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The effect of pre-stressing and annealing on the young's modulus of some nuclear graphites
JOURNAL
OF NUCLEAR
MATERIALS
(1973) 315-323. 0 NORTH-HOLLAND
46
THE EFFECT OF PRE-STRESSING
AND ANNEALING
OF SOME NUCLEAR M. ET0 Japan
Atomic
Energy
Received
ON THE YOUNG’S MODULUS
OKU Tokai-mura,
18 October
Ibaraki-ken,
Studies have been made on the decrease in the dynamic
A et B sont des con&antes.
pre-stressing its recovery found
presented
of some nuclear graphites
caused by
montrent
or cyclic loading in compressive
mode and
restaurent
due
that
the by
annealing
moulded
ones,
fracture
stress
and
A and
periments
E/Eo=
where
at a pre-stress
recover
E,
that
even at 2000 “C. The
1000 “C is about
recovery
activation
of an extruded
“C;
restaurent peratures du graphite Es
spannung
mique
de
quelques
d’une pr&ontrainte par compression On
a trouvb
rep&sent&e (-AS)
pour
pr&ontrainte
les formules
extrudes
et
les graphites respectivement
Untersuchungen
ob-
lichen
einiger
u, celui
pour
cyclique
se
tem-
& 0,6 eV.
Wertes
durch
stranggepressten
Graphit
Konstanten.
B pour exp et EO repour
une pr&ontrainte
une Bgale
ohne
unterhalb eine
Graphit
vollstiindige
gleichen
wobei
Vorspannung ist.
von stranggepressten vollstlindig
Erholung
der Erholung
von
fiir
E/Eo= E der
u, E, der Modul bei einer
Vorspannung
1000 “C fast
bis zu wird
durch (E-E,)/
dargestellt,
(-A&)
der
such bei 2000 “C nicht erreicht energie
des Moduls
A und
Wiirmebehandlungsversuche
dass die Moduln
denen
des urspriing-
durch den Ausdruck
Modul bei einer Vorspannung
du module
est bien
Elastizitiits-
durchgefiihrt,
Abnahme
B und fiir gepressten
VorDruck
eine Wiirmebehandlung
Die
exp
einer
unter
des dynamischen
2000 “C folgten.
(Eo-EC)=B
auf
zur Wiederherstellung
Modul
E, E,
ne
d’activation
Belastung
Reaktorgraphite
Bruchspannung
-A&+
zu der
zyklischen
der
module
de
en dessous de 1000 ‘C
est Bgale & environ
Abnahme
is not
dyna-
(E-E,)/(Eo-E,)=B le
se
dessous & des
L’bnergie
Untersuchungen
der
moul&,
de recuit
extrudes
moul&
m$me
2000 “C.
extrude
par recuit h 2000 “C.
E/Eo=
graphites
& la restauration
moduls
8, la suite
ou d’une mise en charge
que la diminution
les
en
compl&ement,
oder
beruhenden
below
d’Young
nucleaires
et sa restauration
par
les graphites presentant
graphites
que
pas
in the
energy
graphite
wurden
-_A&+ du module
tandis
Les experiences des graphites
compl&ement
atteignant
ex-
0.6 eV.
On a Btudib la d&roissance
presque
correspondant
res-
graphites
1000 “C, while
complete
que les modules
equal to
Annealing
of extruded
below
graphites
tained for the recovery
are the
EO
no pre-stressing,
constants.
show that the moduli
case of moulded
B exp( --A@) and
1000
is re-
B for ex-
-Ad+
E,
with
are
B
is well
u, that at pre-stress
almost completely
attained
2000 “C. It
and (E-E,)/(Eo-EC)=
modulus pectively.
up to
in the modulus
the formulae,
truded graphites for
to
decrease
Japan
1972
Young’s
modulus
CO., AMSTERDAM
GRAPHITES
and T.
Research Institute,
PUBLISHING
und B
ergaben,
Graphiten erholen,
gepressten
EC sind sich
wiihrend Graphite
wird. Die Aktivierungs-
stranggepresstem
Graphit
& la cont,rainte de rupture et celui avant prhcontrainte.
unter
1.
decrease in the Young’s modulus caused by compressive pre-stress was found by Losty and Orchard 2) and Jenkins 3). The latter proposed an empirical formula concerning the relation between the change in the modulus and the level of pre-stress. More extensive investigations of stress-strain properties of graphite were made by Seldin 4) and Greenstreet et al.5). Seldin has also studied the effect of annealing on the residual strain due to tension or compression.
Introduction
It is well known that a decrease in the Young’s modulus of graphite is caused by pre-stressing or cyclic loading in tensile or on compressive mode. Several investigations the subject have been carried out from various points of view. The relationship between compressive stress and deformation and the change in “paraelastic modulus” were first investigated by Arragon and Berthier 1). A 315
1000 “C betriigt
etwa 0,6 eV.
316
ET0
MI.
Recently
Hart 6) has examined
pre-stressing
in compressive,
the effect
tensile
and
static modes on the thermal expansion Young’s modulus of graphite and found all loading
modes
Young’s
modulus
He
also
has
caused
a decrease
of ATJ and AXF
demonstrated
AND
of iso-
and that
in the
graphites.
that# heating
to
1300 “C resulted in partial removal of stressinduced changes in ATJ moduli and complete removal of those in AXF moduli. At the present stage, however, little appears to be known about the recovery of the modulus due to heat-treatments. The purpose of this paper is first to investigate whether the effect of pre-stressing in the compressive mode on the Young’s modulus depends on the kind of nuclear graphite and the an~sotropy of specimens. Secondly, it is to confirm th.e effect of cyclic compressive loading, and thirdly to clarify the recovery process due to annealing treatment by discussing the origin of the change in the modulus. 2.
ExpetimentaZ procedure
The materials used in the present experiments can be classified into three types, i.e. needle coke, Gilsocarbon and fine-grained isotropic graphites. The needle coke graphites are El327 and
SMG which were manufactured
by GLC
T.
and Showa Denko Co., respectively. IM-2 and IEf -24 manufactured by AGL are used as the Gilsocarbon graphite, and for the fine-grained one 7477/PT of LCL is used. These materials are listed diameter
Brand
of the nuclear graphites
in table
1. Specimens
parallel or perpendicular
to the axis of extrusion
seqwant unloading were carried out using an Instron tensile test machine at strain-rates of 5.6 x 10-S and 2.8 x 10.~/SC, respectively. In the case of cyclic loading (zero $0 a fixed maxjmum} both loading and unloading were performed at strain rate of 1.1 x t0-4/sec. Isoohronal annealing up to 2000 “C and isothermal annealing at 300, 500, 700 and 830 “C were performed in the vacuum of 1 X IQ-3 respectively. ton?, 5 X 10-S and
1 used in the experiments Young’s
j Direction
modulus
(108 kg/mm2) H327
6.15
IEl-24 II
I
~
.____ _I_/__ SMG
J” /l _l
1
1.74 1.74
.__--~-~~.~,.--_ 1.75
1.76
in
or moulding. The velocity of an ultrasonic wave of 100 kHz in each specimen was measured to calcuIate the dynamic Young’s modulus before and after pre-stressing or annealing. The modulus was calculated using the formula, E= (e/g)w2 where e, g and II are the apparent density, gravity constant and velocity of the wave, respe&ively. The measurement technique is that of Sate and Miyazono 7). Pre-stressing and the sub-
I
7477JPT
5 mm
and 30 mm in length were cut from
a block of each graphite in such a way t’hat the longitudinal direction of the specimen is
TABLE List
OKU
’
~
1.42
5.35
I,18
8.49 7.96
0.984 0.996
--
4.70 4.47
1-‘-I I
1.08
0,846
YOUNG’S
MODULUS
OF
SOME
NUCLEAR
317
GRAPHITES
o H327U) A SMG(A
I
70.9 w w
o.go Com&ive
Con&&,‘,
Change
(b)
in the Young’s
modulus
of the
specimen
(a) H327 and SMG, (b) IM-2,
I
0 Fig.
2.
specimen
0.2
0.C
Normalized
Pre-stress
Change
1
ReLresLikgimZ?)
(4
1.
( &llld
1
t 0
Fig.
PA-Stress
in
the
perpendicular
to the axis of extrusion
or mouldmg,
and IEl-24.
I
0.6
0.6
parallel
7477/PT
1.o
( .jp/ 0-i )
Young’s
modulus
of
to the axis of extrusion
the or
moulding.
Specimens for isothermal annealing were heattreated at 2000 “C for an hour in order to give them a standard state, although such treatment hardly affected their moduli. To make the effect of annealing on the modulus of pre-stressed specimens clear, those with no pre-stressing were subjected to the same treatments as the pre-stressed ones, and a comparison was made between them.
0 Fig.
3.
Effect
5 Number
10 15 of Loading
25
of cyclic loading on the modulus
H327 parallel to the axis
3.
20 Cycles
of
of extrusion.
Results
Changes in the Young’s modulus due to pre-stressing are shown in figs. la and lb. Here, the modulus is normalized using the formula,
31s
M.
ET0
AND
T.
ORU
Normalized
Fig.
4.
some
Effect
nuclear
trusion
of cyclic graphites
or moulding,
Pre-stress
loading parallel
(a) H327,
(bp/ a;)
on the modulus to the (b) IM-2,
axis
of
of ex-
(0) IEl-24,
(d) 7477/PT and (e) SMG.
on the modulus
0
0.4 0.6 0.2 Normalized Re-stress ( $1 qy8
I 1.0
(c)
E (normalized)=~~~~b, where EB and Et, are the moduli after and before pre-stressing, respectively. The modulus change of the specimens perpendicular to the axis of extrusion or moulding is shown in fig. 2, where the level of pre-stress is represented as the ratio (prestress, a,)/(fracture stress, at). Fig. 3 shows the effect of cyclic loading in the compressive mode
of the material H327 parallel
to the extrusion axis, In figs. 4~, the effect of cyclic loading as well as the dependence of change in Young’s modulus on the pre-stress level is shown for each material. Isochronal annealing curves for 8327 and SMG pre-stressed up to about 0.6 errare shown in fig. 5, while the similar curves for IM-2, IEl-24 and 7477/PT are in fig. 6. Here, the direction of all the specimens is parallel to the axis of extrusion or moulding. Fig. 7 shows isothermal annealing curves for the specimens of H327 parallel to the axis which were prestressed to about 2.1 kg (0.6 UP). 4.
Discussion
Acaording to Jenkins 3) change in the modulus due to compressive stress is best fitted by the
YOUNG’S
MODULUS
OF
SOME
NUCLEAR
following
GRAPHITES
319
equation : E/Eo= exp [-&/(a,-cr)].
(I)
Here, Eo, E, k and crc are the apparent modulus at zero stress, the apparent modulus after pre-stressing to a stress (T,a non-dimensional constant which is found to be about 0.08 and a critical stress, respectively. Figs. 8a and 8b Annealing
0 5.
Fig.
500 Annealmg
1000 Temperature
Isochronal
annealing
stressed specimens of H327
time
l°C
60mm
1500
)
curves
2000
for the pre-
and SMG parallel to the
axis of extrusion.
are obtained by applying the equation to the data shown in figs. la, lb and 2. In figs. 8a and 8b where - [ l/log(E/Eo)] versus the reciprocal of the pre-stress is plotted, eq. (1) is represented as a linear relationship, because the following equation can be obtained by taking the logarithm of the both sides of eq. (1) : 1 1 UC 1 - In (E/Eo) = F (--->. CT uc
Annealing
time
60min
I
0.950 Fig.
6.
stressed
J 2OcO
500 Annealing
T~rature
Isochronal
annealing
specimens
of
&y curves
for
the
IM-2
and
7477/PT
IEl-24,
pre-
parallel to the axis of extrusion or moulding.
The values of k and B for both extruded and moulded materials calculated from the results in figs. 8a and 8b are summarized in table 2. From fig. 8a, however, it is found that the equation of Jenkins is well fitted to the points only over a limited range, i.e. (0.66 to 1) ur for SMG, H327 and IEl-24 parallel to the axis, and (0.5 to 1) ur for SMG and H327 perpendicular to the axis. For moulded materials fig. 8b shows that it can be fitted to the data only in the very small intermediate range of the pre-stress level. Thus, in the present experiments it is believed that eq. (1) is not to be applied to extruded graphites at lower pre-stress levels and to moulded ones either at lower or at higher levels. A better fit to the points for extruded graphites used in the present experiments can be obtained with the assumption that the relation between change in the modulus and the pre-stress is represented by the equation, E - = -Aa2+B. Eo
Annealing Fig.
7.
cimens
Isothermal of H327
Time
annealing
parallel
(min) curves
to the
axis
for
the
spe-
of extrusion.
(2)
This is shown in fig. 9, and the values of A and B obtained are summarized in table 3. It is found that the equation of this type appears to be well fitted to the curve if the lower and higher pre-stress levels can be
M.
ET0
AND
T.
TABLE The values
3.9
5.3
2
of k and gC in the equation
0.067 UC
OKU
1 0.096 6.7
4.8
/ 0.027
~ 8.0
’ 0.020 6.6
of Jenkins
0.022 7.1
0.027
i 8.0
0.021 6.9
160
ReciprocalOdf”
I 0.2 0.L 2o0 Reciprocal of the Re-stress[(kglmm’
the Re-s!r&sIlkglm$
(4 Fig.
8.
Plots
for the calculation
I
(b)
of k and
oC in the
equation
of Jenkins,
(a) extruded
graphites
and
(b) moulded graphites.
considered separately, that is, two different equations of the form of eq. (2) are to be used for these two regions. It should be noted that the value of A for the specimen parallel to the axis becomes larger above a critical pre-stress level. On the other hand, those perpendicular to the axis have a smaller value of A at higher pre-stress levels. It would be possible to believe that the fact above results from the difference between the specimens in microstructure parallel to the axis and perpendicular to it. It is possibly considered that a compressive stress parallel to the basal plane is more effective in causing a change in the modulus than a stress perpendicular to the plane. Cracks and/or
microcracks on the basal plane would be more easily deformed by a stress parallel to the plane than by one perpendicular to it. It is also noted that IEl-24 which is Gilsocarbon graphite obeys eq. (2), although the amount of decrease in its modulus is almost the same as that of IM-2 or 7477/PT. Thus, it would be possible to consider that the behaviour of both needle coke and Gilsocarbon graphites, extruded, is well represented by eq. (2), though there is a remarkable difference in the amount of change in the modulus between needle coke and Gilsocarbon graphites. The effect of grain size may be one of the factors by which this kind of difference is caused. The dependence of
YOUNG’S
MODULUS
OF
SOME
NUCLEAR
321
ORAPHITES
it may be assumed that the change is to obey an equation
such as E-E, Eo-E,
= B exp ( -Aa2),
(3)
where Eo, E, and E are the original value of the
modulus,
the
modulus
at the
pre-stress
level near fracture stress and that at pre-stress
quare
Fig.
9.
Plots
10 of the Redress
of
change
[
in
20 lkg/mm212
the
1
3
modulus
versus
square of the pre-stress.
level of CT,respectively. Eq. (3) gives a better fit to the data in figs. lb and 2 if we assume, as in the case of extruded graphites, that the pre-stress level can be considered to consist of two separate regions, i.e. lower and higher pre-stress levels. The situation is shown in fig. 10 and the calculated values of A and B in eq. (3) are summarized in table 4. It should be noted that for the specimens of both IM-2 and 7477/PT perpendicular to the axis of moulding, the values of A are larger than unity, i.e. the modulus is not to change until B exp ( -A&) becomes smaller than unity.
3
TABLE
The values of A and B in the equation E/Eo=
- Aas+
B for extruded
A
graphites / Pre-stress level normalized to
B
( U(Wmm2)2)
fracture stress
i ;i H327
; 1
I ~ I
’ II SMG
~I~-~ 1
IEl-24
~//
1.00
1
0 to 0.47
1.12
/
0.47 to 1
0.027
1.00 ~
0 to
0.020
0.98
0.72 to 1
0.011
1.00 ~
0 to 0.67
0.023
1.12
0.67 to 1
0.0084
1.00 )
0 to 0.79
0.0059
0.97
0.79 to 1
0.0018
~ 1.00
0 to 0.58
0.0022
1 1.05
0.58 to 1
.~_
~
/
0.72
strength on grain size of graphite has already been pointed out by Knibbs 8). For the moulded graphites, it appears that the modulus change is levelled off at the pre-stress level near fracture stress. Therefore
Square of the Prestress
Fig.
10.
Plots for the calculation
equation (E-E,)/(Eo-E,) the modulus
change
=
of A and B in the
Bexp( - A ~2) by which
of moulded sented.
i ( kg/mm212 1
graphite
is repre-
322
XI .
ET0
AND
T.
4
TABLE
The
values
of A and
B in the
equation
A
( ~/(k/mm2)“)
II
OKU
((E-E,)/(Eo--E,))=B Pre-stress
H
exp (--A+)
It,vel
normalized fracture
tn
&j&J
stress
0.030
1.00
0 to
0.53
0.083
2.35
0.53
to
0.94
1
IM-2 1
7477/PT
0.051
1.82
0 to 0.55
0.098
2.79
0.55
to
0.94
1
~ Ii I /m
~1 Such critical stresses are about 2.2 and 2.45 kg/ mm2 for IM-2 and 7477/PT, respectively. The results on the effect of cyclic loading are in good agreement with those which have been obtained on the stress-strain relationship by the former investigators 135). That is, after being cyclically loaded several times between zero and a fixed stress level, the specimen produces hysteresis loops of the stress-strain curve that do not change with cyclic number and the paraelastic moduli remain the same. A point to be noted in fig. 3 is that the specimen pre-stressed to 0.85 (TI has fractured
except in the temperature range, 750 to 1200 “C, where the modulus decreases slightly. The modulus of IM-2 shows the annealing behaviour similar to that of 7477/PT. From these results it is clear that the complete recovery of the modulus is observed at about 1000 “C in the case of two extruded graphites, i.e. II327 and IEl-24, and another extruded graphite, SMG, also recovers completely at about 2000 “C. It’ is noted that moduli of moulded graphites do not recover completely up to 2000 “C. This fact also suggests that the mechanism of deformation or fracture differs between the
at the fourth cycle. This fact suggests the possibility of fatigue of nuclear graphite due to cyclic loading. The difference in the behaviour between needle coke graphites and Gilsocarbon or fine-grained graphite is that at higher stress levels the modulus change of the former caused by the second or third loading is rather small, while the latter shows a larger amount of decrease by the similar loading. The isochronal annealing curves in fig. 5 show that the moduli of H327 and IEl-24 recover completely at about 1000 “C, while those of SMG, 7477/PT and IM-2 do not. Moreover the modulus of the specimen of 7477/PT rather decreases between 700 to 1000 “C and is levelled off at higher annealing temperatures. Recovery of the SMG specimen is observed up to 2000 “C,
extruded and the moulded. Hart 6) also demonstrated that the degree of removal of stressinduced changes depends on the kind of graphite examined. The isothermal annealing curves for H327 parallel to the axis shown in fig. 7 give us the activation energy for the recovery of the modulus. The values obtained are shown in fig. 11, i.e. they are about 0.6 eV at any stages of the recovery. At present the meaning of this activation energy is not clear. However, it is believed that the energy has a certain relation to the crack closure or other mechanism of the recovery due to annealing 9910). 5.
Conclusions The conclusions
derived
are as follows:
YOUNG’S
MODULUS
OF
SOME
NUCLEAR
(4)
323
GRAPHITES
The results on the modulus change caused
by cyclic loading are in agreement with those which have been obtained from the stressstrain curve by the earlier authors.
H327tll)
(5) The moduli of extruded graphites recover almost completely up to about 1000 “C (H327 and IEl-24)
or 2000 “C (SMG),
while
in the
case of moulded graphites the complete recovery is not attained even at 2000 “C. The activation energy obtained for the recovery of H327 below 1000 “C is about 0.6 eV, although the mechanism of the recovery remains to be the problem for further investigations. Acknowledgements
Tenpercture (IC'I'K)
Fig.
11.
Plots of time versus annealing temperature for calculating the activation
energy.
(1) The curves obtained for the change in the Young’s modulus are well represented by the formula, E/E0 = - Ai+ B, for the extruded graphites, and (E - E,)/(Eo- E,) = Bexp (-A&) for moulded ones. A’s and B’s in both equations appear to differ corresponding to the difference in the direction of specimen. (2) The amount of the modulus decrease is smaller for the Gilsocarbon and fine-grained graphites than for needle coke ones, if the comparison between them is made at the same normalized pre-stress level. (3) In the case of extruded graphites the amount of the modulus decrease is larger for the specimen parallel to the axis than that perpendicular to the axis, while it appears to have almost no dependence on the direction of the specimen in the case of the moulded ones.
The authors wish to thank Dr. Y. Sasaki for permission to carry out the study, and Mr. T. Usui for technical assistance. Helpful advice and suggestion given by the members of the graphite research laboratory in JAERI are also acknowledged. References 1) Ph. P. Arragon and R. M. Berthier, Industrial Carbon and Graphite
(Sot. Chem. Ind., London,
1958) p. 565 2)
H.
H. W.
Carbon
Losty
Conf.,
and J. S. Orchard,
Vol.
1 (Pergamon
Proc.
Press,
3)
p. 519 G. M. Jenkins, J. Nucl. Mater. 5 (1962) 280
4)
E. J. Seldin, Carbon 4 (1966) 177
5)
W. L. Greenstreet, R. S. Valachovic,
6)
J. E. Smith, G. T. Yahr and
Carbon 8 (1970) 649
P. E. Hart, Carbon 10 (1972) 233
7)
S. Sato
8)
R.
9) 10)
5th
1962)
H.
and S. Miyazono, Knibbs,
J. Nucl.
Carbon 2 (1964) Mater.
24
(1967)
103 174
0. D. Slagle, Carbon 7 (1969) 337 I. B. Mason and R. H. Knibbs, Carbon 5 (1967) 493
OF NUCLEAR
MATERIALS
(1973) 315-323. 0 NORTH-HOLLAND
46
THE EFFECT OF PRE-STRESSING
AND ANNEALING
OF SOME NUCLEAR M. ET0 Japan
Atomic
Energy
Received
ON THE YOUNG’S MODULUS
OKU Tokai-mura,
18 October
Ibaraki-ken,
Studies have been made on the decrease in the dynamic
A et B sont des con&antes.
pre-stressing its recovery found
presented
of some nuclear graphites
caused by
montrent
or cyclic loading in compressive
mode and
restaurent
due
that
the by
annealing
moulded
ones,
fracture
stress
and
A and
periments
E/Eo=
where
at a pre-stress
recover
E,
that
even at 2000 “C. The
1000 “C is about
recovery
activation
of an extruded
“C;
restaurent peratures du graphite Es
spannung
mique
de
quelques
d’une pr&ontrainte par compression On
a trouvb
rep&sent&e (-AS)
pour
pr&ontrainte
les formules
extrudes
et
les graphites respectivement
Untersuchungen
ob-
lichen
einiger
u, celui
pour
cyclique
se
tem-
& 0,6 eV.
Wertes
durch
stranggepressten
Graphit
Konstanten.
B pour exp et EO repour
une pr&ontrainte
une Bgale
ohne
unterhalb eine
Graphit
vollstiindige
gleichen
wobei
Vorspannung ist.
von stranggepressten vollstlindig
Erholung
der Erholung
von
fiir
E/Eo= E der
u, E, der Modul bei einer
Vorspannung
1000 “C fast
bis zu wird
durch (E-E,)/
dargestellt,
(-A&)
der
such bei 2000 “C nicht erreicht energie
des Moduls
A und
Wiirmebehandlungsversuche
dass die Moduln
denen
des urspriing-
durch den Ausdruck
Modul bei einer Vorspannung
du module
est bien
Elastizitiits-
durchgefiihrt,
Abnahme
B und fiir gepressten
VorDruck
eine Wiirmebehandlung
Die
exp
einer
unter
des dynamischen
2000 “C folgten.
(Eo-EC)=B
auf
zur Wiederherstellung
Modul
E, E,
ne
d’activation
Belastung
Reaktorgraphite
Bruchspannung
-A&+
zu der
zyklischen
der
module
de
en dessous de 1000 ‘C
est Bgale & environ
Abnahme
is not
dyna-
(E-E,)/(Eo-E,)=B le
se
dessous & des
L’bnergie
Untersuchungen
der
moul&,
de recuit
extrudes
moul&
m$me
2000 “C.
extrude
par recuit h 2000 “C.
E/Eo=
graphites
& la restauration
moduls
8, la suite
ou d’une mise en charge
que la diminution
les
en
compl&ement,
oder
beruhenden
below
d’Young
nucleaires
et sa restauration
par
les graphites presentant
graphites
que
pas
in the
energy
graphite
wurden
-_A&+ du module
tandis
Les experiences des graphites
compl&ement
atteignant
ex-
0.6 eV.
On a Btudib la d&roissance
presque
correspondant
res-
graphites
1000 “C, while
complete
que les modules
equal to
Annealing
of extruded
below
graphites
tained for the recovery
are the
EO
no pre-stressing,
constants.
show that the moduli
case of moulded
B exp( --A@) and
1000
is re-
B for ex-
-Ad+
E,
with
are
B
is well
u, that at pre-stress
almost completely
attained
2000 “C. It
and (E-E,)/(Eo-EC)=
modulus pectively.
up to
in the modulus
the formulae,
truded graphites for
to
decrease
Japan
1972
Young’s
modulus
CO., AMSTERDAM
GRAPHITES
and T.
Research Institute,
PUBLISHING
und B
ergaben,
Graphiten erholen,
gepressten
EC sind sich
wiihrend Graphite
wird. Die Aktivierungs-
stranggepresstem
Graphit
& la cont,rainte de rupture et celui avant prhcontrainte.
unter
1.
decrease in the Young’s modulus caused by compressive pre-stress was found by Losty and Orchard 2) and Jenkins 3). The latter proposed an empirical formula concerning the relation between the change in the modulus and the level of pre-stress. More extensive investigations of stress-strain properties of graphite were made by Seldin 4) and Greenstreet et al.5). Seldin has also studied the effect of annealing on the residual strain due to tension or compression.
Introduction
It is well known that a decrease in the Young’s modulus of graphite is caused by pre-stressing or cyclic loading in tensile or on compressive mode. Several investigations the subject have been carried out from various points of view. The relationship between compressive stress and deformation and the change in “paraelastic modulus” were first investigated by Arragon and Berthier 1). A 315
1000 “C betriigt
etwa 0,6 eV.
316
ET0
MI.
Recently
Hart 6) has examined
pre-stressing
in compressive,
the effect
tensile
and
static modes on the thermal expansion Young’s modulus of graphite and found all loading
modes
Young’s
modulus
He
also
has
caused
a decrease
of ATJ and AXF
demonstrated
AND
of iso-
and that
in the
graphites.
that# heating
to
1300 “C resulted in partial removal of stressinduced changes in ATJ moduli and complete removal of those in AXF moduli. At the present stage, however, little appears to be known about the recovery of the modulus due to heat-treatments. The purpose of this paper is first to investigate whether the effect of pre-stressing in the compressive mode on the Young’s modulus depends on the kind of nuclear graphite and the an~sotropy of specimens. Secondly, it is to confirm th.e effect of cyclic compressive loading, and thirdly to clarify the recovery process due to annealing treatment by discussing the origin of the change in the modulus. 2.
ExpetimentaZ procedure
The materials used in the present experiments can be classified into three types, i.e. needle coke, Gilsocarbon and fine-grained isotropic graphites. The needle coke graphites are El327 and
SMG which were manufactured
by GLC
T.
and Showa Denko Co., respectively. IM-2 and IEf -24 manufactured by AGL are used as the Gilsocarbon graphite, and for the fine-grained one 7477/PT of LCL is used. These materials are listed diameter
Brand
of the nuclear graphites
in table
1. Specimens
parallel or perpendicular
to the axis of extrusion
seqwant unloading were carried out using an Instron tensile test machine at strain-rates of 5.6 x 10-S and 2.8 x 10.~/SC, respectively. In the case of cyclic loading (zero $0 a fixed maxjmum} both loading and unloading were performed at strain rate of 1.1 x t0-4/sec. Isoohronal annealing up to 2000 “C and isothermal annealing at 300, 500, 700 and 830 “C were performed in the vacuum of 1 X IQ-3 respectively. ton?, 5 X 10-S and
1 used in the experiments Young’s
j Direction
modulus
(108 kg/mm2) H327
6.15
IEl-24 II
I
~
.____ _I_/__ SMG
J” /l _l
1
1.74 1.74
.__--~-~~.~,.--_ 1.75
1.76
in
or moulding. The velocity of an ultrasonic wave of 100 kHz in each specimen was measured to calcuIate the dynamic Young’s modulus before and after pre-stressing or annealing. The modulus was calculated using the formula, E= (e/g)w2 where e, g and II are the apparent density, gravity constant and velocity of the wave, respe&ively. The measurement technique is that of Sate and Miyazono 7). Pre-stressing and the sub-
I
7477JPT
5 mm
and 30 mm in length were cut from
a block of each graphite in such a way t’hat the longitudinal direction of the specimen is
TABLE List
OKU
’
~
1.42
5.35
I,18
8.49 7.96
0.984 0.996
--
4.70 4.47
1-‘-I I
1.08
0,846
YOUNG’S
MODULUS
OF
SOME
NUCLEAR
317
GRAPHITES
o H327U) A SMG(A
I
70.9 w w
o.go Com&ive
Con&&,‘,
Change
(b)
in the Young’s
modulus
of the
specimen
(a) H327 and SMG, (b) IM-2,
I
0 Fig.
2.
specimen
0.2
0.C
Normalized
Pre-stress
Change
1
ReLresLikgimZ?)
(4
1.
( &llld
1
t 0
Fig.
PA-Stress
in
the
perpendicular
to the axis of extrusion
or mouldmg,
and IEl-24.
I
0.6
0.6
parallel
7477/PT
1.o
( .jp/ 0-i )
Young’s
modulus
of
to the axis of extrusion
the or
moulding.
Specimens for isothermal annealing were heattreated at 2000 “C for an hour in order to give them a standard state, although such treatment hardly affected their moduli. To make the effect of annealing on the modulus of pre-stressed specimens clear, those with no pre-stressing were subjected to the same treatments as the pre-stressed ones, and a comparison was made between them.
0 Fig.
3.
Effect
5 Number
10 15 of Loading
25
of cyclic loading on the modulus
H327 parallel to the axis
3.
20 Cycles
of
of extrusion.
Results
Changes in the Young’s modulus due to pre-stressing are shown in figs. la and lb. Here, the modulus is normalized using the formula,
31s
M.
ET0
AND
T.
ORU
Normalized
Fig.
4.
some
Effect
nuclear
trusion
of cyclic graphites
or moulding,
Pre-stress
loading parallel
(a) H327,
(bp/ a;)
on the modulus to the (b) IM-2,
axis
of
of ex-
(0) IEl-24,
(d) 7477/PT and (e) SMG.
on the modulus
0
0.4 0.6 0.2 Normalized Re-stress ( $1 qy8
I 1.0
(c)
E (normalized)=~~~~b, where EB and Et, are the moduli after and before pre-stressing, respectively. The modulus change of the specimens perpendicular to the axis of extrusion or moulding is shown in fig. 2, where the level of pre-stress is represented as the ratio (prestress, a,)/(fracture stress, at). Fig. 3 shows the effect of cyclic loading in the compressive mode
of the material H327 parallel
to the extrusion axis, In figs. 4~, the effect of cyclic loading as well as the dependence of change in Young’s modulus on the pre-stress level is shown for each material. Isochronal annealing curves for 8327 and SMG pre-stressed up to about 0.6 errare shown in fig. 5, while the similar curves for IM-2, IEl-24 and 7477/PT are in fig. 6. Here, the direction of all the specimens is parallel to the axis of extrusion or moulding. Fig. 7 shows isothermal annealing curves for the specimens of H327 parallel to the axis which were prestressed to about 2.1 kg (0.6 UP). 4.
Discussion
Acaording to Jenkins 3) change in the modulus due to compressive stress is best fitted by the
YOUNG’S
MODULUS
OF
SOME
NUCLEAR
following
GRAPHITES
319
equation : E/Eo= exp [-&/(a,-cr)].
(I)
Here, Eo, E, k and crc are the apparent modulus at zero stress, the apparent modulus after pre-stressing to a stress (T,a non-dimensional constant which is found to be about 0.08 and a critical stress, respectively. Figs. 8a and 8b Annealing
0 5.
Fig.
500 Annealmg
1000 Temperature
Isochronal
annealing
stressed specimens of H327
time
l°C
60mm
1500
)
curves
2000
for the pre-
and SMG parallel to the
axis of extrusion.
are obtained by applying the equation to the data shown in figs. la, lb and 2. In figs. 8a and 8b where - [ l/log(E/Eo)] versus the reciprocal of the pre-stress is plotted, eq. (1) is represented as a linear relationship, because the following equation can be obtained by taking the logarithm of the both sides of eq. (1) : 1 1 UC 1 - In (E/Eo) = F (--->. CT uc
Annealing
time
60min
I
0.950 Fig.
6.
stressed
J 2OcO
500 Annealing
T~rature
Isochronal
annealing
specimens
of
&y curves
for
the
IM-2
and
7477/PT
IEl-24,
pre-
parallel to the axis of extrusion or moulding.
The values of k and B for both extruded and moulded materials calculated from the results in figs. 8a and 8b are summarized in table 2. From fig. 8a, however, it is found that the equation of Jenkins is well fitted to the points only over a limited range, i.e. (0.66 to 1) ur for SMG, H327 and IEl-24 parallel to the axis, and (0.5 to 1) ur for SMG and H327 perpendicular to the axis. For moulded materials fig. 8b shows that it can be fitted to the data only in the very small intermediate range of the pre-stress level. Thus, in the present experiments it is believed that eq. (1) is not to be applied to extruded graphites at lower pre-stress levels and to moulded ones either at lower or at higher levels. A better fit to the points for extruded graphites used in the present experiments can be obtained with the assumption that the relation between change in the modulus and the pre-stress is represented by the equation, E - = -Aa2+B. Eo
Annealing Fig.
7.
cimens
Isothermal of H327
Time
annealing
parallel
(min) curves
to the
axis
for
the
spe-
of extrusion.
(2)
This is shown in fig. 9, and the values of A and B obtained are summarized in table 3. It is found that the equation of this type appears to be well fitted to the curve if the lower and higher pre-stress levels can be
M.
ET0
AND
T.
TABLE The values
3.9
5.3
2
of k and gC in the equation
0.067 UC
OKU
1 0.096 6.7
4.8
/ 0.027
~ 8.0
’ 0.020 6.6
of Jenkins
0.022 7.1
0.027
i 8.0
0.021 6.9
160
ReciprocalOdf”
I 0.2 0.L 2o0 Reciprocal of the Re-stress[(kglmm’
the Re-s!r&sIlkglm$
(4 Fig.
8.
Plots
for the calculation
I
(b)
of k and
oC in the
equation
of Jenkins,
(a) extruded
graphites
and
(b) moulded graphites.
considered separately, that is, two different equations of the form of eq. (2) are to be used for these two regions. It should be noted that the value of A for the specimen parallel to the axis becomes larger above a critical pre-stress level. On the other hand, those perpendicular to the axis have a smaller value of A at higher pre-stress levels. It would be possible to believe that the fact above results from the difference between the specimens in microstructure parallel to the axis and perpendicular to it. It is possibly considered that a compressive stress parallel to the basal plane is more effective in causing a change in the modulus than a stress perpendicular to the plane. Cracks and/or
microcracks on the basal plane would be more easily deformed by a stress parallel to the plane than by one perpendicular to it. It is also noted that IEl-24 which is Gilsocarbon graphite obeys eq. (2), although the amount of decrease in its modulus is almost the same as that of IM-2 or 7477/PT. Thus, it would be possible to consider that the behaviour of both needle coke and Gilsocarbon graphites, extruded, is well represented by eq. (2), though there is a remarkable difference in the amount of change in the modulus between needle coke and Gilsocarbon graphites. The effect of grain size may be one of the factors by which this kind of difference is caused. The dependence of
YOUNG’S
MODULUS
OF
SOME
NUCLEAR
321
ORAPHITES
it may be assumed that the change is to obey an equation
such as E-E, Eo-E,
= B exp ( -Aa2),
(3)
where Eo, E, and E are the original value of the
modulus,
the
modulus
at the
pre-stress
level near fracture stress and that at pre-stress
quare
Fig.
9.
Plots
10 of the Redress
of
change
[
in
20 lkg/mm212
the
1
3
modulus
versus
square of the pre-stress.
level of CT,respectively. Eq. (3) gives a better fit to the data in figs. lb and 2 if we assume, as in the case of extruded graphites, that the pre-stress level can be considered to consist of two separate regions, i.e. lower and higher pre-stress levels. The situation is shown in fig. 10 and the calculated values of A and B in eq. (3) are summarized in table 4. It should be noted that for the specimens of both IM-2 and 7477/PT perpendicular to the axis of moulding, the values of A are larger than unity, i.e. the modulus is not to change until B exp ( -A&) becomes smaller than unity.
3
TABLE
The values of A and B in the equation E/Eo=
- Aas+
B for extruded
A
graphites / Pre-stress level normalized to
B
( U(Wmm2)2)
fracture stress
i ;i H327
; 1
I ~ I
’ II SMG
~I~-~ 1
IEl-24
~//
1.00
1
0 to 0.47
1.12
/
0.47 to 1
0.027
1.00 ~
0 to
0.020
0.98
0.72 to 1
0.011
1.00 ~
0 to 0.67
0.023
1.12
0.67 to 1
0.0084
1.00 )
0 to 0.79
0.0059
0.97
0.79 to 1
0.0018
~ 1.00
0 to 0.58
0.0022
1 1.05
0.58 to 1
.~_
~
/
0.72
strength on grain size of graphite has already been pointed out by Knibbs 8). For the moulded graphites, it appears that the modulus change is levelled off at the pre-stress level near fracture stress. Therefore
Square of the Prestress
Fig.
10.
Plots for the calculation
equation (E-E,)/(Eo-E,) the modulus
change
=
of A and B in the
Bexp( - A ~2) by which
of moulded sented.
i ( kg/mm212 1
graphite
is repre-
322
XI .
ET0
AND
T.
4
TABLE
The
values
of A and
B in the
equation
A
( ~/(k/mm2)“)
II
OKU
((E-E,)/(Eo--E,))=B Pre-stress
H
exp (--A+)
It,vel
normalized fracture
tn
&j&J
stress
0.030
1.00
0 to
0.53
0.083
2.35
0.53
to
0.94
1
IM-2 1
7477/PT
0.051
1.82
0 to 0.55
0.098
2.79
0.55
to
0.94
1
~ Ii I /m
~1 Such critical stresses are about 2.2 and 2.45 kg/ mm2 for IM-2 and 7477/PT, respectively. The results on the effect of cyclic loading are in good agreement with those which have been obtained on the stress-strain relationship by the former investigators 135). That is, after being cyclically loaded several times between zero and a fixed stress level, the specimen produces hysteresis loops of the stress-strain curve that do not change with cyclic number and the paraelastic moduli remain the same. A point to be noted in fig. 3 is that the specimen pre-stressed to 0.85 (TI has fractured
except in the temperature range, 750 to 1200 “C, where the modulus decreases slightly. The modulus of IM-2 shows the annealing behaviour similar to that of 7477/PT. From these results it is clear that the complete recovery of the modulus is observed at about 1000 “C in the case of two extruded graphites, i.e. II327 and IEl-24, and another extruded graphite, SMG, also recovers completely at about 2000 “C. It’ is noted that moduli of moulded graphites do not recover completely up to 2000 “C. This fact also suggests that the mechanism of deformation or fracture differs between the
at the fourth cycle. This fact suggests the possibility of fatigue of nuclear graphite due to cyclic loading. The difference in the behaviour between needle coke graphites and Gilsocarbon or fine-grained graphite is that at higher stress levels the modulus change of the former caused by the second or third loading is rather small, while the latter shows a larger amount of decrease by the similar loading. The isochronal annealing curves in fig. 5 show that the moduli of H327 and IEl-24 recover completely at about 1000 “C, while those of SMG, 7477/PT and IM-2 do not. Moreover the modulus of the specimen of 7477/PT rather decreases between 700 to 1000 “C and is levelled off at higher annealing temperatures. Recovery of the SMG specimen is observed up to 2000 “C,
extruded and the moulded. Hart 6) also demonstrated that the degree of removal of stressinduced changes depends on the kind of graphite examined. The isothermal annealing curves for H327 parallel to the axis shown in fig. 7 give us the activation energy for the recovery of the modulus. The values obtained are shown in fig. 11, i.e. they are about 0.6 eV at any stages of the recovery. At present the meaning of this activation energy is not clear. However, it is believed that the energy has a certain relation to the crack closure or other mechanism of the recovery due to annealing 9910). 5.
Conclusions The conclusions
derived
are as follows:
YOUNG’S
MODULUS
OF
SOME
NUCLEAR
(4)
323
GRAPHITES
The results on the modulus change caused
by cyclic loading are in agreement with those which have been obtained from the stressstrain curve by the earlier authors.
H327tll)
(5) The moduli of extruded graphites recover almost completely up to about 1000 “C (H327 and IEl-24)
or 2000 “C (SMG),
while
in the
case of moulded graphites the complete recovery is not attained even at 2000 “C. The activation energy obtained for the recovery of H327 below 1000 “C is about 0.6 eV, although the mechanism of the recovery remains to be the problem for further investigations. Acknowledgements
Tenpercture (IC'I'K)
Fig.
11.
Plots of time versus annealing temperature for calculating the activation
energy.
(1) The curves obtained for the change in the Young’s modulus are well represented by the formula, E/E0 = - Ai+ B, for the extruded graphites, and (E - E,)/(Eo- E,) = Bexp (-A&) for moulded ones. A’s and B’s in both equations appear to differ corresponding to the difference in the direction of specimen. (2) The amount of the modulus decrease is smaller for the Gilsocarbon and fine-grained graphites than for needle coke ones, if the comparison between them is made at the same normalized pre-stress level. (3) In the case of extruded graphites the amount of the modulus decrease is larger for the specimen parallel to the axis than that perpendicular to the axis, while it appears to have almost no dependence on the direction of the specimen in the case of the moulded ones.
The authors wish to thank Dr. Y. Sasaki for permission to carry out the study, and Mr. T. Usui for technical assistance. Helpful advice and suggestion given by the members of the graphite research laboratory in JAERI are also acknowledged. References 1) Ph. P. Arragon and R. M. Berthier, Industrial Carbon and Graphite
(Sot. Chem. Ind., London,
1958) p. 565 2)
H.
H. W.
Carbon
Losty
Conf.,
and J. S. Orchard,
Vol.
1 (Pergamon
Proc.
Press,
3)
p. 519 G. M. Jenkins, J. Nucl. Mater. 5 (1962) 280
4)
E. J. Seldin, Carbon 4 (1966) 177
5)
W. L. Greenstreet, R. S. Valachovic,
6)
J. E. Smith, G. T. Yahr and
Carbon 8 (1970) 649
P. E. Hart, Carbon 10 (1972) 233
7)
S. Sato
8)
R.
9) 10)
5th
1962)
H.
and S. Miyazono, Knibbs,
J. Nucl.
Carbon 2 (1964) Mater.
24
(1967)
103 174
0. D. Slagle, Carbon 7 (1969) 337 I. B. Mason and R. H. Knibbs, Carbon 5 (1967) 493