ML20035C504

Crack Propagation in High Strain Regions of Sequoyah Containment

ML20035C504
Person / Time
Site:	Sequoyah
Issue date:	03/31/1993
From:	Bluhm D, Fanous F, Greimann L IOWA STATE UNIV., AMES, IA
To:	NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES)
References
CON-FIN-A-4136 IS-4878, NUREG-CR-4273, NUDOCS 9304080044
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'I Crack Propagation in High Strain Regions of Secuoyah Containment 1 'l l' T ' Prepared by: L Greimann, F. Fanous. D. Bluhm - Ames Laboratory Iowa State University Prepared for U.S. Nuclear Regulatory Commission ~ 4,, 9304080044 930331 ^ PDR ADOCK 05000327 P PDR

m, AVAILABlWTY NDTICE - Availabuny of Reference Matenals Cited m NRC Publications Most documents cited in NRC pubhcations will be available from one of the fobowing sources: 1. The NRC Public Document Room. 2120 L Street, NW. Lower Levet. Washington.' DC 20555 p 2. The Superintendent of Documents. U.C. Government Printhg Office. P.O. Box 37082. Washington, DC 20013-7082 ~ 3. The National Technical lnformation Service. Springfield. VA 22161~ Although the listing that follows represents the rnajority of documents cited in NRC pubHcations, it is not - Intended to be exhaustive. Referenced documents aval!able for inspection and copying for a fee from the NRC Public Document Room. include NRC correspondence and Internal NRC memoranda: NRC bunetins, circulars, information notices, inspection and investigation notices; licensee event reports; vendor reports and correspondence; Commis. slon papers; and applicant and licensee documents and correspondence. The following documents in the NUREG series are available for purchase from the GPO Sal'es Program: formal NRC staff and contractor reports. NRC-sponsored conference proceedings, international agreement : reports, grant pubhcations.' and NRC booklets and brochures. Also avaHable are regJ!atory guides. NRC regulations in the Code of Federal Regulavons, and Nuclear Regulatory Commission issuances.' Documents aval!able from the National Technical Information Service include NUREG-series reports and: technice' reports prepared by other Federal egenctas and reports prepared by the Atomic Energy Commis-sion, forerunner agency to the Nuclear Regulatory Commission. Documents avaBable from public and special technical libraries include all open literature items, such as books. Journal articles, and transactions. Federaf Register notices. Federal and State legislation, and cors : gressional reports can usually be obtained from these libraries. Documents such as theses, dissertations. foreign reports and translations, and non-NRC conference pro-ceedings are avatable for purchase from the organization sponsoring the publication cited. Single copies of NRC draft reports are available free, to the extent of supply, upon written request to the Office of Administration. Distribution and Mail Services Section.- U.S. Nuclear Reguistory Commission,'- Washington, CO 20555. Copies of industry codes and standards used in a substantive manner in the NRC regulatory process are' maintained at the NRC Library, 7920 Norfolk Avenue. Bethesda, Maryland, for use b" the public. Codes and standards are usuaHy copyrighted and may be purchased from the originating organization or, if they are' American National Standards, from the American National Standards institute.143D Broadway New York, NY 10018. DISCLAIMER NOTICE This report was prepared as an account of work sponsored by an agency of the United States Govemment.. Neittwrthe United States Govemment nor any agency thereof, or any of their employees, makes any warranty, expressed or implied, or assumes any legal liability of responsibility for any third party's use, or the results of : such use, of any information, apparatus, product or process disclosed in this report, or_ represents that its use ' by such third party would not infringe privately owned rights.

NUREG/CR--4273 IS-4878 Crack Pro Jagation in Higa Strain Regions 03 Secuoyah Containment l'repared by: L Greimann, F. Fanous. D. I!!uhm Ames Laboratory 1 Iowa State Unisersity Prepared for U.S. Nuclear Regulatog Commission l I i DR DD OO 7

AVAILABILITY NOTICE Availabilny of Reference Matenais Cited in NRC Pubhcations Most documents cited in NRC pubhcations will be available from one of the following sources: 1. The NRC Pubhc Document Room 2120 L Street, NW., Lower Level, Washington, DC 20555 2. The Superintendent of Documents. U.S. Government Prhting Office, P.O. Box 37082 Washington. DC 20013-7082 3. The National Technicat information Service, Springf. eld, VA 22161 Although the listing that follows represents the majority of ducuments cited in NRC publications, it is not htended to be exhaustive. Referenced documents avaltable for hspection and copying for a fee from the NRC Public Document Room include NRC correspondence and internal NRC memoranda: NRC bulletins, circulars, information notices, inspection and investigation notices; licensee event reports; vendor reports and correspondence; Commis-sion papers; and apphcant and licensee documents and correspondence. The following documents in the NUREG series are available for purchase from the GPO Sales Program: f ormat NRC staff and contractor reports, NRC-sponsored conference procewdings, international agreement reports, grant publications, and NRC booklets and brochures. Also available are regulatory guides, NRC regulations kn the Coce of Feoeral Regulations, and Nuclear Regutatory Commission Issuances, Documents available from the National Technical information Service include NUREG-series reports and technical reports prepared by other Federat agencies and reports prepared by the Atomic Energy Commis-sion, forerunner agency to the Nuclear Regu:atory Commission. Documents aval:able from pubhc and special technical hbraries include all open literature items, such as books, journal articles, and transactions. Federaf Reprster notices Federal and State legislation, and con-l gressional reports can usually be obtained from these libraries. Documents such as theses, dessertations, foreign reports and translations, and non-NRC conference pro-ceedings are available for purchase from the organ:2ation sponsoring the pubhcation cited. Single copies of NRC draft reports are avallable free, to the extent of supply, upon written request to the Office of Administration. Distribution and Mail Services Section U.S. Nuclear Regulatory Commission, Washington, DC 20555. Copies of industry codes and standards used in a substantive manner in the NRC regulatory process are maintained at the NRC Library, 7920 Norfolk Avenue, Bethesda, Maryland, for use by the pubhc. Codes and standards are usually copynghted and may be purchased from the originating organizatson or. If they are American National Standards, from the American National Standards Institute,1430 Broadway, New York, NY 10018. I DISCLAllAER NOTICE This report was prepared as an account of work sponsored by an agency of the United States Govemrnent. Neither the Un ted States Govemment nor any apneythereof, or any of their employees, rnakes any warranty. l expressed or imptied, or assumes any legal liability of responsibiitty for any third party's t.se, or the results of such use, of any information, apparatus, product or process disclosed in this report, or represerrs that its use by such third party would not intringe povately owned rights.

NUREG/CR-4273 IS-4878 Crack Propagation in High Strain Regions of Sequoyah Containment l Manuscript Completed: July 1985 l Date Published: March 1993 J Prepared Dy L Greimann, F. Fanous, D. Bluhm Ames 12boratory Iowa State University Ames,IA 50011 Prepared for Division of Engineering OITice of Nuclear Beactor Regulation U.S. Nuclear Regulatory Commission j Washington, DC 20555 j NRC FIN A4136

iii ABSTRACT f f The rate of release of radioactive materials from a containment during a severe occident has a significant impact on the consequences of the occident. One i hypothesis for o containment leakage model states that the containment will develop a controlled, relatively small leak before the pressure reaches the. point where o general rupture of the shell occurs. Another states that overall failure [ will occur with total release of the vessel contents almost instantaneously. The i Sequoyoh ice condenser containment vessel has been studied for some time to predict the possible location and extent of leakage which could occur during a severe occident. In this work, three critical high strain locations were studied to [ predict crack propogotion from on initially small defect. The 1/2-inch plate near the Sequoyoh springline was selected for further study. A detailed finite element model of the region was prepared and a virtual crack i extension method for calculating the J integral was developed for use with the l general purpose finite element program. The pressure in.the model was l increased to 78 psi which produced a maximum membrane strain of 6.5 i percent. At this point the surface crack was assumed to propogote through the plate and leakage began. Using the. ' :tual crack extension method, two through cracks with different lengths were found to be unstable at this pressure which would allow almost instantaneous release of the vessel contents. i p B E i -i h l i i w i

l, r V i i ' TABLE OF CONTENTS t LIST OF TABLES............-............... yt ) LIST OF FIGURES......................... .yjj j

j viii ACKNOWLEDGMENT-..........................

1 P l' j EXECUTIVE

SUMMARY

V 2 1. INTRODUCTION... 2: l 1.1 Objective.......................... 3 ?! 1.2 Approach......................... 4 1.3 References........................ 5 ~ 2. CRACK GROWTH CRITERIA.................... } 5~ { 2.1 Crack Growth Process 5

i 2.2 Review of Criteria........._..........

2.3 J Controlled Crack Growth............... 6 7-2. 4 J - Ap p l i e d........................ a 2.4.1 Crack Idealization and Elastic Solutions 7 r 2.4.2 Analytic Elastic-Plastic Solutions 7-l 2.4.3 Finite Element Elastic-Plastic Solutions 9 l r ') 12 '{ 2.5 J-Resistance...................... 13 t 2.6 References ), 17 3. SEQUOYAH CONTAINMENT 17 3.1 Previous Results 17 3.2 Postulated Crack 3.3 Surf ace Crack-to Through Crack Propagation........ 17 3.4 Propagation of Through Crack 18 j 20 3.5 References .:[' 21-4.

SUMMARY

21-4.1 Conclusion.......................

4. 2 Recommend at i on......................

21 l 1 i i 'I 1 l 1 l l l I 1

~ t I vi- ' i .] LIST:OF TABLES Table 2.1 Typical Steel Properties, Sequoyah A516, Gr.60 ~..... 22. Table 3.1 Surf ace Crack to.Through Crack Propagation.. 22 .I ~ .. i r i h ? I I t 1 ) J - t l l

I

.l l l

vii' j

LIST OF F.lGURES ..t* Figure 1.1 Sequoyah Containment - Azimuth 285* 23 . Figure 1.2 Crack'in-1/2-inch Plate Near Springline of...... 24 Sequoyah Containment .l Figure 2.1 Idealized Crack Crowth Process............. 25 l i Figure 2.2 Definition of J as Generalized Force for'....... 26 Crack Movement e Figure 2.3 Material Resistance to Crack Growth 26 -l t Figure 2.4 Comparison of J Calculations, Center Cracked..... 27 i Plate (CCP) (a/b = 0.1, a = 1, n = 10) j -1 ~ ~ Figure 2.5 Virtual Crack Extension Pattern 27

t Figure 2.6 One-quarter of Center Cracked Plate,..........

28 Finite Element Mesh j (1/2" Plate, a/b =.0.1, a = 1, n = '10) 'l Figure 2.7 Attempted J - CVN Correlation 29 l Figure 2.8 Crack Growth Resistance Values............ ~30 j i Figure.2.9 Idealized Stress-Strain Curve for. A516,. Gr 60 31 Figure 3.1 Membrane Strain in 1/2-inch plate Near the...... 32 Springline of Sequoyah i Figure 3.2 Membrane Strain Near Penetration of 33 Sequoyah Containment j Figure 3.3 Membrane Strain in Sleeve of Sequoyah 34 i Equipment Hatch Assembly. i Figure 3.4 ASME Acceptance Standards for Radiograph....... 35 Welds (Section Ill, Subsection NE, Class MC i Components, Paragraph NE 5320) l +l Figure 3.5 Comparison of J Calculations, Edge Cracked. 36 l Plate (ECPT) (a/b = 1.8, a = 1.5, n = 10) l Figure 3.6 Finite Element Model of a Section of the....... 37 i

Sequoyah Containment Near the Springline j

38 l Figure 3.7 Maximum Membrane Strain ? Figure 3.8 Maximum Radial Displacement 38 i i figure 3.9 Deformed Shape at Different Pressure Levels 39 l 1 I l i ~

1 ? i i viii' ] ~ ACKNOWLEDGMENT-' The authors would like.to express their appreciation to..three members. of the U.S. Nuclear Regulatory Commission, Mr. Goutam Bagchi, leader, Seismic Qualification Section; Mr. James. Knight, Acting' Director. -l Division of. Engineering; and Mr. Robert Wright, NRC - Project Manager, j Division of. Engineering, for their help throughout the course of this - work. The authors also wish to acknowledge,the able assistance of the l Project Secretaries, Connie Bates and Beth Lott, for the word processor. operations and secretarial services associated with this project. i l l } i h j i - 1 j t if n v ,,,-.l a c- .m y

1 i EXECUTIVE

SUMMARY

l r The rate of release of radioactive materials from a containment. during - a severe accident :has a significant 1mpact on the consequences of the 1 accident. One hypothesis.for a containment leakage model states that ,s the containment will develop a controlled, relatively small. leak before the pressure reaches the point where a general. rupture, of..the' shell. occurs. Another hypothesis states that an overall failure will occur: with total -release of the vessel contents almost instataneously. As part of the Containment. Performance Working Group (CPWG). and other studies, the Sequoyah ice condenser containment vessel has been studied for some time to predict the possible location and extent' of' leakage. which could occur during a severe accident. In this work, three criti-i c al high strain locations were studied to predict crack propagation from an initially small defect. Several criteria are presented in the literature for predicting crack' growth in highly ductile materials such as containment steels. EThe J integral approach is adopted herein. In simple.. idealized cases, the J-applied value is given 'by curve-fits of numerical results -that. have a been developed by others. In this work, a virtual crack extension method for calculating .J has been developed for use with a general i purpose N ite element programs. The various methods are compared herein. pproximate values of the material J-resistance are tabu-

lated, f

? An initially small surf ace flaw is first postulated-in each of the critical high strain regions. By comparing the J-applied value to the ' J-resistance, the pressure at which this. surface crack' propagates is estimated for each of these regions. The 1/2-inch plate - near the i Sequoyah springline :is then' selected for further study. A detailed r finite element model of the region was prepared and analyzed with the ANSYS program. The pressure in the model was increased up to 78 psi which produced a maximum membrane strain of 6.5 percent. At this point j ~ the surface crack was assumed to propagate through. the : plate and leakage began. Using the virtual crack extension method, two through cracks with different lengths were found to be unstable at this ~ pressure. ( If the critical membrane strain is about 6.5 percent, the Sequoyah containment vessel will begin to leak at about 78 psi. The resulting. l through crack will not be stable and general failure will occur with the almost. instantaneous release of the vessel contents. i i I i l i .i

2 1. INTRODUCTION f During a severe accident,- a containment may develop a controlled, relatively-small, leak before the pressure reaches the point where a general rupture of the shell occurs. On the other hand, overall fail-ure may occur;with total instantaneous release of the vessel contents. Either possibility may occur, depending primarily upon local geometry, material details and the applied pressure [1.1]. The NRC has established a Containment Performance Working (SARP) Group (CPWG) at the request of the Severe Accident Research Pl an Senior Review Group to study several models of containment leakage. The members of this group have studied many possible leak models [1.2] such as pre-existing leakage, hatch seals, general rupture and flange opening. For many of the containments it was quite clear where leakage would first occur. However, even though the Sequoyah containment vessel (Fig.1.1) has been carefully studied-for. the past several years [1.3,1.4], it is not clear what is the weakest point in this. vessel. Containment Shell The containment shell is estimated to have a strength at which "sig jficant yielding" occurs between 55 and 60 psi [1.5]. This strength it controlled by the 1/2-inch plate near the i springline. The design pressure is 12 psi. Penetrations - A study of all the penetrations in the Sequoyah contain-ment, using plastic collapse mechanism equations, indicates that the weakest penetration is at Elev. 767', AZ 266* [1.3]. Equipment Hatch Seal - The most recent Sequoyah study [1.6] investi-i g ated leakage of t.he equipment hatch seal as the containment - shell deforms the penetration sleeve. The three-dimensional finite element model indicated that relative motion of the flange interf aces was not sufficient to permit leakage at 82 psi. If a through crack develops at any of these-high strain locations (and, possibly,. several others), leakage will begin. The amount of leakage 1 will depend upon how f ar the crack extends. For examnie, a crack in the.1/2-inch containment plate, Fig. 1.2, may be arrened by an adja-cent stiffener or. the adj acent thicker plate; or, it may propagate through both of these. In this and other regions, the high strains may. be sufficiently localized so that the crack arrests _ as it moves from i the region. 1.1 Objective The objective of' this work is to predict the extent of crack propaga-tion which will occur from a postulated small. crack in the high strain regions of the Sequoyah containment.

3 I 1.2 Approach j The general approach to studying this problem is..first, to select a crack growth criteria from the current state-of-the-art of. the elastic-plastic fracture mechanics fielo--the J integral. The analytical tools required to calculate the J integral and the experimental data required to. characterize the material. J resistance are summarized next. After postulating an initial surf ace flaw, the growth criteria is applied to -[ predict when a through crack develops and how far the through -crack-l extends. I i t t t 1 i I 4 i [ J r I i 1

I 4 1.3 References -l t 1.1 Kussmaul, K., et. al, " Crack Arrest Behavior in. Pressure Vessels," Paper B/F 4/10, SMIRT,' August 1983, pp. 337-346. j f 1.2 Containment Performance Working Group. " Containment Leak Rate Estimates," Fourth Draf t, NUREG/1037, March 1984. 1.3 Greimann, L., Fanous, F. and Bluhm, D., " Reliability Analysis of-Containment Strength," NUREG/CR-1891, August 1982. j 1.4 ACRS, Subcor.ittee on Structural Engineering, " Establishing the ) Maximum Internal Pressure that the Sequoyah Containment Structure Can Withstand," Washington, D.C., September 2, 1980. -l 1.5 Greimann, L.,

Fanous, F.,

and Bl uhm, D., " Containment Analysis l Techniques, A St ate-of-the-Art Summ ary," NUREG/CR-3653, March 1984. 1.6 Greimann, L., Fanous, F., and Bluhm, D., "Sequoyah Equipment Hatch l Seal Leakage," NUREG/CR-3952, 15-3052, Final Report, February { 1985. t 'I t ? i l i A i ~h [ .i [ a t e i I + .,.n

= - 1 I 5 2. CRACK GROWTH CRITERIA i l 2.1 Crack Growth Process i \\ For the nuclear containment leakage considered here,_ the crack will be assumed to begin as a partially-through surface crack of approximately elliptical shape. Figure 2.1 shows such a crack (Fig. 2.la) in a flat i plate (Fig. 2.1d) subjected to a uniaxial -stress, c. As the stress is increased, the crack is visualized as first propagating through the { thickness B (Fig. 2.lb). Leakage begins at this point. The extent of leakage is controlled by how f ar the through crack (Fig. 2.lc) propa-l gates across the plate, c l 2.2 Review of Criteria j There are no crack aruwth criteria for ductile materials which are generally accepted by the tracture mechanics community. No single l parameter or combination of parameters have been found which satisf ac-torily characterize the growth of cracks through regions of high strain j and with gross plasticity of highly ductile materials. Currently, the state-of-the-art in fracture mechanics permits the reliable prediction. l 3 i. of small crack growths in regions of limited plasticity. It is beyond-i the scope of this work to review completely the state-of-the-art in j elastic-plastic fracture mechanics (EPFM). 'ndeed, the authors are not qualified to make the judgments necessary for such a review.

However, a very brief listing of the various criteria is justified.

J Integral. The J integral is a measure of the energy release rate as i a crack extends. This approach has become popular in the United States for nuclear reactor vessels [2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8]. ~ CTOD. The crack tip opening displacement (CTOD) hypothesis states that a crack will grow when the opening near the crack tip reaches a criti-cal value [2.3, 2.4, 2.6, 2.7]. Modified R-6 Assessment Diagram. This approach, which is popular in the United Kingdom, presents an interaction type equation between the extreme limits of crack extension in a perfectly elastic material l-(brittle fracture) and plastic collapse ' governed by a limit load [2.9, 2.10,2.11,2.12]. Crack Tip Energy Release Rate. Probably related to the J integral approach, the crack tip energy release rate criterion considers the. amount of plastic energy in the immediate vicinity of the crack tip [2.13]. Strain Energy Density. In the strain energy density criterion, the crack is assumed to grow when the strain energy density-immediately ahead of the crack reaches a critical value which can be r5tained from a uniaxial tensile test [2.14, 2.15; 2.16, 2.17, 2.18]. _........ ~ _ -. _. -,_.m_.- - m, -.. ~ m.._ - -.-- -.--

.=_.- ) 6 1 Each of these criteria has its proponents. They have been reviewed by-i experts in the fracture mechanics field and compared [2.10, 2.11, 2.19, 2.20, 2.21, 2.22]. Each has an area of application and, yet, none is completely satisfactory for the complete description of ductile crack' growth. If.thef number of proponents can be used as a legitimate - measure. of the validity of the criterion, the J integral and CT0D approaches are more accepted _ [2.10,. 2.21]. The J. integral criteria will be adopted herein. l 2.3 J Controlled Crack Growth i The J integral has been. defined in a number of ways but perhaps.the i most physically appealing way is to define J as the generalized force j associated with an increment of crack growth. The energy balance equations for an increment of crack area 6A is -l t J 6A + 60 + 6V = 0 (2.1) where 60 = 6J Wdv (2.2) v j c I W=fode (2.3) ] 0 is the increment in internal strain energy for the increment in strain [ 6c which is associated with the 6 A growth. The quantity W is the } strain energy density. The quantity, 6V = - F 6u (2.4) l is the increment in external energy for the increment in. displacement 6u associated with 6 A. The first term in Eq. 2.1 is the energy required to form the new crack with a surface area of 6 A. The applied J integral can be calculated in a number of ways, as' will be discussed i in Section 2.4. Crack growth is presumed to occur when J reaches some. i critical value J, usually considered to be a material property. The g J. resistance is usually characterized by the JR vs. aa curve (Fig. 2$3) where aa is an increment in lech of crack growth. Hence, crack t '- growth occurs if i J>J (2.5). ] R The amount of growth is controlled by the JR curve. The J criteria j applies to a limited amount of growth [2.1, 2.4, 2.5, 2.7): i U I*y R Cn (2.6)- l J / (dJ ) ] R p-da t l t l - i t l' i I t

7 where C is the remaining' ligament, i.e. the remaining portion of the material ahead of the crack tip (Fig. 2.2}. j r l 2.4 J - Applied 2.4.1 Crack Idealization and Elastic Solutions a j As shown in Fig. 2.1, two crack shapes are envisioned 'as the crack l grows--an initial surf ace crack and a through crack. The surface crack i 4 can probably best be idealized as an eliptic crack. However, there are l limited plastic solutions for this crack shape. If the crack is long l (a < < c), the conditions at the base of the crack are approximated by asingle edge cracked plate under tensi_on (ECPT) in plane strain. After the crack has propagated through the plate, the conditions approximate a center cracked plate (CCP) in plane stress. For these conditions, the elastic solution for J can be written as [2.7] r { 2 2 _ Y 50 a ge E in which (2.71 !1 - v ECPT 1.12 Y= l lsec f CCP ? W The above solution for the ECPT case is limited to shallow cracks j (a ( < B). j 4 2.4.2 Analytic Elastic-Plastic Solutions The application of J in the nonlinear range depends upen the calculation of J and this has been the subject of many studies--both l analytical and numerical (finite element). Here, we will summarize - a few solutions which seem to attract the most attention. Most of these -i solutions use a Ramberg-Osgood approximation to the true stress-true j i strain curve from a uniaxial tensile test of the material -l +a(o ) (2.8) c o = 'y y y 3 i are the material true yield stress and strain, l in which o and c respectively[and 5nd are material constants which are selected a n l to provide a good fit to the experimental curve [2.20]. For purposes i of presentation, the yield J will be oefined by j l 2 2 i Yvo a Y (2.9) l J = E 1 ~.

8 Turner [2.19, 2.22] gives, perhaps, the simplest approximation to J as 2 2 , [(c ') [1 + 0.5 (c )] h < 1.2 C J y y y (2.10) 2.5(c' -0.2) > 1.2 Jy c y y This approximation is intended to 'be an upper bound.to most practical cases, includkng surf ace and through. cracks. The above equation does not include a correction for deep notches which Turner has suggested. Paris [2.1] has presented an equation for surface and through cracks in A533 steel for the ductile range as i i 2 ( )n + 1 I

3. 3(" )

+ 3.14 a Surface = 1 )l Y J (2.11) 2 +1 J (," )n~ Through l Y L-4.3(,y ) + 10.6 a y ? Af ter several years of study, the EPRI [2.2, 2.3, 2.4, 2.23] presents t 4 J solutions as the sum of the elastic and fully-plastic cases 2 l (P )n + 1 (2.12) ah c J = (o ) i 4 2 J o w bY p, y y in which the notation is as follows: f i ECPT CCP t ( c (net width) b-a W/2 - a = b (total width) = B W/2 P (load) oB oW = l 1/2 2 2 Py (limit load) = 1.46 oy [(c +a ) - a] o (W-2a) y a=1) 21.7 4.62 I hi( b = 8 3.02 2.86 I a=1) hi( b = 4 i P P Y = y y o B o W y y f

l 9 i l t -In this equation, h is dependent upon the specimen shape, crack size, i and material shape parameter n. It has been obtained for several i cases by EPRI using numerical methods for the fully plastic solutions, The values tabulated above are for a shape f actor-n = 10. The solution for the plane strain ECPT case are from [2.23]. (not [2.4]) and i for the plane stress CCP are from [2.4].. The "RI correction for i effective crack length in the elastic portion has nos been included. l A modif *ad form of the R-6 assessment diagram has been suggested by i Chell an; 'ilne [2.10] and is given by a parametric equation as l E =8 in sec "-p J my 2 j y i 4 -. - 1) ] ( 1 + gu!"y) l 2 p g p =[p +(1-1 )(o u (2.13) 2 P J o y y in which the parameter p ranges as 0<p<1 and o is the ultimate tensile stress. The term on the extreme right u follows their suggestion to use a flow stress (arithmetic mean of the yield and ultimate) in the evaluation of the limit load. Equation 2.13 is plotted parametrically as p ranges frcm 0 to 1. l 4 l The above four solutions are plotted for a CCP case in Fig. 2.4. Note l

that, in order to plot the results on the strain abcissa, the 1

Ramberg-Osgood relationship, Eq. 2.8, was used in conjunction with l Eqs. 2.11, 2.12, and 2.13 to find the strain corresponding - to any j stress state. 2.4.3 Finite Element Elastic-Plastic Solutions t Most numerical solutions for the J integral are by one of two methods. l In one method, the contour integral formulation of J is used directly l [2.2, 2.3, 2.4, 2.7, 2.11, 2.23, 2.24, 2.25, 2.26, 2.27] by integrating _ along several paths around the crack tip. The virtual crack extension-(VCE) method is a. second popular method [2.6, 2.28, ' 2.29, 2.30, 2.31, 2.32, 2.33,'2.34]. The VCE method, which will be-adopted here, basically uses the J definition in Eq. 2.1. The. crack is given a ~ virtual area - growth 6 A. The virtual change in internal and external-l energy caused by-this growth can be calculated..This is equal to the j amount of surf ace energy released during the growth. The generalized j force J can then be calculated directly by Eq. 2.1. 'l r The virtual crack extension is usually ~ accomplished _ by a series of stress-free nodal shifts and ' releases as the crack propagates [2.3, 2.29, 2.30, 2.33,.2.34]. The virtual crack extension is accomplished l l H 1

r 10 by a virtual change in the nodal. coordinates (stress-free) with ~no j total volume change and is ' not the same' as a virtual displacement.. 1 Hence, in Fig. 2.5, node C is given 'a virtual stress-free coordinate-shift of 6 a to C'. The nodes on the boundary are not permitted to move during this virtual change. (The location. of the outer boundary 'is arbitrary but different J values will be obtained for each because: (1). J is ' not totally path independent for inelastic materials and -(2) i finite element mesh size will have a varying effect.).. The virtual coordinate changes between C' and the boundary. are usually-taken to vary linearly [2.3]. l l To accomplish the virtual coordinate shift in an existing - general 3 purpose finite element program with a minimum of change, phantom l elements are introduced. In the region depicted in Fig. 2.5, the j phantom elements duplicate the real elements except they are connected ' to the node C', The phantom elements are.given a very small th.ickness, say 0.0001 times the real thickness. Hence, as the structure is loaded, these elements accumulate stress and strain, i.e., strain energy density. However, the strain energy is insignificant since-their volume is very small. Suppose the structure with the real and phantom elements has been. loaded to same load level at which - the J calculation is desired. At this point, the crack is given a virtual crack extension, 6a, that is, the phantom elements became real elements and vice versa. Since the boundary does not move, the change ' in external potential energy is zero and, using Eq. 2.1, J= 1 6U ~(2.14) 6A or, using Eq. 2.2, J= 1 (f 6W dV + f WdV) (2.15) 6A V 6V If, for example, the constant strain triangle finite element is 'used, i.e., W is constant within an element, elements 1 (ej j c j + W aV )] J=- [ [ (,2.16) Va j j AA j volume of the real eleme$ are the stress, strain energy density and the in which aj, Wj and V nt i, respectively. The' increments are-Ac = cj ' cj (2.17)' AVj'=.V ' - Vj (2.18) j where c $ '- ' denotes the strain'in the phantom element corresponding to the real element-i. The' volume Vj' is the volume of phantom element using the real ~ thickness, i.e.,

.11 AVj = (Aj' - Aj) Bj (2.19)- where Aj ' represents the area of the phantom element and _- Aj-and Bj l are the area and the thickness of the real element, respectively, i To check this approach and compare it to the analytical methods, it was'- applied to the CCP specimen in Fig. 2.6. The finite. element -idealiza-tion was analyzed with ANSYS [2.35]. (Note the crude' mesh of constant strain triangles.) The virtual crack extension was _0.6 inch. Phantom - elements duplicated the real elements in the lightly shaded area except node C was shifted up 0.6 inch. j First a static analysis procedure was tried. In this procedure, the applied edge stresses.were increased in increments. and a sufficient j number of iterations were run to permit convergence. In _the : ANSYS. i program, convergence criteria are: (1) the charge in displacement { between consecutive iterations must be less than 0.001 inch and, (2) t the charge'in plastic strain divided by' the yield strain must be less than 0.01. It was found that the static analysis requires - several_ - hours of computer time even when these convergence criteria were -l relaxed somewhat. et To reach a converged solution using a reasonable number of iterations, the slow dynamic analysis procedure suggested in' Ref. [2.35] was used. The dynamic solution within ANSYS permits an ' extrapolation procedure i for plastic strains not available in the static solution. Hence, a -[ converged solution can be-obtained more rapidly using _ a dynamic solu-tion. High damping was used to minimize the vibration response, j Physically, this would correspond to placing the structure in' a viscous l fluid during the loading process. Mass-proportional damping was used to approximate the critically. damped case. The fundamental frequency for the plate shown in Fig. 2.6 was estimated as 4300 rad./sec and, l hence, the proportionality constant was taken as 8000/sec. -l The applied edge stress was increased in steps.. For each step, the j applied stress was first increased _ over a rise time of one second, which is larger than several times the structure fundamental period.. Next, the applied stress was held constant for several seconds. In i each step a very small integration step size, At, was used (0.001 i ~ sec.). During the solution, At does not remain constant but changes. j automatically as optimized.by the ANSYS program based - on the -third derivative of the displacement with respect to time (jerk).- l The finite element results were used in conjunction with Eq. 2.14 to c alculate _J-at different applied stress levels. This was accom-plished _ using the MSYS postprocesser and a computer program written by the ' authors. The calculated J for the CCP specimen in: Fig. 2.6 are j plotted in Fig. 2.4. For the elastic case (Linear Elastic Fracture 'j Mechanics), the exact J for an. applied nominal. stress of 10 ksi is ] J = 0'.0636 k in/inz e l ~ j +

12 The finite element procedure using phantom elements give J = 0.0643 k in/inz e which is certainly a favorable comparison considering the coarse mesh. As can be seen from Fig. 2.4, the proposed analysis gives results below ) the results predicted by Paris, EPRI ' and Turner in the high strain region (several times yield). This discrepancy is mostly caused by the coarse mesh around the crack. i 2.5 J-Resistance As in Eq. 2.5 and Fig. 2.3, the resistance of the material to crack extension is characterized by the J resistance. The material in the Sequoyah containment is A516, Gr. 60 steel. Typical properties of the steel in this particular ' containment are listed _ in Table 2.1.- (Note:- these are " typical", i.e., from a very small sample and do not neces. sarily represent the mean values.) As usual, properties such as yield-strength and Charpy values degrade with increasing thickness. No Jg values were available for this material when this study was conducted i To establish an estimate of the J-resistance, similar: steels were considered. Figure 2.7 is a plot of the Charpy value versus the - J resistance, which is a measure of J-resistance defined by Paris [2.I3 1 for reactor steel -( A533B). Attempted correlations by Paris' [2.1] and i Kussmaul [2.8] are illustrated. Using a very gross extrapolation and the Charpy values in Table 2.1,2one could estimate the J value to be i 3o z in the. range of 1 to 2 K in/in fer _3-inch plate and. 3 to 6 K in/in t for 3/4-inch plate at -30' F. Data presented by Rolfe [2.36] for J versus Aa curves for structural steel and others [2.8, 2.37, _2.38] -i suggests that : these values are, at least, the correct order.of magni-tude (Fig. 2.8). r For use in both the analytical and finite element - analyses to follow, j the stress-strain curve for the steel is idealized as in Fig. 2.9. The true stress-true strain curve approximates that found for the steel in j much thinner plate [2.39]. The_ Ramberg-Osgood equation, Eq. 2.8, is used to approximate the true stress-true strain curve for the analyt-- ical J calculations. The piecewise linear, engineering strain curve is used in the finite element analysis. } 'i I i i i 'I l i a

l

+. n

s 1 13 j i i 2.6 References 2.1

Paris, P.C.

and Johnson, R.E.,"' A ' Method of Application of I i Elastic-Plastic Fracture Mechanics to Nuclear Vessel Analysis," Elastic-Plastic Fracture: Second Symposium, Volume II - Fracture Resistance Curves and Engineering Applications, ASTM Special Technical Publication 803, October 1981, pp. II-5 to 11-40. l 2.2 Shih, C.F., Kumar, V. and German, M.D., " Studies of the Failure f Assessment Diagram using the Estimation Method and J-Controlled Crack Growth Appro ach," Elastic-Plastic Fracture: Second j Symposium, Volume II - Fracture Resistance Curves and Engineering Applications, ASTM SDeci al Technical Publication 803, October 1981, pp. II-239 to 11-261. 2.3 Kumar, V., et. al, Advances in Elastic-P1astic Fracture Analysis',- Electric Power Research Institute, EPRI NP-3607, August 1984. [ i 2.4 Kumar, V., German, M.D. and Shih, C.F., An Engineering Approach for Elastic-Plastic Fracture Analysis, Electric Power Research l Institute, EPRI NP-1931, July 1981. i 2.5

Ernst, H.A.,

" Material Resistance and Instability Beyond [ 1 J-Controlled Crack Growth," El astic-Pl astic Fracture: Second Sym>osium, Volume I - Inelastic Crack Anal ysi s, ASTM Special l 3 Tec1nical Publication 803, October 1981, pp.1-191 to I-213. 2.6 de Lorenzi, H.G., "El astic-Pl astic Analysis of the Maximum l Postul ated Fl aw in the Beltline Region of a Reactor _ Vessel," Aspects of Fracture Mechanics in Pressure Vessels and Piping, PVP-Vol. 58, ASME, July 1982, pp. 71-90. t 2.7

Broek, D.,

Elementary Engineering. Fracture Mechanics, Third l Edition, Boston: Martinus Nijhoff,1982. 1 2.8 Kussmaul, K., et. al, " Crack Arrest Behavior in Pressure Vessels," Paper G/F 4/10, SMIRT, August 1983, pp. 337-346. ) i 2.9

Milne, I., " Calculating the Load Bearing Capacity of a Structure J

Failing by Ductile Crack Growth," Advances in Fracture Research, Proceedings of 5th International Conference on Fracture, Cannes, i France, March 29-April '3,1981, pp.1751-1757. 2.10 Chell, G.G. and Milne, I., " Ductile. Tearing Instability Analysis-A Comparison of Available Techniques," Elastic-Plastic Fracture: l Fracture Resistance Curves and i Second Symposium, Volume II Engineering Applications ASTM Special Technical Publication 803, -i j October 1981, pp. 11-179 to II-205. I

14 t i 2,11 Bl oom, J.M., " Validation of a Deformation Plasticity Failure Assessment Diagram Approach to Flaw Evaluation," Elastic-Plastic Fracture: Second Symposium, Volume II Fracture Resistance Curves and Engineering Applications, ASTM Special Technical Publication 803, October 1981, pp. II-206 to 11-238. 2.12 Sarmiento, G.S., et. al, " Failure Internal Pressure of Spherical Steel Containments," Second Workshop on Containment Integrity, NUREG/CP-0056, August 1984. 2.13 Saka, M., et. al, "A Criterion Based on Crack-Tip Energy r Dissipation in Pl ane-Strain Crack Growth Under Large-Scale Yielding," Elastic-P1astic Fracture: Second' Symposium, Volume 1 3 Inelastic Crack Analysis, ASTM Special Technical Publication 803, October 1981, pp. I-130 to I-158. 2.14 Si h, G.C., " Mechanics of Subcritical Crack Growth," Fracture Mechanics Technology Applied to Material Evaluation and structure Design, The Hague: Marinus Nijhoff, 1983, pp. 3-18. 2.15 SiL, G.C. and Tzou, D.Y., " Mechanics of Nonlinear Crack Growth: Effects of Specimen Size and Loading Rate," Modeling Problems in Crack Tip Mechanics, University of Waterloo, Ontario, Canada, August 1983, pp. 155-169. 2.16 Carpinteri, A. and Si h, G.C., " Damage Accumul ation and Crack Growth in Bilinear Materials with.Sof tening: Application of Strain Energy Density Theory," Theoretical and Applied Fracture r Mechanics. Vol. I, 1984, pp. 145-159. 2.17 Gdoutos, E.E., " Stable Growth of a Control Crack," Theoretical and Applied Fracture Mechanics, Vol. 1, 1984, pp. 139-144. t 2.18 Sih, G.C. and Chang, C.I., " Prediction of Failure Sites Ahead of l Moving Energy Source," Fracture Mechanics Technology Applied to Materi al Evaluation and Structure Design, The Hague: Marinus j Nijhoff, 1983, pp. 171-187. 2.19 Turner, C.E., "Further Developments on a J-Based Design Curve and its Relationship to Other Procedures," Elastic-Plastic Fracture:- Second Symposium, Volume II - Fracture Resistance Curves and Engineering Applications, ASTM 5pecial Technical Publication 803, October 1981, pp. 11-80 to 11-102. 2.20 Hodul ak, L. and Blavel, J.G.," Application of Two Approximate-Methods for Ductile Failure Assessment," El asti c-Pl astic Fracture: -Second Symposium, Volume II - Fracture Resistance-Curves and Engineering Applications, ASTM 5pecial Technical Publication 803, October 1981, pp. 11-103_to 11-114. 2.21 Marston, T.V., Et. al, " Development of a Pl astic Fracture Methodology for Nuclear Systems," El astic-Pl astic Fracture: l l

.~ .~ l 15 i Second - Symposium, Volume II - Fracture Resistance Curves and i Engineering Applications, A51M 5pecial Technical Publication 803, October 1981, pp. 11-115 to II-132. 2.22 Turner, C.E., "A Review of El astic-Pl astic Fracture Design Methods _and. Suggestions.for a Related Hierarchy of Procedures ~ to Suit Various Structural Uses," Analytical and Experimental Fracture Mechanics," Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands,1981, pp. 39-58. 2.23 Shih, C.F. and Needleman, A., " Fully Plastic Crack Problems, Part j I: Solutions by a Penalty Method and Part-II: Application of Consistency Checks," Journal of Applied Mechanics, Vol. 106, ASME, March 1984, pp. 48-64. 2.24 Yagawa, G.,

Kashima, K.

and Takahashi, Y., "A Round-Robin in [ Finite Element Elastic-Plastic Stable Crack Growth An alysi s," Aspects of Fracture Mechanics in Pressure' Vessels and Piping, PVP-Vol. 58, ASME, July 1982, pp. 175-184. j 2.25 Watanabe, T., et. al, "J-Integral Analysis of Plate and Shell Structures with Through Wall Cracks _ Using Thick Shell Elements," Paper G/5 3/8, SMIRT, August 1983, pp'. 257-264.

j i

2.26 Dodds, R.H. and Reed, D.T., " Elastic-P1astic Response -of Tensile Panels Containing Short Center Cracks," Computational Fracture Mechanics - Nonlinear and 3-D Problems,. PVP-Vol. 85, ASME, June 1984, pp. 25-34. 2.27 Jung, J. and

Kanninan, M.F.,

" An alysis of Dynamic : Crack l Propagation and Arrest in a Nuclear Pressure Vessel;Under Thermal i Shock Conditions," Aspects of Fracture. Mechanics in Pressure i Vessels and Piping, PVP-Vol. 58, ASME, July 1982, pp. 91-108. [ .( 2.28 Yong, C.F. and Palusamy, S.S., "VCE Method of J Determination for a Pressurized Pipe Under Bending," Aspects of Fracture Mechanics in Pressure Vessels and Piping, PVP-Vol. 58,_ASME, July 1982, pp. 143-157. [ 2.29 Schmitt, W., "Three-Dimensional Finite Element Simulation ' of l Post-Yield Fracture Experiments," Computational Fracture Mechanics - Nonlinear and 3-D Problems, PVP-Vol. 85, ASME, June i 1984, pp. 119-131.- i 2.30 Bakker, A., "On the Numerical - Evaluation of the J-Integral," c Paper G/F 2/4, SMIRT, August 1983, pp. 181-189. 2.31 Cells, A., Squillani, A. and Milella, P.P., " Experimental and-f Numerical Evaluation of 'J Integral on Tubes," Paper G/F 3/2,- i SMIRT,- August.1983, pp. 275-281. l l 1 .i l ) .I 1 l 1

'16-2.32 Beliczey, S. and Hofler, A., " Calculations to Experimental Results of Crack Growth," Paper G/F 4/9, SMIRT, August 1983, pp. 329-335. 2.33 de Lorenzi, H.G., "3-D Elastic-Plastic Fracture Fbchanics with ADINA," Computer and Structures, Vol. 13, 1981,.pp. 613-621. 2.34 de Lorenzi, H.G., "On the Energy Release Rate and the J-Integral for the 3-D Crack Configuration," International Journal of Fracture, Vol. 19, 1982, pp. 183-193. 2.35 ANSYS Engineering Analysis System User's Manual, Swanson Analysis System, Inc.. Houston, PA, (Version 4.lc) 1984. 2.36 Rolfe, S.T. and Bersom, J.M., Fracture and Fatigue Control in i Structures, Englewood Cliffs: Prentice-Hall, 1977. 2.37 De Castro, P.M.S.T., "R-Curve Behavior of a Structural Steel," Engineering Fracture Mechanics, Vol. 19, No. 2, 1984, pp. 341-357, 2.38 Shih, C.F., et. al, Fbthodology for Plastic Fracture, Electric. Power Research Institute, EFRI NP-1735, March 1981. 2.39 Blejwas, T.E.,

Woodfin, R.L.,

Dennis, A.W.

and Horschel, D.S., i " Containment Integrity Program," NUREG/CR-3131/1, SAND 83-0417, j March 1983. l l l i

i i

t l .) J i I ..r

L 17 3. SEQUOYAH CONTAINMENT 3.1 Previous Results As listed-in Sec.1.1, three regions have been selected in the Sequoyah containment as locations. at which through cracks could. develop and. i leakage occur. The results of previous-analyses, summarized here, have j indicated that high strains occur in these regions: j Containment shell, near springline. The maximum membrane strain at 60 psi is. greater than- 0.0025 -in.the 1/2-inch plate (Fig. 3.1). The results were obtained from an axisymmetric approximation to the containment [3.1]. .t Penetration at El ev. 767', AZ. 260*. A three-dimension al - l finite analysis [3.1]_has.shown that the maximum membrane. i strain for this penetration is about 0.003 at - 60 psi (Fig. f 3.2). .j ) Equipment hatch sleeve. A membrane strain of about 0.004 occurs in the 3-inch plate in the sleeve and in the 11/2-inch reinforcement of the Sequoyah equipment hatch-assembly- (Fig. 3.3), according to a three-dimensional finite element analysis l [3.2].

i 3.2 Postulated Crack j

J Following Sec. 2.1 and Fig. 2.1, an initial surface crack is postulated 1 in each of these regions. It is not clear what !is a most' realistic'. crack shape and size. Probably a sensitivity study of dif_ferent possi-. I bilities should be done. For this study, the crack ' is assumed to-be'. long and shallow, i.e., ECPT case in _ Sec. 2.4.1. With reference to i ASME acceptance standards for radiographed welds in containment vessels - -i [3.3], this is a linear indication with length limits, 1, as listed in-j Fig. 3.4. Since 1/a is greater than 3 for linear indications, -the maximum crack depth, a, is also listed, j 3.3 Surface Crack to Through Crack Propagation I l The maximum depth surf ace crack' listed in Fig. 3.4 is postulated to-occur in each of the high strain regions of Figs. 3.1, 3.2, and 3.3, as j listed in Table 3.1. As described in Sec. 2.4.1, this case is approxi-- mated by a flat plate in plane strain with an edge crack- (ECPT). Using -) the analytic solutions summarized in _ Sec. 2.4.2 - for this _ case, the calculated value of the applied J can be obtained for.various levels ~of nominal' true strain (as was done in Fig. 2.4 for the CCP case). Using the Ramberg-Osgood constants ' for the true stress-true strain curve in-Fig. 2.9, the applied J values were obtained for.a crack depth of:1/8 the thickness and plotted in_ Fig. 3.5. The Turner values are repre-sentative and ~. easier to calculate and, hence, 'will be used in the j following. j 1 Lf 1

f 18 l l The J resistance of the material is probably the most uncertain quality. in this analysis but the bounds presented in Sec. 2.5 and listed as J in Table 3.1 are appropriate. Upon setting the applied g J values (Eqs. 2.9 and. 2.10) equal to the material resistance 'R, the nominal strain cR for surf ace crack propagation is _ found anc' listed in Table 3.1. Returning to the pressure versus membrane strain curves in Sec. 3.1, the pressure pR corresponding to the strain cR IS obtained for each of the three high strain regions. The pressure pR j represents the pressure at which the postulated surf ace crack propa-- gates to a through crack and leakage begins. Note that the previous analyses were not extended to sufficiently high strains so as to permit determination of other than a lower bound to pR. However, one can note that, because of the " flattening" of the pressure versus strain curves, the relative uncertainty in pR will not be as large as the uncer-tainty in J-I R 3.4 Propagation of Through Crack l The results of the previous section (Table 3.1) indicate that the postulated surf ace crack will become a through crack at some pressure beyond 65 psi. One area, the 1/2-inch plate at springline, was selected for further study--both to extend the analyses into the high j strain regime so that the p in Table 3.1 can be refined and also to estimate the extent to whick the through crack will propagate. In this regard, the finite element model illustrated in Fig. 3.6 was f ormul ated. The model includes the 1/2-inch plate near the Sequoyah springline and extends into the hemispherical head and into the 5/8-inch plate below (refer to elevations in Fig.1.1). Stringers and } rings are included in the model and the material properties of Table l 2.1 and Fig. 2.9 are used. Symmetry boundary conditions are imposed on both vertical boundaries. The top boundary is constrained in the i tangent pl ane of the hemisphere, but permitted free motion perpen-i dicular to this pl ane. The meridional forces induced by pressure j loading are applied to the lower boundary, which is constrained -to move uniformly in the vertical direction. Internal pressure loading is applied to the shell elements which represent the containment shell. A total of 308 elements and 158 nodes are included in the model. As illustrated in Fig. 3.6, the finite element model has provisions for a 12-inch and 72-inch crack. Phantom. elements, as described in Sec. 2.4.3, are associated with each of these cracks. During the first phases of loading, there is no crack in the model. The pressure is increased from zero in increments and the analysis was accomplished using the s'ow dynamic approach described in Sec. 2.4.3. i At each load increment, the load was increased and then held constant over periods of time equal to 1 and 3 seconds, respectively. An initial integration time step size of 0.001' second was specified. During the solution, this time step size was changed automatically by the program according to third derivative of the displacement (see Sec. 2.4.3). At a pressure of 78 psi, the maximum membrane strain in the entire model was 6.5 percent. This occurred in the 1/2-inch plate at l 4 g-ne p ~- r--,

19 Elev. 783' 5/8". Figures 3.7 and 3.8 are plots of the maximum membrane strain and the radial displacement at Elev. 783' 5/8" (see Fig. 3.6). Figure 3.9 shows the deformation along a meridian at different pressure levels. At a membrane strain of 6.5 percent, the postulated surface crack I (Table 3.1) is assumed to propagate through the 1/2-inch plate forming a crack with a length of 12 inches. The node at the center of this i crack was released and the solution was continued at a pressure level of 78 psi until a converged solution was reached. Using the VCE method j as described in Sec. 2.f.3, the value of the applied J was calculated i as about 120 k in/in This is much larger than any conceivable l 1 J-resistance of the material. One murt conclude, therefore, that at a j pressure of 78 psi, a through crack of 12 inches. will continue to propagata-in the meridional direction in the 1/2-inch plate. l The solution was continued to investigate whether this crack would be } arrested at the 5/8-inch plate below and the ring above at Elev. 788' i 5/8". A 72-inch crack was simulated by releasing all nodes along the ( left vertical edge in the 1/2-inch plate between these elevations. The ,} l solution was continued until convergence. Agai n, the VCE method was l implemented and an applied J of 3860 k in/in was calculated. Ag ai n, this unrealistically high value of J indicates the crack will continue j to propagate through the ring stiffeners at the top and the' 5/8-inch plate at the bottom, i.e., there will be an overall failure. Note that only one cracking sequence has been studied in this work. l If, for example, the postulated surface crack was assumed to propagate through the 1/2-inch plate at a membrane strain of, say, 1 percent (about 60 psi), the resulting through crack could possibly have been arrested. I ( 1 f i l [ t i I i f )

4 . i 20 1 i 3.5 References , j l 3.1 Greimann, L., Fanous, F. and Bluhm, D., " Reliability Analysis of j Containment Strength," NUREG/CR-1891, August 1982. l 3.2 Greimann, L, Fanous, F. and Bluhm, D., "Sequoyah Equipment Hatch Seal Leakage," NUREG/CR-3942, Final. Report, February 1985. i h 3.3 ASME Boiler and Pressure Vessel. Code,- ASME, Section

III, Subsection NE, Class MC Components, Paragraph NE 5320.

I I i I j r - 1 l i f 5 i j -i '*M e ,,p,., s,n-4

l 21 4.

SUMMARY

The rate of-release of radioactive materials from a containment during i a severe accident has a significant impact on the consequences of the l accident. One hypothesis for a containment leakage model states-that the containment will develop a controlled, relatively small leak before l the pressure reaches the point where a general rupture of the shell occurs. Another hypothesis states that an overall failure will occur ~ with total release of the vessel contents almost instantaneously. As l part of the Containment Performance Working Group (CPWG) and other [ studies, the Sequoyah ice condenser containment _ vessel has been studied { for some time.to predict the possible location and extent of leakage which could occur during a severe accident.- In this work, three l critical high strain locations were studied to predict crack propagation from an initially small defect. -f Several criteria are presented in the literature for. predicting crack growth in highly ductile materials such as containment steels. The J integral approach is adopted herein. In simple idealized cases, the J-applied value is given by curve-fits of numerical. results that have been developed by others. In this work, a virtual crack extension method for calculating J has been developeo for use with.a general purpose finite element programs. The various methods are compared herein. Approximate values of the material J-resistance are t tabulated. l An initially small surf ace flaw is first postulated in' sach of the i critical high strain regions. By comparing the J-applied value.to the [ J-resistance, the pressure at wh_ich this surface crack propagates is j estimated for each of these regions. The 1/2-inch plate near the 3 Sequoyah springline is then selected for further study. A detailed finite element model of the region was prepared and analyzed with.the { ANSYS program. The pressure in the model was increased up to 78 psi i which produced a maximum membrane strain of 6.5 percent. At this point' the surf ace crack was assumed to propagate through the plate and leak-l age began. Using the virtual crack extension method, two through cracks with different lengths were found to be unstable at this _j l oressure. f 4.1 Conclusion i If the critical membrane strain is about 6.5 percent, the Sequoyah containment vessel will begin to leak at about ' 78 psi. The resulting i through crack will not-be stable and general failure will occur with the almost instantaneous release of the vessel contents. l 4.2 Recommendation This. study should be considered very preliminary. El astic-pl astic i fracture mechanics has _ clearly been pushed beyond the acknowledged i st ate-of-t he-art. However, the above conclus_ ion for this application I will, most likely, not change, j l

i ts-+

E'

22 1 Table 2.1 ~ Typical Steel Properties, Sequoyah A516, Gr.60 Plate CVN Thickness-o (ksi) u(ksi) elong. @ -30*F(ft-lb) y 7/16" 48.3 66.0 25 'N.A. 1/2" 47.3 66.6 33 N. A'. I i 5/8" 49.2 68.3 29 240 -j 1" 46.6 62.0 N.A. N.A. 1 1/4" -45.5 N.A. N.A. N. A.- 1 1/2" 45.5 67.1 28 N.A. 3" 42.0 62.0 34 -57 t Specification 32.0 60-80 30 -{ N.A. - Not Available I Table 3.1-Surface Crack to Through Crack Propagation I J P1 ate Crack R c p I 2 R R l Location Thickness Depth k.in/in .l Springline 1/2" 0.083" 3.0 1.0 9 3% >'65 psig Penetration 5/8" 0.083" 3.0 1.0 812% '> 65 psig-i Hatch 1 1/2" 0.17" 2.5 0.5 411% > 82 psig Sleeve 3" 0.25" 1.5 0.5' 2 1% '> 82 psig i l l

23 .t*t$It6* t = 9/16" t=1/2" ELEVATIONS 815' 4 )

• 6 809*6}"

8 803'9g"" t 799'9t To6' 0" 79f'i" 789' g." '+ 778'6l"

2 769'I"

,3 759'6)"

3 7 41' l' "

Y =2 730'3)" 721'6l" ) 7f3' 6"

• g 7
• s 70r' q"

'f ( 691'Fj" 680*9f" Figure 1.1 Sequoyah Containment - Arirnuth 285

I 24 '1 \\"N"N t dN 'n NdN f xdx cd .c d( N N NN N ,h d e 1 s N N N N'N o N ed I, . 's = N~ ~ e ~ <N -N o ~ ' NN crock NN sa N N t s 'N 'N Figure 1.2 Crack in 1/2-inch Plate Near Springline of Sequoyah Containment l l f [

l 25 ) i 2c i. a L s i. ,7 / / O' r/ d B i (a) initial Surface Crack f /\\ Y Crack / J / /,' / 2a (b) t, 'l y / /> // l () (c) Through Crack Figure 2.1 Idealized Crack Growth Process

26 A F,8u lf. 80= 8A a ) 80 C BU 9 J B A + BU-F8u =0 Figure 2.2 Definition of J as Generalized Force for Crack Movement Ja) L Jc i w r Ao Figure 2.3 Material Resistance to Crack Growth

27 140 120 t 100 3 1 80 Jy g i / 60 p ? 40 20 1 f f 1 10 20 30 40 50 j e/cy (True) Figure 2.4 Comaprison of J Calculations, Center Cracked Plate (CCP) (a/b = 0.1, a = 1, n = 10) // / -- TT / _ __ s=. a l, L 1 1 / / /- Boundary /' ,y 7 '%, //, /,, / / '/ Figure 2.5 Virtual Crack Extension Pattern i

28 72" = = D- ~ a l 1 1 1

• o 3D g

s w W eEO zN ,736 - x y N i u n E &h Ah k Ib, I v i [ t l Figure 2.6 One-quarter of Center Cracked Plate, Finite Element Mesh (1/2" Pl ate, a/b = 0.1, a = 1, n = 10) t 4

29 I l 8 / i u 6 oo / M. l [ (Kussmoul) ^ = .E m 2; 4 = / 3 T .9 / c Q / p. O q'-' / n ~ f j,. 5&f . p,h(.IcN aris)

1. rh7 E=q O P

~ A533B a Weld l l I I 50 10 0 150 200 250 CVN (ft-lb) L Figure 2.7 Attempted J-CVN Ccrrelation-

30 /* 12 - S EPRI 1 'A5331 B 10 - % ELD \\ \\' * \\ 7 78-C f y 4Q

• W

, ' h ', c,',0 e r 6- ~ "s C s, .~ ni: ,e V li w, e ,,u ^ . jj y_i;,;.. 3; y _ 1. _s 7.q.j.; ' ~~ 4- . ; ;& n " ~ ~ - pw - 1: { Rolfe ...b ' 1 J A572, Gr. 50 2 Sw Kussmol 1 I I I I 0.1 0.2 0.3 0.4. 0.5 Aa (in.) Figare 2.8 Crack Growth Resistance Values 4 s

l 31 T Romberg - Osgood g me a c (n= lO, a = 1.5) / ,/ 0 U g /- Engr. cr-c g T Y O I .] I ,J 'l r F L I I 1 I I I I O.05 0.10 0.15 0.20 0.25 0.30 Q35 STRAIN ENGINEERING Point c 7 1 C c y y 2 0.015 Uy 3 0.035 (Uy +70)/2 4 0.15 70 5 0.35 (7 +7 )/2 y 9 Figure 2.9 Idealized Stress-Strain Curve for A516, Gr. 60

32 L t i l ~ MAXIMUM MEMBRANE STRAIN e ELEVATION 783'0" 70 60 3 50 E n .i y 40 o 1 in $ 30 I ) cca 20 10 m,,I -ll 1 f f 1 .0 01 .002.003 g MAX. MEMBRANE STRAIN Figure 3.1 Membrane Strain in 1/2-inch Plate Near the Springline of Sequoyah

33 i i I l Ring Stiffener (Elevation 769'5 a) j 5.. E /8 Maximum Membrane Strain / P i Elevation 767'0" N /zimuth 266* A 70 60 n d 50 b 1 l =40 E 2 30 ' 20 10 0 O 0.002 0.004 0.006 Maximum Membrone Strain Figure 3.2 liembrane Strain Near Penetration of Sequoyah Containment t 6

34 Stringers / Maximum Membrane Strain } / / / / / / / / Rings / / Elevation 741'I.!" 'A / s 2 ( z.285* Hatch ( [ Sleeve (3 " FP_ ) \\ 10 0 i i i i 80 1 3 60 m $ 40 < m E Q-20 O O.OO4 0.008 0.0120 0.0160 Ma ximu m Membrane Strain Figure 3.3 Membrane Strain in Sleeve of Sequoyah Equipment Hatch Assembly

.i 35 .1 .I 1 .i i .i l' 1. .l, l l A i .i / / i I /,la' / 4 / J l I I Linear Indications ( 2/a > 3 ) 9 i i Thickness Maximum l Maximum a. less than 3 " 1/4" 1/12 " / l 3/4" to 2 /1" t/4 t/9' 4 1 3/4" l/4" j n greater than 2 /4 i ) i f t i i Figure 3.4 ASME Acceptance Standards for Radiograph Welds

l (Section-III, Subsection NE, Class liC Components, Paragraph NE 5320)

.j i

36 5 i i i i i i i 4 i i i i i i 4 i 8 3 N C t' N C 2 1 O 1 I I 5 1 1 1 1 I 1 I I I i O.05 0.10 0.15-True Strain i i Figure 3.5 Comparison of J Calculations, Edge Cracked Plate (ECPT) (a/b = 1.8, a =1.5, n = 10) l I

j 37 i l-l l g 14 h I k 2 799'9 l g ~ I $ 1 ) 796'0" s s< [ 791'f" 5" e 7 d 788'1 N 778'6h" i t 769'5" 8 [ Figure 3.6 Finite Element flodel.of a Section of the Sequoyah l l Containment Near the Springline i.

38 10 0 t 80 Wx 60 o ch W E 40 20 O O.O 1.0 2.0 3.0 4D 50 6.0 7.0 PERCENT STRAIN IN/IN f Figure 3.7 Maximum Membrane Strain l 10 0 80 - v5 Q. W 60 x3(n (nW 40 - x Q. 20 OO 10 20 30 40 50 60 70 DISPLACEMENT IN. Figure 3.8 Maximum Radial Displacement

39 i i M l il 7 PI il /.f i /// i /// i ( / r/ i s\\\\ i \\'\\\\ i \\.g< \\_ PRESSURE II (psi) iI 43 I 99 70 ,jll 75 --~ 78 ~ -~ Figure 3.9 Deformed Shape at Different Pressure Levels l-l l l 1 m

l 1 NRC f OHM 33b u s. NUCL E AH RE Gul ATORY COMMI$5 ION

1. RE PORT NUMBE R

@!$ uc2 i".II f l","u*;m' O di'~""' s l .w.= BIBLIOGRA_PHIC DATA SHEET i NUREG/CR-4273 ismnnr.arwm on e,e,~m .t 3g_4g,g

2. TITLE AND SUBTIT LE I

Crack Propagation in High Strain Regions of Sequoyah Containment 3. DATE REPORT euBoiSsEo l j Mom mn March 1993 4, FIN OR GRANT NUMBER A4136

5. AUTHOR (5)

6. TYPE OF RtPORT l.

l L. Greimann, F. Fanous, D. Bluhm Technical l

1. YE RlOD COV E R E D tracousne Datest I

i

8. PE RF ORMING ORGANIZATION - NAME AND ADDRESS #r hac. pra,dr D won, off.ce os acyton, u.E haceer Repuhrory com msuon. ena meihne madresosrconewser, paw anme end meanna ouressJ Ames Laboratory lowa State University Ames, IA 50011 y

i

9. SPONSORING ORGANIZATION NAME AND ADDR ESS rer wac. rvor ~l;eme e.eso v s #conrracror.prp dae wac o.riuan, otra or Reama. v.A sw*er amatory comme uon,

[ cmr meitmp eaaress) Division of Engineering l Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission l Washington, DC 20555 j

10. SUPPLEME NTARY NOTES i

11. ABSTRACT r200 eword or deal The rote of release of radiooctive materials from o containment during a severe occident hos a significant impact on the consequences of the occident. One hypothesis for o contoinment leakoge model states that the containment will develop o controlled relatively small leck before the pressure reaches the point where o general rupture of the shell occurs. Another states that ' overall foiture will occur with tofoi release of the vessel contents olmost instantoneously.' The Sequoyoh ice condenser containment vessel has been studied for some time to predict the possible locofion and extent of leokoge which could occur during a severe occident. In this work, three criticot high strain locations were studied to predict crock propogotion from on initiolly small defect The 1/?-inch plate near the Sequoyoh springfine was selected for further study. A detailed finite i

element model of the region was prepored and o virtual crock extension method for colculating the J integral was developed for use with the general purpose finite element progrom, lhe pressure in the model was increosed f.e 78 psi which produced a moximum membrone strain of 6.5 percent. At this point the surfoce crock was assumed to propogote through the plate and leokoge begon. Using the virtual crock extension method. two through crocks with different lengths wue found to be unstoble of this pressure which would ollow Olmost instantaneous release of tho vessel contents.

12. KE Y WORDS/DESCH:P10H5 rurr sworas orpnesm aner e m sessst sworeartners en hersna rne sepers.J

13. Ava LAluuT Y 61 AILME NT severe accident, containment leakage, Sequoyah ice condensor unlimited containment, crack propagation, J integral, finite element

• • .S*wa'" "^ = = *

(Tha Pepe) unclassified (7Adp heep,T/ unclassified 18A NUMBER OF PAGES ) 16 PHICE 4 NRC FORM 33b (7 419) t

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NUREG/CR-4273 CRACK l'ROl'AGATION IN lilGli STRAIN REGIONS OF SEQUOYAll MARCH 1993 CONTAINMENT UNITED STATES NUCLEAR REGULATORY COMMISSION FIRST CLASS Mall P STA E AN0 FEES PAID WASHINGTON, D.C. 20555-0001 u 9 PERMIT NO. G-67 OFFICIAL BUSINESS PENALTY FOR PRIVATE USE, $300

.NUREG/CR-4273 CRACK l'ROPAGATION IN llIGII STRAIN REGIONS OF SEQUOYAH - - MARCH 1993 ' CONTAINMENT. UNITED STATES - NUCLEAR REGULATORY COMMISSION - FIRST CMSS MAIU POSTAGE AND FEES PAtD WASHINGTON, D.C. 20555-0001 USNRC PERMIT NO. G-67 OFFICIAL BUstNESS PENALTY FOR FRIVATE USE, $300 I}}