A t û É C e l i & l ^

STRESS RELAXATION TESTING OF SMALL BENT BEAMS:

AN EVALUATION OF SOME OUT OF-PILE TESTS

DE. FRASER

0

It! ' f \ :

Kb* - * -

, i v if? , /

- s ï i " - - -.-Chalk River, .Ontario

STRESS RELAXATION TESTING OF SMALL BENT BEAMS:

AN EVALUATION OF SOME OUT-OF-PILE TESTS

D.E. Fraser

ABSTRACT

The relative stress relaxation behaviour at 300°C ofcold-worked Zircaloy-2, cold-worked Zr-2.5 wt% Nb and heat-treated Zr-2.5 wt% Nb pressure tube materials was evaluatedand compared using a power function from "time hardening"creep theory. The function fitted satisfactorily over thetime range from 1000 h to 10,000 h.

Creep rates calculated from stress relaxation data com-pared reasonably well with experimental creep data.

Relaxation tests to determine relative creep behaviourseem promising, but should not be substituted for creep teststo determine design creep data at the present time.

Chalk River Nuclear LaboratoriesChalk River, Ontario

January, 1971

AECL-3782

Mise à l'essai en relaxation de contraintede poutrelles cintrées: évaluation/de

quelques essais hors pile

).E.\

par

Fraser

Résume

Les comportements relatifs, à 300°C et en relaxationde contrainte, d'alliages employés pour les tubes de force(Zircaloy-2 écroui, Zr-2.5% en poids Nb êcroui et Zr-2.5V enpoids Nb) ont été évalués et comparés au moyen d'une fonctionde puissance provenant de la théorie de fluage avec "durcisse-ment dans le temps". Ladite fonction a été très satisfaisantepour l'intervalle de temps allant de 1 000 a 10 000 heures.

Les vitesses de fluage calculées à partir desdonnées relatives à la relaxation de contrainte se sont avéréesen bon accord avec les données de fluage-recueillies expéri-mentalement..

Les essais en relaxation de contrainte semblentprometteurs pour déterminer le comportement relatif dufluage, mais ils ne devraient pas remplacer, à l'heureactuelle, les essais de fluage pour déterminer les donnéesde fluage employées par les ingénieurs.

L'Energie Atomique du Canada, LimitéeLaboratoires nucléaires de Chalk River

Chalk River, Ontario

AECL-3782^

/.ECL-3782

STRESS RELAXATION TESTING OF SMALL BENT BEAMS:

AN EVALUATION .?OF—SOME* OUT-OF-PILE TESTS

D.E. Fraser

INTROlXJG'nObT

When a material is stressed elastically and held at aconstant strain for an interval of time, the stress neededto maintain the strain gradually decreases. This time depend-ent change in stress with constant strain is stress relaxation,

A program of stress relaxation testing, using beam-typespecimens, has been performed to:

(i) evaluate the technique asi a means ofclassifying the relative time dependentbehaviour of different reactor materials;

(ii) to determine the extent to which stressrelaxation tests can be used to predictthe creep behaviour of reactor materials.

The advantages of stress relaxation testing of beam-type specimens are:

(i) the tests are easy to do and requiresimple equipment;

(ii) many specimens can be tested simultaneouslytherefore a range of material!* can be assessedquickly.

This report presents the results of some transverse

- 2 -

stress relaxation tests in bending at 300°C on zircaloy-2 andZr-2.5 wt% Nb alloy pressure tube specimens and on longitudinaland transverse specimens of zircaloy-4 sheet in differentmetallurgical conditions.

The creep rates predicted from stress relaxation resultsare compared with measured tensile creep rates and with pre-viously published relaxation results. Possible sources oferror and their estimated magnitudes are discussed in anAppendix.

EXPERIMENTAL PROGRAM

Table 1 characterizes the materials which were used forthe stress relaxation tests and Pig, 1 shows their structures.

All test specimens were 0v030 in. thick x 0.150 in. widewith lengths of either 4 in. or 3 in, Specimens cut fromrollnd sheet were 4 in. long; specimens which were cut fromthe circumferential direction of pressure tubes were 3 in.long. Fig. 2 shows the specimen orientations.

The longitudinal specimens were stacked nine deep andclamped in holders as shown in Pig. 3. The transverse (hoop)specimens were stacked six deep and clamped in similar holders.

Nominal muciirum fibre stresses of 15,000 psi, 25,000 psiand 35,000 psi were achieved by stacking specimens in holderswith different radii of curvature on their clamping faces.The maximum fibre stresses were calculated with the followingestablished formula developed *rom the theory of elasticityi,'or the pure bending of a simple beam(i) :

whore ofi is the change in maximum fibre stress when thespecimen radius changes from R to R,;

E is Young's modulus = 11.2 x 10 psi at 300°c forzirconium alloys;

c is the thickness of the beam.

- 3 -

The test specimens were milled from pressure tube orsheet stock so that the width and thickness dimensions werewithin 0.002 in. of the desired^dimensions .i; = 13jie-final-0V002Jin. was removed by chemical polishing. This procedure wasadopted so that residual surface stresses introduced by machiningcould be reduced to a small amount.

After measuring initial dimensions and shapes, thespecimens were stressed in the holders and maintained in waterat 300°C and pH = 9 to simulate the reactor thermal conditions.Periodically, they were removed, released from the holders andthe changes in radius of curvature measured. The change inradius provided a measure of the unrelaxed stress as calculatedby equation (1) .

To measure the radius of curvature, a profile projectorwas used to determine the (x>y) co-ordinates of at least sevenpoints along the central three-quarters of a specimen's length.A computer program was employed to fit the best circular arcthrough these points. The radius of this arc, corrected tocoincide with the specimen's longitudinal centreline, was thespecimen's radius of curvature.

This method was chosen because it calculated radii whichwere most representative of the actual specimen shape over thewidest range of radii. Also, this technique gave a measureof the difference between the calculated shape and the actualshape.

EXPERIMENTAL RESULTS

Fig. 4, which shows the typical shape of a stress relaxa-tion curve, is ftr the hoop specimens of 15% cold-workedZircaloy-2 pressure tube material. The curve shows the averageunrelaxed stress fraction versus time. The unrelaxed stressfraction is the maximum fibre stress at a given time dividedby the initial maximum fibre stress. Generally, the specimensmaintained their relative positions within the range of observedstress relaxation behaviour throughout the testing time. Thir,spread in data is typical of the tests on the other material*when more than one specimen was tested. For the other materials,the average stress relaxation behaviour is shown in Figs. 5 to8. Only the data for initial maximum fibre stresses at ap-proximately 25,000 psi have bean plotted because these twits

continued for the longest time. Appendix 1 lists the relaxa-tion results for each specimen of each material and for allinitial maximum fibre stresses.

ANALYSIS AND DISCUSSION

TO establish a basis for comparing the behaviour of thedifferent materials quantitatively, the stress relaxation datawere analyzed using the time-hardening creep theory in whichthe relationship between creep rate, stress and time is(2,3):

e = K a11 t m (2)P

where e is the creep rate;P

K is a constant for constant temperatures;

cf is the stress; . .......

t is the time; ;.

n, m are constants.

The term "time-hardening" refers to the idea that thestrain rate is a function of the time. The alternative is the"strain-hardening" theory where strain rate is a function ofthe strain. The use of the time-hardening theory is accept-able when considering slowly changing stresses. Its pre-dictions improve when fitted to data for long test times (i.e.,times beyond which the effects of initial rapid transientsare small) . An attractive feature of the tims-hardening theoryfor creep and relaxation is that it is analytically easier toapply than the strain-hardening theory.

For stress relaxation tests, the total strain, £„, isconstant. A fraction of the elastic strain,'ee, transformsto plastic strain, e , as time progresses. Mathematically thisis (4). y

e m ee + e a constant (3)

Differentiating equation (3) with respect to time gives:

- 5 -

m = e + e = oT e p

Therefore: e p

Substituting for efi from Hooke's law for linear elasticityand equation (1)for e g i v e s :

(4)

where the symbols are as before.

If the power, n, is one, then the integration of equation(4) yields:

(5)

where the subscripts o and t refer to initial test conditionsand conditions at some time later in the test, respectively.

If n^l, then, after integration, equation (4) becomes;

1-n

1 + B-.-K t1-n

m+l

(6)

or

m+lt m + 1

(6A)

If the exponent, n, on stress was close to one, a plotof log (cJt/aQ) versus log a Q would give a straight lins withslope near to zero.

Fig. 9 shows a plot of log (stress ratio) at 2000 hoursversus log (initial stress) for the hoop specimens taken frompressure tubes and some specimens taken from sheet materials.•There is not a strong variation in stress ratio with initialstress. Except for 15% c.w. Zircaloy-2 the average slope ofall the lines drawn through the data for different materials

- 6 -

is about -0.2 which is close to zero. For most materials, thetotal range in c?t/ao with initial stress shown in Fig. 9 iswithin the accuracy which could be expected from the beam testresults (see Appendix 2). The scatter in the 15% c.w. Zir-caloy-2 results masks any trend. The power, n, was also checkedusing a method of successive approximations proposed by Lew-thwaite et al(5»6»7K Powers from n=4 down to n=1.5 wereinvestigated. As the value of n decreased towards one, the

[(a/ \i-n _"]experimental data fitted a plot of log I ' oQ\ - 1 versus

log 0 O better than the higher powers, a is the stress whichhas been'adjusted to allow for the nonlinear stress distributionwhich develops with time. Fig. 10 shows such a plot forannealed zircaloy-4 and 79% c.w, zircaloy-4 using n=2 andn«l.5. The slope of the plot should be equal to n-1 when thecorrect value of n is chosen. Thus the value n for the zir-conium alloys is probably in the region 1.0 to 1*5.

The effect of making a small error in. the choice of iton the calculation of the maximum fibre stress in a bent beamstress relaxation specimen has been investigated by HattdnC8).The study showed that for an initial maximum fibre stress of20,000 psi, the error in the calculated .stress by assumingn=l when in fact n=1.5 was less than 1000 psi after 10,000hours (see Fig. 11). For a specimen whose 0 o = 30,000 psi, theerror in calculated stress after 10,000 hours by assuming n=lwhen actually n=1.5 was less than 1500 psi. Smaller errorswere calculated for shorter times. This suggests that largeerrors in stress will not be introduced-by using equation (5)even if n is a little different from one. The parametersdetermined from equation (5) can be used for a relative com-parison of the stress relaxation behaviour of the materialstested because all the materials would be affected similarlyby such an error. The results allow the use of equation (5) inwhich n=l over (6A) to compare the relaxation behaviours ofdifferent zirconium alloys.

The finding that 1 <n Si.5- is consistent with the creeptests in the stress range 10-40 kpsi on airconium alloy pres-sure tube material. Fig. 12, based on information from Del-vecchio^9), summarizes the effect of stress on creep rate forvarious zirconium alloy pressure tube materials at 300°c.Diametral creep rates are reported for the tube specimens. Forall tests, whether internally pressurized closed-end tubes oruniaxial transverse specimens from tubes, the slopes of the

- 7 -

curves are between about 1 and 1.6 at stresses below 40 ksi.

Pigs. 13 and 14 show the stress relaxation data plottedaccording to equation (5). The values of-m determined fromthe slopes of these curves for data beyond 1000 hours and theparameter KE are shown in Table 2. The smaller the value ofKE, the less will be the initial, rapid drop in stress. Thesmaller in magnitude the value of m the more rapidly relaxa-tion will occur later in the test, Generally, thecold-workedmaterials relaxed a large fraction within the first few hours(for example, see KE for 15% c.w. Zircaloy-2, 28,5% c.w.Zr-2.5 wt% Nb and 79% c.w. 2ircaloy-4) but at long times therelaxation rate became lower. The heat-treated or stressrelieved materials (for example; 15% c.w, zircaloy-2 + Etressrelief, and heat-treated Zr-2.5 wt% Nb) tended to relax lessduring early stages of testing, but maintained a higher relaxa-tion rat« at long times. The difference in relaxation behaviourbetween the stress relieved? iarcjd the unrelieved specimens ofpressure tobe 48^sensitivity of tlvis early behaviour to the specimen condition.There appeared to be no obvious advantage to p-quenchihgZircaloy?-4; in ati attempt to improve its stress relaxationbehaviour out-of-pile. The results; suggest that a stressrelief following cold-working will improve the resistance tostress relaxation over both short and long term.

An attempt was made to predict the creep rates for heat-treated zr-2.5 wt% Nb-, 15% cold-worked zircaloy-2 + stressrelief, and annealed Zircaloy-4 from the stress relaxation datafor various times and stress. By combining equations (3A) and(4), a relation between creep rate, stress and time resulted:

where the symbols are the same as for equations (3A) and (4) .

The stress for a given time must be determined fromequation (5). The creep rate was then calculated using thecalculated stress and its corresponding time. The calculatedrates are compared with creep data from Fig. 15 in Table 3.The measured creep rate reported in Table 3 for annealed Zir-caloy-4 was estimated from the creep data for annealed Zir-caloy-2 obtained by Bell(10).

- 8 -

-There is reasonably good agreement between the predictedtrapolated creep rates. The predicted rates are usually

l o w e T S the experimental values. Agreement seem* to improve^longer times if the trend for heat-treated zr-2.5 wt% Nbis true.

The good agreement between predicted and extrapolatedrates Say be fortuitous, the predicted creep rates were cal-l e d Lsuming no difference between tensile and compressxvecreep. Fig. IS is based on data provided by Pr^cet^) and byBelli" .13714). it shows there is a difference between tensionand compression in the longitudinal direction of 15* cold-workedZircaloy-i2 pressure tubes. Whether the same effect occur* xnthe transverse directions has not been established. How thiswould affect a relaxing beam has not been studied yet. Thepredicted rates in Table 3 are based on the averaged behaviourof two or more stress relaxation specimens for -each material,except for annealed zircaloy-4 where ?bnly one specimeniwasavailable. The extrapolated creep rates ̂ ere determined fromcurves such as those of Fig. 15. —

just as there is a spread in the creep rates from dif-ferent creep tests under nominally identical conditions, thereis a spread in the observed relaxation behaviours for a givenmaterial which leads to a spread in the predicted creep rates.Until the effect of different tension and compression creepbehaviours and the effect of anisotropy on beam relaxationare known, this test should not be regarded as a substitutefor a creep test to get design information for creep. Itappears that the relaxation test is useful to determine rel-ative creep behaviours.

The relaxation results for annealed Zircaloy-4, 79%cold-worked Zircaloy-4, and p-quenched Zircaloy-4 were com-pared with the results of Kreyns and Burkart(15) in Fig. 16.Only the data gathered in this study before 1000 hours wereused except for p-quenched zircaloy-4. Kreyns1 and Burkart'sunirradiated specimens were tested for only 1000 hours, exceptfor the p-quenched material which was tested 1992 hours. Thetime exponents, m, and the values of KE which were derivedfrom Kreyns1 and Burkart's data are lower in magnitude thanthose derived from data in this study (see Table 4). However,for each set of data, the same relative behaviours for eachmaterial were observed. That is, the p-quenched zircaloy-4had higher relaxation rates at long times than the annealed

- 9 -

Zircaloy-4 or 79% cold-worked zircaloy-4 but at short timesthe p-quenehed zircaloy-4 dropped less than the other materials.The 79% cold-worked zircaloy-4 relaxed the most for shorttimes but at long times i ts relaxation jcate was about thesame as the annealed zircaloy-4. The values of m arid KE givenin Table 4 differ from those reported in Table 2 because onlythe first three or four points of data were used to determinem and KE. Table 4 is meant for comparison of the two sets ofcJata over the same time range. As Fig. 14 shows, the same powerfunction which would be fitted to data before 1000 hours wouldnot describe the stress relaxation behaviour consistently fortimes much longer than about 1000 hours. This limited ap-plicability of a power function for stress relaxation is con-sistent with the conclusions of Peltham in reference (2),

The differences in m and KE determined from the twosets of data probably arise from different specimen histories.Kreyns and B̂ing. Thfi specimens in this study were tested as received fromthe sheet materials. They were chemically polished to reducesurface stresses which might have been introduced duringmachining.

Stress relieving tends to lower the magnitudes of m andKE. This is consistent with the trends observed betweenKreyns' and Burkart's materials and the sheet materials ofthis study.

Kreyns1 and Burkart's annealed zircaloy-4 and 79% cold-worked zircaloy-4 have different textures from these Eircaloy-4 materials in this study. A comparison of the stress relaxa-tion results from the longitudinal and transverse directionsof Kreyns1 and Burkart's annealed zircaloy-4 suggests thatthe differences in behaviour due to texture is less than thedifferences due to stress relieving.

SUMMARY

1. The stress relaxation data from pressure tube materials(transverse specimens of 15% cold-worked Zircaloy-2, 15% cold-worked zircaloy-2 + stress relief, 28.5% cold-worked zr-2.5wt% Nb, and heat-treated zr-2.5 wt% Nb) and sheet materials(annealed Zircaloy-4 (transverse and longitudinal specimens,79% cold-worked Zircaloy-4 (longitudinal specimens) and £-

- 10 -

quenched zircaloy-4 (longitudinal specimens)) were evaluatedusing the expression:

;•• ; • • • - - • • . - . ;-•-••—-^LfJS ^ •• • • •s--+-----~-

For these zirconium alloys n is between 1 and 1-5, Thisis consistent with out'-of-pile creep test results for 15% cold-worked Zirdaloy-2, cold-worked .zr-2,5 vt% Nb and heat-treatedZr-5,5 wt% Nb pressure tube materials,

2. Hie effect of choosing n~l if, in fact, n=l,5, upon thecalculated maximum fibre stress is small. It should not notablyaffect the ability of the test to show relative differences instress relaxation behaviour,

3. The equation with n=l is not sufficient to describe thestress relaxation behaviour accurately^ from time = O h to10,000 h. it describes the experimental data sufficiently wellin the region 1,000 h to 10,000 h which is the range of interestfor comparing stress relaxation and creep results.

4. Generally, the cold-worked zirconium alloy pressure tubematerials (15% c.w. zircaloy-2? 28.5 wt% c.w. Zr-2.5 wt% Nb)relaxed quickly at first, reaching lower relaxation rates forlong times than the stress relieved or heat-treated materials(15% c.w, zircaloy-2 + stress relief; heat-treated zr-2.5 wt^Nb). The same trend was seen in the sheet materials (annealedZircaloy-4r 79% cold-worked zircaloy-4? p-quenched zircaloy-4).The relative, thermally-induced, stress relaxation behaviourof the sheet materials was consistent with that observed byKreyns and Burkart.

5. The early stress relaxation behaviour of the specimensseems to be influenced by small differences which arise duringfabrication. Stress relief of 15% cold-worked zircaloy-2material reduced the amount of stress relaxation which occurredin the first few hundred hours. This suggests that cautionshould.be taken when trying to predict long term creep behaviourfrom stress relaxation results, which are of too short a term.

6. The bent-beam stress relaxation tests allowed the thermalcreep rates for some zirconium alloys between 1000 and 10,000hours to be predicted within reasonable agreement with experi-mental values.

- 11 -

ACKNOWLEDGEMENTS

/ : ^ ^ the; experimentalprogram, G,A. DelveccTiio and^E.G. Priciii of Orenda Ltd. f orthe unpublished creep ̂ data and P,Av Ross-Ross for guidance andhelpful discussion.

REFERENCES

(1) Timoshenko, s. and Young, D.H., "Elements of strengthof Materials", (5th edition), D, Van Nostrand Company(Canada) Ltd., Toronto, 1968, p. 113.

(2) Feltham, p., "on the Representation of RheologicalResults with Special Reference to Creep and Relaxation",Brit. J. Appl. Phys., 6 (1955), pp. 26-31.

(3) Gittus, J.H., "implications of Some Data on RelaxationCreep in Nimonic 80A", Phil, Mag., 8 (1964), pp. 749-753.

»(4) Oding, I.A. (Editor), "Creep, and Stress Relaxation in

Metals", Oliver and Boyd Ltd., Edinburgh, 1965, p. 280.

(5) Lewthwaite, G.W. and Mosedale, D., "The Analysis ofRelaxation Tests on Specimens with inhomogeneous Stresses",Brit. J. Appl. Phys., 17 (1966), ppo 821-825.

(6) Lewthwaite, G.W. and Mosedale, D., "The Determinationcif^Cr eep ^Irihomogeneous Stresses", J. Nuc. Mat., 31 (1969), pp.

. •226-227.: .•; : . ."••:".. ;:; "•-' . ••' .;.:::;..: : ...: 2 . ; v . . . ;• .•_..-..

(7) Mosedale, ; p. and Lewthwaite, G.w,, "Comments JOIX a Paperby P.H. Kreyns and M.W. Burkart", J. Nue. Mat. 31(1969),pp. 228-229.

(8) Hatton, H., private communication.

(9) Delvecchio, G.A., private communication,

(10) Bell, L.G., "Some preep Properties of Zircaloy-2",Atomic Energy of Canada Limited, Report AECL-1305(June 1961). '••'•,

- 12 -

(11) P r i ce , E.G., p r iva te coirairjnication.

Belf , L ,€^ ' "*Gr^ ip^ i i i »^ loy -2? ? Pressu re Tubes - 1•Longitudinal- bi r^ct ionf , Atomic Energy of Canada

i i t l Report »ECL-128^ (June 1961) .

(13) Be l l , IuG., "Creep of Zircaloy-2 Pressure Tubes - 2.Transverse Direct ion", Atomic Energy of CanadaLimited, Report AECL-1456 (January 1962).

(14) Be l l , Ii,G.f p r iva te communication.

(15) Kreyns, P.H. and Burkart, M.W,, "Radiation Enhanced Re-laxat ion in Zircaloy-4 and a Zirconium-2,S wt% Niobium-0.5 wt% Copper Alloy", J . Nuc. Mat, 26 (1968), pp. 84-104,

Table 1

Characteristics of the Test Materials

Material

(1)15S5 c.w. Zircaloy-2(pressure tube 485)

; ;i5*:;cw. Zircaloy-2: <"•+ '• stress relief ';'(pressure tube 485)

• - > : ; • { 3 ) !••:•-•.• M . : \

Heat-treated Zr-2.5

^ w t i * i ! » » " ; " ; - : " '•••" i!>; (pressure tube 576)!

;••! '••:'.''• V\i-•'--••: '•' ' •• *•

r i f 4 ) j . ; v - •••;-.••• ••' :;

J28.5* c.w. zr-2.5•.:i;wtjs||in> ' ^ ,-.

(pressure tube 603)'

IV '. ;..Annealed zircaloy-4 sheet ' '

History

Typical Pickering i sII type pressure tubewith 13?4 nominal cold-work , ., . . • : .

Same as (I)1 but witha stress relief of 4 'h'at 5lb"C in vacuum

Extruded frdm billetatiJ::ii>but/B50«C;!..;- "';•'quenched from 880»C, :cold drawn about 12%,then aged for 24 hB i ' 5 0 0 ° C " ' ' ; ' • • ' • • '•'••'•• '•• .

Extruded from a ibillet which was p-quenched from 1065 "Cinto water. Extrudede 675"C with ratio12:1. cold-workedin 3 successivedraws aslOX each

As received material.Met ASTH StandardB352-64T forannealed strip

Chemistry

Inaot chemistry (wt%) :Sn^l.SFe 0.05Cr!0.12NiO.06

As above

Ingot chemistry:! Nb 2.4 wt%O 1070 ppmH ; 5 ppmN 34 ppm

Tube chemistry:Nb! 2.65 wt%N 71 ppmH ;10 ppmO 1340 ppm

Alloy elements (wt%):Fe 0.14cr| 0.09Sn 1.66

Orientation(Basal Pole Intensity)

4 times random at 30°from the radialdirection

As above

6 times random intangential directionand longitudinaldirection

6 times random valuein tangentialdirection

6 times random in thesheet normal direction

Second Phase Particle sizeor Grain Size ;

Grain size about 19 pm x! 10 \unwhen looking in the trans-verse direction {Fig. la)

As above

Grain size not resolvable.a-phaae particle size =3 (jn x10 \m {elongated in extrusiondirection) '<•

Not resolvable due to cold-worked structure

//

Grain size is 14 pm

- continued -

Table 1 continued

Material

(6)79% cold-workedZircaloy-4 sheet

(7)p-quenched Zir-caloy-4 sheet

History

As received annealedsheet was cold rolledto a thickness reduc-tion of 79,5*

Annealed material washeated @ 1016="C for7 rain in vacuum.Material was raisedto cold zone (temp.about 150°C) of fur-nace and cooled withari?on (slow ouench)

Chemistry

Alloy elements (wtfc):Fe 0,12Cr 0.11Sn 1.33

Same as (5)

Orientation(Basal Pole Intensity)

3 times random in thesheet normal direction

About 6 times randomin the sheet normaldirection

Second Phase Particle sizeor Grain Size

Hot resolvable

Average lath width i s about0.3 [an :

Table 2

Summary of the Relaxation Parameters for Out-of-Pile Testson Hoop specimens from Pressure Tubes and Flat Specimensfrom Sheet Materials in the Region of 1000 h to 10,000 h

parameters fromEquation (5) in Text

Material initial Max, m

- 8 5

2. Sheet materials

Annealed zircaloy-4 _. .-_ __(longitudinal) 24'400 -*85

Annealed zircaloy-4 • • _3(transverse) 24,300 -.83

4 24 700 - 91(longitudinal) 2 4' 7 0 0 -91

p-quenched(caloy-4 i 24,200 -.84(longitudihal) f ^

1. Pressure tubes

15% c.w. Zircaloy-2 25,200 -.87 4.8 x 10"2

4.52 x

3.73 x

5.69 x

3.355 x

10

10"2

10"2

ID"2

Material

Keat-treatedZr-2.5 vt% 8b(pressure tube576)

15% cold-workedZircaloy-2(pressure tube485) + stressrelief

Annealed zir—caloy-4 sheet

SpecimenOrientation

TransverseM

Transverse

Longitudinal

TestTime(h)

1.000

3,000

10,000

1,000

3,000

1.000

TestTempCO

300n

ii

••

JI

InitialStress(psi)

27,800

27.800

27,800

26,700

26,700

24,400

InstantaneousStress at Tine

(psi)

20,250

18,720

16,800

19,850

17,850

10,300

PredictedCreep Rate

1.2 x 10~7

4.4 x 10~8

1.5 x 10~8'

1.5 X 10"7

6 X 10"8

1.2 x 10~7

ExperimentalCreep Rate

3.5 x 10~7

1.x! lO"7

2.3 x 10-8

1.5 x 10"7

4 X 10"8

2 x 1O"7*

TestStress(psi)

20,500

19,000

17,000

20,000

18,000

10,000

TestTempi*C)

300M

M

H

Time(K)

1,000

3,000

10,000

1,000

3,000 ;

1,000

Remarks

Fig. 15 A

| rig. 15b

•Estimated from datain referencej (10) forZixcalov-2 , '"J!

Table 4

Comparison of stress Relaxation, Resultsfrom this Investigation withKreyns' and Burkart's Results

Material

Annealed Zircaloy-4(longitudinal)

7996 cold-worked 7fc-caloy-4 {longi-tudinal specimensin this investiga-tion,, K & B used

transverse spec.)

(3-Quenched Zir-caloy-4 (longi-tudinal)

This :

af psi)

24,400

24,700

24,200

Investigation*

m

-.94

-.94

-.91

-KE

fh-(m+lh

3.19 x 10~'

4.6 x 10"2

—22.5 x 10

Kreyns & Burkart

(psiy

10,950

23> 600

10,00Q

m

-.89

-.88

-.70

-KE(h-Oa+D-)

1.5 x 10"2

2.5 x 10~2

6.3 x 10

Remarks

*NOTEt m, & KEwere calculatedusing datagathered duringthe same time,period as Kreynsand iBurkart. .Thus, m and KE inthis It able differfrom those re-ported earlierfor longer times.

Fig. 1 (a) . 1596 cold-worked Zircaloy-2(pressure tube 485). Longitudinal section

X500

Fig. 1 (b). 28.596 cold-worked Zr-2.5 wt%Nb (pressure tube 603). Longitudinal sec-U o n X1000

Fig. 1 (c). Heat-treated zr-2.5 wt# Nb(pressure tube 576). Longitudinal eection.

X1000

Pig. 1 (d). Annealed Zircaloy-4 sheet.Looking in the longitudinal direction.

X500

Pig. 1 (e). 79* cold-worked Zircaloy-4.Looking along the sheet normal direction.

X250

Pig. 1 (f). -̂q!uenched Zircaloy-4 sheetLooking along the direction of the sheetn O r i D a l " ~~ - - - - ^ r --. • r ".•.•-;

X100

TRANSVERSE

3 IN. LONG

PRESSURE TUBE

TRANSVERSE

SHEET

LONGITUDINAL

4 IN. LONG

FIGURE 2: A DIAGRAM SHOWINGSPECIMEN ORIENTATIONS

BOLTS

DIMENSIONS:

STACKED SPECIMENS

LENGTH - 6"(l5-25cm)

WIDTH - 0-375" (0-953 cm)

HEIGHT - 10"(2-54cm)

T FIGURE 3 :

SKETCH SHOEING THE SPECIMEN HOLDEf*LOADED WITH A STACK OF SAMPLES f

FIGURE 4: OUT-REACTOR STRESS RELAXATION OF 15% COLOWORKED ZIRCALOY-2 PRESSURE TUBE MATERIAL-

TRANS VERSE DIRECTION

•0•A•

a—

TESTSPECIMEN

All112in114IISIIB

AVER16 EDBEHAVIOB

TEMPERATURE - 300°CINITIAL STRESS(psi)

23,008

25.500

26.tee24.700

25,50025,200

I

-I-

I4 5

TIME - HOURS X 1(T3

UJ

oUJ

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

—"

— I

— . - :

— .

— * •

• ••••:•£ i . \ i.... 1 . i

FIGURE 5: STRESS RELAXATION OF15* COLD WORKED ZIRCAL0Y-2 + STRESS

PRESSURE TUBE MATERIAL —TRANSVERSE DIRECTION

TEST TEMPERATURE = 300°CAVERAGE OF TWO SPECIMENSINITIAL STRESS = 26,700 psi

1 , 1 , 1 , 1 . 1

RELIEF

. 1 .4 5

TIME - HOURS X 10"3

FIGURE 6: STRESS RELAXATION OFHEAT TREATED Zr-2.5 wt« NbPRESSURE TUBE MATERIAL —

TRANSVERSE DIRECTIONTEST TEMPERATURE * 300°CAVERAGE OF TWO SPECIMENSINITIAL STRESS = 27,BOO psi

4 5TIME - HOURS X 1O"3

0.8

M 0.7

FIGURE 7: STRESS RELAXATION OF28.5% COLD WORKED Zr-2.5 wt« NbPRESSURE TUBE MATERIAL—

TRANSVERSE DIRECTIONTEST TEMPERATURE = 300°CAVERAGE OF TWO SPECIMENSINITIAL STRESS = 27,800 psi

4 5TIME - HOURS X 10"3

FIGURE B: STRESS RELAXATION OF ZIRCALOY-4 SHEET MATERIALSTEST TEMPERATURE = 300°C

CONDITION• A N N E A L E D

O ANNEALED

A 7 9 t COLDIORKEDj 9 - Q U E M C H £ D L O N G I T U D I N A L

K R E Y N S ' S & B U R X A R T ' S O U T * C I S )4 ANNEALEO L O N E J T U O I N A L

ORIENTATIONLOBS1TUDIIALTRANSVERSELOH6ITUDINAL

NO.SPECIMENS INITIAL STRESS(osh24,40024,3D024,700

10,950

2,3.600

10.ODD

A 79* COLD1ORKED

TRANSVERSE

4 5TIME - HOURS X 10"3

to00K

1.0

.9

,8

.7

.6

.5

.4

.300COUl

FIGURE 9: STRESS RATIO VERSUSINITIAL STRESS FOR A TIME

OF 2000 HOURS

.2

.1

• 15X c.w. ZIRCALOY-2A HEAT TREATED Zr-2.5 wtX Nb• COLD WORKED Zr-2.5 wt* Nb

— 6 15% c.w. ZIRCALOY-2 + "STRESS RELUiF

A ANNEALED ZIRCA10Y-4(TRANSVERSE SPEC.)

0 79% c.w.. ZIRCALOY-4(LONGITUDINAL SPEC.)

i • I | 1 i 11. 2 . •'• :1 -*"' • J i :•;. 4 . " '• 5',

INITIAL STRESS - psi X 10"4

5.

4.

3.

2.5

2.

1.5

.3

2.5

.2

1.5

.1

FIGURE 10: CHECK ON STRESS EXPONENTUSING THE METHOD OFLEWTHWAITE et a|C5.B,7)

SLOPE = 0.5b

FOR n =1.5

SLOPE =0.48

I

SLOPE =_n-1 JF. CpRJECTVALUE FOR a WAS CHOSElINITIALLY

A ANNEALED ZIRCALOY-4O 79% c.w. ZIRCALOY-4

i i I i I , I , I . I . 1K 1-5 2. 2.i 3. 4. 5. 6. 7. 8, 9 .1 .0

INITIAL MAXIMUM FIBRE STRESS r ?$IX 10"!

MAXIMUM RESfDUAL STRESS - psi

, .H-.

UJ

H E A T T R E A T E D Z r « 2 5 t U Mb P R E S S U R ET U B I N G A F T E RH E A T T R E A T E D Z r - 2 . 5 » t 4 Mb P R E S S U R ET U B I N G A F T E R 1000 h.

^ L O W E S T R E C O R D E D C R E E P R A T E S F O RU C O L D W O R K E D * Z I R C A L O Y - 2 T U B I N G

EST M A T E D HI M. C R E E P R A T E F D R C O L DN O R K E D Z I R G A L O Y - 2 T U B I N G

A C O L D W O R K E D Z I R G A L O T - 2 T U B I N G .E S T I M A T E D lit). C R E E P R A T E S .

C O L D W O R K E D Z l R C H O t - 2 T U B I N G .E S T I M A T E D H I M . C R E E P R A T E SH E A T T R E A T E D Z t - 2 . 5 « t t Nb T U B I N GM I N . R E C O R D E D C R E E P R A T E .

N E A T T R E A T E D Z r - 2 . 5 lit Nb T U B I M G .M I S . C B E E P R A T E E S T I M A T E D .

H E A T T R E A T E I Z r - 2 . 5 i M N b . T R A N S -f E R S E U N I A I I A L THIS A F T E R 1000 h.C O L O W O R I E I Z f - 2 5 H t Nfc T U B I N GM I N . E t T I M A T E B CflEEF R.'IES.

FIG. 12 A SUMMARY OP TEST STRESS VERSUSCREEP RATE FOR VARIOUS PRESSURE TUBE MAT-ERIALS. ALL SPECIMENS WERE INTERNALLYPRESSURIZED, CLOSED-END TUBES EXCEPT ASNOTED IN THE LEGEND. HOOP STRAIN WASMEASURED. TEST TEMPERATURE « 300*C. THISGRAPH IAS PROVIDES BY DELVECCHIQ(B)

10"8

CREEP RATE - H">

10. cr

FIGURE 13: STRESS RELAXATION DATA FOR HOOP SPECIMENSTAKEN FROM PRESSURE TUBES PLOTTED ACCORDINGTO THE EQUATION In-£= -KEt*»»

or0 rn+lTEST TEMPERATURE = 300°C

1.0

• 15X c.w. ZIRCflLOY-2 Cg = 25,200psi

O HEAT TREATED Zr-2.5 Nb Og=27,800psi

A c.w. Zr;-2.5 Nb eg = 27ifitp0psi

A 15X'c.H: ZYRCALOY-2 +; STRESS RELIEF <T= 2A;700psi

i • i . 1 . 1 , 1 , 1 , 1 1 1 1 , 1 . 1 , 1 , hi,1.1,1 I 1 , 1 . I I 1.1,1,1,1.10* 103 10*

TIME - HOURS

10

ANNEALED ZIRCALOY-4 (LONGITUDINAL) cr0 = 24,400 psiANMEALED ZIRCALOY-4 (TRANSVERSE) <r0 = 24,300 psi

79X c.w. ZIRCALOY-4 (LONGITUDINAL) <r9 - 24,700 psi

0- QUENCHED ZiRCALOY-4 (LONGITUDINAL) <r0 = 24,200 psi

FIGURE 14STRESS RELAXATI OH DATA FORSPECIMENS TAKEN FROM SHEETMATERIALS PLOTTED ACCORDINGTO THE EQUATION l n 2 L = H

TEST TEMPERATURE = 300°C

10°

10- ' I I • I , 1 l l . l , 1 , 1 , 1 , 1 S . I , 1 ,1 ,1,1,1.1,1 l i l , i i i i i . l .U i10 102 103 10*

TIME - HOURS

50

- 40VI

30

20

1010

- (A)

i i i 1 1 1

10-7

CREEP RATE - H">10- 8

FIG, 15 GRAPHS OF STRESS v$CREEP RATE FOR TWO ZIRCONIUMALLOYS AT 300*C .

HEAT TREATED Zr-2.5 wt% NbTRANSVERSE SPECIMENS FROMPRESSURE TUBE

• AFTER 1000 H

O AFTER 3000 H• AFTER 10,000 HDATA FROM

(B)

toto

UJ

a:

40

30

20

10

LOHB ITUDIHALC O M P R E S S I 0 H

L O N G I T U D I N A LCOUfXESSIONLONGITUDIML

TENS ION

I I : I I I llA 1 i j I -—-:; I I I I t i l l I

^5% COLD WORKED

ZIRCALOY-2

PRESSURE TUBE

DATA GATHERED BY

ORENDA LTD. FOR

A . E . C . L .

FROM B E L L < I J ' 1 3 )

— - _ EXTRAPOLATION

10" 10-7

CREEP RATE - H ' '

.8

.6

.4

.2

THIS STUDY<ro = 24,200 psi

ft-QUENCHED ZIRCALOY-4 SHEET(LONGITUDINAL)

I I I I

•KREYNS 4 BURKART<T0= 10,000 psi

FIGURE 18A COMPARISON OF THESTRESS RELAXATIONBEHAVIOURS OFKREYNS'S I BURKART'SMATERIALS WITHMATERIALS FROMTHIS STUDY

TEST TEMPERATURE:(i) 300°C - THIS STUDY !( h ) 310°C - KREYNS t BURMRT(IS>

10 20 30 40 50 60 80 100 200 400TIME - HOURS

600 800 1000 2000

79% COLD WORKED ZIRCALOY-4 SHEET (LONGITUDINAL) tr0 = 24.7j

J>°

.0

.8

.6

.4

-ANNEALED ZIRCALOY-4 SHEET (LONGITUDINAL) <r0 = 24,400 psi

-79J5 COLO WORKED ZIRCALOY-4 SHEET (TRANSVERSE) <r0 = 23,600 psi

KREYNS & BURKART

ANNEALED ZIRCALOY-4 SHEET (LONGITUDINAL) <r0 = 10,950 psi

20 40TIME - HOURS

200 -500 600 800 1000

APPENDIX 1

SOMHARY OF EXPERIMENTAL RESULTS FOR SPECIMENS IH THIS REPORT

NOTE: In thisi summary, "t" means cumulative test, time in hours• and "s"; means the unrelaxed stress fraction for that time; and specimen. The accentuated lines separate groups of

^.specimens; iwhich were in similar types of holders. A holderwas classified according to the nominal stress to which it

\« loaded the specimens - initially 15, 25 or 35 kpsi. Actual**', stresses could deviate from the nominal value because specimen•• " thickness or radii could deviate from the designed values.

'!: Material .. ;

15% cold-workedZ i r c a l o y - 2 ; '•••'> ipressure tube. ;n o . 4 8 5 '.'•'•••-')

; • -:.

•1

" ' • *

• • • - ' ^ L

Orientation

transversej

; ; . " •

1 •?•'

•

•

Specimen

AAl

AA2

AA3

AA4

AA5

AA6

AA21

AA22

AA23

Initial Max.Fibre Stress

(PS 11

23,000

25,500

26,600

24,700

26,200

25,500

15,400

21,400

36,500

ts

ts

' ts

« ft

t"s

ts

t"iS :

ts

t, s

All tests were at 300CCRead across for each

5.667

5.557

5.610

.613

5 •"".620

"5 ".660

138.915

138.541

13 B.833

25.585

:"2sr.:.521

25.571

"25i'\'.554

25";" :.575 !

'is;--!.613

638.812

638.454

638.757

125.514

125.461

125.496

125.494

125.516

125.551

1849.83

1849.430

1849.710

625.441

625.377

625.328

625.417

625.428

625.471

2849.802

2849.439

2849.693

in water ofspecimen —

1500.404

1500.350

1500.324

1500.373

1500.394

1500.434

2500.377

2500.308

2500.356

2500.346

2500.366

2500.399

F»"9

4500.361

4500.;.28i ;

4500.338

4500.322

4500-342

4500.375

APPENDIX 1 COMTIHUED

Material

15% cold-workedZircaloy-2 +stress relief;pressure tubeno.485

Heat-treatedZrf-2.5 vt% Hb;pressure tubeno. 576

[28.596 cold-Lorked Zr-2.5rwt% Kb; pres-sure tube no.603

Orientation

! transverse

transverse

transverse

Specimen

AA13

AA14

AA15

AA16

AA39

AA40

AA41

AA42

AA43

AA44

AA29

AA30

initial MaxFibre^frea

25,300

28,100

19,500

37,800

28,100

27,500

36,500

38,000

17,300

19,000

25,300

30,300

All tests were at 300 °C in waiter of pH«9Read across for each specimen -

ts

ts

t8

tS

ts

t8

tS

ts

ts

!•„

ts

ts

•r25T..889

' 2 5 '•"'

.884

138.922

138.797

•"25 r.865

25.867

138.826

138.817

138.854

138.835

25.551

25.484

'''125̂: .8361

K.834!

.845

''638 l'r.712

; ; - . . . . . . ; : • •

125 ;.815:

125.815'

638.754

638.734

638.758

638-767

125: ;;-474 !

125.413

525.786

625.783

1849.796

1849,646

625.750

625.758

1849.718

1849.694

1849.731

1849.752

625.389

625.345

1508.702

1508.714

2849.796

2849.689

1508.691

1508.703

2849.697

2849.673

2849.756

2849.758

1508.333

1508.296

2508.670

2508.685

2508.673

2508.682

2508.314

2508.296

4480.661

4480.653

4480.635

4480.652

448G.267

4480.251

6480.610

6480.581

6480.629

6480.644

APPENDIX 1 CONTINUED

Material

continued28.5% cold-worked Zr-2.5wt% Nbj pres-sure tube no.603

Annealed Zir-caloy-4 sheet

79% cold-workedZircalcy-4sheet

Orientation

transverse

longitudinal

transverse

longitudinal

Specimen

AA33

AA34

AA37

L42

L43

T95

T97

1.3

Lll

L10

113

Initial Max.Fibre Siress

36,000

37,900

17,000

24,400

14,900

24,300

14,800

33,300

24,200

25,100

14,200

34_000

All tests were at 300°C in water of pH=9Read across for each specimen -•

ts

ts

ts

ts

ts

ts

ts

ts

ts

ts

ts

ts

138.413

138.474

138.471

25.527

138.573

25.507

138.611

138.496

25.406

25.403

138.461

138.385

638.326

638.380!

638.365

125.488

638.512

125.548

638.568

638.447

125 :.366

125.356

638.366

638.322

1849.304

1849.364

1849.405

625.455

1849.485

625.521

1849.522

1849.412

625.339

625.318

1849.337

1849.287

2849.275

2849.314

2849.382

1508.410

2849.455

15D8.465

2849.485

2849.388

1508.304

1508.304

2849.323

2849.278

2508.390

2508.441

2508.289

2508.285

4480.344

4480.400

4480.256

4480.246

6480.324:

6480.375

6480.255

6480.255

APPENDIX 1 CONTINUED

Material. . . . . . . •

P-quenchedZircalpy-4s h e e t : '*:;•:'• r

.: • Orientation

longitudinal

Specimen

133

Initial Max.Fibre stress

TDSII

24,200 t8

Read across for each specimen -•

25.621

125.590

625-556

1508.510

2508.485

4480.444

6480.428

- Al -

APPENDIX 2

DISCUSSION OF EXPERIMENTAL ERRORS

Distinction is made between the terms"precision" and"accuracy" in this consideration of errors. Precision is ameasure of the ability to get consistent measurements withrepetition, Accuracy gives a measure of how close to thetrue value a measured property lies. Accurate measurementscannot be.had without precision but precise measurements do notensure accuracy, in this appendix, an effort is made to estimatethe accuracy of the specimen radii and stresses determined fromthe relaxation tests,

1. Tolerances in Specimen Dimensions and Holder Radii

The cross<-seetional dimensions of all specimens werefinished to within ±,001 of the nominal thickness and width.The lengths were within the limits of +.00 in, and -.02 in. Theholder radii were made to within the limits of +.005 in. and-0.000 in. The specimen holders for longitudinal pressure tubespecimens and sheet specimens were designed using equation (1)and assuming that initially the specimens were flat (i.e.,R? = °°) • In designing the holders for transverse pressuretube specimens an initial specimen radius of 2,14 in. was assumed.This was the radius which a specimen taken from the hoop directionof a 4.07 in. I.D. pressure tube was expected to have initially.

2. Errors introduced during Radius calculation

To calculate the radius of an unrestrained specimenitwas assumed that the specimen shape corresponded to a circular .arc. A least squares curve fitting program for the G-20 com-puter was used to fit the best circular arc to the (x,y) co-ordinates obtained for the specimen. The greatest error arosefrom the degree to which the specimen shapa deviated from theassumed shape. This was evaluated in the program by calculatinga standard error between the smoothed data and the measureddata. The standard error was defined as:

• • • N - r l - •' • :"

where ̂ is the standard error (the error estimate in

- A2 -

Table A2.1) ;

(R - R) i.2 the difference between the radius ofthe specimen for a given (x,y) and the smoothedor average radius foe the whole specimen;

N is the number of (x,y)ever which thesummationwas executed,

A measure of &R - (R - R) is given by the formula;

R

where y is the ordinate for the point being considered?

k is the ordinate of the centre of curvature forthe specimen;

•iy is the error in y;

R is the average radius of the specimen.

E l5 u a t i o n (A2.2) represents an approximation to the partial dif-ferential for the general equation for a circular arc. This isfor the case when &y » &x so that ax can be neglected.

To calculate the initial stress in nearly flat specimens(such as L42 and L33, table A2.1), the initial radius wasdefinea to be 2000 in. This was considered to be the upperlimit which could be measured with the profile projector.Because of the difficulty of quickly measuring large numbers ofspecimen* whose radii were greater than about 500 in., allspecimens which fell infco this category were treated as beingflat.

If a perfectly flat specimen were to be bent to a radiusof S00 in., there would be a maximum fibre stress of 336 psideveloped in the outer fibres, Thi* represents the greatestpossible error introduced into the calculation of the initialstress by defining all specimens as flat if their radii exceeded500 in.

Table A2.1

Material

1 5 % c.r.wi.Zircalpy-2

2B.5% c.w.Zr-2.5 jwt# Nb

AnnealedSirbaloy-4

p-quencnedZircalosH4

Some Typical Error

Specimen• ' , 1 . ' ' ' ' .'• - - • '

AA2

AA6.: _

AA29

''•L42- ;-

• •• - - -

L33 :

Test Time{h)

015004500

015004500

015084480

015086480

0150R6480

Estimates for Unrestrained Radii

CalculatedRadius(in«)

2.16072-72462.8052

2.21432.71472.7824

2.07662.74832.7760

2000.11.73610.234

2000.14.24212.205

Error RemarksEstimate{in.)

±.0096 Specimens from pressure±.0019 tube±.00198

±.0026±.0022±.0020

±.0028±,0015±.0018

±1500 Initially flat by dsfini-±.0013 tion. Specimen from±.0019 rolled sheet.

±1500±.0013±.0017

- A4 -

3. Errors in Stress Calculation

The differential of equation (1) was used to estimatethe error in stress caused by variations in specimen thicknessand radii. As long as these are small, then;

(A2.3)

where ACT, AC, AR^ and AR, a r e fche errors in stress, thickness,restrained and free radix respectively. Any error in choosingE = 11.2 x 106 psi at 300°C for the zirconium alloys was neg-lected.

Table A2.2 shows some typical values for the estimatederrors in stress. The error in stress was usually in the range±4% to ±5% of the specimen maximum fibre stress at a given time.

To see how the unrelaxed stress ratio, aVcr , was affectedby this error in stress, the following apprbximatxon to thedifferential was used:

1̂ 1 O t t O

= - 2 '•",' (A2.4)

For example when errors of ACT. = ±0.04 o^ and ACT = ±0.04 at .. t o

are substituted, an accuracy in the ratio of ±0.08 — results.. .... . . - nCTb

Notice that in pig. 4, the scatter in results for eachspecimen is much less than ±0,08 at/aQ. The observation thatspecimens maintained their relative positions throughout thetest and the consistency of the data for each specimen indicatethat the bent beam test has a higher precision than accuracy.That is, the technique allows specimens to be strained repeatedlyand consistently to the same strain. If the precision ofthetechnique was poor, there would be greater scatter along thecurves for each specimen. The spread which is seen in Fig* 4and observed in the data for the other materials is due todifferences from specimen to specimen which experience showsis to be expected when trying to determine a material property.

precision is important when one wants to compare tho

- A5 -

behaviours of several materials as it allows different specimensto be tested and measured consistently, it is this qualityof the bent beam test which allows objective (i) of the intro-duction to be met.

Given the correct functional relationship between stressrelaxation and creep, it is the accuracy of the stress relaxa-tion data which restricts its usefulness in predicting creepX 3X6S

- A6 -

Some

Material

15% c.w.Zircaloy-2

28.5% c-v?.Zr-2.5 wt% Nb

AnnealedZiraaloy-4

(3-quenchedZirealoy-4

Table

Typical Error

Specimen

AA2

AA6

AA29

L42

L33

A2.2

Estimates for Stress

TestTime

(h)

015004500

015004500

014084480

015086480

015086480

CalculatedStress(psi)

2552289377166

25504110609556

282038432

' 7525

24354100287915

241431235210372

ErrorEstimate(psi)

±1278±408±347

±1073±542±485

±1114±380±362

±902±365±297

±901±448±384

r —

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Chalk River, Ontario, Canada

Price • $1.50 per copy

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