ML19340C514

Integrity Assessment of Feedwater Line Indications,Trojan Nuclear Plant

ML19340C514
Person / Time
Site:	Trojan File:Portland General Electric icon.png
Issue date:	09/30/1979
From:	Bamford W, Davidson J WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
To:
Shared Package
ML19340C513	List: ML19340C512 ML19340C514
References
IEB-79-13, WCAP-9613, NUDOCS 8011170601
Download: ML19340C514 (54)

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b INTEGRITY ASSESSMENT OF FEEDWATER LINE INDICATIONS TROJAN NUCLEAR PLANT M

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INTEGRITY. ASSESSMENT ~0F

.FEEDWATER LINE INDICATIONS TROJAN NUCLEAR PLANT i

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j W.H. Bamford J. A. Davidson i

Septemoer 1979 i'

Prepared by Westinghou' e for. Portland General Electric Co.

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.NJ b,O APPROVED:

].

J.N. Chirigos, Manager Structural Materials Engineering I

Work Performed Under P0XN 2018 i

although the information contained in this report is nonproprietary,

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-no distribution -shall.be made outside Westinghouse-or-its Licensees j

without the. customer's approval.

WESTINGHOUSE ELECTRIC CORPORATION-Nuclear Energy. Systems.

P.O. Box-355 Pittsburgh Pennsylvanf at 15230 i

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r TABLE OF CONTENTS Introductiom 1-1 Materials amd Geometry 2-1 Non-Destructive Examination 3-1 Methods of Analysis 4-1 Fatigue Crack Growth Analysis 5-1 Critical Flaw Size Determination 6-1 Results and Conclusions 7-1 References 8-1 s

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-I SECTION,

INTRODUCTION I_n response to a recem: NRC Bulletin (IE 79-13), a series of non-

~ destructive examinations were performed on portions of the feedwater piping of the : Trojan Uluclear Plant in June 1979. Results of the insepction showed a groove or gecmetric discontinuity at the inside surface of-line A near the counterbore associated with the feedline -

feedwater nozzle weld _ Although the indication is not ' thought to be identifiable as symptomatic of the type of cracking which has been found in other PWR pla.nts, an integrity assessment has been carried out to show. that its ' presence will not adversely affect future operat-ion of the plant.

The inspection results are described in cetail, as well as the plant operating history and the feedwater line geometry and materials of construction. This information forms the basis for the evaluation carried out on the feedwater lines, which included fatigue crack grcwth studies, as well as critical flaw size determinations. Results j

of the analysis are s=marized concisely in the last section, where 1

it is stated that.sven if the caserved discontinuity were to be a crack, adequate margins exist for continued operation without repair.

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.i SECTION 2

.l MATERIALS AND GEOMETRY t

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r The steam generator-feedwater. piping assembly is made up of two

-l grades of piping steels. The figure below illustrates the various j

segments.

[

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(

Y

- WP No. 2

/

7 e

M 14" Elbo.v I-q Sch. 60 i

16" Feedwater '

16x14

• "*i Nozzle Red.

r Q~

t WP No.1 i.

t The material used is as follows:

- steam generator feedwater nozzle: SA S08 cl 2-'

- reducer

SA 106 Gr B

- feedwater piping

SA 106 Gr B 4

The area investigated in this report is in the reducer section about

]

-1/2 inch frem the reducer-nozzle weld, WP 1 (Rl 145) at steam gene-rator A. The cross-section geometry of this area is illustrated below.

I 2

.1

=

-.. ~

w w

-e

t Feedwater Nozzle Weld f

Reducer

1. ^

-, y 13 l

~_

0.75 -

Pipe Wall l

/ Q y

7

~

4 x

0 15 Max.

Location of k

Indicar..on Observed Reducer O.D. = 16.16 in.

1 SA 106 Gr B (ASTM A234 WPB) is a piping grade steel with the following ASTM speci-fications:

Carbon, max.

0.3 per cent Manganese 0.29-1.06 Phos., max.

0.048 Sulfur, max.

0.058 Silicon, min.

0.10

- The minimum specified yield and ultimate tensile strength is 35 and 60 ksi, respectively.

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+

2.

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The chemistry and n.er.:hanical proeprties 'of the reducer (ladle analysis, as taken from the _Ladisin test reports, are listed below. As 'may be easily seen, the prorcerties are within the specifications:

Chemical Compositicon per cent Physical Properties Carbon G).28 Yield strength 53.2 ksi Manganese

'l.05 Ultimate strength 88.4 ksi Phosphorus 0.023

% Elongation 29.0 Sulfur-0.035

% Reduction in Area 59.0 Silicon 0.31 3;

Charpy energy obtained for the actual-material is summarized in the table below - these data were obtained on standard Charpy specimens at a test temperature of zero degrees Fahrenheit.

Eneroy (ft lbs)

Per cent shear Lateral Exoansion (in) 23.0 5

0.019 41.0 17 0.035 50.0 29 0.045 The reducer was formed from a 16 inch diameter seamless pipe. by induction heating one third to one half of the starting piece, and then forcing it f

- through a ring type die by press and plunger.. The piece was then nonnalized 0

at 1650 F.

9 f

2-3

r SECTION 3 NON-DESTRUCTIVE EXAMINATION At the request of ~ Portland General Electric Company (PGE), NDT personnel from Wes:tinghouse joined NDT personnel at the Trojan site to perform a detailed examination of the counterbore area of the feedwater mozzle-to-reducer section weld using ultrasonic as well as radiogeaphic techniques. The s;,ecific area investi-gated was the coumterbore area on the reducer side as shown be-Icw. A detailed r eport was creacred on thse examinations, and trans-mitted. to the NRC, but the results will be surrmarized here for completeness.

Nozzle =SA508 Cl. 2 Reducer-SA106 Gr. B Nozzle t

Counterbore Area with Indication Area with L

Indication Wall Thickness Where the Indication p'r 15 Was Observed is 0.75" With An Outside Diameter of.16.16".

n f

S'4

.: & b O.D. Wall

. 6 Figure 31 Detail of Indication Location 3-1 1

l

e A single linear indication was found both radiographically and with ultrasonic examination. The indication appeared on the inside surface of the reducer, one half inch from the weld root of the WP no.1; weld. As illustrated in the above figure, the indication is located at the corner formed by the straight counterbore and the 15 machined transition to the transducer I.D. surface. Figure 3-2 shows a cross section of the reducer section at the counterbore lo-U cation just described. O is taken to be the top of the reducer.

U 0

The observed indication extends clockwise from 180 to 140, i.e.

45 inches of the 50-inch _ circumference. The greatest depth of the U

U indication extends clocks;ise from the' 345 to the 18 position gra-dually becoming shallower counter clockwise from 345 to 180 and clockwise from the 18 to 140 position. It was estimated that the depth of tne indication. is approximately 0.100 inches. The ultra-sonic and radiographic examination were in good agreement.

The weld was ground flusn with the adjacent base metal where the indication was darkest and sharpest, 345 clockwise to 18 -(approxi-mately 5 inches of the circumfarence). The ground area was re-radio-graphed for depth determination by triangulation methods using ultra-fine (Kodak R) film. Ultrasonic examination for estimation of location and depth was also made. The indication was on the inside surface of the reducer and has no detectible crack-like characteristics. The linear indication has the radiographic 'and ultrasonic appearance of a machined groove. Examination of the construction radiographs of the subject weld-counterbore area revealed the same straight line in -

0 l

dication in the same 345 to 18 location as_was the case with_the

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recent radiographs. This suggests that the discontinuity producing the radiographic indication was introduced during fabrication and is.

not the result of service conditions.

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The radiographs were compared with those of a known crack found in the feedwater line of another plant.

The radiograph of the known crack has a distinctly different appearance from those of the feedwater line weld area of interest here (PJ 145).

The FW 145 radiographic image appears as a straight line drawn with pencil and ruler - very regular in appearance.

Radiographs of FW 145 made during plant construction also show the indica-tion, although the image quality is lower because the film used was larger grafn (Type T)e 0

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15445 9 2

4 a

0 0

0 180 345

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0 o0 0

270 t

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i 1400 1800 4

p6nxq Indication Observed Indication with 4

2 Greatest Depth k

i Cross Section View is'One Facing the Steam Generator l

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Figure 3 2 Cross $cctional View 'of Feedwater Line at Indication Location i

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SECTION 4 METHODS OF ANALYSIS In this work, the cbsterved indication is treated as a sharp crack, and analyzed as to i :s behavior in future service. Growth due to l

further cycling is esvaluated in fatigue crack growth analyses, and then the final flaw rize is compared with the critical flaw size for normal and upset anc :sther operating conditi'ons. In this section, the methods used in mese analyses will be detailed.

4-1 FATIGUE CRACK. GROWTH ANALYSIS The fatigue crack growth analysis was conducted in the same manner as sug-gested by ASME Section XI, Appendix A. The operating transients which affect the feecwater line are all considered, and scheduled out over a 40 year period. The initial flaw depth assumed was that of the original indication, but sligr ly greater depths were also considered, to give further information.

Crack tip stress intensity factors (K ) were calculated using an ex-y pression for a continuous flaw oriented circunferentially at the inside surface of the pipe. The stresses were linearized through the pipe wall thickness, and used to calculate K and AK. The fatigue crack growtn 7

y for any single transient was calculated from a crack growth rate law determined to be applicable for the materials of the pipe, exposed to a water environment.

4-2.

DETERMINATION OF CRITICAL FLAW SIZE The feedwater piping'and welds are. fabricated from carbon steel and-operate at. elevated temperature. A great deal of study of the failure aspects of piping and tubing has been undertaken in recent years and 9

4-1

2

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is considerable experimenital data are now available. A large number of failure theories have been develaped, both analytically based and l

i empirically based, whth. varying degrees of success. This section will briefly review varion:s types of theories, and provide the basis for use of the plastic imstability nethod.in predicting the critical flaw

~

size for-the area of interest.

Frncture mechanics was ~ first developed for the case of low energy i --

-fracture which involv>ed small deformations.- This is termed brittle fractura,- and the tneory is called linear elastic ' fracture :aechanics (LEFM). The theory is generally applicable only to brittle materials, for example high strength alloys and those which operate at low tempe-l rature. A further requirement for strict applicability of LER4 is the presence of a heavy section, where the ' stress state is plane _ strain.

Failure in these materials and geometries is abrupt, and the crack pro-pagates at. speeds approaching the speed of sound. The theory predicts l

that failure will occur when the applied stress intensity factor exceeds I

the material's fracture toughness, or resistance to failure.

3

~

There. is a large range of materials _ and geometries where the conditions 1

necessary for linear elastic or brittle fracture do not exist. This -

happens in lower strength carbon ' steels, stainless steels, and Inconel, particularly those with high ductility, and also in~ structures with thin sections with low constraint on the opening of-a crack. A good example of this geometry is piping and tubing. In this case, once a' crack is

-loaded to the point'where it begins-to propagate, failure *does not occur

~

at once. Instead, as the: crack propagates, the ' plastic zone ahead of the.cra'ck grows with the crack, and;a steady increase in the magnitude

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of -the load.becomes necessary to ove.'come-the increasing resistance of-

• In this context " failure" implies. complete loss of function _ for~ the pipe, that is loss of the ability to carry pressurized water.

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l the material to fracture. Consequently a toughness oriented single para-meter fracture criterion becomes totally inadequate to deal with the problem of ductile failure.

A number of concepts have been developed for the prediction of ductile failure, and these are reviewed in detail in a number of recent works, for example references 1,2.3, and 4. Two of the mere popular para-meters for ductile-fracture are the J-integral [5] and the crack opening displacement (COD) E03 concept. These parameters have been shown to be successful at predicting the onset of ductile crack propagation, but 1

are only now being extended to the prediction of final failure. Exten-sions to the point of unstable propagation and final failure have thus far been centered on R-curve technology E73 and development of the Tearing Modulus concept by Paris E3 is an extension of this trend.

Based on the level of Charpy energy at 0 F from tests of the actual material as well as experience with results from similar materials, the transition from brittle to ductile behavior should occur at room tem-perature or belcw so the piping will be always ductile during operation.

-The operating temperature range for the feedwater lines as well as their material and geometry places the fracture mode squarely in the large strain -

general yield regime. As such the crack will not become un -

stable until beyond the point where the entire remaining ligament be-comes plastic. If this occurs the failure will be well predicted by '

the plastic limit load of the structure, corrected to account for the material strain hardening behavior.

There is a considerable body of experimental data which shows that the governing mode of failure for ductile cracked pipes and tubes is that i

4-3 i

c.

0 of plastic instability'. Several series of experiments on piping geo-metries were completec' by both General Electric and Battelle Memorial Institute as early as 1968, and these results, as well as other more recent results are well-predicted by.the plastic instability method, as discussed in Appendix.A. Therefore the cpproach taken in this analysis was to evaluate the pn opensity for failure by the plastic. instability mode. Details of the c:alculation will be provided in Section 6.

4-3.-

SAFETY ASSESSMENT Once the growth of the assumed crack-like defect has been calculated, the resulting flaw is compared with the critical flaw size to deter-mine the margins of safety for further operation. This assessment method is similar to nat used in Section XI of the ASME code, but the details of the calcula:icns are different, especially the critical flaw size calculation for cuctile failure. Note that there are presently no rules or guidelines ir. the ASME code for sucn calculations in secon-dary systems. The assessment method used is therefore based on good engineering practice and is expected to have both general validity and good accuracy.

4-4

SECTION 5 FATIGUE CRACK GROWTH ANALYSIS l

The purpose of the fatigue crack growth analysis is to estimate the grcwth of the observed indication, if it were a sharp crack. Since the indication appears to be a groove rather-than a crack, this is a conservative assumption.

i The growth of a crack is the result' of fluctuations in the crack tip stress field due to coolant pressure and temperature variat' ions' during transients. The analysis is executed by finding the crack growth during each individual transient, and adding this growth to the initial crack si:e before proceeding to the next transient. The transients used as a i

3 design basis for the feedwater lines are listed in Table 5-1, along with the number of expected occurrances in the 40 year design lifetime of the Trojan ~ plant. The transient occurrances were divided up equally for the entire lifetime, and the crack growth was calculated for periods of ten, twenty, thirty, and forty years.

For each transient, the pressure and temperature fluctuations were used to calculate stresses in the following manner. The heat transfer analysis was carried cut by an explicit finite difference technique [9].

i The resulting ter.perature distribution'was then used to calculate ther-mal stresses, using the equations for thermal stress in a hollow cylinder-frcm Timoshenko-and Goodier [10]. The axial stresses were calculated as:

a 2

2 Trdr - T b

a

(

t where T.= temperature inner-radius of pipe a =

b

. outer radius of pipe

=

v Poissen's ratio

- =

aE = the product of the coefficient of thermal expansion and the

• odulus of elasticity, assumed ; constant, requiring a conser--

. vative value to cover the entire temperature range.

l 5-1 p

yr

~ - -

-t-T-

• N W

-t'-

v

J

}'

The mechanical loacimgs.for the pipe which contribute to crack grcwth result from cmanges in internal pressure, and the stress for a given value of internal pressure, P, was calculated from:

a-Z. P (5-2) o =

Z (b - a" )

t The stresses calculated in equations 5-1 and 5-2 are axial stresses, which would tend to propagate a circumferential flaw. The material

~

properties.used in tme stress analysis are given in Table 5-2, and the input stresses for tt's analysis are providea in Table 5-3.

3; -

The next step in the analysis, calculating the range of applied strea intensity factor, was carried out using an expression for a continuous -

circumferential flaw, as shown in equation 5-3. The combined thermal and. pressure stresses were linearized through the pipe wall..The~ value

~

j of aK resulted from replacing the stress values with stress ranges in 7

the expression for Kr.

j b] a (5-3)

Kg = [yem +yb

-l i

where

-o

. linearized membrane stress

=

m linearized bending stress e =

b y.

membrane correction factor -

=

• /t + 18.1 Y/g)E~- 38.5 @/ b *

'S ( lt)

=

t

.yb bending factor

=

l'.99 - 2.47.#/ +12.97 (al)

- 23.2 f/ ) +24.8 (aj )4

=

t t

t 1

4 e

j 5-2

.S..w e

~

v

.c.

s nn--.

,7

- + -.

r y-y

.. ~

1

~

Calculation of the fatigue crack growth for each cycle was then

. carried out using a reference fatigue crack growth rate law deter-mined from consideration of the available data for carbon and low alloy steels exposed to a water environment. The reference law is pro-vided in Figure 5-1, and is actually an improvement over the present ASME Section XI reference crack growth law for water environments.

1 The revised curves ha ve been proposed as a replacement for the pre-sent ASME Section XI : eference curves. The background and basis for the Tevised reference curves are provided in reference 11. The re-vised reference law a' lows for the effect of mean stress or R ratio (Kminimum/Kmaximum) cin the growth rates, and results in slightly higher growth than thie present Section XI reference law in cases of predcminating proportions of high R transients.

Results of the fatigu:e crack growth analysis are presented-in Table 5 4, and show that crack growth due to all design transients is very small, even for the entire forty year operating lifetimes, of

^

which some 3-4 years nave already passed.

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5-3

Table 5-1 DESIGN T RANSIENTS - TROJAN FEEDWATER LINES Transient Number of Occurrences in 40 years Secondary Sider Hydrotest 5

Hot Standby 18,300 Unit Lead - Umload 5% per minute 18,300 Small Step Load Decrease 2,000 Large Step Load Decrease 200 Loss of. awer 40 Partial less cf Flcw S0 Lars of Lead 80 Reactor Trip 400 i

e e

TABLE 5-2 l'ATERIAL PROPERTIES flaterials SA106 Grace B Procerty (550 F) and SA508 Class 2 6

Young's Modulus (psi) 27 x 10 Densi+J (lb/in.3) 0.280 Conductivity (Bru/hr-in. UF) 1.948 Heat Capacity (Stu/hr OF) 0,135 Coefficient of Therral Expansion 7.30 x 10-6 (in/in.0F)

Poissen's Ratio 0.30

?

s TABLE 5-3 STRESSES USED IN FATIGUE CRACK GROWTH ANALYSIS Transient Axial Stress

• Axial Stress

• Inside Surface Outside Surface Maximum Minimum Maximum Minimum Hot Standby 10.57 8.22 9.53 7.34 Unit load-unicad 10.47 7.71 8.49 7.50 5 per minute Small stepload decrease 9.56 7.87 7.89 7.50 Large stepload decrease 12.62 8.56 7.65 5.07 Loss of pcwer 30.13 5.04 4.50 3.95 Partial loss of flow 23.70 8.42 7.52 3.79 Loss of Icad 23.02 8.42 7.52 3.18 Reactor tr.')

22.69 5.21 7.33 2.88 Secondary Side Hydrotest 12.59 0.0 11.34 0.0 all stress values are in ksi

e r

TABLE 5-4 RESULTS OF FATIGUE CRACK GROWTH ANALYSIS Initiai! Crack Crack Depth after year (inches)

Cepth Cinches) 10 20 30 40 0.700 0.1006 0.101 0.102 0.103 0.150 0.153 0.158 0.162 0.168

=

l 1000 700

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s' N

N $

l& $

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g.

e 200

.N

.Y.

4 y

5

• /t/ :

j N

Q 100 (AIR ENVIRONMENT)

D SUS SURFACE FLAWS E

1*. - lo.o2s7xio'3)tx,3.72s 70 e

gg U=

s h

SURFACE FLAWS

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i (WATER REACTOR ENVIRONMENT) 20 APPLICABLE FOR x

/KMAx < oh McN

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x,u/x x>o.s-M M

M, 10 g

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a x-a 7 ~

f n

x 4

k 4

e-5 g

o

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f C

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ejg

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I I I l l l' l 1

2 5

7 10 20 50 70 100 STRESS INTENSITY FACTOR RANGE (AK (KSI TIS.)

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. Figure 5-1 Fatigue Crack Grcwth Reference Curves-- Carbon and Low Alloy Steels.

s s

SECTION 6 CRlTICAL FLAW ZIZE DETERMINATION The determination of the critical flaw size, or that size flaw which would cause piping failure under the loadings considered has been done based cm a plastic instability analysis method. In orde,r to apply such am analysis procedure, care must be taken to demonstrate that crac:ts will not become unstable before this gene-ral yielding stage is reached. The tearing modulus approach [ 8 ]

was used for this purpose.

6-1.

DEVELOPMENT Of METHODOLOGY - PLASTIC INSTABILITY ANALYSIS For materials which are very ductile, linear elastic fracture me-chanics methods are very seldom applicable for calculation of cri-tical flaw size. Elastic-plastic fracture methods have not been de-veloped to the advanced state of linear elastic techniques; however, a number of analytical or empirical solutions are available for spe-cific applicaticns. For the problem at hand (circumferential flawed pipe subjected to internal pressure and a bending moment), the state of the art is reviewed and an appropriate formulation is set forth for determination of plastic instability.

Several series of experiments on piping geometries have been conducted by Battelle Memorial Institute [12,13] and General Electric Company

[14,15]. These tests were conducted on both specimens and full-scale sections of reactor coolant piping, and a considerable amount of data were produced. From these results, an empirical relationship was de-6-1

veloped by Eiber et.al.EI3 for predicting critical flaw sizes for i

piping with longitudinal through-wall cracks, based on a plastic i.n-stability analysis. The prediction method is summarized in figure 6-1.

This expression in figure 6-1 has been shown to be very accurate in predicting burst pressure for a number of different materials and piping geometries [16,17,18,19, 20]. Examples of its applicability

'are shown in figures 6-2 and 6-3.

(

The primary concern in the case of an earthquake condition, the worst case loading here, is that of bending loads superposed on the internal pressure loads alreacy existing in the' piping. Experiments have shown that imposed bending loads do not affect the burst pressure of piping with longitudinally-oriented flaws [21]. Iherefore, the method of fi-gure 6-1 remains valid.

The case of a circumferentially-oriented flaw in piping geometries has j

received very little attention either experimentally or analytically.

Using a plastic instability analysis similar to that employed by Eiber et.a1. for the longitudinal flaw, Bamford and Begley [22] derived a relationship for predicting the burst pressure for circumferentially-flawed pipes. This method is valid only for through-wall flaws which are lest. tan half the circumference of the pipe, because for longer flaws asymmetric loadings are produced. F,or the application of concern, however, such an expressicn is more than adequate, because a flaw measuring half _ of the circumference is more than 25 inches long. A plot of the expression derived is shown in figure 6-4. Very little experi-mental work is available regarding the bursting of pipes with through-wall flaws, but the available data agree well with this prediction method, as also shown in figure 6-4 s

6-2 4

r i

l l

The viability of the above methods is further supported in a recent paper which consider-ed suddenly appearing axial and circumferential through-wall cracks -in pressurized piping [23].

perhaps the most. imp ortant crack geometry to be considered is that of a circumferentially-: flawed pipe subjected to bending loads as well as internal pressure. Again, very little work has been done in this area, and no expressions aire presently available for piping systems. For this reason an expression was derived using a limit load analysis method. The method is detailed im appendix A and allows consideration of internal pressure, externally-applied bending, and axial applied forces.

Based on this analysis detailed in appendix A, the limit moment is calculated as:

4 (3 -a ; 2 R,2 2t ef _y2 R 4 P2 2

[R 2 (2 cos S-sin a)]

,'q 9

b 2(:-a)2 R tof m

(6-1)

= half-ar gle of crack, in radians (refer to figure A-1) where a p-

= internal pressure R

= mean pipe radius, inches m

t

= pipe thickness, inches of = 0.4 (o

• 'u)(flow stress) ys o

= yield stress y

o

= ultimate tensile. strength R

= pipe inner radius, inches 9

'R

= pipe outer. radius, inches g

s

= angular location-of neutral axis (refer to figure A-1)

This expression was applied to the results of a series of experiments i

done by Reynolds [15], and the predictions were quite good. The results as well as the predictions are shown in Figure 6-5.

6-3

=~.

+

j 6-2.

TEARING MODU 1US ANALYSIS The tearing modulus approach is attractive in that it accounts directly-for the stable teariing which occurs prior to fracture.

Characteri-zation of stable cratck growth is based on the J-integral, where the slope of the J versus crack growth resistance curve is given by a nondimensiona-lized parameter calTred the tearing modulus, T. The instability con.11 tion is formulated in a rmanner similar to the LEFM R curve approach.

When the-applied mechanical crack drive of a specimen or structure,- labeled Tapplied, is equal Oc or greater than tne material resistance to crack advance, labeled Teaterial (Tapplied > Tmaterial), the tearing instability ensues.

has been evaluated from test results re-The material proper:y Tmaterial ported in references, 24 and 25, as well as some unpublished data obtained at Westinghouse. This property is determined from the results of J-inte-gral fracture tests, where the resulting value of J is plotted as a func-tion of the amount cf subcritical crack growth, termed Aa. The value of l

JIc, that is J at'tne initiation of crack extension was also determined.

The tearing modulus T may be calculated from the relation:

E da I-l ofa da

]

where E.= Youngs Modulus of = flow stress = 0.5 ( ys.+ 'u)

~

y = slope of J vs ta curve o

= 0.2 offset yield strength ys

= ultimate tensile: strength ou l

1 l

6-4 i

l t

The values obtained f:or the tearing modulus for SA 106 8 and similar materials are summari=ed in Table 6-1. There is very little data now available on these materials, and that which is available suggests that the fracture prcmerties are dependent on the sulfur content.

For the sulfur centent of this steel (from Section 2) of 0.035 weight per cent, the lowest available value for the material tearing modulus,

Tmat, is Tmat. 85.4 (6-3)

The cost likely type of flaw which could exist in the piping is a sur-face flaw, and an e ession is available to estimate T for a applied deep surface flaw.

Although the expression is strictly for a plate geometry, it.can be used to approximate T for the piping geometry. Be-cause the degree of constraint is approximately the same for a surface flaw in the two geometries, the expression should be fairly accurate fer icngitudinal and circumferential surface flaws. (This is not true for a througn-wall crack, as will be discussed later.) The expression derived by Paris ec.al.

is as follows:

2L

.Iapplied

• 7 (6-4) where t = flaw length at the surface (inches) t = tube thickness (inches)

This expression does not involve stress level, because the derivation assumed the remaining ligament was fully plastic, which is conserva-tive for this application. An elastic-plastic fomulation would pro-duce a icwer value for applied tearing modulus.

6-5

\\

^

U h!8@ldNhMh M 'M bM N &NfE NN.NN M-M h$@ M/ MON N O M 7

Consideration of this equation shows that for the piping geometry (thickness in inches) and for the estimated values of Tmaterial (85.4),

required crack lengths for a surface flaw to become unstable are greater than 32 inches (81.2 cm). Therefore, a realistic surface flaw will never beccme unstable in the piping, regardless of whether it has axial or cir-cumferential orientation. Thus the only type of flaw which could con-ceivably lead to an instability before general yield is a through-wall flaw.

Expressions for the tearing modulus 'T for a through-wall flaw in applied the piping geometry are not available in the literature, but can be easily derived from expressions for the crack opening displacement (6) when they are known. Expressions are available for a center cracked a-nel and for a longitudinally-orier ted through-wall flaw in a pipe;U these have been used to derive expressions for Tapplied, as detailed in Appendix 8. No expressions are currently available for 6 for a circum-ferentially-oriented through-wall flaw. However, the expression for-6, and therefore the resulting T for this geometry, should range applied between that for the center cracked panel and that for the longitudinal flaw (based on consideration of the relative amounts of constraint for the two geometries).

For a center cracked panel, Appendix B'shows the following:

applied = 2n log Ul + sin 8)/cos s]

(6-5)

T 6.- 6

(([m__

~ -_ _iM*%C.$4.#EMM$fd$"%TM$. k5fidifdfDs'fpst2MfDY!Z7ndyM A

---.4

= non e,so r e

n

+

I where s = lC f

=. applied stress (tension) o

= flow stress, here taken to equal 0.4 (o

+ "uts) o f

ys This expression'is taken from an elastic-plastic analysis by Erdogan therefore, the applied stress enters the calculation. In determining the for the center impact of the loads and stresses' on the value of Tapplied l

cracked panel, only the worst' case loading situation was used. This is I

for the safe shutdown earthquake applied to the fet:dwater piping. For I

equals 0.87. Therefore, this case, c/of =.20 and the value of Tapplied the through crack in a geometry approximating a center cracked panel will must only exceed 0.87. This finoing always be stable, since Tmaterial agrees with that of Zahoor [26] who did extensive analysis of center cracked panels.

might reach for a circum-l The upper limit en the value which Tapplied i

ferential flaw is obtained by assuming that the longitudinal flaw ex--

1 pression can be used. The actual expression is probably closer to that for the center cracked panel, because the long crack has much less re-striction on opening imposed by the pipe geometry, and does actually bulge in many.csses. Comparable bulging does not occur in the circumfe-rential-flaw case.

Using the worst case-loading condition of the earthquake affecting becomes, from Ap-the feedwater piping, the expression for Tapplied pendix B:

2 3

4 0.248-- 0.108a C O.177a -0.0216a

+ 0.0008a (6-6l T

=

applied 6-7

F-where a

• half cracx length.

actually depends on the pipe dimensions as The expression for Tapplied well as the loading ratio e/d and the crack length, therefore, this f

expression is not eeneral. More general expressions can be determined frcm Appendix B. Fct the feedwater piping subject to a SSE, it can be concluded that T f r a circumferential flaw is as fellows:

ap:: lied 4

0.248 - 0.108a + 0.177a - 0.0216a3 + 0.0008a (6-7) 0.87 < fapolied <

The result of calculation of the instability flaw length can be seen from figure 6-6 which shows the above expression plotted versus flaw length. This calculation of minimum flaw length represents conditions obtained from an aarthquake occurring at operating temperdture and full is 85.4 and the unstable flaw length pressure. In this case, Tmaterial is approximately 25 incnes (63.5 cm) whice is over half the circumf1-rence of the pipe. The actual size of the critical flaw for plastic instability will be less than this.

Determination of the critical flaw size for a longitudinally-oriented through-wall flaw is possibla using the methods described above, but will be very small because the earthquake loadings the resulting Tapplied would not affect the longitudinal crack. The only loading of signifi-cance for the longitudinal crack is internal pressure, which is very small compared to the earthquake load.

Thus, the conclusion reached from application of the tearing modulus

~

for conditions approaching the limit load is that unstable fracture before limit load is highly unlikely; thus the plastic instability mode of failure would be governing. The remainder of the work in this report was carried out on this basis, and the results are presented below.

o 6-8 m

7

--y

i i.

b i

6-3.

RESULTS OF CRITICAL FLAW SIZE DETERMINATION I

all the design loadings were considered in the critical flaw size determination, which was made according to equation 6-3, and is

~

shown in Figure 6-7. The design loads for all four feedwater lines i

of the Trojan Plant are shown in Tables 6-2 and 6-3, and were obtained

}

frca Bechtel calculaticns [20. No loads frem water hamer were in-cluded, because the possibility of water hammer has been eliminated by.

)

ins'tallation af J-tubes. The highest loading was used, even though l

it does not apply to steam generator 1, in whose feedwater line the I

indication.was-observed.-

I i-Figure 6-7 provides the critical flaw depth for a part through con-

~

tinuous flaw oriented circumferentially. Even for the most severe design loading, that of a design basis earthquake (DBE) occurring i

j during operation, the critical flaw depth is 68 per cent of the wall thickness' or 0.510 inches. -For the other load combinations used in j

the design, the critical depth is greater than 80 per cent of the wall i

thickness.

i I

Consideration of through-wall flaws has also been included here, and -

r results show that the critical flaw length for a through wall crack i

is about 23 inches (58.4 cm) even for the worst design loading.

1

~

i i

f 6-9 i

l m

. a

Table 6-1 I

SU.* MARY OF. TOUGHNESS DATA U

T y.

'u o

IC 4

Source:

Gudas-USflRDC (sulfur - 017

.029)

A106C RT 49.5 81 65.3

-1380 20500 144-'

A516Gr70-RT.

l52.0 81 66.5 890~

15000

.101.7

-300F 40.0 69 54.~ 5 664,850

12000, 125.6-4 11500 Source: W unpublished data - TSulfur -.004 - 0.0101 all at~ Room Temoerature-

.'3030.

59320 461 Si6Gr70-RT.

49 75.1

- 62.1 52 74-63 4400 29930 226.2 SA350LF2 Forging RW 81.3_

66.7 41.80 8528 57.51 Source: W WCAP 9499 -(ref. 24) -(S = 0.030

.037) 516Gr70-RT.-

46.7

-71 58.9.

790 10745

-93.07 440F 31. 3 61 46.2 375 6082 85.4

'RT 45.5

.71 58.3 995 440F 32.7 61.2

. 46.9 995 16801 229.1 i

I i

t e

a d

7

((

x

.z by RhR l-.

x-y Plane is Vertical

~

Nozzle STEAM GENERATOR SECONDARY IULET N0ZZ_LE (SG* No.1 & 2 )

I e

, Load F-F F

M i

M M

x y --

z x

y z

i Condi tion N.x V,i ps Kips Kips In-Kips - In-K1ps

!In-Kips I

l

'[

l Thermal

-1

-1

-1 l

250

- 278 282 i

i

. Pressure-i 765 0.

O 0

0 0

1 a

se.

s a.

0.

j.

-1 O

2 1

27

= 1 Deadweight

}

}

~

i OBE

+3

+4

+2

- 48

+ 276 e - 298

+

+

t l

u-E

~

i m

~-

+6

+3 l-80

+ 461

, - 498.

+_

+

+

p M

SSE

-o a

t

-Table 6-2.

Design loads for Steam Generator /Feedwater line functions Units 1 ar.d 2.

j Nozzle STEAMGENERATORSECONDARYINLETN0ZZLEhG No.

3 & 4) l

~

u Lead

-F F

F M,

M M

j 7

y j

x y

z Condi tion \\s,

Kips Kips Kips

!In-Kips In-Kips IIn-Kips i

I j Thermal

-- 2

-2 i

-3 201

- 623

- 307 y

' Pressure l 165 O

O O

0 0

o I

Deadweight 0

-2 0

8 4

63 l

i i

1 6

~+.3 f

OBE l

+2 f

+4

+'288

+ 293

- 441

.+

4i u

2..

i

[~

d j

M SSE.

! I-3 1 7 15 1 481 I.489

!I737-

!~

f Table 6-3. Design lcads for Steam Generator /Feedwater line functions

~

Units'3:ard 4.

1.0 Solid Points are Experimental Failure

- Points. All Fractures in the Experiments g-Were Completely Ductile. [14]

A-

^

0.8 C

A 0.6 U

O E

s e

.c a.

o Prediction am 0.4 0

Nu N

9 24 x 1.7 - In. A10GB Pigm 0.2 24 x 0.7 In. A106B Pi m i

12.75 x 0.7 -In. A106B Pipe 0.0 0

4 8

12 16 20 24 28 Axial Through Wall Flaw Length, Inches E

Figure 6 3 Comparison of Experimental Critical Flaw Size Data from Reference 14 with Predictions

[

a

?

l

1,0 0.0 0.8 0.7 0.6 0.5 0.4 Q

H h-o 0.3.

t R = Radius of Cylinder u = 0.4 (ny3 + u I u

0.2 o=ph.

I I

I I

I I 1.1 I

I I

I 11 o,

0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2

3 4

6 78-910

,\\ = a/ [ikt O = 1.28 - 1,4 A flii. + 0.800

-0.219 Rt 3/2 + 0.0217 ' g2 2 a

(Rt1 1

Tu Figure 6-1 Failure Pressure for Longitudinal Through. Wall Flaws (Reference 12]

[

J 4

~~

.m"s* g 0

1 I

9 I

8 I

7 6

NO

{p I

4 c

0 a

2 t )a0 D2 e

1 n

nl ne er a e e

t mS fe t

I 3

r s R

s o

e f

Fl n o

&i ta a

t u

a iS l

D n

i4 I

2

+

e0 la Z3 tne im re 0

px

0. [

E h

t 1

i l

/

a w

=

's 8

n I

0 A o

i b

I tc id 0

e I

0 rP e

I 5

r fo d

0 n

n o

i l

ly u

4 is C "

I 0

a r

f

+

p o

m 3

s y

u n i

3 o

_l i

(

C 0

_2 d

a a 4 R

2 R 0 p

G j

e

+

r R T u

7 o

l 0

ig 2

F m

t R

1 0

d 0 0 8 7 6 5

4 3

2 i.

1 00 0 0 O

0 -

0 0

o Qe i.1 i

'4 i

d

15445.

1.0 p = Internal Pressure 0.8 ' sQ R = Mean Radius 0

0.6 2

0.4 Note:

g% $

pR

u.

oc " 2t' I

n

!3.

O Experimental Data [121 1

A p"

' 2a t'y 0.1 0.8 1

2 4

6 8

10 A = a/ [

i.

i Figure 6 Failure Pressure for Circumferential Through Wall Flaws 4

l r

]

15445 1 9

\\"

3 7

6 O (0 PSI) l (6000 - -

36 PSI) l

.y-Flaw Geometry

=

• =

'O 3.

.s 5

9 52.-- 4 E-

"'i

\\

p Prediction (0 PSI) 3

\\

/

2 i

Experimental data from [151 1

Prediction (6000 PSI)

N l

I I

l l

l l

l l

l

.s.-

.g 0

20 40 GO SO 100 120 140 160 180 200 220 240 260 280

-2a (Degrees)

Figure 6 5 Com;urison of Limit Moment Predictions With Experimental Results -

i A10GB Piping (15]

15445 7 140 Z

+

~ 2a h=0 e

120 I

X f

winm

_s

- h/

R = 8.08" l

)

Y u

4 T

= 0.0008 a - 0.0216 a3 + 0.177 a2 - 0.11 a + 0.25 app 100

= 0.20 Resulting From Longitudinal Stresses Of E.-

b E

80 Og

~

E=

S j

60 40 20 0

0 10 20 30 40 50 Crack Length,2a, (Inches)

Figure 6-6 Applied Tearing Modulus for Feedwater Piping (Longitudinal Flaw Used to Approximate a Loaded Circumferential Flaw)

r 15445 6 Crack Depth, a/t 0.0 0.2 0.4 0.6 0.8 I

I I

I 7

10 g

t a

/

\\

V For Part-Through Cracks "Ei 1

Ye l

E 5

52

-Thermal + Deadweight

.5

+ SSE a

N Thermal + Deadweight Throu 106

+ OBE I Crack

(~

1

~'

Thermal + Deadweight Only 5x105 O

10 20 30' 40 Crack Length, ( (Inches)

Figure 6-7 Results of Critical Flaw Size Determination

v

.t SECTION 7 RESULTS AND CONCLUSIONS ~

3 i

An integrity analysis has been completed on the feedwater lines of the Trojan Nuclear Plant, to characterize the effect of an indication f

detected during a recent inspection. Although the indication appears to be a groove, for conservatism in the analysis it was assumed to be-a sharp crack.

I

~

l A fatigue crack growth analysis was performed on the assumed crack, and the growth was found to be very sma-ll. Specifically, during the next ten year period the expected growth is less than 0.001 inch, so at the end of ten more years of operation the crack depth will be:

1 1

a = 0.1006 inches Critical flaw size calculaticns were carried out.for all design con-ditions, and the results below were obtained. For a continuous cir-cumferential crack at-the inside surface:

3 i

a = 0.510 inches for Thermal + Deadweight + OBE loads c

a > 0.600 inches -for Thermal + Deadweight + OBE loads c

c. 0.600 inches for Thermal + Deadweight loads l

a Thus there is a margin greater than a factor of five on the critical' flaw size for faulted conditions, a'nd a margin of S.96 on the critical flaw size for normal operating conditions. These margins sshow that the indication is more than' acceptable for further service, and.will have no impact on the, integrity of the feedwater lines.

1 1

4'

-e e

e, e

.~

-~

~

n

P

- e SECTION 8 REFERENCES 1.

Erdogen F., " Ductile Fracture Theories fo'r Pressurized Pipes and ' Container",. International Journal of Pressure Vessels and Piping, Vol. 4 No. 4 1976, 2.

Wilkowski, G.M. and Eiber, R.J., " Review of Fracture Me-chanics Aoproaches to Defining Critical-Size Girth Weld Discontinuities" Welding Research Bulletin 239, July 1978.

3.

Reich, M. and Estergar, E.P., "Ccmoilation of References,

' Data Scurces and Analysis Methods for LMFBR Primary System Components". Nuclear Engineering and Design Vol. 50, 1978, pp. 273-304.

4.

Kanninen, M.F. et. al. "Towards an Elastic-Plastic Fracture Mechanics. Predictive Capability for Reactor Piping". Nuclear Engineering and Design, Vol. 48, 1978. pp. 117-134.

5.

Rice, J.R., "A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks" ASME Journal. of Applied Mechanics, Vol. 35, June 1968, pp. 379-86.

6.

Wells, A.A., "The Application of Fracture Mechanics At and Beyond General Y.ield", British Welding Research Association Research Report M13/63, March 1963.

7.

McCabe, D.M., editor, Fracture Touchness Evaluation by R. Curve Methods. ASTM STP 527, 1973.

8.

Paris,'P.CJ et. al., "A Treatment of the Subject of Tearing Instability", Washington University Report NUREG-0311, July 1977.

9.

~Holman, J.P., Heat Transfer, McGraw Hill Book Co., New York 1963.

8-1 I

c e

v.

. ~,

m.

e 10.

Timoshenko, S.P. and Goodie r, J.H., Theory of Elasticity, McGraw Hill Book Co., New York,1970.

11.

Bamford, W.H., " Application of Corrosion Fatigue Crack Growth Rate Data to Integrity Analyses of Nuclear Reactor Vessels", ASME Trans. Journal of Materials Technology, July 1979.

12.

Eiber, R.J., Maxey, W. A., Duffy,. A.R., and Atterbury. T.J.,

" Investigation of the Initiation and Extent of Ductile Pipe Rupture", EMI-1866, July 1969.

f 13.

Eiber, R.J., Maxey, W. A., Duffy, A.R., and Atterbury, T.J.,

" Investigation of the Initiation and Extent of Ductile Pipe Rupture", BMI-1908, June 1971.

14.

Reynolds, M.B., " Failure Behavior in ASTM A1068 Pipes Con-taining Axial Through-Wall Flaws"' GEAP-5620, April 1968.

15.

Reynol ds, M.B., 'iFailure Behavior of Flawed Carbon Steel Pipes and Fittings", GEAP-10236, October 1970.

16.

Watanabe, M., Mukai, Y., Kaga, S., and Fujihara, S.,

" Mechanical Behavior on Bursting of Longitudinally and Cir-cumferentially Notched AISI 304 Stainless Steel Pipes by Hydraulic and Explosion Tests", Proceedings of Third Inter-national Conference on Pressure -Vessel Technology, Tokyo, April 19-22,1977, ASME, New York, pp. 677-683.

17.

. Adams, N.J.I., "An Analysis and Prediction of Failure in Tubes", Ibid., pp. 68S-694.

18.

Darlasten, B.J.L., and Harrison, R.P., " Ductile Failure of Thin Walled Pipes with Defects Under Combination of Internal Pressure and Bending", Ibid., pp..669-676.

19.

Rodabaugh, E.C., Maxey, W. A., and Eiber, R.J., " Review and Assessment of Research Relevant to Design Aspects of Nuclear Power Plant Piping Systems", NUREG-0307, June 1977.

8-2

20.

Zeibig, H. and_ Fartmann, F., " Fracture Behavior of Ferritic and Austenitic Steel Pipes", Trans. 2nd International Conf.

4 on Structural Mechanics in Reactor Technology, Vol. 2, F-4/8, Berlin, Germany, Sept. 10-14, 1973, Sponsored by Commission of the European Communities, Brussels, Belgium, 1973.

21.

Darlaston,- B.J.L., and Harrison, R.P... " Ductile Failure of.

Thin Walled Pipes With Defects Under Combination of Internal Pressure and Bending", Proceedings of the Third International' Conference on Pressure Vessel Technology, Tokyo, April 19-22,1977, pp. 669-676, ASME, NY,1977.

22.

Bamford, W.H., and Begley, J. A., " Techniques for Evaluating the Flaw Tolerance of Reactor Coolant Piping", ASME Paper 76-PVP-48 Septemoer 1976.

23.

Ayres, D.J.,

" Determination of the Largest Stable Suddenly Appearing Axial and Circumferential Through Cracks in Ductile Pressurized Pipe", Paper No. F7/1, Vol. F Structu-ral Analysis of Reactor Core and Coolant Circuit Structures, Transactions of the 4th International Conference on Structu-ral Mechanics in Reactor Technology, August 15-19, 1977, Sponsored by Commission of European Communities, Brussels, Belgium, 1977.

24.

Palusamy, S., et. al. "Commanche Peak Steam and Electric Station Structural. Integrity Evaluation of Mainsteam and Feed-

• water Superpipes" -Westinghouse Electric Corp. Report WCAP 9499, May 1979, 25.

J. Gudas, US Naval Ship R.and D. Center, Annapolis Md., Per-sanal Communication, May 1979.

26.

Zahcor, A., " Tearing Instability of Elastic Plastic Crack Growth", Ph.D. Thesis, Washington University, St. Louis, M0.,

August 1978.

27.

Bechtel Letter BW - 799, July 10,1975.

8 +

r 1

y.w

m m.

4 N

APPENDIX A -

' DETERMINATION OF THE MOMENT CAPACITY OF PRESSURIZED PIPING WITH CIRCUMFERENTIALLY-ORIENTED THROUGH-WALL FLAWS

.t A straight section of pipe with a circumferential!y-oriented through-wall flaw, as shown in figure A 1, is considered. It is assumed that plane sections remain plane during deformation, and that the flaw is not too large in comparison with-the ' pipe circumference. For flaw lengths which approach one-half of the circumference, the present method is not accurate.'

The pipe is leaded by internal oressure, P, an axial force, F, and a bending moment, M.

-Be,cause of the bending moment the axial stress will be compressive somewhere in the cross section. The point'of demarcation between tensile and ' compressive stresses is the neutral axis, as shown in figure A 1. To determine the. location of the neutral axis,.the axial force on the pipe from the internal pressure and other loads, N, is equated to the integrated stresses over the cross-sectional area of the pipe, N, as follows:

c i

N = P:r R2+F

( A-1) where P = internal pressure _.

.R = mean radius of the pipe F = other axial force (if any) 1 1

~"

-# (7 - og PR N

=2 og Rt.d6 + 2 Rt dB (A-2) e -

-f

-tr T

i where t = pipe thickness.

og = flow stress = 0.4 (oys

• Ou) i.

A1-

'I

,(

a a crack'ang!e as shown in figure A 1.

. # = angle to located neutral axis, figure A-l '

Equating the quantities in (A 1) and (A-2) leads to the definition of the neutral axis which is:

og t a,F 0 " 2 of I - PR

^

Figure A 1 also illustrates that' the angles a and # are related at the limit moment; therefore, equating areas above and below.the neutral axis results in the following:

a=2)

(A-4)

The fully-plastic' limit moment capacity, M, is obtained by taking moments about the 3

neutral axis as follows:

(90.- a)

(2x - g)

Mb=2 R

t of sin 6 de -

R t of sin 6 d6 (A-5) m m

-J.

(: + J) where of = 0.4 (ay3 + o ), that is, of s the flow stress.

i u

After integration and substitution of the limits, the moment capacity for a pipe without' internal pressure is found to be:

A13 = 2 af R 2t (2 cos # - sin a)

'(A 6) o For simple pressure loading with no bending, the limiting force is equal to:

N = 2 (:r - a) R t of (A-7) o m

s 1 For any arbitrary pressure. P, the' force produced is

~

~

N = rR;2 P (A 8)

I l

A-2 I

l

...i.;_-,_,.

~

. r Then, the ratios of axial force to limit axial force and moment to limit moment are defined as follows*

n=N m=M

( A-9) :

o b

Since the internal pressure and bending ' moment interact, the combined effect will cause a reduction in the. moment capacity M to M. From Hodge's interaction theory,Ill the corrected b

limit moment is determined from:

2 M = (1 - n ) M

( A-10) -

b.

Substituting for ~all the parameters from equations (A-6) through (A-9),.we.obtain:

4-(x - a)2 R t _ of2_y2 R;4 2

P2 m

(R 2 (2 cos # - sin a (A-11) ML* 2 (: - a)2 R 2 g m t of 9 Wete [* e e o e a

1. naage, p. a, prostic Anar s s or structures. Mearan n.no coas company, sose, po. sio soo.

~ v 'A3 l~. -4 g .-.w-e= , N., e - e n o.--, e .a, n v - r

.11870 3 n fI N m s m g \\ = l N x / 3+ 2 m } 1 ) co i \\ w a t = \\- is s 0 = 3 O A. 5 2 9 a.b C y. N 2 2, E 4 e 4 ~ ~ j G' a A4

APPENDIX B ~. CALCULATION OF APPLIED TEARING MODULUS FOR TWO GEOMETRIES B 1. ' GENERAL INFORMATION The tearing modulus as defined by ParisOI.an be determined for a given geometry from c knowledge of the crack opening displacement, which leads to the straightforward derivations presented below. Two geometries are considered, the center cracked panel and the longitudinal through-crack in a pipe. Both derivations are based on the crack opening displacement (COD) expressions determined in the elastic-plastic analysis of Erdogan.(21 E-2. CENTER CRACKED PANEL The expression given by Erdogan(21 for the crack opening displacement 6 is S = f d log [(1 + sin #)/cos #] (B-1) where d = 4aga/E S = a:r/2ag of = flow stress = 0.4. (ays + Juts) ys = 0.2 percent offset yield strength a "u ts = ultimate tensile strength a = half crack length (see figure B 1) 4 E = Modulus of Elasticity t o = applied tensile stress

1. Pares, P. C., "A Treatment of the Subsect of Tearing instabihty," NUAEG4311. July 19 77. ~

2.. Ercogan. F., " Ductile Fracture Theories for Pressuraed Pipes and Containers," /nr. J. pres. Ves.,s piping 4, 253083 (19761 4 B1 w

wee ? 2 s 4 a ,-,. +, --ee ex a x, 1 The crack opening displacement'is related to the ~J integral by the following expression: i~ 6-= a J

• f.

(8-2) .where og' i flow stress a = constant for a given material, generally 1 < a < 2 Taking the differential of equations (B 1) and-(B-2) and equating them result in - dJ 200f a-= - log [(1 + sin $)/cos #] da - (B-3) as c I Rearranging terms; i dJ } ag yf' = aTapplied = 2r log [(1 + sin til/cos #} (B-4) -/. 2 1 4 The stabi*ity criterion is tnen a T DIapplied _ = 2:a log [(l' + sin E)/cos #} (B 5) material i. Consider the worst case for-the piping loadings of interest, that is, the reactor vessel outlet nozzle, where o/of a 0.75. For conservatism assume a = 1. These give # = 1.19 radians, and Tapplied = 4.51. This value compared favorably with -the calculations of Zahoor,I)I who found ~ ~ that Tapplied f r a center crack ~ed panel is generally no greater than; 4 or S. B 3. LONGITUDINAL THROUGH WALL CRACK IN A PIPE j [- Erdogan t21 supplies the information on the COD for this ge'ometry in a graphical form, as shown in figure B 2. The information on this figure was put into equation form using.a 4

1. Zanoor. AI, ' Tearing instacal tv of (bst.c Plastic Crack Growth." Ph. Di Thesis. Wash.ngton University. st. Louis, j

i August 1973 {

2. Erdogan 5. "ouctae Fracture Theor.es for Press'urized Pipes and C.antainers." /nt. J. Pres. Ves, & Piping 4, j

253 283 11976), t 4 8._

4 least. squares curve fit. As may be seen lit the figure, the information is provided as a function of' crack length through 'the value A, and a function of loading through the ratio o/of, 4 2 A = (12(1 - v 3)O.25a Rh.50 (B 6) 0 where v = Poissons ratio R = radius to pipe mid thickness h = pipe wall thickness. a = half crack length A nernber of load ratios were chosen to closely follow the load ratios for the pipe sections of interest; the following fits were obtained: if o/of = 0.75, S/dj = 0.65 '- 0.25A + 2.1 A2 e gg,7) if o/of = 0.40, 6/dj =. 0.15 - 0.332A + 0.885A2 - 0.203A3 a (8-8) if o/of = 0.30, 5/d j = 0.119 + 0.051 A '- 0.027A2 + 0.017A3 e (B-9). 2 if a/of = 0.::0, S/d. = 0.062 - 0.049A + 0.199A.- 0.059A3 + 0.008A4 e j (8-10) where dj = 4a og/E The tearing modulus is derived for the case of o/of = 0.75 which represents the worst case, b'ut the same methods could easily be followed to determine Tapplied f r the other load . ratios. The COD from (8 7) can be writtes as 4aaf 6= Q~ E (O'I II where Q = 0.65 - 0.25A + 2.1 A2 ~ B-3 s. A ,,g,,,m.. ""'a p

m - Using the differential for equation (C 11) results in .. ~ 40 (3 G + 3 y. 9 - 4aag dQ dA )da - d5.= = y dog 4aag (4.2A --0.25) [12 (1 - v )j 0.25/Rh.5 da (8 12) I 2 0 -E O I E Now substituting for the dimensions of the pipe, R = 15.75 ano h = 2.5, and letting a = 0.3. the expression ' simplifies to.- aq. .4 ' d5 =. 7 13.4 a - 0.15 a + 2.60 Agair-using the COD-J relationship. J-0""K 1.1 1 dJ d5 =a Uf. l The stability criterion becomes = 0.13 a2 Tmaterial > Tapplied * * - 0.15 a + 2.60 (8 13) 2 . f The results of this expression are plotted in figure 5-1, and further discussed in section 5. ' 8-4

g 13727 20 4-14 1 A L 1'A A -o, I i-1- I i i 1 A t L+a - m-2a -*- 2b a-- Y n i i ! 777777 ' l i I o, Y 7 7 Y T T Center Cracked Panet AZ l +

1. *h h X

wac-u _ _; = k R. s Longitudinal Through Crack in Pipe Figure B 1. Analysis of Two Geometries B5- 'qqaph y : ^ '

13727 19 den 6 5 4 t 2, 3 [ A=4 3 2 2 1 0.5 0 1 l 0 0.2 0.4 0.6 0.8 1.0 Ntha a y 0 a= h y = og o o Figure B 2. Crack Opening Displacement in a Cylindrical ShcIl With a Through Crack B6 . g - _ = -,we,.-,- m_rr.,..,_ yy,...s,.,,m.rm-c,yc ecs,,,. c-y,w,p m -c ss,w-,

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