ML20239A681

Crack Propagation in High Strain Regions of Sequoyah Containment

ML20239A681
Person / Time
Site:	Sequoyah
Issue date:	07/31/1985
From:	Bluhm D, Fanous F, Greimann L AMES LABORATORY, ENERGY & MINERAL RESOURCES RESEARCH
To:	NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES)
Shared Package
ML20234B866	List: ML20239A681 NUREG-1264, Forwards List of Refs from NUREG-1264.Circled Refs Must Be Placed in Pdr.Refs 7,10 & 28 Encl.Ref 4 Already in PDR as Ref J.10.3 of NUREG-1150
References
CON-FIN-A-4136 IS-4878, NUREG-1264, NUREG-CR-4273, NUREG-CR-4273-DRFT, NUDOCS 8709180099
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Text

'

'r NUREG/CR-4273 IS-4878 no 9+c -

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CRACK PROPAGATION IN HIGH STRAIN REGIONS OF SEQUOYAH CONTAINMENT i l

Second Draft of Final Report ,

July 1985 Prepared by L. Greimann, F. Fanous, D. Bluhm Ames Laboratory Iowa State University Ames, IA 50011 Prepared for Division of Engineering Office of Nuclear Reactor Regulation U.S. Nuclear Regulatory Commission Washington, D.C. 20555 NRC FIN N0. A4136 8709100099 NUREG 870916 PDR PDR 1264 C

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. D SCLAIMER This book was prepared as an account of work sponsored by an agency of the United States Government. Neither the United .

States Government nor any agency thereof, nor any of their .

employees, makes any warranty, express or implied, or as- -

sumes any legal liability or responsibility for the accuracy, completeness or usefulness of any'information, apparatus, pro-duct, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trade-mark, manufacturer, or otherwise, does not necessarily con-stltute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not neces-sarily state or reflect those of the United States Government or any agency thereof. l Printed in the United States of America Available from National Technical Information Service U.S. Department of Commerce  ;

5265 Port Royal Road i Springfield, VA 22161

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-1 TABLE OF CONTENTS l l

LIST OF TABLES ......................... iv LIST.0F FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . v l

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AJ!v1WLEDGMENT . . . . . . . . . . . . . . . . . . . . . . . . . .

EXECUTIVE

SUMMARY

. . . . . . . . . . . . . . . . . . . . . . . . I

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . .- '2  !

1.1 Objective .-. . . . . . . . . . . . . . . . . . . . . . . 2

-1.2 Approach ........................ 3 1.3 References. . . . . . . . . . . . . . . . . . . . . . . . 4

2. CRACK GROWTH CRITERIA . . . . . . . . . . . . . . . . . . . . 5 2.1 Crack Growth Process .................. 5 2.2 Review of Criteria .................... 5  ;

2.3 J Controlled Crack Growth . . . . . . . . . . . . . . . . 6 2.4 J - Applied . . . . . . ... . . . ._. . . . . . . . . . . 7 2.4.1 Crack -Idealization and Elastic Solutions ..... 7 2.4.2 Analytic Elastic-Plastic Solutions ........ 7 2.4.3 Finite Element Elastic-Plastic Solutions ..... 9 2.5 J-Resistance ...................... 12 2.6 References ....................... 13

3. SEQUOYAH CONTAINMENT ..................... 17 3.1 Previous Results .................... 17  ;

3.2 Postulated Crack .................... 17 l 3.3 Surface Crack to Through Crack Propagation. . . . . . . . 17  :

3.4 Propagation of Through Crack ............... 18  !

3.5 References ....................... 20

4.

SUMMARY

. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.1 Conclusion ....................... 21 i 4.2 Recommendation. . . . . . . . . . . . . . . . . . . . . . 21 ]

1 l

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' ' iv LIST OF TABLES Table 2.1 Typical Steel Properties, Sequoyah A516, Gr.60 . . . . 22 Table 3.1 Surface Crack to Through Crack Propagation . . . . . . 22

)

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(

1

- _ _ _ _ _ - _ _ _ _ _ _ _ i

, v.

LIST OF FIGURES Figure 1.1 Sequoyah Containment - Azimuth 285* ......... 23 Figure 1.2 Crack in 1/2-inch Plate Near Springline of . . . . . . 24 Sequoyah Containment Figure 2.1 Idealized Crack Growth Process . . . . . . . . . . . . 25 Figure 2.2 Definition of J as Generalized Force for . . . . . . . 26 Crack Movement )

Figure 2.3 Material Resistance to Crack Growth ......... 26 a Figure 2.4 Comparison of J Calculations, Center Cracked . . . . . 27 Plate (CCP) (a/b = 0.1, a = 1, n = 10) i Figure 2.5 Virtual Crack Extension Pattern ........... 27 Figure 2.6 One-quarter of Center Cracked Plate, . . . . . . . . . 28 Finite Element Mesh (1/2" Plate, a/b = 0.1, a = 1. n = 10)

Figure 2.7 Attempted J - CVN Correlation ............ 29 Figure 2.8 Crack Growth Resistance Values . . . . . . . . . . . . 30 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  !

Figure 3.2 Membrane Strain Near Penetration of ......... 33  !

Sequoyah Containment  !

Figure 3.3 Membrane Strain in Sleeve of Sequoyah ........ 34  !

i Equipment Hatch Assembly Figure 3.4 ASME Acceptance Standards for Radiograph . . . . . . . 35 Welds (Section III, Subsection NE, Class MC Components, Paragraph NE 5320)

Figure 3.5 Comparison of J Calculations, Edge Cracked . . . . . . 36 1 Plate (ECPT) (a/b = 1.8, a = 1.5, n = 10) l l Figure a.6 Finite Element Model of a Section of the . . . . . . . 37  !

Sequoyah Containment Near the Springline j Figure 3.7 Maximum Membrane Strain ............... 38 Figure 3.8 Maximum Radial Displacement ............. 38 Figure 3.9 Deformed Shape at Different Pressure Levels ..... 39 l L____ . _ _ _ _ l

' ' vi ACKNOWLEDGMENT i

The authors would like to express their . appreciation to three members s

of the U.S. Nuclear Regulatory Commission, Mr. Goutam Bagchi, Leader, Seismic Qualification- Section; Mr. James Knight, Acting Director, Division of Engineering; and Mr. Robert. Wright, NRC Project Manager, Division of Engineering, for their help throughout the course of.this 1 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. 4 1

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EXECUTIVE

SUMMARY

The rate of release of radioactive materials from a containment during a severe accident has a significant impact on the consequences of the accident. One hypothesis for a containment leakage model states that 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 f ailure will occur with total release of the vessel contents almost instantaneously. 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-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 i 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 i method for calculating J has been developed for use with a general purpose finite element programs. The various methods are compared herein. Approximate values of the material J-resistance are t sbu-lated.

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 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 which produced a maximum membrane strain of 6.5 percent. At this point 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 I' through crack will not be stable and general failure will occur with the almost instantaneous release of the vessel contents, i

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l L_ _ _____z----- - -.. I

' > 2

1. INTRODUCTION

'i During a . severe accident, a containment may develop a controlled, [

relatively small, leak before the pressure reaches the point where a j general rupture of the shell occurs. On th other hand, overall fail- l

.ure may occur with total instantaneous release of the vessel contents. l Either possibility may occur, depending primarily upon local geometry, I material details. and the applied pressure [1.1].' l f

The at the NRC has established request a Containment of the Severe Performance

- Accident Research Plan Working ( Group (CPWG)

SARP) Senior Review . Group to . study several models of containment' leakage. The members of this group have studied many possible leak models [1.2] such r- pre-existing leakage, hatch seals, general rupture and fl ange gening. 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 l

[1.3,.1.4], it is not clear what is the weakest point in this vessel. ,

Containment Shell - Th e containn;ent shell is estimated to have a strength at which "significant yielding" occurs between 55 and 60 psi i

[1.5]. . This strength is controlled by the 1/2-inch plate near the  !

springline. The design pressure is 12 psi. j

, Penetrations' - A study of all the penetrations in the Sequoyah contain- l' 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- *

' g ated leakage of the equipment. hatch seal as the containment shell deforms the penetration sleeve. The three-dimensional finite element model indicated that relative motion of the flege interfaces 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 will depend upon how f ar the crac% extends. For example, a crack in the 1/2-inch containment plate, Fig.1.2, may be arrested by an adja-cent stiffener or the adjacent thicker plate; or, it may propagate through both of these. In this and other regions, the high strains may J' be sufficiently localized so that the crack arrests as it moves from 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.

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4

,. 3 1.2 Approach 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 field--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. surface flaw, the growth criteria is applied to predict when a through crack develops and how far the through crack-extends.

4 4

i l

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.. , 4 1.3 References 1.1 Kussmaul, K., et. al, " Crack Arrest Behavior in Pressure Vessels,"

Paper B/F 4/10, SMIRT, August 1983, pp. 337-346.

1.2 Containment Performance Workin Group, " Containment Leak Rate Estimates," Fourth Draft, NUREG/g1037, March 1984.

1.3 Greimann, L., Fanous, F. and Bluhm, D., " Reliability Analysis of Containment Strength," NUREG/CR-1891, August 1982.

1.4 ACRS, Subcommittee ion Structural Engineering, " Establishing the Maximum Internal Pressure that the Sequoyah Containment Structure Can Withstand," Washington, D.C., September 2, 1980.

1.5 Greimann, L., Fanous, F., and Bluhm, D., " Containment Analysis Techniques, A St ate-of-the- Ar t Summary," NUREG/CR-3653, March 1984.

1.6 Greimann, L., Fanous, F., and Bluhm, D., "Sequoyah Equipment Hatch Seal Leakage," NUREG/CR-3952, 15-3952, Final Report, February 1985.

I l

"*Mhwe---m--_- -_m.__--______ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ,

C ,

5 2.- CRACK GROWTH CRITERIA 2.1 Crack Growth Process 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 plate (Fig. 2.1d) subjected to a uniaxial stress, o. 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. 2.1c) propa- I gates across the plate, j i

2.2 Review of Criteria .]

There are no crack growth criteria for ductile materials which are generaily accepted by the tracture mechanics community. No single  ;

parameter or combination of parameters have been found which satisf ac-torily characterize-the growth of cracks through regions of high strain .]

and with gross plasticity of highly ductile materials. Currently, the l

)

state-of-the-art in fracture mechanics permits the reliable prediction of small crack growths in regions of limited. plasticity. It is beyond the scope of this work to review completely the state-of-the-art in elastic-plastic fracture mechanics (EPFM). .Indeed, the authors are not . p qualified to make the judgments necessary for such a review. However, 1.f a very brief listing of the various criteria is justified.

J Integral . The J integral is a measure of the energy release rate as 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].

-CT00. The crack tip opening d' displacement (CT00) 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]. l 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 il (brittle fracture) and plastic collapse governed by a limit load [2.9, 2.10,2.11,2.12]. l Crack Tip Energy Release Rate. Probably related to the J integral {

approach, the crack tip energy release rate criterion considers the f 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 obtained from a uniaxial tensile test [2.14, 2.15, 2.16, 2.17, 2.18].

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' 6 Each of these' criteria has its proponents. They have been' reviewed by 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 satisf actory for the complete description of ductile crack growth. If the number of proponents can be used as a legitimate j measure of the validity of the criterion, the J integral and CT00 j approaches are more accepted [2.10, 2.21]. The J integral. criteria j will be adopted herein.

2.3 J Controlled Crack Growth The J integral has been defined in a number of ways but perhaps the most physically appealing way is to define J as the generalized force  ;

associated . with an increment of crack growth. The energy balance J equations for an increment of crack area 6A is J 6A + 6U + 6V = 0 (2.1) where 6U = 6f Wdv (2.2) v c

W = f ode (2.3) 0 l 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 I strain energy density. The quantity,  !

6V = - F 6u (2.4) 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 6A. The applied J integral can be calculated in a number of ways, as will be discussed in Section 2.4. Crack growth is presumed to occur when J reaches some critical value J , usually considered to be a material property. The R

J resistance is usually characterized by the JR vs. aa curve (Fig.

2.3) where aa is an increment in length of crack growth. Hence, crack growth occurs if

'I J>J R (2.5)

The amount of growth is controlled by the JR curve. The J criteria applies to a limited amount of growth [2.1, 2.4, 2.5, 2.7]:

J/y R

C >> (2.6)

R JR f [dd )

i

t 7 where C is the remaining li ament, i.e. the remaining portion.of the material ahead of the crack t p (Fig. 2.2}.

2.4 J - Applied 2.4.1 Crack Idealization and Elastic Solutions As shown in Fig. 2.1, two crack shapes are envisioned as the crack grows--an initial surf ace crack and a through crack. The surface crack can probably best be idealized as an eliptic crack. However, there are limited plastic solutions for this crack shape. If the crack is long (a < < c), the conditions at the base of the crack are approximated by a single edge cracked plate under tension (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]

2 2 Je= Y no a E

in which y=

1.12 !1 - v ECPT ,

sec "a

- CCP W

The above solution for the ECPT case is limited to shallow cracks (a < < B).

2.4.2 Analytic Elastic-Plastic Solutions The application of J in the nonlinear range depends upon the calculation of J and this has been the subject of many studies--both I analytical and numerical (finite element). Here, we will summarize a few solutions which seem to attract the most attention. Most of these solutions use a Ramberg-Osgood approximation to the true stress-true strain curve from a uniaxial tensile test of the material:

=

+a( ) (2.8)

C y "y "y in which a and c are the material true yield stress and strain, respectively(and a End n are material constants which are selected i to provide a good fit to the experimental curve [2.20]. For purposes '

of presentation, the yield J will be defined by 2 2 J = Y . (2.9)

1. E l

8 Turner [2.19, 2.22] gives, perhaps, the simplest approximation to J as 2 2 E

J y l (2.10)

Jy L 2.5 (,'y - 0. 2) ,y > 1.2 l I

This approximation is intended to be an upper bound to most practical cases, including surface and through cracks. The above equation does i 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 2

F + 3.14 a ( ," )n + 1 Surface l

3. 3(,7 ) Y J ,1 (2.11) 2 J w Y

4. 3(," ) + 10.6 a ( ," )n + 1 Through y y j l

After several years of study, the EPRI [2.2, 2.3, 2.4, 2.23] presents <

J solutions as the sum of the elastic and fully-plastic cases {

2 J ah e l

= (o ) +

1 (Pp )n + 1 (2.12)

J y o y wbY 2 y in which the notation is as follows:

ECPT CCP c (net width) = b-a W/2 - a b (total width) = B W/2 P (load) = eB oW 1/2 2 2 Py (limit load)

• 1.46 oy (( c +a ) - a] oy(W-2a)

= 21.7 4.62 h1( ba_ 8 =1)

= 3.02 2.86 hi( ba4 = 1)

= P P Y y y

1. y B oyW

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9 j

. In this equation, h is dependent upon the specimen shape, crack size, 1

and material shape parameter n. It has been obtained for several cases by EPRI using numerical methods for the fully plastic solutions. l The. values tabulated above are for 'a shape factor n = 10. The -

solution for the plane strain ECPT case are from [2.23] (not [2.4]) and for the plane stress CCP are from [2.4]. The EPRI correction for i effective crack length in the elastic portion has not been included.

A modified form of the R-6 assessment diagram has been suggested by l Chell and Milne [2.10] and is given by a parametric equation as-J ,8 i n s ec "-- p z

Jy ny 2 P gp 2 /

_ = [p + ( 1 - 1 1 )(o._u- 1) ] ( 1 + " u "y) (2.13)

P J oy 2 y

in which the parameter p ranges as i

0<p<1 j is the ultimate tensile stress. The term on the extreme right j and o u follows their suggestion to use a flow stress (arithmetic mean of the l yield and ultimate) in the evaluation of the limit load. Equation 2.13 is plotted parametrically as p ranges from 0 to 1.

The above four solutions are plotted for a CCP case in Fig. 2.4. Note that, in order to plot the results on the strain abcissa, the Ramberg-Osgood relationship, Eq. 2.8, was used in conjunction with Eqs. 2.11, 2.12, and 2.13 to find the strain corresponding to any stress state.

I 2.4.3 Finite Element Elastic-Plastic Solutions Most numerical solutions for the J integral are by one of two methods.

In one method, the contour integral formulation of J is used directly

[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 i n Eq . 2.1. The crack is given a virtual area growth 6 A. The virtual change in internal and external energy caused by this growth can be calculated. This is equal to the amount of surf ace energy released during the growth. The generalized force J can then be calculated directly by Eq. 2.1.

l The virtual crack extension is usually accomplished by a series of stress free nodal shif ts and releases as the crack propagates [2.3, 2.29, 2.30, 2.33, 2.34]. The virtual crack extension is accomplished .,

l

i 10 by a virtual change in the nodal coordinates (stress-free) with no total volume change and is not the same as a virtual displacement.

Hence, in Fig. 2.5, node C is given a virtual stress-free coordinate shif t 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) 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].

To accomplish the virtual coordinate shift in an existing general purpose finite element program with a minimum of change, phantom elements are' introduced. In the region depicted in Fig. 2.5, the phantom elements duplicate the real elements except they are connected to the node C'. The phantom elements are given a very small thickness, say 0.0001 times the real thickness. Hence, as the structure is l oaded, 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

_ hantom elements has been loaded to same load level at which the J p

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, 1

J= 6U (2.14) 6A or, using Eq. 2.2, 1

J= (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 J=- 1

[ [ (oj Vj ac j + Wj aVj)] (2.16)

AA i in which aj, Wj and Vj are the stress, strain energy density and the volume of the real element i, respectively. The increments are j l

ac =ej' -cj (2.17)

AVj = Vj' - V4 (2.18) l where cj' 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., ,

l

• .- 11 AVj = (Aj' - Aj) Bj (2.19) where Aj ' represents the area of the phantom element and Aj and Bj are the area and the thickness of the real element, respectively.

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.

First a static ' analysis procedure was tried. In this procedure, the applied edge stresses were increased in increments and a sufficient nurnber of iterations were run to permit convergence. In the ANSYS program, convergence criteria are: (1) the charge in displacement between consecutive iterations must be less than 0.001 inch and, (2) 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 relaxed somewhat.

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 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.

Physically, this would correspond to placing the structure in a viscous 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, hence, the proportionality constant was taken as 8000/sec.

The applied edge stress was increased in steps. For each step, the 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 each step a very small integration step size, At, was used (0.001 sec.). During the solution, At does not remain constant but changes automatically as optimized by the ANSYS program based on the third derivative of the displacement with respect to time (jerk).

The finite element results were used in conjunction with Eq. 2.14 to

' calculate J at different applied stress levels. This was accom-plished using the ANSYS postprocesser and a computer program written by the authors. The calculated J for the CCP specimen in Fig. 2.6 are plotted in Fig. 2.4. For the elastic case (Linear Elastic Fracture f Mechanics), the exact J for an applied nominal stress of 10 ksi is Je = 0.0636 k in/in2 1 1 i

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- _ _ - _ _ _ _ _ _ _ _ _ _ _ \

12 l l

I The finite element procedure using phantom elements give Je= 0.0643 k in/inz which is certainly a favorable comparison considering the coarse mesh.

As can be seen from Fig. 2.4, the proposed analysis gives results below i 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.

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 J values were available for this material when this study was conducted.R To establish an estimate of the J-resist ance, 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 [2.13 for reactor steel ( A5338). Attempted correlations by Paris [2.1] and Kussmaul [2.8] are illustrated. Using a very gross extrapolation and the Charpy values in Table 2.1,2one could estimate the J g value to be2 in the range of 1 to 2 K in/in for 3-inch plate and 3 to 6 K in/in 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]

suggests that these values are, at least, the correct order of magni-tude (Fig. 2 8).

For use in both the analytical and finite element analyses to follow, 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 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.

13 2.6 References 2.1 Paris, P.C. and Johnson, R.E.," A Method of Application of 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.

2.2 Shih, C.F. , Kumar, V. and German, M.D., " Studies of the Failure Assessment Diagram using the Estimation Method and J-Controlled Crack Growth Approach," Elastic-Plastic Fracture: Second Symposium, Volume II - Fracture Resistance Curves and Engineering Applications, ASTM Speci al Technical Publication 803, October 1981, pp.11-239 to 11-261.

2.3 Kumar, V., et. al, Advances in Elastic-Plastic Fracture Analysis, Electric Power Research Institute, EPRI NP-3607, August 1984.

2.4 Kumar, V. , German, M.D. and Shih, C.F., An Engineering Approach for El astic-Pl astic Fracture An alysi s , Electric Power Research Institute, EPRI NP-1931, July 1981.

2.5 Ernst, H.A., " Material Resistance and Instability Beyond J-Controlled Crack Gr owt h ," Elastic-Plastic Fracture: Second Sym)osium, Volume I - Inelastic Crack An alysis , ASTM Special Tec1nical Publication 803, October 1981, pp. I-191 to I-213.

2.6 de Lorenzi, H.G., "El astic-Pl astic Analysis of the Maximum Postulated Fl aw in the Beltline Region of a Reactor Vessel,"

As]ects of Fracture Mechanics in Pressure Vessels and Piping, PV)-Vol. 58, ASME, July 1982, pp. 71-90.

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

2.9 Milne, I., " Calculating the Load Bearing Capacity of a Structure Failing by Ductile Crack Growth," Advances in Fracture Research, ,

Proceedings of 5th International Conference on Fracture, Cannes, l 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: ,

Second Symposium, Volume II -

Fracture Resistance Curves and Engineering Applications, ASTM 5pecial Technical Publication 803, October 1981, pp. I1-179 to II-205.

' 14 l

l 2.11 Bl oom, J.M., " Validation of a Deformation Plasticity Failure l 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.11-206 to II-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 Dissipation in Pl ane-Strain Crack Growth Under Large-Scale Yielding," Elastic-Plastic Fracture: Second Symposium, Volume I

- 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 Sih, G.C. and Tzou, D.Y., " Mechan ics of Nonlinear Crack Growth:

Effects of Specimen Size and Loauing 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 Softening: Application of Strain Energy Density Theory," Theoretical and Applied Fracture 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.

2.18 Sih, G.C. and Chang, C.I., " Prediction of Failure Sites Ahead of Moving Energy Source," Fracture Mechanics Technology Applied to Material Evaluation and Structure Design, The Hague: Marinus 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," Elastic-Plastic Fracture: Second Symposium, Volume II -

Fracture Resistance Curves and Engineering Applications, ASTM Special Technical Publication 803, October 1981, pp.11-103 to 11-114.

2.21 Marston, T.V., Et . al, " Development of a Plastic Fracture Methodology for Nuclear Systems," El astic-Pl astic Fracture:

L__________________

l l

15 Second Symposium, Volume II - Fracture Resistance Curves and  !

Engineering Applications _, A5lM 5pecial Technical Publication 803, October 1981, pp. II-115 to 11-132. #

2.22 Turner, C.E., "A Review of. Elastic-Plastic 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, i The Netherlands, 1981, pp. 39-58, 2.23 Shih, C.F. and Needleman, A., " Fully Plastic Crack Problems, Part l 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 El astic-Pl astic Stable Crack Growth An alys i s ," !

As)ects of Fracture Mechanics in Pressure Vessels and Piping, PV)-Vol. 58, ASME, July 1982, pp. 175-184.

2.25 Watanabe, T., et. al , "J-Integral Analysis of Plate and Shell Structures with Through Wall Cracks Using Thick Shell Elements," i Paper G/5 3/8, SMIRT, August 1983, pp. 257-264. l 2.26 Dodds, R.H. and Reed, D.T., " Elastic-Plastic 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., " Analysis of Dynamic Crack Propagation and Arrest in a Nuclear Pressure Vessel Under Thermal Shock Conditions," Aspects of Fracture Mechanics in Pressure 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 Simul ation of Post-Yield Fracture Experiments," Com)utational Fracture  :

Mechanics - Nonlinear and 3-D Problems, PV3-Vol. 85, ASME, June 1984, pp. 119-131.  !

1 2.30 Bakker, A., "On the Numerical Evaluation of the J-Integral," i Paper G/F 2/4, SMIRT, August 1983, pp. 181-189.  ;

2.31 Cells , A. , Squillani, A. and Milella, P.P., " Experimental and .

Numerical Evaluation of J Integral on Tubes," Paper G/F 4/2, '

SMIRT, August 1983, pp. 275-281.

l

• . 16 i

J 2.32 Bel iczey, S. and Hofler, A., " Calculations to - Experimental l' Results of Crack Growth," Paper G/F 4/9, SMIRT, August 1983, pp.

329-335..

l-

'2.33 de Lorenzi, H.G., . "3-D Elastic-Plastic Fracture Mechanics 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 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, Methodology for Plastic Fracture, Electric Power Research Institute, EPRI NP-1735, March 1981.

2.39 Blejwas, T.E. , Woodfin, R.L., Dennis, A.W. and Horschel, D.S.,

" Containment Integrity Program," NUREG/CR-3131/1, SAND 83-0417, 1 March 1983. i l

l l

i i

l l

l

a 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 leakage occur. The results of previous analyses, summarized here, have indicated that high strains occur in these regions

. 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 axisynmetric approximation to the containment [3.1].

Penetration at Elev. 767', AZ. 260*. A three-dimensional finite analysis [3.1] has shown that the maximum membrane strain for this penetration is about 0.003 at 60 psi (Fig.

3.2).

. 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

[3.2].

3.2 Postulated Crack Following Sec. 2.1 and Fig. 2.1, an initial surf ace crack is postulated in each of these regions. It is not clear what is a most realistic crack shape and size. Probably a sensitivity study of different possi-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 ASME acceptance standards for radiographer welds in containment vessels

[3.3], this is a linear indication with length limits,1, as listed in Fig. 3.4. Since 1/a is greater than 3 for linear indications, the maximum crack depth, a, is also listed.

3.3 Surface Crack to Through Crack Propagation 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 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 furner values are repre-sentative and easier to calculate and, hence, will be used in the following.

• . 18 The J resistance of the material is probably the most uncertain

quality in this analysis but the bounds presented in Sec. 2.5 and l listed as J R in Table 3.1 are appropriate. Upon setting the applied J values (Eqs. 2.9 and 2.10) equal to the material resistance Ja, the nominal strain cR for surface crack propagation is found and 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 represents the pressure at which the postulated surface 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 1 determination of other than a lower bound to pR. However, one can note that, because of the " flattening" of the pressure versus strain curves, t the relative uncertainty in pR will not be as large as the uncer-tainty in Jg.

3.4 Propagation of Through Crack The results of the previous section (Table 3.1) indicate that the j postulated surface 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 strain regime so that the p in Table 3.1 can be refined and also to estimate the extent to whic$ the through crack will propagate. In this regard, the finite element model illustrated in Fig. 3.6 was formulated. 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 2.1 and Fig. 2.9 are used. Synmetry boundary conditions are imposed on both vertical boundaries. The top boundary is constrained in the tangent plane of the hemisphere, but permitted free motion perpen-dicular to this plane. The meridional forces induced by pressure j loading are applied to the lower boundary, which is constrained to move j uniformly in the vertical direction. Internal pressure loading is j applied to the shell elements which represent the containment shell. A total of 308 elements and 158 nodes are included in the model. l 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 slow dynamic approach described in Sec. 2.4.3.

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 I

a

. 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 (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 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 as described in Sec. 2.f.3,'the value of the applied J was calculated as about 120 k in/in . This is much larger than any conceivable J-resistance of the material. One must conclude, therefore, that at a pressure of 78 psi, a through crack of 12 inches will continue to propagate in the meridional direction in the 1/2-inch plate.

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' 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 solution was continued until convergence. Again, the VCE method was implemented and an applied J of 3860 k in/in was calculated. Again, this unrealistically high value of J indicates the crack will continue 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 f ailure.

Note that only one cracking sequence has been studied in this work.

If, for example, the postulated surf ace 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

.. ,- 20 3.5 References -]

-3.1 Greimann, L., Fanous, F. and Bluhm, D., " Reliability Analysis of Containment Strength," NUREG/CR-1891,. August 1982.

3.2 Greimann, L., Fanous, F. and Bluhm, D., "Sequoyah Equipment Hatch Seal Leakage," NUREG/CR-3942, Final Report, February 1985. i 3.3 ASME Boiler and Pressure Vessel Code, ASME, Section III, ,

Subsection NE, Glass MC Components, Paragraph NE 5320. l l

'l i

i i

I l

i

• - 21

4.

SUMMARY

The rate of release of radioactive materials from a containment during a severe accident has a significant impact on the consequences of the accident. 0ne hypothesis for a containment leakage model states that 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 instantaneously. As t part of the Containment Performance Working Group (CPWG) and other studies, the Sequoyah ice condenser containment vessel has been studied i for some time to predict the possible location and extent of leakage which could occur during a severe accident. In this work, three critical high strain locations were studied to predict crack propagation from an initially small defect.

Several criteria are presented in the literature for predicting crack j 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 developed for use with a general purpose finite element programs. The various methods are compared herein. Approximate values of the material J-resistance are tabulated, j 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 Sequoyah springline is then selected for further study. A detailed i' 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 the surface crack was assumed to propagate through the plate and leak-age began. Using the virtual crack extension method, two through '

cracks with different lengths were found to be unstable at this  !

pressure, t t

4.1 Conclusion 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 4.2 Recommendation This study should be considered very preliminary. Elastic-plastic j fracture mechanics has clearly been pushed beyond the acknowledged

}

state-of-the-art. However, the above conclusion for this application  ;

will, most likely, not change.

i i

l _-______-_-_ _ a

22 1

f r-Table' 2.'1 Typical Steel Properties, Sequoyah A516, Gr.60 i

Plate - -  % CVN ,

Thickness oy (ksi) ou (ksi) elong. 0 -30*F(ft-lb) j L 7/16" 48.3 66.0 25 N.A. l 1/2" 47.3 66.6 33 N.A.- q 5/8" 49.2 68.3 29 240 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

)

Specification 32.0 60-80 30 N.A. 'Not Available Table 3.1 Surface Crack to Through Crack Propagation JR p Plate Crack c Location Thickness Depth k in/inZ R R Springline 1/2" 0.083" 3.0 i 1.0 9 i 3% > 65 psig Penetration 5/8" 0.083" 3.0 1.0 8 1 2% > 65 psig Hatch 1 1/2" 0.17" 2.5 0.5 4 1% > 82 psig Sleeve 3" 0.25" 1.5 0.5 2 t 1% > 82 psig

- 23 t = 15 /16" t = 9/l6" t e l/2" i

ELEVATIONS

, 815' 4h" bE 809'6{"

e

. 803' e-

=

799'9 "

796'0"

! 791'Y "

, 788'g."

, 778'6l" 3 769'l"

• • l* , 759'6l"

,~~T 741' Ij"

=c L

'+ 730' W

_ 721'6l"

T 713' 6"

'm

. =>

'g , 701' 6]"

• 3-( 691'2}"

680'9{"

Figure 1.1 Sequoyah Cotitainment - Azimuth 285

(

.e , 24 l

l l-1 l

l s

i i

l "N

1 dN;h N l 1

=

e '

N s\ N\  !

N y,

a

<N:N'N N

<h- \ #%g/fg 4

1 j

IN

'N N ,

ctJ i

%s

= '

w ,

5 '

<\ '

~,

s s\[\ Crack Nr. \[N '

'N \

'N

-% /

\

f l

i l

Figure 1.2 Crack in 1/2-inch Plate Near Springline of Sequoyah Containment 1 l

I I

- - _ - - - - - . -_ - -- - - - - - l

I "

-. - as I

, 2c ,

/

g-

" '- - ,c.

e' ( B

// /

(a) Initial Surface Crack f /, V l, f (b) -

, 2a '

u ,, ,

/

i

/ // l w r ~/ l (d) />

(c) Through Crack l

l l

Figure 2.1 Idealized Crack Growth Process .

. 26 A F,Bu

/ / 80= 8A 1

s i

Bo

' ' C - '

BU J 8 A + BU- F8u = 0 j I

Figure 2.2 Definition of J as Generalized Force i for Crack Movement i

Ja J L l

4 Jc i

l 1

l w '

7 80 ,

4 Figure 2.3 Material Resistance to Crack Growth i

l t '. 27 y

[ '.

.l l-  !

l40 i f i i

l 120 -

I 10 0 -

3 4 J-- 80 -

k Jy g 60 '

y /

l 40 -

20 -

t t I I I

10 20 30 40 50 e / cy (True) i Figure 2.4 Comaprison of J Calculations, Center Cracked {

Plate (CCP) (a/b = 0.1, a = 1, n = 10)

{

/E.//

C C'  !

Y Y

-==.

/l

/

Vs

/ ,%' /

b0 /

/. Boundary

/

.W

- i

//l. ,? j Figure 2.5 Virtual Crack Extension Pattern <

0 . 28

,. t 1

i 72" -

i al g  : !

i o

e D  :

l 1

N 30 v.

zN  %

.y Ab x $. _

AA

~

O A e e i e

i e

i Figure 2.6 One-quarter of Center Cracked Plate, Finite Element Mesh (1/2" P1 ate, a/b = 0.1, a = 1, n = 10)  :

2, I

i i

/

8 u .

/ \

6 - o o

7 /

(Kussmoul) l

{ g

~l i

.C g s 4 .

O  !

.e Q-

. C__ x -

F-

^

.o - =

o 2 - -

'1' s f g u.

m o o j a o i

1. m7

.i l '(Paris) ~

A5338 8 Weld 50 lbO lb 200 250 I

CVN (ft-Ib) 1 l

\

Figure 2.7 Attempted J-CVN Correlation i

L i

' . 30 12 -  ;

EPRI i 1

h5331 8 10 - WELD w

78-C C \ _

x

. tgn

' "'t i "' N 6- ^

! ,  ! 'i 'l $'1

.5 , , , : ! , l., ,

- 4 , 1,, Se 60 % v'f,

\  ;;: 8.v,%, ';'N';  :.::i

,, ,, y , .... = ;

- > e .

,c, c y. ;: 3J 4- ,

,,;;;;;;;;,;fp y ',,,:l /.;.. _ , _

(, ',l, j jN:' ': ~ ' . N.

. y ~ ,,1 c ., , o Rolfe

f A572, dr. 50 2  ;;~ _ _

Kussmal .

I I I I I O.1 0.2 0.3 0.4 0.5 Aa 4 (in.)

Figure 2.8 Crack Growth Resistance Values 3

i: 31' l j:

I  !

,i 1

! i I

Rornberg - Osgood True cr 4  ;

(n= 10, a = 1.5)

,7 __

F U.

P/~~~ .

(g)

~/ Engr. cr-e d y 01 O

I

..l l~

J I-I r

I f -l l t 1 i f I I O.05 0.10 0.15 0.20 0.25 0.30 Q35 STRAIN ENGINEERING Point e c l 1 Ey gy 2 0.015' Fy 3 0.035 (7y +70) / 2 4 0.15 79 5 0.35 (Cy +7 U)/2 i

Figure 2.9 Idealized Stress-Strain Curve for A516, Gr. 60

... 32 i

~

MAXIMUM MEMBRANE STRAIN

ELEVATION 783'0" 1

i -

70 -

+

60 -

?%-

/ <~

i -

3

- g 40 -

1 8 "l

O 30 i E 20 l

10 -

- , , , ll l

% i

.0 01 .002 .003 g I

MAX. MEMBRANE STRAIN Figure 3.1 Membrane Strain in 1/2-inch Plate Near the Springline of Sequoyah mm _ - - _ - _ _ _ . _ _ _ . _ . _ -_...

. i 33 Ring Stiffener (Elevation 769'5f ")

- 5"t

/

Maximum Membrane Strain d

i Elevation

' 767'0"

\

/zimuth 266*

A 70 . i . . .

60 -

9 -

2o. 50 -

5 40 - -

!5 3 30 - -

E

' 20 -

10 -

O O O.002 0.004 0.006 Maximum Membrane Strain Figure 3.2 Membrane Strain Near Penetration of Sequoyah Containment

4 . 34 i

Stringers Maximum Membrane Strain

/

/

/

/ 1

/ .

/

Rings '

/

/

s' f s ' Elevation 741'l2L"

( z.285*

i Hatch

\

[ Sleeve (3 "It )

100 i i i i 80 - -

5m 60 - -

m 40 < - -

E 1

20 . -

0 8 ' ' '

l

} O.004 0.008 0.0120 0.0160 Maximum Membrane Strain Figure 3.3 Membrane Strain in Sleeve of Sequoyah Equipment Hatch Assembly

( .__ . _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ - - _ _ - - - - - _ -

• a

• 35 l

/ ,

, / /

/ /

,/a' '

'/

/

N, Linear Indications (1/a>3)

Thickness Maximum 1 Maximum a less than 3/ " 1/4" 1/12 " ,

3/4" to 2 l 4 /" t/4 t/9 greater than 2 /4 l,

3/4" l/4" Figure 3.4 ASME Acceptance Standards for Radiograph Welds ,

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

l L

I i

l

... g . -;, -

l' l

l-i i i i i i i i .i 5 i i i i i 4 -

.- 3 _

s8 _

l

.N

.5

.N c- .

6

'T

@*\ -

E.2 -

1 1 I I I I I I l I l 1 1 O I O.05 0.10 0.15 True Strain i.

Figure 3.5 Comparison of J Calculations, Edge Cracked Plate (ECPT) (a/b = 1.8, a =1.5, n = 10) l l

L___---_-_--__-_-__._.

"d'= 37

\Ao \

\

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k ,

e

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g Og 8 t ,

k' k'} qil

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2.

y ,es'%* . .

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's k

kb \

w T

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Figure 3.6 Finite Element Model of a Section of the Sequoyah Containment Near the Springline '

\

t

• 4 cje 38 l

10 0 . .

f 80 - _

w -

x 60 -

/

O f

@ 40 20 -

O O.O 1.0 2.0 3.0 4.0 50 6.0 7.0 PERCENT STRAIN IN/IN Figure 3.7 Maximum Membrane Strain 10 0 . . > >

80 -

55 Q. -

w 60 -

x b -

d x

40 -

o.

20 -

0 30 40 50 60 70 O 10 20 DISPLACEMENT IN.

Figure 3.8 Maximum Radial Displacement f

l

39 a 4 '9 I

l 1

II i lY

'il M/:

]h

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/// /  :

(.I sxs

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(psi) lll 43

. ,I .................

60

,l ,

70

,jl

,l 75 ,

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I i

l l

I f

l Figure 3.9 Deformed Shape at Different Pressure Levels