ML19326B658

AO 50-313/74-11C:on 741107,reactor Bldg Spray Pump P35B Suction Line Leaked.Cause Discussed in Encl Failure Analysis of Schedule 10S Piping Rept & Corrective Action in Encl Insp & Examination Program

ML19326B658
Person / Time
Site:	Arkansas Nuclear
Issue date:	10/31/1975
From:	ARKANSAS POWER & LIGHT CO.
To:
Shared Package
ML19326B653	List: ML19326B651 ML19326B658 ML19326B662 ML19326B664 ML19326B670 ML19326B676 ML19326B683 ML19326B687 ML19326B691 ML19326B694
References
NUDOCS 8004170504
Download: ML19326B658 (51)

Text

_ _ _ _ . - - . _ _ _ _ . . _ . _ _ . _ _ . __.. _ _ . . , . . , _ _ . _ _ _ . _ _ _ _ _ _ _ _ _ . . _ . _

j O ..s f

, 1. Abnormal Occurrence Report No. 50-313/74-11C

2. Report Date: October 31, 1975 3. Occurrence Date: November 7, 1974 4 Facility: Arkansas Nuclear One-Unit 1 Russellville, Arkansas

5. Identi fication of Occurrenec:

Reactor Building Spray Pump P35B suction line leak.

1 -

6. Conditions Prior to Occurrence:

Steady-State Power Reactor Power 0 MWth Ibt Standby :ct Output 0 MWe Cold Shutdown X Percent of Full Power 0 i Refueling Shutdcten Load Channes Durinn Routine l

' Power Operation )

Houtino Startup ,- I

'Jpera t ica Routine Shutdown Operction Other (specify) 1

7. Description of Occurrence: ~

See AOR No. 30-313/74-11 8 0 04170J04 J i

.4tre! -i , IP 3 NSP-10, 2ev. 2 Page 2 of I

_ _ _ _ . . _ - __ __ _ _ . . _ _ _ . _ _ _ ~ . _ _ - - - - - - -

-- --l

l I

I i.

Abnormal Occurrence Report No. 50-313/74-11C i

8. Desi! ' nation of Apparent Cause of Occutrence:

1

Design Procedure Manufac ture . Unusual Service Condition Including lhvironmental Installation /

Construction Component Failurc Operator Other (specify) X See AOR No. 50-313/74-11, 11A 6 11B

9. Analvnis of Cecurrenec: .

See Attached Failure Analysis Report, " Fatigue Analysis of Schedule 10S Piping".

5 s

March 4, li m NSP-10, . <:v. 2 Page 3 Of 1 -

_ _ . . .~ ._ . . _ . _ _ _ . . . - . - . _ _ _ _ _ _ _ _ . . _ _ . - _ _ - . . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

r J

y5 -l

. Page 3 of.3 I

i; j  : 9.3 .. Cool- sample to room temperature. l r  :

! 9.4 - Check pil of solution with pH paper. . (Do not use. a pH motor.)- If -

, pH is- below :10 add N/5 NaOH solution to raise pH to at least 10.  !

lL '9.5 ' Add 10-20 ml of 30% H2 03 to sample. Rocheck-sample to insure j

! sample is still basic. "  !

9.6 Boil sampic again until reaction stops. l l C 1

- 9. 7 Adiust sample.to a pH of 8.3 with 6M Nitric Acid and N/5 Sodium  :

Hy'droxide.  !

i-- 9.8.~ Add 1 21 of Potassium Chromate Indicator Solution. .i j; -

1

[

- 9.9 Titrate with Silver Nitrate Solution to a light orange color endpoint.

l i i i

i 10.0 CALCULATIO.'S -

l '10.1 PPM C1' =-(A - 3) 5 '

j A = m1 titration for sample B = c1 titration.for blank (% 0.4 al) . .

t ,

i  !

4-  ?

! i 5

r i 2

.an k  !

p 1!

l s l

i.r 2 i

1:  :

1 . , t 1.' *

.,i 1.

e .I r

J. l

1. i 1 ,.

{' .l l t l- .

L ,

je: -

-=

- 4

!< - i

Rev. Oc

~ - -

.. . . . .- = -

l-A

/ 'y V

EXAMINATION AND INSPECTION PROGRAM F0d SCllEDULE 10 STAINLESS STEEL PIPING ASSOCIATED NITIl MATERIAL llEAT NUMBERS 800201 AND 2P 3352 The Tollowing program defines APGL's plan for inspection of schedule 10 stain 1 css steci piping associated with material heat number 300201 and a singic pipe section associated with material heat number 2P 3352. These sections of piping were sing 1cd out in the report to the NRC il50-313/74-11B dated August 29,.197S. This program is designed to prevent conditions which may have contributed to past failures and to detect any future failures.

This program has three parts which include:

1) _ Sampling, draining and flushing, if necessary, of stagnant liquids in the reactor building spray pump suction piping.

2) Visual inspection of the subject piping, and

3) Radiography of welds in the subject piping.

[m

'd '

i The offected piping and associated welds are listed in Tabic 1 and are shown in Figures 'l thru 10. The effected piping and welds covered by this program -_

will be referred to as " subject" piping and " subject" welds throughout this program outline.

In the event sections of the subject piping are replaced during the life of this program, they will be deleted from inspection unless the new welds

' involve some of the subject piping. ,

Sampling. Draining and Flushing of Stagnant Liquids in the Reactor '

-Building Soray Pump Suction Piping The purpose of th'.o phase of the inspection program is to limit chloride concentration in stagnant liquids found in the reactor building spray pump '::

suction piping. Chloridos may be introduced into this piping during quarterly testing of-the sodium thiosulfato discharge valves or leakage thru said valves.

To limit the chloride concentration, a program of sampling, draining and flushing,-if necessary, will be performed as fo11cws: -

1) Following the quarterly test of the valves in the sodium thiosulfate .

' discharge lines, the piping will be drained, refilled and flushed, if necessary. -

2) Samples of stagnant water from low point drains in the reactor building spray pump suction piping are taken the next scheduled

[a working day following the flush to check chloride Icycis. h'cekly be} sarrples - arc then taken _ of stagnant water in both spray pumps

suction pipi.ng to check chloride IcVels and determine if- further

~ flushing or drcining is nee-lcd.

e I

.  ?%

s.

J )-

v

3) 'Sanples are analyzed for sodium thiosulfate first. If the sodium thiosulfato content of the sample is belcw 10 ppm, then die stag-nant conditions are ccceptabic and no further action is taken.

If the sodium thiosulfato content is greater dian 10 ppm, the chloride content is nnaly:cd. If die chloride content is at or below 10 ppm, no further action is taken. If the chloride content exceeds.10 ppm, the piping is drained, refilled and f prie.' If neces-sary to reduce ch.'oride concentration and sampled again the fol-

-lowing scheduled work day.

The above program will be continued as long as the subject piping is part of the reactor building spray pump suction piping.

~~

- Visual Insocction of Subject Piping The purpose of this phase of the inspection program is to locato any thru-wall cracks in the subject piping which results in visible leakage.

All piping listed in Tabic 1 and shown in Figures 1 thru 10 will be visually examined and. documented by a check-sheet filled out by ANO staff personnel appointed by the plant superintendent.

The visual examination will performed once each month for five years from (O)-

the last failure in the subject piping. If at the end of die five year period no visibic lcakage has occurred, the visual inspection and documen- '_.

tation will be discontinued. Should any visibic icakage occur from the subject piping, the visual inspections and dccumentation will be increased to ence ecch week following the leak occurrence and will be continued for one month. At the end of one month, if no new leaks are found, the monthly inspection prograr will be reinstated.

a A daily general walk-thru inspection of accessibic plant areas is a part of normal plant operations personnel's dutics. No documentation of this 3 inspection is made unless a probica is found. This program insures quick location of any visible leakage while die above documented inspection assures records of detailed visual inspection, i

Radiogranhy of Subject Piping In order to detect internal imperfections and cracks which may not be

Icaking, K progran of periodic radiography'will be performed.

This exanination is to cover all welds listed in Table 1 whidi are acces- -

sible to radiography. The welds will be radiographed based on radio-graphy standards for nucicar piping USAS B 31.7.

.This program will begin at the first refueling shutdoun with collection of baseline data for accessible welds listed in Tabic 1. Currently some

['/

(. .f

. baseline ~ radiography has been done per USAS 3 31.7 standards.

.. 'I

O t.

The following program will be folicwed for ten years from the first refuel-ing shutdown:

1) Establish complete baseline radiographs of all accessible wclds listed in Table 1 per.USAS B 31.7 standards during the first refueling shutdown.

2) Subscriuent inspections may be performed dur.ing refueling shut-downs or other plant outages.

3) A set of not less than three examinations shall be performed at approximately equal intervals during the 10 year program, with the third examination coinciding with the end of the 10 year period.

4) Examination of welds from the reactor building spray pump suction piping every 12 to 24 months on a staggered basis for the ten year period with not less than 100'. of the subject suction piping welds examined during the first five years of the program.

5) Unscheduled inspections will be conducted in the event of a detectable Icak in the subject piping. This examination will include representative accessibic wolds in Tcbic 1 associated with

/ x that portion of the system in which the failure occurs. If further

( ) unacceptable structural defects are located, that portion of the

redundant stream in which the defect was found will be examined -

(representative refers to areas to be determined by analysis of failure location, previous radiographs, previous failures, system conditions and operating experience).

This completes the ten year inspection program.

The final phase of the examination dealing with the remainder of the service life of the subject piping will be submitted upon completion of the 10 year ,

.. program based on the examination, any failures which may have cccurred and operating experience.

O e

,.a-b

m ym .

{ TABLE 1, SUBJECT WELDS LISTING WELD it- AND

• !! EAT # l ent,n 1 ;\go 4-HFs\T #

SYSTDI FIGURE #- 0F PIPING SYSTD1 FIGURE il f UF PIPING

~

Reactor Bldg. 69G 800201 Decay licat Re- GC BJ-5il'~ "800I2dl~

] ;moyal l Spray "A" f.oop 69ff " l "A" Loop (Cont'dl GCB-1-8D Figurc n a

(4 Welds) IK:B-6-28 jFigur ." , GCH-1-9 8 .

!!CB-6-29) l ) 48B 800201 48C "

1 49A "

Reactor Bldg. 26A ] l 800201 49B "

Spray "B" Loop 26B l "

49C "

l

.(3 Welds) 26C- 49D "

26E "

50A Figure n Figural 6 s HCB-6-1A- f 1 " '

l GCB-1-17 "

)'  !

HCB-6-1C. I GCB-1-18A l

" '~-

l HC B-6-32 " (

l GCB-1-19 + "

i TREPAN #26J l l GCB-1-20 "

m

-)

Decay Heat 30A '

800201 I GCB-1-20A " >

l 30B " '

Removal "A[ooI ' "

,, GCB-1-46C 1

(.'.9 Welds) GC B-1 -4 8"# "

) - } '

CCB-1-48C /

'GCB-1-4A "

Decay Heat Re- 38A 800201-moval , t

.GCB-1-6 s "

"B" Loop 39B "

F. 32A D 800201 (44 Welds) 39C . "

. - 33A " "

399 .

33C -i " "

42A Figure 34 B r '3"# " "

a 42B

.34C " "

42C

(

v i

( ,/ .GCB-1-3 "

42E ,

GCB-1-8 j 42F "

) .-

. t'

. ~ . -. - _ _ . _ _ _

,m

,s7s l

-l TABLE 1, SLTECT WELDS LISTING (CONT'D)

. NHLD # AND -* IIEAT Il '

ri!!LI) il 'AND #

lil!AT #

LSYSTDI FIGURH fi 0F PIPING SYSTIS! FIGURli # OF PIPING l

Decay lieut Ite- ) lDecayllcatRe-mova 1 -.

42G. 800201 j

moval .GCB-3-4 ) 2P3352 I

l GCP-l-28 " "

l ' "R" ~ 1.co p (Co n td l "B" Loop (Contd) GCB-3-5 ,,

- Figur <.  ; ME"#'

. GCB-t-28A 4 TREPAN f;37 5 o

GCB-1-28D (Two Nelds)

i. GCB-1-28Es 54B 800201 -

-43A .

80020] 54C - "

! l i

'43C l- " "

SSA l

43D " "

. 55B 44C 56A l

b 44G "

57A Figure gure .,

4411

' " 7 " -

'5 ' 57B }

44K " '

- , 57C i

! .GCB-1-26A GCB-1-12 GCB-1-26B , GCB-1-13 "

~

l " i

!= GCB-1-27B GCB-1-15A "

! I GCB-1-27F GC 3-1 -38 "

GCB-1-27G. GCB-1-38AJ .

TREPAN #4 "

l l

l i

• Shopweldshave3digitnumbersandfid1dweldshave

. 6 or'7. digit numbers.

Note'1.). Inaccessible cids will.be determined during

- we first refuelin(g shutdown.

F e

[

~

i 4

i. -

4e - - . . . . - - --.- - - .

4 O~

kh

- b 00 wO I co 9

'N o d \&

A I

3,/ b g 3- cQ i

N J

O r

D i

a e.,s_%

4 CC D

3 tu.

9 4.js.

s M JY l

\ ,

\

Sqs

.s I!Mbh t y , .

%g

~

g Tg; megg

I ' .) 1l l p

st uo t To x

eo Hs 5

H D.

0 7

' 0 3 .

4 0 5

6 ,

1 n ' 0 ,.

O \.

'0 1

dE 2 l

o0 .

I E

C I8 0 C,

c V 3 R t U e

G.

I s F I I g

6 ,s 3 .

_s 1

_N c

6 .

r u -

y s r

'w I , a g m k

0 W -

41 i

a 5 6(g m

z b.y u pc 33 s

g-fi u s

.m b i f

i

Gt h i'8 4

k

'y ..

l6 POOL DDl SPoot 33A t

-)

0  %

I.0 3 0c GCO 5gh e

DDoot h4 A lGca+8Bl s a f

l Seat SZ l, gg l'5 o loca-t >Ib i

1. co TC p6 C'6 s 8

0h4 gc0'I' h'S 1,;j 1 ISeat 34 l Next Na

&'3 ,,,,,,, 8002.01 I

@ f i Is wv one t

[ Ficuae 3 , Iso _ 7-DH-6

(v3 lSpoot 38 l

)

l.(lh.$

3e 4 ~

0'0'y~

..t*

HEAT N S

'e g < < i,,,,, 800 2'O I -

O

,, e .

l Is ocu sel s F

U, 0 c gi.z6 t,,t( a D cc(:0N' a si y'/ Y -;

Gt 4f 3gA t(f,(g'I'lo-

? _ls.cou 42l '

y.g .

t ,z c O '

m.

,I,. A a -

i J  : .

• Ek r

/

I*hr/ Fieunt 4, Iso 7-DH-8 pa vmm p., M

~

fb\

P l 59ect. 46 [ ,35 Y$1 HEAT y 2, ~

I#'p# -!"",::':' 2 P 3 3 5 2

,4' -.,,

50020l a')g'0

,~ ~ ,....

cb p.

.h GC O /

V '

R

o c, a ,,,ay c a a 8 x D ,), y~%q

3 s f i s w ei

-l D

! , g70 144Kl A g j 0

- s, _

,Ecg

,N -t 3%

A Q

3 C0 b 0,,, g 6 D 0 g oC C y.

l Spoot.4 4 s c

/

eb wg  !

/

\O N

{}

\d NJ lseeot as 488 jp GC 69 g p'l*0 A

pf G O ISpoot 48R l g .r M ,r f  % :-

l Spoou a 3 j 490 gg l.gO SPoot EIA

-l'I

) ,

I69 ot 50l

.gf.

9c s

,[

dEAT MB )

MM 800208 (

}r W ge#(([

k( q[ pec $#'

I ,

(*

, e , .

g F',GURE6,

<.m.e,.# Iso. 7~0n- w

, .. ,, ,, I

O O O l Spoot S4 l

- G 00 )

r 5#

{

{% V A .50A g C ' ~' l O *' 5l Y a 0~ '

> qD V

!iS,' f g.r l^ hOO

%, b E3 t c,c F

%g C *> G

%gn ( l Spoet. 56 l h

! H EAT N1 .

iiiii s a 8002.o\

f  ; F%g l '

i i d L i , w

\ 'ff 42NNYN h. -

Flaune T Tso. 7- D H-11

, a , ,, ,, i

O O O I

h 'Q-

/

?

i

p. 9' lSPOOLGSA Spoot 69 8 9

)

+: ' /c0 g) [

1 f_ -

M /

gIj 9 H EAT N '

mymr 800?_O)

' ' 6W-

.!  !) >

m Ja_,!

! : ^>

W m

@p1 NIM avb FIGURE 8, ISO. T-DH'l2

f*'%' ,rh (%

m. .( . -OH- 8 l 1  : - -

)

6

1. .......

C

(.

4 t

Q+ l-* V  ::m

(

u-( #' ,

bon 4Tf D waf fe gt&LE Taste

+ l 7- OH-5 l : - R

,,,y,g,,

to se on.

C  : h  ;,J lc 04  ::

X-O X

X-@

1 l7-DH 6l l 7-DH- ) l

@]: M 4 4

_..th .._..,)

E SSA E%s g, ..-.. g, Dr. CAY llEAT COOLER '

7 7 1* 4"i 4 COOLANT b T hv.

D l'l-OttlO] l7-DH-il l H -

tH

~ #:

v ~ g ,_ 1:

g_

l' 1r dk JL

- A _ l-

-1 il

l.

RF. ACTOR M t. D C.

SUMP e" i =

. .I rm[

s* .#

i f 's a < -4 90 n t l7-DH-12 l i

2}U is

$$MNS6 ,

. . fisunc,,9, DECAY, HDT RgMovAt SYSTEM i

i soseusA TMQ1ULFATC STotAga Taun

.n.

- e .... . .

x .2 MN > ,

M DRu. <

V , x  ;

e-d k  ; ,

........v.

w

- ,= f Q '

i .. ..

m.,o - M.

s,..,

g& 1 0.c.a.r

~. .w.t . av. a.s.u.ov.at Q

.= 6e A y m l

e

(

65-6 l REACTOR PLOG. '%

Speny puuss rj Z

lT-DH 12.l - >

<ip m .v ...T _

S***' h ants '

Q L.

~

x x ,

.tu. e s s. suctio=

-cz  ;

. a.

t 5

g . .

O

flaw and loading stresses specified by Bechtel Power Corporation. Because conclusions are appropriate only for these specified conditions, neither 9 Failure Analysis Associates, nor any person acting on behalf of Failure Analysis Associates:

1) Makes any warranty or representation, express or implied, with respect to the usefulness of the information reported to assess the general .

structural integrity of Schedule 10S piping, or

2) Assumes any liabili' / with respect to use of, or for damages result-ing from the use of any information presented in this report, except for the conditions specified by Bechtel Power Corporation. f Prepared For Mr. E. H. Smith, Project Engr.

Bechtel Power Corporation

/ .

P. O. Box 3965

' ' San Francisco, California 94119 October 1975 LOS ANGELES REG'ONAL OFilCE POST OFFICE Box 24947 LOS ANGELES CA CO24 (2t3) 525 5664

O .. r-

- e

~

SUMMARY

Analyses have been performed to assess the. structural reliability of two j

highly stressed locations in Schedule 105, reactor containment spray lines f

containing a postu'.ated through-trickness 2 inch long, circumferential

. crack. Loading conditions analyzed included accide . mode stresses -and vibratory stresses produced during specified operating and design base earthquakes. Fracture mechanics analyses.were performed to calculate the ,

crack tip' stress intensity factor as a function of crack length, the i

critical crack size for unstable rupture, and the rate and maximum extent of j fatigue crack growth under design conditions. Utilizing published data i

! and conservative extrapolations when data was not available, results show

! that the postulated flaw'will not extend in fatigue to cause pipe rupture

_ under the three specified design conditions. .[

t l

1 l f

, l 4

i 1

4 w/

l -

[

w+ v m- n , - + - , vv,e r -- - - , - , , , - -- m--n-,-e+ , . . ,.-e,-----,---,

rw a----, e,--, ---,-r,-1 v ,n

~

I. INTRODUCTION &' BACKGROUND

%f The ~ containment sprav system piping is 10" diameter Schedule 10,

'and is fabricated from Type 304 stainless steel. Such systems are normally fabricated using. shop and field welds made 'with the gas tungsten arc welding (1)

. process. Past experience with Type 304 stainless steel in light water reactor systems indicates that if the welding procedures are not strictly 1-controlled, excessive. heat input can produce highly. sensitized material.

The residual stresses in conjunction with the borated water environment can lead to stress corrosion cracking in the heat affected zone. In such systems, - -

the stress ' corrosion cracks form in a region in the heat affected zone in which excessive grain boundary carbide precipitation has taken place. The

. exact point at which stress corrosion cracks could occur will depend to a 2

large extent on the t.otal heat input of the weld and whether or not a minimum b thickness exists '(by counterboring) near the heat afvected zone.

Q In this thickness of material, it is likely that the region of worst embrittlement will' be about 0.25" from the fusion line. In this region of the heat affected zone', it is likely that the tensile residual stresses have fallen from the

! - yield ~ stress level 'in the weld material (30 ksi) to about 1/3 of thi.s value (10 ksi). As described in Section II, both these values have been used to determine '.1) the mean level for the fatigue analysis and 2) the peak stress level ' for the unstable failure analysis'. 'I g The containment spray system piping and the pump suction s,ide piping is ;normally maintained .in the full non-flowing condition. In the event of a -

loss of coolant accident (LOCA), the system pumps water from the borated l l

water storage tank (BWST),into the reactor building atmosphere. After exhausting

[ the-contents of the barated water storage tank (BWST), the suction of the pumps v l l

e t Y + r i e m --> i-,- ,, -.

'I

. ,n is transferred to t... reactor _ building sump for the . mainder of building spray.

s operation.

( In addition to this accident mode operation, the system is affected

'I by a normal unit shutdown (in which it is isolated from the decay heat cooling system) and by testing of the pump _(in whic.n water from the borated water

' storage tank, at ambient temperature and pressure, is recirculated by the pump).

.In the operating modes described above, the largest pressure and thermal stresses occur during accident conditions. Therefore, the accident raode operating condition represents the most severe case, and it was used as the basis to -

calculate the stresses given in Table 1.

The purpose of_this analysis is to assess the. structural integrity of I

two specific, high stress locations in Schedule 105, Type 304 stainless steel, reactor containment spray lines in the presence of postulated through-thickness,

\~ **

2 inch long, circumferential flaws. The loading conditions considered include both v1 oratory stresses resulting from seismic conditions associated with design ,

base and operating base earthquakes and system loading (weight, pressure and thermal stresses) during shutdown and testing. 5 i

Fracture mechanics analyses have been performed to:

1) Calculate the crack tip stress intensity factors as a function _

of crack length,

2) The critical crack size for unstable failure, ,

3) The maximum end of life crack size if the postulated crack extends in fatigue, and

4) The conditions required for growth of the postulated flaw to cause O<

s unstable pipe rupture.

• Specified by Bechtel- Power Corporation in Schedule B (Reference 2) shown in Fig.1.

• • Specified by Bechtel Power Corporation in Pg. 8 of Schedule B (Reference 2) and Table ~1. -

a J

^

, n. I'

( ) CALCULATION OF THE CRACK DRIVING ~ FORCE _

/

U 'II. _

Both the rate of fatigue crack propagation and the conditions for '

ck tip -

unstable fracture of_ flawed structures can be.describad by the cra ~

K is quite simply a measure of the cracs stress intensity factor, Ky .

7 It is opening force and magnitude of local stresses, around k length,a crack tip.' . .

proportional to the applied stresses, the square root of the crac That is 4 and the details of. the part geometry and loading conditions.

(1) t K = aha (Bm)*

7 and (2)

AK 7

= ao / U (Bm) .

where *#* -K 7 ")

AK

= range of stress intensity factor (K 7 7

max ,y min),

ao = range of normal stre'ss.(o .

(./ _

o is the nominal tensile stress on the crack plane, a is the half crack length, and .

B is a parameter dependent on geometry and loading conditions.

m 3 Under uniform tensile loading of a flat plate, ir B = 1, and K7 = o h a.

m is a curvature correction factor For a circumferential _ crack in a pipe, 8m h to pipe diameter, greater than unity, which depent.s on the ratio of crack lengt ,

(3) .

Throughout this analysis, the conserva-wall thickness, and Poisson's ratio i ts over the ,

tive assumption will be made tlat the maximum nominal stress ex s entire section of concern. stress ranges, I \ :The calculation of the ap?copriate nominal stresses,

(/ h two positions of interest

.and curvature corrections is presented next for t e ation alone, d

shown in Figure 1, under loading conditions of 1) accident mo d e oper

2) accident mode' operation during operating earthquakes, N mrMdruouakes.

. . = . - _ . - - -

r

'. E ,

s A. --Nomi.ml Stresses' q

Stresses from six sources ' contribute to the crack-driving force and must'be considered. They are:

• Residual welding stresses -(og )

.ght stresses (og)

Pressure stresses (op)

Thermal stresses -(oT)

Seismic x'+ y (og) lf .

Seismic y + z (o3) _

Some of the above stresses are cyclic and contribute to the fatOue loading cycle while; others remain co'nstarit for the conditions being analyzed and contribute to the mean st'ress about which cycling occurs. The mean stress is important because

it affects both the rate of fatigue crack growth, and the maximum K yproduced iv for a given stress range. _

t

1. Accident Mode i

Under accident mode operation, the mean stress (c m

) is given by I * + (3) 5 m R "W .

where'i is the stress concentration factor (stress indices) associated with

- * ~

the weld' bead .

Two different values of the residual stress ( R) were analyzed. One ,

is R = 30 ksi, the flow stress which would be appropriate for a-crack in the ['

w eld itself, and the other is oR = 10 ksi which is the appropriate og at the p *~ Given by'Bechtel, Pg. 4, Schedule B

. (2) e

'4 1

• v y w . - ,. ,,,.s *- n v- - ,r e--,, . . - ,,..-,,m.,- ,c,., -. -y. , , - , - - -s.,r- , - , = - - - + - -

• O' ~

.. position where:hsat(affected zone cracks have bee.Nobserved.(1)

v. The maximum stress range (Ao) 'for accident mode operation is .given by

'Ao = i (OT + "p) (4)

L that is, the stress. range is the total of the thermal and pressure stress magnified by the stress concentration factor, i. Table 2 shows the values of -

mean stress and stress range for both points A and B and for.both weld and.

heat affected' zone cracks. This is a conservative bound on normal operating 1 -.

I ^ stresses ~ because 1) under normal shutdown without testing, thermal stresses are i

produced without o p , 2) if the spray system pump is tested against a closed

) valve,' pressure stresses occur without oT , 3) the individual magnitudes the thermal-and pressure stresses during normal shutdown or testing are less than

- the magnitudes which occur during accident conditions, and 4) for' heat affected i

!' zone cracks, the stress concentration factor is likely to be close to unity rather than the maximum value of i = 1.8' assumed to act for all cracks. Therefore',

i ) -

=,d while this analysis was done for the accident mode, the results envelope normal shutdown and testing.

-For quantitative description of the mean stress effect on fatigue crack growth, the R-ratio,-defined as  :

g min om - A /2 ,

.RE

" max m + Ao/2 is utilized. R is also included in Table 2. .

The thermal and weight stresses also produce a torsional shear stress (TTand Ty) on the pipe' weld. Ahtough their magnitude is generally much less than the tensile stresses and the affect on fatigue crack growth is usually

[ negligible, they have been included for conservatism by' calculating an effective principle: stress given .by

~Ao E- (Ao) + .(AT) (6) v e

• l l

(

. -. r Values of At and Ac e are also included in Table 2. It was not necessary to V calculate a contribution ~ of torsional ' stress t m since it will be shown in r Section III'that the R-ratioLis already so-high as to produce the maximum

• t i materials crack growth law.

2. Operating-Earthquake-(OBE)

During an operating base earthquake, 650 cycles of the stresses specified by Bechtel '(Table 1) are produced. The mean stress for the OBE includes not only the welding residuals, but also the weight, thermal and pressure stresses. Specifically, o (7) m"#R + i b#W+"T+"P].

The stress range is i

p - Ao = (i) (2) (o3) ,

(8) i

,l -~

~

where the factor of 2 -is included to convert the maximum seismic stress og I .into the total range ao3 = og - (-o g) = 2 o3 >

Table 2 summarizes .the mean; stress,' stress range and R-ratio for both ,

weld cracks ( R = 30 ksi) and heat a'ffected zone (HAZ) cracks ( R 10 ksi)

=

located at Points A and B. The torsional stresses have again been included to calculate the' effective principal stress range a e O#) + (AT)* ~

i.

3. . Design Base Earthquake (DBE)

{

(2) -

During a'DBE, 200 cycles of the stresses specified by Bechtel 1 . -

and shownlin Table 1, are produced. The mean stresses during a DBE are identical-

. to those existing for the OBE, but the stress ranges are 1.5 times as large.

O These nominal stresses on the plane of the postulated crack during DBE are

'(-% / l' falso summarized in Table 2.

+ , ----g-- - , - e -g, ,, , ,- _,-,e- w- - -,wg e-- u - re -r--,e

~

.w .,

7

)

Aj.

, B. Calculationof'CrackTipStressIntensityFactors(Kl y As discussed previously, .y K = c /n a B *m. The curvature correction factor (B,)-is a function.of crack length (a), pipe radius (R), wall thickness (t), and Poisson's ratio (v). For any applied stress range or mean stress

~AKI

- [K'

=

3,

- Ca.(B ),m which depend only on geometry and stress state, will The curvature correction, Bm , was obtained from the elasticity

~

be.the same.

! solution of Erdogan and Ratwani,( ) which has been shown experimentally to

~ '

be slightly conservative (3,4) ,

The calculation of K was accomplished by programming yK a /n a (Bm)

{

y

- in subroutine form. The values of B m were read into the routine in tabular

. form as a function of the shell parameter IO 2_ 1/4

(,I A= [12(1-v), (a// lit),' (9) _

where

}~ v = Poisson's ratio = 0.3, R a Tube radius = 5.375",- 5:

t = Wall thickness = 0.165", 1.

. a = Half crack length, [in) .

~

.The subroutine interpolates to calculate K y for any specified a. Figure 2 summarizes the results of the K y calculation as a function of half. crack

- length, a. This routine is also used in the fatigue crack growth program discussed in Section V.

It should be noted again that a uniform nominal stress equal in magnitude to the maximum value is-conservatively assumed to exist over the entire cracked

'[]'d -section for all' calculations.

1

• e

,+w- -y , ,.-_y --

, 9 < - ~ . . , - - - . . , - - . - - - , . r_w,- en+-i-+ q,

. n m

[A}

v III. ' MATERIALS PROPERTIES-DATA i

.The materials properties data required for the fatigue ana-lyses

, relate: the fatigue crack propagation rates at the very high R-ratios (R a o *I") to: the range of crack tip stress intensity factor' AK fo'r very 7

max low " AK suminarized g

in Table .2. The existing data on 304 stainless 4

from published work have been utilized-along with the most appropriate correlations of mean stress effects. Figure 3 shows schematically the ma'terials fatigue crack growth law at two R-ratios. The crack growth rate is proportional to a power of AK over a range '4K, but shows a deviation from ~

! this power law relationship at low AK where the threshold AK;, below which cracks do not. propagate, is approached.

Because testing at very slow fatigue crack growth rates is difficult and expensive, no data is available for Type 304 stainless below growth rates j "

of 3 x 10 4 inches per cycle. In order to perform analyses in the slower ~ '

region, the crack growth curve is approximated by the dotted lines in Figure 3.

Figure 4 summarizes the ambient temperative crack growth rates for >

(5)

Type 304 stainless and R = 0 from James ar.d Schwenk . These data have been it -

(6) confirmed by Shahinian, et al . , whose data fall within the same scatter

. band. These data are represented well for 10-6 1

-4 1 3 x 10 inches / cycle by a

3.365 da =- 5.56 x 10-21 (3g) (10) y ~

dii -

J where da, is in ~ inches per cycle,'aK is psi /i'n. , and 0 < R < 0.05.

df4

'o 9

- --* v , y , y--= ,, y .g =

• wce -y ' -+-,-.9 r- --.iy 3 9

] Although the effect of R-ratio on da_ at ambient temperatures have not.been published for Type 304 stainless, there is extensive' data for

~

(7 ) (8)- (9) .(12)

Aluminums ' , Titaniums , ferritic steels , ' and nickel alloys On a modulus compensated basis, all-show similar increases in g with R reach-dN ing a maximum C /C at R = 0.7 which does not increase further with increasing R 0 R. fiumerous equations have been utilized to describe.the effect of R. Those-

(10 ) (11) of Foreman' , James and Yuen (8) predict only slightly different effects; for e'

ample, C /C = 3.33, 5.05 and 5.72 respectively. Limited experimental 0.7 0 The conservative assumption is 0.7I O results show C to be between 3 and 4.

again made that for all R < 0.7, CR will be 5.72 times that for R = 0.

That is, 3.365 da =

' 3.18 x 10-20 (AK) AK in psi /in. (11) dII The threshold values below which fatigue cracks do not propagate C)

.I . (15) i V were similarly estimated from limited Type 304 stainless data by correlation -

(13,14,12}g (16) l' with extensive data on other alloys on a TH basis . For Type 304 E

stainless, the threshold is conservatively estimated to be s

AK = 7,920 - 5,600 R in psi /in. (12)

TH i

Table 3 compares the existing data with Equation (12). For all of the analysis conditions, specified in Table 2, the initial AK yfor the postulated flaw (a = 1 inch) exceeds the threshold AKTH. Therefore, the postulated flaw should grow in fatigue under acciaent mode operation and earthquake conditions. The ainount of growth is calculated in Section V.

• O -

(v/

e

,--g*y -- e- y- v -w- y w-- ,y--, -mw -

(( )~

u

. I'V . CALCULATION OF THE FATLURE CONDITIONS A. Failure Criteria The fracture' behavior of welded structures may be categorized in one of three ways depending on the mode of failure. 'These are 1) linear clastic. fracture mechanics (LEFM), 2) general yielding fracture mechanics (GYFM) also called elastic-plastic fracture mechanics, or 3) plastic instability. .

1) LEFM For the techniques of LEFM to be appropriate, the failure mustltake place in a nearly brittle manner with limited (contained) crack tip plasticity. This category is,-therefore, only relevant to 1) brittle

-( /-

materials, 2) low temperatures, 3) high strength materihls, or' 4) high -

loading rates in ferritic steels. This categcry is not appropriate for austenitic stainless operating at. or near, ambient temperatures.

2)' GYFM s

In this enegory, stress or toughness level's are such that much larger plastic zones occur in the near crack tip region-before

~:

fracture can occur. Because the energy dissipated in forming the plastic zone must b'e taken into account, the failure conditions require producing a critical crack tip opening displacement (or J integral), which also depends upon the materials flow properties such as yield stress and strain hardening rate. Materials which fall in this category are thin sections

_ of .ferritic steels 'at ambient temperatures and austenitic steels over a-In this category, the fracture properties are also range of temperatures.

M

m ,

,. -s t

G- 1-

%)

[  ; related to the thickness.

3) Plastic Instability This category may often follow category 2) when stable ductile tearing has taken place; i.e. , the failure mode is plastic collapse rather than a' shear fracture mechanism. Plastic instability, when it occurs without prior crack extension, is dominated by the flow properties of the material. In these-circumstances, the failure condition.is .

4 independent of fracture toughness, and limit load analysis is used to define the failure condition.

B. Failure Conditions for Schedule 10S Pipino

- To determine the limiting conditions for the 10" diameter

(% .

schedule 10 piping both GYFM analysis, based on a crack opening displacement (C0D), and plastic instability analyses have been carried out. Each of these is discussed.in detail in the following sections.

1) GYFM Analysis E i

b The critical flaw size for elastic-plastic fracture can be determined by comparing the applied ~ crack opening displacement (C00) with the critical crack tip opening displacement (C00c ). The determina-tionLof the applied C0D is based on work by Burdekin and Dawes , and Merkle (18)'

For total applied stra'in~ values grea# 'r than 0.5 cy,'where c y is yield strain, the non-dimensional C00 (0) is given by 0 =

(c/c) y 0.25 ' (13) v' .

.where cis the nominal strain on the crack plane.

6 9 $. , -- e-. -y...--._y.- m, - . , , , m- **'rw'*M* 9'* * * * ""'W- - - ' - " ' *--"'#~W T

g -.

.For' residual stresses .of the yield stress (30 ksi) level and the m

. peak applied stress:(Table 2, DBE Pt.; A), the maximum' nominal stress is 35.6 i-.

psi- . For' contained plasticity, c/c =

' 1.19 and 9 = 0.94.

The ' critical flaw size is determined by iterative solution of 4

I.I COD c.

a 1 (14) c .2Wf 5~ c,

( *) >

=wheremB is the curvature correction factor which depends on ca and is

~

l conservatively assumed equal to the elastic value. Since critical C00

-values for stainless are not generally available, we have conservatively f assumed a'value of COD c =-44 x 10~3'in, which is equivalent to the upper

sheli value for A533 8 steel. Type 304 stainless will have C00 cconsiderably I greater than this.

~~

A conservative bound on the critical crack size is then i"

a " 2'03 I"'

c

~ This means a through crack of length greater than 5.66 inches is required for

fail u re. *

2) Plastic Instability (Limit Load) Analysis The applied stresses =have been conservatively assumed to exist

! over the entire pipe section. (axial load). The flaw size, 2a,. to cause~ -

, -:)

' plastic collapse at a flow stress . defined. by the average of the yield (30 ksi) l

. and ultimate strength (90 ksi):may be calculated from

[ .

~

1 p x. cA = o lim A*

0; l

'oro (15) o(nDt) = oiim-(nD - 2ac )t

r.

- _ - . - ., . = .

h.

i

-s-

3. 7 7/~ 13

r. .

! -where D- - = mean pipe diameter = 10.59,  ;

i j . t' -= wali~ thickness, olim . = limit;-stress'= (90.+ 60)/2 = 60 ksi, j I

j.

~

l o -= applied stress which is the maximum nominal stress minus the .

l residuals since they'.are.self equilibrating 5 5.6 ksi. l r i i i

!. . I

( \

' Therefore - -

a = 15.1 in, c .;,

1 ,

- The total crack! size to.cause plastic collapse is 90 percent of

~

[

t ..

the circumference.

i J

1- ,

I h

j.

l g

9 .

p

(

l 7, l'  !

t .

~

~

i i .

+..

-I $

j ..

i- ~-..#.

3 .,

J .-, -

y w-t ew w- e w e --- w v y e y-

---evwe w -  : material could not support a high R-ratio.  ;

A ange greater than

. utilizing the appropriate da law, Equation (10), a stress r dN i.

' Ac = 56 ksi. or 12.7 times the maximum DBE Ao of 4.4 ksi would be r The limiting failure condition at the high cause pipe rupture (see Fig. 6).

In any case, extremely high and Ao may also become: limit load rather than c C00 .

ltd l i

unrealistic stress ranges would be required to propagate the postu a e  ;

i flaw in fatigue to failure in 200 cycles.

}  !

1

.{

R ,

i . i j- ,

^1 !

l . ,

i t-a j t j._i \ _

t

, , , . , . . . - 2- ... m _ _ , _ . . . _ , . - . , , , , . _ . _ . . . , --,m . . . , . - - , . _ , . . , . -

.. m 16 I

VI. CONCLUSIONS- t

[

1. The postulated two inch long, through-thickness circumferential j flaws' will not extend in fatigue to cause catastrophic pipe j

. 1

rupture under .the design stress conditions. I it

2. Under accident mode operation alone, the postulated flaw would  !

i require more than 2.5 million cycles to extend in fatigue to the _ ,

I critical size where pipe rupture could occur.

1 i

3. Under the most severe design base earthquake conditions specified, the postulated flaw would require more than 700,000 cycles to '

i extend in fatigue to the critical crack size. ,

4. The specific amounts of fatigue crack extension at the two points I

of concern under design specified conditions are summarized in Table 4.

• I

! 5.~. For fatigue crack extension to critical size to occur within 200 I

cycles, a stress range greater than 56 ksi or 12.7 times the  :

actual design maximum would have to be present. l a

D k

1-n v

1

,,..-4 ~.,_.,i.-, , , _ _ - .

_l_. . _ , , - _ , , - . _ . , _ _ _ .-c__, . . . , _ - , , , _ ,_ . . . , , , ..-- . . , -

n \j VII.. REFERENCES

~ 1. Abnormal Occurrence Report, No. 50-313/74-11.

2. . Agreement'for Technical Services 6600-M-171 between Bechtel Power Corporation and Failure Analysis Associates, August 4,1975.

3. F. Erdogan and M. Ratwani, " Fatigue and Fracture of Cylindrical Shells Containing a Circumferential Crack," Int. J. of Fracture Mech., 6 (1970),379.

4. N. J. I. Adams, " Influence of Curvature on Stress Intensity at l '

the_ Tip of a Circumferential Crack in a Cylindrical Shell,"

ASTM STP, 486, Am. Soc. for Testing and Materials, 1971, 39.

C l _ 5. L. A. James and E. B. Schwenk, Jr. ,," Fatigue Crack Propagation -

Behavior of Type 304 Stainless Steel at Elevated Temperatures,"

Met. Transactions, 2,(2/71),491.

i i

i '

P. Shahinian, H. W. Smith, and H. E. Watson, " Fatigue Crack 6.

Growth. Characteristics of Several Austenitic Stainless Steels at High Temperature," ASTM STP'520, Am. Soc.-for Testing and Materials, 1973, 387. ~:

l.

7. H. P. Chu, "Effect-of flean Stress Intensity on Fatigue Crack

. - Growth in a 5456-H117 Aluminum Alloy," ASTM STP 559, Am. Soc.

for Testing and Materials,-1974, 245.

2

8. A. 'Yuen, et. al. . ." Correlations .between Fracture Surface s

I Appearance and Fracture Mechanics Parameters for Stage II

\~ l. .

. Fatigue _ Crack Propagation in Ti-6Al-4V," Metallurgical Transactions,

. 5,(8/74),1833. - -

 ? T=

• w- 3 - . - + -Aw - w e e-w=n.-g---t ,-s.--.or-w.,mv g--- --vw-,*-v- vv' w+v=i=*r-- W

- I 9 J. R. Griffiths, et. al. , " Influence of Mean Stress on Fatigue s._ -

Crack Propagation in a Ferritic Weld Metal," Met. Sci. J., 5_

(1971),150.

10. R. G. Foreman, et. al . , J. Basic Engineering (9/67), 459.

11. L. A. James, "Estination of Crack Extension in a Piping Elbow Using Fracture Mechanics Techniques," ASME Paper No. 74-PVP-14

12. S. W. Hopkins, et. al. , "The Effect of Various Programmed Overloac on the Threshold for High Frequency Fatigue Crack Growth,"

Presented ASTM Symposium, Toronto, July 1975.

13. R. A. Schmidt, Extremely Slow Fatigue Crack Propagation, Ph.D.

Thesis, Lehigh U., 1972.

I (j 14. R. A. Schmidt, A Threshold in Metal Fatique, M.S. Thesis, Lehigh.l l'70.

15. L. P. Pook and A. A. Beveridge, " Threshold for Fatigue Crack Growth in Ferritic Steels at 300," Faticue at Elevated Temp.

4 ASTM STP 520, Am. Soc. for Testing and Materials, 1973, 179.

16. S. Pearson, " Fatigue Crack Propagation in Metals," Nature, 211

~

1. 5053 (9/66), 1077.

17. Burdekin, F. M. , and Dawes, M. G. , " Practical ilse of Linear Elastic and Yielding Fracture Mechanics with Particular Referenqe to Pressure Vessels - Practical Application of Fracture Mechanics to Pressure Vessel Technology," I. Mech. E. , London ,1971.

m

' d' 18. Merkle, J. G. , " Analytical Relations Between Elastic-Plastic Fracture Criteria," December L,1974.

. Points A and B Producca by Height, , ressure, .nenr.al, and Se; ....c -

L STRESS CALCU/;R${$/2 : During Accident l'cde10peratiork

>Z- = 14.3 in P = 60 psi for Accident Mode

. OD =.10.75" .

THI.= .165-l,-

- Yc = 2Z = 28.6 in A = 5.49 in ~

i TORSIONAL

. DIRECT BENDING PRESSURE SHEAR

, LOADING STRESS STRESS STRESS STRESS

, F/A MB/Z Pd/4t Mt/2Z (PSI) i Pt A PSI PSI See PSI i, Note 1 I Thermal- .9 ' 701 87 i

Weight 0 776 342 Seismic 97 275 164

+

(X+Y) i Seismic 112 ' 320 144 (Y+ Z)

Pt B Thermal 15 386 , 74

- Weight 0 175 60 -

' Seismic . 63 695 456 (X+Y)-

Seismic' 40 455 297 q (Y+Z)

• i *

NOTE 1: For the given pressure of 60 psig,.

P-= 60 psig d=D = 10.75 in ~;

g

'. t-tn"* "

!- The_" nominal" pressure ~ stresses are: ,

Pd -

- Hoop Stress = . g = 1955 psi pei NB.3650 i

i

. Axial' Stress = Pd 4g

- 977 psi per NC.3650, ND.3650 3

• *-rtr -

=ec----m- e - +-m- + ..-.,.r-=--g--v--v v '+- -p w- w- - - - + --*--t-e---- r-=t- ww-" F-w~ ' = - 'r-t-Nm*-MtN*We Ri**W'9-W**--"'e -*-t$fF *eW*y =-

x

(

w_j Table 2 - Summary of the flominal Stress on the Crack Planes of Point A and Point B Under Accident Mode Operation

' Operating Earthquakes (0BE)* and Design Base

Earthquakes (DBE).*

'l cm 0 ao R AT 0#e I(1)

(ksi) Tksi) (ksi) (ksi) (ksi /in.)

Accident Mode Operation

, Point A, Weld Crack 31.4 3.04 0.91 0.157 3.04 6.08 i Point A, HAZ Crack 11.4 3.04 0.76 0.157 3.04 6.08

~~

Point B, Weld Crack 30.3 2.48 0.92 0.133 2.48 4.96 Point B, HAZ Crack 10'.3 2.48 0.79 0.133 2.48 4.96 OBE Operation Point A, Weld Crack 34.4 1.56 0.96 0.590 1.67 3.34

[ j Point A, HAZ Crack 14.4 1.56 0.90 0.590 1.67 3.34 Point B, Weld Crack 32.8 2.73 0.92 1.070 2.93 5.86 Point B, HAZ Crack 12.8 2.73 0.81 1.070 2.93 5.86 DBE Operation Point A, Weld Crack 34.4 2.34 0.93 0.885 2.50 5.00

?

Point A, HAZ Crack 14.4 2.34 0.85 0.885 2.50 5.00 Point B, Weld Crack 32.8 -4.095 0.83 1.605 4.40 8.80 Point B, HAZ Crack 12.8 4.095 0.72 1.605 4.40 8.80

• 0SE and DEE Loading Consist of Accident Mode Operation During CBE and DBE, Respectively.

v

?

s

!' ') Table 3 - The Effect of R-ratio on the Threshold Values for Fatigue Crack Propagation.

aK K 0 "

TH TH TH .

R 7920-5600 R Ty,pe 304 SS (15) A533B (Ferritic)(13) Ti-6Al-4V(12) 0 7,920 5,500-7,000* 8,000 7,200 0.1 7,360 7,400 7,000 0.3 6,240 5,400* 5,200 6,200 0.5 5,120 4,300 5,100 --

0.6 4,560 4,200*

0.7 4,000 2,800 4,000 0.72 3,890 0.76 3,660 3,700* 3,700

/'~'s .

) 0.79 3,500 0.81 3,280 0.85 3,160 0.88 2,990 0.90 2,880 3,000 s

0.91 2,820 0.92 2,770 0.96 2,540 2

• s

• Approximate thresholds only from notched rather than precracked specimens.

,- s ** Values for Ti-6Al-4V have been normalized to account for the difference in 6

clastic modulus, i.e., AK = (30 x 10 psi).

TH 6

e i s.

6  ;

u. . .  !

. f i V. ,

TMLE 4 i O

1 i ~ End-of-Li_fe-Flaw Sizes (a f

) for Highest Stressed Pipe : Locations  ;

Under Actual-Design Loadings i

}i i r ~

i Postulated t Initial l

!  : Loading. . Pipe Ao Design F1aw.aj af l I  : Condition Location - [Ksil Cycles [in.] ,[i n .] l l

l Accident Point-A- 3.04 200 1.0 1.00003G i Mode  !

{ .  !

5-Accident .

Point. B. 2.48 200 1.0 1.000018 ,_,

Mode

! OBE . Point A .1.67 650 1.0 1.000016 i

i i

1 3

OBE Point B 2.93 650 1.0 1.000103 l 4

f-DBE Point A 2.50 200 1.0 1.000019 ,

1 i

f I

l 'DBE' Point 8- 4.4 200 1.0 1.000124 i I .

si i

l 7

i n.

l.

f - ,

I'

.z

s i

t G .

I l

4 l.

i

. . . . . - . ~ . , . - ~ . - - - - - . . _ - . . - . . , - . . - , . - . . -

..._m.,--_ - - - - . ~ _ - . . . . . . _ . , , - . , . - - - - - , . . . . -

-m - , - 4 m 2 .

S -

,** W, e ,

b f3 t

n,

't ti

& ;L

( g/p/;jj j ,

$ \ *$[' h *c, ag s s v<,s s x/ j., . s '

C 4 .

./ 1,S. .

y 'Q ,$ ,. k, -

s4 3

C te

• O O 'Q 'N 5!,

Vi ,

.,3

[ _

5 O 6'

z;>

e M, \, . of2f;s s.

6 ~

.o i }

~. y "

*Q "*s,,

ye ,\

~

..- .i .

. o.

h *%X

.{) e -  % ~

E'

%g sd }2 ,

,'c e- .e 2 g a v ,x,,

t pY /,' T .

h W / rs gJ f, a aJ '

c 4

i 2

'w s

i E

a* ti 9

l i

y 9-i  % R. q <

O I n . \

A

/

8 > ho -

/

n a ,s 3 a 3 :n m n 2

l t ,4/ w a%. i j '?

% s 0 'O

o. 9 ny ,

.k h k-3. 4l $7 4, ,

-. o y fr e7f

$ ]y4R}{1

$ a5 l' '

$N

.] 4 idtB /

. \J n\

L__

a .. cE c .

s '% s G

' R R g M.

• w, 41."> R C p$

4 1 1 a

h e -e .

~

4 R& l - .; .7

I L. c  :;.

• 4 l , 1: :-  : 1.

..j:

p ..i.

a

- ~

+l 4..a .dj. . . . u. . _ : . ;la _  :; . .

. /]! ..!h. .

a_1 . ... :1. .'.:

l..

(g) . , $_ -

.Q

. ']l _. ,

' - ..:..; __S p u ._

6.

.a.-

.r L i

.i :1 .!- r I  ;

a yf.:....:.: .g,._:.. q

. a_:_ .; 2:. u..p ..._jf.g u. i. i.. .;_. .n . l l :J.l

-l. :l: a 1  !

n ..

.  : .p m

l:

p  :.  :;: .  : ...

.r

pf ';

",:._.;.-l'- uul..n a.y.. _.: $r -2.[_aiji=...[:= dji=

~ .li. i _uijia. un _ _ _

n]i2.. :q:,ua t

a 1

' ];

.. . . . .

n ;=. .l-

n... .

y:L. _

=;3 =. . . . . .n ;_ yn_ 9:

.l:.._ n- :t: .f.  : i: :4:

I==

=

=

.f;=.-l:;:l- .. . m==  !.: = ;p

-l  ;- .f- i. .h  : r .-  ;-

10,& , . -

[

-l.

..' :l:

... .. . .l:

. .. :l. :. . i, :... . . .. . .. . .t- . . ..'-.

l .: , .. l: .

~:1. * :f.n: ..

. 1. i::..  : .

):

+ -l-  : d. . f;._ . l-  :!.

l. *{- :l- . .t .{-

+l- , :l: -

.- 1 i. .t: I-I . O  :

.. 1: . . r :- .1. . .

. -l- .1: -

. :. [a . . .

-d 7.. . -:..t. -d . . I' :. . . -]. . . :. .

.i . .... . .

.k.k*.8@

--b IiI' - -

~%it: :r: i: - di 'll ~- .ii' 0 b.

@ . . . :In : .=1 : . . .  ; i- t.= t : . - :: n-  ;...  :;. i~...  ::.

• n  :* h I: .

c nt *=  : .rt. . .1  ;

.t- .3 -

unlunj:.nl:. =: 1 p ..j.

.. t ..:t:...

m .

., ;- .;; - . .. . .. . .. . - g. 8.

o , . . ., ,. .. . .!

.l . .

.p .

8

. } Q; .

1 .:)-

i..

.: :..4n :-6765"}:.

z F' r-- =:J " "

":J..g]:

I:

-n. ....j.

p- ,

i:

i i  :;.

":l: P( / .;:!:.

... . ... a .,.

.7.l.- l--

.. . . : l.:....:... . . . . ..:n. ..:::. h.._5 ... ..l .. ._......

.  : ;j... IM.

,.= .

...:f- W. k__ ...:l:.:;  :=u .n.: . :nn: :;n"u: n n;ua ....L. . n.J r. . t . . . : - -f x : i : .. ..

l.  ;  : ~ 1. . .-.. l ::n  ! -- ~------j--- ~l-- - - ~ ~ - ' -

-- - l - - - - j ."+. j - I "-

! ~ = :- - b  :..1  :. . ':- u.:{p .  : = p, -- .

-- n.c - .. , . . jt!.l. n; :, .:3

.ui. !. q 7

]! - "3. . . n'  !. a. .

3. ..3::p g.. .

.l N ....c. -

. .p + ; 4. -

[q . . . .

n1 s y..

. .+. .

l- .t- 1: .:p 1

i""

. . f; / j. . . - l ,. g....j!

'.h - ~T. . .p-

.it j:. .

.(' . .. .. ,

'il" d -

. d . .h. .: i f 's .Pi t :l : il- .

..'t ;j. 4U.

.a,i . . ..q.  :

.[..=., _;,, .:.  : p , . . . ,. : q . .,  :::. _  ::.  :: a.

..l:

7 . p .. - ( . g . 3 .t.

. ..) ..

.. j . - lit

...t;._.,.._._. .. .:. ..

.. ..q..

._ i.

. , ;, . . . . , .,a.. ..,

.h .- .

a. ..

,. .t. .i.

4

i}L N 4 '- id5Fi E.ils 25ii.i ' 4 F i-55!' 5 EE!!!:$r ~;if  : :-

f

+

....j:. .. kM.;~

.. : . . _. : t, - - - q.-- i 9 d.:4:4: .

3-

h. , ....

. . l. ;.

.. . [. . . 3 _. ... .- j :. . .".q...,.. . . . l:.. . . . l . . h. ...

. 3 j- .

en

.:l. - -y 7 .....n =

. :n

!j" i:. :. .. ..g:

-+"e -

4  :

};.

12 ~ _a l ( -1: --

l- ; 3 :-

7(f' f::-. ' g_F_==l8igct":h=';=.1 g. .. ["-

4 zo , .p . . ..

. ln- .r ~ -

1. f

- ~

r : 5'

b. bd 6M~

~

[r 4 -

b 0

--[' . .-  :

j

M-- ". !:- :b i"-

- [' - '"r". F '.1.' =ih: . h- kl~.."iU-'--h dl h. . :i

+ - .: :: :l,  :  : .- . , - i .; .;..

g

• m

.. .x V ,

1

.I- .e2 c. .i : i . a .t . . .: -.. ...

) . . . . ,

=s - ;

.l  :! .  :.  : h...:. u-l .u q... t . - i s ..

9

..t. -

M =-

.n-t o-y . c ;- =c:on =

=- w .=.20:q: .n:{o:.;.1. [. 1.q:j g, :i:

.b.O-L.lL

,.  : l . -- p. - :... .. ,. ng.

s..  ;

p f . 2. - -

g 1. ' ^ '* -

, '.. . .):. f p L, ..arG,,.

,. 4

. .N' . l ' . P l :Al.G~ CaecKiilLsal. GEN, .. j ...

.. -.?

. Lt L . .:= ' . ===:  %

. p _.

l.

.... t. .

f j iLi_.=a::.a..{_._..!._..a..l.e.j.

.._.a _. j , - 1[. .-__a...., j __ _

Fig. 2 - i'omalized stress intensity factor, K;/o versus half crack length,

- p)

, a, for a through-wall circumferential crack under tension.

\~/

4

-e

.,i ? .

- - - . . . - , . . - . . 2a. . - a. . . - , - -.-.na u.__...n.n ..e., , a w .. u -,.,,, . , , .-. . - -

t i

wo e=0.3 i

da = C3 (6k)"^

dN 1

dN

= co(AK)"

z N

m ,'

f

U /-

o l

um / -

o I

/ --

l- J l I i l i

I l

bn

• 7, l A ( (R=0) j qv-1 AK .

LO$

]

Fig. 3 - Schematic-representation of the materials fatigue crack j . propagation law (solid) and the conservative model of i

threshold behavior (dashed line).

l 4

-e

..-.,,w yy ..m-ge, 9., ,.y,_._. .,p_ , si .m- , . . , , , , . , _ . . .y.,,,,, p, . , , , , ..,.,,,,,w,, ,w.,, . . , , _%,w,, - , _

1 e

r l

l 1

J g 3 b b i-in4 _.

.. ~

f,' $N X IG'IIItAl'

, . ~.

b

! ,c-s _ 8 _

~

i l l

h 'Y 0

s T g ia4  :-

c. c O SrtCietn No. l. aw .

~ ~

3 6 $PIC1'afN NO. 2. AW ]

O $F(Cl!.TN NO. 3. AW O 58!CI'aCN P.O. 4. WR 7 5FICl*2fN NO. 5. nR gg-T l f l 10 id

$T2!$$ (Ni['4511Y f ACICR R AN00 (A, ;si M.

5 Fig. 4 - Fatigue-crack propagation behavior of Type 304 stainless steel at 75 0 F, and R = 0, Ref. 5.

l i

4 )

I

' l l

l I l l .. '

l I

i

{- . - _ . . - . _ - _ _ _ _ . _ . _ . . _ . _ _ _ _ . _ _ _ _ _ _ _ _ _ _ . _ _ . _ _ _ . _ _ . _ _ _ , _ _ _ _ _ _

4

.l~ . .

l. e j j p _ .,

4 l .. .. .s_ _

q_

j

/

/, ; -~ . N' l

.~

. e. .

.....n.

1  ; i . - : . .- - -

l 7

d..

4- ,

s e

. . .a 8

- . i.. . .

',L-

>

• 4

.L

.d. __{ .j... l. . ..;.. .

g

. ;.4 .1

/- . . . . b..

4 -*

. . , .I 4-

. .b J.

s s 4 i i .

.. 3 .

4 . . .

-*t. *r - . s

.j..-[

" - t- * "."**-- . ' ' - -

.i,..p'!..*

,4..

.- 4. . y. ,; .

q, - , ,

, j

. . 4

.a e. .

e..e 4 .._+a-..--.r -

. It . 3 ,

I *

. *l i . . I I  !-

l ._h _. k E ?.

• '.. ! ' ..*. *. -?- *  : .- - - - .

' .:J r-

.-* .; .. . . --":. . . .: -*_: .... .. 1. -  :.:: .. .

.. j- - -

s . . :_ LT.'

.. .U. .

2 . - .. :. Q-

. . ~ . .

u

_ .... 4 . ...I....

. .. g a ~~...

. . . . .. ~ . . ~. . ... . . . . .. -

. ...._. _n. -. ..4.-..-...

. q ... ... .. .. .,c g

.r.,, .y.. .-. . ... .

. . - ,. - . . ... . . . . .. . .. _ .. ~~ , . 3

. . }; < , , .- .-b. . , , , C

. c .. . .

q$a -.

. . . .. > . .. .. _ _ . .. . - . 10 . { .. . . . . . . . ~

-1 N Q

O

. g.i i 6

."."'%.. l . L

.r-s . J  : n ,

n . , s m

p i

t - - : . 2 i ,

A

. t h

.l * " i .! .

I.. * . } . .

g 1

- n.w LJ  % .2 4 .;. W

_ t .; .,, ,

?

- 4.J p.- 4 ,.4 .~ .t' i'*. , nn. ,

e s

s . . I . ,

, x y

.- r- i F. -2  ;. -m..... .s. .u. . . a.

.. 4

. W. . _:

4 i.~. i. .i. . .-- . .

.4 ,

4 ..

.,,r

. v :, .----l

,e v , r- .s . . :s m t sy - - .r. p ; q - F "-- : 1's :r-~ - - 1 ' *.

g

-_..r.

..:. .::.u. -

.. . . . :. r... r n. t~ :.: =_. a..'. -.- .._1.

. . . , .. _ .c. .-  :.~4.2  :: :.. . . .

g

• • = -

a L. .-~  : . :~; :. }. : 7:* ~. . .~  :::.7 --  :; ; :,.' 1:.;'. *C

_. f- --~."= t r r^- -

- . - 1, - - . . . - -:.:- _.::.1. . --.=........ .. ._ - . .a= c

.3

._.._--j_. ..

.. .y.. ._  : . _-. .. .

. n

_. - - . . _.. U

. _. .. .. j .. - 4 m 4

~

... 6. ... . - . ~ .- - . ~ . - -

3

.. . .4 4a. {.. .' . _- . . .

..--..4..~--. y.. % a r~u a t...;

L

j ._

Q Q.J. - y  ;

N r

M 4 t- .3 . a 9- ._ .

. . w.. .. u -. a

. p. .: -. .- . :.. i n. p . . _. .- : . :- .

t. ...-- --

m.

.. .=,

y. .:_c a

.'. - ai4 :y J~. !- .- . .

[- l.

l

%~ .

U g

/

.j..--g 3'

M* g * .., .g 4 . .

g . . . g .y

.j- - e,p-w - . . ..w-*

.." .o

• * - -- - r

. - s .pe.

s r-. -.1

.l. ....e-e6-.-. b. ,- -

..e J.

g

/

. , s -- ., . L. .--:'

• 2 3- ..: i . .

. d . - : .: . . '

1

-* I**"*- .-- ; 4==='M _ . . = = - - ' * - - " = * - S= f**

.-- " .'*.i* . r~ 7 .h.1..J *. s 4.'

. * * - - . - - - - -"'""T . ** - . * * * ' **

m y .

_a

.. i i

p. . . n .- .: 1 - .M.g i L ,3.:. ;. --j f.; a-,u : . . . , , , 4: ,:

- 2 ,u -

-...--- . .-d

. _. .. . .. . . . . 6..-~.

. :8 ...._._.. .. L. .. .. _ .. ... .

. . . .. . . . N._. .

. .:- u

.q .

.. . .. . . . 4. .

J..... _ .. . . . _ . . . . . . . ..... . . . . .e==

.h.

e.. . . . . 9

,. . . .. .. , . . ...e-*..

..e

,. ....g

....1.

. .. . . . , . . .e -. . .. .. . .. 9.

V8

..i....- ... .-

. .m. ... . - . .

. ... , . , .a

.e .. y _..,. 0 0 2

.q

_ ._;. 4 h g

M.j

- - .~ .. -

.2

. . _ . L p .c I.a I

.,e e. x 4.J.

.a..

m -'P re. . , * = * = * . ,-

J.

CQ

_{ -r" ua - ' e a

.e t , -

,. - s a r 4- 4 ._g. 7

$ s 2 ei . -)... -f a 4L: ( .: .i. .--- , . ~ . . -ru i * . L

.i 1 -i d i -

- - j - _--  :{  ;- G

. . .s_.. .

4 .- + r 4- r .- _ "m .

'*"h ""'! h.

+

' * ~ * *.I [ - ' --- * " * ' " a *a f . .-

- ...* * , *- ! *1 f * * " ' "

.;^" *-

.N y .U

-.-J...;.J......_' *

.'. w ; a . , . . . < '  !  :- .: . . L. : ._g g .J 3

4 t 1 .

i= . . . . .. -

. . : - * ..J-+.4, 2 -

g.

.'D i -

' : - g g g

.,h *-

} , ,t _. O .h e."

s.

. f, 9

4

• l

,, j . ,-.

L

. .4*. . , .g .

. M .. .

T.. .

y p

. . ~

'. 7.-f. af g .

. .f*.4 . zi. . ~ .a. .

. T. j 1.. ;. ;.

. . . y, v O-

- ........ . .2.-  : ... . : -

a' "g . , .

. :.: -. .n.

.m -u..

.. .n.-

1,. 8

.s h O. . . - .

r---

. : =. 2..

.. ..:.1 .-

4

.c .

[

W.i.... . .

t..... w

. .. = .. ... .,.. . . _..,..,.$- . y. . . e... ..

.e.

a

..-.--.~ .._.-

.. i..

. i

. . . . ~. .. . . , .

.a. - - . ..r . g . . .. , b.* .

.I.

. s O, ..- g. l n

, i .

. . .. . y . _ . -

r .. . . .

G (N _ _ o%. g, y._. .. ._ .

j.._._._..

.m

_, i t 7

't' i t h . .1 $ v . l .g.,- i s j -

Q. .

L.

7 , . .. j

. u m. - .  : g

' " * * ~ * '

. I * *I - ' '*!.*

f ._] _

. . s . . . .

j .

• P - ? - e ****f- .F, b*=E. b - P. ar r.* == *d. - f.-*++-* i**"'"-f...* * * ' - * * - * '."4* ***,N.

f*

- , . s ,

.g -

e -*****-b-4.-t**=*'**-.-a--=='"-""-t,'..- . ,

J E

• e *

a &..

u**'

e

^*

i g-e .

. ~

O _b. l i

g..

b 5 . . . . . ; . . 3 1 g

{- <

._. ; . - =

.t; . ..: . ;

a.-

.-- ..: ..:w=.....-

)  : .: ~ ,

.a.x , - , . . .:_3: . .. . =. a .. , .

=.s a. _. .i . . . .u a. .. . . ..

. .. . ... t.=.

+ .-. . . d

. . ... ..' ..".I/,"...

. .. . . / .~ .. .- e=.~..

. -.i.... .....L- 4. - . s .

~~..'J..-

.-p_.. __..p._... ---.....t....

. ....r _ . . .

j ..

l .w

...L,..

- - j

.-4 r_..-. .. . . ~I--

- - - . - .-...A.- .

y , _

-41

$' r .

(. h . .I-

..jg ,

n...

9.. o _ . . . _ . . ._ _ m _ ..;..J _ .a i _ . . . g __ .i L_J_ . _.. o .J e ... _ . _. _ . . _ _ - :_._ .. - FIGi. -Comparison ~ opt.N taximudrFa. .gue Crack-Grfwth'fdr V. '

" ~' ~

DeiiUE.Cind'itiims~i{ith._T.hatJot A HypotEitWicaEstre s _

Ohich_Would,seReqQred..To_Causelipe.!Eai16de'_InJ200 87 ._.i- -. H s

(.kg) .

-- H fi 7 t- ! l- ,8- ",._...m

,-- -c .( l ; * , * ~ -

• ',---__1..--

e - ,. .: . _ . i m;. t - m .~ e *

,iI  :.

,s.

. .t  ?-- s- - -- .

A .= j, f :, - ..

, r .i . ..

~,.; d y. ..1-M 4 q~ j . .

A '. :

~. E~ 0 W Ii O ICY' Y2' . ! ~; 5 I

'550 l 'l l' * * - 'H " I ~ ki 232~ . . '---- ,..E':- - EN ~

2..-  : =.v:  :::: = =.: --

.u.~..

.t. . ... -..s: ..

.~

_. ;. :..a .: :.. . ..

- L_. .. -.. .; :

.=:.:=.'i........

..I .- .

.. .- .9 . . . , _ .. . . . .

.. . . l.. .... ... ... ... .. . . . . . ,

....... . 1 ... ..

. . . ., . i /

, . . . . 4.:

. . . . . ,.~.l.

f

.. j..w H 1....

}.. j s) ]. ' / - - - - -

t V- '

l_ I 9 .. . . * ._;, . - '

f 8.. =.G,_,-.,_, ,- , j i , -2 .. -/- t . 2

.r. i -

2

. 7 . - r

- Q -i - - rr .j .1' 4 J r. : m ..: - _ :Q 4. /- l 6.

.r!- a.*  :::- y F-- :-- -: 1- :L  : " .p . .t  !-i i- L

__ 4..

- - f/-. v

- 6 m . .: .--t;j

5. . . -

, , N i" N ' .' ddW ,,.

h4 m, ,. , i . F ' . T- h -"~ . . c

~-""~,1~.

--t ~~.' 4 v-- ~- _Wr ~ g-%~ _ . 34--8 .i . . i:. ca 1

~ p/. + - - L '

• -~1

---.~,,t.-

' 6- .

. 'm :. w' '

• 2- - - - ,:..---1.-;= - 4 . .= . .r.

..- - . . - . . . w i ..  :- ,,-

~ .

t

r y e- zt.=-

~s .

3, .7 = -M-i F-- * - -f-!;i :==T== M- :i - q-6. .- 4 J W: h.1 5 *- I 2-

'.r.O

---.. . 4 Q+ r -.M == -=...-:-~~ .::.

- ~

.M: - - - f/ . ~.u-=. : } : .=. -- r -: =-- =. : a N .  :.  :.  :. -. =

- .= ..:  :=.  : p- =. . - -I e ._.__,____._=..=..._.=.=....g e

W. . . . 2. . .

...t.,-...

.=._,...w--- . . . . . . . , . ..l,.... ,

, ....s f ,,  ;..... .,

t., ;. -.

/ . - . . - . . . .

._....y. .,.. .. . . J.f_ g y g. p g-4,. . . . ..1._./..,.._.._...., _.,..

......-~~- ,..

.._9{ .. .

k,.

O~ 56 /.. - - i..-

.-.-- . { . -- _.. - ,- . ...

i..7 . .% .. .( ..  ! .. j . . . t f. ,[ . . _

9. .

. _ . ..m,. .

. .;._N. .J

.jp F /. ' ,_ ?

__i

. .~ ;_' -

..-  ! f.

g, - . , .

' C l /j  ;~}f -

6  !~ --

b i-

7. ) +

- .. ,; - 4 . . f; i . . . .i:

,,, L - Gi-m. . 4 ,;

s. [_g r . . c _ . % ; .: . - y .-j. f . wje ei_ - ; . _ _ _ .. j - i q 4 y .L,

.m .

-[94'..

- .9 7

.. :.j p.4_ . ,_M-; - - -,

-h J /.j  :.- q . -.:_

• r .l .. . _. - .-i . . - 4. 4 ;- ~

/ ,_m s... . _ . ,

. . j  ! ,.: z. a.

\

....r-

. 2,. i a. . : -

,/5

. ,a

, =..

/

j . . , . - .. ,-

., . .. _ .... .3 s ..

1 j 3

-r . !.{ . r t.: . .. :_ .: M. r : .. --L-) . u. '.  ;

NJ - :: ..~.:--: . .l:_u:

,m r-;.h' 1 .. iA.: MX:-  ::

- ~

T.N --

T. - -  :-

'+.4sq W4  ?-m-- =.

='~ .  ;

h.i.=. . .. .::--  :  :  : L  ?-% .  :.:..  :  : .l

_w.: J '= , == = L=. +:.^ .  : _ r:

\ r - r j

2;-

.~. _~. . T- 1.ii_.{..=.~.M. , FI-~--1=_ =J.I.._R 3 22 ~ ; i . E_E_' ._mO.~ .. . ._i H-_. .=. iW 7a .--I.

.. ri-E.

1. _ . . - 4_ . _ . . _ _ . . .

m _. .

> ._4_.

._u.-._...

.._.L._..__a_..._..

5 ..-.._..

.. 1,. . . ...

3._ _._

+.___,L._... _.

, - ' . ,y -

Q5~ - e

, '91. a 1 -  ;-.

Q~L .h;, _O- . :.

_ . - .r: . n .,. - _,m.c-

' -f - =

-*'. .. / m=_. n__

,, s. - . . 'o. : :. . , . . /. , , e'- v ..

w, 0*

,[ T'"NTi b ./-i.=r: .-----i> - --

- lit N-N @ L v .:m= . - -r- ...e  : /

M ,.

. .;.. ' p - e 2 -:-- : g.: . . 2. p-: . . m. -e .-f f.: -*

o .. .

e__m.......-._.--,.- .

q . F "-r i . . . - *, -. ~. "-- :

r - /- -

. .- + :- . .-- y. e

. ..+ ..._.t_.____s f gra,iy w.. - .. . a g ,

su r. ._ _ 1 ,_ ;

..t4-

.n.g  ; - - .

+

4

. g.m ._

t

,  ; : - .w- . '~~ 3~h: ,( _ ,

Ed ' ' ' .' . ... . . . . . ... ., -: m.. ._. .s..r. .nj- . A , u.,y y

,w __.

.._-._..t.

p". -

... - .g& .-*-

-: : m: . r: .

9 a

• 1

..... .- ::- . .. * ---. L: . . . . .

7,01kn-n

~

• t- . . --

.u n . ; ,

=: . . .

..L..=

-t- . . .

.n --

u .;.. , ,

I  !' j t

j t'

. U.J  ;. - i-7 j

Z .! ...

,. , $_5.... . . . .

4 .. . { . , ,

, . . . . . _ . . . _ . . . . + _;__

r-

.. . _r. .

._ _.g=

1

< . I - t t . - -t

• ? t - .

6 '

i

/

. l.

- I -

I .

3 ._ _

e ,----~.,.. . . - - - - . - . .- .-s

-a. p .,' ,Qj. .

j. g .. .. .-, . j -._- .__

4.

I d- Z

.---_ l :_..

.L. al_1 i 4.5._ ]:T i.; -}.:' .; +-f. ,..._!.* .

~

.i ) .1__ [ t (; -

i i s.

.y sm N. .

1 ..

-1 t..l.. 1 . - -

~'L , _.. _ :.:.:... _. - .

(' :WM

- - ~

t

' . N i 5 i Y E =i" l --

\ v ]'

. . g. ,_. q,_

...-._).

. . -. I . 5

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

.9... . ,

n ..e .2

. .: . .. n. . : . s

...~...

-..t..

. . . . . . ~ . _

. .. J ..._!.. . _

.. g . . g . g

.._ .j ..4.,..., g... .q- ,g g

..., - h.- .

I,

../Q /00

/ 2 '9 b 0 (0 ^

log Crwis, Al .

. . - - - . , ,.,-g .

y +a - .a 4 -