ML20087A526

Analysis of Bellows Expansion Joints in the Sequoyah Containment

ML20087A526
Person / Time
Site:	Sequoyah
Issue date:	12/31/1991
From:	Bluhm D, Fanous F, Greimann L, Wassef W IOWA STATE UNIV., AMES, IA, SANDIA NATIONAL LABORATORIES
To:	NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES)
References
CON-FIN-A-1401 NUREG-CR-5561, SAND90-7020, NUDOCS 9201090203
Download: ML20087A526 (98)

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NUREG/CR-5561 SAND 90-7020 Ana:ysis of Be::ows Ex;pansion Joints in ~::ae Secuoya: 1 Con:ainment Prepared by L Greimann, W. Wassef, F. Fanous, D. Bluhm Institute for Physical Research and Technology Iowa State University Sandia National Laboratories Prepared for U.S. Nuclear Regulatory Commission hbk p

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NUREG/CR-5561-SAND 90-7020 R1, RD lulalysis of Bellows Expansion Joints in the Sequoyah Containment i

Manuscript Completed: October 1991 Date Published: December 1991 Prepared by L Greimann, W. Wassef, F. Fanous, D. Bluhm Ames Laboratory Institute for Physical Research and Technology Iowa State University Ames,IA 50011 i

Under Contract to:

Sandia Nationallaboratories Albuquerque, NM 87185 Prepared for Division of Engineering Office of Nuclear Regulatory Research L U.S. Nuclear Regulatory Commission Wasitington, DC 20555 NRC FIN A1401 l

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ABSTRACT Bellows expansion joints are an integral part of the containment building pressure boundary in some nuclear power plants. They are used at piping penetrations to minimize the loadings on the containment shell due to differential movement between the shell and piping. The purpose of this study was to investigate bellows behavior in the unlikely event of a severe accident inside the containment building. The study began with a survey of available information on bellows design, analysis, 'and past test programs. This information was then used to assess the ultimate behavior of the bellows in the Sequoyah containment.

It.was determined that the bellows at penetration X-47 in the Sequoyah containment would experience the worst loading conditions during a severe accident. Finite element calculations of bellows X-47 were conducted to examine the deformation and resulting strains caused by the combination of axial compression, lateral offset, bending, and internal pressure that would be applied to the bellows during a severe accident. Because of convergence problems, the analyses could not be continued to a point of obvious bellows failure. However, large inelastic bending strains, up to 8%, were calculated.

A test program to determine the ultimate bellows behavior and develop data for validation of analytical methods is recommended.

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TABLE OF CONTENTS EXECUTIVE

SUMMARY

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1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1 Obj ective . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2. ANALYSIS AND DESIGN OF BELLOWS - PREVIOUS STUDIES . . . . . . . . . . 8 2.1 Types of Bellows and Failure Modes . . . . . . . . . . . . . . . 8 2.2 Bellows Analysis and Test Programs . . . . . . . . . . . . . . . 10 2.2.1 Atomics International (1964) . . . . . . . . . . . . . 10 2.2.2 Bar telle Memorial Institute (1968) . . . . . . . . . . . 11 2.2.3 Lockwell International (1984) . . . . . . . . . . . . . 12 2.2.4 Other Studies . . . . . . . . . . . . . . . . . . . . . . 14 2.2.5 Summary of Finite Element Analyses . . . . . . . . . . . 15 2.3 Current Design Criteria . . . . . . . . . . . . . . . . . . . . 16 2.3.1 ASME Code Classes and Service Levels . . . . . . . . . . 16 2.3.2 Bellows Design . . . . . . . . . . . . . . . . . . . . . 17 2.3.3 Design Acceptability . . . . . . . . . . . . . . . . . . 18

3. SEQUOYAH BELLOWS . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1 Bellows Description . . . . . . . . . . . . . . . . . . . . . . 21 3.2 EJHA Design Analysis . . . . . . . . . . . . . . . . . . . . . . 21 3,2.1 Analysis Parameters . . . . . . . . . . . . . . . . . . . 21 3.2.2 Analysis Procedure . . . . . . . . . . . . . . . . . . . 25 3.2.3 Analysis Results . . . . . . . . . . . . . . . . . . . 30

-3.3 X-47 Bellows . . . . . . . . . . . . . . . . . . . . . . . . . 30

4. THREE DIMENSIONAL ANALYSIS OF X-47 . . . . . . . . . . . . . . . . . 32 i

4.1 Features of the Model . . . . . . . . . . . . . . . . . . . . 32 4.2 Execution . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.3 Analysis of the Two-ply Approximation Results . . . . . . . . . 34 4.4 Analysis of the One-Ply Approximation Results . . . . . . . . . 38 4.5 Bellows Failure . . . . . . . . . . . . . . . . . . . . . . . . 49

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SUMMARY

, CONCLUSIONS AND R'ECOMMENDATIONS . . . . . . . . . . . . . 54 5.1 Summary . . . . . . . . . . . , , . . . . . . . . . . . . . 54 5.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.3 Recommendations . . . . . . . . . . . . . . . . . . . . . . 55

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1 APPENDIX. FINITE ELEMENT MODEL PARAMETERS . . . . . . . . . . . . . . . 56 A.1 ABAQUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 A.2 Experimental Correlation . . . . . . . . . . . . . . . . . . . . . 56 A.3 Ply Interface Model . . . . , , . . . . . . . . . . . . . . . . 58

-A.4 Axisymmetric Analysis of X-47 . . . . . . . . . . . . . . . . . 58-A.4.1 Material Properties . . . . . . . . . . . . . . . . . . . 59 A.4.2 Loading . . . . . . . . . . . . . . . . . . . . . . . . . 59 A.4.3 Finite Element Models and Results . . . . . . . . . . . . 63 A 4.4 Nonlinear Solution Parameters . . . . . . . . . . . . . . 67 A 4.5 Combined Effect of the Different Factors . . . . . . . . 67 A.5 One Convolution 3-D Model. . . . . . . . . . . . . . . . . . . . 68 A.6 Modification for Full Three-dimensional Model of X-47 . . . . . 72 REFERENCES . . . . . . . . , , , , . . . . . . . . . . . . . . . . . . . 76 l

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l LIST OF FICURES Figure 1.1 Typical Containment Bellows Penetration . . . . . . . . . 5 Figure 1.2 Typical Bellows Displacement Curve . . . . . . . . . . . 6 Figure 2.1 Bellows Types . . . . . . . . . . . . . . . . . . . . . . 9 Figure 3.1 Ceometry of Bellows at Penetration X-47 . . . . . . . . . 22 Figure 3.2 Effect of Temperature an the Properties of Stainless . . 22 Steel SA 240 Type 304 Figure 3.3 Sequoyah Containment Temperatu.w versus Pressure . . . . 26 Figure 3.4 Displacements of Containment at X-47 Bellows . . . . . . 27 Figure 3.5 EJMA Stresses for X-47 . . . . . . . . . . . . . . . . . 29 Figure 3.6 Equivalent Axial Displacements of X-47 . . . . . . . . . 29 Figure 4.1 Finite Element Mesh of X-47 Three-Dimensional Model . . . 33 Figure 4.2 Deformed Shape of the Compression Side - Two-ply . . . . 35 Approximation Figure 4.3 Change in convolution Pitch, q (Fig. 2.1), Between . . . 36 the Crowns on Tension Side - Two-ply Approximation Figure 4.4 Change in Convolution Pitch Between the Crowns of . . . . 37 Compression Side - Two-ply Approximation Figure 4.5 heridional Surface Strains on the Outer Surface Along . . 39 First and Second Convolutions on Compression Side Up to 30 psi - Two-ply Approximation F.i 4.6 Meridional Surface Strains on the Outer Surface Along . . 40 Third and Fourth Canvolutions on Compression Side Up to 30 pst - Two-ply Approximation Fi u_. 4.7 Meridional Surface Strains on the Outer Surface Along . . 41 Fifth and Sixth Convolutions on Compression Side Up to 30 psi - Two-ply Approximation Figure 4.8 Meridional Surface Strains on the Outer Surface Along . . 42 First and Secc_id Convolutions on Compression Side Up to 61'.34 psi - Two-ply Approximation Figure 4.9 Meridional Surface Strains on the Outer Surface Along . . 43 Third and Fourth Convolutions on Compresrien Side Up to 61.34 psi - Two-ply Approximacion

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Figure 4.10 Meridional Surface Strains on the Outer Surface Along . . 44 Fifth and Sixth convolutions on Compression Side Up to 61.34 psi - Two-ply Approximation Figure 4.1.? Meridional Surface Strains on the Outer Surface of . . . 45 the Crowns on Compression Side - Two-ply Approximation Figure 4.12 Meridional Surface Strains on the Outer Surface of . . . 45 the Aoots on Compression Side - Two-ply Approximation Figure 4.13 Ax(al and Lateral Reactions - Two-ply Approximation . . . 46 igure 4.14 Deformed Shape of the Compression Side - . . . . . . . . 47 One-ply Approximation Figure 4.15 Overall Deformed Shape at 64 psi - One ply . . . . . . . 48 Approximation Figure 4.16 Meridional Surface Strains on the Outer Surface of . . . 50 the Crowns on the Compression $1de - One-ply Approximation Figure 4.17 Meridional Surface Strains on the Outer Surface of . . . 51 the Roots on the Compression Side - One-ply Approximation Figure 4.18 Change of Convolution Pitch on Tension Side - . . . . . 52 One-ply Approximation Figure 4.19 Change of Convolution Pitch Between Crowns on - . . . . . 52 Compression Side One-ply Approximation Figure 4.1 Analytical and Experimental Surface Strains . . . . . . 57 Figure A.2. Stress-Strain Curves for Stainless Steel SA 240 Type 304, 60 Figure A.3 Loading for X-47 Axisymmetric Analysis . . . . . . . . . -61 Figure A.4 Rigid Surfaces and Convolution Mesh for X-47. . .. . . . 62 Axisymmetric Analysis.

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!- Figure A.5 Maximum Meridional Strains at the Inner durface . . . . . 64 l of the Crown l

l Figure A.6 Meridional Strains Along Convolution Inner Surface . . . 65 l

at Touch Figure A.7 Meridional Strains Along Convolution Inner Surface . . . 65 l

St End of Load Step 2 Figure _A.8 Maximum Crown Meridional Inner Surface Strain-Time Curve. 66 Figure A.9 Deformed Shape of Axisymmetric Model at End of . . . . . 66 Load Step 2

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Figure A.10 Three-dimensional Model, Finite Element Mesh. . . . . . . 69 Figure A.ll End Tangent Region . . . . . . . . . . . . . . . . . . . 71 Figure A.12 Original Position of " rigid Surfaces of X-47 . . . . . . . 73 Three-dimensional Modei Figure A.13 Displacement of Rigid Surfaces . . . . . . . . . . . . . 74 Figure A.14 Values of Yield Strength Used in the Finite . . . . . . . 75 Element Model l

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LIST OF TABLES Table 2.1 Bellows Tolerances (ASME Code Case N-290, Class 1) . . . 20 Table 2.2 FJMA Tolerances for Single and Double Bellows . . . . . . 20 Expansion Joints Table 3.1 Sequoyah Bellows Ceometric Parameters . . . . . . , . . . 23

' Tabla 3.2 Sequoyah Bellows Design Conditions . . . . . . . . . . 24 Table 3.3 EJMA Extrapolated Pressures for Sequoyah Bellows . . . . 31 Table A.1 Surface Strains in One Convolution Model . . , , . . . 70

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ACKNOWLEDCMENT  ;

The authors would like to express their appreciation to Mr. David Clauss from Sandia National Laboratories for his help throughout the cours of this work and for running thu final computer runs on Sandia's CRAY-XMP supercomputer.

Special thanks is also extended to Mr. Herman Graves , III, and Dr. James Costello from the U.S. Nuclear Regulatory Commission and Dr. Walter von Rfosemann from Sandia National Laboratories. The assistance of TVA personnel in obtaining information about Sequoyah containment bellows is greatly appreciated.

Very special thanks is also extended to the Project Secretary, Ms. Connie Bates, for the word processor operations and :he secretarial services associated with t this project.

M. B. Parks, Sandia Proj ect Monitor, was intimacely f nvolved with the ds/elopments in this proj ec t . He helped supply much of the background information in Chapter 2. Many of the details described in the analyses of Chapters 3 and 4 were discussed with Dr. Parks in person and vis the telephone.

The authors gratefully ac. knowledge his input.

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, EXECUTIVE

SUMMARY

Bellows expansion joints are an integral part of the pressure retaining boundary of many nuclear containment buildings. They abs wb the normal movement which occurs between the containment building and the pipes that penetrate the containment shell caused by the thermal growth of the pipes and the containment.

The bellows are also designed to withstand relatise movements which may occur durin6 an earthquake. In case of severe accideats, where the containment experiences large movements associated with internal pressures and increased temperature, the bellows may be forced to undergo very large displacements. ,

This combination of end movements and internal pressure could 1.1ciate 14,akage in the bellows. Although recent studies by the Containment Technology Division of Sandia National 1.aboratories and others have investigated several aspects of containment integrity, the behavior of bellows expansion joints during a severe accident has not been thoroughly studied. This study was undertaken to assess current information on the performance of containment bellows with the specific objective to evaluate the performance of the bellows expansion joints in the Sequoyah contairment.

In so far as could be determined, all bellows in containment buildings are circular U shaped convoluted bellows. Most contaira.ent bellows are constructed of two plies of stainless steel mat-rial. However, there are some single ply, stainless steel bellows in Boiling dater Reactor MX 1 units. For the present study, failure of bellows is defined as a loss of the bellows pressure boundary.

This could occur au a result of a tear in the bellows material or in the connection of the bellows to the end spool. In nucicar containments, bellows 1 failure may occur by overpressurization, by application of extreme deformations or by a combination of both pressure and deformation.

Early work on bellows was directed toward the aerospace industry which utilizes small bellows for control systems that operate more or less continuously. Some of the aerospace work was applied to bellows for Liquid Metal Fast Breeder Reactors. Tests vers conducted on several bellows and nonlinear fi..ite element models were applied by several investigators. All of these previous efforts havo focused on the behavior of bellows in the elastic range where the bellows is expected to function repeatedly without permanent damage. For example,= the work at Rockwell was ccaducted primarily to develop American Society of Mechat.ical Engineers (ASME) Class 1 bellows design criteria for commercial breeder nuclear power reactors.

All previous studies er.counte red analytical problems which were not ,

satisfactorily solved. Inters.ction between plies of the bellows has not been modeled acceptably. Material properties for cold formed bellows have not been well described. None of the studies addressed the gross deformation and large strains which would be associated with loadings beyond design. Failure criteria for bellowo leakage are not available.

The Expansion Joint Manufacturers Association (EJMA) has, over the years, formalized design criteria for bellows expansion joints. The design equations are based on elastic shell theory and include empirical factors. The design equations must be verified by each individual manufacturer, using test data obtained from the manufacturer's bellows. ASME has design criteria for bellows which are quite similar to EJMA.

After completing a survey of available information on the performance of containment bellows, the focus of the study changed to an assessment of the behavior of the bellows in the Sequoyah containment. The Sequoyah nuclear power plant has two ice condenser units. Each containment building is a 115 f t, diameter, 174.35 ft. high, free standing steel cylindrical shell with a hemispherical top. The containment design pressure is 10.8 psig. A concrete shield building with similar geometry (125 ft. inner diameter) is built around the steel containment for protection.

All of the bellows in the Sequoyah containment were analyzed using the EJMA equations. Loading for the bellows included internal pressure, temperature, and end displacements. Four possible limit states were investigated: yieldin6, rupture, instability, and squash. Squash is the point at which the bellows are fully compressed between the end pipes. Although the application of the EJMA equations to severe accident conditions represents an extreme extrapolation, it did provide a means to rank the Sequoyah bellows in ,

approximate order of criticality. Based on the EJMA calculations, the bellows at penetration X 47 were determined to be most critical; thus, it was selected for further study.

The obj ec tive of the study of the X 47 bellows was to determine its ultimate pressure and deformation capacity. A complete three dimensional, finite element model of X-47 was formulated and analyzed. An appendix summarizes a study with two- and three-dimensional finite element models to establish efficient mesh sizes, load steps, and convergence tolerances. Contact between adj acent convolutions was modeled with contact surfaces raintained midway between the convolutions. Ply interaction was not modeled. Instead, two bounding cases were investigated. In the first case, it was assumed that the .

two plies are interlocked. Thus, a single ply model with ply thickness equal to twice the individual ply thickness was employed to represent this case. For the second case, the plies were assumed to act independently. The bellows thickness was assumed to equal that of one ply for this case. Because of the varying amount of cold-work along the convolutions, it was difficult to estimate the actual material yield strengths. The yield strengths that were used in the analyses were based on hardness readings taken at various points of bellows with somewhat similar construction. The applied pressures and temperatures were those associated with the saturated steam conditions. The corresponding displacements were based on the re.ults of global finite element analyses of the Sequoyah containment shell. These analyses were conducted by Sandia.

Membrane strains are very small relative to bending strains at the crown and root of the convolutions. Meridional bending strains due to end displacements in the single ply model are about one-half those of the locked two ply model. Meridional bending strains in the single-ply model due to pressure are at least twice those in the two ply modal.

The single-ply analysis was discontinued when the end pipes began to push through the bellows wall. During the two-ply analysis , the runs were stopped because slow convergence of the large strains and nonlinear contact surfaces caused long run times. At the last analysis step, the X-47 bellows conditions are summarized as:

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Single-Plv Igo-P1v Pressure 64.0 psig 61.3 psig Temperature 311' t' 308' F Axial compression 5.34 in. 4.15 in.

Lateral Displacelant 2.39 in. 2.35 in.

Maximum meridional membrane strain 0.11% 0.064 Maximum meridional bending strain 8.24% 4.47%

Maximum effective attain 9.354 4.694 The X 47 bellows han a diameter of 19.25 in, and an initial convoluted length of 12 in. The maximum strains occurred at the bellows crown adjacent to the end pipe.

-Strain failure criteria are not hypothesized. Leakage will probably occur when the end pipes are pushed through the thin wall of the bellows.

Finite element analysis of bellows with gross deformation is certainly feasible but some problems have yet to be solved, such as ply interaction. The convergence criteria of the finite element solution must be improved. Cold-formed material properties are not well defined. Failure criteria for the high strains in bellows need to be postulated and verified experimentally.

Experimental collaboration of strains and displacements with finite element results are also needed. (Strain measurements may be difficult because of the high strain gradients and the large inelastic surface strains.)

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1. INTRODUCTION The Containment Technology Division of Sandia National Laboratories has, on behalf of the U.S. Nuclear Regulatory Commission [1], developed methods for predicting the performance of light water reactor (1VR) steel containment buildings subject to loads beyond their design basis. These methods have been validated by comparison with test results on a 1:8 scale steel containment model and with component tests of penetrations, seals, and gaskets. The next step in the development is to ' apply the predictive methods to an actual containment.

The Sequoyah ice-condenser containment building has been selected both for the pilot demonstration and for a state-of the art estimation of its performance, since it has been used as a reference plant in reactor safety studies.

To initiate the study, all of the structural details in the Sequoyah containment were identified: reinforced penetrations, seals, shell attachments, personnel airlocks, anchorage system, and bellows expansion joints [2]. Each detail was investigated by first order analysis methods or simple finite element models and by on site inspection. The details were then rank- ordered in decreasing order of leakage potential. Bellows expansion joints were high on the leakage potential list, primarily because their behavior with gross deformations has not been studied extensively. Bellows are primarily employed at process piping penetrations in steel containments.1 Their purpose is to minimize the loads imposed on the containment shell which are caused by differential movement between the shell and pipe. A typical application of process piping penetration bellows is illustrated in Figure 1.1. As shown, the bellows form a part of the containment pressure boundary. In most cases (including Sequoyah), the bellows are placed outside the containment shell such that the containment pressure acts upon the bellows as an internal pressure.

Normally, the process pipe is rigidly anchored to the adjacent shield building such that the pipe end of the bellows does not move. However, the containment end of the bellows will displace according to the movement of the containment wall.

The following description assumes that the bellows are located outside the containment wall as shown in Figure 1.1. During a severe accident, increasing pressure and temperature within containment causes a radial and vertical growth of the containment shell. ~

The vertical growth of the containment shell imposes a lateral or snear deflection on the bellows. The radial expansion of the containment acts upon the bellows as axial compression. As shown in Figure 1.2, until containment yielding occurs, the applied deformations are relatively small compared to the undeformed bellows length. However, after the containment pressure exceeds the yield pressure, the r plied axial compression on the i bellows increases rapidly for relatively small additional increases in pressure.

If the pressure continues to increase, the applied axial compression will soon equal the original undeformed bellows length (L in Figure 1.2) which will fully compress or ' squash' the bellows convolutions. Once this happens, rupture of the bellows pressure boundary appears to be inevitable.

1 There are a few applications of bellows in process piping penetrations in concrete containments. Bellows are also used at the penetration of the vent lines into the suppression chamber of Boiling Water Reactor Mark-1 containment structures.

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Penetration Siceve Guard Pipe

._ Expansion Bellows Containrnent 7 n w,.

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Process Pipe Inside -. _ .

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1 Figure 1.1 Typical Containment Bellows Penetration l

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E" Axiol Compression 2e o ga h Bellows E3 8m- Cylindrical 3* Contoinment Laterol

@ Vessel Deformat, ion 5 -

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Contoinment Pressure L Octiowsconvolutedlength PS Contoinment pressure of squoth Figure 1.2 Typical Bellows Displacement Curve

7 At this point, two questions arise:

1) In actual containments, are there cases in which the penetration bellows would be fully compressed before another failure mode of containment would likely occur?

2) Will penetration bellows remain leaktight up to the point of full axial compression while subjected to simultaneous combinations of lateral deformation, rotation, and internal pressure?

The answer to the first question is yes. Based on the Sequoyah shell analysis

[1,3), the estimated mean failure pressure for the containment shell is 75 psi.

Throughout this renort. the notation osi is used to s'up the este cressare when referrine to containment oressure. However, based on the displacement results of this same analysis, the bellows et Sequoyah penetration X 47 will be fully compressed in the axial direction at about 74 psi and subjected to a lateral offset of 2.4 inches. The second question cannot be answered, at present, because sufficient experimental data on the ultimate behavior of bellows is not available.

1.1 objective The initial- obj ective of this study is to determine the state of the art wich regard to bellows analysis capabilities and to deteraine the availability of test data that could be used to answer the second question. Then, knowing the status of-bellows teat data and analytical methods, the second objective was to employ this information to evaluate the performance of the Sequoyah containment bellows when subjected to severe accident pressure and deformation conditions.

1.2 overview A significant effort in this project was devoted toward understanding the current status of bellows analysis, test data, design and fabrication, as summarized in Chapter 2. Current design standards were reviewed. Visits with bellows manufacturers were conducted. Analytical and experimental studies by previous investigators were studied.

Fabrication and construction details for the bellows in the Sequoyah containment building were collected from Tennessee Valley Authority (TVA) and summarized. In order to determine the most critical bellows, each bellows was analyzed for severe accident conditions by extrapolating current design procedures. In Chapter 3, the Sequoyah bellows which, in the authors' judgment, are most likely to develop a leak during a severe accident were selected for furr : c study.

Chapter 4 summarizes a nonlinear, three-dimensional shell, finite element analysis of the selected bellows. Finite element model parameters such as mesh size, load step size, boundary conditions, and convolution interference are I

documented in the Appendix. The analyses were conducted using a finite element code. Based on the analyses results, observations regarding bellows behavior and leakage are presented.

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2. ANALYSIS AND DESIGN OF BEL 1DWS PREVIOUS STUDIES 2.1 Types of Bellows and Failure Hodes The primary function of bellows in containments is to absorb the relative displacements between the containment shell and the pipe to which they are attached. The imposed bellows deformation may be caused by thermal growth, expansion of the containment due to internal pressurization, or seismic motion.

They are also designed to resist the relatively low pressure associated with a design accident.

Bellows are classified according to their cross section, reinforcement, number of plies and the convolution geometry [4). Single and universal bellows expansion joints, as shown in Figures 2.la and 2.lb, are used in nuclear containments. The universal bellows joints are used in locations of relatively large lateral displacements.

Bellows in containment penetrations are typically unreinforced circular U-shaped convoluted bellows [5). Not all containments were surveyed in [5). The ventilation pipes which connect the dry well to the torus of Mark I Units 2, 3, 4, and 5 in - [4] have single-ply bellows. All other expansion. joints in the containment buildings surveyed in [4] are two ply bellows, including joints in the ventilation pipe of Mark I Unit 1. Except for the Mark I Unit 1 joint, all two ply bellows described in [4] are provided with a test connection which allows pressure to be applied between the two plies to check for leakage.

Bellows for all known nuclear containment applications are formed from thin longitudinally welded tubes of stainless steel type 304. All of the bellows forming techniques depend on the application of radial forces on the inner surface of the pipe using hydrostatic pressure or mechanical devices while restraining the radial movement on the adjacent outer surface (4). The amount of localized thinning and the change in material properties due to strain hardening are functions of the forming technique. Bellows in nuclear contain-ment buildings of light water reactors are not annealed af ter cold forming.

The applied end motion of containment penetration hellows consists of a combination of axial and lateral displacements and angulation (see Section 1 and Figure 1.1). Both the pressure and end motions develop membrane and bending strains in the bellows. Membrane strains caused by end motions are relatively small. The maximum bending strains due to internal pressure and axial compression occur at the convolution root.

For general design purposes, potential failure modes of bellows are classified as:

a. Failure due to rupture. For some loading conditions, stresses beyond the-material yield stress may indicate failure. Complete rupture of bellows can occur if membrane strains approach the ultimate strength of the material,

b. Fatigue. The fatigue life of a bellows is affected by various factors such as operating pressure, operating temperature, the bellows material, convolution geometry and thickness, movements per convolution and the heat treatment of the bellows. The strain hardening of austenitic stainless

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steel, induced during the cold forming of the convolutions, Senerally improves the fatigue life of an expansion joint [6). Because of the limit.ed number of load cycles and the relatively small magnitude of applied loadings, fatigue failure is not believed to be a potential failure mode of containment bellows,

c. Instability. Bellows subjected to internal pressure may become unstable.

Instability does not necessarily lead to a failure of the bellows pressure boundary such that leakage vould occur. Two types of bellows instability can be identified: column instability and in plane instability. Column ,

instability (squirm) is similar to the buckling of a slender column under compressive force and is associated with bellows which have relatively is Te length-to diameter ratios. It is defined as a gross lateral shift of the center section of the bellows while tne bellows ends remain fixed

[6). Unlike column instability, the center line of the bellown remains straight under the occurrence of an in plane instability (root bulge). In this case, the plane-of one or more convolutions rotates, increasing the convolution spacing on one side of the bellows and reducing it on the other side. Further increases in pressure will cause the convolution root to bulge through and beyond the crown. This type of instability is associated with the combination of high meridional bending and circumferential membrane stresses due to internal pressure,

d. Ratcheting. As bellows are cycled in the inelastic regino, incremental distortion may occur which would eventually lead to an instability, 2.2 Bellows Analysis and Test Programs The historical evolution of bellows analysis techniques has generally moved from classical clastic shell theory approaches to finite element analyses.

These three stages are represented, more or less, by the three major studies summarized below. The state-of-the-art in the finite element analysis of bellows will be summarized at the end of this section.

2.2.1' Atomics International (1964)

Atomics International 17,8] did much of the early work in bellows analysis. They developed a set of equations to determine the circumferential membrana stresses in the convolutions and the end tangent of bellows due to internal pressure and the maximum meridional membrane and bending stresses due to. Internal pressure and end displacements. The stresses due to end movements I were calculated for any combination of axial, lateral, and angulation movements by transforming the last - two typea of motion into an equivalent axial displacement. These equations were developed utilizing classical elastic shell theory. Some correction factors which were included in the equations to correct l for the assumptions in the development were presented in charts, An equation to i predict the instability (squirm) pressure was also developed for thin tubes. A L reduction factor was applied to the equation for bellow design. Several fatigue tests at room tempera:ure and high temperr.ture were performed and an equation to predict the fatigue life was suggested.

2.2.2 Battelle Memorial Institute (1968)

Trainer, et al., [9] tested several small diameter one- and two ply bellows made of type 347 stainless steel (1 , 3, and 5-in. diameter) and Inconel 718 (1 and 3 in. diameter). An analysis program. NONLIN, was written which utilized direct integration of the governing differential equations.

Ceometric nonlinearities were included but the material was assumed to be linearly clastic. A comparison between the analytical and test results of the single ply bellows showed that the maximum difference in stresses for the 3 and 5 in. - diameter stainless steel bellows was about 14 percent. The difference increased for the 1 in. diameter stainless steel bellows and the Inconel 718 l bellows. No nondestructive methods were available which would provide sufficiently accurate geometric dimensions. The configuration used in the analysis was established by sectionin6 a bellows from the same set of dies.

The 5-in, single-ply bellows mathematical model was further analyzed assuming several small geometrical variations (imperfections). The elastic deflection stresses were sensitive to changes in shape, while the pressure stresses were sensitive to changes in thickness, but relatively insensitive to small changes in shape. The 3-in, single-ply bellows was analyzed once using a variable-thickness and three additional timr using the same shape but different constant thicknesses equal to the nominal, maximum, and minimum measured thicknesses. A comparison between the theoretical analysis and experimental results showed that the theoretical analysis must incorporate the actual thickness and shape variationa of the bellows to provide an accurate prediction of the elastic stresses.

Axisymmetric plastic collapse results in gross permanent deformation of the bellows. An attempt was made to predict collapse by scaling up the elastic analysis results, but the solution was not sufficiently accurate. Even if strain hardening due to forming and fatigua cycling at the root was incorprated , the test results were still higher than the theoretical analysis.

Analysis and test results showed that the buckling pressure was higher for two-ply bellows than for single-ply bellows with the same convolution geometry.

Even though a complete t.nalysis of sidewise beam column buckling (squirm) was beyc,nd the scope of the Battelle work, an appendix described attempts to predict elastic buckling using a beam approximation. The lateral stiffness of the equivalent beam was measered experimentally and calculated analytically usin6 FnNLIN. Agreement was satisfactory. Squirm pressures predicted for the '

perfect case were 3 to 5 times too high. Attempts to include imperfections were only partially successful but did show that geometric imperfections have a significant effect on buckling pressure.

Analysis of the two ply bellows was conducted using a multilayer shell model having the same shape and equivalent membrane and bending stiffness. The t.

model of the _ two ply bellows contains a three-layer sandwich shell with layers of equal thickness. Fictitious values for Young's moduli for the different layers were adjusted to account for the interaction between the two plies under

! different internal pressures. At low pressures, the two plies tended to act l independently. At high pressure, they tended to act as a single ply having a I thickness equal to the total thickness of the plies. With no applied pressure, the two plies acted independently under axial deflection.

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The as built geometry of the individual plies within the two ply bellows was found to be similar to the single ply bellows. Also, the variations of the thickness along the bellows were found to be similar. It was recommended in the Battelle study that, for conservative design under internal pressure, the stresses in two ply bellows be taken equal to the stresses in a single ply bellows with the same cross-sectional shape and with a thickness equal to the thickness of one ply.

2.2.3 Rockwell International (1984)

Reference [10) is a summary of work performed to study the behavior of bellows in elevated temperatures for Liquid Metal Fast Breeder Reactor (IMFBR) applications. The results were used to establish the rules of ASME Code Case 290 [11) which can be used to design IMFBR bellows for Class 1 applications.

The report contains the results of testing three bellows at room temperature.

In the first test, strain gage information was collected to evaluate analytical predictions of strain and characterize the elastic and slightly inelastic strain response of the bellows under various axial and pressure loading conditions.

The second test was conducted to evaluate the effect of angulation on the surface strains. The results were used to evaluate the accuracy of the equivalent axial motion as. a simplifying analytical technique. The ratcheting distortion response of a pressurized bellows was investigated in the third test.

Some conclusions of the Rockwell study [10) are summarized below: ,

(1) The circumferential stresses due to both internal pressure and axial motion are in the rarge of one quarter to three-quarters of the meridional stresses depending on convolution geometry. The meridional stresses are predominantly membrane stresses in the case of internal pressure and a mixture of bending and membrano stresses in the esse of axial motion.

This differs from EJMA [6] which recognizes only the membrane stresses in the circumferential direction. The meridional stresses due to axial motion are sensitive to changes in shape while those due to pressure are sensitive to changes in thickness.

(2) Lateral motion causes larger changes in the convolution pitch near the ends of the bellows than in the middle. The changes in the pitch are extensions on one side of the ballows and compression on the opposite side. The use of an axial motion which is equivalent to the maximum change in the convolution pitch is a conservative approach that ignores the large regions of smaller stresses near the bending axis. Empirical correction curves can be used to account for the unequal distribution o' motion. Angulation motion is similar to lateral motion except t!.at the bellows is in single curvature instead of double curvature.

(3) Fatigue failure can be a result ca flow induced vibration, mechanically induced vibration or functional deflections.

, (4) Squirm pressure is dependent on bellows de fl ec tions and shape I imperfections. Axial er. tension of a bellows will decrease the squirm pressure while axial compression will increase it. In plane instability or root bulge may occur prior to squirm or rupture in some bellows with small length-to-diameter ratio. The critical pressure for in plane instability is also dependent un the convolution shape and can be increased by using deeper convolutions, reducing the convolution pitch or keeping the pressure bending stresses essentially elastic.

(5) Friction between plies of e? 1 ply bellows causes nonlinear response of the bellows to motion loading. a a certain point, the plies act together. The friction force is s... overcome. Increasing the internal pressure will increase the am unt of motion required to overcome the friction force. Internal pressure in a bellows will cause the inner ply to expand outward. At the contact surfaces between the pliet, normal forces will be exerted on the inner ply which will restrain its deflection pattern. This behavior is affected by initial gaps between the different plies. Interply friction tends to increase the stiffness of the bellows and the motion induced stresses. As a simple approach to the analysis of multiply bellows, a modified form of the existing formulae for single ply bellows analysis can be used. Assuming that the plies act independently when calculating pressure stresses and together as a single-ply when  !

calculating motion stresses will give a conservative solution. Another  !

approach is to model the bellows as a multilayered shell in which the gap l between the plies can be modeled as a thin uniform orthotropic layer which I is bonded to the adjacent plies. The material properties of the center layer can be chosen to be rigid in the normal direction and very soft in the meridional direction.

Reference [12] summarizes the history of the development of bellows analysis techniques up to 1984. Much of the perspective for this report was obtained from [12). Elastic end elastic plastic finite element analyses of bellows under internal pressare and deflection are presented in [13).

.Axisymmetric, two-node, thin shell elements in the MARC finite element program were used. The analytical model consisted of three convolutions and an end tangent and contains 60 elements per convolution and 20 elements in the end tangent. Measured dimensions and thicknesses were used. The single ply test specimen was fully annealed. Material properties were considered constant along the bellows and were determined by testing tensile specimens from the same heat of material subj ec ted to the same heat treatment es the bellows. Elastic strains due to deflections correlated well with the test results except for the end tangent region where the d.2 termination of the as built geometry was difficult and inexact. Elastic strains due to internal pressure also correlated well with test data although there was a general underestimation of test strains. This agreement is encouraging particularly when one considers that sharp strain gradients can not be precisely measured with strain gages of finite length. When an incremental elastic plastic analysis was conducted for axial deflection, the finite element strains showed excellent agreement with test results (strains were only slightly into the inelastic regime). The predicted changes in sidewall spacing were within 5 percent below the measured values.

The maximum allowable geometrical tolerances should be used in a bellows analysis model if the actual dimensions are not available.

The same finite element mesh in the previous paragraph but with nominal bellows dimensions was used in [14] to predict the root bulge of bellows. The model consisted of two convolutions. Since the model was axisymmetric while the mode of failure was not, the bellows were assumed to fail when full yielding occurs. -Predictions using the EJMA design equations [6] exceeded the observed failure pressure in [14] by more than a factor of two. The discrepancy is probably because the EJMA equations are specifically for cold-formed bellows

while the tested bellows were annealed after forming. The finite element results were also higher than the test results. An equation based on limit analysis gave results close to the test results for the annealed bellows.

Parther investigations were suggested before using the equation.

A state of the art study of creep instability for single ply bellows is presented in [15, 16). The availabli computer codes and their abilities to solve creep instability problems were discussed. ANSYS and MARC would be acceptable but expensive. Recommendations for improvements, including the development of a special code for bellows, were included. References [17, 18) contain a method of accelerated testing of bellows operating at creep temperatures.

2.2.4 Other Studies Reference [19) summarizes the tests of ten single ply bellows. The tests took the bellows well into the nonlinear range with internal pressure and large lateral deformations. The determination of the axial and lateral stiffnesses, strengths and stability of bellows was included. Some tensile specimens were cut from a bellows and tested. Values of hardness and thickness were measured along the length of the specimen. The linear, elastic mathematical model was taken 'n be a circular bellows with rectangular convolutions, i.e., convolutions were made up of two short circular cylinders with different radii connected by annular plates. The test results compared well with the results of the analysis. The MARC finite element program was used to analyze the linear, elastic behavior of the U shaped bellows under pinched loading, shear created by magnetic fields and internal pressure. The element used in the analysis was a doubly-curved, isoparametric thin shell element. The nominal dimensions of the bellows including nominal thickness were used in the analysis. The material properties were considered constant. A comparison between the rectangular convolution model and the linear finite element enal; sis showed good agreement.

Attempts to analyze the actual nonlinear behavior of the test specimens resulted in no convergence within the proj ect time schedule. The work concluded that EJMA underestimates the meridional stresses and proposes a new design equation.

A two-dimensional axisymmetric inelastic analysis code, KINE-T, was used to analyza bellows in [20). Though the program was based on small displacement-theory, Imrge displacements were taken into account by adjusting element coordinates in - the computation of the stiffness. The finite element model consisted of one half a convolution. Eight node, isoparametric solid elements arranged' in 5 layers through the thickness were used. The calculated strains were used to predict. bellows fatigue life at elevated temperatures.

A bilinear stress-strain relationship was ' used for the finite element i elastic-plastic analysis of single ply bellows in [21). The behavior of the bellows was assumed to be symmetrical in each half convolution. The nominal

-dimensions were used-in the analysis except that the measured thicknesses were -

used. The same assumptions of geometry and thickness were used in [22] to calculate the fatigue life of two-ply bellows. It is not clear how the interface between the two plies was considered. A model consisting of three and one half convolutions and an end tangent was used in [23) to analyze the fatigue life of single ply annealed bellows. The actual measured variable thickness was used in the analysis. In general, a comparison between calculated and measured l

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strains in [21, 22, 23] showed good agreement. An exception was the root strains in [23) which were underpredicted by a factor of two at one root.

Reference [24] presents a comparison of the finite element results and test results of rectangular bellows. Elastic finite elements with small i displacements were used. I Finite element methods were used to analyze large bellows in [25) with a thickness of 0.75 inches. The elastic finite element model consisted of one- '

half of a convolution and contained seven layers through the thickness.

Constant strain axisymmetric elements were used. The calculated stresses were compared with the code allowable to confirm the validity of the bellows design.

Six cold formed bellows (four single ply and two double ply) were tested in [26) to confirm the mechanism of in plane instability. The bellows became unstable after the formation of a plastic hinge in the meridional direct!on. Axial precompression was found to decrease the in plane instability pressure. No conclusions regarding ply interaction were drawn. Stresses due to pressure were calculated using one pty thickness.

A computer program using three node axisymmetric curved thick shell isoparametric finite elements was written and used to analyze bellows in [27).

The analysis of two semi-circular convoluted bellows were conducted using nominal dimensions except for the convolution radius, for which measured values were used. The results were in good agreement with test results of [28). The same program was used to solve a U shaped c,nvoluted bellows with no comparison with tests. Linear elastic behavior was assumed in the analysis.

2.2.5 Summary of Finite Element Analyses The previous review shows that the finite element analysis of bellows with geometric and material nonlinearities is feasible. For elastic strains and relatively small inelastic strains, finite-element / experimental correlation has generally been quite good. The actual bellows dimensions, including shape and thickness, should be used. For design purposea, different combinations of assumed geometrical imperfections within the allowed tolerances should be used.

Actual material properties should also be used so that,_ in the cane of cold-formed - bellows , the variation in material properties due to strain hardening should be taken into account. Analyses to date have left several problems unsolved:

• Ply intert4 lion has not been satisfactorily modeled.

F0r nonannealed bellows, the effect of cold working on the material ,

constitutive equations has not been adequately quantified.

• Analytical models for large inelastic strains and gross distortions in which the convolutions may touch each other have not been attempted. The-effect of geometric imperfections in this regime are unknown.

• Failure criteria which predict leakage of the bellows have not been formulated. Most current bellows design is based upon an assumed linear elastic behavior.

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l 15-L

2.3 Current Design criteria 2.3.1 ASME Code Classes and Service Levels The ASME Code,Section III, [29] provides rules for nuclear construction with the following classes:

Classes 1, 2, and 3 Piping

- Class MC, Metal containment vessels Class CS, Core Supports.

(The 1978 edition of the ASME code is referred to in [29) as a representative of the code in effect at the time of the design of many containment structures.)

The ASME code classifies the bellows connected to the containment penetrations as class MC or class 2. For Class MC, the code requires that the bellows should be annealed. According to the experts in the field, the bellows for apparently all nuclear containments have not been annealed after forming so that they would be considered as Class 2 components.

Each class has different values of allowable stresses for each of four service limits: A, B, C, and D. Each limit is associated with a corresponding loading level which has a progressively lower probability of occurrence.

(1) Level A Service Limits must be satisfied for those loadings which the component must withstand in the performance of its specified service function with no damage, f 2) Level B Service Limits must be satisfied for those loadings which the component must withstand without damage requiring repair.

(3) 1.evel 9 Service Limits permit -large deformations in areas of structural discern taulty and may necessitate the removal of the component from service for inspection or repair efter the loading.

(4) Level D-Service limits permit gross general deformations with some consequent loss of dimensional stability and may require removal of the component from service.

Within each service limit, there are several allowable stresses, each associated with a certain combination of primary, secondary, and peak stresses.

The ASME code defines primary stresses as those stresses that do not

redistribute as yielding occurs. Those stresses that do redistribute are called secondary stresses, The code considers the membrane stresses caused by internal pressure as primary stresses. The bending stresses in bellows caused by internal pressure are considered secondary ctresses for Class 1, 2, and 3 compor.ents and as primary stresses for Class MC. Husever , test-results of a single ply bellows [14) showed that the results could be correlated best by considering the pressure-induced bending stresses as primary and the code was subsequently modified for liquid metal piping in [1.) so that bending stresses in bellows are considered as primary stresses.

1 Stresses due to the end displacements of the bellows are considered as secontlary stresses for Class 1 components [11). The ASME code does not classify these stresses-clearly for the other classes.

2.3.2 Bellows Desi5n The bellows design approach in the EJMA standards [6] are based on the equations developed in [7 _8) with a few modifications. EJMA equations account for localized thinning f rom the forming process by using different thicknesses at the root and crown. The EJMA equations are directly applicable to cold formed bellows. Test results [13) showed the equations gave reasonable stresses at the root except they underestimated the meridional membrane stresses due to deflection. At the crown, the equations underestimated the meridional membrane stresses due to pressure and deflection and the meridional bending stresses due a to pressure. Test results in [14) show the use of the equations for annealed bellows will give unt.onservative values for the allowable pressure. The relatively low yield strength of annealed bellows compared to the cold worked material may permit the root to bulge at a low pressure. EJMA requires that the circumferential membrane stress, meridional membrane stress and 35 percent of the meridional bending stress due to pressure should not exceed the allowable stresses. (The 0.35 factor is justified in [26).) The circumferential membrane stresses have a factor of safety of four against rupture. The stresses due to end displacement are not included in the allowable stress calculation. The maximum shear stress theory is not applied. For fatigue, the sum of the meridional membrane and bending stresses due to deflection plus 70 percent of the meridional me abrane and bending stresses due to pressure should not exceed the allowable fatigue stress corresponding to the expected number of load cycles. The EJMA standards contain equations to predict the bellows spring rate. An equation for the maximum allowable internal pressure for colttan instability (squirm) is also given. The equation, which was originally developed for smooth thin tubes [8), is modified by an EJMA knock down factor of 6.67 to fit first order theory to experiment. This represents a factor of safety for desi n 5 of about 2.25 [5] when compared to test results.

The ASME code [29) does not give a method to calculate the stresses in bellows, although the Code Case N-290 [11) gives an equation to calculate the circumferential membrane stresses due to internal pressure for Class 1. For class 2 bellows, the ASME code requires that the circumferential membrane stress due to pressure not exceed the allowable stress and that the permanent decrease in the spacing between adjacent convolutions not exceed 7 percent of the original spacing after a pressure test of 1.5 times the design pressure. To evaluate fatigue, the sum of the meridional membrane and bending stresses due to pressure and deflection are multiplied by a magnification factor to account for test results and temperatures. Bellows are considered unstable if the maximum convolution pitch under internal pressure exceeds 1.15 times the original convolution pitch. The ASME factor of safety against instability should not be less than 2.25.

By comparison. EJMA and the ASME code have similar limits on the circumferential membrane stress. Test results [30] show that if the EJMA design pressure is controlled by meridional bending stress. the permanent decrease in t

the convolution spacing equals 7 percent at an average pressure of 1.55 times L the design pressure. This satisfies the ASME code requirement of 1.5 times the design pressure. Thus', the meridional bending stress criteria of EJMA satisfies

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the deformation condition of the ASME code. There are some differences in the way that the two codes handle the fatigue analysis. EJMA prescribes a method to combine the pressure and displacement stresses while the ASME code does not.

The ASME code only states that the stress must be combined in the same way as used to establish the fatigue curve. The effect of elevated temperature is accounted f or by a stress magnification factor in ASME and a cycle reduction factor in EJ MA . The magnification of the stresses due to the statistical variation in test results is considered by the ASME code, but not by EJMA. EJMA defines the fatigue curve as the best fit curve of all tho test points. The ASME code defines the fatigue curve as the curve parallel to the best iit curve l but which lies below all the. data points. With regard to column stability, EJMA does not define the deformation at which the bellows are considered unstable but does give a design equation. On the other hand, the ASME code considers the bellows unstable if the change in the convolution pitch exceeds 15 percent of the original pitch.

2.3.3 Design Acceptability The EJMA standards (6) state that the design equations can be used only if a manufacturer correlates them with actual bellows test data to demonstrate '

predictability of rupture pressure, meridional yielding, squirm, - and - cyclic life. The test specimens must be fabricated by the manufacturers using the same equipment and procedures used for ell bellows products designed to EJMA standards. A minimum of five yield, rupture, and in-plane instability tests on be11cvs of varyin6 sizes are required to verify pressure stresses. A minimum of ten squirm tests on bellows with varying diameters and number of convolutions a t ., required to verify the value of the column instability pressure. A minimum of tventy-five fatigue tests on bellows of varying diameters, thicknesses, and convolution profiles are required to construct a cyclic life verr <us combined stress plot. In some cases, the range of tested bellot s does not cover a specific application. In this situation, the EJMA star.dards will allow an individual bellows design if there is a successful history cf similar bellows.

For Class 2 components, the ASME code requires that compliance be demonstrated by any of the following three methods:

(1) The bellows can be designed by analysis if the analytical methods are substantiated by tests. The FJMA equations satisfy this method. It is the opinion of the authors that this method does not dist inguish between Service Limits A, B, C, and D. The factor of safety against rupture should not be less than four. For universal joints, a minimum of twelve tests are required to verify the stability.

(2) An individual expansion joint design complies if at least two identical bellows are tested. One test should demonstrate the compliance with stress and deformation requirements and the second shou:.d determine the fatigue life. For_the squirm test, the number of convolution should be the same as the design. For the other tests, a minimum of three convolutions is required.

(3) Designs are acceptable if the stress intensities, calculated using either elastic shell theory or plastic ana'ysis, are within the allowable values for Class 2 components. This criteria utilizes the more general ASME rules based on the maximum shear stress theory. Service Limits A, B, C, 18-

and D can be applied. Stability of the bellows can be verified by elastic stability calculations (with a minimum factor of safety of ten) or pressure test (2.25 times the design pressure).

Two sets of telerances are available for bellows fabrication. The set of .

tolerances - in Table 2.1 is prescribed in ASME Code Case 290 [11) for Class I construction of the Liquid Metal Fast Breeder Reactor (IRFBR). EJMA established another set of tolerances which are shown in Table 2.2 for single and double expansion joints.

19-

Table 2.1 Bellows Tolerances (ASME Code Case N 290, Class 1)

Dimension Identification Basic Tolerance Convolution Height H +0.06H Crown Apex Thickness t 1[1.05 - 0.95 (Dt/Do)1/2)e Root Apex Thickness t 10.10.

Convoluted Length L iO.015L End Tangent Inside Diameter Dt 11.5t(0.01 inch min.)

Convolution outside Diameter Do 10.005 D(0.1 inch min.)

Sidewall Spacing at Crown S 10.075 S Sidewall Spacing at Root S 10.075 S End Tangent Length T iO.03 T Tolerances relating to bellows and convolution repeatability are not given Table 2.2 EJMA Tolerances for Single and Double Bellows Expansion Joints Dimension Basic Tolerance Bellows assembly length i 1/8" for assemblies up to 3 ft.

i 1/4" for assemblies 3 ft. to 12 ft.

3/8" for assemblies over 12 f t.

Diameter For diameters up to 24": in accordance with pipe specification.

For diameters over 24": outside diameter i 5% of the specified diameter based on circumferential measurement.

Out of-roundness For diameters up to 24": in accordance with pipe specification.

For diameters over 24": difference between major and minor diameters not to exceed 1% of nominal diameter.

i

3. SEQUOYAH BELIMS 3.1 Bellows Description The Sequoyah containment has single and universal bellows (Figure 2.1). {

The identification, location, and geometric properties of each penetration are i listed in Table 3.1. All ne bellows are two ply with a fine wire mesh (0.008 '

in.) between the plies. The wire mesh reduces the friction between the plies during forming. They are cold formed from thin longitudinally welded tubes of stainless steel type 304.

Acccrding to TVA (the owner of Sequoyah) and NRC, several bellows in the Sequoyah containment were misaligned when they were initially installed [31).

It was judged that three may not survive a nominal safe-shutdown earthquake (SSE) or design basis accident (DBA). These three were replaced or repaired.

Fifteen were judged to be capable of surviving an SSE or DBA but would require inspection afterwards. Fourteen would satisfactorily survive a SSE or DBA.

Bellows are leak tested by pressurizing nitrogen between the two plies.

. The allowable leak rate is 0.1 standard cubic foot per hour. The test is performed at every refvning, about every two years. Sequoyah Unit 1 started operation on May 1, 1980 and Unit 2 followed about 2 years later. The two units were shut down in July 1985. Unit 2 restarted in mid 1988 followed by Unit 1 in early 1989. TVA estimates that the Sequoyah Units have been subjected to 8 or 9 start-up/ shut down cycles. The bellows design conditions for end displacement and pressure are listed in Table 3.2.

3.2 EJMA Design Analysis As a method of ranking the Sequoyah penetration bellows in approximate order of leakage potential, the EJMA design equations were used to analyze each penetration for conditions simulating a severe accident. For the large pressures and displacements associated with a severe accident, the analysis {

certainly represents an extreme extrapolation. It is, nonetheless, useful for i selecting a bellows to analyze further by more sophisticated means, i.e., the finite element model in the next chapter.

3.2.1 Analysis Parameters To illustrate the EJMA design analysis procedure, the universal bellows at penetration X 47 will be used as an example. The geometry of X-47 is illustrated in Figure 3.1. The X 47 bellows is located hign on the outside of the Sequcyah containment, only six feet below the springline.

The material modulus of elasticity, E, yield strength, S,y and ultimate strength, S u, for annealed or virgin stainless steel type - 304 varies with temperature as in Figure 3.2, schich is from ASME - [32, 33, 34). (The 1978 Edition of the ASME code is referred to in [32, 33, 34) as a representative of the code in effect at the time of the design of Sequoyah.) Note, again, that EJMA uses virgin material properties even though the bellows are cold-formed.

Loading on the bellows consists of pressure, temperature, and end displacements. Pressure is here taken as the independent loading variable. The

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6 convolutions G convolutions y y,,,,, - - - -

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j u u- .m Containment End Shield Building End Figure 3.1 Geometry of liellows at Penetration X 247 1 1 1 I 80 -

30000

_ b -

60 -

28000 ,@

E .9

- ~ -

+~

.M -

O

$ 40 -

26000 $o 8 m 20 - - 24000 o

~

a 1 l l I 10 0 200 300 400 l Temperature, F Figure 3.2 Effect of Temperature on the Properties of Stainless )

Steel SA240 Type 304

Table 3.1 Sequoyah Bellows Geometric Parameters Bellows Elevation Convoluted Diameter No. of Pitch Conv. Ply Length Id. (ft. in.) Length (d) Cony. (q) Height (t) of (in.) (in.) (in.) (in.) (w) (in.) Central (in.) Pipe (in.)

X12 A,B,C,D 708' 0" 2@6 29.250 2@4 1.5 2.0 0.037 24 X13 A,B,C,D 714' 0" 2 @ 10.5 51.250 2@7 1.5 2.0 0.050 21 X14 A,B 716' 6" 13.0 15.250 13 1.0 1.5 0.031 N/A X14 C,D 711' 5" 13.0 15.250 13 1.0 1.5 0.031 N/A X15 710' 0" 13.0 17.250 13 1.0 1.5 0.031 N/A X17 209' 0" 15.0 27.250 10 1.5 2.0 0.031 N/A X20 A,B 709' 0" 15.0 23.250 10 1.5 2.0 0.031 N/A X21 705'-6" 13.5 21.250 9 1.5 2.0 0.031 N/A X22 707'-3" 12.0 19.250 12 1.0 1.5 0.025 N/A X24 704' 6" 12.0 19.250 12 1.0 1.5 0.025 N/A X30, X32 697' 6" 10.0 15.250 10 1.0 1.5 0.025 N/A X33 697' 6" 10.0 13.250 10 1.0 1.5 0.025 N/A X45 700'-0" 10.0 15.250 10 1.0 1.5 0.025 N/A X46 700'-0" 11.0 17.250 11 1.0 1.5 0.025 N/A X47 A,B 785' 6" 2@6 19.250 2@6 1.0 1.5 0.031 9.5 X81 695'-0" 10.0 15.250 10 1.0 1.5 0.025 N/A X107 694' 11.5" 15.0 29.250 10 1.5 2.0 0.031 N/A X108,X109 688'-6" 7.5 23.250 5 1.5 2.0 0.037 N/A Reforence Elevations:

Base mat top: 679.78' Sprin&line: 796.63' Containment steel vessel top: 854.13'

Table 3.2 Sequoyah Bellows Design Conditions End Disniacements Penetration Axial Lateral Angulation No. Compression Displacement (in.) (in.)

'X12 A,B,C,D 1 13/16 1 5/8 l' X13 A,B,C,D 2 1/16 1 11/16 l' X14, A,B,C,D 1 3/8 1 11/16 ---

X15 1 3/8 9/16 X17 1 3/8 9/16 - --

X20 A,B 1 3/8 9/16 -

X21 1 3/8 1/2 --

X22, X24 1 3/8 1/2 - --

X30, X45, X81 1 3/8 3/8 --

X32 1 3/8 3/8 --

X33 1 3/8 3/8 --

X46 1 3/8 3/8 ---

X47A, B 1 3/8 1 11/16 -

X107 1 3/8 1/2 ---

X108, 109 0.775 0.0825 --

Pressure and Temocrature:

Design internal pressure 10.8 psi @ 220*/

Design external pressure 0.5 psi @ 120'F

' Operating internal pressure 0.3 psi @ 120*F 24-

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

pressurization is assumed to occur under saturated steam conditions so that the temperature for a given pressure can be found from saturated steam tables (Figure 3.3).

The end displacements veJe provided by Sandia National Laboratories [1].

Sandia performed two finite element analyses of the Sequoyah containment:

• A four-degree segment of the containment extending from the base mat to the top of the dome. The model was effectively an axisymmetric approximation to the containment. Where plate or stiffener dimensions varied circumferential1y, minimum values were used. No penetraticns are ine.luded. This model was numerically pressurized to 92 pai.

A 90-degree segment of the containment extending from about mid height to the top. The purpose ot this model was to include nonaxisymmetric effects in what< is considered to be the ' critical region of the Sequoyah c o n t a in'm e n t , i.e., the 1/2-in. shell plate near the containment epringline. Penetrations were included in this model, which was pressurized to 78 psi. This analysis wes used for X-47 which is near the containment springline.

The Sandia analyses included the temperature effects on material properties and -*

dimensional changes. Sandia supplied the results of their analyses in tables and curves of the meridional and radial displacement of the containment in the vicinity of each bellows. Linear interpolation was used to determine the displacements at the bellows' locations. Rotation at the bellows connection was also estimated with the Sandia results from the translations of the two adjacent nodes. Figure 3.4 is a plot of the axial, lateral and angular displacement at the containment end of the bellows. These correrpond to radial, meridional, and rotation displacements of the containment. Note that, initially, a large vertical thermal growth of the containment occurs at low pressurec followed by large radial dispacements as the pressure increases and causes general yielding (above 40 pal).

3.2.2 Av N

• racedure Four liuting pressures are obtained from the extrapolated EJMA analysis:

yield, rupture, stability, and squash. Because of the low number of start-up/ shut down cycles and the small associated bellows displacements, fatigue is not considered to be an issue.

The yield pressure is obtained by equating the EJMA stress to the temperature corrected virgin material yield stress. EJMA [6, Table C 5.2.2) gives eq(ations for calculating six stresses:

S1- Bellows end tangent circumferential membrane stress due to internal pressure S2 Circumferential membrane st ess due to internal pressure 53- Meridional membrane stress due to internal pressure S4- Meridional bending stress due to internal pressure 400 - _

^

u. 300 L

2 0

5w 200' - _

o.

E o

H 10 0 -- _

f i i i i 20 40 60 80 10 0 Pressure (psi)

Figure 3.3 Sequoyah Containment "emperat ure versus Pressure i

12 l

m

.E

{m 8 - X(axial _

compression)

E w

V 2

g 4 - -

5 Y(lateral) -

I I I I 20 40 60 80 Pressure (psi) >

0.004 - -

LO E O.002 - -

E e

c 20 40 60 80 j O -

(1 Pressure (psi) 3 a-

-0.002 - -

Fib ure 3.4 Displacements of Containment at X-47 Bellows S5- Meridional membrane stress due to deflection S6- Meridional bending stress due to deflet. tion.

Using the FJMA s:;uations, S, i S2 and S3 are plotted versus pressure in Figure 3.5 for X-47. The bellows thickness is taken as the thickness of two plies without consideration af the thickness of the wire mesh (0.008 inches). Also shown in Figure 3,5 is the tempera.ture-corrected virgin yield stress which was found using Figure 3. 3 and, then, Figure 3.2. The sudden drop of the yield stress-r low pressures is <' r to the application- of the saturated steam conditions where a significant ins : :.s e in temperature is a m ciated with small increcents of low pressure (see figure 3.3) . The stress, S4 , is not considered in61cetive of a leakage failure and is not shown in Figure 3.5. (EJMA uses 35 percent of this stress for an allowable stress check.) Additionally, FJMA does not define allowabic stresses for SS and S6, implying that EJMA does not consider these stresses to be indicative of failure. The yield pressure for X-47 is found as the point where the maximum stress, Si, in chis case, reaches S y which, according to Figure 3.5, is 141 psi.

The burst pressure is estimated in a similar manner except that the I ultimate stress, S u (Figure 3.2), is used instead of S y. For X-47, the EJMA I extrapolated burst pressure is 420 pii.

The lietting column stability pressure, P, S is calculated by an EJMA equation [6, Table C-5.2.2] based on classical shell theory. The limiting value includes a factor of safrz.y of about 2.25 (Section 2.3.2). The buckling pressure of the two-ply bellows is a::.proximated as twice the buckling pressure of a single-ply bellows (t equals 0.031 in.). (One could possibly argue the use of a buckling pressure of a single-ply bellows with tv.ce the thickness, 0.062 in., which would give values about four times higher.) For X-47, P5 times 2.25 is 157 psi.

The pressure at which the bellows are estimated to squash is a geometric consideration. EJMA converts the lateral and angular rotation of a bellows into i an equivalent ad al motion per convolution, e e, e -e +

+e ,

(3.1)

In Equa t ion (3.1), e x is axial compression of the bellows per convolution

'X/N for single bellows e -<

• (3.2) cX/2N for dual bellows ir. which X 1a the total axial compression and S is the number of convolecions in l cne bellows. The equivalent axial compression, ey, for a lateral displacement.

l Y, is I

KdY P

e -

7 (3.3) 2N(L - C - X/2) in which d pis the mean diameter of the convolutions, L is the length between l

E______________.__ _ . _ - - . .

l l

1 i I i  !

30 - -

- SY f

f 20 -

l-g -

ai c) 0.1 m

g a Si __

el 10 -

-1 -

S2 i S3  !

l i i i 25 50 75 10 0 I25 15 0 Pressure (psi)

Figure 3.5 EJMA Streuses for X-47 I i i i i i n

.d 1.0 -- - - - - - - - - -

"a* -

l 8 0.8 -

a y 0.6 -

~

8 6

- op -

5 /

5

~6 Q ,2 -

/ -

.2 s

17 td i l l { l l ,

10 20 30 40 50 60 66 Pressure (psi)

Figure 3.6 Equivalent Axial Displacements of X-47

t the outermost ends of the convolutions in a single or universal joint, C is the convoluted length of the bellows-(Figure 2.1) and 3L - 3CL

~

2 3L2 - 6CL + 4C Equation (3.3) gives the maximum equivalent axial motion, which occurs'at the first convolution. The term do in the equation implies that the motion is calculated at the mid-height of the convolution. For rotational motion, the equivalent axial motion per convolution is id P

e,- I ( * }

2N where # is the angular displacement in radians. The equivalent axial displacement for X-47 is obtained using Equation (3.1) with Figure 3.4 and is plotted in Figure 3.6. The pressure at which the bellows is fully squashed is taken as the pressure at which the equivalent axial displacement per convolution is equal to the convolution spacing, 1.0 in, for X-47. From Figure 3.6 this occurs at a. pressure ,;f approximately 66 psi. This calculation is independent ,

of the number of plies.

3.2.3 Analysis Results The procedure outlined above was applied to all the bellows listed in Table 3.1 to give the results in Table 3.3. All of the listed bellows exhibit high rupture pressures. For many bellows, the instability pressure is quite high.. For others it is near the squash pressure. As the reader can note by looking at Figure 3.4 and Figure 3.6 for X-47, squash tends to occur just after general yielding of the contaiment shell. After yielding, the containment radius increases rapidly for relatively small additional increases in pressure.

Because the Sequoyah bellows are c.11 located outside the containment shell, this radial growth produ:es an axial compression of the bellows. Penetration X-47 is the highest bellows penetration located near the springline of Sequoyah. Being near the top, the X-47 bellows experiences large lateral motions caused by vertical thermal growth of the containment. As the containment is pressurized, the springline region is the first to experience rapid radial growth (10) as the strains go beyond yield and a generalized state of yielding occurs. These two features combine to make X-47 the most likely bellows candidate for leakage caused by large deformations. Thus, X-47 was selected for further study using  ?

finite element techniques. Again the warning should be emphasized---Table 3.3 is an extreme extrapolation of the EJMA design equations, far beyond their intent. It has been used only as an indication of the most critical bellows.

3.3 X-47 Bellows Penetration X-47 permits the passage of glycol pipes into the containment.

The pipes are designed for 150 psi pressure, with -5'F normal temperature and

-20'F design temperature. Figure 3.4 is a plot of the axial, lateral and angular displacements at the containment end of the bellows. The other end of the universal bellows is rigidly anchored to the shield building (Figute 3.1).

According to TVA, X-47 is not one of the initially misaligned bellows mentioned in Section 3.1.

Table 3,3 EJMA Extrapolated Pressures for Sequoyah Bellows Pressure (psi) at:

Penetration Number Yield Rupture Stability Squash l X12 110 330 255 84 l X13 102 306 345 89 I X14 A,B 176 530 107 74 X14 C,D 176 530 107 78 X15 156 468 120 78 X17 100 297 91 79

- X20 A,B 116 348 81 80 X21 127 380 92 76 X22 113 339 85 77 X24 113 339 85 80 i X30, X32 142 427 97 83 X33 164 491 86 83 X45 142 427 97 81 X46 126 378 90 82 X81 142 427 97 85 X107 93 277 99 92 X108, X109 138 415 529 83 X47 A,B 141 420 157 66 1

4 7

4. THREE DIMENSIONAL ANALYSIS OF X 47

)

4.1 Features of the Model The complete finite element model is shown in Figure 4.1. Several smaller problems were analyzed to determine mesh size, gap elements, rigid surfaces, interface elements, and other model parameters as described in the Appendix.

The bellows, themselves, were idealized as a shell, with one element through the thickness. The model contains 2,480 nodes, 2,135 shell elements, 128 gap elements, 176 rigid surfaces, and 352 interface elements. The boundary conditiens in each load step, at the bellows end connected to the containment, match the corresponding vertical translation, radial translation and rotation of the current Sandia Sequoyah analysis. Other displacements at this end and all displacements at the opposite end were taken equal to zero. The size of the model could be reduced by neglecting the bellows rotation at the containment end, shortening the model by one half, and utilizing asymmetry at the n.id-length.

The model was loaded by increasing internal pressure in steps (0.2, 0.6, 1, 10, 20, 30, 40, 45, 30, 52, 54, 56, 58, and 60 psi). The end displacements and.the temperature corresponding to each pressure were applied. The Appendix describes the selection of the values. The choice of the material properties for the cold formed bellows is also discussed in th; Appendix.

The force tolerances within any load step were taken as one percent of the product of the maximum element force per unit length in the previous load step times the corresponding element side length. A similar tolerance was used for moment. The tolerances were adjusted every load step up to a pressure of 40 psi. The tolerances at 40 psi were used throughout the remainder of the analysis.

l 4,2 Execution l ABAQUS version 4-7-21 was used in the analysis [35). The problem was run twice using the same geometry, loading, and boundary conditions except for the i bellows thickness. To model the case of complete interlockin6 of the two plies, ,

a thickness of 0.062 in., equal _ to twice the ply thickness, was used. The i i problem was then rerun using a thickness of 0,031 in, to model the case of the two plies acting independently. The two cases are identified as the two-ply approximation and the one-ply approximation, respectively. No satisfactory ply-interaction, modeling technique has yet been found.

For the two-ply approximation run, the analyses were carried out up to

- 61.33 psi. To increase the pressure from 60 to 61.34 psi, 100 increments were required which took about two and one-half hours on the CRAY-XMP. For the one-ply approximation run, converged _ solutions were obtained up to 64 psi. To l

increase the pressure from 64 psi to 65.6 psi, 66 increments were required. At ,

this point, the pro 5 ram continued to reduce the increment size but no convergent j solution could be achieved. The run was then terminated with no output.  !

l Convergence was slowed by the interface and gap elements. Within ABAQUS, the interface element solution is taken to be converged if it does not change status, i.e., change from an open to a closed interface or vice versa, in two i 1

l

.l q g__ ----.

7 l

___s a .___ - - -

__1

-r ---

_ _ . , _ ... . ==> .

? ===

)

i

' i l ,

i i i '

t .

j.  ! ,

1. , I -

, i +

I 1 l ,

'i ,

{  !

4' i . - '

t t  :

i ,

l i i

l i i .

i i  ;

I '

! <  : , 4 .

l i

l t l l l l j ,

r 4 a ... - - -

t

! i ,

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t I

t i i

l ,

. I -

7 w p- 4 ;rr - _-

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, . L *

')

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, i A_--

.___ , ----- , c ,

t ::;_. .____

_.,_4 L _ L L.~ .

--~ > I- (.;;; -_

A - ' - ' ' B - -

Figure 4.1 Finite Element Mesh of X-47 Three-dimensional Model 1

consecutive iterations. During iteration at the high pressures , interface elements would " chatter", i.e., a small subset of interfaces would change status during one iteration and another subset during the next. The solution would not settle down in a reasonable number of iterations, even though the displacements and strains had effectively converged. Convergence problems with the interface elements need to be addressed.

4.3 Analysis of the Two-Ply Approximation Results Figure 4.2 shows the deformed shape of the compression side of the bellows (area A - B in Figure 4.1) at 0, 40, 50, 60 and 61.34 psi. The deformed shape of the complete bellows is very similar to that of the single-ply approximation which will be shown in the next section. The crowns of the first and second convolution are the first to touch. The remaining crowns touch in successive order with increasing pressure and deformation. EJMA, Equation (3.3), would also predict this. For the lateral displacement case, the regions near the end of the bellows have larger curvatures and, hence, larger rotations. The numbering system of the crowns, roots and crown spaces that is used in Figure 4.3 through 4.19 is shown on Figure 4.2.

The changes in the crown spaces, A, on both the tension and compression side of one bellows are shown in Figures 4.3.a and 4.4.a. On the tension side, the crown spaces increase up to a pressure of 50 psi. At this point the radial displacement of the containment increases rapidly relative to the meridional displacements. The crown spaces on the tension side then decrease as shown in Figure 4.3.a. The first two crowns touch each other on the compression side at 45 psi. Adjacent crowns just touch each other when A reaches approximately 0.55 in. The gap between the two crowns in contact and the third, fourth, fifth, and sixth crowns was closed at 54, 58, 59, and 60 psi, respectively. Once a convolution touches the adjacent rigid surfaces, it stiffens and the additional displacements are absorbed by the remaining open convolutions. The first two roots started to touch each other at 60 psi. The equivalent axial change in the convolution pitch in both tension and compression sides from the EJMA geometric analysis (Equation 3.1) is also shown in Figures 4.3.a and 4.4.a, respectively.

The EJMA equations for equivalent axial motion are based on the assumption that plane sections remain plane. Further, as noted in Section 3.2.2, the EJMA equations are intended to give the maximum motion at the mid-height of the convolution. The results are in a good agreement with the maximum change calculated using the finite element model. A significant portion of the lateral displacements of the bellows is due to vertical thermal expansion of the containment building. With the application of the saturated steam conditions, a large portion of the thermal expansion takes place at low pressure causing the change in the slope of the curves at 1 psi.

The initial portions of Figures 4.3.a and 4.4.a at low pressures is expanded in Figures 4.3.b and 4,4.b. Again, the EJMA equivalent axial change (Equation 3.1) is reproduced. I t, this early phase of loading, bellows displacements are dominated by vertical, thermal growth of the containment, i.e., lateral displacement of the bellows (Figure 3.4). The EJMA equation, which converts a lateral displacement to an equivalent axial displacement using the plane section assumption, predicts the changes in convolution pitch quite well; or, equivalently, plane sections remain approximately plane in the finite element model.

t

! i t

Root # 1 2. 3 4 5 j j, n n n n n <

- -j s s v v. v a v v Crown # 1 2- 3 4 5 6 1 2 3 4 5 Crown  !  ! l t l l-Space (a) original shape i_

(b) 40 psi 3

I (c) 50 psi l-s R

v v (d) 60 psi t

nen 2,n////

v vvyv (e) 61.34 psi Figure.4.2 Deformed Shape of the Compression Side - Two-ply Approximation

O.4 t = 0.062 in.

O.3 -

.5 [si crown space g 0.2 -

___.__ __ _g

,5 2-O.10 3 4

/ 5 10 2O 30 40 5O Gb 70 Pressure'(psi)

(a) up to 61.34 psi O.2 1st erown space a ~ ~~ ~ _ __ __

c 2 EJ M A

- - /

- O.1

<3

/ 3 4

5

/

< i i i i 1.0 2.0 3.0 4.0 5.0 Pressure (psi)

(b) up to 5.0 psi Figure 4.3 Change it, onvolution Pitch, q (Fig. 2.1) , Between the Crowns on Tension Side - Tuo-Ply Approximation

1 0.8 /

/

t = 0.062 in / EJMA O.6 /

g crown 3pec. -- -

S o'4 -

3 / -

5 0.2 E 4

(' '

5 lO 20 30 40 50 60 70 Pressure (psi)

(a) up to 61.34 psi O.4 lst CrownSpace __

EJMA _ _ _.. -

3 ,_

C 0'2 -

/

<1

//

/ \

N N

1. 3 1 2 3 4 5 Pressure (psi)

(b) up to 5.0 psi Figure 4.4 Change in Convolution Pitch Between the Crowns of Compression Side - Two-Ply Approx,ination

-3/-

The meridional surface strains on the outer surface of the convolutions on the compression side are plotted versus location in Figures 4.5 through 4.7 up to a pressure of 30 psi and up to 60 psi in Figures 4.8 through 4.10. After a convolution closed, the strains remained about constant while the rate of increase of the strain in the still-open convolutions increases. When all the convolution crowns were closed at 60 psi, the strains were about the same for all convolutions. At 61.34 psi, the surface strains in the third convolution were the highest with a maximum of 4.53 percent. The membrane strain at this location is 0.06 percent. The stresses exceed the yield stress at all crowns and roots at a pressure less than 1 psi, that is during the loading stage which is predominantly thermal expansion (see Figure 3.4) .

The meridional strain at the crowns and roots on the compressicn side of the bellows are plotted against pressure in Figures 4.11 and 4.12, respectively.

Since the bending strain due to axial compression and internal pressure have the same signs at the roots and opposite sign at the crowns, smaller strains occur at the crowns than at the roots, Figure 4.13 shows the total axial and lateral reactions at the containment end. The lateral reaction increases rapidly at low pressure while the containment is experiencing thermal expansion. The difference in the pressure-exposed area on the tension and compression sides of the bellows increases as the bellows bend to accommodate the lateral displacements. This difference develops a couple which decreases the lateral reaction and eventually reverses its sign. After all the convolutions touch each other (at about 60 psi.), the difference in the surface area decreases and, consequently, the lateral reaction again increases. The positive direction of the reactions is the same as those of the applied displacements as given in Figure 3.1.

The maximum meridional membrane force per unit length in the end tangent elements welled to the steel tube is 350 lbs/in, at 61.33 psi. If the weld size is about 0.08 inches (equal to the thickness of the two plies and the screen mesh), the throat stress will be 6190 psi, which should be well below the weld strength. _

4.4 Analysis of the One-Ply Approximation Results Figure 4.14 shows the deformed shape of the compression side of the bellows at 0, 40, 50, 60 and 64 psi (area A-B in Figure 4.1). Figure 4.15 shows the deformed shape of the entire model at 64 psi. In the case of the single-ply approximation, the crown closures do not occur in sequence, as they do for the two-ply approximation.

The deformed shape of the end tangent region at 60 and 64 psi (Figures 4.14.d and e) shows that the end tangent, subjected to a relatively high compressive force, moves away from the end pipe between 60 and 64 psi. The large rotations affect the movements of the rigid surface between the end tangent and the first root.

]

The end pipe touches the bellows at about 62 psi. The finite element model did not include a rigid contact surface between the end pipe and the

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-0.01 side fifth side fifth side sixth side roots root wall crown wall root wall crown wall end fangent

-0.02 Figure 4.7 Meridional Surface Strains on the Outer Surface Along Fiftli and Sixth Convolutions on Compression Side Up to 30 psi - Two-ply Approximation

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l !second y third 3 root .n _ -

i u froot_ -zz , -

9_97 4, __ .;

ih side third side y l,- side fourth

.1 wall crown wall 1- wcil crown

.1 .I

\\ \. .\

-0.04 -

t. .i V

Figure 4.9 Meridional Surface Strains on the Outer Surface Along Third and Fourth Convolutions on Compression Side Up to 61.34 psi - Two-ply A proximation

t 0.04 - t = 0.062 in.

/\-; o O.02 -

/ y 61.34 psi j i,

/ ! 50 psi j I,  !

c 40 psi

\

~6

= ,"I

/

^/s ' :: ! -.

• s

+mi

- -h , , , ,

.u ,

s. . ,s m \,, ij

,f l 4 y s.

t f00f#

c-

\t g\ /jfifth l', lt r! fourth t i " root q= taj gent

-0.02 -

i'v,j =p = -

_ _P fifth side - side t. .I side sixth side I r. woi; crown wall 1I wall. crown wall ij

-0.04 -

U u f

l Figure 4.10 Meridional Surface Strains an the Outer. Surface Along Fifth and Sixth '

Convolutions on Compression Side Up to 61.34 psi - Tuo-ply Approximation j A $ t- Y - - - - _ . v..m..

3 i = 0.062 in. 4 0.03 -

2 c go co# -

.e 0.02 2

m 0.01 3 4 5 6

9 f t B f 10 20 30 40 50 60 70 Pressure (psi)

Figure 4.11 Meridional Surface Strains on the Outer Surface of the Crowns on Compression Side - Two-ply Approximation 1

1

-0.05 L t = 0.062 in. /I i

-0.04 -

B'

-ie c -0.03 -

-0.02 3 4

-0.01 L 10 20 3O 4O SO 6O 70 Pressure (psi)

Figure 4.12 eieridional Surf ace Strains on the Outer Surf ace of the Roots on Compression Side - Two-ply Approximation 5.0 --

I t = 0.062 4.0 -

2 3.0 -

9x 7 Axiol Reaction

,9 2.0

~

o 8 r Loteral Reaction

[ I.0 '

I 2O 3O 4O 5O Pressure (psi)

- 1.0 Figure 4.13 Axial and Lateral Reactions - Two-ply Approximation

f.'

m o a n n

([=====

v U U UU U (0) OriginOI shape

\ ,

\:

(b) 40 psi

! I i

(c) 50 psi (d) 60 psi 1

f (e) 64 psi Figure 4,14 Deformed Shape of the Compression Side - One-ply Approximation

$E

~~

___k; $

I

[

W pg p--

Hf 7

i <

l j4  !!- 1  ; [

.lI

--r [Olff k}N' llG. fi.:

i f

I pi b

.' ,,, i: I M. # -

y----

I Figure 4.15 overall Deformed Shape at 64 psi - One-ply Approximation 1

bellows wall. At the time of the formulation of the model, the possible contact between the end pipe and the first convolution was overlooked. At pressure beyond 62 psi, the model shows the end pipe penetrating the bellows (Figure 4.14.e). The locally high strains which would be associated with this phenomenon are not predicted by the model. Therefore, the strain and displace-ments provided in Figure 4.16 through 4.19 are not reliable for pressures beyond 62 psi.

While the surface strains due to displacement of the one-ply approximation bellows are smaller than those of the two-ply approximation, the surface strains due to pressures are higher. The meridional strains on the outer surface of the convolutions at the crowns and roots are plotted versus pressure in Figures 4.16 and 4.17. At low pressure (0.2 psi) where the strains are primarily due to displacement, the strains in the one-ply approximation are about one-half those of the two-ply approximation, as one would expect. As the pressure increased, the pressure strains become much greater than in the two-ply approximation. The meridional strains at the crowns, where the strains due to axial compression and internal pressure are subtracted from each other, were much less than those at the roots where the two strains add to each other, Erratic behavior of the strains in the first root occurs at pressures higher than 60 psi (Figure 4.17).

l At 64.0 psi, the maximum surface strain of 8.35 percent occurred at first root.

l The maximum membrane strain was 0.11 percent.

The difference in the transverse component of the internal pressure acting on the tension crea and the smaller compression area of the curved bellows increases-the curvature of the bellows. It affects the one-ply approximation bellows more than the two-ply because of the smaller lateral stiffness. The change in the crown spaces in the tension and compression sides are plotted in Figures 4.18 and 4.19. The equivalent axial displacement calculated using EJMA (Equation 3.1) is also plotted in these figures. Although they start in a l fashion similar to that of the two ply bellows, the pattern changes with the l increase of the pressure. For example, the change in pitch at the fifth crown space overtakes the change in pitch of the first crown space. Figure 4.19 shows the possibility of an in-plane instability occurring at about 50 psi at the fifth convolution, similar to root bulge (Section 2.1.c). As shown in Figures 4.18 and 4.19, the transverse component of the internal pressure affects local curvatures more-for the single-ply than for the two-ply.

l 4.5 Bellow.s Failure A failure criteria for bellows in the high strain range is not available because of the lack of experimental data. The high strains predicted in the previous section are predominantly bending. As such, the strain criteria recommended by Sandia for the containment shell (1], which relates to membrane strain, does not apply directly.

l l

L 1

0.02 l

0.015 -

r3 l c t = 0.031 in.

~6 4 5 0.01 -

2 0.005 -

,5 ist Crown l_==u__453r4, JZ q je 6 10 20 30 40 50 60 70 Pressure (psi) i l

l Figure 4.16 Meridional Surface Strains on the Outer Surface of the Crowns on the Compression Side - One-ply Approximation l:

l

, . . . i i i

'S

-0.06 -

-0.05 -

-0.04 - -

2 1 = 0.031 in.

-0.03 -

[ j3,4-

'5 /5 2 G -0.02 -

/ -

ist Root c l

-0 01 -

10 20 30 40 50 60 70 -

Pressure (psi)

Figure 4.17 tieridional Surf ace Strains on the outer Surface of the Roots on the Compression Side - One-ply Apprc>.imation

O.3 '

O.2 -

s ist c,,,n pace EJ% f

- 5

~

r'f2f~ ~ ,

O.I S 'T c- . ,

/

<] IO P.O 30 40 50 60'2 70 Pressure 3

- 0.1 - -

t = 0.031 in. 4

-0.2 -

5

- 0. 3 Figure 4.16. Change of Convolution Pitch on Tension Side - One-ply Approximation

- 0.6 4 '

EJMA-nspace ,-;

- - 0. 4 -

ie d '

l 5 /j 5

-0.2 -

, , , , i i t

10 20 30 40 50 60 70 Pressure (psi)

[

l Figure 4.19 Change of Convolution Pitch Between Crowns on Compression Side -

One-ply Approximation

Failure (leakage) will probably occur when the rigid end pipe pierces through- the thin bellows material. However, there is no experimental evidence to support this hypothesis at this time. The rigid end pipe first touches the bellows between 62 and 64 psi for the single-ply case. Although the analyses did not proceed beyond 61.*!4 psi, the two-ply bellows would be expected to touch the end pipe at a pressure slightly above that of the single ply. Contact between the end pipe and bellows materials does not necessarily mean failure (leakage). However, high bending strains will soon develop as the bellows material bends around the corner of the end pipe. (In [1], mean failure pressure of the Sequoyah containment shell is predi::ted to be 77 psi.)

No final judgment regarding the failure (leakage) of the X-47 Sequoyah bellows) should be drawn from this work. The results of this work are based on too many uncertainties. Most important, this work shows that bellows behavior should be studied further to reduce the uncertainties.

l l

5.

SUMMARY

, CONCLUSIONS AND RECOMMENDATIONS 5.1 Summary-As a containment experiences large displacemen.s during a severe accident, the bellows expansion joints are subjected to gross deformations. All of the early work on bellows did not address t'ais behavior but was oriented toward bellows design in the small strain range. Current design criteria are based on elastic shell theory with modification factors to account for experimental observations.

Finite element analysis.of bellows have also concentrated on small strain behavf.or. To extend the knowledge in this area, a bellows expansion joint in the Sequoyah containment vessel was analyzed for large displacements, pressures, and temperatures associated with a severe accident. The three dimensional finite element model included contact surfaces to model the interaction of the convolutions as they are squashed together. Ply interaction was not modeled but bounded by single- and double-ply results.

High strains occurred as the convolutions touched each other. Failure criteria are not hypothesized because of the lack of experimental data but the results indicate failure (leakage) probably will occur when the more rigid end pipe is pushed through the thin wall of the bellows.

5.2 Conclusions Conclusions from this study are:

+ Finite element analysis of bellows with gross deformation is feasible.

+ EJMA equations for the equivalent axial convolution displacement give results comparable to.the finite element results up to the point at which the convolutions come in contact.

+ The bellows at penetration X-47 in the Sequoyah containment will remain leak tight until at least 62 psi. Maximum strains are predominately bending. Membrane strains are well below ultimate. Failure will occur, at -a higher pressure, probably, as the end pipes are forced together to pierce the thin bellows material. Limitations of this study are:

- The effects of corrosion were not investigated.

- The effects of cold-forming on the bellows material were ba: upon limited information.

+

No experimental evidence is available to validate analyses at high strain levels.

l- + Failure criteria which can - be used to predict bellows leakage are not l available.

l l

No satisfactory ply-interaction model has yet been found.

The size of the three-dimensional model used in this study could be reduced by neglecting the bellors rotation at the containment end, shortening the model by one-half, and utilizing asymmetry at the mid-length. A one-convolution axisymmetric model, as studied in the Appendix, vauld also be a useful tool towards predicting bellows strains.

%.tvergence problems with the interface elements need to be addressed.

5.3 Recomendations Recommendations for further work are:

An experimental program is the next logical step to obtain information which could be compared to finite element results. Failure criteria for leakage should be developed as a part of this program.

Materials properties for the cold-formed portions of bellows convolutions need to be defined.

More finite element work should be done to concentrate on the ply interaction problem. Contact between the end pipe and bellows should be included in the model. Convergence criteria f.n ABAQUS should be modified to permit overriding the current criteria for interface elements.

Parametric studies on the effect of ply ar d convolutien imperfections should be considered.

l

APPENDIX. FINITE ELEMENT MODEL PARAMETERf A.1 AB%US The general purpose nonlinear finite element program ABAQUS was selected for use on this project (15;. It is in a special class of programs such as MARC, ADINA, and ANSYS wnich have a fairly large elmont library and are especially suited for the solution of problems with geometric and material nonlinearities. With MARC and ADINA, ABAQUS is recognized as having one of the more efficient nonlincar solvers and can use a full Newton solution technique

[3W . Modified Newtoa solution techniques are available. ABAQUS has an automatic load step feature. It has interface elements that can be used between active nodes and rigid surfaces and gap elements that can be used between two active nodes. ABAQUS was developed by Hibbitt, Karlsson (= Sorensen, Inc. The program was selected over MARC and ADINA primarily because: (1) it was availabic on the Sandia high speed computer and Sandia personnel had experience with the program and (2) it, supposedly, has one of the better concrete elements, which is being used in a concurrent project at Ames Laboratory.

A.2 Experimental Correlation To gain exterience and some level of confidence, a single ply bellows previously tested and analyzed by Becht, Hong, and Skopp [13J was analyzed with ABAQUS. The 18 in diameter bellows had 12 convolutions with an original nominal pitch of 0.6 in. The test bellows was fully annealed after forming.

Consolution depth was 0.75 in. Type 316 stainless steel was used. Becht and Skopp use6 MARC to analyze the bellows up to strains of about two times the yield strain.

Two- and thret node axisymmetric shell elements (SAX 1 and SAX 2, respectively) in ABAQUS were tried in the analysis of the bellows. The two elements gave similar results in the linear range. When f;eometric nonlinearities were included, the convergence of the three node element slowed a :4 at some point the solution would not converge. Decreasing the load it.crement and increasing the number of iterations did not improve the '

performance, The two node element performed satisfactorily. (Input files for both the two- and three nodo models were sent to the ABAQUS authors, who i experit.nced the same problem. No resolution to the problem has been received '

from AbAQUS.) '

Sixty two node elements were used per convolution, just as in the MARC analysis, which elso used a two node element (Element 15 in MARC) . Bellows thickness matched measured va lues. Three convolutions and an end tangent were ne.luded in tht,model. ,

The finite element modul was subjected to 0.4 in, axial compression. The computed surface strains are plotted in Figure A.1 along with expetimental and  ;

MARC resul ts . There is an insignt#! cant difference between ABAQUS and MARC results. The small difference betww malytical and experimental results is acceptable.

i I

56-

o Test Results Meridional Strain [13'

-~ F.E. Results (MARC) '13' ,

F.E. Results ( ABAQUS) 0.003 , , , , , , , , ,

0 o i 0.002 - o .

E 0.001 -

<;[' -

C 0.0 -

/ _

.E s

$ -0.001 - o '

w

-0.002 -

(o -

-0.003

' ' ' ' ' ' L ' '

O O.5 1.0 1.5 202.53.03.54.04.55.0 Arc length along bellows midsurface (in.)

Figure A.1 Analytical and Experimental Surface Strains

A.3 Ply Interface Model The most analytically difficult problem faced and not solved in this project is the modeling of the interface between the plies. Caps occur between the two plies durinr, fabrication (9]. During pressurization and end movement, the plies may separate or contact each other and slide with respect to each other. The thin wire mesh between the plies keeps the plies apart and will affect how they slide.

Conceptually, the interface could be modeled by gap elements which transmit only compression forces normal to the interface when the gap is closed.

The tangential force at a closed gap would be limited to the normal force times a friction coefficient. Such an interface element exists in many computer

. pror, rams for small motions. However, as large displacements occur and the two finite element surfaces slide with respect to each other, nodal equilibrium is not maintained. Two choices are typically available in ABAQUS and other programs,. In the first (CAPUNI in ABAQUS), an interface element between two nodes maintains its original orientation. As the two nodes slide, or ths interface rotates, the interface force maintains its original direction which, in gena,ral, is no longer normal to a rotated interface. Nodal equilibrium is

- destroyed for large displacements. In the second choice (CAPSPHER in ABAQUS) the interface element rotates so as to remain directed along a line between the two nodes. If the nodes slide significantly along the interface, this rotated direction is not normal to the interface surface.

Slight variations of these two choices are possible. For example, in MARC, the user can update the gap element orientation manually. Although not practical, tha user could continually update the orientation to correspond to the current interface orientation. Equilibrium of the element could still be a problem. Interface elements for finite sliding between two meshes apparently are not available in general purpose programs.

The interface could possibly be modeled by a layer of solid elements between the plies with material properties that are very stiff in compression and very flexible in tension. The shear modulus could possibly be modified to model interface friction but it la not clear how to do this and it might cause numerical problems. Since the material would be orthotropic, the orientation of the material axes for finite rotations would have to be considered. A fine mesh would be needed to have a reasonable aspect ratio for the solid elements.

Since no adequate interface element is available, the bellows will be analyr.ed twice: (1) independent plies, i.e., assume the plies are completely independent and analyz* as a single ply bellows with a thickness of one ply and (2) dependent plies, i.e., assume the plies are completely interlocked and analyze as a single ply bellows with a thickness of two plies. Presumably, these two solutions will bound the true selution.

A.4 Axisymmetric Analysis of X-47  ;

To help determine some of the basic parameters for the full 3-dimensicnal model of the X 47 bellows (Figure 3.1), an axisymmetric analysis of one-hall a convolution and a complete convolution of X-47 was conducted. The thickness was

assumed constant and equal to the thickness of two plies for this parameter study. A two noded axisymmetric element (SAX 1 in ABAQUS) was utilized in the analysis.

A.4.1 Material Properties The true stress true strain curvc until failure for type 304 stainless steel is availabic only for the annealed material at room temperature. Curves are available at 200'F and 400'F up to only $ percent strain. In this low strain level, the three curves are approximately parallel. The curves at 200'F and 400'F were assumed to continue parallel to that at room temperature as shown in Figure A.2. Elastic moduli were taken as 28,300, 27,600, and 26,500 kai at 70,200 and 400'F, respectively. The corresponding values of Poisson's ratio are 0.264, 0.271, and 0.281, respectively [36).

The distribution of strain hardening due to co1* working is not well known. Stainless steel does not follow the same type of hysteresis loops as normal steel. The effect of cyclic loading is known only for equal strain cycles in tension and compression [37).

At one tine, the authors considered trying to duplicate the forming process with a finite element analysis. Starting with an annealed tube model and the annealed stainless steel properties (Figure A.2), radial displacement boundary conditions could be enforced to simulate the form ng process. After the convolution was formed, the unloaded and shif ted stress strain curve could be used as the cold worked material properties. This solution was not attempted.

An experimental detarmination of the yield stress after cold forming was not available. Based on limited information from bellows manufacturers and other sources, the yield stress of the material in the crown and root was taken as 2.0 S y and cs 1.8 S y for the side walls. See Figure A.2 for the resulting stress strain curves.

A.4.2 Loading Two load steps were used. In the first load step, the containment temperature increases from 70 to 210*F with zero internal pressure. The containment radial and meridional displacement associated with this temperature change was calculated and converted to an equivalent axial displacement (e) for the bellows. (See section 3.2.2) . Tha temperature and the equivalent axial displacement were assumed to change with the time as shown in Figure A.3. In the second load step, the pressure was assumed to change linearly with time.

The temperature and the equivalent axial displacements of the bellows are plotted and idealized into several straight lines. (The loadings in Figure A.3 are slightly~ different from those in Figure 3.4 because they are based on an earlier Sandia analyses. The loadings in Figure 3.4 are based on the latest analysis.)

The equivalent axial displacements were assumed to be equal for all convolutions. Planes of symmetry normal to the bellows axis exist at each root and at each crown. Two rigid surfaces at these planes were placed at the ends of the model. See, for example, Figure A.4(a). The rigid surface on the right

-59

)

14 0 i i i i i 70 F 12 0 200 F N/ - -

400 F ,,

a u x lo0

//

3 80 _

/f Assumed Curves P

in 4 ,

a) 60 -

//

E / //

i- 6 40 -

/

--Root and Crown (2.OSy) 20 -Side Wall (1.8 Sy) -

1 I I I I 10 20 30 40 50 60 True Strain %

l l

Figure A.2 Stress-strain Curves for St.ainless Steel SA240 Type 304 l

l

400 - 1 -

80

-300 LL 60 m L a 4*/ 2 e $ e gep 40 g

.)200 g b

a & v E q$ &

• 10 0 -

- 20

/

l.0 2.0 Lood Stepi Load Step 2 Time (a) Temperature and pressure I i

, 1.0 -

.E M "o 0.8 - -

4 *. .

p ,8 0.6 -

j-o p, i 9 e 0.4 -

l-sa ,

t3h0.2 l-

- I L 1.0 2.0 Time (b) Equivalent oxial displacement Figure A.3 Loading for X-47 Axisymmetric Analysis

e e U O O O e + e -

O O 'o

'o m

.O m .O m

w a " o .t m m, ., .

en m o,

u c u += c '

m

< S

.o u

s

.o u O u O e < > e >

x O x '

0 C E C E J

l (a) one half convolution (b) one half convolution reduced end elements I

e , e O O Sm e ,

Rm a O a o & w

.t g q = y a , .V g

c y c o ,

o

.o - .o O y O g

O y O E c E J ,

l*

(c) full convolution Figure A.4 Rigid Surfaces and Convolution Mesh for X-47 Axisymmetric Analysis

l is considered to move to the left with the prescribed equivalent displacement,

e. The rigid surface on the left is considered fixed. One node interface elements (IRS 12 in ABAQUS) are attached to the model nodes to measure contact between the model and the rigid surfaces. The rotations at both ends of the model is equal to zero. As the two rigid surfaces approach each other, the convolution is finally fully squashed between the two, i.e., when e (Figure A.3) is equal to the convolution spacing of 1 inch.

A.4.3 Finite Element Models and Results The two node axisymmetric shell element (SAX 1 in ABAQUS) was used in the X-47 axisymmetric finite element model. Three mesh sizes were used: fine, medium, and coarse. Figure A.4 illustrates the coarse mesh. The element size in the crown and the root was calculated to bc /rt/c' where r is the convolu-tion radius, t is the bellows thickness and e is a constant. The value of c was chosen equal to 6, 3, and 1,5 for the fine, medium, and coarse meshes, respectively. The element size in the side walls was taken to be twice that in the crown and the root.

Three mesh configurations were investigated: Figures A.4(a), (b), and (c).

For the mesh in Figure A.4(a), the location of the center of the end elements is different for different element sizes. (The strains are calculated at the center of each shell element. ) There was a significant difference in the maximum strain between the mesh sizes. To improve the comparison, each of the end elements of the medium mesh were divided into two elements and the end elements of the coarse mesh were divided as shown in Figure A.4(b). Now the end element size and, hence, the points of strain calculation are the same for the three meshes. The maximum inner surface strains in the end elements at the load increment just before the bellows touch the rigid surface (at a time of about 1.916, indicated as " touch" on the curves) and at the end of Step 2 (Figure A.3) are presented in Figure A.S.

To place a strain calculation point directly at the center of the crown, a full convolution model was analyzed using the same three mesh sizes (coarse mesh shown in Figure A.4(c)) . The number of elements in the crown was chosen to be an odd number, in addition to the above t' ee meshes, a very coarse mesh similar to Figure A.4(c), which contains only seven elements around the crown and four elemants along each side wall, was analyzed. The maximum inner surface strains for the different meshes are in Figure A.S.

The inner surface strains along the full convolution model at touch and at the end of Load Step 2 are presented in Figures A.6 and A.7, respectivdv. The

. peak strains occur at the crown and root. Figure A.8 illustrates the cha,tges in the strain with time for the crown (medium mesh) . The strain values increase rapidly after the bellows touch at a time of 1.916.

Figures A.6 and A.7 show that the medium and the fine mesh give essentially the same results. The coarse and very coarse meshes gave good answers at the crown and the root (maximum strain) although they are not in perfect agreement along the convolution. The maximum strains at the end of Step

1 I I I

-30 /o -

fig. A.4 (b) mesh

~

-25 % ' -

fig. A.4 (c) mesh End of step 2

-20 % - -

.. '\f ,,

~

u - 3 o/ - -

03 fig. A.4 (c ) mesh __ -

fig A.4(b) mesh

-7of -. --

Touch

-lof, _

i i l I fine medium coarse verycoarse mesh mesh mesh mesh t.

l Figure A.5 Maximum Meridional Strains at the Inner Surface of the Crown l;.

G 0.06 fine mesh medium mesh 0.04 -' -- coorse mesh

- . - - very coarse mesh 0.02 -

Arc 5 ( "

==- -~._qp Length

-0.02 -

i

-0.04 -

root side wall - crown

= ^

.O.06 Figure A.6 Meridional Strains Along Convolution ir ur Surface at 'Iouch O.30

---

fine mesh medium mesh 0.20 -

-- coarse mesh 4-*-+ very coarse mesh k Arc

. Length

.c \ .,,m g.

- 0.10 -

-0.20 -

root =

side wall _

crown _

-0.30 Figure A.7 Meridional Strains Along Convolution Inner Surface at End of Load Step 2

-0.25 -

-0.20 -

.5 0

5 -0.15 -

E.

n E -0.10 -

• n O

e.

-0.05 - -l-time at touch m / I*916 l '

O.0 ..

i

-M i i /

0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0 Time load step i lood step 2 ,

p: - ,g  : ,,

Figure A.8 Maximum Crown Heridional Inner Surf ace Strain-Time Curve s' ,

e s I \

e i l

, 4 i

a l

4 $

4 i

' 4 I g I e i g .

' q

' i t g 4

i i e -

4 i .

I' g 4 6

I 4

(

8 i

/ \

/ \

e .

l' e

Figure A.9 Deformed Shape of Axinymmetric Model at End of Load Step 2

2 for the fine, medium, coarse, and very coarse meshes are -25.3, -24.8, -25.0, and 26.4 percent, respectively. The strains at touch differ -in the third significant figure. The ratios of CPU time for the very coarse, coarse, medium, and fine reshes are 1:2:4:9. Note that, if only the maximum strain is desired, the very coarse mesh will give satisfactory results and save CPU time. (In retrospect, runs of t'd - type could have been used to learn more about the strains in squashed bel .4 At this point in time in the project, these runs were used only to determi.~ model parameters for the 3-D model.)

For all of the above runs, the automatic increment size option of ABAQUS was used with a starting time increment in Steps 1 and 2 of 0.125 and 0.05, respectively. No limit on the maximum increment size was specified. The convergence tolerance for the two steps was tsken as 40 and 80 lbs, respec-tively. These values are equal to aboua; 1 percent of ti,e end forces associated with the EJMA spring rate. Nine integ*ation points through the thickness were used in the ana'ysis. Isotropic material hardening was used in all runs for this parameter study.

The medium mesh was analyzed with 5, 7, 9 and 11 integration points through the thickness. There is no significant difference between the results for the maximum inner surface strain at the end of Load Step ?. Changing the number of the points from 11 to 5 decreased the CPU time by 30 percent. Five points were used in the remaining analyses.

A.4.4 Nonlinear Solution Parameters The medium mesh modc1 was reanalyzje with a starting increment size of two, three, and four times that in the previous section (i.e., 0.25, 0.375, and 0.5 for Load Step 1 and 0.1, 0.15, and 0.2 for Load Step 2). Automatic incrementation was used. The difference in the strains at touch and at the end of Load Step 2 was in the third significant figure. The ratio of the CPU time between the two runs with the largest and smallest increment sizes was 1:1.4 at touch and 1:1.2 at end of Step 2. Further increases in the initial increment size were not beneficial.

The medium mesh was again reanalyzed using a force tolerance equal to twice, three times, and ten times that above. The difference in the strains at the end of Step 2 was in the fourth significant figure. Increasing the tolerance ten times resulted in a reduction in the CPU time equal to 30 percent.

The end forces and the maximum strains (Figure A.8) increase rapidly after the bellows touch the rigid surface. At that point, the force tolerances become very tight (0.15 percent of the nodal forces at the end of Step 2). The tolerances should be increased after the bellows touch the rigid surface, which will decrease the CPU time.

A.4.5 Combined Effect of the Different Factors The full convolution model with the very coarse mesh was reanalyzed using the largest values of the increment size and force tolerances and five integration points through the thickness. The maximum strains were compared to those calculat a using the fine mesh with small increment size, small force tolerance and nine points through the thickness. The very coarse mesh gave

strains three perc ent higher than the fine mesh at the end of Step 2 and 6 percent higher at touch. The ratio of the CPU time of the fine and very coarse meshes was 12:1.

Figure A.9 is a plot of the displaced shape at touch. Note that the convolutions first touch each other near the transition from the root to the sidewall. Figures A.6 and A.7 show there is a significant strain reversal between touch and the end of Load Step 2 near the point where the convolutions touch. Isotropic hardening was used in these runs but kinematic hardening would be a better choice because of the unloading [38). Kinamatic hardening was used in the full three-dimensional model.

A.5 One Convolution 3-D Model A three-dimensional model of one full convolution of X-47 using the four-node shell element with five degrees of freedom per node (S4R5 in ABAQUS) and five intn, ration points through the-thickness was analyzed. (The six degree of freedom element (S4R in ABAQUS) did not converge. ABAQUS personnel told us that they are in the process of eliminatin6 this element from the program and recommended that we use the other element in our work.) A vertical symmetry plane exists through the bellows (the X-Z plane in Figure 3.1 and -Figure .

A.10.a). The mesh size along the convolution is the same as the very coarse mesh of the axisymmetric models (Figure A.10.b) . The minimum length of the elements in the meridional direction was 0.112 in. An aspect ratio of 40 was used to determine the element size in the circumferential direction. This gives seven elements along half of the bellows circumference. This aspect ratio is very severe but success has been achieved with this approach in an analysis of the 1/2-in, eccentricity in the 1/8 scale steel model for Sandia [2]. A smaller aspect ratio would be preferable in theory but it would results in a significant increase in the bandwidth and the number of elements for the full model.

The material properties and the load steps (axisymmetric compression, internal pressure, and temperature change) were similar to those for the axisymmetric models (Figures A.2 and A.3). The increment size and force tolerance were similar to the largest used in the axisymmetric elements.

The planes normal to the bellows-longitudinal axis and at the convolution crown and root are planes of symmetry, llence , rigid surfaces were placed at these locations as in the axisymmetric model. Two node interface elements (IRS 13 in ABAQUS) were used to model the interface between the bellows and the rigid surfaces. The movable rigid surfaces were moved toward the fixed surface according to the . equivalent axial displacement (Figure A.3.b). Table A.1 ,

compares the strains at the crown at touch and Load Step 2 for the 3 D model and the axisymmetric model. The results do not agree perfectly on the outer surface at the end of Step 2. Ilowever the other strains in the table are in better agreement.

Figure A.11.a shows a typical connection of the bellows end tangent to the piping. A 3 D model with one convolution and an end tangent (Figure A.11.b) was ,

analyzed to check the gap elements (CAPCYL in ABAQUS) between the end tangent and the 0.5 in.-thick pipe. The initial gap width was defined equal to one half the sum of the bellows and the tube thickness. The program considers the gap

)

x (symmetry plane)

A -

A 4 y_

(a) Cross sectional subdivision of bellows e e U y 2 e 2 5 8 E w ~ m S E s

.e m o

.e m

o

• Eu

.9?

o 2  ?, E (b) Sec A- A F1 tre A.10 Three-dimensional Model, Finite Element Mesh

.. .. - _ .- - . - . . . - . _ . , . - = - - - . _ . . - . . _ . . . _ .

!. J r

Table A.1 Surface Sttiins'in One Ct.nvolution !! ode)

Touch 1-:nd of sup 2 F lIult.I outer Joner Juter Axisymmetric 0.027 0.025 0.283 0.161 3-D -0.026 0.026 0.262' O.222

'! i i

s j

l f

e I

L l

l-l l

i

~

coupling screen r1 i

2 pliesecch mesh >

1 ei O.03l in. thick $M:; I/2', pipe N  : R/

gL y bg p

, I

=

-2 - i (a) Typical bellows end tangent

/ gap elements I/2" thick pipe

{ elements p W4 t t bellows end rigid beam tongent elements element (b) Finite element model Figure A.I1 End Tangent Region

, _ _ , . ..gy.,.*1 w t u-~ - ~'- -

+M - -

• E open, i.e., transmits no force, if the distance between the nodes exceeds this value. These elernent s include friction between the two surfaces. (The amp elements have the weaknesses described in Section A.3 but they were considered the best choice here.) The weld between the bellows and the outet pip- as rnodeled by rigid et a traints between the end tangent and the pipe. The s u or E pipe is made up of carbon steel, SA516 CR60. The stresses in this pipe asi iar below .ne yield stress. The moduli of elasticity at different temperatases i t' the A 'E Code [32) were used. The planes normal to the bellows lont,i tudinal axis .a the convolution crown .r root are no longer planes of synanetry due to the presence of the end tangent. (No rigid surfaces or interface olenet ts were used in this model and the analysis could not be carried until the bel'.ows were squashed.) The val es of the strains at the crown are similar to those frr,a the J model in Figure . 10. The gap elements worked satisf actu tly and were inecrporated into che full 3 D model. , .

A.6 Medific it 'n for Full Three-dimensional Model of X 47 4 Moveable cigid surfaces were incorporated in the full three dimer ali al noi el of A 47. These surfaces were applied at the rnidpoint be tw w the ri ts .

and the crowns of the cotspression side of the model as shown in Figare A.12.

The trcnslations of the rigid surface were taken as those of poi t 5 in FJ iure A.13, which were taken as the average of the displacements it points 1 -hi ugh

4. The ro t a t i or.5 of point 5, about x and y, were calcu'.uted using ths displacements of the four nodes aa shown in Figure A.13. Yht rotations aboat the z axis have no significant effect on the distance betweu tne ntedes eid the rigid surfaces. Therefore, it was assumed equal to zero.

The material properties of the calculated parts at different temperatures were taken as shown in Section A.4.1. In the end tanen. . ugior. , a shown 4.n -

Figure A.11, a gradual change of the yield strength was used. A yield 1t ingth of Sy was used for tho elements in the end tangent then increar3d to L. 3S,y '

1.5 Sy , and 1.75 S y for the next rows of elements (Figure A.14).

As mentioned in Section A.4.5, kinematic hardening w: , usted in this a del. '

A plastic modulos of 300,000 psi was used in the antlysis.

72-

X h

-Symmetry N

Root Y- Z , out A

ASi N

(a) Cross Section of 15e110ws Finite Element Model (See Figure 3.1)

,, Rigid surface O 4' 5O 2

9&

kj ,s D Rigid surface (b) Section A - A Figure A.12 Original Position of Rigid Surfaces at X Three-dimensional Model l

i l

Undeformed Position

- -- Deformed Position  ;

l nX

'% l s " ~s

.3 g g 3 $- 5 4 i1 5 12 o

'g }'bx

& $ I ,I I s' I l

I l

/ BYI I

/ + 8 1

/ I I

/ I I

/ f i

>Z A - A 4 A + A &A /4

• 1 *2 *3 *4, A - 'A + A +A +A /4 Y Y1 Y 2 Y3 Y 4, A - A 4 A + 6 +A /4

, 1 *2 *3 *4, A +A - A +A

~

• 1 3 *2 *4 0

y

, 2 2 ,

/A x 0 e is calculated similarly.

l X

Figure A.13 Displacement of Rigid Surfaces M

2.0 F

_ O .y l.8 F y I.8 Fy 1.5 F l hl l  ?

F' '

l 2.0 Fy 1.75 Fy 1.25 Fy Figure A.14 Values of Yield Strength Used in the Finite Flement Model

REFERENCES

[1] Miller, J.D., " Analysis of Shell-Rupture Failure Due to Hypothetical Elevated Temperature Pressurization of the sequoyah Unit 1 Steel Containment Building," NUREG/CR 5405 SAND 98 1650, Sandia National Laboratories, Albuquerque, New Mexico (1990).

[2] Creimann, L. , Fanous , F. , Rogers , J . , and Bluhm, D. , "An Evaluation of the Effects of Design Detai!s on the Capacity of LVR Steel Containment Buildings," NUREG/CR 48, SAND 87-7066, Ames Laboratory, EMRRI (1987).

[3] M111ct, J.D. and Clauss. D. B., " Evaluation of the Performance of the Sequoyah Unit 1 Containment Under Conditions of Severe Accident Loading,"

Fourth Workshop on Containnent Integrity, Arlington, Virginia, NUREG/CP.

M95, SAND 88 1836 (June 14-17,1988) .

[4]

.stny. R.J.. " Metallic Convoluted Expansion Joints: Application, Specification, and Installation," ASME Special Publications, Metallic Bellows and Excansion Joints. Part 11. PVP Vol. 83 (June 1984), pp.1 15.

[5] Shackelford, M.H., et al., Characterization of Nuclear Reactor Containment Penetrations, Sandia National Laboratory Report No. SAND 84 7180, NUREG/CR-3855 (1984).

[6) Standard of Exoansion Joint Manufacturer's Association. Inc. 5th Edition, EJMA, Inc., 25 North Broadway, Tarrytown: New York (1985 Addends).

[7] Anderson, W.F. , " Analysis of Stresses in Bellows, Part I: Design Criteria and Test Results," NAA SR 4527 (Pt I) Atomics International Division of North American Aviation (Oct 1964).

[8] Anderson, W.F., " Analysis of Stresses in Bellows, Part II: Mathematical,"

NAA-SR-4527 (Pt-II) Atomics International Division of North American Aviation (May 1965).

[9] Trainer, T.M., et al., " Final Report on the Development of Analytical Techniques for Bellows and Diaphragm Design," AFRPL TR-68 22, Battelle Memorial Institute, Columbus Laboratories (Mar 1968).

[10] Jaquay, K., Summary Report for IRFBR Flexible Pine Joint Development Procram 1975-1984, ESG DOE-13422 (DE84026260), Atomics International Division, Rockwell International (Feb 1984).

[11) Exoansion Joints in Class 1. Liould Metal Pininc, Codo Caso N 290, American Society of Mechanical Engineers (April 1983).

[12) Becht, C., "Pred*cting Bellows Response by Numerical and Theoretical Methods ,"' ASME Special Publications, Metallic Bellows and Excansion Joints. Part II, PVP Vol. 83 (June 1984), pp. 23 40.

[13) Becht, C., Hong, C., and Skopp, G., " Stress Analysis of Bellows." ASME Special Publications, Metallic Bellows and Exnansion Joints, PVP W 1. 51 (June 1981), pp.11-28.

[14] Bt .:h t , C., llo ton, P., and Skopp, C., " Root Bulge of Bellows," ASME Special Publications, Metallie Bellows and Exosnsion Joints, PVP Vol. 51 (June 1981), pp.105 113.

[15) "Research and Development Needs to Develop Design Tools for Prediction of Creep Indtability of Flexible Piping Joints," Report prepared by Engineering Decision Analysis Company, Inc. for Energy Systems Group, Rockwell International (Dec 1978).

[16] Campbell, R.D., Cloud, R.L., and Bushnell, D., ' Creep Instability in Flexible Piping Joints," ASME Special Publications, Meta 111e Bellows and ,

Exoansion hints, PVP Vol. 51 (June 1981), pp. 29-52.

[17) Campbell, R.D., and Kipp, T.R., " Accelerated Testing of Flexible Piping Joints Operating at Creep Temperatures," Report prepared for Atomics International Division, Rockwell International (Dec 1977).

[18) Campbell, R.D., and Kipp, T.R. , " Accelerated Testing of Flexible Piping Joints Operating at Creep Temperature," ASME Special Publications, Metallic Bellows and Exoansion Joints. PVP Vol. 51 (June 1981), pp. 75 89.

[19) Sned' N.W., "The Strength and Stability of Corrugated Bellows Expansion Joir.. Ph.D. Thesis, University of Cambridge (Nov 1981).

[20] Kobatake, K., et al., " Fatigue Life Predietion of Bellows Joints at Elevated Temperature," ASME Special Publication, Meta 111e Bellows and Exoansion Joints, PVP Vol. 51 (June 1981), pp.91-104.

[21) Kobacke, K., Ooka, Y., and Shimakawa, T., " Simplified Fatigue Life Evaluation Method of Bellows Expansion Joints at Elevated Temperature,"

ASME Publications, faritue and Fracture Assessment by Analysis and Testine, PVP Vol. 103 (1986), pp. 73-78.

[22) Abe, 11. , Shimoyashikis, S., Maeda, 0., and Mizuno, S., " Fatigue Strength of Two-ply Bellows at Elevated Temperature," ASME Publications, Fatirue and Fracture Assessment by Analysis and Testing, PVP Vol. 103 (1986), pp.

79 85.

[23) Yamamoto, S., et al., " Fatigue and Creep-Fatigue Testing of Bellows at Elevated Temperature," ASME Publications, Fatirue and Fracture Assesement by Analysis and Testing, PVP Vol. 103 (1986), pp. 87-93.

[24] Johnson, J.J., Tiong, L.V., and Campbell, R.D., " Redesign of the Neutral Beam Pivot Point Bellows: Validation of Stress Analysis " SMA 18502.01, Lawrence Berkeley Laboratory (Feb 1984).

[25] Misvel, H.C., and Chakrabarti. C.S., " Analysis of Convoluted Shell Expansion Joint for Straight Tube LMFBR Steam Generators ," ASME Special Publications, Metallic Bellows and Exoansion Joints. Part II, PVP Vol. 83 (June 1984), pp. 65-73.

[26) Li, Ting-Xin, et al. , " Instability of Several Convoluted Bellows Subjected to Internal Pressure," ASME Publications, Design and Analysis of Pioing.

Pressure Vessels. and Components, PVP 120 (1987), pp. 93-98.

l 1

77-

[27] Singh, A.V., "On Stresses in Pipeline Expansion Bellows," UNIDAl_21 Pressure Vessel Techno1ory, Vol. 110 (May 1988), pp. 215 217.

[28) Turner, C.E., and Ford, H., " Stresses and Deflection Studies of Pipeline Expansion Bellows," Proceedines of the Institution of Mechanical Engineers, Vol. 171, No. 15 (1957), pp. 526-552.

[29) ASME Code.Section III, American Society of Mechanical Engineers (1978).

[30) Thomas, R.E., " Validation of Bellows Design by Testing," ASME Special Publications, Metallie Bellows and Exoansion Joints. Part II, PVP Vol. 83 (June 1984), pp. 55 64

[31) G111 eland, J.E., (TVA), Letter to James P. O'Heilly, Nuclear Regulatory Commission, regarding misaligned bellows in Sequoyah Unit 1 (1979).

[32) ASME Code. Anoendix 1. Table I-6.0, American Society of Mechanical Engineers (1978).

[33] ASME Code. Annendix I. Table 1 3.2, American Society of Mechanical Engineers-(1978).

[34) ASME Code. Anoendix 1. Yable I-2.2, American Society of Mechanical Engineers (1978).

[35) Hibbitt, Karlsson and Sorensen, Inc., ABAQUS Manuals, Version 4-7-19 and 4 7-21 (1988).

[36] Rack, Henry J. and Khorousky, Gerald A. , "An Assessment of Stress-strain Data Suitable for Finite Element Elastic Plastic Analysis of Shipping Container," NUREC/CR-0481, SAND 77 1872 (Sept 1978) .

[37] Jaquay, K., " Summary Report for LMFBR Flexible Pipe Joint Development Program 1975-1984," Rockwell International ESG-DOE-13422 (1984).

[38) Mendelson, A., Plasticity: TF;9ry and Apolleati2D, Robert E. Krieger Publishing Company, Malabar: FL (1983).

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<s mmur, o. .,, ,~ ,,,'"

NUREG/CR-5561

2. mLE AND SUBilTLE SAND 90-7020 Analysis of Bellows Expansion Joints 3 DATE REpOni PUstisHED in the Sequoyah Containment Mom u Aa l

December 1991

4. FIN OH GR ANT NUMBE R A1401 b, AUTHOR (S) 6 TYPE OF REPORY L. Greimann, W. Wassef, c. Fanous, D. Bluhm Technical

7. PE RIOD COVE R E D fiastww perees k

B, PE Rf ORMING ORGANIZ ATION - NAME AND ADDR E SS (ir sec pronae Desmo. Offere er mernm U.5 No.cw Re* dere. Commeessoa, e Hr medsene ed**ss. JF rearra for, provide neue esd mean't estMI Ames Laboratory Under Contract to:

Institute for Physical Research and Technology Sandia Na :onal Laboratories Iowa State University Albuquerque, NM 87185 Ames, IA 50011

9. SPONSORING ORG ANIZ ATION - NAME AND ADDRE SS (sf Nac. tree "5ame es ecow". coatractor. pramde 48C O'ea**. O ace a' 8* yen. v14 rw neevereev Commmww.

eut maaine edeweLI Division of Engineering Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Cormiiss ion Washington, DC 20555

10. SUPPLEMENT ARY NOTES

11. ABSTR ACT (Joo werse or mass Bellows expansion joints are an integral part of the containment building pressure boundary in some nuclear power plants. They are used at piping penetrations to minimize the loadings on the containment shell due to differential movement between the shell and piping. The purpose of this study was to investigate bellows behaviorin the unlikely event of a severe accident inside the containment building.

The study began with a survey of available information on bellows design, analysis, and past test programs. This information was then used to assess the ultimate behavior of the bellows in the Sequoyah containment.

It was determined that the bellows at penetration X-47 in the Sequoyah containment would experience the worst loading conditions during a severe accident. Finite element calculations of bellows X-47 were conducted to examine the deformation and resulting strains caused by the combination of axial compression, lateral offset, bending, and internal pressure that would be applied to the bellows during a severe accident. Because of convergence problems, the analyses could not be continued to a point of obvious bellows failure. However, la:ge inelastic bending strains, up to 8%, were calculated.

A test program to determine the ultimate bellows behavior and develop data for validation of analytical me'.heds is recommended.

12. KE Y WORDS/DESCRf PTORS fter wores cre rows a faer we# essst everseraers er 'ecerme rhe '* port. A i3. Av AiLAsit.T v a f A ItuthT Unlimited Bellows Expansion Joints, Nuclear Containment Building, ,,,, c , , ct.33,,,c. no ,

Sequovah Nuclear Power Plant, Severe Accident, Piping, ,,,,,,,,,,,

Containment Penetrations Unclassified a r.= a e,o Unclassified

16. NUMBER Of PAGES 16 PRICE l

NRC FORM 335 149)

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a OFFICIAL BUSINESS PEN ALTY FOR PRIVATE USE. 4300 4

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