THE MECHANICAL PROPERTIES OF REACTOR GRAPHITE

Cmbon 1967,Vol. 5, pp. 519-531. Pergamon Press Ltd.
Printed in Great Britain
THE MECHANICAL
OF REACTOR
PROPERTIES
GRAPHITE
R TAYLOR+, R G. BROWN, IL GILtZHIUST, E. HALL, A. T. HODDSf,
B. T. KELLY and F. MORRIS
United Kingdom
Atomic Energy Authority,
Warrington,
Reactor Materials Laboratory,
Lams.,
Culcheth,
England
(Receiued 12$zmuzy 1967)
Abstract-The following mechanical properties of three types of isotropic reactor graphite have been
measured, before and after fast neutron irradiation at 150°C in DIDO: Young’s modulus, Poisson’s
ratio, stress-strain curves in tension and compression, shear strength, uniaxial tensile and compressive
strength, triaxial compressive strength and Vicker’s hardness. The propagation of cracks in these
graphites has been examined microscopically and measurementn made of the work of fmcture. The
accumulation of irradiation damage has been followed by measuring changes in linear dirnen&ms of the
specimens and of pyrolytic graphite samples which show that the graphite is heavily damaged.
The experimental data have been compared with theories of the mechanical properties of u&radiated
and irradiated graphite. A model in which large porea act as “G&F&’
flaws is compatible with the data
on irradiated graphite, but in unirradiated graphite, plastic flow modifies the failure in compression.
1. INTRODUCTION
SMALLdoses of fast neutrons can produce improvement in the mechanical properties of reactor
graphite, but there has been no systematic investigation of the effect of heavy irradiation damage,
which might cause deterioration in strength.
Irradiation of graphite crystals with fast neutrons
over a wide temperature range, causes changes in
dimensions which can reach very large magnitudes.“) The majority of reactor graphites are well
crystallised, fairly randomly orientated polycrystals, and it is therefore to be expected that the
anisotropic crystal dimensional changes as well as
changes in the mechanical properties of individual
crystals would affect the bulk mechanical properties of graphite.
Irradiation at 150°C can produce large crystal
dimensional changes in relatively small doses and
thus we have undertaken a detailed study of the
*Present address: Department of Metallurgy, University of Manchester Institute of Science and Technology,
Sackville Street, Manchester 1, England.
tSandwich
course
London, England.
student,
Borough
Polytechnic,
519
mechanical property changes after irradiation at
this temperature. The dose dependence of various
mechanical properties and their absolute values
before and after irradiation are also compared with
existing theories of the mechanical properties of
well-crystallised graphites.C3)
2. EXPERIMENTAL
DETAILS
2.1 Materials and samples
Samples were taken from each of three blocks of
isotropic reactor graphite manufactured to the
specification of HUTCHEONand THORNE.(~)All
were manufactured from coke obtained from
residues from the petroleum refinery process
using coal tar pitch binders. The graphites
designated as Types 1,2 and 3 were manufactured
as hollow extrusions 164~ dia., 33 in. long and
were graphitised at temperatures greater than
2800°C. Metallographic examination showed Types
1 and 2 to contain spherical coke particles of sizes
ranging up to 1 mm whereas Type 3 graphite contained anisotropic coke particles up to 1 mm long.
Physical properties characterising these graphites
are listed in Table 1.
520R. TAYLOR, R. G. BROWN, K. GILCHRIST, E. HALL, A. T. HODDS, B. T. KELLY andF. MORRIS
Two graphite blocks 2 in. thick by 4 in. square
cross-section were cut from each graphite extrusion, with the 2 in. axis (a) parallel and (b) perpendicular to the direction of extrusion. Each of the
six blocks was then subdivided into 64 bars 2 in.
long by + in. square cross section (i.e. an 8~ 8
matrix). The bars thus obtained were machined to
provide 1 tensile and 1 compressive specimen from
each. Alternate bars provide specimens for irradiation whilst the remainder were used as controls.
The compressive specimens were 0.500 in. long
x O-245 in. dia. cylinders and the tensile specimens,
which were 1.125 in. overall length, had a gauge
length 0.375 in. long x 0.200 in. dia., with transitional fillets of 2 in. radius to end grips O-245 in. dia.
Four each of tensile and compressive specimens
were withdrawn from the reactor after irradiation
to each of several doses at 150°C. In addition to
tensile and compressive strength, measurements
were also made of Poisson’s ratio, dynamic
Young’s modulus
and hardness.
Dimensional
changes were measured after each withdrawal
from the reactor and pyrolytic graphite specimens
were irradiated
concurrently
to obtain crystal
dimensional changes.
Specimens were cut from other regions of the
extrusion for triaxial compression, shear strength
measurements, and observations of crack propagation under slow tensile strain. Specimens of Pile
Grade “A” graphite (Type 4) were also tested in
triaxial compression, and the specimens used for
this test were cylinders O-245 in. dia. by 0.500 in.
long. Type 2 graphite was tested in triaxial compression after neutron irradiation using the broken
ends of the tensile specimens
machined
into
cylinders 0,375 in. long x 0.200 in, dia. Shear
strengths were measured on specimens 1 in. long
by 0.245 in. dia. Special strip tensile specimens
were used for observations of crack propagation.
2.2 Irradiation conditions
The specimens were irradiated in a standard
triple magazine Wigner rig located in a hollow fuel
element in the core of DIDO, as described by
BELL et aZ.(5)Each sample hole in the magazines of
the rig contained two tensile and two compressive
specimens, eight holes in each magazine being
occupied in this way.
The irradiation doses are all determined from
the 5sNi (n,p) 5sCo reaction using a cross-section
of 107 mb.(6) The instantaneous
flux in these
facilities measured by this reaction is 5~ lOi
n.cm%ec-’
and the maximum total dose achieved
was 11.5 x 10zo n .cme2 .
Irradiation temperatures were controlled within
the range of 0 to +lO”C of nominal.
2.3 Measurements
Stress-strain
curves and static Young’s moduli
were measured in a Hounsfield or Mand testing
machine. Initially tensile strains were measured
using
a 5 mm Huggenberger
extensometer
mounted on the gauge length, and compressive
strains were measured
using a Boulton-Paul
differential inductance transducer mounted across
the compressive platens. The efFects of compression of the platens over the load range employed
was checked using a steel sample and found to
amount to 7% error for the largest loads employed
and proportionately
less for smaller
loads.
Subsequently,
both tensile
and compressive
strains were recorded using a 4 in. gauge length
extensometer consisting of two differential inductance transducers
mounted
either side of the
specimen using radial knife edge clamps. It is
estimated that strains at fracture are accurate to
f5”/, in tension and compression.
Unirradiated
stress strain values are listed in
Table 1 together with standard deviations. After
neutron irradiation the stress strain curves show
increasing linearity as the irradiation dose increases.
This is illustrated in Figs. 1 and 2 which compare
u&radiated
stress strain curves with curves
obtained for specimens irradiated to doses of 1.55
and 11.5~ 102’ n.cmW2. These also indicate the
increase in fracture stress and decrease in strain to
fracture after irradiation.
However, because of
statistical scatter in the data these should be considered to be merely indicative of the changes.
Table 2 lists the average fractional changes in
stress and strain to fracture at each neutron dose,
calculated
from unirradiated
strength
values
inferred from adjacent control specimens. Tensile
strengths of Types 1 and 2 graphites increase by a
factor of -2 after a small neutron dose and show
little variation with subsequent dose. For Type 3
graphite this increase is not as marked and the
data show considerable scatter. Strains to fracture
decrease to &_8 the u&radiated
value and stay
roughly constant. In compression however, the
l-85
jZO.04
1.86
2
3
0.17
16.5
5.9
6.6
:
1
-
:
0’
‘!
*z%iin
perpendicular
parallel
parallel
perpendicular
parallel
perpendicular
Direction
of cut
0.64
0.13
36
11.2
10.3
0‘64
0”‘4$
0.75
1.85
Im3
0‘17
55
13.3
12.3
I.55
2.09
2.02
0.66
0.63
2.51
2.55
0.70
0.64
0.19
70
121
13.0
2.91
1.71
I.90
0.53
O-68
2.90
2.90
0.71
0.64
Type I
022
79
13.3
13.6
3-60
2.07
1.97
0.97
0.77
2.99
3.04
0.84
0.86
0.13
147
11.9
12.0
:‘z.
0.49
0.62
3.11
3.23
0.62
0.59
7-5
*t:
.
0.14
167
11~5
I.75
2.05
0.59
0.69
3.21
3.47
os3
0.51
0.75
2.11
I.97
0.74
0.71
I.95
I.97
0.63
0.58
0.17 42
0.17
19.8
9.85 18.2
9.4
160
0,
I
I
I
1
1
1
1
1
0.17
64
28.7
19.2
I.55
2.40
I.95
I.30
0.85
2.32
2.30
0.69
0.59
6.85
6.75 >
7-6s >
7.23
4.95
4.78
tiverag
*-----Ye
strengh I.
(kg mm-“)
GRAPHITPS
0.18
90
18.0
17.8
2.70
2.00
1.90
0.69
0.98
2.65
2.54
0.75
0.58
:‘tf
.
0.97
0.93
2.76
2.90
O-88
Ial
3.60
g:;
o-21
100
Type 2
0.10
135
14.9
16.9
X.
0,48
0.95
3.02
3.00
0.58
046
7.5
NEUTRON IRRADIATION
@20
0.19
0.215
0,215
0.244
0.260
Neutron dose n.cm-1 x 10’0
AETER
0.22
o-21
0.13
frazre
o/0 strain
n.~ , a Average
wanaara
deviation
(kg mm-‘)
PROPERTIES
1*34
I.13 >
1.51 )
140
1.06 >
1.07
OF UNIRRADIATED
Tension
PROPRRTIES
.m~
Average
strength
(kg mm-‘)
MRCWANICAL
0.370
0.390
0.320
0.290
0.335
0.315
TABLE 2. CHANGE IN
;:I:
3.5
4.1
3.4
3.8
?ean
?,
tccars. cm sec.-l. “K-l)
AND MECHANICAL
*See Table 1 for absolute values of fracture strength and strain.
(dmaxl
smin=%f
Pohaon’E
Hmdncu r&J
(kizmm-‘)
rtmintoflacwre
Chmge
in compressive
ChongE in tensile
eh.enfth arlol
change in ten&!
Btraintofr~
Changein compressive
strenstbm/m.
PIWWW
Material
fOGI
1.78
fO.05
1
Density
Type (gms cm-y
&i?WCAL
Mean
Z.T.E.
(2612OOC)
( x l[)d deg K-l)
TABLE 1.
:::(:
0.09
158
1
:
1
I
_
18.5
5.25
8.2
1
:‘E
.
0.56
0.47
0’
I
1
11~5
1.98
1.71
0.63
0.38
0.57
0.43
0.35
34
4.5
7.2
:4;
*
0.57
0.55
2-08
I.88
0.61
065
O-85
2.50
2.56
;:;t
0.77
0.94
2.58
244
0.83
I.12
Z-90
Type 3
-75
7.8
IS,4
2.75
3.02
2.15
2.42
A-..:^,:^..
UCVI~CIVII
(kgmm-3
f__?w_
Compression
1;:;
100
;X0.51
0.52
E
0.53
0.72
4.70
11.0
12.0
11.4
10.4
9.7
8.7
1.45
38’:
*
0.53
0.56
8’%
.
7.5
1.65
‘Z .
122
UC’)
Dynamic
3
8
=;
ii
g
B
z
%
g
$
!!
R
?I
8
522 R. TAYLOR,
R. G. BROWN,
K. GILCHRIST,
E. HALL,
A. T. HODDS,
B. T. KELLY
and F. MORRIS
2s
r
‘0
t
STRAIN, *lo.
FIG. 2. Variation in strain-strain curves in compression
with increasing neutron dose-Type
2 graphite.
The Young’s moduli were determined at very
small strains, on compressive specimens only, by
measuring the fundamental
resonant frequency.
The changes in modulus on irradiation are obtained from:
FIG. 1. Variation in stress-strain curves in tension with
increasing neutron dose-Type
2 graphite.
strength increases with increasing neutron dose
and tends to saturate at a value 3-3.5 times
greater than the u&radiated
stress to fracture.
Here again the strains to fracture are I&j the unirradiated value. The fracture angle in uniaxial
compression (the angle between the applied stress
and the fracture plane) decreases as the neutron
dose is increased (Table 3). At high doses specimens generally tended to fragment and it was not
possible to measure a fracture angle.
E/E,, - 1= cflfo)2 - 1
where E, E. are the irradiated and unirradiated
moduli respectively, and f, f. the corresponding
resonant frequencies. No corrections were made
for length and density changes. Since maximum
growth in the specimens was 3%, this would
amount to a maximum error of 3% in modulus and
this may be neglected.
TABLE 3. FRACTURBANGLBS
Specimen
type
IN CNIAXIAL
Irradiation dose
0
0.75
1.55
x
COMPRJBSION
lOa ncm-*
2-70-29
3.6
7.5
16”-+10”
36”&
6”
21°*12”
28”&17”
23”&19”
Typell
34”&
5”
40”*12”
26”&
24”&
Type211
Type21
29”&14”
39”f23”
30”&12”
23”cb 7”
23”zk 7”
30°&
18”~lS”
24”jcl7”
25”&
25”&
‘bwl
II
6”
(1)
8’
8’
6’
6”jc
5”
6”
11.5
+
I
l
+
0°*
l
a
”
*One specimen of Type 2 // graphite exhibited a fracture plane parallel to the compression direction. Ail other
specimens at doses of 75 and 11-S x lOso shattered into many pieces and a fracture angle could not be determined.
THE MECHANICAL
PROPERTIES
NEUTRON
523
OF REACTOR GRAPHITE
DOSE, n C6’
FIG. 3. Changes in small strain (dynamic) moduli.
Figure 3 shows the fractional changes in Young’s
modulus measured by the dynamic method. These
show the usual form: an initial rapid increase
followed by a slight fall, and at higher doses, a
slow rise.
Poisson’s ratios were measured on compressive
specimens taken from the parallel to extrusion
(axis of symmetry) direction, lateral and longitudinal strains being measured over the stress
range 0.33-1.70 kg/mm2. The longitudinal strains
were measured by the 5 mm Huggenberger extensometer and the lateral strains by two Boulton
Paul transducers mounted on either side of the
specimen held in a U-shaped clamp bolted to the
lower compression platen.(‘) The longitudinal
strains were determined four times and averaged,
lateral strains were determined sixteen times,
rotating the specimens or transducers after each
determination. The results tabulated in Table 2
indicate that there is little change after neutron
irradiation and that Poisson’s ratio for these
graphites lies in the range 0.1-0.2.
Shear strengths were measured using the simple
double shear apparatus illustrated in Figure 4.
The 1 cm long central portion of the specimen was
sheared using a direct tensile pull. No attempt was
made to measure shear strain at fracture. Two
specimens of Types 1 and 2 graphite were measured after three irradiation doses up to 2.9 x 1020
n.cme2 and these are compared with tensile
strengths in Table 4. Shear strength increases on
neutron irradiation similarly to the tensile strength
and the tensile strength/shear strength ratio is
roughly constant at a value slightly less than 0.5.
The hardness was measured on the end grips of
broken tensile specimens using a Vickers pyramidal indenter, after lapping to a smooth finish
with 520 y alumina and coating with a thin layer
of aluminium to improve the visibility of the edges
of the indentation. Two samples of each type of
TABLE4. COMPARISON
OFSHEAR
ANDTENSILE
~TRENGTHLI
‘Ibe
1
2
Neutron dose
(n.cm-*)
Shear strength
(kg/mm*)
Tensile strength
(average)
(kglmm’)
Tensile strength
0
1 x 10”
1.79
2.91
2.31
6.08
4.76
5.60
l-09
2.17
2.17
2.05
0.465
O-360
O-460
0.370
0
1 x 10’0
1.79
2.70
3.37
6.10
6-00
6-00
l-46
3.10
3.36
2-66
0.435
O-510
0.560
0445
Shear strength
524 R. TAYLOR, R. G. BROWN, K. GILCHRIST,
E. HALL, A. T. HODDS, B. T. KELLY and F. MORRIS
b WI. dla
,
,
Specimen
f in.dia
FIG. 4. Double shear apparatus.
graphite were measured after each irradiation, ten
to twelve indentations being made on each sample.
The results listed in Table 2 show that hardness
continuously
increases up to the highest dose
measured.
Triaxii
compressive
strength
measurements
were carried out in the apparatus shown in Fig. 5.
The Nimonic plunger, which transmitted
the
axial load, was the same diameter as the specimen
to ensure that no correction need be applied to
compensate for an axial component
of hydrostatic pressure. The pressure vessel was made of
stainless
steel. Measurements
were made at
hydrostatic pressures rising by increments of 0.7
kg/mm2 up to 562 kg/mm2. The specimens were
sheathed in 4.76 mm i.d. silicone rubber tubing to
TABLE5.
COMPARISON
OF OBSEFWXJ
IN TRIAXIAL
prevent oil entering the pores of the graphite. For
the unirradiated specimens radial pressure exerted
by this sheath is O-014 kg/mm-‘which
is negligible
in comparison with the hydrostatic pressures used.
For Type 1 graphite eight specimens were tested
per increment of hydrostatic pressure, but for
Types 2 and 3 graphites and Pile Grade “A” cut
perpendicular
to extrusion only four specimens
were used per increment.
The results of triaxial tests on four unirradiated
graphites in Fig. 6 show the usual form noted by
other workers (cf. PRICE@), MIJFIRELL’~)),namely
that the axial compressive strength increases with
increasing hydrostatic pressure. Fracture surfaces
generally showed a smooth appearance similar to
those noted by MURRELLon coal, and enabled the
fracture angle to be measured. However, a few specimens did not fracture completely even though the
usual drop in load was noticed and a fault line
appeared on the specimen surface. The data on
Type 2 irradiated specimens is presented in Fig. 7
where each point represents an individual determination (the total number of specimens tested is
given on each graph). Specimens irradiated to low
doses show well defined fracture angles, but at
high doses the specimens generally fragmented
and very few yielded a sufficiently large piece to
enable a fracture angle to be determined.
The propagation of a crack across a plate was
observed microscopically at magnifications up to
x480 and photographed,
using equipment
as
illustrated in Fig. 8. A notched graphite plate is
rigidly clamped to a brass block which is slowly
heated by flowing water circulated from a temperature controlled
bath. Due to the differential
thermal expansion of brass and graphite, a tensile
strain is applied to the sample and a crack is
slowly propagated.
AND
CALCULATED
FRACTURE
ANGLE3
COMPRESSION
1
kl~ WXd
Graphite
tan
type
Qw
1
z::
Pile Grade “A”
P=
38”
36p
362
364
39” &6”
35O f7”
36” &7”
35Ff7”
0.25
0.31
0.30
0.31
20
THE MECHANICAL
PROPERTIES
OF REACTOR
GRAPHITE
PRESSURE
VESSEL
525
TOP
FIG. 5. General arrangement of triaxial assembly.
Pores were observed as large as 060 mm and
cracks generally tended to link up these large pores
although not necessarily by the most direct path.
Spherical coke particles deflect cracks, cracks
peter out in numerous branches, and cracks often
initiated at a pore surface and ran back to meet an
advancing crack.
The failure of unirradiited compressive specimens was photographed using a high speed tine
camera (16,000 frames/set). A number of interesting points emerged from these observations. A
crack is often visible on the specimen surface a
significant period of time before failure occurs.
When failure occurs this crack forms an integral
part of the fracture path and failure is catastrophic.
Fracture is invariably accompanied by a cloud of
fine dust similar to that obtained when two rough
surfaces are abraded one over the other.
The dimensional changes of three isotropic
graphites and the pyrolytic graphite specimens as a
function of neutron dose are shown in Figs. 9 and
10 respectively. Due to the fact that specimens
jammed in the rig, results on pyrolytic graphite do
not extend to the same dose as data on the isotropic
graphites.
4. DISCUSSION
The most important practical result arising
from this work is the observation that the strength
of the graphite is not reduced by the large internal
strains due to crystal dimensional changes caused
by irradiation-indeed the strength is increased
over the wide range of conditions examined. The
data on pyrolytic graphite* (Fig. 10) shows that
*The materialemployed was ,9 type in the notation of
KELLY,MARTINand NBTTLEY.(~)
526 R. TAYLOR, R. G. BROWN, K. GILCHRIST,
E. HALL, A. T. HODDS, B. T. KELLY and F. MORRIS
TYW1
2ot
Hydrostatic
FIG. 6.
~reswe.
Wmmz
Triaxial stress data for four u&radiated
graphites.
crystal growth in the c-axis direction in excess of
29% and basal plane contractions in excess of 4%
have been obtained while the work of KELLY,
MARTIN and NETTLW(‘) shows that similar
dimensional changes occur in the crystals of the
polycrystalline graphites. Thus to a radiation induced differential crystal strain in excess of 33%
the isotropic graphites examined show enhanced
strength. Although modulus and creep may affect
structural
irradiation
damage in graphite the
principal factor will probably be the differential
crystal strain irrespective of the absolute magnitudes of c axis expansion and a axis contraction.
The results are also of interest in relation to
theories of the mechanical properties of graphite
(cf. REYNOLDS(~)). The changes in dynamic
Young’s modulus are very similar to those observed in other well crystallised graphites irradiated
at 150°C and have been explained as follows, It is
generally accepted that the increase in modulus
observed at small strain and low doses is due to the
pinning of glissile dislocations in the basal planes
Cc)Irradiotion
(b) Irradiation
dose
I.55 x 10% cme2
2s
1
dose
16
24
.;
20
16:
0123456
I
I
/L=o.34
p=o39
8 = 359
8 =35*
I
L”
I
(9)
]
P,,
.
, , , ,
(II)
Hydrcslotic
(IO)
0123456
$123456
pressure,
kg/mm2
FIG. 7. Triaxial stress data for irradiated graphite-Type
2.
THE MECHANICAL
PROPERTIES
527
OF REACTOR GRAPHITE
FIG. 8. Equipment for tensile testing of notched specimens.
3
Type
p0
I
*/w-*
-rt
Perpendnlw
Neutron
I
I
I
dose.
n cm-’
FIG. 10. Dimensional changes of graphite crystals at
150°C.
Neutron
dose,
n cm-’
FIG. 9. Dimensional changea of polycrystalline graphite
at 150°C.
of the component crystals which, in the unirradiated state, contribute a large strain component. As
the dislocation strain component decreases, the
effective shear constant, CM, of the component
crystals tends towards the true value for the
crystal lattice. At higher doses, the elastic constants
of the crystal lattice are changed and C&
decreases,(“) thus causing a reduction in the
moduli of the polycrystal. At higher doses still the
large crystal dimensional changes modify the pore
space of the solid in such a way as to increase the
moduli once more. The marked dependence of the
moduli of the present graphites on the Cd4 of the
component crystals shows that these too approximate more closely to the Reuss uniform stress
condition than to the Voigt uniform strain condition, as noted by REYNOLDS for other graphites.(3)
If we now consider observations at larger
strains, then in tension the stress-strain relation is
fairly linear up to fracture before irradiation and
truly linear up to fracture after irradiation (Fig. 1).
In compression, before irradiation, the stressstrain curve is very non-linear, conforming
roughly to the form proposed by WOOLLEX.(~‘)
After irradiation the stress-strain relation becomes
increasingly linear with increase in dose. At the
two highest doses no deviation from linearity is
observed. However even after irradiation the
static modulus determined from the linear portion
of compressive stress-strain curves is some lS-20%
lower than the modulus determined dynamicallythis suggests a strain amplitude dependent dislocation pinning effect such as that observed by
528R. TAYLOR, R. G. BROWN, K. GILCHRIST,
E. HALL, A. T. HODDS,
GOGGIN”~’ in low temperature
irradiation. The
lateral strains decrease with dose in much the
same way as the longitudinal
strain, and thus
Poisson’s ratio is not much changed. This is not
true of all graphites on irradiation at 15O”C.(‘) In a
solid graphite body in the uniform stress condition
the Poisson’s ratio is expected to be 0.5 because the
shear strain of the crystals dominates and introduces no volume change. The observed low value
of Poisson’s ratio thus shows the importance of the
pore space in the deformation of these graphites.
The low value of Poisson’s ratio shows that
different groups of crystals are deformed in shear
when orthogonal
stresses
are applied to the
graphite, and this is only possible because of the
presence of porosity.(3)
A number of mechanisms have been proposed to
account for the non-linear stress-strain relation in
graphite in the unirradiated
state. It is not proposed to examine these here but it is clear that an
increasing proportion of the material is deforming
plastically with increasing stress, and the work of
JENKINS
and HALL
shows that the component of dislocation strain is also increased. At the
large strains observed in compression, changes in
stress-distribution
due to changes in pore volume
are also possible. The changes in shape of stressstrain curves show that irradiation inhibits plastic
flow and also apparently, the formation of new
dislocations.
The fracture stress in tension (or) increases
rapidly at low doses and is little changed by
further increases in dose, while the fracture strain
quickly decreases with increase in dose to about
O-6 its pre-irradiation
value. The compressive
fracture strains behave in much the same way as
the tensile fracture strain, but the fracture stresses
increase over a wider dose range. It was suggested
by LOSTY and ORCHARD that tensile fracture in
graphite occurs at a constant value of the elastic
strain energy/unit volume (F) in the u&radiated
and irradiated states, that is,
F==
4
= constanl
(2)
where E is the modulus. MACON
concluded that
in tension graphite could be described as a
Griffith solid, which would obey the same condition.
B. T. KELLY and F. MORRIS
It is important
to consider only recoverable
energy in using equation
(2). For irradiated
graphite Hookean behaviour
is observed and
equation (2) defines the total area under the stressstrain
curve.
However,
because unirradiated
graphite exhibits non-linear
stress-strain
curves
(a<&),
there is a permanent set which
amounts to up to 25% of the total strain. The
energy associated with this deformation’ is not
recoverable and does not appear in equation (2).
The static moduli of irradiated graphite tensile
specimens
agree very well with the dynamic
moduli and for unirradiated
graphite the static
modulus at fracture (i.e. the modulus by unloading
the specimen just prior to failure) is slightly lower
than the dynamic value. However, this difference
has been found to be not greater than 10% in
agreement with the observations
of SLEDIN.
We have evaluated F for our graphites as a function of neutron dose and the results are shown in
Table 2. In Types 1 and 2 graphite the strain
energy shows an initial increase and is then fairly
constant or slowly decreasing, while in Type 3
graphite the average behaviour shows reasonable
constancy, but there is a large fluctuation.
The GRIFFITH crack hypothesi@u
postulates
that failure will occur due to the presence of
randomly orientated cracks which are sufficiently
separated to be considered as isolated cracks. The
following criteria are predicted by the GRIFFITH
theory (c.f. ref. 19) when or -as > 0 and 30~ +a2
<o:
61 -a2)2+8a,(q+a2)=0
-02)
(Ql
--*(ol+c72)-cos
(3)
2e
and for : 3trr +a~ > 0 :
bl=bT
(9
8-O
(6)
for multisxial stress systems where:
frr is the major principal stress
02 is the minor principal stress
UT is the m&z&l tensile strength
8 is the angle between the critical crack and the
normal to the direction of maximum principal
stress.
THE MECHANICAL
PROPERTIES
Equations 3 and 4 imply a compressive/tensile
strength of 8 and a parabolic relation(20) between
the principal stresses at fracture. Since the principal stresses are related to the shear stress S, by(19)
61 -Qs=SO
(7)
this when substituted in equations 3 and 4 predicts
that the shear strength is twice the uniaxial tensile
strength. For both Types I and II graphite thii
criteria is reasonably well obeyed (Table 4) and
highly irradiated graphite does have a compressive/
tensile strength ratio of N 8 (Table 2).
However, unirradiated graphite exhibits a compressive/tensile strength ratio less than 8. The data
obtained in triaxial compression, certainly in the
unirradiated graphite, does not obey the parabolic
GRIFFITH criterion. It is found that the COULOMBNAVIER theory (cf. ref. 21) describes the unirradiated triaxial results very well and is a good representation of the irradiation results. This theory
postulates that the shear strength S, is increased
by ,u times the normal pressure (a) across the fracture plane where p is the coefficient of internal
friction. If c and r are the normal and shear
stresses across a plane, fracture will occur in that
plane when
.
r=S,-/Xr
(8)
Resolving cri and 02 into normal and shear stress
components
acting on the crack, and following
usual practice where tensile stresses are positive
(ai is thus the hydrostatic pressure, 02 is the axial
stress) gives
C,[P + (P2 +
I>“1
+ g2b
-
(P2
+
1>*1=
2so(9)
where p= l/tan 2 0.
8 defines the fracture plane as before.
The results in Fig. 6 show very good agreement
with equation (9) for four unirradiated
graphites
having
very different
microstructures.
It is
interesting to note that the coefficients of friction
determined from the slope of the plot of axial
stress vs. hydrostatic pressure are roughly the same
for all graphites, in fact three have the same value.
The fracture angle 8 was found to be independent
of hydrostatic pressure and agrees very well with
the calculated angle (Table 5) although the values
of 0 are higher than those obtained from &axial
tests (Table 3).
H
OF REACTOR GRAPHITE
529
For irradiated graphite the same linear dependence between axial stress and hydrostatic pressure
is observed at low doses, although at higher doses
the results show considerable scatter. Values of CL
and 8 calculated from the slope of ~1 vs. 62 are
listed in Fig. 7 and suggest a trend to an increasing
coefficient of friction and a decreasing fracture
angle with increasing dose. Thii could not be
checked since the inaccuracies in measuring fracture angles were too great to enable the small
changes at low doses to be measured contidently.
At the two highest doses the specimens generally
fragmented; but from a few specimens the fracture
angle was assessed at 30 & 4”, in agreement with the
calculated value for specimens irradiated to 7.5 x
102* n.cm2. At the highest doses however, there is
considerable scatter in the results and these could
just as readily be fitted by a parabolic law as
predicted by the Griffith relation.
MCCLINTOCK and WALSH(“) derived equations
8 and 9 from the Grifhth model by assuming
the critical cracks to be closed in compression, and
this model has been shown by HOEK and
BIENIAWSKI(~~) to apply to a wide range of rock
materials. However, unless the cracks are initially
closed, this predicts a compressive/tensile
strength
ratio between 8 and 10; moreover, this model
merely predicts the critical angle of the crack(s)
from which fracture is initiated. This need not
necessarily be the macroscopic fracture angle. In
fact, the observations of BRACEand BQMBOLAKIS(~~)
on glass show that the crack, which is initiated at a
point near to, but not at, the crack tip(25) runs out
by following a curved path, and having gone out of
critical orientation the crack ceases to grow.
Although the COULOMB-NAVIER relation provides a good qualitative picture of the uniaxial
results, it does not explain why the observed fracture angle coincides with the critical crack orientation. Whilst in tension a single crack can produce
failure it is extremely unlikely that graphite in
compression will fail by the propagation of a single
crack. Rock failure due to natural faults has been
observed to occur from an echelon system of
cracks (MCKINSTRY 1941,‘26’ BRACE1963’27’), and
it seems possible that graphite fails in similar
fashion. Ultimate failure will occur by the shear of
thin slabs of graphite still connecting cracks which
have ceased to grow. Since the maximum shear
stress acts along this plane of critical orientation,
530R. TAYLOR, R. G. BROWN, K. GILCHRIST, Ft.HALL, A. T. HODDS, B. T. KELLY andF. MORRIS
which is moreover weakened by these cracks,
would expect shear along this plane and
macroscopic fracture angle to correspond to
critical crack angle. The failure of graphite in
stages is substantiated by:
one
the
the
two
1. The observation that certain triaxial specimens
had not broken even though the drop in stress
corresponding to crack propagation, and usually
failure, has occurred.
2. The high speed tine photography of compression tests which showed a visible surface crack
for a significant time before failure occurred.
Additional evidence is that a specimen subjected to
a large irradiation creep strain has been found with
large surface cracks even though the specimen as a
whole was still intact.(“)
In order to explain the effects of irradiation
using a crack concept the strain energy associated
with the cracks must be entirely associated with
crystal shear. This limits the cracks to either
macroscopic flaws sufficiently large to sample the
average modulus of the polycrystal, which depends
upon crystal shear almost entirely, or to microscopic cracks inside crystals which propagate
under shear stresses. REYNOLDS(~) considers the
GIUFFITH flaws in graphite are the microcracks
while MASON
suggests that the larger flaws are
appropriate.
The microscope
observations
of
tensile fracture suggest that the large pores are the
sources of weakness. Our metallographic observations of tensile fracture of a limited number of
Type 1 graphite specimens suggests pore sizes up
to a maximum of 0.6 mm, but detailed visual
examination indicates that the largest pores have
dimensions as high as 2 mm. If values of crack
length (2c) lying in this range are inserted in the
Griffith equation :
(11)
using for E the Young’s modulus of the polycrystal, values of y lying in the range 06-2.4 x 10’
ergs.cms2 are deduced.
We have determined
the work required to
initiate fracture of Type 1 graphite specimens
having artificially induced cracks about 0@04 in.
wide using GILMAN’s
technique
and determined this to lie in the range 0.7-2.5 x lo4
ergs.cmb2. Substituting
the mean value ~-1.5~
lo4 ergscm”
and c=O*l cm in equation (11)
yields a value for o+r2/2E=4*8 x IO4 dynes.cm-2
which is in good agreement with the value of
strain energy derived from our tensile stress strain
curves (see Table 2). The calculated and observed
surface energy values show very good agreement
but are considerably
higher than the energy
expended by the propagation of cracks along the
basal plane of the graphite crystal (119 ergs.cm-2(30)
and 150 ergs.cm-2(31)) and less than work of fracture values obtained from controlled crack growth
in polycrystalline graphites (N 105(32’ and l-5 x
lOS(33’).
The former value is not applicable to polycrystalline graphites since a basal plane crack can
only propagate for one grain diameter. After that
more energy must be expended to cross a grain
which is not suitably oriented.
The work of fracture determination
from controlled crack growth experiments are derived from
measurements of the nominal fracture surface area
and are not applicable to tensile failure for the
following reasons :
The true surface area may be many times the
nominal fracture area. LOSTY
has estimated
this difference from fractographic analysis to be
a factor of S-10.
Our observation of crack growth show that
many minor cracks are opened up. These are
not allowed for.
Crack growth in u&radiated
graphite is modified by plastic flow around the crack tip.
Crack interaction
occurs.
For these reasons we feel that our work of fracture which measures the energy required to
initiate complete fracture from a crack is more
directly applicable and it seems therefore that the
large pores constitute the GRIFFITH cracks in
graphite. Since the pores themselves are often
blunt it is entirely probable that the effective
crack comprises the pore plus the microcracks
radiating from it and that an effective c is fractionally greater than the values we have quoted.
The assumption
that one can use the bulk
modulus of the aggregate in equation (11) is open
to question and it may be argued that a crystal
modulus such as Css may be more applicable. If
the large cracks are indeed the sources of weakness,
then the change in tensile strength on irradiition is
THE MECHANICAL
PROPERTIES
due in part to the change in crystal moduli. The
modulus of the polycrystal reflects the effective
crystal C44 which increases whereas other crystal
moduli decrease or remain unchanged.(lO) Thus,
since these larger pores persist after irradiation
and c is relatively unchanged, it is more appropriate
to use the measured modulus.
After neutron irradiation the strain energy to
failure of these graphites shows an initial increase
followed by a subsequent fall. The increase may be
caused by an increase in y or a reduction in c. Our
hypothesis suggests that c will be relatively unchanged by neutron
irradiation
at low doses;
therefore we postulate that y must increase. An
increase in 2’is most probably due to the fact that,
due to the decrease in plasticity, the crack is
propagating in an elastic stress field. At high doses
crack generation(‘)
is known to occur and the
subsequent decrease in strain energy is probably
due to an increase in c.
The increase in hardness of graphite on irradiation is, we believe, due to two effects, the first the
decrease in permanent
set or plastic flow on
irradiation
and the second, the reduction
in
into which deformation can take
microporosity
place.
531
OF REACTOR GRAPHITE
7. BROC~BHUR~T
J. B. and LYNAMJ. T., U.K.A.E.A.
Report TRG Report 901(C) (1965).
8. PRICEN. J., Mechanical Properties of No-n-Met&c
Materiak (editor W. H. Watton), p. 106. Butterworth (1958).
9. MURRBLLS. A. F. Ibid. p. 123.
10. S~MMERB
L., WALKERD. C. B. and KELLY B. T,,
Phil. Msg. 14, 317 (1966).
11. WOOLLWR. W.,Phil. Mag. 11,475 (1965).
12. GOC~IN P., Second International Conference on
Industrial Carbons and Graphite, S.C.I., London
(1965).
13. JENKINSG. M., Phil. Mug. 8, 903 (1963).
14. HALL E., J. Nucl. Mat. 15, 137-139 (1965).
15. LOSTY H. H. W. and ORCHARDJ. S., Proceedings of
the Fifth Carbon Conference, p. 519. Pergamon
(1961).
16. MAsONI. B. Ibid. p. 597.
17. SELDINE. J., Carbon 4, 177 (1966).
18. GRIFFITH
A. A., Proceedings of the First Int. Congress
Appl. Mech. p. 5.5 (1924).
19. YOKOBORI T., Strength Fracture ond Fat&e
of
Materials, p. 127. Noordhof, Groningen (1964).
20. OROWANE.. R&orts on Promess in Phwics 12, 485
(1949).
’ 21. JAEGER J. C., Elasticity, Fracture and Flow (3rd
edition). Methuen.
22. MCCLINTOCK
F. E. and WALSHJ. B., Proceedings
of the Fourth U.S. Congress Appl. Mech., Berkeley,
1962. Aw.
Sot. Mech. Engs. New York, 1015
(1963).
23. HOEK E. and BIENIA~SKI2. T.., Int. 7. Fruct. Mech.
”
Acknowle&men~The
authors wish to acknowledge the
assistance of the reactor operators, rig technicians and
R.M.L. site staff at A.E.R.E. HarweII.
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