The temperature dependence of the irradiation induced creep of graphite

Co&on

1966,

Vol. 4, pp. 67-72.

Pergamon

Press Ltd.

THE TEMPERATURE IRRADIATION

Printed in Great Britain

DEPENDENCE

INDUCED G. U JENKINS*

OF THE

CREEP OF GRAPHITE

and D. R. STEPHENS

(Received 15 Septemb

1965)

Abstract-An experiment is described in which the irradiation induced creep extensions of helical springs under constant load are recorded continuously at various controlled temperatures between 70 and 350°C. The load can be adjusted without removing the rig. Some resuhs are reported for specimens of graphitiaed E Y 9 graphite. Many well-known features of . creep in graphite have been confirmed and among new data the following are of interest: (1) The continuous creep constant increases by a factor of ~1.6

between 100 and 3OO’C.

(2) Reactor transients causing temperature changes result in strain increments corresponding substantial internal stresses. These can result in fracture under constant load at low creep strains.

to

1. INTRODUCTION MUCH

experimental data has accumulated since the early work of LOSTY et al.(‘) from many sources, but notably from Kmm~~y(~) and Pms and SIMMONS,(~*~)to show that graphite exhibits greatly enhanced creep when it is subjected to neutron irradiition. A corresponding number of theories have been put forward to explain this behaviour (cf. WILLIAMSON and JENKINS(~)). In order to distinguish between the rival classes of theories it was considered important to measure the effect of changes in temperature and load on a given specimen without disturbing it by removal from the irradiation facility. In the normal test reactor the irradiation history of a stressed specimen is complicated by the many trips, shut-downs and other transients which normally occur. It is therefore desirable that a continuous record of the extension be made. These requirements have been satisfied in the experiment described here. 2. RIG DETAILS The general design of the rig is shown in Fig. 1, and its position in the HEMLD Reactor, Aldermaston, is indicated in Fig. 2. The reactor is lightwater moderated, enriched-uranium fuelled and is *Faculty of Applied Science, Swansea, U.K.

University

tAtomic Weapons maston, U.K.

Establishment,

Research

College

of

FIG. 1. Details of the creep rig showing the loading and transducer stage at platform level (to the left) and the specimen stage at core level (to the right).

Alder-

67

G. M. JENKINS and D. R. STEPHEN

SPRWGuMu,TESTRlG

Frc, 2. Position of the creep rig in the core of the HERALD reactor, Aldermaston.

running currently at 5 MW. The rig consists essentially of two concentric aluminium tubes about 26 ft long leading down to a fuel eIement position in the centre of the core. The test spring is located inside the lower end of the inner tube to which it is attached. A wire leads from the upper end of the specimen up the inner tube to the top of the reactor where it runs over a low-friction pulley and is brought into tension by high density tungsten weights prescribed by the limited volume available. The wire is matched with respect to length and tension by two others leading from the bottom of the inner tube to the top of the reactor.

Despite the care taken to match the specimen and control wire systems, there is a small discrepancy of about 0*005 in. on changing the temperature through 100’. However, this is a constant and instantaneous error for each temperature change and is therefore easily eliminated. The differential movement between the wires gives the extension of the spring. This is measured by a soft-iron core fixed in series with the specimen lead wire which is threaded through the centre of an inductance transducer suspended from the two control wires. The output of the transducer is recorded continuously in the control room of the reactor. Extensions of 04005 in. can be detected in this manner as compared with a typical initial elastic extension of O-50 in. The friction in the system is such that a movement due to the addition of only 0.2 g suspended on a normal load of 200 g is just detectable. The temperature is measured by thermocouples placed as shown in Fig. 1 and ia recorded continuously alongside the extension of the spring and details of the reactor operation. The~~ouple junction A is set in the gas stream in the centre of the spring while thermocouple junction B is set against the inner wall of the lower end piece of the spring. The actual temperature of the spring was deduced from A and B readings with reference to a preliiary experiment. The tempera~re is varied by blowing down air or nitrogen at different inlet pressures in between the aluminium tubes and up through the inner one. The gas flow was designed so as not to disturb the specimen by turbulence or to affect the Ioading. With the reactor running at 5 MW, the temperature of the test spring (which is subjected to gamma heating) can be brought down to 70°C. The temperature can be allowed to rise above 350°C but the highest temperature used in any experiment referred to herein is 300°C. The temperature is controlled to about 22°C using a sensitive automatic valve and flow-meter. The neutron beam proceeding up the tubes from the reactor core is blocked by constrictions at the top and also by heavy polythene shielding above the water line. The neutron flux was determined by the Nickel (58) (n,p) Cobalt (58) activation, suitably corrected for flux spectrum perturbations. Ail neutron exposures quoted will therefore correspond to neutronswith energy in excess of O*lBMeV.

TEMPERATURE

DEPENDENCE

3. TEST

OF THE IRRADIATION

SPECIMENS

Graphite specimens were machined out of 1 in. dia. rods of fine grain graphite (E Y 9 ex Morgan Crucibles). Coarse thread of -4 mm pitch was cut to a depth of N 2 mm’ into the solid rod machined to 20 mm dia. which was held in a tubular jig in a chuck while the centre core was drilled out. The result is a square cross-sectional helical spring with plane ends designed to facilitate connection to the rig, as shown in Fig. 3. The springs were heattreated in an argon-filled furnace to 2800°C to ensure complete graphitization.

FIG. 3. A drawing of a typical test-specimen-square cross-sectioned helical spring with plane ends designed to facilitate connection to the test rig.

INDUCED

CREEP OF GRAPHITE

69

(spring 2) is shown in Fig. 4 as an example. The detailed history is much more complicated because of temperature changes due to trips, shut-downs, or pre-arranged gas flow changes and also as a result of the movement of neighbouring rigs and the control rods. These disturbances were reflected in the recorder traces from the transducer, making analysis complicated. These transients are inevitable in any test reactor and the details are useful. For instance, it was found that rapid thermal cycles produced significant increments in extension. This would not have been detected if continuous recordings were not made. Spring (1) was subjected to a constant load of 200 g while the temperature was varied. The creep rate results were similar to those obtained for Spring (2) over the initial period and under the same loading. Fracture took place after a dose of 2-l x 10” nvt with a total spring extension of 1.03 in., soon after a reactor trip. Spring (3) was subjected to fewer transients and remained intact under a constant load of 200 g up to an extension of 1.3 in. The creep rate results corresponded with those for springs (1) and (2). Since the main object of the exercise was the measurement of the temperature dependence of continuous creep, readings of this creep rate were not made until the region of transient creep was passed (at doses N 1 x 1020 nvt). Creep rate data was only used when the temperature and other reactor conditions were constant over a period of at least 24 hr.

The specimens are set in the rig free of stress and their connections locked while the rig is lowered into position. The connections are freed and the load applied only when the rig is set in position and the transducer is recording to check loading transients. 4. RESULTS

Three graphite specimens have been tested consecutively in the same rig. The test programmes were designed not only to determine the creep characteristics of the graphite specimens but also to check the performance of the rig. The tests on each specimen thus differed but, even so, the overall behaviour was very similar. This is indicative of the general reliability of the experimental technique. The overall strain history of one specimen

u100* 0

I

r&m”dose

I

I 2 I

10’0 t

I

I

NwLt

s

I 6

Ieke1

FIG. 4. A typical overall strain history of a graphite test specimen. (Specimen 2).

G. M. JENKINS and D. R. STEPHEN

70

The degree of oxidation was measured by determining the density of the spring material before and after irradiation. The density decreased by Iess than 0.1% for doses of 25 x 10zo nvt. Checks were made to see if even this small amount of oxidation could effect the creep by blowing down alternately streams of air and nitrogen (99.99% purity) at the highest temperature used (300°C). No sign&ant change in the creep rate was observed. It was therefore concluded that the effect of oxidation could be neglected. From the detailed strain histories the following was observed: (1) The transient creep strain is equal to about 0.31 x the initial elastic strain (a,) and its contribution is negligible beyond 6 x 1Org nvt. (2) The transient creep is wholly recoverable on irradiating free of stress (part is recoverable with time without irradiation). So also is the large permanent set produced by the increase in modulua due to the accumulated irradiation damage. (3) The steady-state creep rate at 300°C is 0.26 f O+OS & per 10zQ nvt (fast flux). This form of presentation eliiates the di%culties due to the complex geometry of samples. (4) The effect of temperature on the creep constant at doses greater than 10zo nvt is shown in Fig. 5. It is clear that the creep constant increases slightly with the temperature (by a factor 1.6 between 100 and 300°C).

TI

%

x O-5 -

s 0

04

X

x

i//

I

0

.a

0

0

X

_ 0.3

% -

3 u t w

I

x

o-2

0

Spriq

(1)

x

*iq

(2)

t

L 0’ka

% tem$emtun,

600 *K

on the steady state (derived from two experiments, specimens 1 and 2).

FIG. 5. The effect of temperature creep constant

I

I 500

400 Xrrodiotion

(5) Most of the. steady-state recoverable.

creep strain is not

(6) Temperature excursions result in increments in the extension which vary approximately linearly with the temperature range of the excursion. (7) Fracture occurs without any noticeable acceleration in the creep. It is associated, however, with the non-equilibrium conditions immediately following a reactor transient. 5. DISCUSSION The amount of transient creep is about the same as that reported by KENNEDY(~’ (-0.35 ~0). It differs from that observed by PERKSand SI~UMONS(~) ( - 1-O s,,). The discrepancy may be due to the fact that both in this experiment and in KENNEDY’Sthe strain measurements were made directly on specimens in the reactor. The other measurements involved the removal of specimens from the conditions with some delay. It is conceivable that this procedure could introduce a further strain increment since an extra thermal cycle is involved and the reiease curve of a specimen irradiated under stress may be singular and unrepeatable. The effect of temperature on the steady-state creep differs from that observed by KEXNEDY(~) who reports a factor of three increase on iowering the irradiation temperature from 350 to 150°C. In defence of the present experiment it should be noted that our observations were made on the same specimen and under the same irradiation conditions. The other measurements were made using different specimens and involved large corrections due to the presence of neutron flux gradients. The present results are in agreement with BLAKELOCK@) who has observed an increase by a at 200 and factor of -2 between experiments 400°C using a restrained growth technique (cf. LOSTY et al.(‘) Again, BARNETT,~‘)using the same technique, has measured the steady-state creep rate at 40°C and finds it to be 0 + 1.8 x lad as opposed to 0.10 x 10V6 per 1,000 MWD per lb/in2 as measured by BLAKELOCK at 200°C. The results are consistent with the following picture of irradiation creep in graphite. The transient creep, since it is wholly and easily recoverable, is probably caused by the further movement of basal plane dislocations which have already

TEMPERATURE

DEPENDENCE

OF THE IRRADIATION

contributed to the elastic strain. The mechanism for this may be the removal of so far unidentified pinning points allowing dislocations to glide further (cf. &ZYNOLDS’*‘) but more probably it is mainly due to the intergranular stresses induced by the highly anisotropic growth of the component graphite crystals (cf. WSLL~N and JENKI~#)). This would also account for the strain increments due to temperature excursions by analogy to those observed on thermal cycling the virgin material, (cf. JENKINS and WILLIAMSON(~)). The process, being recoverable, essentially stores elastic energy and so does not add to the ductility of specimens. Fracture occurs because transient influences, such as thermal cycling, and possibly load excursions, bring about too large an accumulation of internal stresses which have not had sufficient time to relsx. The steady-state creep has been shown to increase the ductility of graphite (cf. PERKSand SIMMON.#~)) and, indeed, some process must be available to lower the accumulation of inter-granular stresses. The various possibilities have been discussed in another paper (WILL~~VSON and JENKINs(‘)).The one which corresponds the best with the present experimental data is that involving the migration of point defects produced by irradiation down stress gradients before they reach stable positions in the lattice (cf. Appendix). The activation energy consistent with the results shown in Fig. 5 is 0.15_+0*05 eV. This may be compared with the migration energy of an interstitial which is calculated by COULSONet QL(~*) to be cy O-14 eV. AcknowZedgemmtr-The research was supported by the Central Electricity Generating Board while one of the authors (G.M.J.) was a Research Officer at the Berkeley Nuclear Laboratories. The authors are indebted to Dr. G. K. WILLXAMSON (B.N.L.) for discussion related to both the theory and the design of experiments and to Mr. M. TODD (A.W.R.E.) for discussions related to the design of rig. REFERENCES

Carbon Conference,

Cleveland (1965).

SIMMONS J. H. W., Carbon 1,441

(1964). PWKS A. J. and SIMMONS J. H. W., Paper presented at the Seventh Carbon Conference,

6. 7. 8.

9. 19. 11. 12.

13. 14. 15. 16.

CREEP OF GRAPHITE

WKLLXAMEON G. K. and J-m

Cleveland (1965).

71

G. M., Proctmdinga

of the Second Conference on Industrial Carbon and Graphite. To be published. BLAKELOCK H. D., Private communication. Barxrr J. T., Private Communication. REYNOLDS W. N., Phil. Mug. 11, 357 (1965). JENKINSG. M. and WILLIAMSON G. R., 3 Appl. Phys. 34,2837 (1963). COULsON c. A., SENENT S., HEM. A., ti M. and SANTOSE., Carbon 3,445 (1966). SUTTON A. C. and Howm V. C., J. Niul. Mater. 7, 58 (1962). NAB-O F. R. N., Report of a Conference on Strength of Solids, p. 75. Physical Society, London (1948). WI~A~ R. O., Acta Met. 5, 55 (1957). DE Hht~s D. R., Nu&ar Graphite. Academic Press, New York (1962). Luc.~ M. W. and MITCHELL E. W. J., Carbon 1,345 (1964). Eats W. T., Private communication.

APPENDIX

Polycrystalline graphite contains a widespread population of micro-cracks due to the inability of the material to sustain large plastic deformations on experiencing the highly anisotropic thermal contractions of individual crystals on cooling from the firing temperature. Since these cracks are on the average only lo4 cm apart (Svno~ and HOWARD(~ very sharp stress gradients are to be expected as a result of both intergranular stresses and the externally applied stress. A simplified theory follows with typical values showing the feasibility of the hypothesis that these stress gradients can explain irradiation induced continuous creep in graphite. The creep strain due to interstitial migration down stress gradients has been derived by NnARRo’ra) and WILLU?&‘~) from whose work we take it that the ~on~uous creep rate (8), neglecting geometrical factors, is given by: OV

LOSTY H. H. W., FIELDER N. C., BXL 1. P. and T-INS G. M.. Proceedinm of the Fifth Cm-bon &&mnce. Vol. i, p. 266. Pergamon Press, Oxford (1962). WY C. R., Paper presented at the Seventh PIIRKSA. J. and

5.

INDUCED

idVX--x

kT

Dt L2

where fi is the number of intemtitials formed per second per atomic site. L is the distance between microcracks. If every interstitial manages to migrate this distance, i= I$. D is the coefficient of diBusion of an interstitial and lJ is its volume, u being the maximum stress normal to the plane in which it diEuses.

72

G. M. JENKINS

t is the actual time in which the average interstitial is free. z will depend on how interstitials are captured. If they are captured at boundaries which are a distance S apart: eS2/D in which case, substituting

in (1):

ovs . frz--N. kT L2 In a fast neutron flux of lOi nvt/sec L$’will be about 3 x lo-’ displaced atoms per lattice site per sec-i.(14)* is estimated by EELEP) from X-ray data to be about 3 x 10B5 cm and L- lo4 cm (see above). V is assumed to be N 3 x 1O-24 cm3. Thus at 300°C the continuous creep rate/unit stress, This value is calculated assuming a displacement energy of 25 eV. Recently, LUCASand ~‘~TIX-IELL(~‘) have measured a displacement energy of 60 eV and, if this is accepted, a correspondingly reduced N would be expected. This would bring the value of the creep rate predicted nearer to that measured experimentally here. This is not of great importance since the theoretical assumptions are such that a correspondence within a order of magnitude is all that is required to show that the theoretical treatment is at least possible.

and D. R. STEPHEN

neglecting geometrical considerations, will be 2.5 x 10-i’ dyn-’ set-’ cm2. This is somewhat greater than that actually found by PERKSand SIMMONS(~) (- 1W2’ dyn-’ se& cm2). The discrepancy can be explained by inserting a suitable geometrical factor and also by reasoning that the interstitials are captured at isolated vacancies/interstitial clusters before they reach the boundaries. This would lower the creep strain rate but it is diflicult to predict T since on raising the temperature the stable defect population decreases while the migration rate increases. One can but assume that r is approximately constant with temperature in which case (1) becomes : . e=NiLlA2 on substituting

exp [-E,,,/kT]

DzA2 7kT exp [ - E,,,/kT]

where 1 is the distance travelled/jump Em is the activation

energy for movement.

Thus the activation energy from an Arrhenius plot should be equal to h’,,, as is assumed in the text of the article.