The effect of compressive prestressing on the mechanical properties of some nuclear graphites

Carbon, 1973, Vol. 1 I, pp. 639-647.

Pergamon

Press.

Printed

in Great Britain

THE EFFECT OF ~~M~RESS~VE PRESTRESSING ON THE MECHANICAL PROPERTIES OF SOME NUCLEAR GRAPHITES TA!XJO OKU and MOTOKUNI ET0 Japan Atomic Energy Research Institute, Tokai-mura,

Ibaraki-ken, Japan

(Received 13 February 19’73) Ahstraet-The effects of prestressing in compression at room temperature on the Young’s modulus, the tensile strength, and the compressive strength of some nuclear graphites were examined. Also the effects of strain rate in the range of 10e5 - 10W2se@ on the room temperature tensile and compressive strengths were investigated. The Young’s modulus and the tensile strength of the graphites decreased as the compressive prestress increased above a particular prestress level. However, the compressive strength of the graphites did not change appreciably for the above range of strain rates. The decrease in Young’s modulus and tensile strength with increasing prestress is considered to be due to two factors: an increase in the dislocation density and an increase in the size and number of cracks produced. It is inferred that the decrease in the strength at higher prestress levels is due to the formation and propagation of cracks with increasing prestress, since some growth of cracks was observed in the higher prestressed graphites.

1. INTRODUCTION The

core

region

possibly because of the limitations of the performance of tensile test machines. The effect of prestressing on the tensile and compressive fracture stress has never been investigated; it is considered to be important, however, from the viewpoint of the strength of graphite blocks in a high temperature gas-cooled reactor core in the event of an earthquake. It is considered that prestressing produces increases in the size and number of cracks and an increase of the dislocation density in graphite materials. Therefore, prestressing should have an influence on the Young’s modulus and the strength of graphite. Some results[7-91 have already been published on the effect of prestressing on the Young’s modulus of some nuclear graphites, and the authors [lo] have also examined the subject phenomenologically. The purpose of this paper is to investigate

of the high temperature

gas-cooled reactor consists of fuel blocks which contain fuel and fuel sleeves, and reflector blocks which are mainly made of high density graphites except for the fuel itself. These graphitic materials, in particular graphite blocks, are considered* to receive repetitive stressing with strain rates of lop5 to 1 set-‘. Smith has investigated the effects of prestressing at high temperatures[l] and strain rate]21 on the tensile properties of molded graphites. Fatigue behavior of graphites has been preliminarily examined [3,4] and investigated by Green[5], and by Leichter and Robinson {6]. In these investigations, however, little is known about the effect of strain rate in the range of lo+ to 1 set-‘, *Ikushima, private communication. 639

CARBON-VOW.

II. Nat%E

640

TASUO OKU and MOTOKUNI ET0

the effect of prestressing and strain rate in the range of 10m5 to 10m2set-r on the tensile and compressive fracture stress of some graphites which include the graphites explored particularly for the high temperature gas-cooled reactor, and to reexamine the expression for the Young’s modulus vs prestress from the point of view of crack formation due to prestressing. P. EXPERIMENTAL 2.1 Materials Three kinds of graphites were used as test materials. They were: isotropic gilso carbon coke graphites (extruded and molded), isotropic petroleum coke fine grained graphites (molded), and anisotropic needle coke graphites (extruded). The five brands of graphite which were tested are tabulated in Table 1 together with some mechanical properties. Young’s modulus, tensile and compressive specimens were cut from each graphite block. The Young’s modulus specimens were 5 mm dia X 30 mm long. The tensile specimens, which were 60 mm overall length, had a gage length 21 mm long X 5 mm dia with transitional fillets of 30 mm radius to 8 mm dia cylindrical end grips. The compressive specimens were 12 mm long X 6 mm dia. All specimens were cut out in the direction of the extrusion axis for the extruded materials and in the press direction for the molded materials. 2.2 Testing and meamrements Young’s modulus was obtained at room temperature from the equation, E = pv2 (E: Young’s modulus, p: density, V: sonic velocity) by measuring the velocity of propagation of 100 kHz longitudinal waves. Prestressing was carried out by an Instron testing machine after the dynamic modulus measurements were made. After loading, the modulus was measured again. Tensile and compressive tests were performed at strain rates of - 10e5 to - 10m2se@ at room temperature by using an Instron

testing machine after removing the prestress in order to investigate the effect of the prestressing on the tensile and the compressive strength. 3. RESULTS The effect of compressive prestressing on the normalized Young’s modulus (E/E,,) of various graphites is shown in Fig. 1. (See Section 4 for definitions of E and E,.) Generally, the Young’s modulus decreases as the prestress level increases. The behavior of the decrease in Young’s modulus of nuclear graphites has been discussed in detail elsewhere[lO]. In the range of low prestress level, the modulus gradually decreases with increasing prestress and then, above a certain prestress level, the modulus decreases abruptly as the prestress increases. Fig. 2. is a plot of normalized Young’s modulus vs a normalized prestress which we define as the ratio of the compressive prestress (up) to the compressive fracture stress (a,). As can be seen in Fig. 2, the normalized

w

0.7-

06. 0

1

1

1

I

2

3

Compressive

0

m-2

.

IEI-24(//l

(11

.

7477PT

0

H-327(//)

I 4

I 5

pre-stress

(//)

I 6

I 7

I 8

C kg/mm21

Fig. 1. Changes in Young’s modulus of some nuclear graphites with increase in compressive prestress.

(El)

E = Extruded,

SMG (E)

H-327 (E)

7477/FT (M)

IEl-24

IM-2 (M)

Brand

M = Molded.

l-76

1.75

Ii I

1.79

1.77

/J I

1.74

1.74

ll _L

1.79

Ii _I_

1.82

I/ 1.78

1.78

Dir.

I

Apparent density (g/cm3)

1.10

l-49

I*00

1.08

1.01

BAF

8.72

7.57

7.76

4.56

17.4

16.9

9.89

8.16

10.7

10.8

Resistivity (1O-4 Sz . cm)

0.846

1.08

0.705

1.51

0.990

0.984

1.18

1.42

1.21

1.22

Young’s modulus (lo3 kg/mm?

0990

1.68

0.70

1.23

2.07

2.24

1.54

2.84

2.12

2.24

Tensile strength (kg/mm*)

4.47

4.70

2.80

3.20

796

8.49

5.32

6.15

7.31

7.98

Compressive strength (kg/mm?

Table 1. Some mechanical properties of nuclear graphites

needle coke, anisotropic

petroleum coke, fine grained, isotropic

gilsonite coke, isotropic

Coke

642

TASUO OKU and MOTOKUNI

I

ET0

I

I

0

0.6

0

0.2

0.4

0.6

IO

6

pre-stress

Cl

06

I

I

4

Compressive A 7477PT(/I)

I

I

2

o’7

I

I

t

e

Ckg/mm21

Fig. 3(b). I

I

H-327

up 101

Fig. 2. Changes in Young’s modulus of some nuclear graphites with increase in normalized prestress.

(//I

0

7.9 x IO-5sec-’

8

Mean

value

I.6 0

0

Young’s moduli decreases at stresses of more than about O-2 CT,almost independently of the brand. It was found that there are some differences in the normalized Young’s modulus (E/E,) vs normalized prestress relation of various brands of nuclear graphites, which depend upon whether the brand

-1

IM-2

C/i)

Compressive

pre-stress

Ckg/mm21

Fig. 3(c). Fig. 3. Changes in tensile strength of some nuclear graphites as a function of compressive prestress level. (a) gilsonite coke, isotropic graphite (IM-2). (b) petroleum coke, fine grained, isotropic graphite (7477PT). (c) needle coke, anisotropic graphite (H-327).

Compressive

pre-stress

Fig. 3(a).

Ekg/mmz3

belongs to an isotropic graphite (gilsonite coke and petroleum coke fine grained) or an anisotropic one (needle coke). The fractional decreases in Young’s modulus of gilsonite coke graphites (IM-2, IEI-24) and petroleum coke fine grained graphite (7477PT) were

MECHANICAL

PROPERTIES

OF SOME NUCLEAR

below about 10% even near the compressive fracture stress, while those of needle coke graphites (H-327, SMG) were below 15 to 30% near the fracture stress. The effects of compressive prestressing on the tensile strength of some nuclear graphites are shown for strain rates of the order of lo-’ and 10-2sec-1 in Fig. 3(a), (b), (c). No changes of tensile strength of IM-2 (11) were found below 0.6 a, for the two levels of strain rate 7.9 X 10m5see-’ and 7.9 X lo-* set-‘. The tensile strength of IM-2 f/i) at a strain rate of 7.9 X lOA set-’ decreased for the normalized prestress above 0.6 a,. However, the tensile strength of IM-2 (//) at a strain rate of 7.9 X lo-* see-’ seems not to change with compressive prestress. The tensile strength of 7477PT(//), petroleum coke fine grained graphite, decreased with increasing compressive prestress up to O-24 af and was almost constant above 0.24 cfi In the range above 0.24 af, the tensile strength of 7477PT(//) became maximum at a strain rate somewhere between the maximum and minimum of 7.9 X 10e5 set-’ and 3.3 X 10-l set-I. On the hand, the tensile strength of H-327(//),

643

GRAPHITES

anisotropic needle coke graphite, at a strain rate of 7.9 x 10e5 set-‘, abruptly decreased above 0.5 uf, but seemed almost not to change below 0.5 ofi Fig. 4 shows the compressive strength of nuclear graphites as a function of compressive prestress. As can be seen from the figure, it was found that the compressive strengths of these graphites changed very little with compressive prestress. The compressive strengths of all of the graphites did not appear to be affected at strain rates of 10e5 to 10m2set-’ , as shown in Figs. 5(a), (b).

0

a

.A

I/ 1

IM-2 t-

b”

IE i-24

3

0

10-5

I

I

10-4

10-S Strain

rate

I 10-z

I

IO-'

Csec-‘I

Fig. 5(a).

5o IM-2(N) 43m_

.7477/PTl//) h n


01

a H327(fl)

!O#

I

I

IO-* Strain

2-

0

I

10-X rote

1O-2

I

IO-'

Csec-‘I

Fig. 5(b). Fig. 5. Changes in compressive strength of some nuclear graphites as a function of strain rates. I I 12345678 Compressive

I

I

pm-stress

I

I

I

[kg/mm21

Changes in compressive strength of some nuclear graphites as a function of compressive prestress level.

4. DISCUSSION

It is well known[3,7,8] that the Young’s modulus of graphite decreases with increasing prestress level. This effect is considered to be

644

TASUO

OKU and MOTOKUNI

the result of two factors: the formation and propagation of cracks, and an increase in the dislocation density which is associated with an increase in the prestress level. At first, we consider the formation and propagation of cracks with increasing prestress. Microphotographs which show the growth of cracks associated with increasing prestress level are shown in Fig. 6. The growth of cracks becomes definitely noticeable above the stress level of 0.6 ufi It has been already found[ll] that the electrical resistivity increases with increasing stress level, and this is considered to be due to the growth of cracks which already exist mainly in the coke grains. The deviation from linearity of the compressive stress-strain curve occurs at a point at which the remarkable growth of cracks is seen. This point corresponds to the starting point of the increase in dpldu, as the prestress level increases, where p is the electrical resistivity and op is the prestress level (Fig. 7a-c). We deduce from the simple consideration of strain energy based on the presence of the crack [12] that the growth of cracks produces the decrease of Young’s modulus. The effective Young’s modulus, E, of the cracked specimen, when E,, is the Young’s modulus for the material which does not contain cracks, is given by the following equation[I2]: E = __2L_Eo, y + 2?rc2

1

IM--2(//l

Fig. 7(b). H-327(N) oObservation

point

(1)

where a cylindrical specimen of unit crosssectional area and length y experiences an axial tensile stress u, and the specimen extends when a crack of width 2c extending right through the specimen is introduced perpendicular to the applied stress. According to the three dimensional theoretical analysis [ 131, the effective Young’s modulus of a specimen containing some cracks is expressed by the following equation: E=l+KN+

I

ET0

(2)

Fig. 7(c). 7. Changes in electrical resistivity of some nuclear graphites as a function of normalized prestress level. (Points show where crack observations were made). (a) IM-2 (b) 7477PT (c) H-327.

Fig.

IM-2W)

a/cTf

(4

c/of

=o

c/cf

=0.76

o/of

q0.26

=0.96

Fig. 6(a).

(Facing page 644)

7477fPTfhq

’I ,i I I cr/crf=O

(bf

a/CT-f =o-21

obf=O-64

H-327(//)

o-/of

=o

o&f

=I 0.2mm

Fig. 6. Formation of cracks in graphite associated with increase in compressive prestress level.

MECHANICAL

PROPERTIES

OF SOME NUCLEAR

where K depends upon the volume of cracks and whether cracks are open or closed, N is the total number of cracks, and c is the average crack length as defined by I? = i

$/N.

(3)

i

In this analysis, the shape of the crack is assumed to be an ellipsoidal slit which has circular cross-section of radius c, and plane stress or plane strain is assumed. Therefore Nz? is the average of the total crack volume. The electrical resistivity of graphite is known [14] to increase proportionally with pore volume over the narrow porosity the resistivity in Fig. 7 range; therefore, may be replaced by the crack volume, Nz?, since NP is considered to correspond to pore volume. Then, as seen from Fig. 7, NZ can be taken to be proportional to the compressive prestress, up, below the critical stress, crO; above co the normalized Young’s modulus for the isotropic graphites abruptly decreases. Also, NP is assumed to increase as an exponential function of (a, - ao) above cro, since the resistivity increases as shown in Figs. 7(a) and (b). If VU is defined to be the value of Ni? when u, = co, then for the isotropic graphites the following equations may be written: for up s cro

E/E,=

and for up Z u. E/Eo= l/[l+K NZ3=A(u,-uo)z.

*A(u,--o)~~

Nc32(~~

E/E0 = Aup2+B,

-E--E, Eo-E,

_ - A * exp(-

Bup2),

which are different from the expressions mentioned above.

\ -

\

QO

0

IM-2(//j

. A

IEI-24(N) 7477PT

0

H-327

I

SMG(//)

and for u, B u.

v/j (//I

.(5)

Nz3 = 0,

I

-

(4)(51

---

(6) (7)

:5

I

--(N(7)

0

1 I

1

2

Compressive

(6‘) .

cr, vP

1

3

E/E,

(kghd) ‘,

0.61

(9)

theoretical

Equation \

E = En,

(8)

and for molded graphites

(4)

In the same manner, the following equations for the anisotropic graphites may be drawn from Fig. 7(c): for up 5 u.

(7)

These expressions only give a rough approximation for the decrease of Young’s modulus with increasing prestress level as shown in Fig. 8. However, Fig. 8 indicates that the theoretical expressions, equations (4) to (7), are comparatively well consistent with the data points in Fig. 1. On the other hand, the expressions which are best fitted to the experimental data are the following[lO]: for extruded graphites

l/(l+K$u,J 7

645

GRAPHITES

1

4

pre-stress

1

5

1

6

246

::::

2

0.92

1

7

1

6

[ kg/mm21

Fig. 8. Comparison of the theoretical expressions with decreases in Young’s modulus of the graphites which were measured associated with increase in commessive orestress level. 1

TASUO OKU and MOTOKUNI ET0

646

The decrease in modulus, particularly at higher stress levels, may be well illustrated since definite formation and propagation of cracks can be seen in microphotographs (Fig. 6). However, the effect of increase in the dislocation density cannot be neglected, particularly at lower prestress levels, because an increase in the dislocation density in graphite is expected with increasing prestress. Friedel[l5] gives the following expression, similar to that for cracks, as the equation which shows the decrease of modulus with increasing strain: E/E,=

1/(1+advL3),

(10)

where N is the dislocation density, L is the average length of a pinned dislocation, and a! is a constant. At present, it cannot be determinded. whether the increase in dislocation density or the formation and propagation of cracks is the major factor which produces the decrease in Young’s modulus as the prestress increases. The tensile strength of graphite after prestressing appears to be correlated with the decrease in Young’s modulus since the compressive prestress produces the decrease in the modulus as shown in Fig. 1. The prestress dependence of Young’s modulus depends upon the type of graphite, as seen from Fig. 1. Also it has been shown@] that there is a good correlation of the tensile strength with Young’s modulus of nuclear graphites. If we assume that the tensile strength of graphite follows the Griffith equation

uf=

$YE Z’

(11)

the tensile strength of graphite after prestressing may be expected to decrease as the Young’s modulus decreases, if the change in y/.?iis neglected. In fact, the tensile strength of graphite was observed to decrease with increasing compressive prestress level

(Fig. 3). As already pointed out, however, the increase in the tensile strength of graphite at lower prestress levels may possibly be due to the increase in the dislocation density, although no direct evidence of this type of an effect has been found yet.

5. CONCLUSIONS The effects of compressive the Young’s modulus and compressive strength of graphites were investigated. following conclusions may be

prestressing on the tensile and nuclear some As a result, the drawn:

(1) Young’s modulus of nuclear graphites decreases with increasing compressive prestress. (2) The reduction in Young’s modulus occurred after prestressing above approximately 0.3 of for all brands of graphite tested. (3) The tensile strength of nuclear graphites tested in this experiment decreased as the prestress increased. (4) In the case of gilsonite coke graphites, the tensile strength at a prestress below O-6 uf decreased as the strain rate increased. (5) The compressive strength of nuclear graphites changed little with increasing prestress level for strain rates in the range of 10m5to 10T2 set-‘. (6) The theoretical expressions which are based on the cracks produced in graphite with increase of compressive prestress are comparatively well consistent with the data points. (7) The decrease in Young’s modulus and tensile strength of some nuclear graphites with increasing prestress level seems to be explained by the formation and propagation of cracks in graphite, particularly at higher prestress levels. Acknowledgement- The authors would like to thank Dr. Y. Sasaki for valuable discussions, and Mr. T. Usui for help with the experiments.

MECHANICAL

PROPERTIES

OF SOME

REFERENCES 1. Smith M. C., Carbon 2,269 (1964). 2. Smith M. C., Carbon 1,147 (1964). 3. Arragon P. and Berthier R. M., Indwttil Carbon and Graphite, p. 565, Sot. Chem. Ind. London (1958). 4. Greenstreet W. L. et al., Carbon 8,649 (1970). 5. Green L. Jr.,J. A@. Mech. 18,345(1951). 6. Leichter H. L. and Robinson E., J. Amer. Cer. sot. 53,197 (1970). 7. Jenkins G. M., J. Nucl. Mat. 5,280 (1962). 8. Losty H. H. W. and Orchard J. S., Proc. Fifth

9. 10. 11. 12. 13. 14. 15.

NUCLEAR

GRAPHITES

647

Carbon Conf. vol. 1, p. 519. Pergamon Press, Oxford (1962). Hart P. E., Carbon 10,233(1972). Eto M. and Oku T., J. Nucl. Mat. 46,315 (1973). Eto M., Usui T. and Oku T., J. Nucl. Mat. 45, 347 (1972/73). Petch N. J., Fracture vol. 1, (Edited by Liebowitz)(1968) chapt. 5, p. 351. Walsh J. B., J. GeophysicalRes. 70,399 (1965). Armstrong P. E., Proc. Conf. Continuum Aspects GraphiteDesign, Nov. 9-12, p, 3 (1970). Friedel J., Phil. Mug. 44,444 (1953).