Reactor Here poet-weld-heat-treated. A 106 grade B

pipe, J decreaed from 1714 in-lb/lnz (300KJ/m2) at rooaic

temperature to 286 in-lb/in2 (50KJ/m2) at 280°C. Hence, the drop

In toughness is a factor of six.

The demonstration of LBB for the piping eyetern requires the

loads resulting fron the most severe operating conditions. These

loads are usually determined from the static and dynamlo piping

analysis of the uncracked piping system. However, the presence of

a large leakage crack causes a significant changes In the

flexibility of the region iteelf and the additional material

plasticity, thereby redistributing the loads which can be carried

by the cracked pipe section. The resulting load can be reduced

significantly for the large leakage crack in a pipe. Battele

Columbus, Ohio group has performed dynamic analysis of cracked

pipe and also performed experiments at HDR in Germany. The cracked

pipe is represented by a nonlinear spring placed at cracked

location. The spring stiffness is defined by prediction using

J-estimatlon schemes analysis. The response is characterised by a

nonlinear moment-rotatiojo (stiffness) in place of a crack at a

point in piping system. Analysis using this model with seismic

loading have shown that even very large crack (i.e. a 360 , 75%

deep internal surface crack with 40 % long leaking TWC in a 406 mm

diameter having 12 mm wall thickness) did not result in a double

ended guillotine break at three times the plant design basis SSE

loading. Any other flaw evaluation procedure would have suggested

that this flaw could not have survived for euch loading.

Therefore, the realistic forces can be only determined if staticand dynamic analysis model of the crack in the piping is made.

This aspect will be studied in fature.

44

Dynamic strain-ageing Is well known to be not only

sensitive to temperature but also strain rate. This brings op an

Interesting question about the fracture behaviour that would occur

at seismic load rates. Seismic loading rates are approximately

four order of magnitude higher than quasi-static loading rates

[8]. At this higher rates, it is possible that some material may

be pushed above the dynamic stain-ageing effects. Therefore, the

ductile material at high strain rate may behave in semi-brittle

manner. The strain rate sensitive aspect of dynamic strain ageing

makes charpy impact test results misleading, since it cannot

simulate crack tip strain rates due to blunt notch. This is an

area which should be studied in detail.

45

CHAPTER IV

CONCLUSIONS

The presenae of flaws In piping induces • reduction in load

carrying capacity. This reduction can be quantified through the

fracture Mechanics estimation schemes. Finite Element Method and

estimation schemes predict crack initiation load, amount of stable

crack orowth and maximum load carrying capacity satlfaotorily. The

following conclusions can be drawn from this study

1) Though the limit moment for pipe with 50% oircumfereone crack

is 113.5 T-H without the axial force, the screening criteria

shows that vhe EPFM analysis is to be applied for the load

carrying capacity of the pipe. All the estimation schemes give

the conservative J estimation when the crack size is less than

25% of the circumference. For crack angles less than 25% of

the circumference the differnce between upper bound and lower

bound values are of the order of around 20%. For crack sixes

more than 25% of the circumference, there is considerable

difference in J values calculated by different estimation

schemes. The stability analysis has been done by each method

to get the conservative value.

2 ) For crack angles less than 22% of circumference no crack

growth (either stable or unstable) is possible in the absence

of axial force with a applied moment of 100 T-m. However, if

the axial force is considered, the moment required for

initiating the growth, for the same crack length is,

decreased to around 70 T-H. It should be mentioned here, that

the above conclusion has been arrived by comparing applied

46

crack initiation with Material crack Initiation toughness

(Jlc) value at 280°C. This value ie chosen to be 50 KJ/mZ

£8]. For SA 106 grade B pipe J c decreases from 300 KJ/n2 at

room temperature to 50 KJ/m at 280°C C8]. This reduction is

due to dynamic strain ageing. It is noted that ASME Sec. XI

permit the usage of Jje of 300 KJ/mz. If ASME J^ value is

used, then initiation crack length will be 38% of the

circumference at a moment of 100 T-m. With axial force of 260

T-m acting the initiation crack length will be 28% of the

circumference. The maximum variation in upper and lower bound

crack initiation length is 16X. It implies that irrespective

of the estimation scheme used, the initiation load predicted

by different schemes will be nearly same.

3) From the extrapolated J-T . [24] it is seen that the crackmat

of else 50% of the circumference will be unstable at a moment

of 90 t-n as predicted by GE-EPHI scheme. The limit moment

calculations show that crack of 50% of the circumference can

take 113.5 T-M moment in the absence of axial force. But

detailed EFFM shows that the same crack will be unstable at a

moment of 90 T-M that is a reduction of load carrying capacity

by a factor of 1.26. The same crack will become unstable at a

moment of 35 t-m when axial force is acting on the pipe i.e.

the axial force due to internal pressure in the pipe will

reduce the maximum load capacity of the pipe by 2.8 times for

the same crack length. The growth of the same crack size is

initiated at a moment of around 23 t-m.

4) The maximum bending moment during SSE is 33 t-m. As per ASME

code applying a factor of safety of 1.5 for faulted load (SSE)

and adding the expansion moment for which stability shall be

47

checked is 33 x 1.5 •»• 54 = 103.5 t-m. Crack size of 40X of the

circumference will becoae unstable with this aoaent. It is

seen that the cracks sizes less than 33% of the circumference

are stable for the applied aonent of 105 t-» and axial force

of 260 T. Hence after detailed EPFM analysis it is concluded

that suction pipe having a through wall clrcuaferentlal crack

sizes upto 33X of circumference would not lead to sudden

rupture under safe-shutdown earthquake loading with the

supposition that the plant is operating.

5) From the leak rate calculations it is seen that the leak rate

of 0.5 Kg/sec is detected during SSK when the pipe carrying

the coolant which has a circumferential TWC of 38°. It is

coaparable with the 33.5° reported [25], The critical flaw

size which becone unstable is around 120 , as predicted by

GB-EPBI estimation. This gives a factor of 3.15 on the flaw

slae which is acceptable by ASMS Sec.XI code.

6) The axial crack does not show any initiation under the

operating conditions. The effect of the axial teneile load on

the axial flawed pipe is not significant. The compreesive load

on the pipe nay lead to crack propagation as the the net load

carrying capacity of the pipe decreased with the presence of

flaw. This will be a case of elastic stability.

48

REFERENCES

1. ASME Boiler and Pressure Vessel code section III .HB 1986.

2. Bartholone, 6. et. al., "LBB for KWO"-Plants". Nuclear Bngg.6

Design, Vol 111, PP. 3-10, 1989.

3. Pan, J. "Some Considerations on Estimation of Eneroy Release

rates for Circunferentially Cracked Pipe", Journal of

Pressure Vessel Technology, Vol-106, pp.391-404, 1984, .

4. Pan, J. "Estimation of Energy Release Bates and Instability

Analysis for a Pipe with Circumferential Surface Crack

Subjected to Bending", Jour, of Pressure Vessel Technology.

Vol. 108, pp.33-40, 1986, .

5. Chaottopadhyay, J. B.K. Dutta. and H.S. Kushraha, "Application Of

Leak Before Break concept in design of High Temperature High

Pressure Primary Heat Transport Piping", BAHC Report

1992/E/033, 1992.

6. Shin, C.F. "Methodology for Plastic Fracture", General Electric

Corporate Report to EPRI, RP 601 - 2 ,1976-1979.

7. Haricchiolo, C. and Hilella, P. "Fracture Behaviour of Carbon

Steel pipes Containing Circumferential Cracks at Room

Temperature and 300°C", Nuclear Engg. & Design, Vol. Ill,

pp. 35-46, .1989.

8. Wilkowski, G.H and Scott, P.M. "A Statistical based Circumfer-

entially Cracked Pipe Fracture Mechanics Analysis for Design

or Code Ijoplementalon", Nuclear Engg. & Design, Vol. Ill,

pp. 173-187, 1989.

9. ABAQDS, version 5.2, Hibbit.Kalsson & Sorensen, Inc.

49

10. Bakker, A. "An Analysis of the Numerically Path Independence

of J-integral", Int. Journal of Pressure Vessel and Piping;,

Vol. 14, pp. 153-179, 1983.

11. Hays, R. et. al.,"Pipe Fracture Analysis using Limit Load and

J-integral Technique". Nuclear Engg. & Design, Vol.96,

PP.225 -253, 1986.

12. Broek, D. "The Practical Dee of Fracture Mechanics", Kluwer

Academic Publishers, 1991.

13. USNRC, "Evaluation of Potential Pipe Break Report of the

0.S.Nuclear Regulatory Conaisslon piping Review",

NOREG-1061, Volume 3, 1984.

14. Kumar. V, et al., "An Engineering Approach. For Elasto-Plastio

Fracture Analysis", lPRI-Report,»P-1931 1984.

15. Xuaar. V, et. al., "Advances in Elaeto-Platlc Fracture

Analysis", EPR1-Report, NP-3607, 1984.

16. Paris, P.C and Tada, H, "Application of Fracture proof design

nethod using Tearing Instability to Nuclear Piping

Postulating Circumferential Through vail crack",

NDRE6/CR - 3464, Sept. 1983.

17. Sander, J.L. Jr. "Circumferential Through Cracked Cylindrical

ShellUnder Combined Bending and Tension", Journal of Applied

Mechanics, Vol.50, March 1983.

18. Vasquez, J.A. and Paris, P.C. "A Plastic Zone instability

Phenomenon Leading to Crack Propogation", Proceedings of

CSNI Specialists meetings on Plastic Tearing Instability,

USNRC, NUREG/CP-0010 and OECD Nuclear Energy Agency CSNI

report No.30, pp.601-631, Sept. 1979.

19* Klecker, R. et. al., " NRC Leak-Before-Break Analysis Method

for Circumferntlally Through-Wall Cracked Pipes Under Axial

50

Plus Bending Loads", HOBEG/CR-4572, 1986.

20. Brust, F.W. "Approximate Methods for Fracture Analyses of

TWC pipes", HOREG/CR-4853, 1987.

21. Zahoor, A. "Ductile Fracture Handbook", Vol 1, 1969.

22. "Evaluation of Flaws in Ferritic Piping", EPRI-NP-6045,

Oct. 1988.

23. Rahaman, S. and Brust, F.W. "An Estivation Method For Evaluating

Energy Release Rates of ClrcuBferential TWC Pipe Welds",

Engineering Fracture Mechanics, Vol 43, 1992

24. Wilkowei, G.M. et. al., "Degraded Piping Program - Phase II ",

HDREG/CR-4082, 1986.

25. Nathwani, J.S. et al., "Ontario Hydro's LBB Approach :

Application to the Darlington (CANDD) Nuclear Generating

Station", Nuclear Engg. & Design, Vol 111, pp. 102-104, 1969.

26. International Journal of Pressure Vessel and Piping, Vol.

43, Special Issue, "Leak-Before-Break in Water Reactor

Piping and Vessels", 1880.

27. Ahead, J. et. al., " Elastic-Plastic Finite Element Analysis of

Crack Growth in Large Compact. Tension and Circumferentially

Through-Wall-Cracked Pipe Specimen", NUREG/CR-4573, 1986.

28. Scott, P and Brust, F.W. " An Experimental and Analytical

Assessment of Circumferential Through-Wall Cracked Pipe Under

Pure Bending", NOREG/CR-4574, 1986.

29. Wilkowski, G.M. et al.,"Progress and Results from the

Degraded Piping Program-Phase II", Proceedings of the

Fourteenth Water Safety Information Meeting, NOREG/CP-0082,

Volume 2, 1987.

51

TABLE 1

COMPABISIOH OF J-T CALOLATIONS WITH NOVITECH LTD SAMPLE PROBLEM

CRACKANGLE

42.96

42.96

48.71

54.43

54.43

54.43

63.00

MOMENT(IN-KIPS)

1000

1500.

2000

2000

2500

3000

3500

ZAHOOB

66.

172.

557.

608.

1831.

3978.

18025.

1

8

8

7

5

9

0

J (LB/IN)PRESENT X

66.1

174.1

672.0

832.0

1926.0

4267.0

19810.0

variation

0.0

0.76

2.54

2.88

5.16

7.24

9.90

ZAHOOB

0.3

0.9

3.3

5.0

12.7

30.4

169.5

TEARINGPRESENT

0.2786

0.7115

3.369

5.280

14.64

34.60

124.87

MODOLOS(T)X variation

-7.1

-20.9

+2.9

+5.6

15.2

14.47

-26.80

Table 2

Validation of Cede with R«ff8)

MOMENT BEF (25) J ESTIMATED (PRESENT) KN/H X VAHIKN/M PARIS NRC BCL1 BCL2 GH-EPRI (8)2 0.0265 0.0265 0.265

4 25.27 12.576 12.74 19.13

6 106.09 35.365 40.32 84.24

8 390.091 89.63 121.64 284.39

9 708.59 148.13 217.39 480.98

NOTE : COLOMN (8) SHOWS THE X PERCENTAGE DIFFEBENCE OF J ESTIMATED BYBCL2 WITH REF VALUES

0.02652

23.41

114.385

405.35

695.4

0.035

30.96

151.07

536.51

919.19

-7.

-7.

3.

1.

41

60

7

9

52

TABLE 3 : LIMIT LOAD CALCOLATIOH FOB DIFFERENT CRACK AH6LB8

Crack angle (&)

(degrees)

10

20

30

40

50

60

70

80

90

Limit nonent (M )

(T-M)

499.86

447.015

392.745

339.90

287.06

236.50

191.37

150.53

113.97

Screening (rl/r2)

parameter

5.7

6.38

5.06

4.72

4.37

4.05

3.72

3.37

3.04

53

Table 4 : J values by 6E-KPRI estimation echene

crack

angle

11

22

27

31

36

45

5463

72

81

90

.34

.50

.00

,50

.00

.00

.00

.00

.00

.00

.00

1

1

2

3

30

.0611

.1454

.1956

.2544

.3222

.4879

.7890

.1958

.7293

.4227

.3460

1

2

3

4

6

applied monent(t-m)

40

.1090

.2594

.3491

.4541

.5756

.8731

.4155

.1556

.1477

.4995

.4835

1

2

3

5

711

50

.1712

.4077

.5491

.7147

.9068

.3796

.2460

.4484

.1166

.5513

.5789

1.

1.

2.

3.5.

7.

12.

19.

60

2484

5925

7986

0408

3225

0210

3111

1452

8113

0380

9109

with

.

out

70

3420

.8171

1.

1.

1.

2.

4.

7.

11.

18.

33.

1026

4393

8327

8163

6577

3558

5027

6711

4578

axial force

1

1

1

2

3

6

10

16

28

55

80

.4537

.0862

.4682

.9205

.4522

.8018

.3534

.2380

.5808

.4747

.0677

90

.5857

1.4064

1.9048

2.4983

3.2010

5.0129

6.4906

14.0078

23.5791

42.8493

88.6350

100

.7413

1.7852

2.4251

3.1909

4.1054

6.5059

11.1909

18.9494

33.1990

63.6368

139.2819

Table 5 : J values by Paris-Tada estimation scheme

crack

angle

11.34

22.5

27

31.5

36

45

54

63

72

61

90

30

0.0619

0.1419

0.1815

0.2268

0.2786

0.4079

0.5860

0.8409

1.2193

1.8034

2.7558

0

0

0

0

0

Applied moment(t-m) with out axial

40

.1102

.2526

.3235

.4043

.4969

0.7286

1

1

2

3

5

.0496

.5126

.2099

.3206

.2241

50

0.1724

0.3954

0.5067

0.6337

0.7794

1.1456

1.6557

2.3992

3.5447

5.4252

8.878

0

0

0

0

1

1

2

3

5

8

14

60

.2485

.5708

.7320

.9162

.1282

.6622

.4138

.5234

.2675

.254

.1835

70

0.3387

0.7793

1.0002

1.253

1.5447

2.2842

3.3324

4.9053

7.4437

12.0167

21.9314

0

1

1

1

2

3

4

6

10

16

33

force

80

.4431

.0214

.3121

.6456

.0323

.0155

.4251

.578

.1668

.9781

.461

90

0.5618

1.2977

1.6696

2.097

2.5928

3.8635

5.7076

8.5603

13.5417

23.5827

51.3893

0

1

2

2

3

4

7

10

17

32

82

100

.6949

.6099

.0731

.6077

.23

.8361

.1988

.9715

.7251

.447

.2

54

Table 6: J values by LBB.HHC estimation scheme

crack

angle

11

22

27

31

36

45

54

63

72

61

90,

.34

.50

.00

.50

.00

.00

.00

.00

.00

.00

.00

crack

angle

11.22.

27.

31.

36.

45.

54.

63.

72.

81.

90.

34

50

00

50

00

00

00

00

00

00

00

30

.0619

.1416

.1812

.2262

.2777

.4058

.5812

.8296

1,1915

1.7304

2.5446

1

1

2

3

4

Applied moment(t-m) with

40

.1101

.2519

.3224

.4026

.4943

.7226

.0355

.4786

.1246

.0873

.5430

50

.1721

.3941

.5046

.6302

.7741

1.1323

1.6238

2.3207

3.3376

4.8548

7.1531

Table 7 : J values

30

.0619

.1437

.1814

.2265

.2781

.4072

.5827

.8333

1.2032

1.7730

2.7210

•

1.

1.

2.

3.

5.

60

.2480

.5686

.7283

.9102

1.1185

1.6379

2.3517

3.3653

4.8469

7.0622

10.4302

1

1

2

3

4

6

9

14

out axial force

70

.3380

.7761

.9947

.2440

.5299

.2440

.2276

.6276

.6793

.7587

.4732

1

1

1

2

2

4

6

8

13

19

by LBB.BCL1 estimation

Applied moment(t-m) with

40

1100

2613

3234

4037

4962

7289

0422

4950

1768

2773

3297

50

.1719^

.4240

.5076

.6338

.7799

1.1523

1.6452

2.3728

3.5035

5.4599

9.6604

60

.2474

.6456

.7361

.9193

1.1335

1.6694

2.4067

3.4993

5.2738

8.6202

16.8899

1.

1.

1.

2.

3.

4.

7.

13.

28.

80

.4422

.0175

.3054

.6341

.0118

.9575

.2642

.1301

.8759

.0222

.4557

scheme

out axial force

70

.3367

.9477

.0121

2644

5632

3584

3495

9248

6274

2216

8384

1.

1.

1.

2.

3.

4.

6.

10.

19.

48.

80

.4396

3610

3401

6748

0782

1859

5067

7219

7656

9308

1266

1

1

2

90

.5610

.2943

.6626

.0840

2.569P

3

5

7

11

16

25

.

1.

1.

2.

2.

4.

5.

8.

14.

29.

78.

.7879

.4791

.9053

.4967

.9739

.6951

90

.5561

.9278

.7263

1585

6910

2080

9234

9897

9634

6597

3381

1

2

2

3

4

6

9

14

21

33

22

3.

5.

100

.6946

.6084

.0692

.5980

.2063

.7483

.8970

.9987

.6279

.8003

.8556

100

.6861

.7037

.1790

.7261

.4181

.4722

7.6592

11.8586

20.5828

43.

124.

6078

1861

55

Table. 8 t J values by LBB.BCL2 estimation scheae

crack

angle

11

22,

27,

31.

36.

45.

54.

63.

72.

81.

90.

.34

.50

.00

50

00

00

00

00

00

00

00

30

.0619

.1416

.1813

.2264

.2780

.4070

.5654

.8353

1.2120

1.8055

2.8385

1.

1.

2.

3.

5.

Applied nonent('t-B)

40

1101

2520

3227

4033

4958

7281

0543

5041

2161

4226

8543

1

1

2

3

5

11

50

.1721

.3944

.5055

.6324

.7786

.1497

.6636

.4018

.6290

.9235

.3344

60

.2480

.5694

.7306

.9156

1.1301

1.6827

2.5061

3.5740

5.5977

9.8165

21.2101

with out

70

.3379

.7778

.9997

1.2560

1.5556

2.3437

3.5711

5.0914

8.3494

15.8685

38.4684

axial force

80

.4419

1.0209

1.3153

1.6579

2.0631

3.1563

4.9505

7.0553

12.2113

25.2712

67.4101

90

.5604

1.3003

1.6805

2.1275

2.6631

4.1534

6.7422

9.6049

17.6307

39.5127

113.9158

100

.6936

1.6184

2.0997

2.6725

3.3697

6.3778

9.0753

12.9227

25.1962

60.6492

185.7204

Table 9 : J values by GE-KPRI estimation scheme

crack

angle

10.0

26.0

42.0

58.0

74.0

90.0

40

0.1911

0,7359

1.9447

5.2553

18.2998

103.801

Applled

50

0.266

0.996

2.6856

7.5115

27.4901

163.497

nonent(t~m)

60

0.3534

1.3362

3.684

10.6621

40.6879

249.559

tilth axial

70

0.4633

1.7712

5.0015

14.9678

59.2005

370.759

force of

80

0.5992

2.3196

6.7153

20.7538

84.656

537.818

260 t

90

0.7660

3.0046

8.9199

28.4176

119.044

763.697

56

Table 10 : J estimation by Paris-Tada method

crack Applied moment(t-m) with axial force of 260 t

angle 40 50 60 70 80 90

11.26 .5110 .5254 .6543 .7978 .9560 1.101

26;0 1.3801 1.6105 2.0071 2.4515 2.9454 3.4909

42.0 3.3338 4.2035 5.2812 6.4679 7.7800 9.2560

58.0 7.8014 9.4595 12.4316 15.7405 18.7367 22.5853

74.0 20.1369 26.9158 34.0114 43.8675 55.9554 71.4772

90.0 64.9321 134.4438 326.7276 367.6117 412.4225 461.0410

Table 11: J estimation by LBB.HRC method

crack

angle

11.26

26.0

42.0

58.0

74.0

90.0

40

.4104

1.2541

2.6905

5.4490

11.4486

25.9588

Applied

50

.5249

1.6047

3.4434

6.9662

14.6270

34.0799

moment (t-m)

60

.6543

2.0045

4.3126

8.7439

18.4489

46.1985

with axial

70

.7989

2.4575

5.3130

10.8305

23.1017

61.5237

force of

B0

.9595

2.9686

6.4641

13.2904

28.8631

76.4627

260 t

90

1.1367

3.5442

7.7907

16.2084

36.1612

97.9710

57

Table 12

Crack Initiation angle predicted by different estimation schenea

(Jic considered 50 KJ/M2)

Applied Predicted Initiation flaw size (©)Monent Paris NRC BCL1 BCL2 GK-EPRI

Applied axial force - 0

50 T-M

70

90

100

82.0 83.8 75.7 74.0 72.0

64.0 04.7 64.1 63.1 60.0

52.0 54.0 51.0 49.2 49.0

48.0 48.2 42.2 42.0 43.0

Table 13

Crack Initiation angle predicted by different estimation schenes(Jic considered 50 KJ/M )

AppliedMoment

Predicted Initiation flaw size (©•)Paris NRC GE-EPBI

Applied axial force = 260 T

40 T-M

60

80

54.58

45.10

36.7

56.0

45.2

37.2

56.7

49.9

38.4

Table 14

Crack Initiation angle predicted by different estimation BchetoeB

<Jic considered 300 KJ/M2)

AppliedMoment

Predicted Initiation flaw sizeParis NRC BCL1 BCL2 GE-EPRI

Applied axial force = 0

70

80

100

NOTE

NI8 7 .

8 0 .

0

0

NINI

8 6 . . 0

NI8 5 .

7 6 .

0

0

868 1

74

. 0

. 2

. 0

8 8 .8 2 .

7 0 .

00

0

NI -no initiation of crack in the range considered

58

Table 15

Crack Initiation angle predicted by different estimation schemes(Jic considered 300 KJ/M )

Applied Predicted Initiation flaw size (©)Moment Paris NRC GE-BPRI

Applied axial force = 260 T

50 T-M

70

80

78.

68.

58.

00

00

0

88.

79.

64.

0

0

0

77.

66.

52.

8

0

0

Table 16: Unstable crack angle prediction( Without axial force)

Applied Predicted Critical flaw aize (e)Moment Paris NRC BCL1 BCL2 GE-EPRI

Applied axial force = 0

90 T-M HO HO NO 87.0 89.0100 ND HO 86.0 82.5 82.0HOTE: HO stands no unstable crack in the range of crack length

considered

Table 17: Unstable crack angle prediction

( With axial force)

Applied Predicted Critical flaw size

Moment GB-EPRI PARIS LBB.NRC

Applied axial force = 260 T

40SO60708090105NOTE:

T-M

NO stands noconsidered

86.082.079.076.074.069.063.0

unstable

NO82.0

84.082.081.078.070.0

crack in the

NONONONDNO88.082.0

range of crack length

59

Table 18: Leak rate calculation by Parls-Tada estimation

tfoaent acting Flaw else correspond to leak rate of 0.5 Kg/sec

(T-») with out axial force with axial force

30 29 20.550 25 171570 20 16.390 17 14.2

Mote : axial force applied is 260 T

Table 19

Sunaary of BPFM analysis of pipe

51. Crack Length Monent Axial force CommentsHo. X Circumference T-M T

No crack initiation

No orack initiation

No crack initiation

Crack initiates

Onetable crack

Unstable crack

Unstable orack

Unstable crack

1,

2.

3.

4.

5.

6,

7.

8.

10.5

10.5

22.0

22.0

50.0

50.0

44.0

33.0

100

100

80

80

90

35

105

105

0.0

260

0.0

260.0

0.0

260.0

0.0

260.0

60

1.0. , R-6Curve

0.0 Sr

5o

Oisaptacemenf

FIG. 2.1 FAILURE ASSESSMENT DIAGRAM FIG. 12 LOAD-DISPLACEMENT CURVE

S

APPLIED J-T

MATERIAL*CURVE

Tearing modulus

1

Applied moment

INSTABILITYMOMENT

FIG. 23 J - T CONCEPT OF INSTABILITY

61

FIG. 2.4 PIPE CONFIGURATION

M

FIG. 2,5 PIPE WITH CIRCUMFERENTIAL CRACKSUBJECTED TO BENDING

62

4.00 T

3.00 -

I0 2.00 :

A j

1.00 :

<taaa» Parit-Toda •stimation<uuuu> L8S.NRC« u t f LBB.Bdl* * * * * LBB.Sd2»»i«« GE-EPR1

0.000.00 20.00

FIG. 3.1

40.00 60.00 60.00HALF CRACK ANGLE (DEGREE)

COMPARfStON OF J-ESTIMMON SCHEMES(MOMENT 30T-M)

100.00

8.00 n

0.00 -

(4.00 -

aflBAV Pori»-Tada estimationttjuuui LB8.NRCtitAfe* LBB-Bdl***** LBB.Bd2t u u GE-EPRI

2.00 -

0.000.00 20.00 40.00 60.00 60.00

HALF CRACK ANGLE (DEGREE)

3.2 COMPARtSION OF J-ESTNATON SCHEMES(MOMENT 4OT-M)

63

100.00

12.00 j

10.00 ;

8.00 -.

6.00 :

4.00 -

2.00 i

0.00

%aaap Poria-fodo estimationOOflflP UM.NRC» 4 * » * L8fl.Bd1* & U U LBB.Bd2

C£—EPRI

0.00 20.00 40.00 60.00 60.00 100.00HALF CRACK ANGLE (OEGREE)

F » . 3J COMPAREtON OF J-ESTMATON SCHEMES(MOMENT 50T-U)

25.00 -j

fcfctft* LBB.Bd2t t t f t GE-EPB

0.000.00 20.00 40.00 60.00 80.00

HALF CRACK ANGLE (DEGREE)FKJ. 3.4 COMPARISON OF J-ESpMATON SCHEMES

(MOMENT flOT-M)

100.00

40.00 -i

30.00 -

E

120.00 -

10.00 -

0.00

0£££ff Poris-Todo estimation•UUULP L8B.NRC***** LBS.Bclit&£&# LBB.BdZ

GE—EPRI

0.00 20.00 40.00 60.00 80.00HALF CRACK ANGLE (OEGREE)

3.3 COMPARISION OF J-ESTIMATION SCHEMES(MOMENT 70T-M)

100.00

80.00 -i

60.00 -

(40.00 -

20.00 -

0.00

qaasa Paris-Toda eMlmaUcnUUUL0 LB3.NRC•**»« LB3.Bc(1t&U* LBB.Bd2f t t t * GE-EPRt

o.coFK>.

20.00 40.00 60.00 60.00HALF CRACK ANCLE (DEGREE)

100.00

COMPARBION Of J-ESTIMATJON SCHEUES{MOMENT 8 0 T - M )

65

120.00 3

100.00 ;

80.00 -.

60.00 :

40.00 :

20.00 :

0.000.00

oafiAo Poni-rodo MtbnoUon

F».

20.00 40.00 60.00 80.00HALF CRACK ANGLE (DEGREE)

COMPMRtSION OF J-ESTIMATON SCHEMES{MOMENT 9OT-M)

100.00

200.00 n

150.00 -

100.00 -

60.00 J

0.000.00

«£fiAP Porh-Tado mtknaUoovumB LBB.NRC* * U * LBB.Bdit * l A * LBB.Bc/2r t i t i CE—EPRI

20.00 40.00 60.00 80.00HALF CRACK ANGLE (DEGREE)

F)C. 3.8 COMPARBKIN Of J-ESTIMATWN SCHEMES(UOMEHT 100T-M)

100.00

6 6

120.00 q

100.00 -

40.00 :

20.00 z

0.000.00

ooooa Paria—Toxta ««tlrnattor>«»o»» L69.NRC estimationt-»*«•* GE— £PRI estimation

20.00 40.00HALF CRACK

100.00

F10. 3.9 COMPARISON Of J-EST1MM1ON SCHEMES(MOMENT 4OT-M AND AXIAL FORCE 260 T)

200.00 -,

150.00 -

100.00 -

50.00 -

0.000.00

USilP PcrH-Todo eatimatloniiAi* LBO.NRC estimation»+-»tt GE-EPRJ esb'irvotlor)

20.00 40.00 60.00 80.00HALF CRACK ANGLE(DCGREE)

FW. 3.10 , COMPARISON OF J-ESTIMAT10N SCHEMES(MOMENT SOT-M AND AXlAt FORCE 260 T>

100.00

400.00 n

300.00 -

(200.00 -

100.00 -

0.00

P«r»Tado « l m a*&*i.i LBB.NRC estimationt-Ht-t GC-EPW estimation

0.00 20.00 40.00 60-00 80.00 tOO.00HALT CRACK ANGLG(DCGREE)

(Vi. 3.11 COMPARISJOH OF J-ESTIMATION SCHEMES(MOMENT «OT-M AND AXIAL FORCE 260 f )

400.00 n

300.00 -

200.00 -

100.00 -

0.000.00

aopao Paris-Tuda esvirnatf« « < « • LB8.NRC «stinr)dtk>n***** GC-EPRI b ' t i

20.00 4OJX> 60.00 80.00HALT CRACK ANGUEXDECREE}

3.12 COMPARISON OF J-EST1MATI0N SCHEMES(MOMENT 70T-M AND AXIAL fORCE 280 7)

100 JO

68

WOOO -3

500.00 :

"^400.00 ~

ft 300.00 :

200.00 -

100.00 i

0.00o.oo

qfioop Poria-Toda «etlmotioft»»«»» L8B.NRC estimation»«,«»« GE-EPRI estimation

20.00 40.00 60.00 B0.00 -f>OX»OHALF CRACK ANGLEXDEGREE)

FK). 3 . t J COMPARISJOM OF J-ESTIMAT10N SCHEMES(MOVCNT 80T-M ANO AXIAL fOfiCE 2 * 0 T)

800.00 -i

600.00 -

• 400.00 -

200.00 4

o.oo

Porfs-Tada» » P » LBB.NRC estimationt-t.+tf GE-CPRI «sb'motion

000 20.00 40.00 6OJ3O 80.00HALF CRACK ANCL£(DCGR£E)

100.00

FJC. 3.14 COMPARISON OF J-ESmtAWH SCHEMES(MOMENT 90T-M AND AXIAL FORCE 26O 7)

6 3

moo -

150.00

ttU&» oppiitd J-T 70 t-m«AA4* 60till* 90

toono

mct«riijl J-T curve

100.00 -i

80.00 -

60.00 -

40.00 -

20-00 :

0.000.00 40 M 80.00 120CO

TEARING MOOULUS

0.00

MOMENT 30 T-Maaae* 40 T-M

SO T-4160 T-M

•***t 70 T-Mtu&r 80 T-M4JUUJT 00 T-M«***# 110 T-M

0.00 20.00

FIG. 5 . J 5 WSTA8IUTV PPSOCTtiJM BT J - r CONCEPT(PAWS-TAT* ESTIMATION} nc. s.ie

40.00 60.00 80.00HALF CRACK A N O £ (DECREE)

J VS 1HCTA FOR VARIOUS APPUC5 MOMENT(PWWTJAOA, ESTHMTIOH)

100.00

I

»-

rl

71

MOOO - ,

-41JO.00 -

eo.00 •

4000 •

QAAfiP OppJted J-T 10 t - mUA4* 70

80SO

uiu 100u m rr»«t«rto( J-T curve

0.5B0.00

I I I I I I I I' I I I -I40.00

i i ' i 'i 'i ri i i i i i i i i i i8 0 JOB 190.00

TEARINC MCOUUUS1S0.OD

FIG. WSTABUTr PROMCTI0N Br J - T CONCEPT(OE-EPRl ES"nu*nO>

ieooo -i

120.00 -

t

IS 80.00 1

40.00 -

0.000.00

MOMENT 30 T-MWftfiP 40 T-M

50 T-M60 T-M70 T-M80 T-M90 T-M

TOO T-M

20.0C 40.00 60.00 50.00CRACK ANCLE (DECREE)

100.00

FIC. S.22 -/S 7HETA FOR VARIOUS *PPUET MOMENT(GE--EPFa ESTIMATION)

8 8d

8 8d8

2

74

aw.co -

coo

U U P opplM J—T moment 50 t—muui 00

***** QQuiti 105«»»f» moUrid J-T curv*

fere* 260 t

cooi i T r i i i i i i i i i

40.00

FIG. 3.2S

i f i i i i i r r - i - i T T130.00

TEARINS MODULUS

IMSTAeiUTY PREDICTION BY J -T CONCEPT( LE'B.NRC ESmMATIC+4)

1BCJ0O

200.00 -1

150.00 -

100.00

50.00

0.00

« ftp n»

• • i i •

MOMENT 40 T-M AXIAL FORCE 260 T50 T-M - „ -60 T-M - „ -70 T-M -Z-80 T-M90 T-M

TO* T-M

0.00 20.00

PS. 3.26

40.00 60.00 60.00HALT CRACK ANCLE (DEGREE)

VS THETA. FOR VARIOUS APPUEO MOMENT(18S.NPC ESTIMATION )

100.00

l0\

leoooo i

120000 -

|

eoo.00 -

«oo.oo -

0.00

J-T moment 40 t -m * «rtjj fora 260 tSO9070

105««««« mottoal J-T curv«

«•»->••

o.oo 50.00 100 DO 150.00 200.00TEARIHC MOOJCUS

2SOXI0

FIG. 3.27 INSTASJIl/TY PREDICTION BY J - T CONCEPT(CE-EPR1 ESTIMATION)

1600.00 ->

1200.00 -

g 800.00

400.00 -

0.00

4LW&JP

MOMENT 40 T-M AXIAL FORCE 260 T5Q5Q80 T-M70 T-M80 T-M90 T-M

103 t - m

0.00 20.00 40.00 60.00 80.00HALF CRACK ANGU (OEGREE)

too.oo

FIG. \26 J VS THETA FOR VARIOUS AFPUEO MOMENT(CE-EPRI ESTIMATION )

2.00 -t

1J50 -

6,

aeo -

aooI0J1O

naaua moment 30 t~m 4xM force O4Jubt* 50tlAAJ 90fctifc* 100

20J3O 30.00 40.00 50.00CRACK ANGLT (DECREE)

00 00

HO. 3 .29 LEAK RATE vs CRACK LtMGTH(PARIS ESTIMATION)

100 -2

2.50 -

£ 1 JO -

090 -

0.00

UOO0 momant 30 t -m oxW tore* 2«0 tSO7090

20i» 30.00

no. 130

40.00 SO.OCCRACK ANCLE (DEGREE)

LEAK RATE vs CRACK LENGTH(PAWS ESTIMATION)

60.00 Taoo

77

9.00 - |

•*••» ran MBMM. mesamc or 10 « *

O J O O

0.0fl 200.00 « 0 i » «00u00 MOJOCRACK LENGTH (mm)

ooico taxxco

HO. J.31 J vs AXIAL CRACK LENGTH(OC-EPR) EST»*WH»)

78

Published by : Dr. M.R. Balakrishnan, Head, Library & Information Services DivisionBhabha Atomic Research Centre, Bombay - 400 085, INDIA.