A16402, Irradiation-Induced Creep in Graphite:Review

Irradiation-Induced Creep in Graphite:Review

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i 1 IRRADIATION-INDUCED CREEP IN GRAPHITE:  :

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A REVIEW by R. J. PRICE l

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! Preparedunder Contract DE-AT03-76ET35301 for the San Francisco Operations Offica Department of Energy GENERAL ATDMIC PROJECT 7400 DATE PUBLISHED: AUGUST 1981 l

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ABSTRACT Data on irradiation-induced creep in graphite published since 1972 are reviewed. Sources include restrained shrinkage tests conducted at Petten, the Netherlands, tensile creep experiments with continuous strain registra-tion at Petten and Grenoble, France, and controlled load tests with out-of-reactor strain measurement performed at Oak Ridge National Laboratory, Petten, and in the United Kingdom. The data provide reasonable confirmation of the linear viscoelastic creep model with a recoverable transient. strain component followed by a steady-state strain component, except that the steady-state creep coefficient must be treated as a function of neutron fluence and is higher for tensile loading than for compressive loading. The total transient creep strain is approximately equal to the preceding elastic strain. No temperature dependence of the transient creep parameters has been demonstrated. The initial steady-state creep coefficient is inversely proportional to the unirradiated Young's modulus of the graphite, and the decline in creep coefficient at high fluences parallels the increase in

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i Young's modulus. There is no conclusive evidence for a flux-dependency of the creep coefficient. The creep coefficient increases with irradiation temperature, but the temperature dependence is still not well defined. For l

i a uniaxially stressed specimen the ratio between the transverse creep strain j and the longitudinal creep strain is about 0.3, with a tendency toward a higher strain ratio at high strains. Tensile creep strain tends to reduce the thermal expansivity, while compressive creep strain has the opposite effect. Poisson's ratio is reduced by compressive creep strain. The I

effects of creep strain on Young's modulus and tensile strength are negli-gible. Creep equations recommended for mechanical design of graphite reactor components are presented.

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CONTENfS ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

1. INTRCDUCTION . ......................... 1

2. VIS 00 ELASTIC CREEP MODEL . . . . . . . . . . . . . . . . . . . . . 3

3. THEORIES OF IRRADIATION CREEP ...... . . . . . . . . . . . . 6

4. EXPERIMENTAL TECHNIQUES ................ . . . . . 10 4.1. Restrained Shrinkage . .... . . . . . . . . . . . . . . . 10 4.2. Fully Instrumented Creep Tests . . . . . . . . . . . . . . . 12 4.3. Controlled Load Tests with Out-of-Reactor Strain Measurement .. ... . . . . . . . . . . . . . . . . 16

5.

SUMMARY

OF EXPERIMENTAL RESULTS . . . . . . . . . . . . . . . . . 21 5.1. Transient Creep and Recovery . . . . . . . . . . . . . . . . 21

. 5.2. Steady State Creep . . . . . . . . . . . . . . . . . . . . . 32 5.2.1. Dependence on Stress . . . . . . . . . . . . . . . . 32 5.2.2. Dependence on Material Properties . . . . . . . . . 33 5.2.3. Dependence on Temperature and Neutron Flux . . . . . 38 5.2.4. Dependence on Neutron Fluence . . . . . . . . . . . 45 5.3. Transverse Strain Ratio ... . . . . . . . . . . . . . . . 48 5.4. Effect of Creep Strain on Physical Properties . . . . . . . 49 5.4.1. Thermal Expansivity . . . . . . . . . . . . . . . . 49 5.4.2. Young's Modulus . . . . . . . . . . . . . . . . . . 54 5.4.3. Poisson's iC c io .. . . . . . . . . . . . . . . . . 56 5.4.4. Stren?f>. and 7ailure Strain . . . . . . . . . . . . 56 5.4.5. Irrid %

3 @ ; @ ced Dimensional Change Rates . . . . 58

6. RECOMMENDED DESIGN ZQUATIONS . . . . . . . . . . . . . . . . . . . 61 6.1. Creep Model ........................ 61 6.2. Transient Creep ...................... 61 6.3. Steady State Creep . .. . . . . . . . . . . . . . . . . . . 62 6.4. Tranverse Strain Ratio . .. . . . . . . . . . . . . . . . . 63 6.5. Effect of Creep Strain on Physical Properties. . . . . . . . 65

7. REFERENCES . . . . ........................ 66 v

l FIGURES

1. Rheological model for irradiation-induced creep in graphite . . . 4

2. Creep specimen and restraining pads for restrained j shrinkage tests . . . . . . . . . . . . . . . . . . . . . . . . . 11

3. Example of the stress build-up and dimensional changes of a graphite creep assembly as a function of neutron fluence. . . . . 13

4. Schematic illustration of R-135 continuous-registration creep assembly. . . . . . . . . . . . . . . . . . . . . . . . . . 15

5. Cross-sectional view of in-core portion of compressive creep assembly OC-1 . . . . . . . . . . . . . . . . . . . . . . . 17 l

6. Schematic illustration of DISCREET creep capsule assembly . . . . 19

7. Creep strain record of experiment ORFHEE 03 . . . . . . . . . . . 22

8. Creep strain record of experiment FLACH 02. . . . . . . . . . . . 23 l

9. Creep strain record of experiment FLACH 04. . . . . . . . . . . . 24 l 10. Creep strain record of experiment FLACH 03. . . . . . . . . . . . 26 l 11. Creep strain record of experiment R-135 . . . . . . . . . . . . . 29 l 12. Creep strain record of experiment D-166-01 at 850*C l with tensile stress of 6 MPa. . . . . . . . . . . . . . . . . . . 30 ,

13. Creep strain as a function of compressive stress for different graphites at a fluence of approximately 10 21 n/cm2 (DNE). . . . . 34 i

14. Creep strain as a function of neutton fluence for ATR-2E graphite (axial orientation) at 500*C: (a) tension, (b) compression . . . . . . . .................. 35

15. Steady-state irradiation creep data from restrained shrinkage tests: (a) creep coefficient as a function of temperature; (b) creep coefficient multiplied by initial Young's modulus as a function of temperature . . .................. 37

16. Steady-state irradiation creep data from restrained shrinkage tests: creep coefficient moultiplied by initial Young's modulus for different flux ranges as a function of temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

17. Composite plot of creep coefficient multiplied by initial Young's modulus as a function of temperatures . . . . . . . . . . 44

18. Creep coefficients divided by the value at 0.8 - l'.4 x 10 21 n/ d , DNE, as a function of neutron fluence for ATR-ZE graphite at 500*C, with structural factor S . . . . . . . . . . . 47 ,

19. Composite plot of transverse creep strain as a function of longitudinal creep strain. . . . . . . . . . . . . . . . .... 50 vi

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20. Composite plot of thermal expansivity of creep specimens

• divided by the thermal expansivity of irradiated unstressed companion specimens, as a function of creep strain. . . . . . . . 52

21. Composite plot of thermal expansivity of creep specimens divided by the thermal expansivity of irradiated unstressed companion specimens, as a function of creep strain. . . . . . . . 53

22. Composite plot of Young's modulus of creep specimens divided by Young's modulus of irradiated unstressed companion specimens, as a function of creep strain. . . . . . . . . . . . . 55

23. Poisson's ratio of creep specimens divided by Poisson's ratio of irradiated unstressed companion specimens, as a function of creep strain. . . . . . . . . . . . . . . . . . . . 57

24. Tensile strength of creep specimens of pressed gilsocarbon graphite irradiated in the Dragon reactor, as a function of tensile Creep strain. ... .. . . . . . . . . . . . . . . . . . 59

25. Dimensional changes as a function of neutron fluence of UK isotropic graphite specimens subjected to a tensile or compressive load for the first part of the irradiation, with unstressed controls. . . . . . . . . . . . . . . . . . . . . 60 TABLES

1. Transient creep characteristics. . . . . . . . . . . . . . . . . . 27

2. Steady-state creep coefficients from CEA/KFA continuously measured creep tests . .... . . . . . . . . . . . . . . . . . . 41

3. Values for steady-state creep parameters . . . . . . . . . . . . . 64 i

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1. INTRODUCTION Irradiation-induced creep in the graphite core and reflector components of a high-temperature Sas-cooled nuclear reactor (HTGR) permits the relaxa-tion of stresses arising from differential irradiation-induced shrinkage and differential thermal strains. The creep phenomenon needs to be well characterized for mechanical design calculations to be realistic.

A report written in 1972 (Ref. 1) reviewed the existing literature on irradiation creep in graphite relevant to HTGR conditions. The 1976 Petten conference on the measurement of irradiation-enhanced creep in nuclear nate-rials (Ref. 2) included nine papers on irradiation creep in graphite, and provides an excellent overview of world-wide creep programs and measurement techniques. The present report reviews work published since 1972, including experiments inter.ded to verify the basic viscoelastic creep model, refine-ments in the determination of creep parameters, and the effects of creep strain on physical properties. The report attempts to present the data in a form useful to designers; the experimental techniques and the theory of irradiation creep are only touched on briefly. Details of measurement tech-niques can be found in the papers in Ref. 2, while the theory of irradiation creep in graphite is discussed in a series of papers by Kelly and co-workers (Refs. 3 through 5).

Most of the original data reviewed in this report express neucron fluence in terms of the Dido nickel equivalent (DNE) fluence. Conversion to other fluence units are made as follows (Ref. 6):

Equivalent fission fluence for damage in graphite

= 1.77 x DNE fluence.

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2. VISCOELASTIC CREEP MODEL Virtually all the reported irradiation creep experiments have been analyzed in terms of a linear viscoelastic creep function which can be rep-resented by the rheological model illustrated in Fig. 1. The Kelvin element (spring and dashpot in parallel) represents the transient creep strain com-ponent, while the spring of the Maxwell element represents the elastic com-ponent and the dashpot of the Maxwell element represents the steady-state

! creep component. Two " black box" elements are shown in the model to repre-sent the thermal strain and irradiation strain components, which are inde-pendent of applied stress. Figure 1(b) shows the mechanical strain response (disregarding the black box elements) when a constant stress is applied to a creep specimen for a time period and then removed. There is an instanta-neous elastic strain, CE, which is followed b3 a period of transient creep.

The transielt creep strain saturates at T c after a short interval. The r steady-str.te creep strain, cS, increases linearly with neutron fluence.

When the stress is removed, an elastic strain cR is instantaneously recov-l ered. cE may be smaller than the original elastic strain, c ,E because Young's modulus of graphite increases with neutron fluence. The transient creep strain, c T, is recovered over a short interval, but the steady-state creep strain, c S, is not recoverable. The total mechanical strain, c, is given by the expression:

c = f + fE [1 - exp(-by)] + key , (1) o o where o = applied stress, Y = fast neutron fluence, and Eo = initial value of Ycung's modulus.

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STRAIN 1RRADIATl0N STRAIN (c) MODEL Fig. 1. Rheological model for irradiation-induced creep in graphite 4

The three material parameters that characterize the creep behavior of.the graphite are a = ratio of the maximum transient creep strain to the initial elastic strain,

. b = transient creep exponential coefficient (reciprocal of the time constant),

k = steady-state creep coefficient.

The extent to which the experimental data conform to Eq. I and to the rheological model of Fig. 1 is discussed in subsequent sections of this report.

Equation 1, as written, refers to uniaxial loading, which is the mode in which all experiments to date have been conducted. However, in several experiments the transverse strain was measured in addition to the strain in the loading direction. These data are described in Subsection 5.3.

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3. THEORIES OF IRRADIATION CREEP Although a detailed discussion of the theory of irradiation creep

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is beyond the scope of this review, a brief outline may be useful in interpreting some of the experimental data.

The relationship between the macroscopic creep rate of polycrystalline graphite and the deformation of individual crystallites has been analyzed in papers by Kelly and co-workers (Refs. 3 through 5). The elastic deforma-tion of polycrystalline graphite is dominated by shear parallel to the basal planes of the constituent crystallites. It may be assumed that creep defor-mation is likewise controlled by basal slip. Equating the work done by the macroscopic and microscopic creep rates leads to the following expression for dcxx/dY, the rate of change of creep strain in the x direction with respect to neutron fluence Y:

l dc /C44 3

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dY "xx kE xx/

where K = a constant, o xx = the uniaxial stress in the x direction, C4 4 = the sing 1. crystal elastic constant for basal s? tear, and l

l Ex x = Young's modulus in the x direction.

Equation 2 implies that, for the same irradiation conditions, the creep rate for different graphite grades and orientations will be inversely proportional to Young's modulus. It also implies that the creep rate will not be affected by those changes in Young's modulus that result from changes in C44 (such as the rapid initial rise in E xx at low neu.ron fluences),

because the ratio C44/Exx remains constant. However, the creep rate will be 6

Influenced by changes in E xx arising from changes in the structure of the graphite aggregate (such as the slow rise in Young's modulus at high fluences or the reduction in Young's modulus due to oxidation). Another prediction of the theory is that the ratio of lateral creep strain to longitudinal creep strain will be equal to the elastic Poisson's ratio.

The constant K.in Eq. 2 is related to the strain rates in the individual crystal 11tes. Two theories have been proposed to account for these microscopic strain rates. According to a model originally developed by Roberts and Cottrell (Ref. 7) to explain irradiation-induced creep in uranium, creep is considered to result from the anisotropic dimensional changes of the crystallites causing internal yielding. The creep strain rate, dcxx/dy, is given by

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where Y = the yield stress of the crystallites, and X e and X a= the crystallite dimensions in the e and a directions, respectively.

The quantities (1/X e + dXe /dy) and (1/Xa

• dX a/dy) are fairly well known functions of irradiation temperature obtained from experiments on graphite crystals and highly oriented pyrolytic graphite. However, there is no inde-pendent estimate of the internal yield stress, Y, which is likely to be a function of temperature and fluence.

An alternative model proposed by Kelly and Foreman (Ref. 4) assumes that basal slip in the crystallites is activated by dislocations moving through an array of pinning points that are continually being created and destroyed by irradiation. The theory predicts that the steady-itate creep coefficient shor3d be directly proput-ional to the dislocation density and 7

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t inversely proportional to the pinning point density. An additional prediction is that the linear relationship between creep rate and stress would break down at high stresses.

The relationship between macroscopic and microscopic strain creep rates (Eq. 2) seems to be fairly well supported by experimental evidence. The dependence of creep coefficient on Young's modulus, and the change in creep rate in highly' irradiated or oxidized specimens, agree at least qualita-tively with the predictions, but the lateral-to-longitudinal creep strain ratios tend to be greater than Poisson's ratio (Refs. 3 and 5).

Agreement between experiment and the two theories of microscopic creep rates is more controversial. The observed temperature dependence of the steady-state creep coefficient is roughly similar to the temperature depen-r dence of the crystallite dimensional change rates, and this similarity has I .

been cited as support for the Roberts-Cottrell sect:anism (Eq. 3) . However, agreement would be expected only if the internal yield stress, Y, is inde-l pendent of temperature. The Kelly-Foreman mecnanism does not explicitly l

predict the temperature dependence of the creep coefficient, and it implies that the dislocation density must be similar in all graphites. The creep rate calculated from the Kelly-Foreman dislocation pinning-unpinning model appears in reasonable agreement with experiments. In one experiment speci-fically designed to test the alternative models, the irradiation creep rate of a standard nuclear graphite was compared with the creep rate of graphite l

doped with 0.27 wt % boron (Ref. 8). Creep rates in t' e two materials were l similar, despite a factor of 3 higher crystallite dimensional change rate in the boron-doped graphite. This result appears to favor the Kelly-Foreman model over the Roberts-Cottrell model.

A seniempirical model for irradiation-induced creep in graphite has been proposed by Cords (Ref. 9) as an extension of his model for the irradiation-induced changos in physical properties, which assumes three saturating atomic processes with different activation energies (Ref. 10).

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By adjusting the "importance factors" for the different processes, the reported temperature dependence of the steady-state creep coefficient could be matched. Similarly, the strain-fluence curves from the French step-change creep experiments (FLACE-02, -03, and -04 and ORPREE-03) could be matched through the fitting of free parametres. However, the temperature dependence of the creep coefficient predf',ted by the fitted parameters from the step-change experiaants differed cc asiderably from the observations; in one case the creep coefficient was predicted to become negative below about 1000*C. It seems that the model needs further development before it can be used for extrapolating experimental data into unexplored temperature and fluence regions.

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4. EXPERIMENTAL TECHNIQUES 4.1. 2ESTRAINED SHRINKAGE In this technique a dumbbell-shaped tensile specimen is fitted with a split cylindrical rastraining pad made from a different grade of graphite (Fig. 2). The pad material is chosen sa that the difference in irradiation-induced shrinkage between the specimen and the pad subjects the specimen to a tensile stress during irradiation. A modified version can be used to stress a specimen in compression. After the test, the difference in shrink-age between the specimen and an unrestrained companion irradiated in the same capsule at the same temperature gives the irradiation-induced creep strain. The end-of-life stress can be estimated by heating the specimen plus pad assembly to the irradiation temperature and measuring the specimen expansion, and then repeating the test with the restraining pads removed.

The difference in thermal strain gives the elastic strain present at the end -

of irradiation. A final measurement of the tensile stress-strain curve gives the corresponding stress. The whole assembly can be reirradiated to obtain additional data.

This method was developed by the ECN, Petten (the Netherlands) laboratory and has been used extensively to generate creep data on several hundred specimens of many varieties of graphite (Refs.11 through 14). Its principal advantages are that the restrained shrinkage assemblies are self-actuating and require no external loading device, the capsule experiments are fairly inexpensive,.and up to 50 specimens can be included in one cap-sule. The disadvantages are that the load on the specimen varies during the test and is only known at the end of life (from an indirect measurement out

' of the reactor), and the method of analyzing the results assumes a specific creep model. This method is therefore most suitable for generating a large number of measurements when the creep laws have been determined from other, 10

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4 more direct, experiments. The method cannot be used at high fluences where dimensional change rates reverse (" turn around"), and is limited at low temperatures (below 500*C to 600*C) because of low shrinkage rates.

The procedure for analyzing the test results is explained in detail (in Ref. 12). Refefly, the unrestrained dimensional changes in the speci-men and the pad material are expressed as polynomial functions of fluence.

Using the measured end-of-iradiation stress as input, an iterative calcula-tion is performed to derive a value for k, the steady-state creep coeffi-cient (Eq. 1). As a check, the restrained dimensional changes in the speci-men and restraining pad can be compared with the calculation. An example of the measured and calculated stress buildup and dimensional change is shown in Fig. 3.

Aside from the necessity for assuming a specific model, this technique is subject to several sources of error. The stress determination is very sensitive to the irradiation temperature of the particular assembly, and the i

dimensional change-versus-fluence curve for a particular specimen may devi-ate from the assumed polynomial expression because of statistical varia-l tions. The assemblies must be machined to very close tolerances and must be reassembled in precisely the same way after out-of-reactor measurements.

The differential thermal expansion measurement, necessary to determine the end-of-life stress, requires high precision. Finally, the tensile test on the dumbbell specimen is performed at room temperature, but the data are assumed to apply at irradiation temperature. The cumulative effect of the sources of error could be large. No formal error analysis has been pub-lished, but an accuracy of 120% for the determination of k has been claimed (Ref. 15).

4.2. FULLY INSTRUMENTED CREEP TESTS The most fundamental, but also the most difficult, method for measuring in-reactor creep is to use a fully instrumented in-reactor uniaxial creep 12

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l assembly in which the specimen can be subjected to a known load and the strain recorded as a function of neutron fluence.

This technique has been applied to reactor graphites in tests in the Siloe' reactor, Grenoble, France (Refs.16 through 19) and in the High Flux Reactor, Petten, the Netherlands (Rafs. 20 through 22). A single tensile specimen is loaded through pneumatic bellows and a sensor is used to measure the difference in length between the tensile specimen and an unstressed reference specimen. Figure 4 shows a schematic illustration of the R-135 creep experiment at Petten. The unstressed reference specimen consists of a pair of half shells fitting around the cylindrical gauge section c2 the tensile specimen. A measuring sensor is located between the head of the ten'ile specimen and the top of the reference specimen. The sensor can be moved up and down by actuating a second set of pneumatic bellows; the motion is recorded by a pair of linear displacement transducers. The French FLACH creep capsules used at Grenoble operate on similar principles, except that double sensors are used (one for each half of the split-shell reference ,

specimen) and displaccients are measured with a microwave resonant cavity.

In the French ORPHEE creep capsules the tensile specimen and reference .

specimen are placed side by side and their length changes are measured by two separate sensor rods coupled to transducers. The displacements are actually measured with a motor-driven mictometer, the transducers serving only as null detecturs.

This technique is capable of high precision strain measurements (displacements of a few microns can be reliably recorded) at short inter-vals, revealing fine details of the creep curve. The load is known and can be changed at will; the temperature can be changed over a limited range.

Thermal expansion and stress-strain measurements can be made in situ. The principal disadvantages are the high cost and complexity of the rigs, the limitation of one specimen to a capsule, and the vulnerability of the single tensile specimen to fracture from an accidental overload.

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In spite of the inherently high precision of the measurement technique, corrections have to be made for dimensional changes in the sensor material and for the difference in unrestrained shrinkage between the tensile speci-men and reference specimen arising from their different length. These cor-rections are obtained from the average dimensional change-versus-fluence curves for the materials being tested; differences between the individual specimen behavior and the average curves are estimated from the final out-of-reactor dimensional measurements. The sources of error are discussed in Re f . 19 . Possible variations in individual specimen shrinnsge rates could contribute an error of 10% to the values of the creep coefficient, k; and uncertainties in the measurements of fluencc, load, and displacement could increase the uncertainty in the absolute value of k to 25%.

4.3. CONTROLLED LOAD TESTS WITH OUT-OF-REACTOR STRAIN MEASUREMENT ,

To increase the number of specimens tested while retaining the -

advantage of a controlled load, strings of tensile or compressive specimens loaded in series can be irradiated together with unstressed companions.

Creep strains are determined from the difference in dimensions of the stressed and unstressed specimens when the irradiation capsule is dis-assembled. Curves of creep strain versus fluence can be constructed by repeated encapsulation and reirradiation of the same specimens, augmented (in the case of isothermal capsules) by data from specimens in different axial locations which receive different neutron exposures.

At present two series of graphite creep experiments of this type are being conducted, one at Oak Ridge National Laboratory and one at the Euratom Joint Research Center, Petten. Three capsules in the DC-series of compres-sive creep tests have been irradiated in the Oak Ridge Reactor (Refs. 23 l through 28). Figure 5 shows a cross section of the OC-1 capsule. The cap-sule contains four columns of 14 cylindrical graphite specimens; two of the l columns are subjected to a compressive load applied by pneumatic bellows and )

the other two are unstressed. The capsules are designed to operate iso-thermally at a nominal temperature of 600* or 900*C. A load cell is located 16

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?  ! P-4 A s'O SECTION Fig. 5. Cross-sectional view of in core portion of compressive creep assembly OC-1 (from Ref. 23)

s at the opposite end of each loaded column to the bellows to verify that the load is transmi.tted along the specimen train without, binding. In the first capsule some binding occurred, but this was corrected in subsequent capsules.

The DISCREET series of capsule experiments being conducted at the Euratom laboratory, Petten (Refs. 29 through 33), uses principles similar to those of the OC-series. Three individually controlled specimen columns are irradiated simultaneously in relcadable thimbles (Fig. 6). Each column con-sists of either 5 tensile specimens or 10 compression specimens, together with unstressed reference specimens. The temperature is maintained by gas-gap control. In a complete test series the specimens would be irradiated in four increments, with dimensional measurements being made between each increment. Along one specimen column there are flux differences of 30% for tensile specimens and 60% for compressive specimens.

Compared to creep experiments with continuous strain registration, the main disadvantage of this technique is that creep strain data points for one specimen are measured only at wide fluence intervals. To obtain more points for analysis, data trom all the specimens in a column, incorporating l

1 the axial range in fluences, are usually included. If there is any flux dependence of the creep rate, this plotting method may obscure it.

Because the specimen strains are obtained from direct dimensional measurements in the laboratory, the measuring precision is good. The meas-urements must be corrected for irradiation-induced changes in thermal expan-sivity and Young's modulus. The stress applied to the end of the specimen column is known from the gas pressure in the bellows, which is held constant to within a few percent. However, any sticking or binding in the load train induces uncertainty; binding is more likely to occur in compression than in tension. The tenperature along the specimen column of both the OC-capsules and the Petten capsules can be held constant to within about 130*C (Refs. 24 l and 30). Since the creep strain is obtained from the difference in shrink-age between the stressed specimen and the unstressed reference specimen, 18 l

1 l  ;

.,1) isJi w

,- M

=gl E1 i l3 i

7

-5 / a d I r of

,.; l \.

,N h .-J 1.2 5 5 Qt n

e lA -  :

r E

..a 4

- P 3r

'N d 11

.3,,

s -

1

'{ O '

20

=

} 4 v -

%oa i

-6

.i =

A, L -

1

• b

- i 1. TENSILE SAMPLES WITH I REFERENCE HALF SHELLS

, r' 2. COMPRESSIVE SAMPLE WITH (INTERNAL) REFERENCE PIECE

+

5 3. TENSILE SAMPLE HOLDER (2X)

I 4. COMPRESSIVE SAMPLE HOLDER I 's 5. LOAD SYSTEM BELLOWS f, gQ 6. LEAD SHIELDING p . 7. THIMBLE HEAD WITH DISPLACEMENT UNIT l

Fig. 6. Schematic illustration of DISCREE* creep capsule assembly (from Ref. 30) 19

I the absolute accuracy is limited by the statistical scatter in shrinkage determinations.

l l

\

l l

i 20

5.

SUMMARY

OF EXPERIMENTAL RESULTS 5.1. TRANSIENT CREEP AND RECOVERY The fully instrumented creep tests at Grenoble and Petten provide detailed records of the transient creep strain at start-up and at load increments, and of the recovery of the creep strain when the load is removed. Controlled load tests with out-of-reactor strain censurements can provide an estimate of the total transient creep strain by extrapolating plots of strain versus fluence back to zero fluence, but the extrapolation procedure is not very accurate, and these tests give no estimate for the transient creep exponential ccefficient b (Eq. 1), unless the fluence increments are very short.

An analysis of four fully instrumented creep tests conducted at Grenoble, FLACH-02, -03, and -04, and ORPHEE-03, is contained in Ref.19.

The specimens in all four tests were made from coal tar pitch - coke graph-ite: Sigri gisde AS2-M-500 in FLACH-02, Sigri grade AS2-F-500 in FLACH-04, and Pechiney P 3JHAN in FLACH-03 and ORPHEE-03. The creep curves are shown in Figs. 7 through 10. In the ORPHEE-03 (Fig. 7) test the mean operating temperature was 945*C. The stress was held at 2.5 MPa for the first irradi-ation period, then lowered to 0.5 MPa, then increased to 4.5 MPa, then reduced to 0.5 MPa. A third irradiation step at a higher stress is not depicted because of instrumentation failure. In test FLACH-02 (Fig. E9, the temperature was raised from 893* to 1088*C during the second irrad:-

ation period, and reduced to 893*C for the third period. Finally, the rig was moved to anotter reactor test hole acd reirradiated at 845*C in a neu-tron flux lower by a factor of three. In all four steps the stress was set at 4.9 to 5.0 MPa. In test FLACH-04 (Fig. 9), the temperature was held constant at 895*C while the stress was increased from 2.8 MPa to 4.9 MPa i to 7.0 MPa in the first three steps. For the final step, the rig was 21

l l

0.6 g , , ,

Creep strain %

L.

Ie I

a5 - ~

tim = 945 'C I I

l l l l

! I i

I l 0.4 -  ! l -

, , , I l , o = 2.5 .! I

~

i i l

1 o = 0.5 3 i o=0.5 '

i

, r -

i g 0.3 -

l l 1 I l I 8 l

l l .

I o  ;

I 6

1 0.2 - i 3 i -

1 I i l i 1 j L o = 4.5 i l r ,

4 0.1 - * -

l l

-2 Fluence x 10-21 cm DNE 0.

O.5 1.0 1.5 Fig. 7. Creep strain record of experiment ORPHEE 03 (from Ref. 19) 22

I I I Creep strain %

4 i

l 1 1

0.8 -

. 1 -

T = 893 C _!_ T = 1088 *C I , T = 893 C _

T= 845 *C i i l i I I i i 1

I I

1 I l

0.6 -

i 8 i t I I  ! -

, g l 1 I i

! l l I m'  !

I I l l 8

I I i i l g 0.4 -

i i -

I

• s = 1.72 , i,$ 3= 0.6,

, i-I

, I I l l I l i 0.2 -

Xi i l

I l

l

,j_L o = 0.5 j !_ o=0.5 l I g

, . g i  ! _ o = 4.9 d  ! o=50 _ ! _o =54 .

~

o = 4.9 _! e i 'I I I Fluence x 10-2 cm-2 DNE

0. ) ' '- L 8 ' R 1 2 3 Fig. 8. Creep strain record of experiment FLACil 02 (from Ref. 19)

l s Creep strain % i ,

i L T = 895'C !  !

O.8 -

i g

• I I -

, T = 894 C 1 l

T = 893 *C l /I,T= 874*Cl ,

I l l I l l l 8 0.6 -

l l l  ! -

I 1 I l

I

' i I  : l

, p 1 I i l i l

I i ,

t

't 0.4 - I I

1 l 8

I l

m $s = 1.59 ,

l _ I,$ s = 0.65, i

' 8 I e I l

l l

l 1 I l l 1

l l 1 I

I l l R2 -

1 I e l I o = 4.9 3  !, o = 7.0

., .l l 1, -

i l I o = 0.3 .! L o = a5 I a <

i o = 2.8 I '

_ . ! l lI 2 I 1  ! Fluence x 10-21 cni DNE

0. ' ' ' ' I 1 2 3 Fig. 9. Creep strain record of experiment FLACil 04 (from Ref. 19)

. O mm a

reirradiated in the low flux test hole at 874*C, under a stress of 7.0 MPa.

Test FLACH-03 (Fig.10) followed a similar pattern to FLACH-02, except that there was no low flux step.

Taken together, these four experiments provide direct verification of several points implicit in the rheological model shown in Fig. 1. All irradiation steps at a constant stress level show a saturating transient creep followed by steady-state creep. When the stress is reduced during irradiation, the instantaneous elastic recovery is followed by a slower recovery of the transient creep. The recovery time appears similar to the saturating time for transient creep.

The transient creep parameters calculated by a least-squares fitting method from the four experiments are shown in Table 1, taken from Ref. 19.

The first line in the table shows the average ratio of the total transient creep strain to the preceding elastic strain (a in Eq.1). The ratios range between 0.75 and 1.45, averaging 1.10. The second line shows the ratio of the total recovered creep strain to the preceding transient creep strain.

The values range from 0.5 to 1.5. Since partition of the recovered strain between the instantaneous elastic recovery and the slower creep recovery is somewhat arbitrary, the third line shows averaged ratios of the total recov-ered strain to the sum of the preceding elastic and transient creep strains.

With the exception of the FLACH-02 results, the ratios range from 0.7 to 0.8, compared with a theoretical maximum of 0.9 (because the shut-down stress is 10% of the preceding stress). Since the recovered strain would be expected to increase if the recovery period were extended, these results are consistent with full recovery of the transient creep strain. The final line in Table 1 shows the averaged transient creep exponential coefficient (b in Eq . 1) . The values range from 0.15 to 0.4 x 10-19 (n/cm2, DNE)-1, with an average of 0.3 x 10-19 A continuously monitored tensile creep experi=ent using near-isotropic petroleum coke graphite (Great Lakes Carbon Corporation grade H-451) was conducted at Petten under the designation R-135. The same specimen was 25

---

4..

1.4 I I l 4 Creep strain %

1.2 -

i l

1 I -

1.0 -

, T = 893 C <_!. , ,

T =1075 oC !_I I

I I T = 893 *C _!

m l -

0.8 -

l 1 I I II I .

l l I

I i l I

i l :

l 0.6 -

l  : l l 1

I lI I 1I i lll I1 1I i

II ' --

0.4 -

I i1 l l1 o = 4.9  !, o = 4.9 _

3 3

[ o = 0.5 ] l] o = 0.5 'i I

'I r 1 i -

0.2 - i i i 8 1 I i 8

I I I

' I I i l o = 4.9 -2

-21

~

' l cm DNE 0

' ' l '! Fluence x 10' 1 2 3 l

Fig. 10. Creep strain record of experiment FLACH 03 (from Ref. 19) 1 26

1

• 1 l

TABLE 1 TRANSIENT CREEP CHARACTERISTICS (from Ref. 19)

FLACH-02(a) FLACH-04(a) FLACH-03(a) ORPHEE-03(*)

AS2-M-500(b) AS2-F-500(b) p3JHAN(b) P3JHAN(b)

Ratio of total primary 0.74 1.17 1.45 1.03 I

creep strain to prece-ding elastic strain l

Ratio of total creep 1.7 0.5 1.45 0.80 recovery strain to preceding primary creep strain Ratio of total recov- 1.28 0.70 0.76 0.80 ered strain to prece-ding elastic and primary creep strain Primary creep expo- 0.28 0.40 0.15 0.80 nential coefficient B in (1019 cm-2 DNE)~1

(* Experiment.

(b) Graphite grade.

27

I reencapsulated and the irradiation was continued under the designation D-166-01 (Refs. 21 and 22). The flux levels reported in Ref. 21 were subse-quently revised (H. J. Veringa, private communication). The revised fluxes are u sed here. In test R-135 (Ref. 20) the temperature was held in the range 820* to 850*C. Thr stress was set at 4.56 HPa for the first step and was increased to 5.98 MPa for the second step. ,For the third step the cap-sule was moved to a higher flux position; the stress setting remained at 5.98 MPa. The strain measuring system failed before the end of the test.

The strain-versus-fluence history up to this point is shown in Fig.11. In the follow-on experiment, D-166-01 (Ref. 21), the same specimen was reirra-diated at 850*C under a stress of 6.0 MPa. The stress was removed for a period and reimposed for the remainder of the test. The recorded creep curve ix shown in Fig. 12. The specimen was accidentally fractured during removal of the capsule shortly afterwards. In a follcw-on experiment (D-166-02), a fresh specimen of H-451 was irradiated at 850*C under a load of 6

~

MPa to a fluence of about 2 x 1021 n/cm2 (DNA) without interruption (M. R.

Cundy, private communication). This test also ended with the accidental fracture of the specimen during a reactor shutdown.

The transient creep characteristics observed during the R-135/D-166 tests on H-451 graphite were very similar to those found during the French

, tests on pite.n coke graphites, except that in the initial loading of the R-135 test both the total transient creep strain and the fluence required for saturation were unusually low (Fig. 11). This is believed to have been caused by the application of a large tensile preload (84% of the expected tensile strength) before irradiation, which caused a considerable " permanent set." If this permanent set was recovered early in irradiation, the appar-ent transient strain would be reduced (Ref. 21). The transient strains '

associated with the second loading in test R-135, the start-up and second loading in test D-166-01, and the start-up of test D-166-02 ranged from 0.7 .

l to 1.5 times the elastic strain, with an average of 0.9. These ratios are in good agreement with the French tests (Table 1). The transient strain recovery at the unloading point in test D-166-01 (Fig. 12) continued for a I l

longer period than in the French tests, suggesting that a portion of the 28 l

E no . '

14 sco

$s00 .

J -6 598 MPa -

m to -

U -5 4.56 MPa

.b @-

• 26 -4

.24 - ,

22 - 4 l . .* *. * -

neutron flux density 0 87 x 10"ncm,s i .**

.20 - .

• • d neutron flux. density 2.46 x10"rtcrd's -

.18

,o .16 f e '

14 ..,.. ,.

./

12 -

I# -

.-. 10 -

- E- ___etastic strain

6. . .

c,u 08 -

$ .06 -

h04 o .

02 # irradiation time s ,M [ ,M ,m j,n,m ,m ,a ,2 m ,2 M 0'

0 ') '2 '3 '4 'S '6 '7 '8 '9 '10 '11 2e neutron iluence (10 n.cm-2 DNE)

Fig. 11. Creep strain record of experiment R-135 (from Ref. 21; fluence values revised)

0.20 K = 4.5 X 10-31 p,-1(n/cm-2)-1.fr,e 0.16 -

,,,,o*.**** y' *

.yw ....

1. .e

• l 0.12 -=

.R ...t'."- '% .

'N 0.08

• • es

a. .......

• • * 'K = 3.8 X 10-31 p,-1(n/cm 1 0.04

. f-f :- '

0 1 2 3 4 5 6 h 8 9 1O FAST FLUENCE 1020 n/cm--2 DNE -

Fig. 12. Creep strain record of experiment D-166-01 at 850*C with tensile stress of 6 MPa (from Ref. 22) l l

30

steady-state creep may be recoverable in the highly strained (0.56%)

i specimen. However, the recovered creep strain was again similar in magni-tude to the preceding transient creep strain. The transient creep exponen-tial coefficients may be estimated graphically from Figs. 11 and 12;

~

excluding the startup of test R-135, the coefficients range from 0.3 to 1 i x 10-19 (n/cm2 , DNE)-1, which is a little higher than the values from the French tests because of faster saturation after the second loadings.

I Some useful confirmatory data on the total transient creep strain can be obtained from tests with out-of-reactor strain measurements, espe-cially when the fluence increments are short. In reviewing earlier creep data obtained on a variety of graphites irradiated in the BR-2, Pluto, and Calder Hall reactors between 140* and 650*C, Kelly and Brocklehurst (Ref. 5) concluded that the ratio of total transient creep strain to elastic strain was close to 1 and that the exponential coefficient was about 0.4 x 10-17 (n/cm2, DNE)-1 No temperature dependence was seen. Reference 5 also includes some data on the recovery of strain in a tensile and a compressive specimen irradiated under a 6-MPa stress to strains of about 0.7% and 1%,

respectively. During subsequent irradiation without stress, almost half the creep strain was eventually recovered, which is considerably greater than the transient creep strain. These data are discussed further in Subsection 5.4.5 The experiments outlined above provide reasonably satisfactory verification of the basic points of the rheological model depicted in Fig.

1. They confirm the existence of a transient creep stage followed by s'teady-state creep, and show that the transient creep strain is slowly recovered when the load is removec. There are some indications that a por-j tion of the steady-state creep strain in highly strained specimens is also recoverable, but there are not sufficient data to quantify this. The total transient creep strain is approximately equal to the elastic strain; thus, a in Eq. 1 is equal to 1.0. Values for the transient creep exponential coef-ficient, b, fall in the range 0.15 to 1 x 10-19 (n/cm ,2 DNE)-1, with a best-guess estimate of 0.3 - 0.4 x 10-19 There is no evidence for a temperature 31

dependence of a or b; the data do not confirm an earlier indication that the transient creep strain might be higher at higher temperatures (Refs. 34 and 35).

5.2. STEADY STATE CREEP 5.2.1. Dependence on Stress Early experiments on irradiation creep in graphite pointed to a linear dependence of creep rate on stress (Ref. 1), and the recent tests confirm this conclusion. The fully instrumented tests at Grenoble and Petten included step changes in the applied load. The steady-state creep rates before and after the load change were used to calculate the creep coef-ficient, k (Eq. 1); a linear stress dependence requires that k remain con-stant. When the tensile stress applied to the specimen in the R-135 test at Petten was increased from 4.56 MPa to 5.98 MPa (Fig. 11), the creep coef-ficient was essentially unchanged (Ref. 20) [4.03 x 10-31 (Pa-n/cm 2, DNE)-1, compared wi'h 4.10 x 10-31 before the change *]. The values for k for the various steps in the Grenoble experiments, taken from Ref.19, are listed in Table 2. In the ORPHEE-03 experiment k remained unaltered af ter an increase in stress from 2.5 to 4.5 MPa. However, the effect of the load changes in the FLACH-04 experiment was more erratic; as the stress was ircreased in steps from 2.8 to 4.9 to 7.0 MPA, k changed from 5.8 to 7.5 to 7.1 x 10-31 (Pa-n/cm2, DNE)-1 These apparent differences were believed to have been caused by a discrepancy in free shrinkage rates between the stressed speci-t men and the reference specimen; no real departure from a linear stress i dependence was postulated.

Controlled load experiments with out-of-reactor strain measurements can also be used to verify the linear stress dependence. Reference 5 includes a

• Revised calculations of the neutron flux during the two steps give values of 4.08 and 3.02 x 10-31 (r a-n/cm2 , DNE)-1, respectively (M. R.

Cundy, unpublished data).

32

-t_.

plot of the compressive creep strain rate at a fluence of about 10 21 n/cm2 versus applied stress for creep experiments in the PLUTO and DRAGON reactors at 840* and 1040*C. The plot is shown in Fig. 13. The plots are essen-tially linear, except for some suggestion of an increased creep rate at the highest stress at 1040'C. Such an increase in strain rate at high stresses would be predicted from Kelly's dislocation model for irradiation creep (Ref. 4). The compressive creep tests being conducted at ORNL include spe-cimens under stresses of 13.8 MPa and 20.7 MPa; no difference in creep coef-ficient has been found for these two sets of specimens (Refs. 25, 27, and 28).

The possibility of a higher steady-state creep coefficient for tensile loading compared with compressive loading was suggested by early experiments by Brocklehurst and Brown (Ref. 36), but the data were not con-clusive. Recent experiments at Petten, utilizing controlled tensile and compressive loads with out-of-reactor strain measurement (Refs. 30 through 33), show a clear difference in creep rates for tension and compression in specimens of Sigri ATR-2E graphite tested at 500*C. The data are shown in Fig.14, taken from Ref. 33. At a given fluence, the creep coefficient for

~

compressive creep is 20% to 30% lower than the coefficient for tensile creep.

5.2.2. Dependence on Material Properties Early irradiation creep experiments on grades of graphite with a l pronounced preferred crientation showed a higher steady-state creep coeffi-cient in the against-grain direction than in the with grain direction. This orientation dependence is consistent with Kelly and Brocklehurst's analysis of irradiation creep (Ref. 3), which predicts that the steady-state creep coefficient should be proportional to C44/E (Eq. 2), where C44 is the single crystal elastic constant for basal shear and E is Young's modulus. At low neutron fluences dislocation pinning causes C64 and E to rise rapidly to a plateau, with their ratio remaining constant. Later in irradiation, structural changes cause a secondary increase in E, this time without a l

33

--Sa, 2

Compressive stress, MN/m 20 40 0 , , , ,

e O

l 100 -

I\

I l

e 3

l t

840*C -

200

\

\

\

\

300 -

\

Creep strain 1040*C X

Initial Young's modulus j Fig. 13. Creep strain as a function of compressive stress for different graphites at a fluence of approximately 10 21 n/cm2 (DNE) (from Ref. 5) 34

1.2 -

MEAN CREEP COEFFICIENTS -

R = 2.70 X 10-31 Pa-1(n/cm-20N E)-l 1.0 -

E3= 1.83 .

n .

0.8 . . . -

5 *

=

E 0.6 -

. E -

3 N

w

$ 0.4 -

• E 0 .2 _

K g 2 0

0 2 4 S 8 10

=

FAST NEUTRON FLUENCE 1021 n/cm-l EDN (a)

FAST NEUTRON FLUENCE 1021 n/cm'-2 EDN -

0 2 4 6 8 10

. MEAN CREEP COEFFICIENTS  ;

R R = -2.07 X 10-31 pa-1(n/cm-2 DNE)-l 2

,.'.. R3 = -1.42 X 10-31 p,-1(n/cm-20NE)-I

-0.2 -

. R4 = -1.08 X 10-31 Pa-l'(n/cm-2 DNE)-I -

d

. K 3

E .

q -0.4 -

. K,,

m S

w m . .- -

u - .S K -

4

-0.8 -

(b)

Fig. 14. Creep strain as a function of neutron fluence for ATR-2E graphite (axial orientation) at 500*C: (a) cension, (b) ccapression (from Ref. 33) 33

4 concurrent change in C44 Oxidation also causes drastic changes in E due to structural modifications. The implications are that the creep coefficient should be inversely proportional to the unirradiated Young's modulus for any grade or orientation of graphite, and the same relationship should hold for oxidized graphite. High fluence irradiation should result in a declining creep coefficient until porosity generation reduces Young's modulus, at which stage the creep coefficient should increase.

The inverse dependence of the creep coefficient, k, on unirradiated 4 Young's modulus, Eo, is well supported by experimental data. This depen-dence is illustrated by the Petten data obtained by the restrained shrinkage method (Ref. 12), which covers a wide range of graphite types including both with-grain and against-grain orientations. Figure 15(a) (from Ref. 12) shows the creep coefficient, k, plotted as a function of temperature for all graphite types for neutron fluxes in the range 0.2 to 2.5 x 10 14 n/cm2 ). In Fig. 15(b) the same data are replotted using k x Eo as the ordinate. The ,

scatter is greatly reduced, supporting an inverse relationship between k and E o.

This relationship also holds for graphite whose Young's modulus has been reduced by oxidatien (Refs. 3 and 5). Data reported in Ref. 5 show very different creep rates at 300' to 650*C for isotropic graphite, the same material prexoidized to 25" to 28% weight loss, anisotropic PGA graphite both parallel and perpendicular to extrusion, and highly oriented pyrolytic graphite. However, when the same data were plotted in terms of creep strain i per unit initial elastic strain (cEo/c), the scatter was much reduced.

• l l Similar conclusions may be drawn from the Oak Ridge constant load compressive creep tests at 600* and 900*C (Refs. 25, 27, and 28). The tests included an anisotropic graphite (H-327) in both parallel and perpendicular i direction, and two isotropic graphites (H-451 and AXF-8Q). Values for the initial Young's modulus, ranged over a factor of 2. The measured steady-state creep coefficients increased with decreasing Young's modulus, and the data were in good agreement with the predicted inverse relationship.

36 ,

GILSO G RAPHITE ~

_N" +O EXTRUDED PITCH C0 KE GRAPHITE k h "T EXTRUDED PETRO LEUM C0KE GRAPHITE Blackstane et.al ."

Y ,a PRESSED PETROLEUM C0KE GRAPHITE ,

15 - A ISOSTATICALLY PRESSED + -

3 MATRIX MATERIAL "

52 ** s PRESSED MATRIX , "

MATERIAL

• - - + e -

_S 10 - e + -

gg - + + y e d , 7 ,a +' ~

7 "

+ A a ,

94 lT

+ 7 MS

1. 4, T -

+ , o , O y5 -

+ 3 +, + o 0

@4 w

+, + -

+

5 -

3 W

Backstone etd. ' '

2 300 1300 1400 300 400 500 600 700 800 900 1000 1200 IRRADIATION TEWERATURE ('C)

(a)

~f90 +

80 . +

Yb -

70 -

+

60 - * , , -

+o & +,

J ,k ? t

• A a- 50 + 7{, A, a4 g o= -

&+

h *

+

A , 4 +0 yG -

+ ,=

++ o GILSO GRAPHITE 30 -

+ EXTRUDE 0 PITCH C0KE GRAPHITE x PRESSED PETROLEUM C0KE GRAPHITE O

W & IS0 STATICALLY PRESSED MATRIX "

g 20 -

MATERIAL e PRESSED MATRIX MATERIAL b 10 -

T EXTRUDE 0 PETROLEUM C0KE GRAPHITE O

300 400 500 600 700 800 900 1000 110 0 1200 1300 1400 IRRADIATION TEMPERATURE ('C)

(b)

Fig. 15. Steady-state irradiation creep data from restrained shrinkage tests: (a) creep coefficient as a function of temperature; (b) creep coefficient multiplied by initial Young's modulus as a function of temperature (from Ref. 12) 37

Changes in the creep coefficient at high fluences are discussed in Subsection 5.2.4.

5.2.3. Dependence on Temperature and Neutron Flux Much effort has been expended at several laboratories to characterize the dependence of the steady-state creep coefficient on temperature and neutron flux. The bulk of the data were derived from isothermal restrained shrinkage or controlled load tests with out-of-reactor strain measurements.

Additional data were obtained from tests with continuous strain registration where a step change in temperature was imposed, or where the neutron flux was changed by moving the entire capsule assembly to a different position in the test reactor.

l The restrained shrinkage tesci conducted at Petten (Refs.11 through

15) covered a wide temperature range (350' to 1400*C) and flux range (0.24 ,

to 2.4 x 1014 n/cm 2-s, DNE). A progressive increase in creep coefficient with temperature is clearly apparent (Fig. 15). Veringa and Blackstone (Refs.12 and 13) noted that if the neutron flux is taken into account, coefficients derived from specimens irradiated at a low neutron flux tend to fall high, while data from specimens irradiated in a high flux tend to fall low. This trend was most noticeable if early UKAEA high flux data from restrained shrinkage tests in the Dounreay fast reactor (Ref. 37) and low-flux data from tensile strings for the Dragon reactor (Refs. 34 and 35) were included. The data are shown in Fig. 16. Veringa and Blackstone system-atized the data by assuming that the product of the creep coefficient, k, and Young's modulus, E, has a flux-dependent part and a flux-independent l

part:

i i

( (4) kE = + g(T) ,

l where $ is the neutron flux and f(T) and g(T) are functions of the irradi-ation temperature, T. Lines based on Eq. 4, assumi.;g that f(T) and g(T) are linear functions, are shown in Fig. 16. It was suggested that the first i

38 l

c as _

, C

~

100 - sa s'#

'E \ g N 90 - (=.20 x 10 \ /

9 e .27 $= .40 x 10 h Io 80 - . 37 I fM -

C '

Dragon ta y 70 - . ss',_ ,ss,, y,, g'.ss _

+

~

.ms

.47* e.54

.6, 7N

/ , AA $8o 8

~

Y un e .46 7 9 g 14 oo

{g o +

• 50 YA' 9 .24

= "

A 8

H . 91 40 -

. 37 e.3s . . s3, .se _

hi s

')

30

• f.% *f= / 60x 10 u

5 neutron flux densitg range _

a -,.2s Pluto [ 42 \ o>=1.00x

= 1080 x 10,% e 29 .80 x 10" nerdse[.

I2i n2 y V .81 -100 -

$ 20 + 0.ER A 101-180 z o 181 -2.40

+ > 2.41 -

0 y 10

+ D.ER Q

n 0 400 500 600 700 800 900 1000 110 0 1200 1300 1400 300 IRRADIATION TEMPERATURE ( C)

Fig. 16. Steady-state irradiation creep data from restrained shrinkage tests:

creep coefficient multiplied by initial Young's modulus for different flux ranges as a function of temperature (from Ref. 12)

l term in Eq. 4 might correspond to the Kelly-Foreman creep mechanism if the dislocation pinning point density is assumed to be proportional to the flux, and the second term might correspond to Roberts-Cottrell creep (Section 3).

The flux-dependent lines in Fig.16 are certainly a plausible representation of'the data. It is worth noting that the early Dounreay fast reactor points (Raf. 37) may not be directly comparable to mors scent measurements because of the high neutron fluence (see Subsection 5.2.4) and the unsophisticated technique.

To clarify the temperature and flux dependence of the creep coefficient, step changes in both temperature and flux scre included in the continuous-registration test series at Grenoble (Refs.16 through 19).

Table 2 summarizes the results. In the FLACH-02 experiment, when the temperature was changed from 893* to 1088'c and back to 893*C, the creep coefficient changed from 5.4 to 6.9 to 5.3 x 10-31 (Pa-n/cm 2, DNE)-1 These changes were about as expected. A similar series of step temperature ,

changes during the FLACH-03 experiment produced less consistent results; the creep coefficient changed from 8.3 to 8.0 to 5.6 x 10-31 (Pa-n/cm 2, DNE)-1 .

The apparent inconsistency was attributed to differences in the shrinkage curves of the tensile specimen and its unstressed companion (Ref.19). When the neutron flux in the FLACH-02 experiment was reduced from 1.72 to 0.60 x l 1014 n/(en 2 -s) (DNE), the creep coefficient increased from 5.3 to 8.6 x 10-31 (Pa-n/cm2, DNE)-I . However, a similar step change in the FLACH-04 test produced the opposite result: the creep coefficient decreased from 7.1 to 5.6 x 10-31 (Pa-n)/cm 2, DNE)-1 The flux change was created by moving the experimental rig to a different test hole in the reactor, which may have disturbed the sensitive in-reactor measurement system. The authors there-fore judged that the experiment did not allow any conclusions either for or against the existence of a flux-dependency of the creep coefficient.

The continuous-registration creep tests on H-451 graphite conducted at Petten (Refs. 21 and 22) included a step change in flux. The first two steps of the R-135 experiment (Fig. 11) were conducted at a flux of 0.87 x 1014 n/cm2 -s (DNE), and the rig was moved to a high flux position (2.46 40

TABLE 2 STEADY-STATE CREEP COEFFICIEIES FROM CEA/KFA CONTINUOllSLY HEASURED CREEP TESTS (from Ref. 19)

Steady-State Creep k u Young's Graphite Temperature Stress Neutron Flux Coefficient, k 16dulus Experiment Grade Step (*C) (HPa) (10 n/cm -s, DNE) [10 (Pa n/cm . DNE) ] [10' (n/cm . DNE)~ ]

FLAct-02 AS2-N-500 1 893 4.9 1.72 5.40 1 0.07 4.50 2 1088 4.9 1.72 6.93 1 0.09 5.78 3 893 5.0 1.72 5.31 1 0.09 4.45 4 845 5.0 0.60 8.64 1 0.12 7.21 4- FLACil-04 AS2-F-500 1 894 2.8 1.59 5.84 1 0.19 4.65

" 2 893 4.9 1.59 7.52 1 0.10 5.99 3 895 7.0 1.59 7.06 1 0.10 5.62 4 874 7.0 0.65 5.62 1 0.11 4.47 d

FLACil-03 P3JIIAN 1 893 4.9 1.85 8.26 1 0.10 5.88 2 1075 4.9 1.85 7.99 1 0.15 5.69 3 893 4.9 1.85 5.57 1 0.09 3.97 ORPHEE-03 P3JilAN 1 945 2.5 1.45 8.85 1 0.30 6.20 2 945 4.5 1.45 8.85 1 0.16 6.20 1

l x 1014 n/cm2-s, DNE) for the third step. The initial analysis indicated that the creep coefficient fell from 4.03 to 2.46 x 10-31 (Pa- n/cm ,2 DNE)-1 between the second and third step, but these values were later revised to 3.02 and 2.53 x 10-31, respectively (M. R. Cundy, unpublished data). When the specimen was reirradiated in test D-166 in a high flux position (about 2 x 1014 n/cm 2-s, DNE) the creep coefficient returned to a higher value [3.8 x 10-31 (Pa-n)/cm2, DNE)-1, later revised to 4.04 x 10-31] . Thus the Petten experiments, like the Grenoble experiments, failed to confirm the earlier indication of a systematic effect of flux on the creep coefficient.

In their review of UKAEA creep work, Kelly and Brocklehurst (Ref. 5) showed a composite plot of the steady-state creep coefficients from con-trolled stress tests in the BR-2, Pluto, and Dragon reactott as a function of temperature. The data indicate no significant temperature dependence between 300* and 700*C, then a progressive accelerating increase with temperature up to 1200*C. No separate effect of flux was postulated. .

The OC-series of compressive creep tests at ORNL (Refs. 25, 27, and 28) show creep coefficients at 900*C to be 1.5 to 2 times higher than at 600*C.

The authors suggested that the temperature dependence of the creep coeffi-cient may be explained by the Roberts-Cottrell model (Eq. 3). If the crys-tallite yield stress, Y, is independent of temperature, the creep coeffi-cient should have the same temperature dependence as the differential crys-tallite dimensional chauge rate, [(1/Xe dKc/dY) - (1/Xa a dXa/dy)]. This quantity is known to decrease with irradiation temperature up to about 400*C, pass through a shallow minimum, then increase rapidly. Early mea-surements for the creep coefficients for oriented graphite grades are in reasonable agreement with the predicted temperature dependence (Ref. 28).

The Petten controlled-load tests on ATR-2E graphite (Refs. 30 through

33) showed a creep coefficient at 300*C about 15% higher than at 500*C.

Early data appeared to show a trend toward a higher creep coefficient at low flux levels (Ref. 30), but later tests did not confirm this trend (Ref.

33).

42

To summarize, the tests reviewed above did not confirm earlier indications of higher creep coefficients at low fluxes. In spite of the increased complexity of the test facilities and more sophisticated data analysis, the more recent tests have also done little to improve the knowl-edge of the temperature dependence of the creep coefficient. Figure 17 is a plot of the product of the steady-state creep coefficient and unirradiated Young's modulus (kE o ) versus irradiation temperature for the tests reviewed in this section, restricting the data to points obtained at fit 9nces below 3 x 1021 n/cm2 (DNE) because of the trend towards lower creep coefficients at high fluences (see Subsection 5.2.4). The fluxes are indicated for each point. Figure 17 also includes the flux-dependent lines for 0.6,1.0 and 3.0 x 1014 n/cm2 -s (DNE) from Veringa's analysis of the Petten restrained shrinkage data (Ref.12 ind 13); the empirical temperature dependence line from Kelly and Brocklehurst's review of UKAEA data (Ref. 5); and the temperature dependence line based on Roberts-Cottrell creep proposed by Kennedy (Ref. 27). None of the lines represent all the data points to within the claimed 225% accuracy; and the scatter in the data is such that it is not possible to say which line best conforms to the new measurements.

The high scatter in the 830" to 900*C temperature range of the Grenoble and Petten continuous-registration experiments coincides with a steep slope in the ORNL and UKAEA temperature dependence curves, suggesting that a part of the discrepancy could result from deviations between the recorded tempera-ture and the actual specimen temperature. Since the thermocouples in the experiments are located in a container drum separated by a gas gap from the specimen and gamma heating in the specimen generates much of the heat, such deviations can be considerable.

The data points in Fig. 17 for H-451 graphite, the reference grade for the fuel elements in the US HTGR program, appear to fall closer to the UKAEA line than the other lines shown, and this line therefore seems to be more 43

ORNL LINE --*[ [

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CONTINUOUS STRAIN REGISTRATION:

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Fig. 17. Composite plot of creep coefficient multiplied by initial Young's modulus as a function of temperatures g

• e

appropriate for design purposes. The following equation represents the UKAEA line:

T < 650*C : kEo = 2.3 x 10-21 ,

T > 650*C : kEo - 2.3 x 10-21 + 7 x to-28(T - 650)2.6 where T is the ter.9rature in *C and kEo is in the units (n/cm , 2DNE)~1 5.2.4. Dependence on Neutron Fluence As discussed in Subsection 5.2.2, Kelly and Brocklehurst's analysis of irradiation creep predicts that the steady-state creep coefficient should decline as Young's modulus undergoes its secondary increase at fluences greater than about 3 x 1021 n/cm 2 , DNE. Ultimately, the creep coefficient should rise again as porosity generation lowers Young's modulus. Kelly and Brocklehurst (Ref. 3) divide the irradiation-induced change in Young's modulus, E/Eo, into components, one due to dislocation pinning and one due i to structural changes:

l E= --

x , (6) o [o/p (Eoj 1

Since the component due to pinning (E/E o )p, is caused by a parallel change in the crystal elastic constant, C44, it follows from Eq. 2 that the creep coefficient should be inversely proporticnal to (E/Eo)S. (E/Eo)p reaches saturation after a low fluence and is assumed to remain unchanged there-after. (E/Eo)g is therefore equal to E/E*, where E* is the plateau value I of Young's modulus when dislocation pinning is saturated. The creep coefficient, k, at a fluence y should therefore be given by:

k(T) = k* = k* S(y) , (7)

E 45

where k* is the creep coefficient in the plateau region (fluence less than about 3 x 1021 n/cm2, EDN). S is the fluence-dependent structural factor.

Kelly and Brocklehurst (Ref. 3) used a plot of (E/E o)3 versus fluence to predict creep strains in graphite specimens previously irradiated to fluences of about 1.5 x 1022 n/cm2. The measured creep strains were less than would have been predicted using the plateau value for the creep coeffi-cient, k*, but somewhat greater than would have been predicted from Eq. 7.

The controlled load tests conducted at Petten on ATR-2E graphite (Refs. 32 and 33) show a progressive decline in the creep coefficient with fluence, both in tension and compression (see Fig. 14). The coefficients at 500*C divided by the plateau value at 0.8 - 1.4 x 1021 n/cm2 (k*) are plotted against fluence in Fig. 18, taken from Ref. 33. Figure 18 also shows the structural factor, S(Y), calculated from Eq. 7, and the high fluence points from Ref. 3. The reduction in creep coefficient at high fluences measured in the Petten tests is somewhat more than predicted, in contrast to Kelly ,

and Brocklehurst's observations (Ref. 3).

The continuously monitored tensile creep experiments at Grenoble and Petten (Refs.19 and 22) extended to fluences of about 3 and 3.5 x 1021 n/cm2, DNE, respectively, but neither test series showed a clear reduction i in creep coefficient with fluence. However, the ORNL compressive creep

, tests on H-451 graphite at 900*C (Ref. 28) show a trend toward a lower c.sep l

l coefficient at higher fluences; at a fluence of about 1.7 x 1021 n/cm2, DNE, and a compressive creep strain of 1.5% to 2%, the coefficient was about 30%

lower than the initial value. At this fluence and temperature Young's modulus would not be expected to have increased above the plateau level, and no reduction in creep coefficient would have been predicted by Eq. 7. The compressive creep strain in this experiment was higher than in the other work described above, and it is possible that the greater-than-expected reduction in creep coefficient was caused by the specimens approaching a

( compressive strain limit. Gray's compressive creep tests (Ref. 38) had earlier suggested that isotropic graphites approach a compressive strain limit at 2% to 3% strain.

t l

l 46 l

STRUCTURAL FACTOR = YOUNGS MODULUS AT LOW FLUENCE PLATEAU VALUE A A OUNG3 MODULUS 1.0 - -

0.8 -

o. ,

• 0.6 - .

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14 - ...

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u 2 4 6 8 ' 14 16

=

FAST NEUTRON FLUENCE 1021 n/cm-2 EDN 21 Fig. 18. Creegcoefficientsdividedbythevalueat0.8-1.4x10 n/cm , DNE, as a function of neutron fluence for ATR-ZE graphite at 500*C, with structural factor S (from Ref. 33, with added points from Ref. 3 )

{

47

To summarize, there appears to be a trend toward lower creep coefficients at high fluences although the data are not all consistent.

There are theoretical grounds for expecting the creep coefficient to decline as Young's modulus undergoes its secondary increase, according to Eq. 7.

Two quantitative comparisons below the observed and predicted decline in the creep coefficient have been made: in one case the decline was overpre-dicted, and in the other case it was underpredicted. For design purposes it seems reasonable to assume that the creep coefficient decreases with neutron fluence as predicted by Eq. 7, at least until more high fluence data become available. A further reduction in creep rate is probable in compression as strains approach 2%. It has not yet been determined whether the creep coef-ficient increases again at very high fluences where Young's modulus declines.

5.3. TRANSVERSE STRAIN RATIO Kelly and Brocklehurst's analysis of irradiation creep (Ref. 3) predicts that in a uniaxially loaded specimen the ratio between the creep strain transverse to the loading axis and the creep strain parallel to the loading axis should be equal to the elastic Poisson's ratio (typically 0.1 l ~

to 0.2). During fully plastic creep at constant volume the ratio would be 0.5. Experimental measurements generally give a value somewhere between, with a tendency towards a higher strain ratio at high creep strain.

The mean strain ratio observed in UKAEA tests (both tension and compression) was reported to be approximately 0.3 (Ref. 5). In early stages of the Oak Ridge compressive creep tests on H-451 graphite at 900*C, the transverse-to-longitudinal creep strain ratio was about 0.1 to 0.2 (Ref.

25), but at higher strain levels the ratio increased with creep occurring at constant volume (Raf. 28); thus, the ratio between strain increments in the transverse and longitudinal directions approached 0.5. A similar ratio was l

reported by Gray (Ref. 38) for high-strain compressive creep in AGOT and H-337 graphites at 550*C. At 800*C the strain ratio tended to be a little lower (about 0.4). Transverse strains were also reported for the Petten 48 t

constant load tension and compression creep tests at 500'C (Refs. 32 and 33). The creep strain ratio averaged 0.27 i 0.08 in both tension and compression for fluences up to 5.5 x 10 21 n/cm2 , DNE, and for creep strains up to about 0.6%. At higher fluences the data were insuffucient to define the strain ratio.

Figure 19 shows a composite plot of transverse creep strain versus longitudinal creep strain, replotted from the references cited above. The data at low strains can be fairly well represented by a strain ratio of 0.3; the ratio tends to increase at higher strains. The overall relatienship between the transverse creep strain, ci, and the longitudinal creep strain, cll, can be represented by the expression c1=-cll(0.3+5cll) . (8) 5.4. EFFECT OF CREEP STRAIN ON PHYSICAL PROPERTIES I

5.4.1. Thermal Expansivity The thermal expansivity of isotropic graphite specimens that had undergone irradiation creep at 300* to 650*C was measured by Brocklehurst and Brown (Ref. 36). They found that the thermal expansivity of specinens irradiated under compression increased more rapidly than that of unstressed companion specimens, while the thermal expansivity of tensile specimens increased more slowly than that of their stress-free companions. This difference in thermal expansion behavior between tensile, compressive, and stress-free specimens could be removed by postirradiation annealing to 1400' to 2000*C. The thermal expansion of polycrystalline graphite is controlled by microcracks which absorb much of the thermal expansion of the constituent crystal 11tes. It was suggested that the externally-applied stress modified the microcrack closure which accompanies irradiation, with compressive stresses accelerating crack closure and tensile stresses retarding crack closure.

l 49 l

l

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V o o OO O -

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$ V V O g ,

Y I

t; E y e u o a:

$ $ TENSION: y 8

E A ATR-2E AT 500 C(PETTEN) 4 4 C0MPRESSION:

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$ OATRE-2E H 651 AT900 T " 'L (0.3-5 eLI A AT 500Cf0RNL)

C(PETTEN) 8 V AGOT AT 550 C(PNL) 0 Q AGOT AT 800 C(PNL) 8 O H-337 AT 550 C(PNL) 8 G H-337 AT 800 C(PNL)

! I

-2 O 1 2 3 LONGITUDINAL CREEP STRAIN (%)

Fig. 19. Cornposite plot of transverse creep strain as a function of longitudinal creep strain m

9 e O O

This pattern of behavior has been confi'ned in compressive creep specimens irradiated at Pacific Northwest Laboratories (Ref. 38) and Oak Ridge National Laboratory (Refs. 25, 27, and 28). Compressive loading increased the thermal expansivity compared with unstressed control specimens irradiated under the same conditions, with the greatest changes occurring at I

high creep strains. Greater fractional increases in thermal expansivity were seen in the needle coke graphite grades AGOT and H-327 (which have low initial expansivity) than in the near-isotropic grades H-337 and H-451. It was also noted (Refs. 25 and 27) that creep increased both the temperature-dependent and the temperature-independent components of thermal expansivity.

The continuously monitored tensile creep tests at Grenoble and Petten (Refs.19 and 22) confirmed the UKAEA observation of lower thermal expan-sivity in tensile creep specimens than in unstressed companions. The magnitude of the effect was similar to the earlier UKAEA work.

The data from the references cited above are replotted in Figs. 20 and 21. Figure 20 shows the thermal expansivity of a creep specimen, ae, divided by the thermal expansivity of an unstressed companion irradiated under the same conditions, ao, plotted against the creep strain, for near-isotropic graphite grades. Figure 21 is a similar plot for needle coke graphites. For near-isotropic graphites the thereal expansivity change, ac/so, may be related to the creep strain, cc (considering compressive strain to be negative and tensile strain positive), by the expression a

(9)

-[Io = (1 - 18 c ) .

ls For needle coke graphites the dependence on creep strain is greater and may be represented by a

(10)

-[io = ( 1 - 30 c ) .

51

l 2.0 0

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8 A H-451 AT900 C (ORNL) )

Y H-337 AT 550 0C(PNL) )

V H-337 AT 800 8C (PNL) 0

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Fig. 20. Composite plot of thermal expansivity of creep specimens divided by the thermal expansivity of irradiated unstressed companion specimens, as a function of creep strain (near-isotropic graphites) 52 l

l

2.4 9 H-327 AT 600 8C(ORNL)

O H-327 AT900 8C(ORNL)

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Fig. 21. Composite plot of thermal expansivity of creep specimens divided by the thermal expansivity of irradiated unstressed companion specimens, as a function of creep strain (needle coke graphites) 53

_ _ - __ _ _ ._ . - - _ - _.____ _ _ ~ _ . _ _ . _ . _

Figure 21 also appears to show that the fractional changes tend to be higher at 550' to 600*C than at 800* to 900*C. However, the comparison is not straightforward because the thermal expansion tests were made over different temperature ranges and the temperature dependence of the expansion coeffi-cient may be altered by the creep strain, as noted above.

5.4.2. Young's Modulus The early UKAEA work by Brocklehurst and Brown (Ref. 36) included measurements of Young's modulus on tensile and compressive creep specimens.

Within the scatter of the data, no difference could be seen between Young's modulus changes in tensile, compressive, and unstressed specimens. The tensile creep specimens from the Grenoble and Petten experiments (Refs.19 and 22) also showed very little difference in Young's modulus between stressed and unstressed specimens, although the Petten tests on H-451 graphite showed a tendency toward a higher Young's modulus in the tensile .

specimens. The first set of Oak Ridge compressive creep tests at 900*C (Ref. 25) appeared to indicate a marked tendency toward a lower Young's mod- .

ulus in the stressed specimens than in their unstressed companions. How-ever, this trend was largely due to the behavior of "overstressed" specimens in a column which experienced high but unknown stresses due to a jammed load system (Ref. 28) . Later tests at 900* and 600*C (Refs. 27 and 28) showed ,a smaller difference in Young's modulus between stressed and unstressed speci-mens, although there was still a tendency toward lower values at high creep strains.

i The data from all these tests are replotted in Fig. 22, where the ratio q between Young's modulus of a creep specimen (Ec ) and Young's modulus of an l unstressed companion (Eo) is plotted against the creep strain (ce ). If the J overstressed points are excluded, the data can be represented by the i

relation l l

E (11) jf!=(1+3c) o e

54

~ .

1.4 O AS2 - M - 500 AT 845 - 10880 C (GRENOBLE) 9 AS2 - F - 500 AT 8958 C (GRENOBLE)

O P3JHAN AT 893 - 10758 C(GRENOBLE)

W H-451 AT8508 C(PETTEN)

A H-451 AT 6008C(ORNL)

A H-451 AT 9008 C (ORNL)

H-451 AT 900 8C,DVERSTRESSED (ORNL) 1.2 @

+

$ E

$ 1.1 -

E s

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6 A

AA O

$ 1.0 -

9 O'

$ a s b O 0.9 -

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-3 -2 -1 0 1 2 COMPRESSION TENSION CREEP STRAIN (%)

Fig. 22. Composite plot of Young's modulus of creep specimens divided by Young's modulus of irradiated unstressed companion specimens, as a function of creep strain (near-isotopic graphites) l 55

s 5.4.3. Poisson's Ratio Following the Oak Ridge compressive creep tests, Poisson's ratio of the specimens was derived from sonic measurements of Young's modulus and the shear modulus (Refs. 25 and 27). While Poisson's ratio of unstressed specimens was unaffected by irradiation, the creep specimens underwent a progressive decrease in Poisson's ratio. The.results are shown in Fig. 23 (data from Refs. 25 and 27), plotted as a function of compressive creep strain. The three near-zero Poisson's ratio points at about 2.5% strain are from the overstressed specimens. Neglecting these three points, the data can be represented by v

E = (1 & 30 cc ) , (12) o where ve and v oare Poisson's ratios of a creep specimen and a control ~

specimen, respectively, and cc is the creep strain (negative value for compressive strain). .

5.4.4. Strength and Failure Strain The strain-to-failure of a tensile specimen of typical nuclear l

graphite, tested in the laboratory, is typically 0.1% to 0.2%. Under irradiation creep, tensile strains up to 1.8% without fracture have been reported (Ref.12) . Oxidized specimens can withstand even greater creep strains; a creep strain exceeding 7.5% under an applied stress of 6 MPa has been reported in one case. The specimen remained intact, although visibly deteriorated (Ref. 39). A few tensile creep specimens have fractured in the reactor during restrained shrinkage or controlled load tests, but such frac-tures have always been attributable to inadvertent stressing beyond the ten-sile strength. There was no evidence that any specimen had reached a tensile strain limit.

56 l - . _ _ . . - _ _ - _ - - - - _ _, _ . _ . _ _ _ _ __

0.20 e H-451 GRAPHITE,6008C O H-451 GRAPHITE,9008 C 8

@ H-451 GRAPHITE.900 C UNSTRESSED CONTROLS -(OVERSTRESSED) 0.15 -

o I

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• O e 9 O

h 0.10 -

$ $ b (1 + 30 ey a  % / "a O

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0 -

e e

i I l l l 0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 l

COMPRESSIVE CREEPSTRAIN (%)

l l Fig. 23. Poisson's ratio of creep specimens divided by Poisson's ratio of irradiated l

unstressed coispanion specimens, as a function of creep strain (H-451 graphite; data from Ref. 25 and 27)

I

Very little data are available on the effect of creep strain on the tensile strength. Manzel et al. (Ref. 35) reported the strength of six specimens of a pressed gilsocarbon graphite creep-tested in the Dragon reac-tor, together with two unstressed companions irradiated under the same con-ditions. The ir.adiation temperature was 850*C for four specimens and 1240*C for the remaining four. The measured strengths are plotted against creep strain in Fig. 24. The tensile strength appears to be unaffected by creep strain. Additional indirect evidence that this is the case comes from measurements of the sonic attenuation on compressive creep specimens at Oak Ridge National Laboratory (Ref. 28). The sonic attenuation is related to the size of defects in the material, and correlates well with the tensile strength of many graphites. The sonic attenuation was the same in the creep specimens as in their unstressed companions, indicating that the tensile strength is probably unaffected by compressive creep strain.

5.4.5. Irradiation-Induced Dimensional Change Rates .

Figure 25 shows the dimensional changes in specimens of UK isotropic ,

graphite as a function of fluence, taken from Ref. 5. One specimen was irradiated under a tensile load for the first part of the test period, one l

i was irradiated for a time under a compressive load, and two were unstressed companions. After removal of the load, a portion of the creep strain was recovered and the dimensional change curves for the formerly stressed speci-mens approached those of the unstressed specimens (see Subsection 5.1). The major part of the creep strain remained in the specimens af ter recovery had saturated, but the dimensional change rates appear to have been the same as those of the unstressed companions at the same total neutron fluence. Thus, unrecovered creep strain appears to have no effect on the rate of radiation damage accumulation in a subsequent stress-free irradiation. ,

1 l

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1 0 0 0 0.2 0.4 0 0.2 0.4 0.6 03 1A 1.2 1.4 1.8 CREEP STRAIN (%)

l Fig. 24. Tensile strength of creep specimens of pressed gilsocarbon graphite irradiated in the Dragon reactor, as a function of tensile creep strain (data from Ref. 35).

• ? ,

Unstressed oGraphite type (1)

Stressed ~~ 6MN/m' x Graphite type (2)

'" 8 ' I' Fast neutron dose n/cm*

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Fig. 25. Dimensional changes.as a function of neutron fluence of UK isotropic graphite specimens subjected to a tensile or compressive load for the first part of the irradiation, with unstressed controls (from Ref. 5) l l

l l

l l

60 i

6. RECOMMENDED DESIGN EQUATIONS 6.1. CREEP MODEL The basic elements of the linear viscoelastic creep model represented by Fig. I and Eq. 1 should be retained, except that the steady-state creep coefficient, k, should be treated as different for tensile and compressive I loading and as a function of fluence. Most of the other basic features of the model have been verified reasonably well by experiments. These features include a transient creep stage followed by a steady-state creep stage, slow recovery of the err.asient creep strain when the load is removed during irra-diation, and linear dependence of both transient and steady-state creep strain on the applied stress. A portion of the steady-state creep strain, in addition to the transient creep strain, may be recoverable, but it is not possible at present to say how much.

6.2. TRANSIENT CREEP l

The total transient creep strain is approximately equal to the elastic l

strain, independent of irradiation temperature. The transient creep strain, eT, may be represented by c

7 =fh[1-exp(-by)] , (13) where o is the applied stress and E is Young's modulus when the load is applied or changed. For virgin material, E is the value for unirradiated graphite, but for irradiated material E is the value for the appropriate 4..

51

fluence and irradiation temperature. The value for b, in the various fluence units currently being used, is b = 0.35 x 10 19 (n/cm 2, DNE)-1

= 0.20 x 10-19 (n/cm2 , equivalent fission flu. ace for damage in graphite)-1

= 0.25 x 10-19 (n/cm2 E > 0.18 Mev, HTGR)-1 .

6.3. STEADY STATE CREEP The experimental data reviewed in Subsection 5.2 lead to the following conclusions about steady-state creep:

1. Creep rates in tension are about 25% higher than creep rates in compression. .

2. At low fluences the creep rate is inversely proportional to the ,

unirradiated Young's modulus.

3. There is no conclusive evidence for a flux-dependent creep coefficient.

4. The best representation of the temperature dependence of the creep coefficient in near-isotropic graphites such as H-451 is the UKAEA line given by Eq. 5.

5. The change in creep coefficient with neutron fluence correlates with the change in Young's modulus according to Eq. 7.

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o t

Based on these conclusions, the following expression for the steady-state creep strain, es, is reconnnended:

T < 650*C : -=

EE o

T) '

(14)

T > 650.C : "S " oE* [c + d(T - 650)2.6) '

dy E E(y,T) o where T = irradiation temperature (*C),

y = neutron fluence (n/cm 2),

o = applied stress, Eo = the unirradiated value of Young's modulus, E(y,T) = the value of Young's modulus after irradiation to a fluence y at a temperature T, E* = the " plateau" value of Young's modulus at a fluence of about 1 x 1021 n/cm2 , DNE (1.8 x 1021 n/cm2 , equivalent fission fluence, or 1.4 x 1021 n/cm2 , E > 0.18 MeV, HTGR).

Stress and Young's modulus must be expressed in the same units. Values for e and d are listed in Table 3 for tension and compression, and for various fluence units. Equation 14 can be assumed valid at temperatures between 300* and 1100*C, and for total creep strains up to 2%.

6.4. TRANSVERSE STPAIN RATIO The recommended value for the transverse creep strain, ci, can be calculated from Eq. 8:

c1 = -cll (0.3 + 5 cll) ,

where cll 1s the longitudinal creep strain.

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TABLE 3 Vt. LUES FOR STEADY-STATE CREEP PARAMETERS (in Eq. 14)

Stress Parameter Value Direction Parameter Fluence Units (n/cm2 )-1 Tension e Dido Nickel Equivalent (DNE) 2.6 x 10-21 Equivalent Fission Fluence 1.5 x 10-21 for Damage in Graphite (EFFDG)

E > 0.18 MeV, HTGR spectrum 1.8 x 10-21 d DNE 7.8 x 10-28 EFFDG 4.4 x 10-28 E > 0.18 MeV, RTGR ~5.5 x 10-28 Compression e DNE 2.0 x 10-21 EFFGD 1.2 x 10-21 E > 0.18 MeV, HTGR 1.4 x 10-21 d DNE 6.2 x 10-28 EFFGD 3.5 x 10-28 E > 0.18 MeV, HTGR 4.4 x 10-28 64

..o 6.5. EFFECT OF CREEP STRAIN ON PHYSICAL PROPERTIES The thermal expansivity (a), Young's modulus (E), and Poisson's ratio (v) of graphite subjected to a creep strain will differ slightly from those of aa unstressed companion at the same irradiation conditions. The relative difference in property can be estimated from Eqs. 9 through 12. For near-isotropic graphites (including grade H-451) the following expressions apply:

a g" = (1 - 18 c,) ,

o E

dE = (1 + 3 ec) ,

I v

f=(1+30c) o where cc is the creep strain (pos'itive for tensile, negative for compres-sive). The subscripts e and o respectively indicate a creep specimen and an unstressed specimen irradiated under the same conditions. For needle coke graphites (such as grade H-327) the expression for thermal expansivity is different:

l a

c g- = (1 - 30 cc)

• l The tensile strength and rate of irradiation-induced dimensional change can be assumed to be unaffected by creep strain.

65

O

7. REFERENCES

1. Price, R. J., "Ra' view of Irradiation-Induced Creep in Graphite under HTGR Conditions," General Atomic Report GA- 12332, November 1, 1972.

2. Measurement of Irradiation-Enhanced Creep in Nuclear Materials, (Proc.

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M. R. Cundy, P. Von der Hardt, and R. H. Loelgen), North Holland Publishing Company, Amsterdam, 1977. (Also published in J. Nucl.

Mater., 65, 1977.)

3. Kelly, B. T., and J. E. Brocklehurst, " Analysis of Irradiation Creep in Reactor Graphite," Proc. Third Conference on Industrial Carbons and Graphite, Society of Chemical Industry, London, 1971, p. 363.

4. Kelly, B. T.,- and A. J. E. Foreman, "The Theory of Irradiation Creep in Reactor Graphite - The Dislocation Pinning-Unpinning Model," Carbon, _

12, 151 (1974).

5. Kelly, B. T., and J. E. Brocklehurst, "UKAEA Reactor Group Studies of l

Irradiation-Induced Creep in Graphite," J. Nucl. Mater., 65, 79

(1977).

l I 6. Morgan, W. C., " Neutron Fluence and Atomic Displacement Rates for Graphite Irradiations," Nucl. Technol., 21, 50 (1974).

7. Roberts, A. C., and A. H. Cottrell, " Creep of Alpha Uranium during Irradiation with Neutrons," Phil. Mag., 1, 711 (1956).

8. Brocklehurst, J. E., "The Irradiation Induced Creep of Graphite under Accelerated Damage Produced by Boron Doping," Carbon, 13, 421 (1975).

9. Cords, H., R. Zimmermann, and G. Kleist, "Model Analysis of Irradiation-Induced Creep Experiments," Extended Abstrcets of the 14th

! Biennial Conference on Carbon, p. 455 (American Carbon Society, 1979).

j 10. Cords, H. , and R. Zimmermann, "A Model for Irradiation Induced Changes in Graphite Material Properties," Proc. 5th London International Carbon and Graphite Conference, v. II, Society of Chemical Industry, London, l 1978, p. 918.

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11. Veringa, H. J., and R. Blackstone, "Righ Temperature Irradiation-Enhanced Creep in Graphites for HTR Applications," Extended Abstracts of the 12th Biennial Conference on Carbon, p.143 ( American Carbon Society, 1975).

12. Veringa, H. J. , and R. Blackstone, "The Irradiation Creep in Reactor Graphites for HTR Applications," Carbon, 14, 279 (1976).

13. Veringa, H. J., "The Irradiation-Induced Creep in Graphites for HTR Applications," Carbon, 76, p. 322 (Deutsche Keramische Gesellschaft, 1976).

14. Blackstone, R., " Radiation Creep in Graphite: An Introduction,"

J. Nucl. Mater., 65, 72 (1977).

15. Blackstone, R., L. W. Graham, and M. R. Everett, "Eigh Temperature Radiation Induced Creep in Graphite," Dragon Project Report D.P. 665, 1969.

16. Kleist, G., et al., " Continuously Measured Irradiation Creep Strain of Two Reactor Grade Graphites," Carbon, 76, p. 345 (Deutsche Keramische Gesellschaft, 1976).

17. Masson, M. , " Graphite High Temperature Creep Rigs," J. Nucl. Mater. ,

65, 142 (1977).

18. Jouquet, G. , G. Kleist, and H. Veringa, " Review of a Test Program on Irradiation Creep of Graphites and Systemization of Results," J. Nucl.

l Mater., 65, 86 (1977).

19. Jouquet, G., et al., " Continuously Measured Irradiation Creep Strain of Two Reactor Graphites," High Temperatures-High Pressures, 9, 151 l

(1977).

20. Hansen, H., R. Lolgen and M. Cundy, " Uniaxial Tensile Graphite Creep l Capsules with Continuous Strain Registration," J. Nucl. Mater., 65,148 (1977).

21. Veringa, H., and M. R. Cundy, " Irradiation Creep and Its Flux l Dependence on Near Isotropic Graphite at 850*C," Extended Abstracts of the 13th Biennial Conference on Carbon, p. 344 (American Carbon Society, 1977).

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.b.

1 i

22. O'Connor, M. F., et al., "FRG/US Cooperation on the Characterization of Reactor Graphites," Carbon, 80, p. 586 (Deutsche Keramische Gesellschaft, 1980).

23. Senn, R. L., et al., " Design, Operation, and Initial Results from a Series of Graphite Creep Irradiacion Experiments," J. Nucl. Mater., 65, 96 (1977).

24. Senn, R. L. , et al., " Design and Operation of a Graphite Creep Irradiation Experiment," Extended Abstracts of the 13th Biennial Conference on Carbon, p. 340 (American Carbon Society, 1977).

25. Kennedy, C. R. , W. H. Cook, and W. P. Eatherly, "Results of Irradiation Creep Testing Graphite at 900*C," ibid., p. 342.

26. Senn, R. L. , and J. A. Conlin, " Operation and Control of the Second of a Series of Graphite Creep Irradiation. Experiments," Extended Abstracts of the 14th Biennial Conference on Cafbon, p. 451 (American Carbon Society, 1979).

27. Kennedy, C. R., and W. P. Estherly, "Results of the 600*C Compressive .

, Creep Irradiation Experiment," ibid., p. 453.

28. Kennedy, C. R. , W. P. Eatherly, and R. L. Senn, " Compressive Creep Characteristics of Graphite under Irradiation," presented at the 33rd Pacific Coast Regional Meeting of the American Ceramic Society, San Francisco, Oct. 26-29, 1980.

29. Lolgen, R. , and F. Mason, "Reloadable Graphite Creep Facility for

Tensile or Compressive Experiments," J. Nucl. Mater., 65, 131 (1977).

l 30. Cundy, M. R., et al., " Irradiation Creep in Graphite at 500*C," Proc.

5th London International Carbon and Graphite Conference, II, Society of l

Chemical Industry, 1978, p. 959.

l 31. Kleist, G., M. F. O'Connor, and M. R. Cundy, "High Fluence Graphite Creep Experiments Relevant for the Pebble Bed HIR," Extended Abstracts of the 14th Biennial Conference on Carbon, p. 457 (American Carbon Society, 1979).

32. Kleist, G., and M. F. O'Connor, " Irradiation Creep Performance of Graphite Relevant for Pebble Bed HTRs," Proc. Specialists Meeting on Mechanical Behavior of Graphite for HTRs, Gif-sur-Yvet':e. France. June 11-13,1979, p.103 (IAEA Report IWGHTR/3,1980) .

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33. Cundy, M. R., M. F. O'Connor, and G. Kleist, "High Fluence Creep Behavior of Near Isotropic ritch Coke Graphite,* Carbon, 80, p. 569 ,

(Deutsche Keramische Gesellschaft, 1980).

34. Manzel, R., M. R. Everett, and L. W. Graham, "A High Temperature Graphite Irradiation Creep Experiment in the Dragon Reactor," Extended Abstracts of the 10th Biennial Conference on Carbon, p. 178 (American Carbon Committee, 1971).

35. Manzel, R., M. R. Everett, and L. W. Graham, "A Righ Temperature Ctaphite Irradiation Creep Experiment in the Dragon Reactor," Dragon Project Report DP-752, 1971.

36. Brocklehurst, J. E. , and R. G. Brown, " Constant Stress Irradiation Creep Experiments on Graphite in BR-2," Carbon, 7, 487 (1969).

37. Perks, A. J., and J. H. W. Simmons, " Dimensional Changes and Radiation Creep of Graphite at Very High Doses," Carbon, 4, 85 (1966). ,

38. Gray, W. J., " Constant Stress Irradiation-Induced Compressive Creep of Graphite at High Fluences," Carbon, 11, 383 (1973).

39. Gray, B. S., et al., "The Irradiation-Induced Plasticity of Graphite under Constant Stress," Carbon, 5,, 173 (1967).

l l .

l i

l l

l l

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. _ _ , _ _ _ .