- Email: [email protected]
The irradiation induced plasticity in graphite under constant stress
Carbon
1967, Vol. 5, pp. 173-180.
THE
Perpamon Press Ltd.
IRRADIATION
IN GRAPHITE B. S. GRAY,
Printed in Great Britain
INDUCED
UNDER
PLASTICITY
CONSTANT
J. E. BROCKLEHURST
STRESS
and A. A. McFARLANE
L;nited Kingdom Atomic Energy Authority, Reactor Materials Laboratory, Culcheth, Warrington, Lanes. (Hec&ed
17 March 1966; in revised form 4 August 1966)
Abstract-The irradiation creep behaviour of graphite has been studied in the reactor BR-2 at Mol, Belgium, up to fast neutron doses of 5 x lo?’ n.cm-” within the temperature range 300-500°C. Results are presented in the paper for graphites irradiated under constant uniaxial compressive and tensile loads. The graphites studied include the nxmal Pile Grade ‘A’ and a number of improved graphites at present being considered for future nuclear power reactors. It is shown that the presence of an applied stress greatly modifies the irradiation induced dimensional changes up to high doses and that the graphites are capable of absorbing large creep strains without failure. In addition it is found that the stress also modifies the thermal expansion coefficient of irradiated specimens.
1. INTRODUCTION
stressed control specimens included in each capsule together with the thermocouples and flux monitors. Figure l(b) shows the steel struts used to stress the specimen in tension using the external hydrostatic pressure. The operating temperature is achieved solely from the nuclear heating which can be as high as 18 W/g. The capsules are filled with a heliumneon gas mixture and for a given rate of heat generation the specimen temperature is determined by the heat transfer across the gap between the outer graphite sleeve and the wall of the bellows which is in contact with the coolant water at about 40°C. Capsules can, therefore, be designed to operate at the required temperature by choosing appropriate values of gas mixture and gas gap. For a given reactor power, the exact temperature is dependent on the control rod position. The capsules at the top and bottom of the rig show the largest temperature variations during a reactor cycle; the temperature of the top capsule rising and that of the bottom capsule falling as the control rods are withdrawn and the flux peak moves up the core. Table 1 summarises the temperature history of the specimens.
AN IMPORTANT property of any graphite intended for use as a reactor moderator is its ability to deform plastically under an applied stress in the presence of fast neutron irradiation. The rate of this creep determines the magnitude of the stress in the moderator due to the differential dimensional changes caused by flux and temperature gradients. The experiments to be described in this paper were constant stress experiments, both tensile and compressive, performed in the Belgian reactor BR-2 up to fast neutron doses of 5.0 x 10” n.cm-‘, at a nominal temperature of 41O”C, using normal Pile Grade ‘A’ graphite (P.G.A.) and a number of improved isotropic graphites.(‘*‘) 2. EXPERIMENTAL
METHODS
2.1 The irradiation experiment The apparatus developed for these experiments uses the 180 lb/in’ gauge pressure of the light water coolant to apply a compressive or tensile stress to the specimens.(3) To achieve this the specimens are sealed in stainless steel convoluted bellows capsules and an assembly of five capsules, suspended in line inside a support tube, is irradiated in a hollow fuel element. Figures ‘l(a) and (b) depict typical compressive and tensile specimen assemblies showing the unF
2.2 Determination of in-pile stress The load produced by the pressurisation bellows was determined experimentally. 173
of the
174
B. S. GRAY,
J. E. BROCKLEHURST
and A. A. McF~L~E
n
Thermocouples
S/S
n
Holes for thermocouples
canvuloted
bellows t0.005
in. wall
thickness)
Spacer
Cross
Stressed
section
specimen outer
sleeve
Control specunen
spacer
Flux
monitor
Specimen
w.-_----Gas
filling
assembly_
tube
FIG. l(a). Bellows assembly containing a graphite specimen under compressive load in a BR-2 creep rig.
The stainless steel bellows shown in Fig. 1 are approximately 3 in. long and have 42 convolutions for an overall capsule length of about 4 in. The total cross-sectional area including the convolutions is 0+X2 in2 and, excluding the convolutions, the area is 0.248 ir?. Standard stainless steel end caps were welded to one of the bellows units, one end cap containing a narrow tube through which the capsule was pressurised internally to gas pressures up to 200 lb/in’, see Fig. 2(a). A close fitting sleeve was placed around the bellows to prevent distortion. The differential pressure was plotted against the force exerted by the bellows as measured by a hydraulic load cell. Two sets of measurements were carried out in this way. The end cap containing the tube was then removed and an outer sleeve brazed to this end,
FIG. l(b). Diagram of tensile creep capsule.
Hestramnq tube to Gdewoys
prevent
(c)
inlerool
preesutisotibll
(bl
Solid bar to it pressure
External
pressurisotion
FIG. 2. Schematic diagram of apparatus for pressurising the bellows capsule and measuring the resulting load.
IRRADIATION
INDUCED
PLASTICITY
IN GRAPHITE
UNDER
CONSTANT
STRESS
175
TABLE 1. TEMPERATURE HISTORYOF CREEPSPECIMENS IN FIGS. 2 AND 3
$ Lpecimen
Compressive
Tensile
Fast neutron dose (n.cMs X 10mzo)
Graphite
Approximate* range of irradiation temperature T+R.T. (“C)
P.G.A. P.G.A. P.G.A. P.G.A. P.G.A. P.G.A. P.G.A. P.G.A. P.G.A.
L.14 L.14 L.14 L.14 L.141 L.14 L.14 L.14 oxidised
3.2 13.0 25.8 43.0 2.3 3.3 15.0 20.2 35.5
3201 30 350-400 450 -350 350-450 270& 70 3201 40 350-450 300-400 450-350
Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic
expt’l PI-l PI -1t PI-1 PI-l PI-l PI-2 PI--2t PI-2 PI-2 PI-5 PH-2 PH-3 PO-1
3.6 8.6 10-6 11-6 15.5 50.5 13.0 19.8 21.2 26.1 17-o 25.8 10.0 12.5
3303 20 300 -450 500-3.50 500-350 400* 20 420f 20 250-3.50 500-400 500-400 400% 20 450-350 450-350 450-350 300 -400
Isotropic Isotropic Isotropic
PI-4 PI-4 PH-3
23.0 24.0 33.5
300 -400 500-350 450-350
*Where a temperature range is quoted the first value is that at the beginning of a typical reactor cycle and the second that at the end of the cycle. iSpecimens
are cut parallel to the extrusion direction of the graphite except where indicated by t.
The designations PH. PI. PO refer to different isotropic materials and - 1, -2, generally atdifferent stages’of development.
leaving the other end of the bellows free, see Fig. 2(b). The bellows could then be pressurised externally by filling the interspace with gas, and the force exerted on a steel rod inserted in the bellows was transmitted to a hydraulic load cell. Three sets of measurements were carried out, the differential gas pressure (up to a maximum value of 400 lb/in2) being plotted against the load exerted by the bellows. In carrying out the measurements, the pressure as indicated by the gauge was set at predetermined values, and the corresponding load obtained using a hydraulic compression capsule. The compression capsule was connected to a 10 in. dia precision gauge reading up to 200 lb in 1 lb divi-
- 3 etc. refer to different blocks,
sions with an accuracy of LO.5 lb. The pressure gauge was a 5 in. dia Bourdon gauge reading up to 400 lb/in2 in divisions of 10 lb/in2 with an accuracy of f2 lb/in’. All five sets of results are in good agreement and give a linear relation between the differential pressure and the resulting load corresponding to an effective area of 0.316 in2. The stress levei in the experiment may therefore be calculated from the coolant pressure and specimen geometry. Except for the prototype rig, irradiated before BR-2 attained full power, the latter has been chosen to produce a stress in the range 800-1~0 lb/in’. For the first rig shorter specimens were used than for most of the later work and this allowed for
176
B. S. GRAY,
J. E. BROCKLEHURST
two specimens with stress levels differing by a factor of two in each capsule. For that rig only, several specimens were therefore irradiated at 400-500 lb/in2, but at irradiation temperatures somewhat lower (maximum 360°C) than in subsequent rigs. The results from this rig were used to optimise the heat transfer calculations for the later rigs. 2.3 Nfrutro?r dose ??waxrments Fast neutron doses were obtained from the activation of “Fe in the form of enriched (95% 54Fe) iron monitors, encapsulated in silica, in each capsule. The nuclear constants used are those determined by MARTIN and CLARE(~) based on a cross section of 107 mb for the reaction “*Ni (n,p)“Co in a DID0 hollow fuel element facility. The doses for each specimen are corrected for the axial variation down a rig. 2.4 Laboratory measurements thermal expansion and Young’s Length, modulus measurements were made on specimens and controls and the stress-strain behaviour of stressed specimens determined over the appropriate stress range. Normally length measurements were made using a Sigma comparator and slip gauges, but an optical comparison method had to be used for the tensile specimens which have fiduciary marks engraved on the gauge length. The accuracy of these measurements is &to*01 per cent better, depending on the specimen type. Thermal expansion measurements were made in a silica dilatometer with an accuracy of lo-’ deg C-r. After irradiation the thermal expansion coefficients for the gauge length of the tensile specimens were estimated by assuming that the irradiation induced changes of the coefficients of the ends of these specimens were comparable to those of the unstressed control specimens.
and A. A. McFARLANE
2.5 The calculation of creep strain For purposes of calculation the irradiation induced creep strain is here defined as the additional length change arising from the applied stress o, as measured at temperature in the stressed condition, and tensile stresses will be considered positive: L,=measured length of specimen at room temperature (R-T.) before irradiation; L =measured length of specimen at room temperature (R.T.) after irradiation. Considering a mean irradiation temperature (T+R.T.): Length of specimen
at start of irradiation
L’,=L*(l Length of specimen
+@kT+o/EJ at end of irradiation
L’=L(l The in-reactor
+aT++‘)
strain is
but for the unstressed
control specimen
$f=F+T 0
. Aa,
Hence the ‘creep strain’ is given by W --=Al’ I_ L6 I’,
AL Al L_-T-+(Ag-A~JT-; 0
0
(3)
Each of the four terms on the R.H.S. of equation (3) has a probable error of fO.01 per cent, hence the probable error in the creep strain is less than 0.02 per cent. 3. RESULTS
AND
DISCUSSION
For the P.G.A. and isotropic graphites Figs. 3 and 4 show the variation of ‘creep strain’ with dose up to a maximum of 5 x 102’n.cm-2 and normalised to a stress level of 900 lb/in2 assuming
Fost neutron dare, n cm-2
FIG. 3. Compressive creep strains for P G.A. ‘graphite. (Normalised to 900 lb/in-s).
IRRADIATION
INDUCED
PLASTICITY
IN GRAPHITE
UNDER
CONSTANT
.
STRESS
177
PC.2 I
b Pi 5-N I
I
0
v P1.4.N x RI.2.N
. .
.
k\
PH.S.//
+ PO.,.//
.5-
Compressive I 10
0
I 20
*\ 50x10~
40
30
Fast neutron dose,
n cm-2
FIG. 4. Creep strains for isotropic graphites. (Normalised to 900 lb/ine2).
a linear dependence on stress. All the isotropic graphites behave similarly, despite differing sources and temperature histories. After stress normalisation, the data from the prototype rig fall together in Figs. 3 and 4 irrespective of initial stress level confirming that, for the initial creep at least, a linear stress dependence is a reasonable assumption. In compression, Figs. 3 and 4 show a large primary creep followed by a period which may be represented by a linear dose dependence. The primary creep is not associated with the change in Young’s modulus on irradiation, this has been allowed for. The data are too imprecise to be sure that the secondary creep rates are linear and not decreasing or even leading up to a tertiary creep.
o-4r
0.3
-
/
8, 0 g
1 5
/ 0.2
----C
f 3,=
l
O.I-
!?G.A. perpendicular
-
5
$
+
Isotropic
RG.A. parallel
/
Initial
elastic
strain,
%
FIG. 5. Relation between linear creep and initial elastic strain.
However, Fig. 5 shows a correlation between the linear creep rates shown in Figs. 3 and 4 and the average initial elastic strain for each graphite type. The increase in creep rate with initial elastic strain is also demonstrated by the irradiation under stress of a parallel cut P.G.A. graphite specimen which had been previously oxidised radiolytically to 18 per cent weight loss as described by HAWKINS.c5) A creep strain of over 7Q per cent resulted from a dose of 3.5 x 1021 n.cmp2 under a stress of 870 lb/in2 for an initial elastic strain of 0.20 per cent by comparison with a creep strain of 0.6 per cent for 0.07 per cent elastic strain for unoxidised material. After the irradiation the specimen was intact but visibly deteriorating. These results show that the plastic and elastic deformation modes are closely related, perhaps through the stress distribution within the aggregate. Except for the oxidised specimen, the observed compressive strains are smaller than the fracture strain observed in laboratory tests of either irradiated or unirradiated materialc5-‘) even when the elastic strains are included. In tension, however, the total strains are significantly greater as has been reported previously.@-lo) Thus, strains to fracture of comparable material have been studied in a series of laboratory tests. Table 2 gives values of the tensile strength and strain to failure of a number of unirradiated specimens of improved isotropic graphites while other results in both tension and compression have been reported by TAYLOR et a1.c7) whose work includes a study of the effects of irradiation at 150°C. Figure 6 (unpublished work by GRAY and HALL(~‘) illustrates
some
tensile
data
for
unirradiated
178
B. S. GRAY, J. E. BROCKLEHURST
and A. A. McFARLANE
TABLE 2. THE UNIRRADIAW~ TENSILESTRENGTH AND TO FAILUNZ OF SOME INDIVIDUAL SPECIMENS OF THE
STRAIN
IMPROVED
ISOTROPIC
GRAPHITES
Ultimate tensile strength (lb/in*)
Strain to fracture (%)
PH2
1050 1520 1590 990
0.23 026 0.22 0.25
PH3
1510 1420 1780
o-14 0.15 0.16
PH4
2420 1800 2550 2450 2650 2360
O-26 0.28 O-36 0.28 o-34 o-41
PI4
1850 1560 1620 1780 1950 2070
o-19 0.16 0.21 o-22 0.25 0.28
2450 2170 2300 2300
o-35 0.29 0.36 O-29
PO1
1370 1450 1820
0.11 0.16 o-13
PP
1660 1850 1260
0.30 O-24 O-16
Graphite
PI6
Note: All specimens direction.
cut parallel to the extrusion
P.G.A. and Table 3 includes the results of tensile tests on P.G.A. irradiated at 250 and 350°C in DID0 and PLUTO at AERE Harwell. Figure 4 shows that the creep strains observed in tension and compression are comparable for the present experiment, but this could be a coincidence resulting from the limited dose range of the tensile data. Thus, extrapolation to 1000 lb/in’ of the low dose data reported by MORGAN(‘~’supports the existence of primary strains of the order of 0.1 per cent in compression, but other workers have reported much smaller values in tension.(s’12*13) There
is a difficulty
in comparing
present
results
Perpendicular to extrusion
0
L_, Ultimate
FIG. 6. The strength
1000
tensile strength,
Ib/inz
of unirradiated
P.G.A.
graphite.
with other data since the dose scales are very different and the primary creep is estimated by extrapolation of the secondary creep curve to zero dose. HESIUXTH(~‘) has estimated the magnitude of the primary creep, on the assumption that it is due to dislocation climb, to be similar to the initial elastic strain. KENNEDY(~)reports that the primary tensile creep is somewhat less than the elastic strain using the irradiated moduhts and JENKINS and STEPHEN report a similar value in torsion, while the present results in compression yield a large value. However, if the primary creep strain is lower in tension than in compression, as the combined data suggest, then the average secondary creep rate must be somewhat greater in tension to account for the data in Fig. 4. KENNEDY(~)reported a recovery equal in magnitude to his primary tensile creep on removal of the stress during an irradiation and a recovery of similar magnitude was observed in the present experiment when a P.G.A. compressive specimen was irradiated without stress in DID0 at 350°C. These recoveries are also of similar magnitude to the strain due to the doubling of the modulus and may be readily explained on the basis of the
IRRADIATION
INDUCED
PLASTICITY
IN GRAPHITE
UNDER
CONSTANT
179
STRESS
T.WLB 3. RBSUL~ OF “L”W$ILBFRMXURE ~esfg ON XWLATED PILE GRADE A DRAPHIT@) 1rradiatiork+ temperature CC)
x
Irradiation dose+ lOa (n.cmvR)
Direction of cut
Ultimate tensile strength (lb/M)
Strain to fractm!
Parallel
0.074 o@so OGS5
(%)
250
1.2
Pq*
1700 1900 1700
350
0.2s
Parallel Perp.
1820 1380
-
WJ9
Parall@ Perp.
1560 1700
-
2.0
Parallel
1430
0.078
2.1
Pa&k?1 Pcl-p.
1490 1120
O-098
*Irradiations
carried out in hoilaw 6uef element faGties in DID0
1 0
IO
!
1
20
30
40 ---AP
dose,
n cm2
Fost neutron RG.
7. The
changes
reactor at A.E.R.E.
c!
;o
of the coefficients of thermal unstressed specimens.
temporary pinning of dislocations, as proposed by PERKS and ~1~~~~~~~‘~ if this applies to the permanent set due to the change of modulus only. In any consideration of the possible major source of plastic creep strain it is important to examine whether or not the method of analysis of the experimental data is correct. In fact, Fig. 7 shows that different changes are observed in the thermal exparrsion coefficients of stressed and unstressed specimens. Results from unstressed spe&nens irradiated at 3WC in I3IDU are showa. It may he seen that a compressive
20
Fast neutron
expansion
30
dose,
-
HaxwelI.
40
50X10
n cm-3
of stressed and
stress accelerates the changes whereas the tensile stress retards them and difkences in the structure may be inferred. Rence, while the compressive cxeep strains shown in Figs- 3 and 4 are increasing linearly, the plastic strain in the graphite may be increasing more rapidly sincean enhanced growth component should be considered to exist in the specimens in comparison with the controls. A similar conclusion may be drawn for the tensile specimens. The creep strain must, therefore, occur in a maxmer which affects the closure of the small
180
B. S. GRAY, J. E. BROCIUEHURST
porosity and a non linearity in the bulk behaviour would be expected at large strains and possibly also a difference between the creep coefficients in tension and compression. There is no evidence from the unstressed reirradiation for any recovery of linear or secondary creep strain. Depending on their position with respect to the mid-plane of BR-2 the temperatures of some specimens varied systematically and cyclically over a wide temperature interval in the range 300500°C while others remained substantially constant at about the nominal rig temperature of 410°C (see Table 1). The fact that no systematic variation is detectable in the calculated creep values suggests that irradiation creep is insensitive to temperature in this range. Nor does it appear that thermal cycling has substantially affected the results, as suggested by JENKINS and STEPHEN.(’5, However, the high dose results are few and one would not necessarily expect to detect a dependence of the magnitude proposed by KENNEDY.@) Nevertheless, the experiments described have demonstrated creep strains of over 0.5 per cent in both tension and compression and support a correlation with the elastic deformation of unirradiated material.
4. CONCLUSIONS
Isotropic and P.G.A. graphites have been irradiated under uniaxial compressive and tensile stresses, and it is shown that substantial creep occurs with no evidence of saturation up to a fast neutron dose of 5.0 x 10zl n,cm’ and creep strains of more than O-5 per cent. The mechanisms involved appear to be related to those for elastic deformation in unirradiated material.
and A. A. McFARLANE
Acknowledgements-The work of the Irradiation Physics Group of the U.K.A.E.A. at the Reactor Materials
Laboratory, Culcheth, the staff of the U.K.A.E.A. Reactor Engineering Laboratories, Risley, and of the operating staff of the BR-2 reactor, is gratefully acknowledged. REFERENCES 1. HUTCHEON J. M. and THORNE R. P., Improoed Graphite for Nuclear Purposes. The Second Conference on Carbon and Graphite. The Society of The Chemical Industry (1966). 2. GRAY B. S., HANSTOCK R. F., KELLY B. T. and NETTLEY P. T., The Mechanism of Radiation Induced Contraction in Polycrystalline Graphite. Presented at the Seventh Biennial Conference on Carbon (1965). 3. GR~ENSLADE G. K., U.K.A.E.A. TRG Report 821(R), to be published. 4. MARTIN W. H. and CLARE D. M., Nucl. Sci. and Eng. 19,461 (1964). 5. HAWKINSN., The Effect of Radiolytic Corrosion on the Mechanical Properties of Graphite, The Second Conference on Carbon and Graphite, The Society of the Chemical Industry (1966). _ 6. LOSTY H. H. W. and ORCHARDI. S.. Proceedings of the Fifth Conference on Carbon, Vol. 1, p. 516. Pergamon Press, Oxford (1961). 7. TAYLOR R., KELLY B. T., BROWN R. G., HALL E., MORRIS, F., HODDS A. T. and GILCHRIST K., The Mechanical Properties of Reactor Graphites, to be published. Creep of Graphite, 8. KENNEDY C. R., Irradiation presented at the Seventh Biennial Conference on Carbon (1965). 9. PERKS A. J. and SIMMONS J. H. W., Carbon 4, 85 (1966). 10. HE~KETH R. V., Phil. Mag. 11, 917 (1965). Internal 11. GRAY B. S. and HALL E., U.K.A.E.A. Document. 12. PFRK~ A. J. and SIMMONSJ. H. W., Carbon 1. 441 (1964). 13. JACKSONJ. L., The Effect of Tensile Stress on the Radiation Induced Contraction of Graphite, HW-SA-3592 (1964). 14. MORGANW. C., Carbon 1, 255 (1964). 15. JENKINS G. M. and STEPHEN D. R., Carbon 4, 68 (1966). 16. MARTIN W. H., private communication. ”
_
.
1967, Vol. 5, pp. 173-180.
THE
Perpamon Press Ltd.
IRRADIATION
IN GRAPHITE B. S. GRAY,
Printed in Great Britain
INDUCED
UNDER
PLASTICITY
CONSTANT
J. E. BROCKLEHURST
STRESS
and A. A. McFARLANE
L;nited Kingdom Atomic Energy Authority, Reactor Materials Laboratory, Culcheth, Warrington, Lanes. (Hec&ed
17 March 1966; in revised form 4 August 1966)
Abstract-The irradiation creep behaviour of graphite has been studied in the reactor BR-2 at Mol, Belgium, up to fast neutron doses of 5 x lo?’ n.cm-” within the temperature range 300-500°C. Results are presented in the paper for graphites irradiated under constant uniaxial compressive and tensile loads. The graphites studied include the nxmal Pile Grade ‘A’ and a number of improved graphites at present being considered for future nuclear power reactors. It is shown that the presence of an applied stress greatly modifies the irradiation induced dimensional changes up to high doses and that the graphites are capable of absorbing large creep strains without failure. In addition it is found that the stress also modifies the thermal expansion coefficient of irradiated specimens.
1. INTRODUCTION
stressed control specimens included in each capsule together with the thermocouples and flux monitors. Figure l(b) shows the steel struts used to stress the specimen in tension using the external hydrostatic pressure. The operating temperature is achieved solely from the nuclear heating which can be as high as 18 W/g. The capsules are filled with a heliumneon gas mixture and for a given rate of heat generation the specimen temperature is determined by the heat transfer across the gap between the outer graphite sleeve and the wall of the bellows which is in contact with the coolant water at about 40°C. Capsules can, therefore, be designed to operate at the required temperature by choosing appropriate values of gas mixture and gas gap. For a given reactor power, the exact temperature is dependent on the control rod position. The capsules at the top and bottom of the rig show the largest temperature variations during a reactor cycle; the temperature of the top capsule rising and that of the bottom capsule falling as the control rods are withdrawn and the flux peak moves up the core. Table 1 summarises the temperature history of the specimens.
AN IMPORTANT property of any graphite intended for use as a reactor moderator is its ability to deform plastically under an applied stress in the presence of fast neutron irradiation. The rate of this creep determines the magnitude of the stress in the moderator due to the differential dimensional changes caused by flux and temperature gradients. The experiments to be described in this paper were constant stress experiments, both tensile and compressive, performed in the Belgian reactor BR-2 up to fast neutron doses of 5.0 x 10” n.cm-‘, at a nominal temperature of 41O”C, using normal Pile Grade ‘A’ graphite (P.G.A.) and a number of improved isotropic graphites.(‘*‘) 2. EXPERIMENTAL
METHODS
2.1 The irradiation experiment The apparatus developed for these experiments uses the 180 lb/in’ gauge pressure of the light water coolant to apply a compressive or tensile stress to the specimens.(3) To achieve this the specimens are sealed in stainless steel convoluted bellows capsules and an assembly of five capsules, suspended in line inside a support tube, is irradiated in a hollow fuel element. Figures ‘l(a) and (b) depict typical compressive and tensile specimen assemblies showing the unF
2.2 Determination of in-pile stress The load produced by the pressurisation bellows was determined experimentally. 173
of the
174
B. S. GRAY,
J. E. BROCKLEHURST
and A. A. McF~L~E
n
Thermocouples
S/S
n
Holes for thermocouples
canvuloted
bellows t0.005
in. wall
thickness)
Spacer
Cross
Stressed
section
specimen outer
sleeve
Control specunen
spacer
Flux
monitor
Specimen
w.-_----Gas
filling
assembly_
tube
FIG. l(a). Bellows assembly containing a graphite specimen under compressive load in a BR-2 creep rig.
The stainless steel bellows shown in Fig. 1 are approximately 3 in. long and have 42 convolutions for an overall capsule length of about 4 in. The total cross-sectional area including the convolutions is 0+X2 in2 and, excluding the convolutions, the area is 0.248 ir?. Standard stainless steel end caps were welded to one of the bellows units, one end cap containing a narrow tube through which the capsule was pressurised internally to gas pressures up to 200 lb/in’, see Fig. 2(a). A close fitting sleeve was placed around the bellows to prevent distortion. The differential pressure was plotted against the force exerted by the bellows as measured by a hydraulic load cell. Two sets of measurements were carried out in this way. The end cap containing the tube was then removed and an outer sleeve brazed to this end,
FIG. l(b). Diagram of tensile creep capsule.
Hestramnq tube to Gdewoys
prevent
(c)
inlerool
preesutisotibll
(bl
Solid bar to it pressure
External
pressurisotion
FIG. 2. Schematic diagram of apparatus for pressurising the bellows capsule and measuring the resulting load.
IRRADIATION
INDUCED
PLASTICITY
IN GRAPHITE
UNDER
CONSTANT
STRESS
175
TABLE 1. TEMPERATURE HISTORYOF CREEPSPECIMENS IN FIGS. 2 AND 3
$ Lpecimen
Compressive
Tensile
Fast neutron dose (n.cMs X 10mzo)
Graphite
Approximate* range of irradiation temperature T+R.T. (“C)
P.G.A. P.G.A. P.G.A. P.G.A. P.G.A. P.G.A. P.G.A. P.G.A. P.G.A.
L.14 L.14 L.14 L.14 L.141 L.14 L.14 L.14 oxidised
3.2 13.0 25.8 43.0 2.3 3.3 15.0 20.2 35.5
3201 30 350-400 450 -350 350-450 270& 70 3201 40 350-450 300-400 450-350
Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic Isotropic
expt’l PI-l PI -1t PI-1 PI-l PI-l PI-2 PI--2t PI-2 PI-2 PI-5 PH-2 PH-3 PO-1
3.6 8.6 10-6 11-6 15.5 50.5 13.0 19.8 21.2 26.1 17-o 25.8 10.0 12.5
3303 20 300 -450 500-3.50 500-350 400* 20 420f 20 250-3.50 500-400 500-400 400% 20 450-350 450-350 450-350 300 -400
Isotropic Isotropic Isotropic
PI-4 PI-4 PH-3
23.0 24.0 33.5
300 -400 500-350 450-350
*Where a temperature range is quoted the first value is that at the beginning of a typical reactor cycle and the second that at the end of the cycle. iSpecimens
are cut parallel to the extrusion direction of the graphite except where indicated by t.
The designations PH. PI. PO refer to different isotropic materials and - 1, -2, generally atdifferent stages’of development.
leaving the other end of the bellows free, see Fig. 2(b). The bellows could then be pressurised externally by filling the interspace with gas, and the force exerted on a steel rod inserted in the bellows was transmitted to a hydraulic load cell. Three sets of measurements were carried out, the differential gas pressure (up to a maximum value of 400 lb/in2) being plotted against the load exerted by the bellows. In carrying out the measurements, the pressure as indicated by the gauge was set at predetermined values, and the corresponding load obtained using a hydraulic compression capsule. The compression capsule was connected to a 10 in. dia precision gauge reading up to 200 lb in 1 lb divi-
- 3 etc. refer to different blocks,
sions with an accuracy of LO.5 lb. The pressure gauge was a 5 in. dia Bourdon gauge reading up to 400 lb/in2 in divisions of 10 lb/in2 with an accuracy of f2 lb/in’. All five sets of results are in good agreement and give a linear relation between the differential pressure and the resulting load corresponding to an effective area of 0.316 in2. The stress levei in the experiment may therefore be calculated from the coolant pressure and specimen geometry. Except for the prototype rig, irradiated before BR-2 attained full power, the latter has been chosen to produce a stress in the range 800-1~0 lb/in’. For the first rig shorter specimens were used than for most of the later work and this allowed for
176
B. S. GRAY,
J. E. BROCKLEHURST
two specimens with stress levels differing by a factor of two in each capsule. For that rig only, several specimens were therefore irradiated at 400-500 lb/in2, but at irradiation temperatures somewhat lower (maximum 360°C) than in subsequent rigs. The results from this rig were used to optimise the heat transfer calculations for the later rigs. 2.3 Nfrutro?r dose ??waxrments Fast neutron doses were obtained from the activation of “Fe in the form of enriched (95% 54Fe) iron monitors, encapsulated in silica, in each capsule. The nuclear constants used are those determined by MARTIN and CLARE(~) based on a cross section of 107 mb for the reaction “*Ni (n,p)“Co in a DID0 hollow fuel element facility. The doses for each specimen are corrected for the axial variation down a rig. 2.4 Laboratory measurements thermal expansion and Young’s Length, modulus measurements were made on specimens and controls and the stress-strain behaviour of stressed specimens determined over the appropriate stress range. Normally length measurements were made using a Sigma comparator and slip gauges, but an optical comparison method had to be used for the tensile specimens which have fiduciary marks engraved on the gauge length. The accuracy of these measurements is &to*01 per cent better, depending on the specimen type. Thermal expansion measurements were made in a silica dilatometer with an accuracy of lo-’ deg C-r. After irradiation the thermal expansion coefficients for the gauge length of the tensile specimens were estimated by assuming that the irradiation induced changes of the coefficients of the ends of these specimens were comparable to those of the unstressed control specimens.
and A. A. McFARLANE
2.5 The calculation of creep strain For purposes of calculation the irradiation induced creep strain is here defined as the additional length change arising from the applied stress o, as measured at temperature in the stressed condition, and tensile stresses will be considered positive: L,=measured length of specimen at room temperature (R-T.) before irradiation; L =measured length of specimen at room temperature (R.T.) after irradiation. Considering a mean irradiation temperature (T+R.T.): Length of specimen
at start of irradiation
L’,=L*(l Length of specimen
+@kT+o/EJ at end of irradiation
L’=L(l The in-reactor
+aT++‘)
strain is
but for the unstressed
control specimen
$f=F+T 0
. Aa,
Hence the ‘creep strain’ is given by W --=Al’ I_ L6 I’,
AL Al L_-T-+(Ag-A~JT-; 0
0
(3)
Each of the four terms on the R.H.S. of equation (3) has a probable error of fO.01 per cent, hence the probable error in the creep strain is less than 0.02 per cent. 3. RESULTS
AND
DISCUSSION
For the P.G.A. and isotropic graphites Figs. 3 and 4 show the variation of ‘creep strain’ with dose up to a maximum of 5 x 102’n.cm-2 and normalised to a stress level of 900 lb/in2 assuming
Fost neutron dare, n cm-2
FIG. 3. Compressive creep strains for P G.A. ‘graphite. (Normalised to 900 lb/in-s).
IRRADIATION
INDUCED
PLASTICITY
IN GRAPHITE
UNDER
CONSTANT
.
STRESS
177
PC.2 I
b Pi 5-N I
I
0
v P1.4.N x RI.2.N
. .
.
k\
PH.S.//
+ PO.,.//
.5-
Compressive I 10
0
I 20
*\ 50x10~
40
30
Fast neutron dose,
n cm-2
FIG. 4. Creep strains for isotropic graphites. (Normalised to 900 lb/ine2).
a linear dependence on stress. All the isotropic graphites behave similarly, despite differing sources and temperature histories. After stress normalisation, the data from the prototype rig fall together in Figs. 3 and 4 irrespective of initial stress level confirming that, for the initial creep at least, a linear stress dependence is a reasonable assumption. In compression, Figs. 3 and 4 show a large primary creep followed by a period which may be represented by a linear dose dependence. The primary creep is not associated with the change in Young’s modulus on irradiation, this has been allowed for. The data are too imprecise to be sure that the secondary creep rates are linear and not decreasing or even leading up to a tertiary creep.
o-4r
0.3
-
/
8, 0 g
1 5
/ 0.2
----C
f 3,=
l
O.I-
!?G.A. perpendicular
-
5
$
+
Isotropic
RG.A. parallel
/
Initial
elastic
strain,
%
FIG. 5. Relation between linear creep and initial elastic strain.
However, Fig. 5 shows a correlation between the linear creep rates shown in Figs. 3 and 4 and the average initial elastic strain for each graphite type. The increase in creep rate with initial elastic strain is also demonstrated by the irradiation under stress of a parallel cut P.G.A. graphite specimen which had been previously oxidised radiolytically to 18 per cent weight loss as described by HAWKINS.c5) A creep strain of over 7Q per cent resulted from a dose of 3.5 x 1021 n.cmp2 under a stress of 870 lb/in2 for an initial elastic strain of 0.20 per cent by comparison with a creep strain of 0.6 per cent for 0.07 per cent elastic strain for unoxidised material. After the irradiation the specimen was intact but visibly deteriorating. These results show that the plastic and elastic deformation modes are closely related, perhaps through the stress distribution within the aggregate. Except for the oxidised specimen, the observed compressive strains are smaller than the fracture strain observed in laboratory tests of either irradiated or unirradiated materialc5-‘) even when the elastic strains are included. In tension, however, the total strains are significantly greater as has been reported previously.@-lo) Thus, strains to fracture of comparable material have been studied in a series of laboratory tests. Table 2 gives values of the tensile strength and strain to failure of a number of unirradiated specimens of improved isotropic graphites while other results in both tension and compression have been reported by TAYLOR et a1.c7) whose work includes a study of the effects of irradiation at 150°C. Figure 6 (unpublished work by GRAY and HALL(~‘) illustrates
some
tensile
data
for
unirradiated
178
B. S. GRAY, J. E. BROCKLEHURST
and A. A. McFARLANE
TABLE 2. THE UNIRRADIAW~ TENSILESTRENGTH AND TO FAILUNZ OF SOME INDIVIDUAL SPECIMENS OF THE
STRAIN
IMPROVED
ISOTROPIC
GRAPHITES
Ultimate tensile strength (lb/in*)
Strain to fracture (%)
PH2
1050 1520 1590 990
0.23 026 0.22 0.25
PH3
1510 1420 1780
o-14 0.15 0.16
PH4
2420 1800 2550 2450 2650 2360
O-26 0.28 O-36 0.28 o-34 o-41
PI4
1850 1560 1620 1780 1950 2070
o-19 0.16 0.21 o-22 0.25 0.28
2450 2170 2300 2300
o-35 0.29 0.36 O-29
PO1
1370 1450 1820
0.11 0.16 o-13
PP
1660 1850 1260
0.30 O-24 O-16
Graphite
PI6
Note: All specimens direction.
cut parallel to the extrusion
P.G.A. and Table 3 includes the results of tensile tests on P.G.A. irradiated at 250 and 350°C in DID0 and PLUTO at AERE Harwell. Figure 4 shows that the creep strains observed in tension and compression are comparable for the present experiment, but this could be a coincidence resulting from the limited dose range of the tensile data. Thus, extrapolation to 1000 lb/in’ of the low dose data reported by MORGAN(‘~’supports the existence of primary strains of the order of 0.1 per cent in compression, but other workers have reported much smaller values in tension.(s’12*13) There
is a difficulty
in comparing
present
results
Perpendicular to extrusion
0
L_, Ultimate
FIG. 6. The strength
1000
tensile strength,
Ib/inz
of unirradiated
P.G.A.
graphite.
with other data since the dose scales are very different and the primary creep is estimated by extrapolation of the secondary creep curve to zero dose. HESIUXTH(~‘) has estimated the magnitude of the primary creep, on the assumption that it is due to dislocation climb, to be similar to the initial elastic strain. KENNEDY(~)reports that the primary tensile creep is somewhat less than the elastic strain using the irradiated moduhts and JENKINS and STEPHEN report a similar value in torsion, while the present results in compression yield a large value. However, if the primary creep strain is lower in tension than in compression, as the combined data suggest, then the average secondary creep rate must be somewhat greater in tension to account for the data in Fig. 4. KENNEDY(~)reported a recovery equal in magnitude to his primary tensile creep on removal of the stress during an irradiation and a recovery of similar magnitude was observed in the present experiment when a P.G.A. compressive specimen was irradiated without stress in DID0 at 350°C. These recoveries are also of similar magnitude to the strain due to the doubling of the modulus and may be readily explained on the basis of the
IRRADIATION
INDUCED
PLASTICITY
IN GRAPHITE
UNDER
CONSTANT
179
STRESS
T.WLB 3. RBSUL~ OF “L”W$ILBFRMXURE ~esfg ON XWLATED PILE GRADE A DRAPHIT@) 1rradiatiork+ temperature CC)
x
Irradiation dose+ lOa (n.cmvR)
Direction of cut
Ultimate tensile strength (lb/M)
Strain to fractm!
Parallel
0.074 o@so OGS5
(%)
250
1.2
Pq*
1700 1900 1700
350
0.2s
Parallel Perp.
1820 1380
-
WJ9
Parall@ Perp.
1560 1700
-
2.0
Parallel
1430
0.078
2.1
Pa&k?1 Pcl-p.
1490 1120
O-098
*Irradiations
carried out in hoilaw 6uef element faGties in DID0
1 0
IO
!
1
20
30
40 ---AP
dose,
n cm2
Fost neutron RG.
7. The
changes
reactor at A.E.R.E.
c!
;o
of the coefficients of thermal unstressed specimens.
temporary pinning of dislocations, as proposed by PERKS and ~1~~~~~~~‘~ if this applies to the permanent set due to the change of modulus only. In any consideration of the possible major source of plastic creep strain it is important to examine whether or not the method of analysis of the experimental data is correct. In fact, Fig. 7 shows that different changes are observed in the thermal exparrsion coefficients of stressed and unstressed specimens. Results from unstressed spe&nens irradiated at 3WC in I3IDU are showa. It may he seen that a compressive
20
Fast neutron
expansion
30
dose,
-
HaxwelI.
40
50X10
n cm-3
of stressed and
stress accelerates the changes whereas the tensile stress retards them and difkences in the structure may be inferred. Rence, while the compressive cxeep strains shown in Figs- 3 and 4 are increasing linearly, the plastic strain in the graphite may be increasing more rapidly sincean enhanced growth component should be considered to exist in the specimens in comparison with the controls. A similar conclusion may be drawn for the tensile specimens. The creep strain must, therefore, occur in a maxmer which affects the closure of the small
180
B. S. GRAY, J. E. BROCIUEHURST
porosity and a non linearity in the bulk behaviour would be expected at large strains and possibly also a difference between the creep coefficients in tension and compression. There is no evidence from the unstressed reirradiation for any recovery of linear or secondary creep strain. Depending on their position with respect to the mid-plane of BR-2 the temperatures of some specimens varied systematically and cyclically over a wide temperature interval in the range 300500°C while others remained substantially constant at about the nominal rig temperature of 410°C (see Table 1). The fact that no systematic variation is detectable in the calculated creep values suggests that irradiation creep is insensitive to temperature in this range. Nor does it appear that thermal cycling has substantially affected the results, as suggested by JENKINS and STEPHEN.(’5, However, the high dose results are few and one would not necessarily expect to detect a dependence of the magnitude proposed by KENNEDY.@) Nevertheless, the experiments described have demonstrated creep strains of over 0.5 per cent in both tension and compression and support a correlation with the elastic deformation of unirradiated material.
4. CONCLUSIONS
Isotropic and P.G.A. graphites have been irradiated under uniaxial compressive and tensile stresses, and it is shown that substantial creep occurs with no evidence of saturation up to a fast neutron dose of 5.0 x 10zl n,cm’ and creep strains of more than O-5 per cent. The mechanisms involved appear to be related to those for elastic deformation in unirradiated material.
and A. A. McFARLANE
Acknowledgements-The work of the Irradiation Physics Group of the U.K.A.E.A. at the Reactor Materials
Laboratory, Culcheth, the staff of the U.K.A.E.A. Reactor Engineering Laboratories, Risley, and of the operating staff of the BR-2 reactor, is gratefully acknowledged. REFERENCES 1. HUTCHEON J. M. and THORNE R. P., Improoed Graphite for Nuclear Purposes. The Second Conference on Carbon and Graphite. The Society of The Chemical Industry (1966). 2. GRAY B. S., HANSTOCK R. F., KELLY B. T. and NETTLEY P. T., The Mechanism of Radiation Induced Contraction in Polycrystalline Graphite. Presented at the Seventh Biennial Conference on Carbon (1965). 3. GR~ENSLADE G. K., U.K.A.E.A. TRG Report 821(R), to be published. 4. MARTIN W. H. and CLARE D. M., Nucl. Sci. and Eng. 19,461 (1964). 5. HAWKINSN., The Effect of Radiolytic Corrosion on the Mechanical Properties of Graphite, The Second Conference on Carbon and Graphite, The Society of the Chemical Industry (1966). _ 6. LOSTY H. H. W. and ORCHARDI. S.. Proceedings of the Fifth Conference on Carbon, Vol. 1, p. 516. Pergamon Press, Oxford (1961). 7. TAYLOR R., KELLY B. T., BROWN R. G., HALL E., MORRIS, F., HODDS A. T. and GILCHRIST K., The Mechanical Properties of Reactor Graphites, to be published. Creep of Graphite, 8. KENNEDY C. R., Irradiation presented at the Seventh Biennial Conference on Carbon (1965). 9. PERKS A. J. and SIMMONS J. H. W., Carbon 4, 85 (1966). 10. HE~KETH R. V., Phil. Mag. 11, 917 (1965). Internal 11. GRAY B. S. and HALL E., U.K.A.E.A. Document. 12. PFRK~ A. J. and SIMMONSJ. H. W., Carbon 1. 441 (1964). 13. JACKSONJ. L., The Effect of Tensile Stress on the Radiation Induced Contraction of Graphite, HW-SA-3592 (1964). 14. MORGANW. C., Carbon 1, 255 (1964). 15. JENKINS G. M. and STEPHEN D. R., Carbon 4, 68 (1966). 16. MARTIN W. H., private communication. ”
_
.