Text

Forwards Draft Safety Evaluation of SEP Topic III.5.A, Effects of Pipe Break on Structures,Sys & Components Inside Containment. Recommends Util Utilize Guidance Provided in Encl 2 to Resolve Open Items
	ML18046B128
Person / Time
Site:	Palisades
Issue date:	12/04/1981
From:	Crutchfield D; Office of Nuclear Reactor Regulation
To:	Hoffman D; CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.)
References
	TASK-03-05.A, TASK-3-5.A, TASK-RR LSO5-81-12-015, LSO5-81-12-15, NUDOCS 8112100255
	Download: ML18046B128 (39)
	v • d • e

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Docket No. 50-255 LS05 l 2-0l 5:

Mr. David P. Hoffman Nuclear Licensing Administrator Consumers Power Company 1945 H. Parnall Road Jackson, Michigan 49201

Dear Mr. Hoffman:

December 4, 1 981

SUBJECT:

PALISADES - SEP TOPIC III-5.A, EFFECTS OF PIPE BREAK ON STRUCTURES, SYSTEMS AND COMPONENTS INSIDE CONTAINMENT Enclosed is our draft safety evaluation of SEP Topic III-5.A. This assessment compares your facility with the criteria currently used by the regulatory staff for licensing new facilities. Please inform us if your as-built facility differs from the 1 icensing basis assumed in our assessment within 30 days of receipt of this letter.

This eva 1 uation wi 11 be a basic input to the integrated safety assessment for your facility unless you identify changes needed to reflect the as-built con-ditions at your facility. This assessment may be revised in the future if your facility design is changed or if NRC criteria relating to this subject is modified before the integrated assessment is completed.

As noted in Enclosure 1, we require additional information to complete our review.

We have provided, in Enclosure 2!t guidance for resolution of open items identified in the safety evaluation.

Please provide your schedule for supplying the requested information within 30 days of receipt of this letter.

The reporting and/or recordkeeping requirements contained in this letter affect fewer than ten respondents; therefore, OMB clearance is not required under P.L.96-511.

ll~J.- (. f'111eho. lL s

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S. f'aw J.1 c K '

R. r.'.3CSJ'\\o..t<'

Dennis M. Crutchfield, Chief S£tJ.t/

Operating Reactors Branch No. 5 Sd, PGIA. et.P'E ISi {r;.4-)

Division of Licensing

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Enclosure:

rs112100255 s11204" 1!t:

As stated i PDR ADOCK 05000255'

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P PDR' cc w/enclosures:

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Sincerely, OFFICE~ ***** ~.~.e.. ~./!.v?}.

EMcKENNA:dp SURNAME~ ********* ;., ************

. __ 11 /81;:) /81 DATE~ ****************.. ******

NRC FORM 318 (10-80) NRCM 0240 OFF.ICIAL RECORD COPY

' USGPO: 1,81-335-960

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Mr. David P. *H.offman

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M. I. Miller, Esquire*. :.

Isham, Lincoln &-Beale'-_:::

Suite 4200 On~ First National Pl~za Chicago, Illinois. 60670:

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Mr. Paul A. Perry,*secretary Consumers Power Company 212 West Michigan Avenu~

Jackson, Michigan 49201 Judd L. Bacon, Esquire. _

Consumers Power Company

212 West Michigan Avenue Jackson, Michigan 49201 Myron M. Cherry, Esquire Suite 4501 One IBM Plaza Chicago, Illinois 60611 Ms. Mary P. Sinclair Great Lakes Energy Alliance 5711 Summerset Drive Midland, Michigan 48640 Kalamazoo Public Library 315 South Rose Street Kalamazoo, Michigan 49006

Township Supervisor Covert Township Route 1, Box 10 -

Van Buren County, Michigan Office of the Governor (2)

Room 1 ~Capitol Building*

Lansing,-Michigan 48913 William J. Scanlon, Esquire 2034 Pauline Boulevard Ann Arbor, Michigan 48103 Palisades Plant ATTN:

Mr. Robert Montross

~

Plant Manager Covert, Michi~an 49043 49043

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.. PALISADES.

.. * *_ ":* Docket No. 50-255

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EIS COORDINATOR

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230 South Dearborn Street

Chicago, _I~linois. 60604 *

Charles Bechhoef er, Esq*., Chairman Atomic Safety and Licensing Board Panel

U. s*. Nuclear ReguUtory Commission,:

Wqshington, O. C.

20555 *-:.-.

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Dr. George C. Anderson Department of Oceanography*

Unive~sity of Washington Seattle, Washington 981~5

Dr. M *. Stanley Livingston

1005 Calle Largo Santa Fe, New Mexico 87501 Resident Inspector c/o U. S. NRC Palisades Plant Route 2, P. O. Box 155 Covert, Mich1gan 49043

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*e TABLE OF CONTENTS..

Enclosure.1:

EVALUATION OF EFFECTS OF PIPE *BREAK ON SYSTEMS, STRUCTURES AND COMPONENTS INSIDE CONTAINMENT,* TOPIC :III-5.A, "FOR THE PALISADES NUCLEAR POWER PLANT I.

INTRODUCTION II.

REVIEW CRITERIA III.

RELATED SAFETY TOPICS AND INTERFACES IV.

REVIEW GUIDELINES V.

EVALUATION A.

BACKGROUND B.

REVIEW CRITERIA USED ON THE PALISADES NUCLEAR STATION

1.

HiGH ENERGY SYSTEMS

. 2.

PIPE BREAK LOCATION AND TYPE

/

a.

MECHANISTIG.APPROACH.

b..

EFFECTS ORIENTED APPROACH

-~;--,.~-

3.

PIPE WHIP AND JET IMPINGEMENT

a.

CRITERIA FOR JET THRUST AND JET IMPINGEMENT LOADS

b.

CRITERIA FOR PIPE WHIP ANALYSIS

c.

FINDINGS OF EVALUATIONS VI.

CONCLUSION

1.

STRUCTURE EVALUATIONS

2.

SYSTEM INTERACTION EVALUAT.IONS 3.. LICENSEE 1 s RECOMMENDATION FOR RESOLUTION OF UNRESOLVED PIPE BREAK LOCATIONS :

GUIDANCE FOR RESOLUTION OF OPEN ITEMS FOR TOPICS III~S.A AND III-5.B FOR THE PALISADES

Attactrnent - Guidance for Resolution of High Energy Pipe Break Locations.Where Remedial Modifications Appendix 1 - Alternativ.e Safety Assessemtn for Selected High Energy Pipe Break Location:s*-ut SEP *Fac;lHd~s

- *-----*-*=-

-- -Append1x**-2~~E-s"t1mai'lori.. *ar-~i"tr*e*s-5:*rn*t~-nsTt:Y-~Factorscanci"the- **----------*-

crack* opening Area of a Circumferential and a

Longitudinal Through-crack in a pipe.*

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EVALUATION OF EFFECTS OF PIPE BREAK ON STRUCTURES,

-e SYSTEMS AND COMPONENTS INSIDE CONTAINMENT

- TOPIC II I-5.A FOR THE PALISADES-NUCLEAR POWER PLANT

JI(' J e*

SYSTEMATIC EVALUATION **PROGRAM.

TOPIC III.:.5.A PALISADES-.

I.

INTRODUCTION The safety obj-ective of Systematic. Evaluation Program (SEP) Topic III-5.A, 11 Effects of Pipe Break on Structures, Systems and Components Inside Containment," is to assure that pipe breaks would not cause the loss of needed function of 11 safety-related 11 systems, structures and components and to assure that the plant can be safely shutdown in the event of such breaks.

The needed functions of 11safety-related 11 systems are those

. functions required to mitigate the effects of the pipe break and safely shutdown the reactor plant.

II.

REVIEW CRITERIA General Design Criteria 4 (Appendix A to 10 CFR Part 50) requires in part that structures, systems and components important to safety be appropriately protected against dynamic effects,*such as pipe whip and discha:r-ging fluids, that may: result from equipment fa i 1 ures.

Regulatory Guide-l.46,.

11 Protection Against *Pipe Whip Inside Containment 11 provides an acceptable basis for selecting break 1 ocations and orientati ans for assessing pipe whip consequences.

The current criteria.for-review of pipe breaks inside containment are contained in Standard Review Plan 3.6.2, 11Determination of Break Lotations and Dynamic Effects Associated with the Postulated Rupture of Piping, 11 including its attached Branch Technical Position, Mechanical Engineering Branch* 3-1 (BTP MEB 3-1).

III.

Attachment:

"SYSTEMATIC EVALUATION PROGRAM_ HIGH ENERGY LINE BREAKS INSIDE CONTAINMENT, PALISADES NUCLEAR STATION

SUMMARY

REPORT.

11 Prepared by EDS Nuclear Inc., July.1981.

2.

Letter from D. L. Ai emann to D.

B'ix~l dated January 11, 1 979, "PIPE BREAKS I'NSIDE CONTAINMENT FOR THE PALISADES FACILITY".

3.

Draft ANSI Standard N176, "DESIGN BASIS FOR*PROTECTION OF NUCLEAR POWER PLANTS AGAINST EFFECTS OF* POSTULATED PIPE RUPTURE",* November 1978.

4.

EDS _Nuclear Report 0540~001-03, Pro~edures for Evaluating the Structural Response of Piping Targets to Pipe Rupture Loadings, June 1980.

5.

Draft ANSI/ ANS-58. 2, "DESIGN BASIS FOR PROTECTION OF NUCLEAR POWER ---

PLANTS AGAINST EFFECTS OF POSTULATED PIPE RUPTURE, 11 November J,91'8.

i

Enclosure 2

___ -*-*-.. GUI DANCE FOR RESOLUTION OF OPEN ITEMS FOR

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I.

INTRODUCTION Criterion No*. 4 of the Atomic. Energy Commis.sion's General Design Criteria~

as listed in Appendix A of 10 CFR. Part 50, requires in part that structures, systems and components important to *safety be appropriately protected against the dynamic effects, such as pipe whip and jet impingement, of equipment failures.

The plant must be designed *such that the reactor can be shutdown and maintained in a safe shutdwon *condition in the event of a postulated rup_ture of a piping system containing hi.gh energy fluid, up to and including the double-ended rupture of the largest pipe in the reactor coolant systems.

II.

BACKGROUND On July 20, 1978, the Systematic Evaluation Program (SEP) Branch sent a

lett_er to KMC, Inc. {SEP Owners Group) which provided thr~e general approaches that could be used to evaluate the effects of fluid systems breaks inside containment.

The three approaches, as described in Refer-ence 1, are:

1) mechanistic approach

2).effects-oriented appr_oach

3)

~implified mechanistic approach A com bi nation of_ the three approaches was permi ssi bl e if justified.

III..* DISCUSSION As the topic reviews.on pipe break effects continu~d, the need for addi-tional guidance became clear. Using the methodology adopted by the.licensee,..

approximately four hundred break locations inside containment were ident-ified. Considering the effects of the fnteractions, the number with potentially adverse consequences were reduced to approximately two hundred.

Based bn these preliminary results, the staff has determined that supple-mental guidance is desirable for resolution o*f these open items.*

A.

Selectio~ of Break Locaiicins Break locations need only be postulated at welds and structural dis-continuities '{i. e., terminal ends, elbows~ branch connections) rather than at any point along the pipe.

B~eJk 1~c~tjqns_previously_..

selected under an effects-oriented revie~ may be eliminated\\from con-sideration f -f they°-:-do--riotco-nstTt-ute---~ structural -cifs-cori-t.inuity or a we 1 d.

-* ---*--*-------*--. _,/

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e B. *Effects on Plant Shutdown In assessing the effects of the break on plant safety. the mai.n.

objectives are:

a. to maintain a cool able core geometry following any postulated:

break.

b.

to maintain the capability of safe plant*shutdown (definition of safe shutdown consistent with that of safe shutdown reviews).

c. to maintain containment integrity.

The intent of this review should be to* determine if the reactor* can be safely shutdown following a high energy line break considering a single active failure occurring after the passive event (pipe failure). This does not infer that systems beyond those necessary to handle the pipe break and the postulated-active failure must necessarily remain operable.

For instance. if the initiat1ng pipe

-break is not in the *reactor coolant pressure boundary (RCPB) and does not cause a rupture of the RCPB. the review should deterni1ne the ability to safely shutdown the reactor.

In this case operability of systems needed only to mi ti gate a* lo*ss of coolant acci de.11t **woi.11 d-not be required.

-~"'

The following factors should be considered when performing the systems reviews:

(1) components that would limit-loss of fluid. i.e.-. check valves.

etc.;

(2) energy contained in the reservoir. i.e-**. positive displacement pump discharge energy versus stored energy within the reactor coolant pressur~ boundary or within a steam generator;

( 3) redundancy and separation of syst~ms; (4) consideration of non-safety related systems which are unaffected by the event for cooling;

( 5) operator action that could be taken to *mi ti gate the event *.

considering any needed access to the equipment; and (6) other-defined bases *.

c. Resolution of Unacceptable Locations When the potentially unacceptable locations have been culled down by the above methods,. the licensee *can use the following methdology for resolution of the remaining locations: *

(a) demonstrate why corrective measures such *as piping restraints,.

shields or equipment relocation are not practicable; (b) perform a fracture mechanics evaluation_ to show~that the pipe of interest will "leak-before-break" -and. that the leakage will be detected well before a break could occur. Guidance on fracture mechanics evaluation as well as augmented inservice inspection and 1oca1i zed 1 eak detection is prov1 ded in th~-.. _

~

att.achment.

IV.

SUMMARY

Described above are techniques*that may be_. used by the licensee.in the evaluation of the effects of*pipe breaks. This guidance is :intended to supplement the information previously provided in Reference l.

The guidance provided for a "leak-before-break" approach for resolution of.

open items is not to make a determination that the current Regulations are met,. but to ascertain the safety implications in a plant that was designed prior to current r~quirem~nts.

REFERENCE

l. Letter, D. Davis (NRC) to J. McEwen -(KMC, Inc.)

SUBJECT:

Assessment of Postulated Pipe Breaks Inside Containment for SEP plants, dated July 20, 1978:.

I'.

I

GUIDANCE FOR RESOLUTION OF HIGH ENERGY PIPE BREAK LOCATIONS WHERE REMEDIAL MODIFICATIONS*

ARE IMPRAcntAl From the results of reviews conducted to date, the staff has con.eluded that the relocation of equipment or other modiflcations to m_itigate the consequences of some postulated pipe breaks may be impractical due to physical plant configura-tions. Ot'.' other considerations. Therefore, _the staff has determi.ned that for specific locations wh*ere relocation of equipment or other modifications to mitigate consequences of pipe breaks are shown to be impractical, fracture mechanics evaluation of the piping should be performed to determine if unstable ruptures could occur in piping that contained service induced lar~e undetected flaws.

The intent of the guidance provided by the staff is to provide reasonable assurance that the mitigation of pipe breaks are addressed.

The *approach taken is to provide assessment that condition which could lead to a double ended pipe rupture do not exist thereby making it unecessary for high energy pipe break considerations to mitigate effects of a guillotine rupture *. This would be *accomplished using a defense in*depth.approach that is*a combinatfon of augmented inservice.inspection (ISI), local leak detection and fracture mech-anics evaluations. Augmented inservice inspections would* be perfor~4,:..with the goal of detecting and limiting any service induced flaws tQ limits prescribed by the ASME B&PV Code,Section XI, approximately 10% thru wall. Should the flaws go undetected, a local leak detection system would-be provided with the requisite sensitivity to identify leakage from a through crack, either longitudinal or circumferential, of a length of twice the wall thickness for minimum flow rates associated with normal (Level A) operating conditions. Fracture mechanics evaluations would be performed to determine that for a circumferential or longitudinal through crack of four wall thickness subjected to maximum ASME-design code loads (Le~el* D) that:

(1) substantial crack growth does not occur:

(2) local or general plastic collapse (instability) does not occur.

(3) flow through the crack or the effects of.a jet from the crack

does not impair safe sys.tern shutdown.

To provide assurance that a double ended rupture could not occur by unantici-pated loads being applied to a larg~ undetected crack, a-fracture mechanics..

evaluation would be performed to demgnstrate that a.through crack of a length of four times the wall thickness, 90 total circumferential length, or a larger crack if justified for system service experience would remain stable for local

-- -- ~-

fully plastic large deformation bending conditions. The-basis for performance of this more conservative fracture mechanics evaluation to assure a double ended pipe rupture would not occur is as follows:

(1) operating experience has shown that unanticipated and undefined loads in access of design can and do occur in piping systems, i.e., water hannner events have failed piping system *supports.

(2) uncertainty in:

(a) current analysis methods to accurately predict piping loads analysis and (b) prediction of the energy and frequency content of earthquakes and their effect on* piping loads.

(3)

SEP criteria for evaluation of structures and system resistance to postulated earthquake loads depend on global -structural ductility.

This assumption is based on the ability to have load redi-stributions occur. For unflawed piping,. t~e necessary local ducti_lity is cer-tainly provided.

However, for' flawed sections of piping the __ ability to sustain fully plastic behavior without crack instability is required to assure prudently that _local ductility is preserv~d.. _

The details of the guidance for the combined augmented ISI, leak detection and fracture mechanics evaluations are appended as Ap~endix 1:

e*

e*

~ -Ap~endix.1 '_-:.,~~---]

....:..-~ --------*-*-------

ALTERNATIVE SAFETY ASSESSMENT FOR SELECTED HIGA ENERGY PIPE BREAK LOCA110NS

~AT.. SEP_.FACILITIES

This assessment is required only if a LWR high energy piping sys~em (i_.e.,.

275 psi or higher; or 200 F or higher, etc.) is being considered. It is only required, if a postulated double ended pipe break would *impair safe system shutdown by pipe whip (lacking pipe whip co.nstraints) consequenc*es, or by the consequences of the implied leakage or its* jet action. The following guidance is for a safety assessment that may be permitted as an alternative to other system modifications.or alterations for locations where the mitiga-tion of the consequences of high energy pipe break (or leakage) have been shown to be impr:actical.

Guidance for Alternate Safety Assessment The suggested guidance are as follows:

A.

Detectability Requirements Provide a leak detection system to *detect thro~gh-cracks of a length of twice the wall thickness for minimum flow rates associated with nor~l -

(Level A) ASME B&PV Code,operating condition._ -:_B~.:th cir:cumfer:~ntfa-r*a-nd-~:~--

I longitudinal cracks must be considered for all critical break or leak.-------~~***~---

locations. Methods-for estimation of crack opening areas are attached in Appendix 2.Surface roughness... o*f-the cra~-k shoul*d-be considered.

B.

Integrity Requirements (1)

Loads for Which Level Dis Specified (a)

Show that circumferential or longitudinal through-cracks of

four wall thicknesses in *1ength sub:lected to maximum Level D loading conditions do not exhibit substantial mono~onic load-ing crack growth (e.g., staying below J or K by plastic zone*corrected lineaf7elastic fracture ~~cha~ibE methods or a suitable alternative-.

Also assure-that.local or general plastic instability *does not occur for these loading conditions and crack* sizes.

17

-r*or 4t flaws that are calculated to be greater than K Cor JI *" con-sideration will be given to; (1) flaw growth argumentL (2) ~ostulation of small flaws sizes than 4t if justified by leak detection sensitivity.

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(b) *Under conditions in 11B."(1 )

11 show that the flow through the crack and the action of the jet through the crack will not impair safe shutdown of the system.

Acceptable methodology.for the estimation of crack opening area for*a circumferential through crack in a pipe in tension and bending and for longitudinal cracks.subject to internal pressure a re attached.

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(2) - Extreme Conditions to Preclude a Double-Ended Pipe Break Using el as tic-pl as tic fracture-niechani cs or suitable *alternative show that circumferential through-crack*s will remain stable for local fully plastic large-deformation bending conditions under the following addi-tional conditions: *

(a) Fully plastic bending of the cracked s~cti~n is to be assumed.

unless other load limiting* local conditions (such as elbow collapse) dictate maximum bending loads. for all critical

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(b) Assume all system anchors are effective *. To simplify. the analysis, supports may conservatively be considered inoperative.

If supports are included, cons1deration should 'be given to the adequacy of the suppo.rt to resist 'large loads.

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(c)_ Other as built displacement limits or constraints may be assumed as especially _justified (such as displacement limits of a pipe running through a hole in a sufficiently strong concrete wall or floor. etc. )

0 (d)

Assume a through-crack size of 4t or 90 total circumferential length whichever is greater; or a larger crack only if especially justified.

(e}

Assu:me large deformations means def_ormations proceeding to as built displacement limits or other especially justified li.mits.

(3)

Materia~ -Properties

conservative material pr.operties. should be used in the analyses.

Sufficient ju~tification 1111st be provided for the properties. both weldment and base metal. used in the analyses.

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Subcri~ical Crack Development Consideration should be given to the types of subcritical cracks which may be developed at all locations* associated with this type of analysis.

From prior experience and/or di rec:t analysis it should be sho\\in that:

(1) there is a positive tendency to develop through-wall cracks.

(2) if there is a tendency to develop long surface cracks in_ addition.

to through-wall cracks. then it should be further demonstrated that the long surface crack will remain sufficiently shallow.

D.

Augmented Inservice Inspection Piping system locations for ~hich corrective measures are not practicable should be inspected volumetrically in accordance with ASME Code. *Section XI for a Class l system regardless of actual system ~lassifi.cation.

Acknowledgement f

Assistance in developing this guidance have been provided by Dr. Paul* C.-Paris.

Del Research Corporation (and *washington* University. St. Louis. MO) under sub-contract K-8195 in support of technical assistance provided* by Idaho -~~tiona1*

Engineering Laboratory. Idaho Falls. Idaho (FIN A.;,.6456).

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ESTIMATION OF STRESS INTENSITY FACTORS AND THE CRACK OPENING

~*

Introduction AREA OF A CIRCUMFERENTIAL AND A LONGITUDINAL THROUGH-CRACK IN A. PIPE

-. by.

H. Tada and P. Paris Del Research Corporation St. Louis, Missouri Formulas for estimating the crack opening area are developed for a c1rcumferential and a longitudinal through-crack in a pipe subjected to severa 1 types of.1 oadi ng.

For the ci rcumfere.nti al crack, estimation for-mulas are presented for axial force and be.nding moment applied to-the pipe far from the cracked section and.for internal "~pressure -loading. _J>:.or-the longitudinal crack, an estimation formula for th.e _case of internal pres-sure is presented.

Estimation is based on the method of linear elastic fracture mechanics, which requires the knowledge of the solution of stress intensity factor, K, for each problem.

For the internal pressure loading, K-solutions are readily available for both circumferential and longitudinal cracks as func-tions of a single geometric parameter, A(= a//Rt), relating crack size and pi'pe geometry.

Consequently, the crack opening area fonnulas are al so formulated as functfons of this single parameter.. For _the case of tension and bending of circumferential crack, however, the stress intensity factors are not formulated as fµnctions of a sin~le parameter and no simple formula is readily available. Therefore, in this discussion, a typical value of

mean radius to thickness ratio, R/t = 10, is specifically_ selected and for-mulatfon is made for this value.

Estimation formulas are expected to yielc:I'.

a slight overestimate for. R/t = 10.

For smaller R/t ~atios, degree.of overestimate would increase.

The formulas )resented here may* be used with a reason.able accuracy when R/t ratio is about 10.

Formulas.for the c.rack*

opening for these cases are not available in simple closed forms, but here*

moderately long power series approximations based directly on the estimating

. formulas for K are given.

A Circumferential Through~Crack in Tension and Bendfng The K formulas are first deve 1 oped here based on the.results recently obtained by Sanders [l, 2].

As stated above,.,.the* K solutions for-these-

-~~-

loadings are not expressed as functions of a single geometric parameter..

Sanders presented approximate formulas for the energy release rate for these loadings, which a re readily converted i.nto K formulas.

The formulas are, in essence, functions of two geometric pa.ramet~rs for given elastic constants, which may be written in.either of the following forms:

or K = er h (Re ) F (I., e ).

R K = er/ir(Re) F(e,t)

(1) where er is ~n applied stress, 2Re is the total circumferential length of through-crack.

e*

In this discussion, e and R/t are chosen as geometric parameters ana

~*

the second form of Eq.(1) is employed for the stress intensity expression.

Approximate K. formulas and the subsequent *estimation _formulas for *the crack opening areas are developed spec-ifically *for R/t = lQ, whi~h is_ con..:

. sidered to be a typical value of interest in the present study.. That is, the function F ( e*) in the subsequent discussion represents F ( e, 10).

Let P and M be the axial tensile force and bending moment, respec-tive~y, applied to the pipe far from the crack location and let subscripts

t. and b represent respectively tension and bending.

The nominal stresses o*

due to tension and bending are defined by p

0 t *= 21TRt

- -?--;??"

(2)

M a

= --

b if R2t The stress intensity facto.rs are expressed in the following forms.

(3)

where* Ft(e) and *Fb(e} are* non-dimensional functions.* The numerical.. values of the functions Ft(e}

and Fb(e) are calcu.lated from Sanders' approximate formulas for R/t = 10, which.are tabulated as follows.

I v

' e

(:f~;.rr (Ft(e) and Fb (e) for R/t = 10)

~

e Ft(e)

Fb (e) oo 1.000 1.000 9

1.039 1.037 18 1.151 1.140 27

1. 314 1.278 36 1.505 1.425 45

1. 725 1.580 54 1:987

1. 747 63 2.305 1.934 72 2.702 2.154 I

81 3.209

2.406 90

. 3.872 2.760 99 4.764 3.209

- ~7;..-=--

108 6.003 3.827 These values repres-ent slight overestimates of Ft (e) and Fb(e) [1,2].

The following approximate expressions of the functions Ft(e) and Fb(e) represent the values of the table with a reasonable a,ccuracy (within a few percent).

3/2 5/2 7/2 Ft(e) = 1. + 7. 5( 8'1T)

... 15{~-) + 33(!)

'1T

'1T.

(4) e 3/2.

e s/2 7/2 Fb(e) = 1 + 6.8(:;)

- 13.6(:;}

+ 20(;).

(0< 9< 100°}

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. When the pipe is subjected to axial force and bending moment at the same time, the total stress intensity facto.r is obtained simply by super-*

position of these separate factqr~.

(5)

The crack opening areas due to tension and bending, At and Ab, may be conveniently expressed in the following form.

(6) where E* is the Young's modulus, and It(e) and Ib(e) are non-dimensional functions.

The crack opening ~rea for the tensile loading, At' is obtianed by energy method (Castigli~no's theorem) as follows:

1 out e

K. 2 A = - -

= 2S (_t* )Rde t

t oat 0 oat E

since

2.

1 aut Kt G=---=-

Rt ae E

where ut is the total strain energy i~ the cra~ked pipe.

Combining Eqs. (3), (6) and (7), the functions It(e) is obtained as follows:

(7)

(8)

~.

i.-

,..'}

\\' '

( 9) 1.

Substituting Ft_(e) given by Eq. (4), It(e) is written as*

[

3/2

. 2 It(e) = 2e 2 1 + <!)

{8.6.- 13.3(!) + 24(!) }

+ (!)

3122.s - 75(!) *+ 2os.1(i) 2

. n*l 1T 1T (10)

(O < e < 100°)

I The crack opening are~ for bendi_ng l cad, Ab, however, can not be~ obtained as readily because the "crack-absent stress distribution" is not uniform -

along the crack (direct application of the energy method is difficu_lt).

Therefore, Ab or Ib(e) _will be estimated in the following way.

First, comparison of the crack abs~nt stress distributions for tensile

~nd bending loads, the following bounds are im~ose~ on Ab:

or

( 11)

Where Ab(ab) is the _crack opening area by bending," and At(ot = abcose*) and At(ab = ab) are the crack opening area due to axial force with tension stress ab' respectively.

The first approxfmation would be to take the

')

. *;.\\

average unifonn stress between these extremes and II.

)

.1 + cose) e 2

Ab(ob

~ At(ob.. 2

. = At(ob(cos !) )

or (12)

Ib(e) = (cos ~/rt(-e)

Since the function Ib(e) given by Eq. (12) may yield underestimated values of the crack opening by bending, the stre'ss intensity factor~s Kt and Kb are compared in a similar manner.

Corresponding to Eq. (11), it is obvious that or

( 13).

(cose)Ft(e) < Fb(e) <.f t(e)

Averaging the extremes

(14)

. Comparison of the numerical values of Ft{e)

~nd Fb(e), however, shows that Eq. (14) always underestimates

~b(e) and that the va\\ues of Fb(e) lie be-tween* the following two bounds (15)

Therefore, taking the following expression for Ib(e) instead of Eq. (14),

*.e the risk of excessive underestimation of the crack opening.area caused by ':

bending load may be avoided

. 2 1 + {cos ~).

3 + cose

=

2 It(e) ~

4 It(e)

(16) where It(e) is given by Eq. (10).

The total crack opening area caused by axial tension and bending can be written as

~ ;t (,R2)It(ei[1 +/~3 \\cose~

or (17)

The effect of the yfelding near the crack tip may be incorporated by the customary method of plastic zone corrections in which e in these fonnulas is replaced by eeff" eeff is obtained by using.

9eff = 0 +

2 Kto.tal 2*

2~Rcry (18) for plane stress (maximum) plastic corrections, Repeated iterative proce-dures may be necessary for obtaining eeff"

c '.

~

~

. \\)

t e*

Circumferential.Through-Crack.Subjected to Internal Pressure

~*

For a pipe subjected to internal pressure, p, the membrane stress, a, in the axial direction is estimated by a=l£B.

2 t

{19)

The stress intensity factor for a circumferential through-crack is normally expressed in the following form.

{20) where 2a = 2Re is the total circumferential length of the crack, F (A} is

. P-"-*--

nondimensional function of A = a//Rt and the s~bscri.pt p repfl!~ents pres-sure loading.

Contrary 'to the cases of axial force and bending load, the geo-metric factor FP(A) for this case is a function of a single geometric para-meter as mentioned earlier.

The following fonnula empirically. represents the curve of Fp(A) presented in Rooke-Cartwright's work [_3]..

The approximate *formula is, for convenience, expressed in a form consistent with the fonnula for longitudinal crack which J;J will _be subsequently discussed*. *Accuracy of the formula is within a ~ew per-cent over the rang~ specified.

where A =

a/ v'Rt *

. 2 ih

= (1 + 0.3225). )

= 0.*9 + 0. 25A

{O~A~l).

(1. ~A~ 5)

(21)

I*

i' Apply1ng the energy method again, ~he crack opening area, AP, is

~*

readily obtained as follows A = £.. (2'1TRt) p E

(22) where GP(A) is given by an integral Corresponding to Eq. (21), GP(l) i~ evaluated as*

I 2

4

= A* + 0.16:\\

2

-~3.

- 4

= 0.02 + 0.81A + 0.30A

+ 0.03:\\.

( 1 ~,;~-~ *5 }

{O< A< 1)

(23)

The effect of yielding near the crack tip may be similarly incorporated using the effective {plastic zone corrected) crack size which is calculated from the iterative relation (24)

Longitudinal Through-Crack Subjected to Internal Pressure For a pipe subjected to internal pressure, p, the hoop stress, d, is estimated by

. a = ~

(25)

~*:*

I

(' *.. ~

e-. 't'/ j,

'~'.(

e*

The st.ress intensity factor for a longitudinal throu.gh-crack of length 2a is given by K = o&*F(A.).

(26) where again A. = a/ /Rt.

The geometric factor F(A.) can be empirically*expressedover~the range of interest by 2 1/2

= (1 + 1.25A. )

~-: {27)

(1~ A.~5)

Eq. (27) *provides a good approximation for the she11 factor F(A.) with accuracy of the order of one percent [3' 4, 5, 6].

The crack opening area, A, can be obtained by the method in the previous discussion.

A = a* (2wRt}*G(A.}

E (28) where G(A.) corre~pondin~ to Eq', (27) is given* by *.

(O< A.< 1)

.. (29)

= 0.14- + 0.36A.2 +. 0.72A. 3 + 0.405A.4 (1 < A.< 5(

Iteration with a plastic zone correction* similar to' Eq.(24} can be* applied to account-for the yielding effect near the crack tip.

References

[l]

J. L. Sanders, Jr., "Ci rcumferenti a 1. Through-Cracks in. Cylindrical

Shells Under Tension, "to-be published in Journal of Applied Mechanics.

[2].

J. L. Sanders, Jr., Under Bending, Private Communication, November,.1981.

[3]

D. P. Rooke and D. J. Cartwright, "Compendium of Stress Intensity Factors, 11 Her Majesty's Stationary Office,.London, 1976. * *

[4]

F. S. Folias, "An Axial Cra,ck in a Pressurized Cylinqrical Shell, 11 Int. J. of Fracture Mechanics, Vol. 1, 1965, pp. 104-113..

I

[SJ F. Erdogan and J. J.. Kibler,.Cylindrical and*Spherical Shells* with Cracks," Int. J. of Fracture Mechanics*; Vol.5, 1969, pp. 22~--237.

-~~

[6]

S. Krenk, "Influence of Transverse Shear on an Axial Crack* in *a Cylindrical Shel-1," Int. J. of Fracture, Vol. 14, 1978~ pp. 123-143.

ML18046B128

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