Irradiation-induced dimensional changes and creep of isotropic carbon

IRRADIATION-INDUCED DIMENSIONALA CHANGES AND CREEP OF ISOTROPIC CARBON J. L. KAAE and J. C. BOKROS Gulf General Atomic Incorporated, P.O. Box 608, San Diego, Calif. 02112, I!.S.A (Kcceiued

23

April

1970)

Abstract-This paper describes an investigation of the dimensional behavior of unrestrained and spherically ,restrained isotropic carbons deposited at both high temperatures (> 1500°C; HTI carbons) and low temperatures (< 1500°C; LTI carbons) during irradiation at 600”, lOOo”, and 1250°C to fast-neutron fluences near 2 X 10” n/cm” (E > 0.18 MeV). The investigation covered, in particular, the effect of the initial density on the unrestrained dimensional changes and on the total strain accommodated without fracture in the spherically restrained specimens. For isotropic carbons (Bacon anisotropy factor < 1 .I), the unrestrained dimensional changes were primarily those due to irradiation-induced densification, and the strain accommodated consisted mostly of irradiationinduced creep strain. The largest dimensional changes and highest total strains accommodated were in low-density carbons. At 1000°C the accommodated strain rates were 0.04 per 10” n/cm2 and 0.05 per 10“’ n/cm2 for LTI and HTI carbons, respectively. At 600°C the respective accommodated strain rates were 0+28 per 10” n/cm’ and OGk’j per 10zl n/cm”. At 1250°C both an upper and a lower limit on the density of the restrained LTI carbons that survived irradiation were observed. The lower density limit apparently revealed the maximum densification strain rate that can be tolerated. The existence of the upper density limit is discussed. 1. INTRODUCTION A

variety

of

high-temperature

graphite

reactors currently in operation or under construction use carbon-coated fuel particles [l]. In reactor service the carbon coatings have been found to change dimensions and to creep due to fast-neutron irradiation [2,3]. In particular, the dimensional changes are a complex function of both the structure of the carbon and the irradiation conditions [3]. Irradiation-induced creep also probably depends on structure, but the dependence is not yet known. Because the dimensional changes are considerably smaller in isotropic carbons than in anisotropic carbons, the former have been generally adopted for use as fuel coating materials. At low fluences, the dimensional changes that occur in isotropic carbons are the result of irradiation-induced densification which is

isotropic and first order with respect to the density defect[4). At high fluences, and especially at high-irradiation temperatures, the behavior changes. The densification at first departs from first-order kinetics and then ceases, and finally the carbons expand. Simultaneously, the lineal changes accelerate and become anisotropic. This behavior has been described in Ref. [5]; an interpretation has been given in Ref. [6]. For illustrative purposes, data from Refs. [5] and [fil for irradiations at 1200”-1250°C are plotted in Fig. 1. Although the strains accurnmulated in particle coatings due to the irradiationinduced dimensional changes are relieved somewhat by irradiation-induced creep, in some coating designs they can lead to high stresses during reactor operation [7- 10 I. This is particularly true for designs that

J.

1.. KAAE

and J. C. BOKROS

the effect of density on the behavior of unrestrained and totally restrained specimens during irradiation. In particular, the low-density limit below which carbons fracture due to the densification strains was sought. Isotropic carbons deposited at temperatures above about 1500°C (HTI carbons) and those deposited at temperatures below 1500°C (LTI carbons) were both considered.

-600

4. EXPERIMENTAL

-.

-40

‘.

II

2I

3I

Fast-neutron

4I

5I fluence,

6,

7I

8I

11P. 91

IO

IO"n/cm’

Fig. 1. Length change vs. fluence (E > 0.18 MeV) for a low-density and high-density isotropic (BAF < 1.1) carbon irradiated at 1200”-1250°C (data from Refs. [5] and [6]. employ a silicon carbide barrier layer, which provides a nearly unyielding support. For such designs and for low-density carbons, the data in Fig. 1 indicate that the stresses that arise from the circumferential shrinkage of the coating reach their maximum value early in life. For high-density carbons, the densification strains are substantially lower early in life. At high fluences, however, the accelerations in the dimensional changes become large. Consequently, for highdensity carbons the stresses generated by the dimensional changes become large late in life. The effect of the structure of isotropic carbons on irradiation-induced creep is not known. If creep does not depend on structure, the above observations suggest that the choice of a low-density carbon which just survives the stresses generated by the initial densification will lead to the lowest possible coating stresses late in life and thus prolong the life of the coating. If creep does depend on structure, or if restraint affects the subsequent dimensional changes, the selection of the optimum carbon for particle coatings could be more complex. The purpose of this study was to determine

The carbon specimens used in this study were prepared by depositing carbon in a fluidized bed on both small graphite disks and &in. sapphire spheres in the same deposition run. Small strips of carbon were removed from disks, characterized by their density, crystallite size (L,.), and Bacon anisotropy factor (BAF), and then prepared for irradiation as unrestrained strips using methods that have been reported previously [4]. The density of the carbon on the spheres was obtained by cracking the coating off one of the spheres from a given deposition run, and determining the density by the usual sink-float method. This density agreed closely with the density of the carbon deposited on the disks in the same coating run. It was assumed that the coatings on the spheres also had the same crystallite size and BAF as the coatings on the disks. The deposition conditions and structural parameters for each carbon irradiated are listed in Table 1. All LTI carbons were deposited at < 1500°C from propane; all except one HTI carbon were from methane. The irradiations were conducted in the Engineering Test Reactor. The temperatures were measured with thermocouples, and fast-neutron fluences (E > 0.18 MeV) were obtained from analysis of nickel and iron flux wires. Details of the design and operation of the irradiation capsule have been reported [ 111. The irradiation conditions are listed in Table 2. In each irradiation experiment, unrestrained strips of carbon that had been

IRR/ZDIAl‘ION-ISDC(:~D Table

1. Deposition

Coating run SO.

4174-105 4174-109 4174-151 4344-13 4344-5 4174-95 4174-143 4344-2 1 4174-101 4344-15 4174-111 4344- 17 4174-117 4174-129 4174-137 4344-7 4174-141 4253-63 4033-125 4174-121 4174-127

DIILIENSION:\l.

CH.L\N(:E:S

conditions and structural parameters the specimens irracliated

I I3

characterizing

Deposition conditions Structural parameters Hydrocarbon in He (‘%,) __-_ L,. (:al-bon Ljensity Temp. (g/cm”) BAF” (:\) ‘)Il” ("C) CH, C,Hx 15u0 1450 1450 1400 1400 I450 1400 1375 1400 1350 1400

11.50 1koo 1600 1700 1600 1700 1HO0 1800 1800 1900

-. 20 15 20 10 20 15 20 20

30

l,i’i

I .I0

1.TI

30

I .T,:i

30 4;) ‘55

1 .i:i 1a? I.65 I alibi 1 .(;!I I ,il 1% 1 .HL’ 1.x.5 I .xX 1 .fi!) I.ll-ld(i I .:‘,i 1 60 I G? 1 66 1.67 I .‘i(i 1.HH

I .o’; I .oi I .()!I I ai 1 .0x I.13 I a!) 1 ai I .lO I IO I ,lO I .O!l l.lT 1.18 1.18 1 .:iv

1:1-l I>l‘I 1.‘I‘1 1:1-I 1 .TI 1.‘I-1 I.l‘I I.FI.I I.-I‘1 1.1‘1 I.‘I‘I HTI HI‘1 H’l’l IH~I‘I

1.0;)

HI;.I HI.1 H.1‘1 11’1‘1

40 30 40 30 40 ‘r 3,, ii “0

1.Ol 1.10 1.07

“Bacon anisotropy facto]. [ 121. “The B.4F of this carbon is too high to be desc-Abed as isotropic. Table 2. Irradiation

Cell No. 1 2 2’1‘ 3 3

Irradiation temp.

(T)~

conditions

F,ist fluence” (E y 0.1X MeV) (10” n/cm*)

600 1000 I ‘,.50 Go0 6.W

“The uncertainties in temperature are estimated to he t 75°C. “Tie uncertainties in fluence include a systematic error of about 15 per cent due to uncertainties in the cross section of the dosimetry wires and an additional unknown random error due to countilig errors, burnout, and flux distribution across sl)ecimcn the chamber.

removed along

from

with

spheres.

The

density

the

the

disks

methods

carbon

used

strips

dimensional

sapphire

rods

due

was measured

to that used before 3. RESULTS

to the of

as

measured on a toolmakers’ density of the carbon on irradiation

of the

[4 1. The uncoated

controls

microscope. the spheres in

a

the un-

irradia-

previously

changes

employed

sapphire

to measure

changes

tions have been described small

irradiated

coated

and dimensional

restrained

were

companion

manner

were The af’ier similar

irradiation. AND

DISCUSSION

3. I Unrestrained specimms The postirradiation densities pr of unrestrained specimens are plotted in Figs. !!(;I). 2(b), and 2(c) as a function of the preirratli:~tion densities p,, for irradiations at 600” and

J. L. KAAE and J. C. BOKROS

114

1000°C. At 1000°C the densification rate of both the HTI and LTI carbons is consistent with first-order kinetics. At 600°C the densification of the HTI carbons is also consistent with first-order kinetics, but that of the LTI carbons is not. This is apparent from the fact that an extrapolation of the data for the LTI carbons does not intersect the required point p,, = pf = 2.22 g/cm3. An interesting feature of the data in Fig. 2

I4

I.5

l-6

I.7 Original

I.8 density,

I,9

2.0

2-l

g/cm3

Fig. 2(c). Fig. 2(a-c). Postirradiation density vs. preirradiation density for carbons irradiated at (a) 600°C to 2.0 x 10zl n/cm2, (b) 1000°C to 2.1 X 10zl n/cm2, and (c) 1000°C to 2.3 X 10zl n/cm2.

15 14

I

I

I

I

I

I

I

I.5

I.6

I.7

I-6

I.9

20

2 I

Original

density

2.2

, g/cm3

Fig. 2(a).

1.5L 1.4

I

I

I

I

I

I

I

1.5

I.6

I.7

18

I.9

2.0

2.1

Original

density

, g/cm’

Fig. 2(b).

I

2.2

is that at 600°C the LTI carbons densify at a higher rate than the HTI carbons, but at 1000°C the HTI carbons densify at a slightly higher rate. The latter observation is somewhat surprising since all previous data that relate lineal dimensional changes to crystallite size suggest that the materials with the smaller crystallite sizes would be more unstable than materials with the larger crystallite sizes [13]. The effect of crystallite size in the ran e being considered here (L, from 25 to 100 1 ) would be expected to be most pronounced for irradiations near 600°C which is in accord with the above observations, but the slightly higher densification rate for HTI carbons at 1000°C is pointed out without explanation. The densifications are more advanced in Fig. 2(b) than in Fig. 2(c) even though both irradiation temperatures are reported as 1000°C and the reported fluence is lower for the data in Fig. 2(c) than for the data in Fig. 2(b). Such variations are due to uncertainties in either the temperature or the exposure, or both.

.2

IRRADIAI‘ION-INDU<:ED

DIMENSIONAL

Densification constants Kd calculated from the slopes of the pr vs. p,, plots are listed in Table 3. Comparison of these data for 1000°C with those plotted in Fig. 55 of Ref. [14] for carbons with I,,, in the range loo-180 A shows that the corresponding values in Table 3 are Aside from the usual substantially higher. Table 3. Densification

Temp. (“(J 600 1000 1000

(X

Fluence 102’ n/cm’)

(:HAN(;ES

II5

premise that, at temperatures near lOOO”C, kd is independent of I>,. in the range I,,. = 25-170 A, and that the low values reported for the high-density carbons (p,, > 2.0 g/cm”) in Table 4 of Ref. [15] are probably in error because of departures from first-order kinetics. At about 1000°C the kd value is

constants for HTI and LTI carbons

HTI carbons (43 x G L,. S 100 A) [X 10,” (n/cm”)--‘]

LTI carbons (28Ai&S33ii) [X 10? (n/cm”)-‘]

1.9 5.7 4.1

5.0 3.6

2.0 2.1 2.3

uncertainties in the true irradiation temperature and fluence, these discrepancies have been attributed to two possible sources [15]. One possibility is that kd depends on L,. Since the data in Table 3 do not indicate a dependence on L, for L, < 100 A, the dependence of kd on L,, if it exists, must be important only when L, is greater than about 100 A. An alternate possibility is that the apparent dependence of kd on L, may result when the densification departs from the firstorder approximation. The departure would become apparent first for those carbons with the highest density. Because of the correlation between the L, parameter and the density (for HTI carbons), an apparent dependence on the L, parameter might result. An example of the latter behavior in an advanced stage of departure from firstorder behavior has been given in Fig. 6(b) of Ref. [3]. The data in this figure for a fluence of 0.7 X 10zl n/cm2 show precise first-order behavior over the full range of densities, 1.55 to 2.15 g/cm3 (L, = 50-170 A). The kd corresponding to the data in Fig. 6(b) of Ref. [3] for 900°C is 2*!1 x 1O-22 (n/cm2)-‘. The present data, together with those from Fig. 6(b) of- Ref. [3] for YOO”C, support the

4.3 x lo-*’ (n/cm”)-’ with an uncertainty of about & 1.4 X 10-** (n/cm”)-‘. The large uncertainty is thought to be due to uncertainties in both the fluence and the irradiation temperature. The linear dimensional changes that correspond to the density changes plotted in Fig. 2 are plotted in Fig. 3. At 6OOY: the I.TI carbons are less stable than HTI carbons and, in addition, the dimensional changes in the LTI carbons caused by the irradiation are more anisotropic than those in the HTI carbons. At 1000°C [Figs. 3(b) and 3(c)] the dimensional behaviors of HTI and 1,TI carbons are not significantly different. ‘l‘he data for the slightly anisotropic HTI carbons (structures 4174-219. 4174-137, and 4174141) are not included on Figs. 3(b) and 3(c). These carbons are much less stable than the isotropic (BAF < 1.1) carbons. For example, the data for the carbon with a BAF of 1.Y:i and a density of 1.63 g/cm” show that at 1000°C and 2.1 X 10zl n/cm2, the perpendcular and parallel shrinkages are -1.8 1)~‘ cent and -10 per cent respectively. It is interesting to note that the single HTI carbon deposited from propane (rather than methane) behaved dimensionally like the other HTI carbons. This is in accord with the

116

J. I.. KAAE

common

assumption

behavior

of all carbons

structure, preferred

that

the

depends

i.e. their orientation,

and

J. (:. HOKROS

irradiation

2

only on their

density, degree of and crystalline per-

0

0

-2

Direction

0”

-4

x

blJ

-6

+ S c -E

-IC

-n

74

I

I

I

I

l-5

l-6

I.7

I.6

Original

density

-Ii

I.9

r

, g/cm3

I

I

I

I

15

I.6

l-7

l-6

Original

demty

Fig. 3(a).

3

, g/cm3

Fig. 3(c). Fig. 3(a-c). Length change vs. preirradiation density for carbons irradiated at (a) 600°C and to 241~ lo*’ n/cm*, (b) 1000°C and to 2.1 X 1021 n/cm*, and (c) 1000°C and to 2.3 X 102’ n/cm’.

fection.*

This

substantiated the

premise

dimensional

deposited

has

in a recent propane

of

carbons

structural

were

the

parameters

same,

the

were indistinguishable

LTI

and those deposited mixtures were

from acetylene-propane compared. It was reported the

further in which

behaviors

from

been

paper[l7]

that

as long

as

for the specimens

dimensional

behaviors

[17].

3.2 Restrained specimens The

carbon

coatings

on

the

sapphire

spheres can be treated as biaxially restrained without serious error since the coating thickness was small compared to the diameter and,

-141 I.4

I

I

I

I

1.5

1.6

I.7

I.8

Original

density,

Fig. 3(b).

g/cm2

*The I_,. parameter is most often quoted to characterize the crystalline perfection of a carbon. The ambiguity of this parameter as a measure of‘ crystalline perfection has been discussed [ 161.

IRRADIA?‘ION-INI)I!(:ED

thus, the radial stresses were small compared to the tangential stresses. For the same reason, the anisotropy that developed between the dimensional changes in the radial and tangential directions in some of the carbons can be neglected, and only the important tangential dimensional changes need be considered. The total accommodated strain in the carbon, Ed, c-an be written as

where qe = elastic strain in the carbon, E,, = creep strain in the carbon, Ed= parallel dimensional change in the carbon, E.~= dimensional change of the sapphire, and Ebb = preirradiation mismatch due to thermal expansion differences between the carbon and the sapphire. Measurements of uncoated sapphire rods employed as controls showed that at 650” and 1000°C the sapphire expanded 0.08 and 0.05 ‘I’able 4. Strains accommodated

DIMENSIONAl.

per cent, respectively. Since these values are small compared to the dimensional changes of the carbon, qs can be assumed to be zero. The mismatch strain (a gap) arises because the irradiation temperature is lower- than the deposition temperature. Values of eXI calculated from the coefficients of thermal expansion have been taken into account in the total accommodated strains reported below. At IOOOY:, these values were less than 6 per cent of the total strain. At 600”(;, they were less than about 20 per cent of’ the total strain. The total strains accommodated without fracture for all the specimens irradiated at 1000°C are listed in Table 4. Both specimens of the methane-derived carbon with an initial density of’ 1.(i3 g/cm” failed at < 0.097 total accommodated strain. These specimens, with a BAF ol‘ I-33, ex-perienced the largest dimensional change in the parallel direction of any of’ the methanederived carbons deposited above 1500”1:. Since, at least before irradiation, the elastic strains to fracture and the fracture stresses of all of the methane-derived IlTI carbons were similar [lS], this specimen il; exlwctect

iI1 spherically restrained

carbons irradiated

2.1 X 10”’ n/cm” (E > 0.18 MeVj

No. of’ specimens 1

‘) i !2 ‘) ‘)

Deposition temp. (“C) 1 GO0

1700 1800

1ioo

‘)

14.50 1400 1400 1400 137:i

” ‘)

1350 1GO

‘)

‘)

“Both specimens failed. *One specimen failed.

II7

C;H.lN(;ES

Hydrocarbon used in preparation

(-1)

BAF

Methane Methane Methane Methane Propane Propane Propane I’ropane Propane Propane Propane

33 63 HO 74 00 _. 30 3) 3I :10 30 30

I .I7

I

l.iH I.18 1-3

I4’i 1.(,!b 1*(Hi 1.13 I .O!f I.10 1 IO

;It lOOO”(1IO

118

J. L. KAAE and J. C. BOKROS

to have had the highest stress level in the coating. It is interesting to note, however, that the lowest density HTI carbon had nearly the same accommodated total strain and did not fracture. One LTI carbon specimen with an initial density of I.88 g/cm” failed at < O-040 total accommodated strain. An identical companion sample, however, did not fail. All of the other LTI samples with lower initial densities survived larger strains. Before irradiation the elastic strains to fracture of the LTI carbons were all similar[l9]. It is possible that the failure of the single highdensity sample was atypical, caused possibly by a flaw in the coating. On the other hand, as also suggested by the results for the methane-derived carbons deposited above 15OO”C, at an equivalent stress the highdensity carbons may creep at a slower rate than the low-density carbons, or possibly have a smaller strain contribution during the initial transient creep. It is cohcluded from the data in Table 4 that for id&ally spherical specimens that are shrinking due to irradiation at 1000°C onto an unyielding support, the density limit below which the low-fluence densification leads to fracture is less than 1*46g/cm” for HTI carbons and less than I.52 g/cm” for LTI carbons. All of the coatings on sapphire spheres irradiated at 650°C in cell 4 survived. These specimens were not accompanied by unrestrained strips in rhe same cell. Accordingly, the data from unrestrained specimens irradiated in cell 1 at 600°C to 2.0 X 10zl n/cm2 have been used as controls since the uncertainties in temperature and fluence make the two irradiation histories indistinguishable. The strains accommodated in these specimens ranged from O-043 to 0.027 for the methane-derived carbons, with densities of I.46 g/cm3 and 1.63 g/cm3, respectively, and from 0.051 to 0.025 for the LTI carbons, with densities of 1.53 g/cm3 and I.88 g/cm3, respectively. For the 650°C irradiation, the low-density limit imposed by high densi-

fication strains was below I.46 g/cm” for HTI specimens and below I.53 g/cm3 for LTI specimens. Seven carbon-coated spheres were also irradiated in a special high-temperature hole of cell 2 (labeled 2T in Table 2). These specimens were irradiated at 1250°C to a fluence of 2.3 X 10zl n/cm”. Because of space restrictions, no unrestrained specimens could be included in this cell. The results are listed in Table 5. The data are particularly interesting Table 5. Results from spherically restrained LTI carbons irradiated at 1250°C to 2.3 X 10zl n/cm2 (E > 0.18 MeV) Density (g/cm”) 1.53 1.62 1.65 1.69 1.71 1.82 1.88

BAF 1.07 1.09 1.06 1.13 1.09 1.10 1.10

No. of specimens

Behavior

1 1 1 1 1 1 1

Fractured Fractured Fractured Survived Survived Fractured Fractured

because for a fluence of 2.3 X 10zl nvt they bracket an optimum density for LTI carbons such that, when restrained on an unyielding support, the coatings did not fracture during irradiation. The lower density limit undoubtedly corresponds to that density below which densification strains cause fracture. The high-density limit is probably due to an in dimensional-change rate acceleration with fluence corresponding to that which has been reported for HTI carbons. (See Fig. 11 of Ref. [5] for HTI carbons.) Relevant data at 1250°C for LTI carbons do not exist, but it is possible that, in parallel with the HTI carbons, the high-density LTI carbons have entered a region of increasing dimensionalchange rate. Notice that if this is the case the high-density limit is peculiar only to the present irradiation and at a given irradiation temperature will be expected to decrease with increasing fluence. Another possible explana-

IRRADIATION-INDUCED

tion of the high-density limit is that, for an equivalent stress, the low-density carbons may creep at a faster rate than the highdensity carbons. The total strains accommodated at 1000°C (corrected for lJT) are plotted as a function of fluence in Fig. 4 for LTI and HTI carbons, along with data from Ref. [S]. In Fig. 5 the total strains accommodated ar 650°C (corrected for +) are plotted as a function of fluence; some previously unpublished data [20] are included. The strains accommodated per unit fluence iu the present study are substantially higher than those attained previously. It is thought that the strains were higher because the nearly perfect sapphire spheres do not have the stress-concentrating features, such as corners, fiducial holes, and identifying marks, that were present in the previously used graphite disks. The maximum accommodated strain rates at 1000°C were 0.05 per lo”’ n/cm? and 0.04 per 10zl n/cm’ for HTI and LTI carbons, respectively. The elastic strain component can represent no more t.han about 10 per cent of these values [2, 181. The maximum accommodated strain rates at 650°C were 0.025 per lo” n/cm2 and 0.028 per lo”’ n/cm” for HTI and LTI carbons, respectively. Elastic strain represents no more than 20 per cent of these values. The postirradiation densities of the LTI and HTI carbons that survived irradiation on the sapphire spheres are compared with the postirradiation densities of unrestrained controls in Figs. 6 and 7 for the irradiation temperatures of 1000” and 65O”C, respectively. At both temperatures, restraint reduced the densification of the carbon. If the creep constants of the carbon are isotropic, the above observation indicates that Poissou’s ratio in creep, F,., must be less than 0.5. A previous calculation of this parameter for some carbons restrained on graphite disks produced values of about 0.4 for a considerable range of creep strain [21]. Due to the unknown elastic strain component, an

DII\IENSIONAL>

(:HANGES

119

12.

LTI, A

Ok

0

900”-IOOO”C

Present

I

I

I

I

2

3

Fast -neutron

fluence

work

1

4

, IO” n/cm’

Fig. 4(a)

HTI ,900’=‘- 1000°C o Present work . Ret C31

Fast -neutron

fluence , 102’ n/cm2

Fig. 4(b). Fig. 4(a, b). Total strain accommodated without fracture during irradiation at 900”-1000°C to various tluences: (a) LTI carbons, and (b) HTI caroons.

.J. I.. KAAE and J. C. BOKROS

LTI -500°-700°C A Present work . Ref C203

2 a % per

5

IO”

n/cm”

I A

: j

0

2

I

4

3

Fast-neutron

fluence

5

6

l-4

7

,

,

1.5

I.6

, IO” n/cd

,

t-7 Original

,

I-B density,

,

,

,

I.9

20

2-l

2.0

2.1

: 2

g/cm’

Fig. 6(a).

Fig. 5(a).

HTI - 5OO”- 700°C 0 Present work l Ref. C3I 52.5%

per

102’ n/cm’ \I6

4-

/

8

3-

.

.

‘9 ,I

. .

.

/

. .

.Q

. 8 .

. 16-

. . 0, 0

2 Fast-neutron

4

3 fluence

, IO”

5

6

n/m*

_I 1‘4

13

lb

I.7

Original

Fig. 5(b). Fig. 5(a, b). Total strain accommodated fracture during irradiation at 650°C: carbons and (b) HTI carbons.

7

1.9 I.8 densaty , g/cm3

22

Fig. 6(b). without (a) LTI

exact calculation of pe from the present results is not possible. However, for the large values of total accommodated strain where the creep strain was relatively large compared to the elastic fracture strain, values of p, ranging from 0.26 to 0.40 were calculated when the total strain was assumed equal to the creep strain.

vg. 6(a, b). Postirradiation density vs. preirradianon density for unrestrained control samples and carbon coatings restrained on sapphire spheres during irradiation. Irradiated at 1000°C to 2.1 X 10zl n/cm’: (a) LTI carbons, and (b) HTI carbons. 4. CONCLUSIONS

Irradiation of HTI and LTI carbons to fast-neutron fluences near 2 X 10zl n/cm2 (E > 0.18 MeV) at temperatures near 600°C confirm earlier observations that the irradia-

IRRADIATION-INI>ll<:FU

.

HTI restrained

A

LTI

restraned

DI!vfESSIONAI.

I”1

(:H.AS(;ES

support due to densification at low fluences causes fracture is < 1.5 g/cm:%for both Ll‘I and HTI carbons. At 1250°C the corresponding limit for LTI carbons is between 1 G5 and 1.70 g/cm 3. An upper density limit of 1.72-I .X3 g/cm3 was also observed for 1,TI carbons at 1250°C and a fluence of 2.3 X 10”’ nvt. This

may be due to an acceleration

dimensional

change

rate

in

of the

which

case

it

pertains only to these irradiation conditions. The results show that HTI carbons deposited propane

above

1500°C from

behave

similarly

either

methane

as long

ot

as their

and crystallite si/es anisotropies, are the same. Comparison of the strains realized in and unrestrained specimens restrained shows that Poisson’s ratio for irradiation creep is about 0.35. ‘I‘he lineal dimensional changes caused in the length of sapphire rod by fast-neutron irradiation (2 X 102’ n/cm”; E: > 0.18 MeV) at 600” and 1000°C were OW and 0.05 per cent respectively. densities,

Fig. 7. Postirradiation density vs. preirradiation density for spherically restrained specimens irradiated at 650°C to 2.0 X lo” n/cm2. The dashed lines are for unrestrained specimens and are i‘rom Fig. ‘L(a). All of the unrestrained specimens irradiated at fi5O”Csurvived the irradiation.

tion-induced dimensional changes are more rapid for LTI than for HTI carbons. For lowdensity specimens of both LTI and HTI carbons restrained on sapphire spheres, strains in excess of 0.04 can be accommodated (primarily by irradiation creep), and strain rates at least as high as 0.025 per 102’ n/cm” can be sustained without fracture during irradiation at temperatures near 600°C. At irradiations near 1000°C to fluences near ‘1 X IO”’ n/cm2 (E > 0.18 MeV), the dimensional behavior of HTI and LTI carbons is nearly identical. Data from spherically restrained low-density specimens irradiated at 1000°C show that for LTI carbons, total strains at least as high as 0.08 and rates at least as high as 0.04 per 10”’ n/cm” can be accommodated without fracture; for lowdensity HTI carbons, corresponding values of 0.10 and 0~05 per 102* n/cm2 were determined. The results for irradiations at 600” and 1000°C indicate that the minimum density below which shrinkage onto an unyielding

- The authors thank M. H. Ellis, H. H. Evans, F. J. Gagnon, I,. J. Noble, and V. Slivenko for experimental asststance, and the Irradiations Group at (;ulf General Atomic for including the samples in the P23 irradiation. Also, the authors are indebted to D. W. Stevens for computational work and to R. J. Price for useful discussions. The work was supported in part hy the U.S. Atomic Enern Commission, (&tract AT(04-3)-167. Project Agreements 12 and 17, and in part by Gulf General Atomic.

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