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Carbon 1966. Vol. 4. pp. 177-191. Pergamon Press Ltd. Printed in Great Britain

STRESS-STRAIN PROPERTIES

OF POLYCRYSTALLINE GRAPHITES IN TENSION

AND COMPRESSION AT ROOM TEMPERATURE

E. J. SELDIN

Union Carbide Corporation, Carbon Products Division, Parma Technical Center, Parma, Ohio

(Received 11 February 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

THE STRESS-STRAIN relationship of a polycrystalline graphite is characterized by nonlinearity, by hysteresis loops formed under cyclic stressing, and by an attendant residual deformation when the applied stress is released. These effects were first reported by ARRACON and BERTHIER(~’ for graphite under compression, and shortly afterwards by ANDREW, OKADA and WOBSCHALL@’ for graphite rods deformed as cantilevers. LOSTY and ORCHARD(~) observed nonlinear stress-strain curves for graphite in both tension and compression and found that precompression caused the Young’s modulus of a graphite to decrease but did not appear to affect the tensile strength. JENKINS(“) proposed a mechanical model and a set of equations containing two parameters to describe the stress-strain curves upon application, release, and reapplication of the stress, and he fitted the equations to the stress-strain curve for a reactor grade graphite subjected to a relatively low compression stress. JENKINS and WILLIAMSON(‘) further elaborated upon the model to predict the stress-strain properties of graphite under the com-

bined effects of mechanical stressing and annealing. These authors also reported that the permanent set could be recovered either by annealing to approximately 1500°C or by neutron irradiation.

The previous investigations have been concerned only with the longitudinal stress-strain curves of graphite, and the measurements have been limited by the sensitivity of the apparatus used to measure the strain. A prime objective of this investigation was the observation of both the longitudinal and transverse stress--strain curves for several polycrystalline graphites in tension and compression in order to obtain a set of elastic constants for the different graphites. Where possible, sonic resonance measurements were made on the specimens before they were subjected to static testing so that the sonic moduli could be compared with the static moduli in the limit of zero strain. A complete set of elastic constants has been obtained for ATJ graphite from the static tensile data. Another objective of this investigation was the comparison of the stress-strain behavior of a graphite in tension with its behavior in compression. The effects of annealing prestressed

C 177

178 E. J. SELDIN

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 against- grain direction and as the 3-axis. The l- and 2- axes are then equivalent. Although any direction perpendicular to the Saxis is a with-grain direction, the l-axis will always be taken as the with- grain 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

E3 =S33t73.

(1)

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 3- axis, 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 &I3 and transverse strains ~‘1 and $2, given by

EIl =S’13d3,

E’2=S123 3 CJ’ and

E’3 ==S’33d3.

(3)

The compliances in the primed coordinate system can be shown@) to be related to the original com- plianees 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 in equations (41, we obtain

S44=2(S’33-S’23). (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 GRAPHITES 179

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 cross- head 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 simul- taneous 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

direction were desired, the Instron recorder was also used as an X-Y recorder. The longitudin~ and transverse stress-strain curves were all auto- matically 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 BAUMBERGER and 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 succes- sively 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 4 TENSION

x

STRAIN (PER CENT)

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 0’0 .4 .8 1.2 1.6 2.0

TRANSVERSE E, ~~GITWINAL 6,

STRAIN (PER CENT1

FIG. 2. Longitudinal and transverse stress-strain curves for ATJ graphite, oriented with-the-grain. Compression

test.

2 3 .4

TRANSVERSE E, LONGITUDINAL E,

STRAIN (PER CENT)

FIG. 3. Longitudinal and transverse stress-strain curves for ATJ graphite, oriented with-the-grain. Tension test.

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 manu- factured 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.


TABLE 1. T~PICALTENSILEDATA FOR SEVERAL GFZADESOFPOLYCRYSTALLINEGRAPHITE

Initial Grain Llensity Strength Sonic Static Compliances Poisson

Grade orientation (g/cm*) (psi) modulus modulus (IO-‘scma/dyne) (IO-‘*ems/dyne) ratio (10s psi) (10’ psi)

ATJ RVA

RVC

RVD

CFW

CFZ

CHQ ZT4

ATJ RVA

RVC

RVD

CFW

CFZ

CHQ ZTA

ATJ against-grain 1.72

RVA 1.85

RVC 1.86

RVD 1.92

CFW 1.91

CFZ 1.93

CHQ 1.58

ZTA 1.95

with-grain 1.72 3,800

1.87 3,170

1.84 2,385

1.88 3,915

1.90 1,950

1.93 3,510

1.61 2,760

1.94 4,400

with-grain 1.72 3,900

1.86 3,385

1.84 2,400 1.88 4,050

1.90 1,915

1.93 3,568

1.61 2,860

1.96 4,350

1 bll l/S,, $11 - s12

1.64 1.64 8.85 0.84

2.01 2.01 7.22 0.78

1.82 1.76 8.25 1.26

2.28 2.33 6.23 0.71

1.60 1.63 8.90 1.07

2.06 2.04 7.11 0.89

1.28 1.30 11.12 2.42

2.75 2.56 5.67 0.37

3,000

2,400 1,500

2,840

1,720

2,345

1.66

2.01

1.83

2.12

1.62

2.06

1.26

3.07

1 I& 1.12

1.30

1.42

1.36

1.52

1.52

1,630 0.71

1.67

2.01

1.83

2.31

1.65

2.06

1.25

2.89

1 l&J 1.17

1.30

1.44

1.36

1.49

1.54

.96

.66

8.70

7.22

7.93

6.28

8.80

7.05

11.60

5.02

%I3 12.36

11.17

10.08

10.67

9.75

9.43

15.10

22.00

- %s 1.36

1.15

1.73

1.37

1.31

1.21

2.05

1.28

1.40

1.24

1.61

1.32

1.31

1.15

2.06

1.19

- s1*/sn 0.10

0.11

0.15

0.11

0.12

0.12

0.22

0.07

-%3/%1 0.16

0.16

0.22

0.22

0.15

0.17

0.18

0.25

_ kllSJ8 0.11

0.11

0.16

0.12

0.13

0.12

0.14

0.05

TABLE ~.TENSILEDATA FOR ATI GRAPHITE~~~CUT

Specimen Density (g/cm”)

s 33

Static compliances ( 1@‘scm2/dyne)

-S’13 I

--s 2s

a4 = w*s - S’OEJ (1 0-%m*/dyne)

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 (T by drawing a line with a slope of 2 which best

to the two-parameter equation 6 of JENKINS.(~) fitted the data at the lower and intermediate stress

The parameter A, equal to either $11 or ~33, was levels. In this manner, a good fit was usualIy ob-

obtained from the initial slope of the curve in the tained for the entire envelope stress-strain curve in

limit of zero strain. The parameter B was deter- tension and for the envelope curve in compression

mined graphically from log-log plots of s--Au vs. up to approximately 60 per cent of the breaking

‘in, / , , ( , , 1 0 .4 .a 1.2 I6 20

STRAIN (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 stress- strain 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 curve- fitting 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

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 equal to iBa2,,,. Experimentally, the residual 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

182 E. J. SELDIN

TABLE 3. TYPICAL COMP~I~NDATA FORSEWRALGRADES OFP~LYCR~~TALLINR GRAPHITE

Grade, Grain’ Density

orientation (g/cm?

Strength

(psi)

Initial A B static modulus

(lo6 psi) 10-g(psi)-’ lO-‘a(psi)-”

ATJ

RVA

RVC

RVD

CFW

CFZ

CHQ

ZTA

WG 1.72 11,400 1.72 581 43

AG 1.72 9,150 1.22 817 100

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 grain ; AGagainst grain.


loops were close to those predicted by JENKINS’

model f4f The transverse residual strain was posi- . tive 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, OKADA and 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

8 z

R 6 I 2 E4 E 2 m

0 E _A

0 4 .8 I2

STRAIN E, (PER CENT)

FIG. 5. ATJ graphite, oriented with-the-grain; heat- treated to 3000°C; compression test. Solid curve: Original envelope stress-strain curve of previously un- stressed 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 group, showing the excellent correlation 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. Further- more, all of the stress-strain curves were reproduced once again after another anneal to 3000°C.

The length measurements given in Table 4 indi- cate 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. How- ever, 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

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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 heat- treatment, 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.

-‘i 100

IOMIN

75 gz $2

IOMIN s:, 50 L.J

9 c-

ANNEALING 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.

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 ob- taining 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 with- the-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 heat- treated 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-tension- compression. 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

186 E. J. SELDIN

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 against- grain 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 stress- strain curves for this particular ATJ specimen CO-

incided 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, compari- sons between tension and compression data must

TRANSVERSE STRAIN E, (PER CENTI

6, .9’ 0 02 .04 06 08 IO I I I I

7

= 6

2 “0 5

J :

b- 4b

9 b+ 3 t

2

I , I

I I

n I I 2-J “0 .2 .4 .6 .6 10 12 14

I ONGITUDINAL STRAIN 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.

8

TRANSVERSE STRAIN E, (PER CENT)

02 0 02 04 06

/ I ’ ’ / I

7 I

4 2 ,9

/ /‘/

,’ ’

LONGITUDINAL, +. ,’ /’

/ ,

.I / /

/&’ ,@

,‘TRANSVERSE

/ I

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I’

/I I I I _

6 1.0 12 1.4

LONGITUOINAL STRAIN <, (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.

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 GRAPHITES 187

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

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 dimen- sion is always increased.

In another series of experiments, cyclic stress- strain tests combining tension and compression to equal and opposite stresses were run on -4TJ and ZTA graphite specimens oriented with- and against-the-grain. The maximum stress was 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

188 E. J. SELDIN

.I6 .08 0 .06 .I6 24

LONGITUDINAL STRAIN C, (PER CENT)

b .Ol _L-_-J--d

.02 .03 .x%4

TRANSVERSE STRAIN GE, (PER CENT)

FIG. 10. Stress-strain curves for ATJ graphite, oriented with-the-grain, stressed between ffi00 psi,

tension and then in compression. first in

.24 .I6 .06 0 .oe 16 24 32

LONGITUDINAL ‘STRAIN Et (PER CENT)

41-I

4 Ldi 02 .OI 0 .Ol .02 .03 04

TRANSVERSE 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 with- grain 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 posi- tion 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 with- grain 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


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 stress- strain 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 !- 1-._1_J- id .a 6 .4 2 0 2

LONGITUDINAL STRAIN E, (PER CENTI

TRANSVERSE 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.

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 stress- strain 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 stress- strain 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 c- direction 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 a- axis 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 micro- crack formation. This relief of the c-axis tensile stress component in the internal stress distribution


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 stress- strain 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. How- ever, 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

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 in- accessible to gases if this mechanism is to be eEec- tive. 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 stress- strain 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.

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REFERENCES

ARRAGO.L‘ P. P. and BERTHER K. M., ~~~~ustr~a~ Carbon and Graphite, p. 565. Sot. Chcm. Ind., London (1958).

ANDREW J. F., OKADA J. and WOBSCHALL D. C., Proceed&s of the Fourth Carbon Conference. n. 559. Pergamon Press, Oxford (1960). _ . LOSTY H. H. W. and ORCHARD J. S,, Proceedings of the Fifth, Carbon Conference, Vol. 1, p. 519. Pergamon Press, Oxford (1962).

JENKINS G. M., &it. J. Appl. Phys. 13, 30 (1962).

JENKINS G. M. and WILLIAMSON G. K., r. Appl. Phys. 34, 2837 (1963).

HEARMO~V R. F. S., An Introduction to Applied Anisotropic Elasticity. O.U.P., London (1961).

BAC’MBERGER R. and HINES F., Proc. Sot. Exp. Stress Anal. 2, 113 (1944).

WV C. T., Proc. Sot. Exp. Stress Anal. 19, 338 (1962).

SIMMONS J. H. W., Proceedings of the Third Carbon Conference, p. 559. Pergamon Press, London (1959).

KELLY 13. T., Phil Msg. 9, 721 (1964).

MROZOWSKI S., Proceedings of the First and Second Carbon Conferences, p. 31. University of Buffalo, N.Y. (1956).

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