Steady-state creep of zircaloy-4 fuel cladding from 940 to 1873 K

Journal of Nuclear Materials 82 (1979) 286-297 0 North-Holland Publishing Company

STEADY-STATE CREEP OF ZIRCALOY-4 FUEL CLADDING FROM 940 TO 1873 K H.E. ROSINGER, P.C. BERA Atomic Energy of Canada Research Company, WhiteshellNuclear Research Establishment, Pinawa,Manitoba, ROE ILO, Canada

W.R. CLENDENING Atomic Energy of CanadaEngineering Company, Shertian Park, Ontario, Canada Received 9 November 1978; in revised form 23 January 1979

Steady-state creep rates of as-received zircaloy4 fuel cladding have been determined from 940 to 1073 K in the a-Zr range, from 1140 to 1190 K in the mixed (a + p) phase region and from 1273 to 1873 K in the @Zr phase region. Strain rates of between lo-6 and 10-2/s were determined under constant uniaxial load conditions. Assuming that qeep rates can be described by a power law-Arrhenius equation, the creep rate for a-phase zircaloy-4 is given by: kss = 2000 c5*32 exp(-284 6OO/k7’)s-1; for the p-phase zircaloy4 by: ess = 8.1 03*79 exp(-142 300/k7’) s-1 ; and for the mixed (a + p) phase of zircaloy4 (for creep rates <3 X 10-z s-t) by: kss = 6.8 x 10-s ore8 exp(-56 6OO/kn s-1. For the both the a and p phases, the activation energies for creep are in agreement with those of self-diffusion. For the mixed (a + 0) phase region, the low creep rate range is controlled by grain boundary sliding at the a/((~ + p) phase boundary.

development of an analytical model which will properly describe cladding deformation and rupture behaviour. Detailed knowledge of the dependence of creep rates on stress and temperature is basic to an understanding of creep. The technique that has been used most often for obtaining a quantitative description for creep behaviour is to observe the creep strain rates for specimens acted upon by a nearly constant stress while they are at constant temperature and then to identify an empirical correlation between their strain rate, applied stress and absolute temperature. The creep behaviour of as-received zircaloy-4 fuel cladding has been studied in the temperature range 940 to 1873 K. Uniaxial creep testing was performed in an inert atmosphere in order to obtain a base-line of zircaloy4 deformation data which are unaltered by strengthening mechanisms such as those due to oxygen. The generated data * [4] and all the other

1. Introduction The creep rates of zircaloy4 are one of the basic property parameters required as input to sophisticated computer codes dealing with transient fuel behaviour during hypothetical Loss-Of-Coolant Accident (LOCA) conditions. It is essential that the expansion of fuel cladding be defined quantitatively for temperature histories typical of those that might be postulated to occur during a LOCA. This requires a knowledge of the deformation properties of the fuel cladding and a complete understanding of the stressstrain-temperature-time relationship which governs the behaviour of the fuel cladding in all possible environments. A number of experimental studies [l-3] to evaluate the influence of internal gas pressure and heating rate on the rupture temperature and ductility of zircaloy cladding have been performed. Although they have enabled the geometry of tube deformation to be described, they have not provided the basic materials data necessary for the

* These data are tabulated in ref. [4]. 286

HE. Rosingeret al. /Steady-statecreep of zircaloy-4fuel chdding

published data * on zircaloy-4 have been analyzed and mathematical equations for the steady-state creep in the cu-Zrrange, duplex (a! + 0) phase and /I-Zr phase [5,6] are presented. Because these equations describe the similar behaviour observed in tests done using various different test rigs, they are not biased by being associated with only one experimental procedure and are consequently believed to be good equations to use in safety analyses for any type of zircaloy4 nuclear fuel cladding. A comparison with zircaloy-2 is also presented. The creep of zircaloy4 was studied independently at two laboratories; by Clendening * at Westinghouse Canada Limited [7,8] and by Rosinger and Bera at Atomic Energy of Canada Limited. The data have been combined since the same material was studied and the same experimental approach was employed.

2. Experimental procedure The isothermal creep tests were performed in an argon environment using axially-oriented unirradiated Pickering-type zircaloy4 fuel cladding with nominal values for mean outside diameter and wall thickness of 15.24 and 0.44 mm, respectively. The polycrystalline fuel cladding was tested in the as-received condition, i.e., 70% area reduction at ambient temperature followed by a four hour stress relief at approximately 795 K followed by a furnace cool. The grain size was approximately 5 pm with a slight elongation in the circumferential direction. Creep tests were conducted under isothermal conditions at temperatures from 940 to 1873 K at creep rates of from 10m2 to 10-6/s.

281

levels of from 0.9 to 100 MPa under a variety of test environments, certain special features are incorporated in the design of the test apparatus. The specimen is heated directly (Joule or Ohmic heating) and the load cell and test chamber are electrically insulated from the test specimen by a ceramic coupling (sintered lava) between the load cell and specimen grip. Similarly, a nylon coupling is used to electrically insulate the test apparatus from the MTS electro-hydraulic testing machine. The 250 kg load cell, located on the inside of the chamber to avoid any friction drag during the test, is isolated from the specimen’s heat by a water cooled baffle plate. It is possible to test the specimens in vacuum, inert gas and/or stream. For this work, creep tests were conducted in an inert argon gas atmosphere. The test chamber is mounted-on an MTS electrohydraulic testing machine; this is used to apply the constant uniaxial load to the specimen and to measure the strain of the specimen while at constant load and temperature. Specifically, the strain is determined by measuring the displacement of the MTS ram by mean of a linear variable differential transformer (LVDT). The displacement of the ram is recorded on an X-Y recorder as a function of time. An 89 mm long section of zircaloy-4 fuel cladding is welded in an argon atmosphere with two endfittings, giving an overall length of 140 mm, as shown in fig. 2. Prior to installing the specimen in the apparatus, thermocouples are tack-welded at, and 12.5 mm from, the center of the outer surface of the specimen’s gauge length. The specimen is also marked with heat resistant marks using a carbon-base grease pencil along the entire gauge length. The specimen is then fitted into the test apparatus by threading the bottom and pinning the top.

2.1. Test apparatus 2.2. Testing procedure A schematic of the test apparatus is shown in fg 1. In overall appearance, it consists of a cylindrical chamber 20 cm in diameter and 50 cm high. Since the creep tests are to be performed at isothermal temperatures ranging from 873 to 1973 K and at load

* W.R. Qendening has since joined Atomic Energy of Canada Engineering Company.

** 1 Torr = 133.332 Pa.

Once the specimen is installed in the test apparatus, special procedures are adopted to ensure that the test environment is as free of contamination as possible. The vessel is evacuated to a vacuum of 5 X 10m3Torr * and backfilled with ultra high-purity argon flowing through a titanium gettering system to further remove any contamination. This procedure is repeated at least five times before a steady flow of inert gas is introduced prior to starting the test. An ac

H.E. Rosinger et al. /Steady-state creep ofzirca1oy-Qfuel ciadding

288

I

MTS CROSS HEAD

TEST CHAMBER

I

LOAD CELL

OUTER COOLING

BAFFLE PLATE WITH COOLING' COIL

ERT GAS INLET

THE~~OCO~LFS IN SERIES Zr-FUEL CLADDING SPECIMEN OPTICAL PYROKEZTERAND -SAMPLE ACCESS

INFRARED PYROMETER AND SAMPLE ACCESS

.b. TO T/C MONITORING -INSTRUMENT (PIRAN TYPE)

GAS ODTLET

VACWM IMP

ELECTRO-EDRAULI OF WS-SYSTEM AN TRANSMISSION To X-Y RECORDER

; 1

MTSFRAME

1 LOAD

I--,

Fig. 1 Schematicof high temperaturecreep apparatus.

electrical power supply is used to heat the specimens at 50 to 100 K/s to their test temperature. The temperature is measured by the three thermocouples, by an optical pyrometer and, in some cases, by an infrared pyrometer, and is controlled at k3 K by a manual adjustment of the power supply. The test temperature is achieved in about lo-20 s; a further lo-20 s delay before foading ensures that the axial temperature distribution has stabilized. Upon stabili-

zation of the temperature, the sample is loaded to a predetermined load level in exactly one second for the majority of tests. The constant load is maintained by utilizing the load control mode of the MTS system, and a continuous recording of the strain versus time is made on an X-Y recorder. The creep test is terminated after either 10 min or 0.15 strain. At the end of the creep test at temperature, the load and heat are removed and the specimen allowed to

H.E. Rosinger et al, / study-state creep of zimaloy4 fuel c~ddin~

289

for each specimen tested, rather than yielding only a single post-test measurement, as occurred in earlier testing done by other experimenters [2,3]. A polynominal equation was fit to the strain (e) versus time data. Since the instantaneous strain rate, P = de/dt, the polynomial equation was numerically differentiated to get the strain rate. Typical curves for true strain versus time are shown in fig. 3 for tests conducted at 1573 K for stresses ranging from 1.73 to 4.5 MPa. Increasing the stress increases the strain rate. Typical curves for true strain versus time are shown in fig. 4 for tests conducted at a stress of approximately 1.5 MPa for temperatures ranging from 1473 to 1873 K. Increasing the temperature increases the strain rate. The creep curves obtained at T > 1273 K alway exhibited inverted primary creep in which the work

Fig. 2. Dimensions of fuel cladding test specimen.

cool to ambient tem~rature. The total strain of the specimen is then measured and compared to the strain-time data. 3. Results The test facility, described above, allows a continuous recording of strain versus time to be made 0. IO

0.09

0.08

0.07

0.06 5 2 G 0.05 % E 0.04

IS73 K 0.00

L

0

5

IO

IS

20 Ti M

Fig. 3. Typical true strain versus

25

30

35

40

45

E, SECONDS

time curvesfor tests conducted at 1573 K for stresses ranging from 1.73 to 4.5 MPa.

290

HA’. liositger et al. / Steady-statecreep of zhuluy-4 jkel cladding

TIME. SECONDS

Fig, 4. Typical true strain YWSUS time curves for tests conducted at temperatures from 1473 to 1873 K.

softening effects are greater than those of work hardening.Hence,in the p-21phase the creep strain rates increasedwith time rather than decreasedas occurs for normal creep. Similarresults have been observedby ~enden~g [7,8] and exited in detail by Ho&and Si% 191.No inverted primary creep was found in the cu-Zrphase. Since a constant axialload acted on the test specimens,a true steady-statedeformation never occurred; the axialstressacting on 8 specimenwas never a constant but increasedwith strain. Nevertheless,the creep curvesindicate that strainingwas alwaysoccurringat a very nearly constant rate at 0.05 strain,Hence, the steady-statestrain rate, &, is defmed to be the strain rate at 0.05 strain and the stressis the s~~~en’s true axial stressat the same strain ievel.

4. Jliscussion The ~~~~~~~0~0~~~ equation to describethe creep of any materialis usury of the form:

where & = steady-statestrain rate or creep rata (s-I), e = strain, T= absolute temperature (K), u = stress (MPa),ST = representsthe structure of the material under consideration. Crussard[IO] and Darn [ 131Tamong others, have found that t&es~ad~s~te or secondarycreep of ditute metals or dilute s&d neutron alloys can usu&y be describedby a power maw-~rhenius equation of the form:

H.E. Rosinger et al. f Steady-state creep of zircaloy-4be1 chiding

de . -.-Zf

dt

”

= Afo, r, ST) u(e)@* z ST)

x exp (- Q(o, T, ST)~~~ , (2) where A, the stress exponent n, and the activation energy for the process Q, can all be functions of stress, temperature and structure. k, the gas constant = 8.3 16 J/mol * K. In agreement with Dorn [ 111, one can assume that the activation energy for a particular structure is a constant. The activation energy can be a function of the applied stress but this is usually ignored. Pahutova and Cadek [ 121 have shown that, for creep in fy-Zr, the activation energy decreases with stress for tests performed at 673 to 823 K. Similar results were reported by MacEwen and Fleck [ 131. For creep tests at 823 to 1023 K, Pahutova and Cadek found the activation energy to be a constant, independent of stress, of (27 1.7 + 5.9) kJ/mol. For temperatures in excess of 873 K, it is therefore assumed that the activation energy is independent of stress. The activation energy is, however, a function of the structure. It will be different for the o-phase, duplex phase region and P-phase. The ma~itude of the activation energy for the creep beha~our of a metal or dilute solid solution alloy is frequently found to be in very close agreement to the activation energy for self-diffusion or for the diffusion of the primary alloying element. There is contradictory information in the literature about the value of the stress exponent, n. Dorn [ 1 l] found that, for pure metals or dilute solid solution alloys, the value of n is almost always greater than four and less than seven, while most metals that creep by a diffusion-controlled process exhibit an n = 5 stress-creep rate relationship. Ardell and Sherby [ 141 found that the value of n for cr-Zr decreased from 7.5 to 4.7 with increasing stress. Clendenlng [73 found that, for the creep in zircaloy-4, n was essentially independent of both applied stress and temperature but was dependent on the structure. The value of the constant, A, in eq. (2) is found, in general, to be dependent on the structure and independent of the stress and temperature. Eq. (2) can thus change to: de o ;ii = fss = Au” exp(-Q/kT)

,

where A, n and Q are st~cture dependent.

(3)

291

In the following, all the published creep data for zircaloy-4 combined with that of this work are analyzed to determine the values of A, n and Q for the cr-Zr phase, duplex phase region and &Zr phase. Eq. (3) in the form: In ess = In A + n In (I - Q/RT

(4)

was fit to the experimental data using a multiple linear regression analysis for a dependent variable (ln &) and a set of independent variables (ln u and 7’) to obtain numerical values of In A, n and Q. If the original data were given in terms of the hoop stress, they were changed to the uniaxial stress state by multiplying by m, i.e., isotropy was assumed. 4.1. &Peeprate equation for the ar-Zrphase ie, T Q 1095 K

The creep rate test data for zircaloy-4 in this temperature range are given by this work, Clendening [7],Chungetal. [lS],BusbyandMarsh [16],and Busby and White 1171. The creep rate for the cu-Zrphase (940 Q T Q 1095 K) of zircaloy-4 only is given by: i,, = 2000 u(s*32’ *-14) exp(-284 600~~~) ,

(5)

with a correlation coefficient of 0.961. The standard deviation of this equation’s fit to the natural logarithm of all available zircaloy-4 creep data is 1.05. Hence, there is an average deviation of approximately 30% between an observed creep rate and that predicted by eq. (5). This fit is considered to be extremely good considering that the correlation was done using data obtained from various different laboratories, which would be expected to be associated with different expe~ent~ errors due to tem~rature and strain measurement accuracy as well as, possibly, different amounts of oxygen contamination. If Luton and Jonas’ [ 181 data for the creep of Zr0.7 wt% Sn (similar in tin composition to zircaloy-4)’ are also used for the regression analysis, the stress exponent in eq. (5) increases to 5.82 and the correlation reduces to 0.948. For comparison purposes, the activation energies and stress exponents for the creep of the a-Zr phase of zircaloy4, zircaloy-2 and o-zirconium are documented in table 1, It can be seen that the stress

H.E. Rosinger et al. /Steady-state creep of zircaIoy-4fuel cladding

292

Table 1 Vafues of activation energy (Q) and stress exponent (n) for the creep of the o-21 phase (T < 1095 Kf Material

Activation energy (kJ/moI)

Stress exponent n

zr4 Zr4 22-4 Zr4 Zr4 Zr-4 Zr4 Zr-0.7 wt% Sn zr-2 Zr-2 Zr-2 Zr-2 Zr-2 Zr-2 cu-Zr o-Zr ol-Zr q-Zr o-Zr

284.6 288.9 305.6 320.3 288.5 290.0 360 280 a) 287 244.9 287 286.8 295 +5 300 418.7 266 aJ 271.7 + 5.9 234.5 328.5 to 213.5 cJ

5.32 * 0.14 5.3 6 5.8 5.3 5.3 5.27

o-Z1 o-Zr ar-Zr

281.8 217.0 96.6

5.0 5.0 f: 0.2 4.5 to 5.5 b) 5 i 0.3 5 5.2

6 to 7 b, 7.5 to 4.7 c)

Temperature range WI 940-1073 873-1023 923-1073 940-1040

1033-1075 988 873-1073 588- 773 921-1067 793- 893 973-1073 973-1073 973-1073 998 823-1023 793- 893 933-1118

Selfdiffusion of Zt Selfdiffusion of Zr Gra~~oundary diffusion

Reference

This work Clendening [ 71 Clendening [ 71 Clendening [ 71 Holt and Sills [ 91 Sills and Holt [ 191 Busby and Marsh [ 161 Luton and Jonas [18] Hindle [ZO] Holmes [ 211 Rose and Hindle f 221 Bernstein [ 231 Clay and Redding [ 24) Clay and Redding [ 251 referenced by T. Healey et al. [ 261 Gilbert et al. [27] Luton and Jonas [ 181 Pahutova and Cadek [ 121 Bernstein [ 231 Ardeil and Sherby [ 141 Dot&as [ 281 Neik and Agarwala [ 291 Ritchie and Atrens [ 301

a) Values based on yield condition. bJ Stress exponent vahtes in the high-stress region. cJ Decreasing with increasing stress.

exponent of 5.3 and the activation energy of 284.6 kJ/mol is in excellent agreement with the values reported for the creep of zircaloy-4 and zircaloy-2. In addition, the activation energy is in agreement with that found for the self-diffu~on of zirconium in the cu-Zrphase. This agreement suggests that creep in this temperature range is controlled by a mechanism in which diffusion plays an important role, possibly either gliding or climbing of dislocations. The stress exponent value of 5.3 suggests that the deformation for the cu-Zrphase of zircaloy4 is likely to be controlled by dislocation climb. Shown in fig. 5 are the steady-state creep rates of zircaloy-4 and zircaloy-2 at 973 and 1073 K. It can be seen that there is good agreement between the zirca.loy-4 and zircaloy-2 data of various authors. In general, the trend is toward better agreement between the zircaloy-4 and zircaloy-2 data as the temperature

is increased. This is no doubt due to the different fabrication routes employed for the alloys. As the temperature is increased, any effects of the fabrication route are removed and the materials exhibit identical creep behaviour. The solid line drawn on the figure is the least square fit given by eq. (5). 4.2. Creep rate equationfor the @Zrphase, i.e., T 2 I245 K The creep rate data for zircaloy-4 in this temperature range are given in this work, and by Clendening [7], KizkalIa et al. [32] and Busby and White [17]. The steady-state creep rate equation for the &Zr phase of zircaloy-4 is given by: i,, = 8.1 u(3*7Q* 0*02)expf-142 300/W) , with a correlation c~f~cient

(6)

of 0.975. The standard

293

973

K

DATA

,o_j, , &‘r:Jg$$tj$ IO

IS

20

30

STRESS, Fig. 5. S~ady~tate

40

50

70

MPa

creep rate versus applied stress for tests conducted at 973 and 1073 K in the a-Zr phase range.

deviation of this equation’s fit to the natural logarithm of the experimental data is 1.02. There is thus an average deviation of approximately 28% between an observed creep rate and that predicted by eq. (6). Again, the fit is considered to be extremely good considering that the correlation was done using data from various laboratories. Table 2 lists the activation energies and stress exponents reported for the creep of ~-~co~~. The agreement with eq. (6) is excellent. Again, the activation energy calculated for the steady-state creep is in excellent agreement with the self-diffusion of zirco-

nium in the &Zr phase. The value of the stress exponent of 3.8 is somewhat lower than the reported by Dorn [ 1 l] for the climb controlled creep of bee metals (4 to 7). A contribution from a viscous glide creep mechanism, having a stress exponent of 3, would give a stress exponent lower than four. It would appear that a modified gIide/climb creep mechanism is rate contro~g. The steady-state creep rates of zircaloy-4 and zircaloy;2 are shown in fig. 6. Again, there is excellent agreement. Indeed, there is excellent agreement between the two zircaloy alloys at all test tempera-

HE. Rosinger et al. / Steady-state creep ofzitcaloy-l fiber cladding

294

Table 2 Values of activation energy (Q) and stress exponent (n) for the creep of the p-Zr phase (T > 1245 Kf Material

Activation energy (kJ/mol)

Stress exponent n

Temperature range (K)

Reference

Zr-4

142.3

3.8

1273-1873

This work

Zr-4

151.6

3.7

1273-1473

Clendening ]7J

Zr-l

143

3.6

1273-1473

Rizkalla et al. [32]

Zr-4

130

3.6

1272-1673

Sills and Holt [19]

Zr-4

129.8

4.0

1273-1673

Clendening 171

Zr-4

123.5

3.9

1290-1710

Clendening 171

Zr-2

174

3.7

1300-1500

Burton et al. [34]

Zr-2

191.6

3.4

1248

Pardoe, refenced by Healey et al. [35] Clay and Redding 1241

Zr-2

238

4.2

1273-1413

Rose and Hindle [22]

Zr-2

150

4.4

1273-1473

Clay and Stride [ 36j

ZI-2

150

4.0

1273-1773

Clay and Stride f 371

Iodide-zr

146.5 * 4

3.25

1323-1653

Ivanov and Yamushkewich [38]

tures (up to 1873 K) in the &Zr temperature range. The solid lines in the figure are the least square fit as given by eq. (6). 4.3. Creep rate equation for the mixed fol + (3)phase range, i.e., 1095 < T < 1245 K The creep data available in the mixed (ol + /3)phase range are given in this work, and by Clendening [7], Chung et al. [ 151 and Busby and White [ 171 on

zircaloy-4 and by Luton and Jonas [ 181 on Zr-0.7 wt% Sn. The data for the mixed (o + 0) phase field are shown in fig. 7. It is obvious that contrary to the good agreement in creep rates exhibited in the cu.Zr (fig. 5) and &Zr (fig. 6) the creep rates in the mixed ((w+ /3)phase range do not show good agreement. The lack of agreement could be due to a difference in the starting structure, i.e., difference in the (Y-and P-phase grain sizes, difference in the morphology and distribution of phases, second-phase particle, dislocation structure, substructure plus other variables. Because of the lack of agreement, the analysis of the data to obtain a unique creep rate in this (cu+ p) phase temperature interval is consequently ambiguous. If all the creep data of this work (at 1173 K) and that of Clendening at 1140 and 1190 K are employed in the multiple linear regression analysis, the creep rate equation becomes: P,, = 84 uf2*2s ’ 0*06)exp(-155

100~~~) 9

(-0

with a correlation coefficient of 0.948 and an average deviation of approximately 27% between an observed creep rate and that predicted by the equation. For creep rates less than 3 X 10m3s-l, the steadystate creep rate for the mixed phase region is given by: ess = 6.8 X 10V3a’*’ exp(-56 600/H) .

03)

This equation suggests that grain boundary sliding controls the observed creep at rates <3 X 10s3 s-* since such diffusion~ontrolled behaviour is usually associated with an n value of 2. When the creep rate exceeds about 3 X 10m3s-r, the stress dependence of the creep rate for the mixed phase increases significantly. This suggests that another mechanism controls the higher creep rates. Garde et al. [S] have studied the uniaxial tensile stress-strain behaviour of zircaloy-4 at temperatures 973 to 1673 I(. They observed a superplastic peak near 1123 K. At 1123 to 1173 K, they found that at low strain rates (104 s-r) dislocation creep was dom~~t. Rosinger [39] has also shown that zircaIoy4 conta~~g up to 0.4 wt% oxgyen will be superlastic at 1173 K. BoiSeket al. f33] have shown that gram boundary sliding becomes

H.E. Rosinger et al. / Steudy-stute creep of zircdoy-4 fuel ckzkihg

ZR-4:

+THIS

WORK

o~~E~~~~tK”G ZR-0

7 Sn: t

RIZKALLA

1 2

+

C7 I et 01 1321

ZR-41

B

295

ZR-0.7 ZR-2:

I 3

/

THIS WORK CT3 AT 1230 8 CLENOENINO 0 BUSBY If WHITE AT 125! SnlV RIZKACLA et 01 t323 ACLAY a STRIDE C36,373

I

II11Illl

45

STRESS,

678

IO

I

MPa

Fig. 6. Steady-state creep rate versus applied stress for tests conducted in the @-Zrphase range at 1273 and 1473 K. Note the excellent agreement betweenzircaloy4 and zircaloy-2.

the dominant mechanism at the CX/(CY + 0) phase boundary, Because of the dramatic change in stress exponent and the scarcity of data, it is not possible, unambiguously, to identify the mechanism operating in the

mixed (a + 8) phase. Additonal experimental effort is required to determine the exact nature of the creep equations with their limits of applicability and to identify the mechanisms controlling the creep in the mixed (ar + p) phase.

H.E. Rosinger et al. / Steady-state creep of zircaloy-4fuel cladding

296

P-

and for the P-phase zircaioy-4 by: P,, = 8.1 u3*79exp(-142 3OO/k~ . For both the cr-Zr and @-Zrphases, the activation energies for creep are in agreement with those for the self-diffusion of zirconium and dislocation climb and climb/glide as the rate controlling mechanisms, respectively. The excellent agreement between the creep rates of zircaloy-4 and zircaloy-2 has also been shown. For the mixed (a! + 0) phase range, it has been shown that the equation for creep rates lower than 3 X 10-s s-l is given by: r& = 6.8 X 10m3ur*’ exp(-56 6~~k~

,

The low creep rate region has been identified as being due to gram-boundary sliding. Because of a scarcity of data for strain rates >3 X 10M3,it is not possible to determine the rate equation unambiguously nor to identify the mechanisms for the creep in the mixed (a + fi) phase.

I !5

I 7

I IO

I

I

I

I

I!5

20

30

40

STRESS,

l-d 60

MPG

Fig. 7. Steady-state creep rate versus applied stress for tests conducted in the mixed (a! + p) phase region.

5. Conclusions In this work, the steady-state creep rates of as-received zircaloy-4 fuel cladding have been determined from 940 to 1073 K in the ar-Zr range, from 1140 to 1190 K in the mixed (or + @)phase region and from 1273 to 1973 K in the &Zr phase region. The strain rates between 10S6 and 10m2s-r were determined under uniaxial load conditions. An analysis of all available zircaloy-4 creep data was carried out to determine the equations for steady-state creep which would not be biased by being associated with only one experimental procedure. Assuming that the creep rates can be described by a power law-Arrhenius equation, the creep rate for a-phase zircaloy4 is given by:

f,, = 2000 r.P2 exp(-284 6~/~~

,

The work performed by W.R. Cfendening at Westinghouse Canada Ltd was carried out under a common development contract with Atomic Energy of Canada Ltd and Ontario Hydro. The authors wish to thank these organisations for permission to publish.

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