Carbon
1966. Vol. 4. pp. 177-191.
Pergamon Press Ltd.
STRESS-STRAIN
OF POLYCRYSTALLINE
Printed in Great Britain
PROPERTIES
GRAPHITES
AND COMPRESSION
IN TENSION
AT ROOM TEMPERATURE
E. J. SELDIN
Union Carbide Corporation,
Carbon Products
(Received
Division, Parma Technical
11 February
Center, Parma, Ohio
1966)
Abstract-Longitudinal
and transverse stress-strain curves were obtained by static tension and compression tests for several grades of polycrystalline graphite. The stress was applied cyclically either in
tension or compression to observe hysteresis effects and residual strain as a function of stress. The
stress, o, was measured by an Instron load cell and the strains, E, by strain gages. The longitudinal
curves were fitted to Jenkins’ equation (E = Aa TBa’) ; generally good fits were obtained in the region of
low stress, and consistent deviations were found in the region of high stress. The transverse curves had
different curvature in tension and compression, but the residual strain was positive in both cases. A
series of cyclic tests in which the stress was alternately applied in tension and compression also demonstrated differences between the behavior of graphite in tension and compression. Some specimens were
annealed after stressing and then retested; these experiments indicated that the residual strains were
relieved and that the stress-strain properties were partially restored by a low temperature anneal and
completely restored by an anneal to the graphitization temperature. A qualitative interpretation of the
stress-strain properties of polycrystalline graphites, based on these results, is given.
1. INTRODUCTION
bined effects of mechanical stressing and annealing. These authors also reported that the permaTHE STRESS-STRAIN
relationship of a polycrystalline
nent set could be recovered either by annealing to
graphite
is characterized
by nonlinearity,
by
approximately
1500°C or by neutron irradiation.
hysteresis loops formed under cyclic stressing, and
The previous investigations
have been conby an attendant residual deformation when the
cerned only with the longitudinal
stress-strain
applied stress is released. These effects were first
curves of graphite, and the measurements
have
reported by ARRACONand BERTHIER(~’for graphite
been limited by the sensitivity of the apparatus
under compression,
and shortly afterwards by
used to measure the strain. A prime objective of
ANDREW, OKADA and WOBSCHALL@’for graphite
this investigation was the observation of both the
rods
deformed
as cantilevers.
LOSTY and
longitudinal and transverse stress--strain curves for
nonlinear
stress-strain
ORCHARD(~) observed
several polycrystalline
graphites in tension and
curves for graphite in both tension and comprescompression in order to obtain a set of elastic
sion and found that precompression
caused the
constants
for the different
graphites.
Where
Young’s modulus of a graphite to decrease but did
measurements
were
not appear to affect the tensile strength. JENKINS(“) possible, sonic resonance
made on the specimens before they were subjected
proposed a mechanical model and a set of equato static testing so that the sonic moduli could be
tions containing two parameters to describe the
compared with the static moduli in the limit of
stress-strain curves upon application, release, and
zero strain. A complete set of elastic constants has
reapplication
of the stress, and he fitted the
been obtained for ATJ graphite from the static
equations to the stress-strain
curve for a reactor
tensile data. Another objective of this investigation
grade graphite subjected to a relatively low compression
stress. JENKINS and WILLIAMSON(‘) was the comparison of the stress-strain behavior of
a graphite in tension with its behavior in comfurther elaborated upon the model to predict the
prestressed
pression. The effects of annealing
stress-strain properties of graphite under the comC
177
E. J. SELDIN
178
graphites were investigated, and the technique of
annealing was utilized for the comparison of tensile and compressive data on individual specimens.
In addition, a series of experiments
was performed in which individual
specimens
were
stressed alternately in tension and compression.
The results of these experiments shed new light on
the mechanical
properties
of polycrystalhne
graphite in that they reveal fundamental
differences between the behavior of graphite under tension and compression.
2. ELASTIC CONSTANTS AND STRESS-STRAIN
PROPERTH% OF POLYCRYSTALLINE
GRAPHITES
We shall be concerned here only with polycrystalline graphites formed by molding. For the
determination
of elastic constants, we shall define
an orthogonal coordinate system with three axes.
The direction of the applied molding pressure
forms an axis of symmetry for the material, which
we shall refer to interchangeably
as the againstgrain direction and as the 3-axis. The l- and 2axes are then equivalent. Although any direction
perpendicular to the Saxis is a with-grain direction, the l-axis will always be taken as the withgrain direction along which the stress is applied in
a tension or compression test on a with-grain
specimen.
In the low-strain elastic limit, there are five
independent
elastic compliances
for a molded
polyc~st~l~e
graphite: ~11, ~12, $13, 53s and ~44.
For an against-grain specimen, where the stress as
is applied along the 3-axis, there is a longitudinal
strain sr and two transverse strains ~1 and ~2,
given by
it =st303 =~a and
(1)
E3 =S33t73.
For a with-grain specimen, where the stress ur is
applied along the l-axis, there is a longitudinal
strain ~1 and two transverse strains ~2 and es,
given by
E1=Sll~lt
et =si201
and
(2)
83 =s13c1.
The shear compliance ~44 may be obtained from
a static tension or compression test where the 3axis, or axis of symmet~, is inclined at a known
angle with the specimen axis. Let us consider a
rotation of the 2- and 3-axes by an angle of 45”
about the l-axis so that the new specimen axes are
given by 1, 2’, and 3’. If a stress u’s is applied
along the 3’-axis, there will be a longitudinal strain
&I3and transverse strains ~‘1 and $2, given by
EIl
=S’13d3,
CJ’ 3
E’2=S123
E’3
and
(3)
==S’33d3.
The compliances in the primed coordinate system
can be shown@) to be related to the original complianees by the relationships
S’13
=h+S13)/2,
s’~~=(s~~+s~~+~s~~--s~~)/~, and
(4)
S’33=(S1i+S33+2S13+%4)/4-
From the last two relationships
obtain
S44=2(S’33-S’23).
in equations (41, we
(9
The shear modulus i/s44 can also be determined
directly in a static torsion test.
For large stresses, the stress-strain relationship
for a poly~rystalline graphite is nonlinear. A good
approximation
to the longitudinal
stress-strain
curve is the equation of JENKXNS’~)
&=Ad+-BCr2,
(6)
where A is equal to sss for an against-grain specimen and srr for a with-grain specimen. According
to JENKINS’ model, the longitudinal
residual
strain so after the graphite has been subjected to a
maximum stress a, is
so =+Bo2,,,.
(7)
3. ~~~AL
The stress-strain tests were run on an Instron
test machine at constant strain rate. Pure tension
tests were made on dogbone specimens which
were cut from rectangular blanks measuring 6$x la
x 4 in.; the gage sections of the tensile specimens
were 24 in. long and had either 4 x 4 in. or 3 x b_in.
cross-section. Pure compression tests were made
on + in. dia. cylinders approximately 1 in. long and
on specimens
with square cross-sections
of
similar length. A special tension-compression
specimen was made from a 1 x 1 x 4 in. blank into
a dogbone shape with a square gage section of
STRESS-STRAIN
PROPERTIES
OF POLYCRYSTALLINE
4 in.2 area by 2 in. long; this specimen had flat,
plane-parallel
ends so that it could be tested in
compression, and it also had a hole for a pin near
each end so that it could be tested in tension. The
specimen was placed in a specially designed cage
which sat on the compression load cell. The upper
half of the cage was attached to the moving crosshead of the Instron, and the lower half was held
against the load cell by means of a lever arm,
pinned at one end and loaded with weights at the
other end, which passed through the base of the
lower half of the cage. By thus preloading the
compression load cell, the specimen within the
cage could be tested in compression and/or tension.
In each case, sonic resonance tests were also made
on the tension and tension-compression
specimen
blanks before they were machined into dogbone
shapes.
Strains were detected by pairs of foil strain
gages on opposite faces of the specimen. The foil
gages all contained four fiducial marks to designate
the positions of the longitudinal
and transverse
gage axes. The specimen was held in a fixture on
the base of a travelling microscope, and the gages
were cemented to the specimens with the fiducial
marks aligned under the cross hairs of the microscope. It was estimated that a strain gage could be
positioned so that the gage axis was no more than a
few tenths of a degree out of line with the longitudinal axis of the specimen. The use of pairs of
gages on opposite specimen faces for the measurement of strain led to a cancellation of the effects of
smaI1 bending moments within the specimen and
gave a good average tensile or compressive strain
for the volume element between the gages.
Stress was measured by either the tension load
cell or the compression load cell on the Instron.
Strain was measured by means of a full strain gage
bridge and a Sanborn
Amplifier-Indictor,
a
device which supplies a high frequency excitation
of constant voltage to a strain gage bridge and
amplifies and rectifies the output to produce a
d.c. voltage proportional to the strain. Two such
Amplifier-Indicators
were used for the simultaneous me~urement
of longitud~al
and transverse strains. The strain signals were applied to the
X-axes of separate X-Y recorders, and the output
of the Instron load cell was applied to the Instron
recorder and to the Y-axes of the X-Y recorders.
If the measurement of strain in a second transverse
GRAPHITES
179
direction were desired, the Instron recorder was
also used as an X-Y recorder. The longitudin~
and transverse stress-strain
curves were all automatically recorded while the specimen was being
stressed.
The measurement
of strain is estimated to be
accurate to within about 2 per cent in the longitudinal direction and to within about 3 per cent in
the transverse direction, The estimates of the
accuracy of the strain measurements are based on
the gage m~ufacturer’s
estimate of the accuracy
of the gage factor and on calculations which were
made of the corrections to the strain measurements due to the transverse sensitivity of the
gages. The
transverse
sensitivity
correction
formula has been given by BAUMBERGERand
HINES,(~) and the transverse sensitivity coefficients
for type FAP foil strain gages were taken from the
data of Wu.@)
The modulus was determined directly from the
slope of the initial part of the stress-strain curve. In
order to improve the accuracy of this determination, the gain on each of the X-Y recorder scales
was increased for the initial application of the
stress. ‘Il%h a full scale stress on the recorder
chart somewhere between 100 and 200 psi, the
stress-strain curve was usually linear over a length
of several inches, and the residual strain was
extremely small.
4. RESULTS
J.I
Simple tension and compression
The Iongitudinal stress-strain
curves for polycrystalline graphites have similar shape in tension
and compression. The similarities and differences
are illustrated in Fig. 1, which is a composite
stress-strain
plot for two specimens
of ATJ
graphite oriented with-the-grain,
one of which was
stressed in tension and the other in compression.
The stress was cycled between zero and successively higher values of maximum stress in both
tests, and Fig. 1 shows the envelope stress-strain
curves and some of the hysteresis loops which
were obtained. The loops increase in width as the
m~imum stress is increased, the effect being more
apparent in the compression
data because the
compression strength of a polycrystalline graphite
is greater than its tensile strength.
The transverse stress-strain
curves for polycrystalline graphites have different shapes in ten-
180
E. J. SELDIN
I
TENSION
x
4
STRAIN
(PER CENT)
2
TRANSVERSE
LONGITUDINAL
E,
STRAIN
3
.4
E,
(PER CENT)
FIG. 3. Longitudinal and transverse stress-strain curves
for ATJ graphite, oriented with-the-grain. Tension test.
FIG. 1. Composite tension and compression data for two
specimens of ATJ graphite, oriented with-the-grain.
sion
and compression.
The differences are illustrated here for ATJ graphite in Figs. 2 and 3, but
the results are typical of all the graphites which
were tested. Figure 2 shows the longitudinal and
transverse stress-strain
curves for a with-grain
ATJ specimen stressed in comprefsion. The transverse strain represents an expansion and the longitudinal strain represents a contraction. The ratio
of the transverse strain to the longitudinal strain is
constant, independent
of the stress, yielding a
constant Poisson ratio. The transverse curve in
Fig. 2 shows the strain ES for the applied stress ur ;
the corresponding
transverse curve for ~2 was
similar, but the total strain was smaller.
Figure 3 shows the longitudinal and transverse
stress-strain curves for a with-grain AT J specimen
in tension. The transverse curve is nonlinear but
has a curvature opposite to that of the longitudinal
curve. The transverse strain is negative when the
tensile stress is applied, indicating a contraction;
but there is a positive residual strain when the
stress is released, indicating that the specimen has
~~~~
0.2
01
TRANSVERSE
0’0
.4
.8
1.2
~~GITWINAL
E,
STRAIN
1.6
2.0
6,
(PER CENT1
FIG. 2. Longitudinal and transverse stress-strain
for ATJ graphite, oriented with-the-grain.
test.
curves
Compression
increased in width. The longitudinal
and transverse data, taken together, demonstrate that, after
a tensile stress, there is an overall increase in
volume, the linear dimensions
increasing in all
directions. The stress-strain
curve for transverse
strain ~2 was similar in character to the curve for
ss shown in Fig. 3, but the strains were smaller.
There were no observable hysteresis loops in the
transverse stress-strain curves, the curves tending
to be linear as the stress was cycled between zero
and the previous maximum stress. The ratio of
transverse strain to longitudinal
strain decreased
as the stress increased; the Poisson ratio in tension
is, therefore, a function of the stress.
Representative
values of elastic constants and
strengths as obtained from tensile tests on several
standard grades of polycrystalline graphite manufactured by Union Carbide Corporation, Carbon
Products Division, are listed in Table 1. The sonic
moduli agree fairly well with the initial static
moduli. The values for the compliances were all
taken from the slopes of the stress-strain
curves
in the limit of zero strain, and the Poisson ratios
were obtained from these compliances.
Table 2 gives the elastic constants obtained in
tensile tests on three specimens of ATJ graphite
having the J-axis, or axis of symmetry, inclined at
an angle of 45 degrees with the specimen axis. The
primed compliances given in equations 3 were
determined directly from the data, and equation 5
was used to obtain the shear compliance $44 from
s’as and ~‘3s. The values of $44 which were thus
obtained agreed very well with sonic resonance
measurements
and with measurements
made
independently
in static torsion tests on other ATJ
specimens.
STRESS-STRAIN
PROPERTIES
TABLE 1. T~PICALTENSILEDATA
OF POLYCRYSTALLINE
181
GRAPHITES
FOR SEVERAL GFZADESOFPOLYCRYSTALLINEGRAPHITE
Initial
Static
modulus
(10’ psi)
Grade
Grain
orientation
Llensity
(g/cm*)
Strength
(psi)
Sonic
modulus
(10s psi)
1bll
l/S,,
$11
ATJ
with-grain
1.72
3,800
1.64
1.64
8.85
0.84
0.10
RVA
1.87
3,170
2.01
2.01
7.22
0.78
0.11
RVC
1.84
2,385
1.82
1.76
8.25
1.26
0.15
RVD
1.88
3,915
2.28
2.33
6.23
0.71
0.11
CFW
1.90
1,950
1.60
1.63
8.90
1.07
0.12
CFZ
1.93
3,510
2.06
2.04
7.11
0.89
0.12
CHQ
1.61
2,760
1.28
1.30
11.12
2.42
0.22
ZT4
1.94
4,400
2.75
2.56
5.67
0.37
0.07
1.72
3,900
1.66
1.67
8.70
- %s
1.36
-%3/%1
0.16
RVA
1.86
3,385
2.01
2.01
7.22
1.15
0.16
RVC
1.84
1.83
1.83
7.93
1.73
0.22
RVD
1.88
2,400
4,050
2.12
2.31
6.28
1.37
0.22
CFW
1.90
1,915
1.62
1.65
8.80
1.31
0.15
CFZ
1.93
3,568
2.06
2.06
7.05
1.21
0.17
CHQ
1.61
2,860
1.26
1.25
11.60
2.05
0.18
ZTA
1.96
4,350
3.07
2.89
5.02
1.28
ATJ
with-grain
Compliances
(IO-‘scma/dyne)
(IO-‘*ems/dyne)
-
Poisson
ratio
- s1*/sn
s12
0.25
_
1 I&
1.12
1 l&J
1.17
%I3
12.36
1.40
kllSJ8
0.11
2,400
1,500
1.30
1.30
11.17
1.24
0.11
1.42
1.44
10.08
1.61
0.16
1.92
2,840
1.36
1.36
10.67
1.32
0.12
CFW
1.91
1,720
1.52
1.49
9.75
1.31
0.13
CFZ
1.93
2,345
1.52
1.54
9.43
1.15
0.12
CHQ
1.58
.96
15.10
2.06
0.14
ZTA
1.95
.66
22.00
1.19
0.05
1.72
3,000
RVA
1.85
RVC
1.86
RVD
ATJ
against-grain
1,630
0.71
TABLE ~.TENSILEDATA
Specimen
Density
(g/cm”)
s 33
FOR ATI
GRAPHITE~~~CUT
Static compliances
( 1@‘scm2/dyne)
-S’13
w*s- S’OEJ
(10-%m*/dyne)
a4 =
I
--s 2s
1
1.69
11.12
1.15
1.51
25.3
2
1.69
11.24
1.19
1.37
25.2
3
1.71
10.92
1.13
1.45
24.7
The longitudinal stress-strain curves were fitted
to the two-parameter equation 6 of JENKINS.(~)
The parameter A, equal to either $11 or ~33, was
obtained from the initial slope of the curve in the
limit of zero strain. The parameter B was determined graphically from log-log plots of s--Au vs.
(T by drawing a line with a slope of 2 which best
fitted the data at the lower and intermediate stress
levels. In this manner, a good fit was usualIy obtained for the entire envelope stress-strain curve in
tension and for the envelope curve in compression
up to approximately 60 per cent of the breaking
182
E. J. SELDIN
‘in,
0
/,,
.4
.a
STRAIN
(
,
I6
1.2
,
1
20
(PER CENT)
FIG. 4. Comparison of longitudinal stress-strain curves
in tension and compression for two ATJ graphite specimens of the same density, oriented with-the-grain.
Compression data was fitted to equation (6).
strength. Figure 4 illustrates the fit obtained for
the two specimens of ATJ graphite, the stressstrain curves of which are also given in Fig. 1. The
significant feature of the plot is that the observed
strain increases more rapidly with stress than the
strain predicted by equation 6 if one uses the
values of A and B which are found by curvefitting at the lower stress levels. This type of
deviation between observed behavior and that predicted by equation 6 was found for almost all of the
graphites which were tested. Table 3 lists representative data obtained from compression tests on
TABLE
3. TYPICAL
COMP~I~NDATA
several standard grades of graphite. The parameters A and B, determined by curve fitting at the
lower stress levels, are given in engineering units.
The ratio of B to A is a measure of the nonlinearity
of the stress-strain curve.
According
to equation
7, the longitudinal
strain aa after a maximum stress a, should be
the residual
equal to iBa2,,,. Experimentally,
strain in a tension test was found to be proportional to the square of the stress and to be greater
than +Buzm. A different value of B could be
obtained from a plot of co vs. 02,, using equation 7,
which was 15-20 per cent higher than the value of
B obtained from a log-log plot of a- Au vs. u,
using equation 6. The residual strain in a compression test was found to vary with the stress as
o”, with n falling between 1.6 and 1.9 for different
graphites, in such a manner that the residual strain
was less than $Ba’,. In brief, the longitudinal
residual strain was found to be greater in tension
and lower in compression than the value predicted
by equation 7. Further evidence of this inequality
of the residual strains in tension and compression
is presented in Sections 4.3 and 4.4. The shapes of
the stress-strain
curves on release and reapplication of the stress and the widths of the hysteresis
FORSEWRALGRADES
OFP~LYCR~~TALLINR
Initial
static modulus
(lo6 psi)
GRAPHITE
Grade,
Grain’
orientation
Density
Strength
(g/cm?
(psi)
ATJ
WG
1.72
11,400
1.72
581
43
AG
1.72
9,150
1.22
817
100
RVA
RVC
RVD
CFW
CFZ
CHQ
ZTA
A
B
10-g(psi)-’
lO-‘a(psi)-”
WG
1.84
10,250
1.90
525
62
AG
1.87
10,375
1.34
745
100
WG
1.84
11,000
1.79
558
50
AG
1.85
10,475
1.34
748
110
WG
1.93
12,900
2.31
433
45
AG
1.88
12,480
1.16
860
133
WC
1.89
8,840
1.66
602
78
AG
1.90
9,000
1.51
663
83
WG
1.93
12,160
1.88
532
44
AG
1.92
11,600
1.44
696
77
WG
1.61
14,850
1.37
732
11
AG
1.58
10,000
0.96
1043
28
WG
1.96
8,400
3.34
300
55
AG
1.97
14,700
0.70
1425
155
*WG-with
AGagainst
grain
;
grain.
STRESS-STRAIN
PROPERTIES
OF POLYCRYSTALLINE
loops were close to those predicted by JENKINS’
model .f4f The transverse residual strain was positive for all of the graphites which were tested,
regardless of whether the applied stress was in
tension or compression. In addition, the positive
residual strain was slightly greater for a given tensile stress than that obtained for an equal, but
opposite, compressive stress.
4.2 Annealing experiments
The residual strain in a graphite which is
stressed in tension or compression has been sometimes referred to as a “permanent set”. We have
observed the permanency of the residual strain by
tensile tests on several specimens of ATJ graphite
which were retested several months after the
original tests. It was found that the residual strain
was, indeed, permanent, in that it did not increase
until the previous maximum stress was exceeded.
However, it has also been found that the residual
strain, whether introduced
by tension or compression, can be relieved by a high-temperature
anneal; thus, in this sense, the strain is not permanent. The recovery of residual strain by a high
temperature anneal was also observed by ANDREW,
OKADAand WOBSCHALL'~) in cantilever and torsion
tests.
We shall describe, first, a series of compression
tests combined with annealing which were run on
some ATJ and ZTA graphite cylindrical specimens 1 in. long with 0.2in2cross-section.
The order
of the tests and the dimensional
changes after
compression and annealing are given in Table 4.
Specimens 1 to 4 were annealed together at each
step, and specimen 5 was annealed by itself. The
cylinders were machined
before receiving any
heat-treatment,
and their lengths were carefully
measured before and after each test with micrometer calipers capable of reading to within 0.0002
in. The first heat-treatment
to 3000°C caused the
with-grain ZTA cylinder to contract and all the
other cylinders to expand, indicating
that the
original graphitization
temperatures
were below
3000°C and establishing
3000°C as the new
graphitization temperature. The compression test
was a cyclic test in which the stress was increased
in increments of 1000 psi to 8000 psi; the only
exception was the against-grain
ZTA cylinder,
where the maximum stress was 10,000 psi. Each
specimen was given exactly the same test after
z
R
2
183
GRAPHITES
8
6
E4
E
I
E
2
m
0
0
4
_A
.8
I2
STRAIN E, (PER CENT)
FIG. 5. ATJ graphite, oriented with-the-grain; heattreated to 3000°C; compression test. Solid curve:
Original envelope stress-strain curve of previously unstressed specimen tested up to a maximum stress of
8000 psi. Points: From the cyclic stress-train data for
the same specimen after annealing to 3000°C.
annealing as it was given before annealing: the
same stress-strain
curves were obtained after
annealing as were obtained before annealing.
Figure 5 is the stress-strain
plot for the with-grain
ATJ graphite cylinder, which is representative of
the excellent correlation
the group, showing
between the original stress-strain
curve and that
obtained after the first anneal. Only one of the
hysteresis loops is shown, but the other hysteresis
loops for this specimen were also reproduced in
faithful agreement with the original data. Furthermore, all of the stress-strain
curves were reproduced once again after another anneal to 3000°C.
The length measurements given in Table 4 indicate that the lon~tudinal
strain is completely
relieved by annealing the graphite back to the
graphitization
temperature.
According
to the
notation used in Table 4, this condition requires
that L2 and L4 be equal to LO_The condition holds
very well for the data for the ATJ cylinders. However, for the ZTA cylinders, the length Lz differs
from Lo by an amount greater than that which can
be attributed
to normal experimental
error. A
reasonable explanation of this behavior is that, on
heating the ZTA specimens a second time to
3OOO”C, the graphite continued the shrinkage in
the with-grain direction and the expansion in the
against-grain direction which was observed after
the initial heat-treatment
at 3000°C. This result
indicates that further graphitization
occurs while
the hold time at 3000°C is increased. However, the
stress-strain
curves show that the mechanical
properties are not noticeably changed by increasing the hold time at the annealing temperature.
Tension tests combined with annealing were run
on some against-grain
ATJ specimens
which
___..
-__.
1
2
3
4
5
Specimen
No.
TABLE4.
G
ATI
_.._-.
with grain
against grain
with grain
against grain
against grsin
ATJ
ATJ
ZTA
ZTA
-
,..,
0.9982
0.9936
0.9976
0.9986
0.9866
Before
heattreatment
OF CY&1NDRtCAl..
Orientation
1N INCHES
rsphite
LENGTHS
.”
-
- 0.0027
- 0.0052
-0.0021
- 0.0065
-0.0050
AL =L1-_L,
. . .,~ - ..,
0.9971
0.9902
0.9937
0.9968
0.983 1
0.9998
0.9954
0.9958
1.0033
0.9881
-.
L1
h
AS MEASURED
_.
WlTH
_
.-
-
0.9998
0.9951
0.9953
1.0039
0.9878
0
-0.0003
- o.ooos
0.0006
0.0003
-
,.
Calls
-
-
0.9971
0.9902
0.9932
0.9977
0.9833
cmpression
teat
L,
After second
MICROMRTZR
After anneal
to 3ooo”C AL XL,-_L,
L*
l?XPJZRIMENTS
OF GRAPHXTR
ANNFALING
SPECIMENS
After heat
After first‘re;gF’
to com;;’
COMPRESSION
- 0.0027
-0.OOs2
- 0.0026
-0.0056
-0.0048
AL=L,-LO
0.9996
0.9947
0.9951
1.0040
Lb
to 3WC
After anneal
AT VMZXOUS STAGES DURMG
p
E;
2
3
‘;4
STRESS-STRAIN
PROPERTIES
OF POLYCRYSTALLINE
apparently had been graphitized at a temperature
below 3000°C. This fact was demonstrated
by
testing an “as received” specimen, heating it to
3OOO”C, and then retesting it. After the heattreatment, the initial modulus was lower and the
residual strain was higher. These tensile specimens were, therefore, heat-treated
initially to
3ooo”C to establish this temperature as the graphitization temperature. Then a single against-grain
ATJ tensile specimen was tested, annealed at a
low temperature,
tested again, annealed at a
higher temperature, again tested and so on up to an
annealing temperature
of 3000°C. The tension
tests were identical and went to a maximum stress
of 1400 psi. Both longitudinal
and transverse
stress-strain
curves were obtained. Because the
residual strains in these tests were too small to be
tested by micrometer calipers, the strain gages
remained the sole source of the residual strain
measurements.
Figure 6 is a plot of the longitudinal
residual
strain as a function of the annealing temperature
for one ATJ specimen, with the holding time at
temperature shown beside each point on the plot.
The residual strain increased monotonically with
the annealing
temperature
and equalled
the
original residual strain when the annealing temperature was equal to the graphitization temperature.
The same statement
applies to the positive
residual strain in the transverse
stress-strain
curve. These results imply that the residual strain
is completely recovered after an anneal to the
graphitization
temperature
and is partially recovered after an anneal to a temperature below the
graphitization temperature. Thus, the right-hand
IOMIN.
100
-‘i
IOMIN
75
IOMIN
50
ANNEALING
gz
$2
s:,
L.J
c- 9
TEMt? (‘Cl
FIG. 6. Residual strain vs. prior annealing temperature
for ATJ graphite, oriented against-the-grain. Tested to
140Opsi tension Holdingtime at temperature is indicated.
GRAPHITES
185
ordinate of the plot in Fig. 6 shows the percentage
recovery of residual strain. This reasoning leads to
the conclusion that the polycrystalline
graphite
was completely restored by an anneal at the
graphitization
temperature
to its original state
before the external stress was applied.
4.3 Comparison of tension and compression data
by annealing (ATJ
and ZTA graphites)
The main obstacle in designing a test which will
compare the tension and compression properties
of a polycrystalline graphite is that a static tension
or compression test introduces residual strains and
thereby causes the stress-strain
properties of the
graphite to change. The problem, then, is to
determine a method whereby one can compare the
original tension
and compression
stress-strain
properties of a given specimen of graphite when
either type of test introduces residual strains and
causes the properties to change. Fortunately,
an
anneal at the graphitization temperature seems to
restore the graphite to its original condition, so that
the technique of annealing offers a means of obtaining a true comparison of original tension and
compression stress-strain data on the same specimen of graphite.
A series of experiments was performed in which
there were four ATJ specimens, two oriented withthe-grain and two oriented against-the-grain,
and
a similar set of four ZTA specimens. The specimens were of the type which could be tested in
tension and/or compression in the tension-compression cage. All of the materials were heattreated at the same time to 3000°C to establish the
graphitization
temperature
before the specimens
were machined. Each specimen was then alternately tested and annealed to 3000°C for a total of
three tests. The tests on a given specimen were
performed either in the order tension-compression
-tension
or in the order compression-tensioncompression. The third test was made identical to
the first test as a check on the effectiveness of the
annealing procedure. Although different sets of
gages were, of necessity, used for each test on a
given specimen, the same volume element in the
center of the gage section of the specimen was
examined in each test.
In the limit of zero strain, the initial static
longitudinal modulus for a given specimen was the
same, within the limits of experimental
error, in
E. J. SELDIN
186
tension and compression and was equal to the
sonic modulus which was determined from the
specimen blank. In the first approximation,
the
longitu~n~
stress-strain
curves were identical in
tension and compression for all but the againstgrain ZTA specimens, and there was generally
very good agreement in both the longitudinal and
transverse data between the first and third tests on
each specimen.
For the ATJ graphite, the agreement between
the tension and compression data is illustrated in
Fig. 7, which shows that the longitudinal stressstrain curves for this particular ATJ specimen COincided almost perfectly, as did the transverse
curves of the first and third tests which were in
tension. The data for the other three ATJ specimens (not shown) also indicated excellent agreement between the first and third tests, which were
of the same type except that, at the higher stress
levels, slightly greater strain was observed in the
tensile data than in the compression data. There
was also definitely greater lon~~dinal
residual
strain for a given value of stress in tension than in
compression.
For the ZTA graphite, there was also excellent
agreement in both the longitudinal and transverse
stress-strain data between the first and third tests,
which were of the same type. However, comparisons between tension and compression data must
TRANSVERSE
6,
.9’
STRAIN E, (PER CENTI
0I
02
I
.04I
06I
08
IO
7
=
6
2
“0
J
b-
5
:
4b
9
b+ 3
t
TRANSVERSE
8
STRAIN
E, (PER CENT)
02
0
02
04
06
/
I
’
’
/
I
7
I
2
/‘/
LONGITUDINAL,
+.
.I
,’
,’
/
/&’
/
,
/
/’
/
,9
4
’
,‘TRANSVERSE
,@
I
I
/
I’
/I
I
1.0
6
LONGITUOINAL
STRAIN
<,
I
12
I
1.4
_
(PEA CENT1
FIG. 8. Longitudinal and transverse stress-strain curves
for ZTA graphite, oriented angst-the-gun.
Curve 1: First test in tension after heat treatment to
3oOO”c.
Curve 2: Second test in compression after anneal to
3000°C.
Curve 3 : Third test in tension after anneal to 3000°C.
be made separately for each grain orientation. For
the with-grain ZTA specimens, the tension and
compression
stress-strain
curves were almost
identical except that there was possibly less strain
for a given stress in tension than in compression.
Even the longitudinal
residual strains in compression were comparable to those obtained in
tension, being possibly slightly greater in compression than in tension at the higher stress levels.
For the against-grain
ZTA specimens,
much
greater longitudinal
strain was obtained at the
higher stress levels in tension than in compression.
This fact is illustrated by Fig. 8, where the tension
curves can be seen to be quite different from the
compression curve even though the initial static
moduli are the same. The longitudinal
residual
strain for a given stress was very much greater in
tension than in compression.
2
,
I
n
“0
I
I
I
.2
.4
I
.6
I ONGITUDINAL
.6
STRAIN
I
10
2-J
12
14
E, (PER CENT1
FIG. 7 Longitudinal and transverse stress-strain curves
for ATJ graphite, oriented with-the-gram.
Curve 1: First test in tension after heat treatment to
3ooo”c.
Curve 2: Second test in compression after anneal to
3000°C.
Curve 3 : Third test in tension after anneal to 3000°C.
and ZTA graphites)
With the use of the tension-compression
cage,
several stress-strain tests were made in which the
stress was cyclically varied between tension and
compression. The results of one such test on a
with-grain ATJ specimen are shown in Fig. 9. The
stress was cyclically reversed from compression to
tension while increasing the maximum stress on
successive cycles by uniform increments of 400
STRESS-STRAIN
PROPERTIES
OF POLYCRYSTXLLINE
1
.I6
TRANSVERSE
STRAIN
EJPER
CENT)
Frc. 9. Cyclic compression-tension
test for ATf
graphite, oriented with-the-grain.
Letters designate in
alphabeticat sequence the load-reversal points.
psi. The letters in Fig. 9 denote in alphabetical
sequence the stresses at which the load was
reversed. Since the first applied stress was in compression, the specimen was taken to an equal and
opposite value of stress in tension, and the stress
was increased on each compression cycle to a maximum stress of 2000 psi, the test concluding with a
second compression to 2000 psi.
The longitudinal
stress-strain
curve in Fig. 9
contains loops which increase in length and width
as the stress is increased. The slope of the curve in
the initial compression (i.e. the initial modulus) is
greater than the slope at zero stress when the
stress was reversed into tension. This result is in
agreement with the observation
of LOWY and
O~cwmd~~
that the Young’s modulus in tension is
lowered by precompressing
the graphite. In a
similar manner, the Young’s modulus in compression can be lowered by prestressing a graphite
in tension. At the end of each complete cycle (the
stress in a complete cycle varying from zero to
- of in compression, back to I~CQ in tension, and
then back to zero), there was a positive residual
strain, i.e. a tensile strain, which increased as (rl
increased, Increasing the stress in compression by
an increment of 400 psi caused the longitudinal
residual strain to be reduced almost to zero, and it
GRAPHITES
187
would have been possible, of course, to give the
graphite a negative residual strain by further
increasing the stress in compression. The introduction of a positive residual strain when the
graphite is cyclically stressed between equal and
opposite stresses can be related to the observations
on the pure tension and pure compression tests,
where it was found that the residual strain was
always greater in tension than in compression.
Here, in a cyclic test on a single specimen, is
evidence that for a given stress the residual strain
is greater in tension than in compression.
The transverse stress-strain
curve in Fig. 9
further illustrates
the difference between the
behavior of graphite in tension and compression.
For a stress to 400 psi, there was no noticeable
transverse
residual strain;
but as the stress
increased, the residual strain increased and was
positive for both tensile and compressive stresses.
Figure 9 shows only the stress-strain plot with the
transverse strain ~3~but the stress-strain plot with
the transverse strain EZ was similar in character.
Though the longitudinal
residual strain can be
reduced to zero by appropriately
varying the
tensile and compressive stress, Fig. 9 demonstrates
that, once a polycrystalline graphite is stressed, it
cannot be worked back mechanically to all of its
original dimensions because the transverse dimension is always increased.
In another series of experiments, cyclic stressstrain tests combining tension and compression to
equal and opposite stresses were run on -4TJ and
ZTA graphite specimens
oriented with- and
The maximum
stress was
against-the-grain.
chosen to be about 10 to 20 per cent below the
tensile strength, and both the longitudinal
and
transverse stress-strain curves were observed.
The type of behavior which was observed is
illustrated in Figs, 10 and 11 where the results for
two with-grain ATJ specimens are shown. In Fig.
10, the stress was applied first in tension and then
in compression; in Fig. 11, the stress was applied
frst in compression and then in tension. On the
first complete cycle, the stress was increased in
increments to the maximum stress in both directions. On the second complete cycle, shown by the
dashed curves, and on further cycles, the stress
was cycled between its two limiting values. The
results for the against-grain
ATJ specimens and
the ZTA specimens were so similar that the
E. J. SELDIN
188
.I6
.08
0
LONGITUDINAL
.06
STRAIN
.I6
b
_L-_-J--d
.Ol
.02
TRANSVERSE
24
C, (PER CENT)
.03
.x%4
STRAIN GE, (PER CENT)
FIG.
10. Stress-strain
curves for ATJ graphite, oriented
with-the-grain,
stressed between ffi00
psi, first in
tension and then in compression.
.24
.I6
.06
LONGITUDINAL
0
.oe
16
24
32
‘STRAIN Et (PER CENT)
41-I
Ldi
4
02
.OI
0
TRANSVERSE
.Ol
.02
.03
04
STRAIN Es (PER CENT)
FIG. I I * Stress-strain cur&s for ATJ graphite, oriented
with-the-grain,
stressed between&3200
psi, first in
compression and then in tension.
pattern of behavior shown in Figs. 10 and 11 is
deemed to be representative.
In the longitudinal direction, the residual strain
after one comnlete cycle was generally positive,
regardless of whether the initial stress was in tension or compression. The only exception was withgrain ZTA graphite which was stressed first in
tension, where the residual strain for a given compressive stress was equal to or slightly greater than
the corr~ponding
residual strain for an equal
tensile stress. For both grades of graphite, however, the difference between the residual strain
in tension and compression was greater for the
against-grain
orientation than for the with-grain
orientation. On the second cycle, there was always
a shift of the stress-strain loop on the compression
end toward the positive strain direction,
i.e.
toward lower compressive strain, while the tension
end of the stress-strain loop either remained fixed
or shifted slightly in the positive strain direction,
This shift was greater when the initial stress was
in compression. A careful comparison of the data
for ‘identical’ specimens indicated that the position of the loop for the second and successive
cycles may be independent
of whether the initial
stress was in tension or compression. The loop for
the third complete cycle (not shown) tended to fall
close to that of the second cycle. The end points
of the thiid loop were close to those of the second
loop, being sometimes displaced with another
small shii in the positive strain direction, and the
third loop was always slightly narrower than the
second. On further cycles, the width of the loop
tended to remain constant.
In the transverse
direction,
the interesting
feature of the data is that the residual strain
became more positive after the stress was reversed, regardless of whether the initial stress was
in tension or compression.
The one exception
which was found to this general rule was for withgrain ZTA specimens which were first given a high
compressive stress to 8000 psi and were then
stressed in tension;
as the tensile stress was
increased,
the transverse
residual strain fist
decreased slightly and then increased. With-grain
ZTA specimens stressed in compression to 4000
psi followed the general rule stated above. For all
of the specimens, the transverse residual strain
increased slightly on the second cycle.
With repeated cycling beyond the third cycle,
the residual strain in the against-grain
direction
increased gradually in both ATJ and ZTA specimens. For the with-grain specimens, the loops on
the longitudinal
stress-strain
plots generslly did
STRESS-STRAIN
PROPERTIES
OF POLYCRYSTALLINE
not shift after the third cycle, whereas the curves
on the transverse
stress-strain
plots shied
slightly with each cycle. For the against-grain
specimens, the loops on the longitudinal
stressstrain plots shifted slightly with each cycle,
whereas the curves on the transverse stress-strain
plots showed no shift after about the third cycle.
Two ZTA specimens with each grain orientation were cvcled at the Instron rate of 0.01 in. min
until they failed, which was in tension in each case.
The two with-grain specimens were stressed to
+4000 psi, and they failed after 20 and 21 cycles.
The two against-grain specimens were stressed to
+ 1400 psi, and they failed after 30 and 56 cycles.
The fatigue failure appeared to be associated with
the slight increase with each cycle of the strain in
the against-grain direction.
The
with-grain
ZTA
graphite
specimens
showed anomalous
behavior in two respects.
First, the longitudinal strain was slightly greater
in compression
than in tension. Secondly, the
transverse stress-strain curve in tension showed a
curious reversal as the stress was increased. This
behavior is illustrated in the stress-strain
plot of
Fig. 12, where the specimen was stressed first to
4400 psi in tension and then to 8000 psi in compression. In the longitudinal direction, a compressive stress equal and opposite to the maximum ten-
* ! &‘:i
.a
LONGITUDINAL
TRANSVERSE
id
!- 1-._1_J-
6
.4
2
STRAIN
E,
0
2
(PER CENTI
STRAIN c3 (PER CENT)
FIG. 12. Stress-strain curves for ZTA graphite, oriented
with-the-grain, stressed first in tension to 4000 psi and
then in compression to 8000 psi.
GRAPHITES
189
sile stress caused a reversal in the sign of the
residual strain. In the transverse direction, the
strain reached a maximum at a tensile stress of
about 2000 psi and then decreased as the stress was
increased further. The transverse strain in Fig. 12
is EJ ; this type of behavior was not observed for the
transverse strain ~2. The transverse tensile stressstrain curves for against-grain
ZTA graphite
specimens did not show the strain reversal effect
seen in Fig. 12, but the effect may not be observable because of the lower tensile strength of ZTA
graphite with this grain orientation.
5. DISCUSSION
A comparison of the elastic constants of polycrystalline
graphite with those of the single
crystal reveals that the polycrystalline moduli are
much lower than ‘/srr and i/s33 for the single
crystal. The only single crystal modulus which is
low is the shear modulus ‘/sbd, and this modulus
is much lower than any longitudinal
modulus
for a polycrystalline
graphite.
Assuming
that
the stress-strain
properties of a polycrystalline
graphite are related to the elastic and plastic
properties of the individual
crystallites and to
their physical
arrangement
as an aggregate,
SIMMONS(‘)has suggested that the elastic moduli of
a polycrystalline graphite depend primarily on the
single crystal shear modulus, since the only easy
mode of deformation
in a graphite crystal is
through
shear. With this same assumption,
KELLY
has proposed a model for the small
strain elastic constants of polycrystalline graphites
in which the moduli depend primarily on the
single crystal shear modulus and for which the
dominant mechanism is the motion of dislocations
along basal planes. The model of JENKINS,(~~~)
which describes the larger strain deformations and
hysteresis effects, also is based on the concept of
slip and shear deformation along the basal planes
of the crystallites. Both of these models assume
some type of retarding force for the shear deformation, either in the form of pinning points for the
dislocations or local stresses which oppose slip.
The origin of the local stresses in polycrystalline
graphites is generally conceded to be due to the
large differences in the coefficients of thermal
expansion of the crystallites along and normal to
the basal planes; the nonuniform
contraction of
the crystallites which takes place as the polycrystalline aggregate cools from the graphitization
190
E. J. SELDIN
temperature leads to shrinkage cracks and shear
deformation and results in internal stresses within
the crystallites. These internal stresses, which
were first postulated by MROZOWSKI,(~~)provide
the basic initial conditions
for the models of
KELLY
and JENKINS. We suggest here a further
extension of these ideas to interpret the differences
between the tension and compression properties
and, in particular, the peculiar and distinctive
transverse stress-strain
properties of polycrystalline graphites.
The longitudin~
stress-strain curves in tension
and compression
are nearly identical for most
polycrystalline
graphites and are described very
well in the first approximation by JENKINS’model.
However, closer inspection
of the longitudinal
stress-strain curves reveals that, for a given stress,
there is in general slightly greater strain in tension
than there is in compression, and there is also
greater residual strain than there is in compression.
Furthermore,
the transverse stress-strain
curves
have different curvature in tension and compression, and the residual strain is always positive
regardless of whether the applied stress is in
tension or compression.
Within the individual
crystallites, the external stress can lead to a combination of (1) elastic deformation, (2) irreversible
shear (or plastic) deformation, (3) relief of internal
stresses, and (4) local stresses greater than the
breaking strength which can cause microcracks.
The first two processes cited above have been
used to account for the general shape of the longitudinal stress-strain curves. A combination of the
last three processes may be used to account for the
small differences in the longitudinal stress-strain
curves and for the large differences in the transverse stress-strain
curves for tension and compression.
We suggest that the differences in the stressstrain behavior of a polycrystalline
graphite in
tension and compression are due to the different
manner in which the internal stress distribution is
affected by the external tensile and compressive
stresses. The internal stresses are frozen in when
the graphite cools from the graphitization temperature as the crystallites contract more in the cdirection and less in the a-direction
than the
average contraction of the polycrystalline
aggregate. As a result, there is a complex distribution of
internal stresses, with individual crystallites being
subjected to stresses which are either tensile, compressive, or shear, or a combination of more than
one type of stress. Since the polycrystalline
graphite is in equilibrium
at room temperature,
there must be a balance between the different
types of internal stresses. However, the crux of
our argument is that there is a statistical imbalance in the distribution of internal stresses such
that there exists an excess of crystallites with their
c-axes in tension and an excess of crystallites with
their a-axes in compression. The external stress
then causes a change in the internal stress distribution and some relief of the internal stresses, but the
changes which take place in the internal stress
distribution depend on the type of external stress
which is applied; thus, it is this combination
of
forces which causes the stress-strain properties to
be different in tension and compression.
If an external compressive stress is applied,
there will be a decrease in the internal c-axis tensile stress component
and a corresponding
increase in the internal a-axis compressive stress
component. On the other hand, if an external tensile stress is applied, there will be an increase in the
internal c-axis tensile stress component
and a
reduction in the internal u-axis compressive stress
component.
This discussion is certainly not a
complete
description
of the actual processes
which are occurring, because the major part of the
deformation which takes place under an external
stress is through shear strain; but the changes in
the statistical imbalance in the internal stress
distribution are as stated. The changes in the aaxis stress component
involve relatively small
changes in strain in the crystallites because of the
high a-axis modulus, but the changes in the c-axis
stress component involve much larger strains. The
decrease in the c-axis tensile stress component by
the application of an external compressive stress
of the magnitude
used in our annealing tests
(between 65 and 95 per cent of breaking strength)
is apparently not accompanied by any failure in the
crystallites. However, the increase in the c-axis
tensile stress component by the application of an
external tensile stress should lead to an increase in
the c-axis stresses in individual crystallites and
should cause the relief of some of the c-axis stress
components
either through shear or by microcrack formation. This relief of the c-axis tensile
stress component in the internal stress distribution
STRESS-STRAIN
PROPERTIES
OF POLYCRYSTALLINE
under the action of an external tensile stress, then,
must be accompanied by a corresponding
reduction in the a-axis compressive stress component of
the internal stress distribution. During the application of the tensile stress, the relief process causes
the longitudinal
strain in the polyc~stalline
graphite to be slightly greater and the transverse
negative strain to be smaller in magnitude than
they wouId otherwise be. When the tensile stress is
removed, the transverse dimensions of the graphite
are larger than the original dimensions, i.e. there
is a transverse positive residual strain. For the
highly anisotropic
ZTA graphite, the internal
stress relief was so great that the transverse stressstrain curve, as shown in Fig. 12, showed a
reversal in the strain as the tensile stress was
increased.
The stress relief process leads to a slight
increase in the n- and c-axis dimensions of the
crystallites after the tensile stress is removed. However, the annealing experiments on compressed
specimens give direct evidence that the original
longitudinal dimensions of a specimen are restored
by reheating the graphite to the graphitization
temperature.
Since the longitudinal
and transverse stress-strain curves can be reproduced after
this type of anneal, the implication is that the
original structure of the material, including the
original crystallite dimensions,
can be restored.
This restoration of original structure is possible
because the thermal expansion of a polyc~stalline
graphite is much greater than the residual strain
introduced in any tension or compression test at
room temperature.
Although there is no direct
evidence that any of the dimensional
changes
introduced by a tensile stress are affected by an
anneal to the graphitization temperature, the fact
that the longitudinal
and transverse stress-strain
curves are reproducible implies that the original
structure is restored by an anneal to the graphitization temperature.
The problem which remains is that of deducing
the mechanisms by which the internal stresses are
relieved by an external stress. One possibility is
that microcracks are formed between layers as the
c-axis tensile strength in some of the crystallites is
GRAPHITES
191
exceeded. The main objection to this mechanism is
that the microcracks must then be healed by
annealing. If the cracks are large enough to expose
surfaces which can absorb gases, they probably
cannot be healed by a thermal anneal. Therefore,
the microcracks should be so small as to be inaccessible to gases if this mechanism is to be eEective. The other possibility is that the stress relief
and crystallite growth occur entirely through
plastic deformation by shear along layer planes.
The definitive choice of a mechanism is made
difficult by the fact that the strains which are
involved in the internal stress relief mechanism are
small compared to the longitudinal strains and give
only a slight correction to the longitudinal stressstrain curves; however, these strains give a major
contribution to the transverse stress-strain curves.
_~ckno~led~ements-The
author wishes to aclcnowledge
the able assistance of D. N. WOODS. The strain gage
instrumentation and early exploratory testing were done
with the collaboration of Dr. T. WENG. The sonic
moduli were determined by 0. L. BI.AKSLEF:and Mrs.
E. C. ~INFOSSAN.
REFERENCES
1. ARRAGO.L‘P. P. and
Carbon and Graphite,
London (1958).
BERTHER
p.
K.
565.
Sot.
~~~~ustr~a~
Chcm. Ind.,
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