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ELESTRES Code Description

by M. Tayal

February 1987

CAND4V6-1 1 0AMc-9331

. 7 --. . - *

by M. Tyal par M. Tayal

,.

ABSTRACTIn nuclear fuel elements, sheaths provide a barrier againstrelease of radioactive fission products to the surround-Ing coolant. Hence the Integrity of the sheath and of thesheathendcap weld, Is an Important consideration In thedesign of fuel elements.

The finite element code ELESTRES models the two-dimensional axdsmmetric behaviour of a CANDU fuelelement during normal operating conditions such as steadypower power changes, and load following. The main fousof the code Is to estimate temperatures, fission gas re-lease, and axial variatons of dofohfatikx t s In thepellet and In the sheath. Thus the code models details likestressesJtalns at clrcumferentlal rldge

This repoxt descries the mator feasures of an tmprovedverslon d =*ELESR ;.

Predictions d ELESTRES show good agreement withabout 80 mof fission gas release. In thUsrepot, we iWso presn MELE prREd oSpdjhoopsransI h fhs, for two lradivl For both Irhadons,

*prectoscmae favourbl wt meAsr ent.Wust e ediipshows that near cldrcufdrentlal rldgbodIng t to mutlatda1 stresses In t sheahThis can have a s tgnican effect on sheath Integrlt,such as during ss corrosion crackdng due to powerIncreases, or during corroso df due to .pawer-:llng.

Ri-SUM§-Los galnes des 6l6ments combustibles nucl6alres constl-tuent une barriere contre 18 Uberation de prodults de fissionradioactifs dans le caloporteur qul les entoure. 11 faut doneaccorder une grande Importance a l1ntdgrlt6 de la soudureentre la gaine et le bouchon d'616ment au moment de laconception des 6l6ments combustibles.

-Le code A 6elments finis ELESTRES modellse to com-portement asxisymtrlquo bldlmenslonnel dun 6l6mentcombustible du CANDU, dans des conditions de fonction-nemont normales, conune une puLssance constante, deschangements do puissance ou le suM de charge. La prIn-cipale fonction du code eat d'uvaler Iastemperature, ia1libraion des gaz de fission et los varatios ales dedfomaton et de contraintes dAas la pasthfe et dans lagalne. A1nsi, le code mod6lise des detais teos quo les con--traintes et lea d6formatfos survenues A [a ckoorderence.

Le pr~sent iapport decrit.lea prInp caractqd'une version umEliorde d'ELESTRES

Les pMVW s dEL0ES saccordent awoc peupros 80 mesures de batidon de gaz de fisson; VoAst*viez 6galement dans b prdsen rapport es prXyl-slons dElESTRES relatvement aux conradntes cIroon-

* fMrontle danm in galnes, pour deux kmdlation Cesprvisions correspondn t sse au mesures, dans lesdeux cas cdtes. Un exemple graphique demontre que, prbs ide la clmonfetnoe, la fiexion augmente los contraintesmultladals dans la galne, go qul pout avoir in effet not-able cur ltegrtE do la Ialne, comme durant la fissuration*par corrosion sous tension caus~e par P'augmentation dela puissance, ou encore pendant la fatigue avec corrosiondue au clage.

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of .Canada LimitedCANDU Oet'

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CANDEV486-1 10AECL-9331 !

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CHAPTER PAGEUST OF TABLES AND FIGURES i

1 INTRODUCTION 11.1 Need 11.2 Delinitions 11.3 Applications 21.4 Features and Evolution 4

2 CODE OVERVIEW 62.1 Input 62.2 Calculallon Proodure 62.3 Output 6

3 THERMAL MODELS 63.1 Neutron Flux 6

. .2 tHeat Transfer Coefficient 7'3.3 Temperature - 8

4 F ION GS 94.1 Graln Growth 94.2 Stable Fission Gases 104.3 Radoacti Isotopes 104.4 Gas Pressure 10

.5 DEFORMATIONS AND STRESSES 115.1 Dlametral Charnes 115.2 Hourglassing 115.3 Yield Strength 135.4 Shapes of Finit Elements 145.5 Stresses 155.6 Creep of Sheath .165.7 Stress Corrosion Ccddng 17

6 PROPERTIES AND FEEDBACKS, 186.1 Materlal PropertIes 186.2 Feedbacks 18

7 VALIDATION Is7.1 Irradiation ASS 217.2 Irradiation GS 217.3 Sensitivity to Axdal Nodes 21

8 ILLUSTRATIVE EXAMPLES 229 SUMMARY AND CONCLUSIONS 23

ACKNOWLEDGEMENTS 24REFERENCES 24

TITLE PAGEFigure I Fuel Bundle. IFigure 2 Fuel ElemenL tFigure 3 Circumferential Ridging and Hourglassing: Measured and

Calculated. 2Figure 4 Unks Between ELESTRES and Related Codes. 3Figure 5 Strain at Ridge: Effect of Pellet Geometry. 4Figure 6 Gas Pressure During a Loss of Control of Reactivity. 4Figure 7 Temperatures During Refuelling. 4Figure 8 Major Calculations In ELESTRES. 5Figure 9 Illustrative Profile of Heat Generation Rate across

the Pellet Radius. 7Figure 10 Illustative Variation of Heat Transfer Coefficient. 7Figure 11 Illustrative Profile of Temperatures In the PelleL 8Figure 12 Thernal Conductivity of (° 8Figure 13 Mlcrostructurs In U02 Pellets Irradiated In Canadian Reactors. 9Figure 14 Storage of Fisson Gas at Grain Boundaries. 10Figure 15 Reasons for HourgiassIng of Pellets. 11Figure 16 Possble Cracks In a Pellet. 12Figure 17 Yield Strength of UOr, 13Figure 18 Staln Increase Due to Reduction In Yield Strength. 13Figure 19 Convergencet Mesh Patterns. 14Figure 20 Thermal Stress In a Cy~lnder Analytical Solutions vs.

Finite Element Calculaton. 14Figure 21 Finite EBement Mesh Inthe Pellet 15Figure 22 Loads on the Sheath, and a Finite Element Mesh. 15Figure 23 Examples of Possible Cracks In the Sheath of a Nuciear

Fuel ElemenLt 17Figure 24 Temperatures at the. Center of the Pellet. 18Figure 25 U02 Grain Sizes After Irradiation In Pickering. . 19Figure.26 Measured and Calculated Values of U02 Grain Size Across

a Secton of a Pickering Element. 19Figure 27 Change in U02 Volume During Irradiation. 19Figure 28 Final Values of Sheath Plastic Strains: Measured vs.

Predicted. 20Figure 29 Fission Gas Release: Measurements vs. PredictIons. 20Figure 30 Hoop Strain at the Ridge In Blement ASS: Measurements vs.

ELESTRES. 20Figure 31 Ptastic Hoop Strain at Circumferential Ridges In Bundle GO:

Measurements vs. ELESTRES. 20Figure 32 Sensitivity of ELESTRES calculations, to Axial Subdivision

of the PelleL 21Figure 33 Elasto-Plastc Stresses In the Sheath. 22Figure 34 Strains Across the Sheath Wall. 22Figure 35 Sheath Strain During a Loss-of.Reacthvty.Control Accident. 23Table I Major Outputs of ELESTRES 6Table 2 Radioactive Isotopes Calculated by ELESTRES 11

i

CANDEV-86-110AECL-9331

Hodelling CANDU Fuel Under Normal Operating

Conditions: ELESTRES Code Description

by

H. Tayal

1 * INTRODUCTIOW

1.1 Need

A nuclear fuel element consists of acylindrical tube containing sintered uraniumdioxide pellets. The tube, called the sheath, iss^aled at the two ends by velds to the endcaps.

'">m sheath provides a barrier against release ofWdloactive fission products -to the surroundingcoolant. Bence, the Integrity of the sheath andof the *beath/endcap weld, Is an importantconsideration In the design of fuel elements.

In the reactor, the pellet beats up andexpands, potentially pushing the sheath and theendcap. The resulting stresses can combine withcheatcalfletallurgical effects such as corrosionfrom flssion tpoducts like iodine/cesluu, witheabrittlesent due to bydridealdeuterlies, andwith embrittlezent due to irradiation. Thesecoaibnations are Important contributors [i] topotential failures during normal operatingconditions such as -0ower rsaps, load following,and even long steady powers.

The computer code ZLESTRES* models t2]the thermal and mechanical behaviour of anIndividual fuel element, during Its irradiationlIfe ud r normal operating conditions. A recentpaper 3J briefly described the current versionof the code. This report describes ELESTRES inmore detail.

This report first lists theapplicability of ELESTRES, summarizes itsevolution and then describes the physical modelsIn ELESTRES end how they are linked. Details ofthe major features of the code, folloved by some

sparlsons of predictions to measurements, are__ven. Finally, two specific applications arediscussed.

Figure 1 Fuel 8undle

1.2 Definitions

Figure l shows the geonetry of aCAND** fuel bundle. Figure 2 sho.s a fuelelement. The two figures also illustrate some

'terms relevant to this report. The bundlecontains 20-40 fuel elements. Each element hasone sheath made of Zircaloy-4. Each sheathcontains 20-40 pellets of U02, which produce heatIn the reactor. Reference 4 describes the fuelbundle In more detail.

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ELESTRES: ELEment Simulation and sTRESses

** CANDU - CANada Deuterlum Uranium - Is arealsterei-trademark of Atomic Enerre of

Figure 2 Fuel Elemeon -

1

AECL-9331

Figure 3a shoua measurements [5] ofsheath diameter after an irradiation at Chalkliver Nuclear Laboratories. The sheath diameter,and strain, are larger at interfaces ofneighbouring pellets than at midplanes ofpellets. The larger strain at pellet Interfaceis called a circumferential ridge. It is aresult of axially - non-uniform, radial expansionof the pellet. In Figure 3a, the permanent hoopstrain at the ridge is 1.71 - well Into theplastic range. Figure 3b shows a calculatedshape of the pellet and the sheath, duringinitial rise to power.

(11) Fission gas release and the associatedinternal gas pressure.

(iii) Strains at and near circumferentialridges.

(iv) Probability of sheath failure due tostress corrosion cracking.

Strains should be kept loy to avoidrupturing the sheath. High strains can also leadto channelling (6] of dislocations. Channelltngcan anneal the hardening due to Irradiation. Ifthis occurs at a localized spot, e.g. atcircumferential ridges, then a weak spot iscreated In the sheath. Subsequent strains dueto, say fission gas, can then concentrate at theweak spot, rendering the sheath more prone tofailure.

Expansion of the pellet is a. majorsource of stresses and strains In sheaths, and insheath/endeap velds. Stresses should be kepc lowto avoid failure by stress corrosion-cracking.

1.3 Applications

The following are the main parameterscalculated by ELESTWES:

(I) Temperature along the radius of thepellet and the sheath.

b

Stress corrosion cracking may occur dueto the combined effects of: (a) stresses due topower Increase, and (b) corrodants in the fissionproducts. ELESTRES Includes an estimate for theprobability of fuel failure due to stresscorrosion cracking, based on an empiricalcorrelation.

One application of ELESTRES is toevaluate the ability of a given fuel design tosurviVe the Intended environment (eog. power,burnup) during normal operation. This is done bycalculating temperatures to check for melting, bycalculating Interail pressure to check forbursting, and by calculating ridge strains andstresses to check for the possibility of stresscorrosion cracking.

Other applications include:calculating fission gas release as Initialconditions for subsequent analyses of sheathstrain during hypothetical accidents; andcalculating pellet expansion for subsequent useIn assessments of stresges near weids betweensheaths and endcaps. For these applications,ELESTaES tS frequently linked to other codes likeFEAST [7], ELOCA (8], and ELOCA-A [9J. aeeFigure 4.

The following are some specificprevious applications of ELESTRES:

- Determine the Impact of the followingparameters. on fuel performance:pellet density; surface roughness;shape and length of the pellet.Figure 5 shows an application ofELESTRES, for studying how ridgestrains can be reduced by chamfers andby shorter pellets. The predictedtrends agree with Carter's Irradiations(10].

- Calculate the power that can causecentral melting during normaloperation.

(b) Ca~culatod

Figure 3 CArcutrnfrentalFUdging and Hourgtasslng:Measured and Calculated (

2

CANOEV-86-tioAECL-9331

Figure 4 Unks between ELESTRES and Related Codes

Determine the pattern of altiaxialstre'sses and s t ra In n ea rcircumferential ridges.

- Assess the Impact of pover cycling, onfatigue of the sheath nearcircumferential ridges. The fatiguemay be assisted by corrosion fromfission products.

- Assess the pattern of stresses nearsheath/endcap welds, in an effort toIdentify and remove the cause of fuelfailures [i] in the Bruce reactor.

- Determine the acceptable distributionof unbonded areas In endcap velds.

3

AECL-9331

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0

0.

a I

aI

With chamfer

IL1.4

AWo of Length toDobreter of Plout

Figure 5 Strain at RUdge: Effect of Pellet Geometry 8umrrup (MWJ&g U)

Figure 7 Temperatures During RefuellingPredict: the performance of fuel duringhypothetical transients involving:Loss of Reactivity Control; toss ofHain Feedvater; and Loss of Coolant.In Figure 6, ELESTRES shows that thegas pressure can be kept below thecoolant pressure, during i Loss ofReactivity Control.

Predict the probability of fuelfallure, during multiple ramps inpower.

Calculate temperaturem duringrefuelling. Figure 7 shows thetemperatures predicted by ELESTRES, for& fuel element that first residem In alow power position in the channel, thenIs -shif ted to a higher pover. Duringthe initial Irradiation at the lowpowers densification of U02 results inhigher thermal conductivity, whichreduces the pellet .temperature. Theshift at 80 UW.bfkgU results In muchhigher pellet temperature, and In ahigher rate of densification.

Reference 11 discusses some of theabove applications.

1.4 Features and Evolution

Before. we describe the details ofELESTRES, we give a summary of Its predecessor,ELESzI [12, 13, 14].

Over the years, ELESIH has beenfrequently used for modelling the performance ofCANDU fuel during normal operation. Itsconstituent models are physically (rather thanenpirically) based, and Include such phenomenaass

- heat transfer between the pellet andthe sheath;

- densification of U02 as a function oftime and temperature;

- Influence of temperature, and ofchanges In porosity/density, on thethermal conductivity of the pellet;

effect of burnup on the radialdistribution of neutron flux;

- equLaxed and columnar grain growth inthe pellet;

- fission gas release as a function ofaicrostructure and of irradiation;

- swelling of U02 due to fissionproducts;

- creep of the sheath as a function ofstress, of temperature, and ofneutron-dose.

ELESIH has been verified [14]extensively against numerous irradiations inexperimental and In coomercial reactors.

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a

I

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Figure 6 Gas Pressure dudng a Loss of Control of Reactity

4

CANDEV-86110AECL-9331

Figure 8 Major CaicutaUons In ELESTRES

ELESTRES retains all the precedingsub-models of ELESIH. In addition, ELESTRES alsocalculates the deformation of the pellet, by atwo-dimensional, axisymmetric, finite elementmodel. The calculations include the effects ofthermal, elastic, platic, and creep strains.Cracking Is also simulated. The pelletcalculations use an earlier version of the FEASTcode [7].

ELESTRES continues to provide theInformation provided by ELESIH, on temperaturesand on fission gas release. in addition,ELESTRES also provides Information oncircumferential ridging, and, to a limitedextent,.on stress corrosion cracking.

The first version of ELESTRES was'ntroduced In 1977. Reference 13 gives the

tails of those portions of ELESTRES that arecommon with ELESIK. Reference 7 describes thedetails. of the finite element model FEAST, whoseearlier version was used ln ELESTRES to calculatepellet deformations. Reference 2 describes how

the two major parts, ELESIH and FEAST, wereconbined in the initiaL version of. ELESTRES.Reference 11 describes some recent applicationsof ELESTRES, la design/analysis of CANMW fuel.

Reference 15 describes a counterpart ofELESTRES for .Light Water Reactors: the FEHAXIcode. Many features are cocoon between ELESTRESand FEHAXI, although some details differ.

The current version of ELESTREScontains improvements over the original, In thefollowing major areas: link to FEAST fordetailed calculations of sheath stresses; yieldstrength of the pellet; creep rate of Zircaloy;transient temperatures; calculations atend-of-life; ANS 5.4 correlation for gapinventory; densification of U02; and additionalconveniences in Input/output/lnterfacing withother codes. This report describes thesignificant changes. To provide a perspective,however, we first give an overview of the variousphysical processes included In ELESTRES.Figure 8 shows how they are linked.

AECL-9331

2. CODE OVERVIEW

2.1 Input

ELESTRES assumes that the fuel elementconsists of a cylindrical tube of Zircaloy or ofsteel (steel has been used in some experimentalfuel), containing a stack of U02 pellets. Aplenum may also be Included. The tube Is sealedat both ends. The pellets may be solid orannular, dished or undished, or may be chamfered.The pellets nay also contain grooves forInstrumentation.

The user specifies the details of thepellet and of the sheath, such as: shapes;dimensions; clearances; density; grain size;surface roughness; type of CANLVB coiting; andenrichment. The user also specifies thecomposition-and the pressure of the filling gas.The temperature and the pressure of the coolantare specified as a function of tile. The powerhistbry is specified In -terms of li-ear heatgeneration rate vs burnup.

2.2 Calculation Proceduire

routine that plots the results of ELESTRES.Another file preserves pellet deformations. Thisis used by FEAST to calculate stresses in thesheath near ridges and near endcap welds. Thethird file contains data needed by ELOCA foraccident analyses. Fission gas release is themost Important Information in this file.

3. THEERMAL MODELS

.0

3.1 Neutron Flux

In ELESTRES, the neutron flux isallowed to be non-uniforu along the radius of thepellet: It is normally higher near the outersurface, and lower near the center. The radialdistribution of neutron flux Is a function ofCellet diameter, of U02 enrichment, and of

bnup. ELESTRES also conslders the build-up ofplutonium near the outer surface of the pellet.

To account for these effects, ELESTRESuses an equation fitted to the results of theneutron-physics code KAMMER [17]. Figure 9 shows

The power history is divided Into aseries of increments of powers and burnups. Aseparate calculation is done for each increment.

An extra set of calculations is done atthe end of the specified power history, where thefuel element I assigned a uniform temperature of*20-C. Hence, this calculation glves results thatcan be compared to post-Irradiatfonmeasurements.

ELESTRES contains several features thatpermit large calculation-Increments. Theseinclude: a special. formulation [16] forpermittifti kin finite elements to simultaneouslycross the boundary from elastic to plasticbehaviour; accommodation of large drops Inyield-strength t7] due to changes In localtemperature; and a three-step predictor/correctormethod for elastlc/plastic analyses. Thesefeatures reduce computing costs. For typicalirradiatlon-histories. (powers up to 80 kW/a,burnups up to 300 JW.b/kgU), ELESTRES requiresless than one minute of computing time on aCD/CYBER 175 computer.

Table 1: Hajor Outputs of ELESTRES

- Temperatures: - Sheath- Surface of the pellet- Center of the pellet- Volume-average la the

pellet

- Heat transfer coefficient between thesheath and the pellet

- Fission Gas: - percent release- free volume- pressure- Isotopic composition

- Interfacial pressure between thepellet and the sheath

- Radial gap between the sheath and thepellet

- Radial and axial deformations of thepellet

- Sheath strain: - at the uidplane- at the end of the

pellet

- Stresses In the pellet

- Stresses In the sheath

- Probability of failure due to stresscorrosion cracking

I

2.3 Output

The output of ELESTRES can becontrolled by the user, and ranges from one lineper calculation, to one page per calculation.Table 1 lists the major parameters printed byELESTRES. They include: temperatures, fissiongas release, displacements, stresses, strains,and defect probabilities.

In addition, ELESTRES stores selectedresults In three files for future processing, asshown In Figure 4. One fIle is linked to a

CANDEV-86-110AECL.9331

a typical distribution of heat generation rate- long the radius of the pellet. Near the surface

the pellet, build-up of lsslle plutonium'gives a sharp increase In the heat generation

rate.

3.2 Heat Transfer Coefficient

ELESTRES assumes that the heat transfercoefficient between the sheath and the pellet Isa function of:

- radial gap/contact-pressure between thepellet and the sheath;

- the composition of gases inside thefuel element; and

- the Initial roughnesses of the surfacesof the sheath and of the pellet.

ELESTRES allows cite first twoparameters sbove to change continuously durlngirradiation. For example, the pellet firstexpands thermally, then shrinks due todensification, then swells due to solid fissionproducts (discussed later). The sheath creepsdue to coolant pressure. Thus the diametralclearance/contact-pressure, between the pelletand the sheath, changes continuously, not onlyfor the preceding reasons, but also due tochanges in power. As more fission gases arereleased, from the pellet, the composition of gaschanges Inside the fuel element. All these.effects combine to give a complex variation ofheat transfer coefficient between the pellet andthe sheath, during the residence of fuel in thereactor.

ELESTlES will predict the resultingchanges in the heat transfer coefficient, usingthe empirical wodel by Campbell, Borque,Deshales, Slls, and Notley (18].

Figure 10 shows an Illustrativeprediction of beat transfer cQefficient during anIrradiation. Initially, pellet expansion createsa high Interfactal pressure between the pelletand the sbeath. This gives a high heat transfercoefficient. Then, over the first 100 HW.b4kgU,stress relaxation causes a rapid drop in contactpressure; This decreases. the heat transfercoefficient. By then, fission gases accuulateto become a significant fraction of the Internalgases, causing further decreases In the heattransfer coefficient. By 200 HW.h/kgU, thecontact pressure and the initial filllng gas areplaying an insignificant role In determining theheat transfer coefficient.

8 60

40

20 _

0 100 200 300 400

Bunup (MWtftg U)

Figure 10 Iflustraive variation of heat trnsfer coefficlent

(6cL 4 wa, p-il.t/siec%) 7

Fract)onal radal distance

Figure 9 IllustratUve profile of heat generation rateacross the pellet radius

AECL-9331

3.3 Temperature

The temperature in the pellet isnormally highest at the center, and lowest nearthe pellet/sheath Interface. Figure 11 shows atypical distribution of temperature.

The code assumes uniform neutron fluxalong the length of the pellet. thus, end fluxpeaking is not considered explicitly. It is,however, considered Implicitly. via normalizationof predicted gas release to measured (discussedlater). In any case, since end flux peakingaffects only SZ of the stack length (19], itlikely does not contribute significantly to thetotal gas released in the fuel element.

Two-dimensional calculations using theFULMOD code [201 showed (21] that except for endflux peaking, axial variations in temperature arelow: less than 20-C along the length of anindlvidual pellet. These are insignificantcompared to the normal temperatures in thepellet: - 1800-C at the center. Crain growthsmeasured [22. 23] in the pellets after numerousirradfatlons also show no axial variations alongpellet length, confirming that axial heatconduction Is not significant. Therefore, fortemperatures, one-diLensional calculations aredone In EtESTRES. That Is. heat flow ISconsidered along the radial direction, 'but notalong the length, nor around the circumference.

The following classical eaustiondescribes transient conduction of heat (24J

k2T + k 6T + v - Tk - .-- + WiPs~

Here, k Is thermal conductivity, Ttemperature, r radial distance, w rate of heatgeneration per uni t volune, p density, s specificheat, and t time.

The above equation Is solved [2] usingthe finite difference method.

The transient effects are Important forsome short-term situations, e.g. for postulatedaccidents Involving loss of control ofreactivity. For these, the full equation aboveIs solved.

For the majority of normal operatingconditions, however, the fuel power is ucuallyheld constant for a long tine, say for more thanone hour. This Ins liniftcantly longer than thethermal time-constant of the fuel element: about9 * for volume-average temperature, and 11 a atthe center of the pellet. For these conditions,ELESTRES saves on computing cost by bypassing thetransient calculations, and solving directly forsteady-state (2].

Figure 12 shows, the thermalconductivity of U02, obtained from HkTZRO [25].HATPRO does not refer to the effect ofIrradiation on the thermal conductivity of U02.Reference 26 showe, however, that at lowtemperatures, the thermal conductivity Is also afunction of the number of fissions and of thetemperature at whieh the fission damageaccumulated. ELESTRES simulates the lowtemperature damage by assumIng that. theconductivity is constant below 454C.

Figure 12 shows that at operatingteoperatures, the thermal conductivity of U02varles by about a factor of 2. This makes theabove equation non-linear.

2000

a

I

Temperature (eC)Radal Wistanoe from Pellet Center (mm)

Figure11 Illustrative Profile of Temperatures In the Pelleti

Figure 12 Thermal Conductivity Of U02

8

CANDEV-86-110aAECL.9331

The equation Is solved by dividing the

pellet into a number of concentric annuli,*sually 100, see Figure 11. Another annulus

_represents the sheath, and one annulus models thegap between the sheath and the pellet. Withineach annulus, the temperature is assumed to varyparabolically vith distance.

An implicit, Incremental formulation ofthe above equation is obtained by using theone-step, Euler, backward-difference formula[24]. The Incremental equations are firstformulated for each annulus, then assembled intoa matrix to represent all the annulisimultaneously. This system of noo-linearequations In solved Iteratively, employing themodified Nevton-Raphson scheme. The Iterationscontinue until the net flov of heat has a lowresidual error at each time-step.

4. FISSION GAS

4.1 Crain Crowth

High temperatures promote diffusion of

U02 atoms to and along Iraln bo ndaries. Thisresults In grain growth a22, 23J, equLaxed andcolumnar. Figure 13 shows some examples.

For equiaxed grovth, ELESTRES uses themodel by Bastings, Scoberg, and Mhackenzle [22].This empirical model gives the rate of graingrovth as a function of: local temperature;enrichment; and the diameter of %2.

in somepovers.movement

Columnar grains have been observed (231experimental fuel irradiated at highColumnar grain grovth occurs by bubblein a thermal gradient. This can occur

. z

(a) draIns A*sire Porsta (b) Equ(ad Gr inh Irradiated P*ts

ColumnarGmkins

(C ColUnnai -Grains In Irradiatid PeRset (d) Graln Growth Assumed In ELESTRES

Flgure 13 Microstnictures In U02 Pellets Irradiated In Canadian reactors (221

.9

AECL-9331

(a) observed aer kIndgeUon 1231 (b) Awmwd in CLESTRES

Flguro 14 Storage of Fission Gas at Grain Boundas.- * * ' - - -- - " : - -'

by surface diffusion, bywlue diffusion, or byvapour phase transport J27J. The ELESTRES modelIs taken froo Reference 14, which in based on alogarithmic aierage between the rates for surfacediffusion and for vapour phase transport (28].The resulting equations provide the rate ofgrowth of columnar grains, as a function ofslocal temperature and Its gradient; pressurevithin the gas bubble; ad radius of the grain.

gaS. It Is calculated In ELESTRES using themodel by Notley and Hastings [14].

4.3 RAdioactive Isotopes

ELESTRES *lso calculates theradioactive isotopes in the free gas, using theANS 5.4 model [30]. This Is an empiricalcorrelation of measurements from a wide range ofexperiments. It correlates gas release mainly totemperature and to burnup; more details areavailable from Reference 30.

1, .1 1%

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4.2 Stable Yisslon Cases

Irradiation generates fission productswithin the grains of UO. Some of the ficlionproducts are gaseous. The gas Is assumed to'..diffuse through U02 grains; ELESTRE usesBooth's 'equivalent sphere' model J29J for thiscalculation.. The amount of diffusion to-fian-boundaries depends, among others, on thelocal temperature and on the site of the grain.

The diffused .a accumulates Ingrain-boundary bubbles [IL see Figure 14. Thebubbles grow as more gas reaches the grainboundary, either by diffusion or duringgrain-boundary sweeping due to grain growth(equlaxed and columnar).

ELESTRES assumes that a change In powergenerates thermal stresses In the pellet. Thisproduces microscopic (and -acroscopic) cracks Inthe pellet. A path, called tunnels, is forcedlinking the grain-boundaries to the pellet/sheathgap.

When the bubbles grow big enough totouch each other (i.e. to interlink), any excessgas In the bubbles ts assumed to be released fromthe bubbles, via the tunnels, to thepellet/eheath gap. This gas is called the free

ELESTRES calculates the freeInveatories, of 59 radioactive Isotopes of19 elements, selected for their relevance tosafety analyses and to radiation shielding.Table 2 lists the pertinent Isotopes.

For Isotopes whose half-lives aregreater tha one 'year, ELESTRES uses-. the AFSmodel for stable gas release. For the remaininglsotopes- fractional release is based on themaxteum temperature reached during the last twohalf-lives of *the isotope, accounting. forradioactive decay during diffusion.

4.4 Cas Pressure

The gas pressure inside the fuelelement depends -on: the mass of the gas; thevolume available to store this gas; and thetemperatures of the storage locations. ELESTREScalculates the gis pressure by using the Idealgas law.

The total mass of the gas is the sum ofthe free gas discussed earlier, plus the fillinggas used during the ftbrication of the fuelelenent.

10

CANDEV-86-1 IOAECL-9331

, tIonsELESTRES considers the follovingfor storing the gases:

Axial gaps between neighbouring pelletsand between pellets and the endcaps.

* Non-unilorm stiffness

- Dishes, chamferc, grooves, and holes Inthe pellets.

- Cracks In the pellets.

- Surface roughnesses of the sheath andof the pellets.

- Flenums.

- Radiallgap beteven the pellets and thesheath.

- Open porosity.

5. DEFORMATIONS AND STRESSES

5.1 Dfametral Changes

The following processes affect thediameter of the pellet sad of the sheath:deasification; svwllLug;....creep; ..tbormalexpansion; and hourglaasin-.

Densaficatloa Ls caused primarily bylrradLatLon-iLduced s*nterLng of U02 la thereactor. It Ls calculated li ELESTRES as afunction ofs Initial density of the ,pellet;

Il^1 temperature; and time In the reactor..Lling is caused by solid products of fission,

iElch have a larger Volule than the parentmaterial, amd by unreleased fission gases. Forthese calculations, -LESTRES uses the model (31]by Eastligs, Yehrenbach, aikd nosbons.

Creep due to external coolant pressuredecreases the diameter of the sheath. However,outvard creep of thae sheath can be expected Ifthe Internal- Sas pressure significantly exceedsthe cooluia prcisure. In calculating 'thermalexpansion, melting of U° 2 Is also considered.

More stiff Stiff

* Axial compression

-h V s

ANo A

* Non-aonn hifa denit

More dert. Less den"

Fgure 15 Reaons tor ftourglsng of PeUets

5.2 Nourglsssaig

Eourglapsing of the. pellets can becaused by three factors: non-uniform temperaturealong the radius of the pellet;' axialcompression; and variations In initial density.These are showv schematically In Figure 15.

Table 2: Radioactive Isotopes Considered by ELESTRES

Antimony (128H, 129. 130H, 131)

Barium (140. 141. 142)

Bromine-84

Cerium (141, 142)

Cesium (137, 138)

Iodine (131, 132; 133, 134, 135)

Krypton (83H, 85H, 85, 87, 88, 89)

Lanthanum (140, 142, 143)

Molybdenum (99, 101)

Niobium (95, 97H, 97)

Praseodynius - 146

Rubidium (88, 89)

Ruthenium (103, 106)

Strontium (89, 90, 91, 92)

Technitium (101, 102)

Tellurium (131M, 131, 132, 133H, 133134, 135)

Xenon (133M, 133, 135K, 135. 138)

Yttrium (91M, 94, 95)

Zirconium (9S, 97)

11

AECL-9331

The temperature prof ile along thepellet radius Is, approximately, parabolic.Hence the thermal expansion does not produce thesame radial displacement, nor hoop strain, atadjacent radial locations. The resultingIncompatibility causes stresses and strains thatchange radially and axially. The local strainsand stresses are determined by, among others, thelocal stiffness of the pellet.

At the pellet midplane, the deformationof a transverse cross-section is resisted notonly by the stiffnes6 of that cross-section, but

also' by the stiffness of the neighbouring U02.However, near the pellet end, the transverse

cross-section In surrounded by less U02.Therefore it can, and does, expand more than thecross-section at the pellet midplane, seeFigure 31 The pellet thus takes the shape of anhourglass. This Is one reason forcircumferential ridges.

The amount of hourglassing Is affectedby many other paraceters, for example: thetemperature profile; the coolant pressure; theresistance offered by the sheath; the amount ofradial interaction between the sheath and thepellet; the amount of cracking in the pellet; thediameter and the length of the pellet; and thesizes of the chaafers, of the lands, and of thedishes at the ends of the pellet.

WAxil compression also contributes tohourglassing. When the pellet expands axially,there way be 'axial Interference betweennelghbouring pellets, and/or between the stack ofpellets and the endcap. This causes compressiveaxial forces on each pellet. Hydraulic drag Isanother source of compressive axial forces. Thisadds to the hourglassing of the pellet. Axialcompression has a larger Influence on ridging Ifthe force 1is applied near the surface of thepellet than towards the center.

Another contributor to hourglaasing Isthe initial variation of densities in the pellet:higher -at the ends, lower at the widplane.Densification In. the reactor then leads tohourglassing. This component, however, ispresently not considered In ELESTRES.

Veeder presented (3f] a polynomialexpression for the theroo-elastic hourglassing ofthe pellet. The solution was obtained byminimizing the strain energy of a right circularfinite cylinder.

In ELESTRES, a finite element model isused to calculate the axisymmetric deformation ofthe pellet (2, 71. The code uodelp thermal,elastic, plastic, and creep strains and stresses.The code also considers: axial loads; variationof yield strength with temperature; andcracking.

Figure 16 shows that duringirradiation, a significant fraction of the pelletcan crack. ELESTRES assumes that a radial crackforms when the local tensile hoop stress exceedsthe rupture strength. Upon cracking, theprevious hoop stress Is redistributed touncracked locations, and no new hoop stress isassigned to the cracked material.

Geometry of the pellet Is considered.For example, the code accounts for the length andthe diameter of the pellet, and for the sizes ofthe chamfers/lands/dishes at the ends of thepellet.

The following fundamental laws ofmechanics are satisfied: equilibrium;compatibility; constitutive relations; yieldcriterion; and flow rule.

The preceding calculations employtwo-dimensional, axisymmetric calculations. Thedlsplacements, stresses, and strains are assumeduniform around the circunference. Bowever, theirradial and axial variations are considered.

0

Gkcumfre RadWCracks Trmnrse

. Ctadft

POW

RadW Cracks In a Tnrmveme Section 1231

Figure 16 Possible Cracks In a Pellet

12

CANDEV-86-1 10AECL-9331

5.3 Yield Strength

Figure 17 shows that at operatingtemperatures, the yield strength of U02 varies bya factor of 2. A drop In yield strength causesadditional plastic flow, and redistributesstresses/strains.

Reference 2 describes how the originalversion of ELESTRES accounted for the drop inyield strength. This has now been changed. Forthe current version of ELEStRES, special finiteelement equations were formulated for plasticflow during large changes In yield strength.Reference 7 gives the details and the resultingequations.

Figure 18 shows the results of a testcase using this model. The test case sliulates acylinder under unixrial tension In the plasticrange, with a stress of 400 IU' and a strain of0.46%. At Increase in temperature then reducesthe yield strength, which Increases the plasticflow. The new strain Is 0.63%. Figure 18 showsthat the fInite element method agrees well withthe closed-form solution.

Temperatur (c)

Figure 17 Yield Strength of U0 2 (251

Tlne t1. 7z. ~t

Addl a Wraindue So drop hiyed strengn

soo

4001

TOMPerature

a

I 3001

_ Cosxod Form Sokhbn , f

0

Code Predictions:Origina) Version oCurrent Version .

1 I _ t - I_ _ _ - -I I I

200

100

u .

0 O.t 0.2 0.3 OA 0.5 0.6 0.7

Strain (%)

(b) Results

0.8

(a) Conditions SibMted

Figure 18 Strain Increase Due to Reduction In Yield Strength

13

AtCL4JJ:5i1

5.4 Shipes of Finite Elements

The finite element method Is used forcalculating deformations, stresses, and strains,in pellets and In sheaths. Finite elements areavailable in two basic shapes: triangles, andrectangles. Rectangles are easier to use,because the nodes generally lie on grid-lines,and because the lines that connect the nodes areparallel to the coordinates axes. It Is alsoeasier to formulate the stiffness matrix ofrectangular elements than of triangles; thedifference Is especially noticeable In elementsof higher order. Below, we compare theaccuracies of the two types of elements.

0

The stiffness matrix of a rectangularelement can be generated by first dividing therectangle Into four triangles connected at thecentroid of the rectangle, and then *dding thestiffnesses of the four triangles [33J. Hence,for purposes of accuracy, a rectangular elementis equivalent to four triangles assembled into arectangular shape.

h represents the spacng betweenneighbng nodes

0(h) means that the dtsretlZationerror is of orderh

Figure 19 Convergence: Mesh Pattenms (341

%MP;

a) octanguta Patterwn of Triangles b) Hexagonal Pattern of TrIangles

Figure 20 Thermal Stresss In a Cylinder: Analytical Solutions (Unes) vs. Finite Element Calculations (PoInts)

tI14

CANDEV-86-i 10AECL-933 1

RADIAL DIRECTION

. ILCHAMFER

- -

I

ICENTERLINE I M"z

II FUEL PELLET I

I .

1, - - - - - - - - - .-

FRguro 21 Finite Element Mesh In the Pellet

Udoguchi et. al. [341 have studied theaccuracy of the solution vs the pattern Intowhich frdividual f lit# eleaent are arranged.Figure 19 ahove some of the patterns studied by,lfchi et. .1. for plane-stress problems. They

d Taylor series to represent thete-eleent equations, and determined the

dis cretiration error of the series at a functionof spacing between nodes. They found that whentrLanular elements re arranged In a rectangularpateern, the aolution coaverges slouly. Also, Xtsalwys retalns a residual error. Eovever, if thetriangular ftn~te elements are assembled into ahexagonal pattern, the solution coaverges rapidlyto the true solution. This occurs because thetwo patterns compensate differently for shear.

Ylinte elements of higher order canaccelerate the convergences of both thetriangular and the rectangular elements [33].

We checked If the theoretical resultsif Udogucti et. al. have a signif itant effect onstresses In pellets. We modelled a solid:ylInder experlencing a parabolic distribution ofcemperature along Its radius. We calculated the1xtsynnetric stresses due to thetempersture-gradLent.

Triangular elements have anotheradvantages complex profiles can be more easilyrecreated by assembling triangles than byassemblinag rectangles.

For these reasons, EVESTRES usestriangular elements arranged In a hexagonalpattern.

5.5 Stresses

The dominabt source of stresses -on thesheath, Is expansion 'and hourglassing of thepellet. In ELESTRES, the pellet Is representedby 50-60 triangular finite elements assembledInto a hexagonal pattern, see Figure 21.Reference 2 describes the details of this model.

During irradiation, the sheath developsprimary and secondary stresses. The primarystresses depend on factors like: coolantpressure; fission gas pressure; and hydraulicdrag; see Figure 22. The primary stresses aremaily In the hoop and in the axial directions.The stresses and strains are well into theplastic ranges Hoop strains of -1U have beenmeasured.

Figure 20a shovs the calculatedatresses when the elenents were arranged In arectangular pattern. Compared to the analyticalrolutions, the rectangular pattern, hencerectangular elements, provide reasonable

dIctions for hoop and axial stresses, but the.isl stresses show large scatter. The

%exagonal pattern, hovever, gives betterpredictions for all three components, and the

scAtter Is negligible, see Figure 20b.

4 /

*~ ~ ~ iU 1 * i

_neU ( ? AN I "f 'IA m " o'

Figure 22 Laods on the Sheath, and a Finite Element Mesh

is

AECL.9331

For normal values of element power,pellet expands more than the available radclearance between the sheath and the pellThls leads to secondary stresses In the sheaBecause of hourglassiLg, the stresses are higlnear the circumferential ridge than nearmidplane of the pellet. This generates Insheath, hoop, bending (axial), shear, and rad:stresses. Additional secondary axial stresearise from axial interaction between neighbourlpellets, and from axial Interaction between Iendcap and the stack of pellets. The secondsstresses relax rapidly due to creep.

For sheath stresses, the default optlin ELESTRES uses (2] a simple force-balancethe hoop direction. These calculations considethe coolant pressure, the Internal gas pressurand the Interfacial pressure betideen the pelland the sheath.

A more detailed study using the FEMcode showed (11] that near the ridge, the strairare highly multiaxial. The multiaxialit3however, makes a significant difference to thlevel of stresses. For example, If othecomponents of stresces were not present, the hocstress cannot exceed the uniaxial tensile yielstrength. 'ut because of multiaxielity, tbmaximum hoop stress can be significantly highethan the "niAxi-l tensile yield strength.

All components of stresses contributto the damage of the sheath. For exampleReference 11 investigates the influence oaltfaxiality, on the fatigue of the sheath

during power-cycling. The conclusion is thawhen the entire stress-systen Is applied on th4sheath, the cycles to failure are half of thosiwhen only the hoop stress Is applied.

For this reason, an-optlon in ELESTIBEnou permits more accurate and detalledcalculations of sheath stresses. When the optLotIs actir'edif-for example to calculate sheathstresses after a power-boost, ELESTRES createsand preserves pertinent data In a computer file.This data is then used by a more versatilestress-analysis 'code like FEAST (7]. The mostiSportant information in this file relates to thehourglassed shape of. the pellet. Figure 4 showsthe links aong the codes. The followingparagraphs describe the detailed calculation ofsheath stresses.

The calculations using FEAST aremultLaxial, axisymmetric, and elastic-plastic.They account for. the axial variations IndisplacementslstraLns/stresses of the sheath, dueto: pellet expansion and hourglassing; Internalgas pressure; coolant pressure; and axialInteractions.

Sheath stresses are calculated bysolving simultaneously, the multiaxial classicalequations describing the following funtamentallaws of mechanics: equilibrium; compatibility;constitutive relations; yield criterion; and flowrule. Since the solution ls obtained by usingthe FEAST code, these calculations are similar to

those for pellet deformation [2J. Reference 7gives a more detailed description of the methodsof solution.

Figure 22 shows a typical mesh in thesheath. The sheath contains a finer mesh thanthe pellet; this reflects the need to knowdetailed local variations In the sheath. Themesh in the sheath Is tied to the mesh of thepellet; this precludes the need forInterpolations and extrapolations.

The study reported In Reference 11showed that strains can change rapidly along thethickness of the sheath, and along Its length.Because of the Importance of stresses near theridge, we use S nodes across the thickness atthat location. Stresses are less critical nearthe midplane of the pellet, so 2 nodes aresufficient there. The comparatively coarse meshnear the midplane helps reduce computing-cost.

.The transition from big to smallelements is gradual; this preveaits the largerelements from dwarfing the stiffnesses ofneighbouring smaller elements. For maximumaccuracy, the aspect ratio Is kept close to l.The sheath Is usually represented by about 200nodes, forming about 300 triangular finiteelements in a hexagonal pattern. Our experienceshows that this combination gives sufficientaccuracy at low cost.

5.6 Creep of Sheath

Stresses lead to creep of the sheath.t Anisotropy of the sheath plays an important roleet In the rate of creep. At 300-350C, the rate ofI creep of Zlrcaloy can be calculated using the

model by Hosbons, Coleman and Halt (35]. Thismodel considers athermal and thermal creep due to

S chaages In dislocation densities, and the effectof Irradiation. Reference I describes theapplication of this model to ELESTRES.

For off-normal conditions, thetemperature of the sheath may be higher than350C. Then, the above model Is not adequate,and ELESTRES uses the model by Sills and Halt(36]. This model is applicable for temperaturesabove 350C, and accounts for creep due tos:

- thermal and athermal strains due tochanges in dislocation densities,

- diffuslonal creep due to sliding atgrain boundaries, and

- transformation strain due to expansionat the crystal lattice, during thetransition of Zircaloy from a to f

phase.

The rate of creep from the above threecomponents depends on: temperatures; stresses;and mLcrostructures of Zircaloy. Temperaturesand stresses have already been discussed. Thefollowing paragraph summarizes the three majormicrostructural parameters considered inELESTRES: recrystallization; fractions of a andP phases; and grain size.

P OW71-

(

.0 ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~CANDOEV-86-1 10AECL-9331

Sheath

Sheath

L VbW Transvrs Sections

Figre 23 Exanqes, of Poss*bte Crcks In the Sheath of a Nudear Fuel Element

RecrystallizatIon, or annealing, occurs;ircaloy above - 430-C. Within the old

Veins, nucleation and growth of recrystallizedigrains give areas vith low densities ofdislocations. These areas grow thermally, thusannealing the material. The rate of removal, ofdislocations Is estimated from the empiricalmodel by Sills and Holt [36]. The distributionof a and F phases depends on the temperature, and-Is obtained from the phase dlagram. The size ofgrains is also a function of temperature. It Isobtained from an empirical correlation based ondicroscopic examinations of fuel sheaths afterheating to various temperatures. Further detailsof. the creep model are available fromReference 36.

During' creep calculations, ELESTREScontinually updates the microstructure ofZircaloy, to reflect the temperature transient.

5.7 Stress Corrosion Cracking

The failure rate, about O.lZ In 500,000bundles irradiated [l], Is very low In.currentCANDU fuel, which contains a layer of CANLUB. Inthe pase, however, fuel failures have beenreported (37] at circumferential ridges, andrelated to stress corrosion cracking during powerramps. The initiation of the cracks cansometimes be assisted by delayedhydrideldeuteride cracking. Some types of cracks

ve been reported previously (I, 37, 38], and,town Schematically In Figure 23.

Stress corrosion cracking occurs when alarge stress Is maintained for a lono tiee.

*Inultaneously with high concentrations ofcorrodante (active species). Initiation ofstress corrosion cracks is easier In the presenceof suitably orlented platelets of zirconiumhydrides (deuterides). Another way In whichirradiation promotes stress corrosion cracking,Is by embrittlLng the Zircaloy-

Fuel failures discussed In Reference 37were eliminated from CANDU fuel by Introducing alayer of CANLUB, which reduces the exposure ofthe Sheath to fission products, and by changingto new fuel-management schemes that give lowstresses in the sheath.

For stress corrosion cracking, ELESTRESuses an. empirical correlation based onirradiations at Pickering, Douglas Point, andChalk River. The probability of failure iscalculated from:

- ramped power;

- change in power;

- burnup;

- dwell tine at high power; and

- the presence of a protective layer ofCANLUB at the Inner surface of thesheath.

For this calculation, algebralcequations are used, based on the empiricalcorrelations Fuelograms (37] and Fulooo.

17

ALLUL-%4J1

6. PROPERTIES AND FEEDBACKS

6.1 Haterial Properties

The following properties of U02 and ofZircaloy, are used in ELESTRES: thermalconductivity; specific heat; coefficient ofthermal expansion; Young's modulus; Poisson'sratio; yield strength; plastic modulus; creeprate; and stress for fracture. For use InELESTRES, the values of these properties wereobtained largely from the MATPRO data base (25].Hany of the properties depend strongly oan localtemperature, especially the diffusivity of gas inU02; the thermal conductivity of U02; the yieldstrength of U02; and the creep rates of U02 andZircaloy.

For creep of U02, ELE TS uses theequations suggested by Armstrong j39J. The rateof U02 creep depends on: local temperature;local stresses; and local rate of heatgeneration. The strain rate can be. high atoperating conditions: At 1200-C and 100 Wsa, thecreep rate In U2 Is 0.3Z per day.

the temperature, which slovs furtherdensification. Similar examples can beconstructed for fission gas release, for sheathstrain, and for internal pressure. ELESTRESaccounts for the interdependence of theseparameters.

7. VALIDATION

Many of the physical processes arerepresented In ELESTRES by the same models as inELESIH. The major difference is that theinteractions among the sub-models are arrangedslightly differently, and that some models arenew in ELESTRES (e.g. hourglassing). Comparisonsfor about 80 Irradlations show that, as expected,ELESTRES and ELESIH predict similar temperaturesIn the pellet, see Figure 24. Hence, previousvalidations of ELESIH *lso apply to ELESTRES, forprocesses that are driven largely bytemperatures: UO. grain sizes (14], Figures 25and 26; poroslty [40], Figure 27; and fission gasrelease.

Figure 26 shows (14] the sizes of Uograins across the pellet radius, In bundle 14672irradiated at Pickering. The. grain size, Is.largely A function of time-at-temperature, andthe figure reflects the Influence of theparabolic temperature.

The trends shown In Figure 27 are dueto a cocpetition between volume reduction due todenslfication, and, volume Increase due toswelling from unreleased fission products (solidand gaseous) in U02 grains and at grainboundaries:

- Center. of the pellets Densification Ishigh. It Is balanced by a moderatelevel of unreleased fission products.

0

6.2 Feedbacks

Most of the preceding processesinteract, and influence each other. For example,thermal expansion of the pellet Increases theInterfacial pressure between the sheath And thepellet, tuich lovers the temperature of thepellet, which reduces the amount of thermalexpansion. Similarly, densification of 002Increases Its thermal conductivity, which reduces

.

3000- Fractional radius of

Densification is high. But gasiS low, giving high 'sellingunreleased fission products.

0 . 4 :releasedue to

&

i(2w)-J

2000 _ - Fractiona3 radius of O.7:Densification Is high. The fissionproducts are aostly ln the D02 matrix,where they do not coatribute toswelling.

Ioor _-- Pellet surface: Temperature Is

There is neither densiftcation,fission product swelling. Thevolume In the pellet Is nearas-fabricated value.

low.nor

voidthe

0

III I-

0 1000 2000 3000

Reference 2 compared the predictions ofELESTRES, against irradiation measurements offission gas release (1S irradiations). and ofsheath strains at circumferential ridges (10Irradiation&). The Irradiations were done Inexperimental reactors at Chalk River NuclearLaboratories, and In commercial reactors InOntario, Canada. The data base covered elementpowers of 50-120 kW/a, and burnups of1-300 MV.h/kgU.

ELESTRES Calculauion ('C)

Figure 24 Temperatures at the Centerof the Pellet (18

-lCANOEV.866110

AFCIt .ciiv=- =s

--

-

~92E

E

E0VRertstfication

*01

U- 2

Volume Decoease due to O~nstiscation

_

0 20 40 60 80 100

ues rd (m ._.) _. 1.

Figure 25 U02 raln diesater Iradhatlon In Picketing 114 1

Volkm. kwoe du, to Unreased Rdlon Proouct

Centerr

Surfacey

5

FE0

,7A-Measured

Predicted

I I I I

I C9a.

0 02 0.4 0.6 0.E 1.0

Fractional Radius of PNOet

Fractional Radius of the Pallet

Figure 26 Measured and Calculated Values of U02 Grain

Slze Across a Section of a Pickering Element 1141

Not Chsang In Vocum

Figure 27 Change In U02 volume during Irradiation(P1icketing bundle 097943 (l41

19

AECL-9331

kWlm

F

01:S

TIME (DAYS)

1.00.0 05 S1.s

Measured Sheath SUIM N

Figure 28 Final Values of Sheath Plastic Strains:Measured vs Predicted 12J

TIME (DAYS)

Figure 30 Hoop Strain at the Ridge In Element ASS:Measurements vs. ELESTRES

F-

e

SX

gI-00

if I" * I I0 100 200 300

DURNUP (MW.hlkgU)0

UEASUREO (%)

Figure 29 Fission Gas Release: Measurements vs.Predictions

so

Figure 31 Plastic Hoop Strain at Crcumferentlat Ridges InBundle GO: Measurements vs. ELESTRES

20

CANDEV-86-1 10AECL.9331

On average, the predictions of ELESTRES5tffered from measurements, by 0.2 percentage

nts for hoop strain In the sheath, see,gure 28, and by 1.2 percentage points forpercent release of fission gas.

The never version of ELESTRES has nowbeen compared against about 80 Irradiations inexperimental reactors and in commercial reactors.The predictions continue to show reasonableagreement with measurements of fission gasrelease, see Figure 29. The next two sectionspresent two more valldations of ELESTRES againstirradiation data: element ABS and bundle CB.

7.1 Irradiation ABS

Element ABS was irradiated (41] forabout one month at Chalk River NuclearLaboratories, Canada. The power ranged from 30to 60 kVIK. Hoop strain in the sheath wasmeasured during the Irradiation, using theIn-Reactor Diameter Heasuring Rig (IRDHI).Figure 30 shows the power history. It alsocompares the predictions of ELESTRES Ys themeasurements for hoop strains at the ridge, as afunction of time. On average, the predictionscompare vell with measurements.

7.2 Irradiation CB

In this experiment (42], the outerre^ nt was Irradiated at powers between 48 and

kWUm, to a burnup of )0 EW.b/kgU. Figure 31Wws that the predictions of &LESTRES are withinthe ranges of post-irradLation measurements, forhoop strains at circumferential ridges.

7.3 Sensitivity to Axial Nodes

Hore detailed calculations of ridgestrain require 7 axial nodes in the pellet, and55 CPU seconds to simulate irradiation CB.

0

a1

U.

60

40

20

02

Measured range

I I I I I,_3 4 5 6 7 "

iC.1

Figure 32 illustrates how the resultsBad the computing qosts of ELESTIES areLufluenced by the size of the finite element meshLn the pellet. For Irradiation CB, the figureshows the following parameters as a function ofthe number of axial nodes: fission gas release;?ermanent hoop stran at the ridge; and computing:Ime for the Central Processor Unit (CPU) of aDC/CYBER 175 computer.

Fission gas release Is primarily a!unctlon of temperature, which does not dependsuch on the details of the finite element mesh:.00 radial nodes are always used for this finitelifference calculation.

I

As expected, finer subdivision (moretxial nodes) improves the calculations for hoopstrains.

Also as expected, the computing cost.ncreases with more axial nodes. When 3 axialtodes are used to simulate irradiation CB,:LESTRES requires 19 seconds of CPU time -

¢liar to the 21 CPU seconds required by ELESIK: simulating the same irradiation. This

todalization permits a hexagonal arrangement of'minte elements, and Is sufficient if the primary,un is to calculate fission gas release.

2 3 4 5 6

Axial nodes In penet

7

Figure 32 Sensitivity of ELESTRES Calculatlons.to Axial Subdilvison of the Pellet

21

AECL-93314-

HOOP

8. ILLUSTRATIVE EXAHPLES

Reference 11 discusses some previousapplications of ELESTRES. Below, twoIllustrative examples are presented. They do notnecessarily represent conditions In fuel elementsIn experimental or In commercial CANDU reactors.Rather, the Intent here ls to demonstrate somecapabilities of the code that are not apparentfrom the previous section on validation.

The first example demonstrates howELESTRES and FEAST are linked to calculate thepatterns of sheath stresses and strains in thesheath, for a pover-boost of 40 kw/m at140 HW.hbkgU. Figure 33 shows the results. Themultiaxiality of stresses Is clear. The axialstress shows sharp gradients across the thicknessof the sheath. The shear stress shownsignificant variation. along the length of thesheath. The maximum principal stress is 500 MPa.This, however, relaxes rapidly due to creep.

AXMU

Figure 33 EMastlo4astlo Stresses (MPa) In the Sheath

L�� SHEATH THICKNESS I- SHEATH THIKESS f- !-

4

_ I

| _ | I

--I1.4

1.2

1."

EFFECTIVE

SHEAR0.6

0A

0.2Se

U. --

-02

-0.4

-0o.

-1.0-t.o

-t.2

OUTER SURFACE OF SHEATH -_-

RADIAL

-*-INNER SURFACEOFSAT

RADIAL OISTANCE ALONG SHEATH WALL __1 4...

AT CIRCUMFERENTIAL RIDGE AT 0.04 mm FROM THE RIDGE

Figure 34 Strains across the Sheath Wall

22

CANOEV-86-110AECL-9331

Figure 34 shows the distribution offains near a circumferential ridge, formed by aut-length-pellet, at a power of 56 kW/n at, ro burnup. At the inner surface, the hoop andshear strains have similar magnitudes. At theouter surface, shear strains are low, but theaxial strain is significant. The radial strainIs compressive, but the absolute magnitude ofpeak radial strain Is similar to that of hoop andshear strains. Thus, all four componentscontribute significantly to yield, creep,fatigue, and brittle fracture of the sheath.

The third Illustrative example Involvesa Loss-of-Reactivity- Control accident (LORA).An excursion of power, at 80 W.b/lkgU, graduallyincreases the power by 18Z. The coolant Ismaintained at full system pressure, but, theoverpower is assumed to cause dryout, whichresults in a low coefficient of heat transferbetween the sheath and the coolant.Conservatively, it is assumed that the drypatchcovers the entire element: all around thecircumference, and All along the length. Theseassumptiona are not realistic, but neverthelessused bere to show that the code ncam-be used. for.....simulatiug transients such as LORAs. Figure 35shows the prediction of ELESTRES, for sheath hoopstrains near the ridge and near thi uidplane ofthe pellet. During the Fraasient, the elevatedteeperatures In the pellet increase the hoopstrain at the ridie. The ridge height also.reases.

W

9. SUHXkRY AND CONCLUSIONS

(1) An Improved version of ELESTRES has beendeveloped for modelling the performance ofnuclear fuel elements. The two-dimensional,axLsynmetric calculations account for radialand axial variations.

(2) For given conditions of design andirradiation, the values of the followingparameters can be calculated: temperatures,fission gas pressure, circumferentialridging, sheath stresses, and probability offailure due to stress corroslon cracking.

(3) Temperatures are calculated by aone-dimensional model. The standard finitedifference method Is used for steady-statetemperatures, using 100 nodes across theradius. Transient temperatures use animplicit formulation and an iterativeNewton-Raphson method.

(4) The finite element method is used fortwo-dimensional, axisymnetrlc calculations

-- - of--diaplacements,-*tresses, and *str&Sa*-Sinthe pellet. The pellet is represented by40-S0 finite elements. A link with FEASTpermits detailed calculations of sheithstresses, using 200-300 finite elements.Elastlcity, plasticity, creep and crackingare considered. Above 3SOC, creep ofZircaloy Is calculated from a model thatconsiders diffuslonal creep and dislocatioaclimb. This model accounts for changes Inthe sicrostructure of Zircaloy, such asgrain size, and fraction of a and P phases.Special numerical techniques keep thecomputing time below 1 minute on aCDCjCYTBR 175 computer.

(5) Triangular finite elements arraoged in ahexagonal pattern, give better accuracy thanrectangular elements.

(6) ELESTRES shows good agreement withmeasurements of fission gas release, from- 80 irradiations. The code also predictswell, sheath strains at circumferentialridges in experiments ASS and GB.

(7) By linking ELESTRES and FEAST, Illustrativeexamples show a high degree of multiaxlalityin sheath stresses and strain.. Thestresses/strains change rapidly withdistance along the length of the sheath, andalong the thickness.

2 3 4 5 6 7Tkme dwing the Irsnslon( (wminues)

Figure 35 Sheath Strain during a Loss-of-Reactlavty.ControlAccident

23

t~t~dlLV'Jt# ..

AECL-9331

ACKNOWLEDGEMENTS

The work reported in this document wasfunded partially by COO (CANDU Owners Croup) R&DProgram, as part of the 'Operating FuelTechnology' project: Work Package Number 2840.The author thanks the current members of'Operating Fuel Technology' : Ontario Nydro,Atomic Energy of Canada Limited, Hydro Quebec,and New Brunswick Electric Power Corporation.

The author gratefully acknowledges theencouragemaent, support, and contributions ofR. Sejnoba, H. Cacesa, D.R. Pendergast,D.B. Primeau, J.C. Wood, P.J. Fehrenbach,H.E. Sills, and J. Runge. ELESIN, the startingpoint for ELESTRES, was developed largely byH.J.F. Notley. Special thanks to H.E. Sills(CRNL), for his permission to Include in thispaper, 8ome of his unpublished results(Figures 24, 29), and to A. Banas for Figure 35.

* ~~~~EFRZENCES'

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24

a CANDEV-86-1 10AECL-9331

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Cas Diffusion from U02 Fuel and ItsApplication to the X-2-f Loop Test', AtomicEnergy of Canada Limited, Report AECL-496,1957.

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Commercial U02 Fuel: Comparison With Model1redictionsi, Journal of Nuclear Materials,Vol. 75, 1978, pages 301-303.

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U02 Fuel', Communications of the AmericanCeramic Society, Vol. 67, No. 2, p C-24,1984.

25

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