THE MECHANICAL PROPERTIES OF REACTOR … CAES...using a 5 mm Huggenberger extensometer mounted on...

Cmbon 1967, Vol. 5, pp. 519-531. Pergamon Press Ltd. Printed in Great Britain

THE MECHANICAL PROPERTIES

OF REACTOR GRAPHITE

R TAYLOR+, R G. BROWN, IL GILtZHIUST, E. HALL, A. T. HODDSf, B. T. KELLY and F. MORRIS

United Kingdom Atomic Energy Authority, Reactor Materials Laboratory, Culcheth,

Warrington, Lams., England

(Receiued 12 $zmuzy 1967)

Abstract-The following mechanical properties of three types of isotropic reactor graphite have been measured, before and after fast neutron irradiation at 150°C in DIDO: Young’s modulus, Poisson’s ratio, stress-strain curves in tension and compression, shear strength, uniaxial tensile and compressive strength, triaxial compressive strength and Vicker’s hardness. The propagation of cracks in these graphites has been e xamined microscopically and measurementn made of the work of fmcture. The accumulation of irradiation damage has been followed by measuring changes in linear dirnen&ms of the specimens and of pyrolytic graphite samples which show that the graphite is heavily damaged. The experimental data have been compared with theories of the mechanical properties of u&radiated and irradiated graphite. A model in which large porea act as “G&F&’ flaws is compatible with the data on irradiated graphite, but in unirradiated graphite, plastic flow modifies the failure in compression.

1. INTRODUCTION

SMALL doses of fast neutrons can produce improve- ment in the mechanical properties of reactor graphite, but there has been no systematic investi- gation of the effect of heavy irradiation damage, which might cause deterioration in strength. Irradiation of graphite crystals with fast neutrons over a wide temperature range, causes changes in dimensions which can reach very large magni- tudes.“) The majority of reactor graphites are well crystallised, fairly randomly orientated poly- crystals, and it is therefore to be expected that the anisotropic crystal dimensional changes as well as changes in the mechanical properties of individual crystals would affect the bulk mechanical properties of graphite.

Irradiation at 150°C can produce large crystal dimensional changes in relatively small doses and thus we have undertaken a detailed study of the

*Present address: Department of Metallurgy, Univer- sity of Manchester Institute of Science and Technology, Sackville Street, Manchester 1, England.

tSandwich course student, Borough Polytechnic, London, England.

mechanical property changes after irradiation at this temperature. The dose dependence of various mechanical properties and their absolute values before and after irradiation are also compared with existing theories of the mechanical properties of well-crystallised graphites.C3)

2. EXPERIMENTAL DETAILS

2.1 Materials and samples Samples were taken from each of three blocks of

isotropic reactor graphite manufactured to the specification of HUTCHEON and THORNE.(~) All were manufactured from coke obtained from residues from the petroleum refinery process using coal tar pitch binders. The graphites designated as Types 1,2 and 3 were manufactured as hollow extrusions 164~ dia., 33 in. long and were graphitised at temperatures greater than 2800°C. Metallographic examination showed Types 1 and 2 to contain spherical coke particles of sizes ranging up to 1 mm whereas Type 3 graphite contained anisotropic coke particles up to 1 mm long. Physical properties characterising these graphites are listed in Table 1.

519

520 R. TAYLOR, R. G. BROWN, K. GILCHRIST, E. HALL, A. T. HODDS, B. T. KELLY and F. MORRIS

Two graphite blocks 2 in. thick by 4 in. square cross-section were cut from each graphite extrusion, with the 2 in. axis (a) parallel and (b) perpendicular to the direction of extrusion. Each of the six blocks was then subdivided into 64 bars 2 in. long by + in. square cross section (i.e. an 8~ 8 matrix). The bars thus obtained were machined to provide 1 tensile and 1 compressive specimen from each. Alternate bars provide specimens for irradiation whilst the remainder were used as controls.

The compressive specimens were 0.500 in. long x O-245 in. dia. cylinders and the tensile specimens, which were 1.125 in. overall length, had a gauge length 0.375 in. long x 0.200 in. dia., with transi- tional fillets of 2 in. radius to end grips O-245 in. dia.

Four each of tensile and compressive specimens were withdrawn from the reactor after irradiation to each of several doses at 150°C. In addition to tensile and compressive strength, measurements were also made of Poisson’s ratio, dynamic Young’s modulus and hardness. Dimensional changes were measured after each withdrawal from the reactor and pyrolytic graphite specimens were irradiated concurrently to obtain crystal dimensional changes.

Specimens were cut from other regions of the extrusion for triaxial compression, shear strength measurements, and observations of crack propagation under slow tensile strain. Specimens of Pile Grade “A” graphite (Type 4) were also tested in triaxial compression, and the specimens used for this test were cylinders O-245 in. dia. by 0.500 in. long. Type 2 graphite was tested in triaxial compression after neutron irradiation using the broken ends of the tensile specimens machined into cylinders 0,375 in. long x 0.200 in, dia. Shear strengths were measured on specimens 1 in. long by 0.245 in. dia. Special strip tensile specimens were used for observations of crack propagation.

2.2 Irradiation conditions

The specimens were irradiated in a standard triple magazine Wigner rig located in a hollow fuel element in the core of DIDO, as described by BELL et aZ.(5) Each sample hole in the magazines of the rig contained two tensile and two compressive specimens, eight holes in each magazine being occupied in this way.

The irradiation doses are all determined from the 5sNi (n,p) 5sCo reaction using a cross-section

of 107 mb.(6) The instantaneous flux in these facilities measured by this reaction is 5~ lOi n.cm%ec-’ and the maximum total dose achieved was 11.5 x 10zo n cme2 . .

Irradiation temperatures were controlled within the range of 0 to +lO”C of nominal.

2.3 Measurements

Stress-strain curves and static Young’s moduli were measured in a Hounsfield or Mand testing machine. Initially tensile strains were measured using a 5 mm Huggenberger extensometer mounted on the gauge length, and compressive strains were measured using a Boulton-Paul differential inductance transducer mounted across the compressive platens. The efFects of compression of the platens over the load range employed was checked using a steel sample and found to amount to 7% error for the largest loads employed and proportionately less for smaller loads. Subsequently, both tensile and compressive strains were recorded using a 4 in. gauge length extensometer consisting of two differential inductance transducers mounted either side of the specimen using radial knife edge clamps. It is estimated that strains at fracture are accurate to f5”/, in tension and compression.

Unirradiated stress strain values are listed in Table 1 together with standard deviations. After neutron irradiation the stress strain curves show increasing linearity as the irradiation dose increases. This is illustrated in Figs. 1 and 2 which compare u&radiated stress strain curves with curves obtained for specimens irradiated to doses of 1.55 and 11.5~ 102’ n.cmW2. These also indicate the increase in fracture stress and decrease in strain to fracture after irradiation. However, because of statistical scatter in the data these should be considered to be merely indicative of the changes. Table 2 lists the average fractional changes in stress and strain to fracture at each neutron dose, calculated from unirradiated strength values inferred from adjacent control specimens. Tensile strengths of Types 1 and 2 graphites increase by a factor of -2 after a small neutron dose and show little variation with subsequent dose. For Type 3 graphite this increase is not as marked and the data show considerable scatter. Strains to fracture decrease to &_8 the u&radiated value and stay roughly constant. In compression however, the

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FIG. 1. Variation in stress-strain curves in tension with increasing neutron dose-Type 2 graphite.

strength increases with increasing neutron dose and tends to saturate at a value 3-3.5 times greater than the u&radiated stress to fracture. Here again the strains to fracture are I&j the unirradiated value. The fracture angle in uniaxial compression (the angle between the applied stress and the fracture plane) decreases as the neutron dose is increased (Table 3). At high doses specimens generally tended to fragment and it was not possible to measure a fracture angle.

2s r

STRAIN, *lo.

FIG. 2. Variation in strain-strain curves in compression with increasing neutron dose-Type 2 graphite.

The Young’s moduli were determined at very small strains, on compressive specimens only, by measuring the fundamental resonant frequency. The changes in modulus on irradiation are obtained from:

E/E,, - 1= cflfo)2 - 1 (1)

where E, E. are the irradiated and unirradiated moduli respectively, and f, f. the corresponding resonant frequencies. No corrections were made for length and density changes. Since maximum growth in the specimens was 3%, this would amount to a maximum error of 3% in modulus and this may be neglected.

TABLE 3. FRACTURB ANGLBS IN CNIAXIAL COMPRJBSION

Specimen

type 0 0.75

Irradiation dose x lOa ncm-*

1.55 2-70-29 3.6 7.5 11.5

‘bwl II 36”& 6” 21°*12” 28”&17” 23”&19” 16”-+10” + I

Typell 34”& 5” 40”*12” 26”& 8’ 24”& 8’ 6”jc 5” l +

Type211 29”&14” 39”f23” 30”&12” 23”cb 7” 23”zk 7” 0°* a

Type21 30°& 6” 18”~lS” 24”jcl7” 25”& 6’ 25”& 6” l ”

*One specimen of Type 2 // graphite exhibited a fracture plane parallel to the compression direction. Ail other specimens at doses of 75 and 11-S x lOso shattered into many pieces and a fracture angle could not be determined.

THE MECHANICAL PROPERTIES OF REACTOR GRAPHITE 523

NEUTRON DOSE, n C6’

FIG. 3. Changes in small strain (dynamic) moduli.

Figure 3 shows the fractional changes in Young’s modulus measured by the dynamic method. These show the usual form: an initial rapid increase followed by a slight fall, and at higher doses, a slow rise.

Poisson’s ratios were measured on compressive specimens taken from the parallel to extrusion (axis of symmetry) direction, lateral and longitudinal strains being measured over the stress range 0.33-1.70 kg/mm2. The longitudinal strains were measured by the 5 mm Huggenberger extensometer and the lateral strains by two Boulton Paul transducers mounted on either side of the specimen held in a U-shaped clamp bolted to the lower compression platen.(‘) The longitudinal strains were determined four times and averaged, lateral strains were determined sixteen times, rotating the specimens or transducers after each determination. The results tabulated in Table 2 indicate that there is little change after neutron

irradiation and that Poisson’s ratio for these graphites lies in the range 0.1-0.2.

Shear strengths were measured using the simple double shear apparatus illustrated in Figure 4. The 1 cm long central portion of the specimen was sheared using a direct tensile pull. No attempt was made to measure shear strain at fracture. Two specimens of Types 1 and 2 graphite were measured after three irradiation doses up to 2.9 x 1020 n.cme2 and these are compared with tensile strengths in Table 4. Shear strength increases on neutron irradiation similarly to the tensile strength and the tensile strength/shear strength ratio is roughly constant at a value slightly less than 0.5.

The hardness was measured on the end grips of broken tensile specimens using a Vickers pyra- midal indenter, after lapping to a smooth finish with 520 y alumina and coating with a thin layer of aluminium to improve the visibility of the edges of the indentation. Two samples of each type of

TABLE 4. COMPARISON OF SHEAR AND TENSILE ~TRENGTHLI

‘Ibe Neutron dose

(n.cm-*) Shear strength

(kg/mm*)

Tensile strength (average) (kglmm’)

Tensile strength

Shear strength

1 0 2.31 l-09 0.465 1 x 10” 6.08 2.17 O-360

1.79 4.76 2.17 O-460 2.91 5.60 2.05 0.370

2 0 3.37 l-46 0.435 1 x 10’0 6.10 3.10 O-510

1.79 6-00 3.36 0.560 2.70 6-00 2-66 0445


b WI. dla

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f in. dia

FIG. 4. Double shear apparatus.

graphite were measured after each irradiation, ten to twelve indentations being made on each sample. The results listed in Table 2 show that hardness continuously increases up to the highest dose measured.

Triaxii compressive strength measurements were carried out in the apparatus shown in Fig. 5. The Nimonic plunger, which transmitted the axial load, was the same diameter as the specimen to ensure that no correction need be applied to compensate for an axial component of hydrostatic pressure. The pressure vessel was made of stainless steel. Measurements were made at hydrostatic pressures rising by increments of 0.7 kg/mm2 up to 562 kg/mm2. The specimens were sheathed in 4.76 mm i.d. silicone rubber tubing to

prevent oil entering the pores of the graphite. For the unirradiated specimens radial pressure exerted by this sheath is O-014 kg/mm-‘which is negligible in comparison with the hydrostatic pressures used. For Type 1 graphite eight specimens were tested per increment of hydrostatic pressure, but for Types 2 and 3 graphites and Pile Grade “A” cut perpendicular to extrusion only four specimens were used per increment.

The results of triaxial tests on four unirradiated graphites in Fig. 6 show the usual form noted by other workers (cf. PRICE@), MIJFIRELL’~)), namely that the axial compressive strength increases with increasing hydrostatic pressure. Fracture surfaces generally showed a smooth appearance similar to those noted by MURRELL on coal, and enabled the fracture angle to be measured. However, a few specimens did not fracture completely even though the usual drop in load was noticed and a fault line appeared on the specimen surface. The data on Type 2 irradiated specimens is presented in Fig. 7 where each point represents an individual determination (the total number of specimens tested is given on each graph). Specimens irradiated to low doses show well defined fracture angles, but at high doses the specimens generally fragmented and very few yielded a sufficiently large piece to enable a fracture angle to be determined.

The propagation of a crack across a plate was observed microscopically at magnifications up to x480 and photographed, using equipment as illustrated in Fig. 8. A notched graphite plate is rigidly clamped to a brass block which is slowly heated by flowing water circulated from a temperature controlled bath. Due to the differential thermal expansion of brass and graphite, a tensile strain is applied to the sample and a crack is slowly propagated.

TABLE 5. COMPARISON OF OBSEFWXJ AND CALCULATED FRACTURE ANGLE3

IN TRIAXIAL COMPRESSION

Graphite type

1 kl~ WXd P=

tan 20

Qw 1 38” 39” &6” 0.25

z:: 36p 35O f7” 0.31 362 36” &7” 0.30

Pile Grade “A” 364 35Ff7” 0.31


PRESSURE VESSEL TOP

FIG. 5. General arrangement of triaxial assembly.

Pores were observed as large as 060 mm and cracks generally tended to link up these large pores although not necessarily by the most direct path. Spherical coke particles deflect cracks, cracks peter out in numerous branches, and cracks often initiated at a pore surface and ran back to meet an advancing crack.

The failure of unirradiited compressive specimens was photographed using a high speed tine camera (16,000 frames/set). A number of interesting points emerged from these observations. A crack is often visible on the specimen surface a significant period of time before failure occurs. When failure occurs this crack forms an integral part of the fracture path and failure is catastrophic. Fracture is invariably accompanied by a cloud of fine dust similar to that obtained when two rough surfaces are abraded one over the other.

The dimensional changes of three isotropic graphites and the pyrolytic graphite specimens as a function of neutron dose are shown in Figs. 9 and 10 respectively. Due to the fact that specimens jammed in the rig, results on pyrolytic graphite do not extend to the same dose as data on the isotropic graphites.

4. DISCUSSION

The most important practical result arising from this work is the observation that the strength of the graphite is not reduced by the large internal strains due to crystal dimensional changes caused by irradiation-indeed the strength is increased over the wide range of conditions examined. The data on pyrolytic graphite* (Fig. 10) shows that

*The material employed was ,9 type in the notation of KELLY, MARTIN and NBTTLEY.(~)


2ot TYW 1

Hydrostatic ~reswe. Wmmz

FIG. 6. Triaxial stress data for four u&radiated graphites.

16

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crystal growth in the c-axis direction in excess of 29% and basal plane contractions in excess of 4% have been obtained while the work of KELLY,

MARTIN and NETTLW(‘) shows that similar dimensional changes occur in the crystals of the polycrystalline graphites. Thus to a radiation induced differential crystal strain in excess of 33% the isotropic graphites examined show enhanced strength. Although modulus and creep may affect structural irradiation damage in graphite the principal factor will probably be the differential crystal strain irrespective of the absolute magni- tudes of c axis expansion and a axis contraction.

The results are also of interest in relation to theories of the mechanical properties of graphite (cf. REYNOLDS(~)). The changes in dynamic Young’s modulus are very similar to those observed in other well crystallised graphites irradiated at 150°C and have been explained as follows, It is generally accepted that the increase in modulus observed at small strain and low doses is due to the pinning of glissile dislocations in the basal planes

(b) Irradiation dose

1 I.55 x 10% cme2

2s

Cc)Irradiotion dose

p=o39

8 =35* L”

P,, , , , , . (I I) (IO)

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FIG. 7. Triaxial stress data for irradiated graphite-Type 2.


FIG. 8. Equipment for tensile testing of notched specimens.

3

Type I */w-* -rt Perpendnlw

p- I I I 0

Neutron dose, n cm-’

FIG. 9. Dimensional changea of polycrystalline graphite at 150°C.

of the component crystals which, in the unirradiated state, contribute a large strain component. As the dislocation strain component decreases, the effective shear constant, CM, of the component crystals tends towards the true value for the crystal lattice. At higher doses, the elastic constants of the crystal lattice are changed and C&

Neutron dose. n cm-’

FIG. 10. Dimensional changes of graphite crystals at 150°C.

decreases,(“) thus causing a reduction in the moduli of the polycrystal. At higher doses still the large crystal dimensional changes modify the pore space of the solid in such a way as to increase the moduli once more. The marked dependence of the moduli of the present graphites on the Cd4 of the component crystals shows that these too approxi- mate more closely to the Reuss uniform stress condition than to the Voigt uniform strain condition, as noted by REYNOLDS for other graphites.(3)

If we now consider observations at larger strains, then in tension the stress-strain relation is fairly linear up to fracture before irradiation and truly linear up to fracture after irradiation (Fig. 1). In compression, before irradiation, the stress- strain curve is very non-linear, conforming roughly to the form proposed by WOOLLEX.(~‘) After irradiation the stress-strain relation becomes increasingly linear with increase in dose. At the two highest doses no deviation from linearity is observed. However even after irradiation the static modulus determined from the linear portion of compressive stress-strain curves is some lS-20% lower than the modulus determined dynamically- this suggests a strain amplitude dependent dislocation pinning effect such as that observed by


GOGGIN”~’ in low temperature irradiation. The lateral strains decrease with dose in much the same way as the longitudinal strain, and thus Poisson’s ratio is not much changed. This is not true of all graphites on irradiation at 15O”C.(‘) In a solid graphite body in the uniform stress condition the Poisson’s ratio is expected to be 0.5 because the shear strain of the crystals dominates and intro- duces no volume change. The observed low value of Poisson’s ratio thus shows the importance of the pore space in the deformation of these graphites. The low value of Poisson’s ratio shows that different groups of crystals are deformed in shear when orthogonal stresses are applied to the graphite, and this is only possible because of the presence of porosity.(3)

A number of mechanisms have been proposed to account for the non-linear stress-strain relation in graphite in the unirradiated state. It is not proposed to examine these here but it is clear that an increasing proportion of the material is deforming plastically with increasing stress, and the work of JENKINS and HALL shows that the component of dislocation strain is also increased. At the large strains observed in compression, changes in stress-distribution due to changes in pore volume are also possible. The changes in shape of stress- strain curves show that irradiation inhibits plastic flow and also apparently, the formation of new dislocations.

The fracture stress in tension (or) increases rapidly at low doses and is little changed by further increases in dose, while the fracture strain quickly decreases with increase in dose to about O-6 its pre-irradiation value. The compressive fracture strains behave in much the same way as the tensile fracture strain, but the fracture stresses increase over a wider dose range. It was suggested by LOSTY and ORCHARD that tensile fracture in graphite occurs at a constant value of the elastic strain energy/unit volume (F) in the u&radiated and irradiated states, that is,

4 F== = constanl (2)

where E is the modulus. MACON concluded that in tension graphite could be described as a Griffith solid, which would obey the same condition.

It is important to consider only recoverable energy in using equation (2). For irradiated graphite Hookean behaviour is observed and equation (2) defines the total area under the stress- strain curve. However, because unirradiated graphite exhibits non-linear stress-strain curves (a- <&), there is a permanent set which amounts to up to 25% of the total strain. The energy associated with this deformation’ is not recoverable and does not appear in equation (2). The static moduli of irradiated graphite tensile specimens agree very well with the dynamic moduli and for unirradiated graphite the static modulus at fracture (i.e. the modulus by unloading the specimen just prior to failure) is slightly lower than the dynamic value. However, this difference has been found to be not greater than 10% in agreement with the observations of SLEDIN. We have evaluated F for our graphites as a function of neutron dose and the results are shown in Table 2. In Types 1 and 2 graphite the strain energy shows an initial increase and is then fairly constant or slowly decreasing, while in Type 3 graphite the average behaviour shows reasonable constancy, but there is a large fluctuation.

The GRIFFITH crack hypothesi@u postulates that failure will occur due to the presence of randomly orientated cracks which are sufficiently separated to be considered as isolated cracks. The following criteria are predicted by the GRIFFITH theory (c.f. ref. 19) when or -as > 0 and 30~ +a2 <o:

61 -a2)2+8a,(q+a2)=0 (3)

(Ql -02) -- -*(ol+c72)-cos 2e

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bl=bT (9

8-O (6)

for multisxial stress systems where:

frr is the major principal stress

02 is the minor principal stress

UT is the m&z&l tensile strength

8 is the angle between the critical crack and the normal to the direction of maximum principal stress.


Equations 3 and 4 imply a compressive/tensile strength of 8 and a parabolic relation(20) between the principal stresses at fracture. Since the principal stresses are related to the shear stress S, by(19)

61 -Qs=SO (7)

this when substituted in equations 3 and 4 predicts that the shear strength is twice the uniaxial tensile strength. For both Types I and II graphite thii criteria is reasonably well obeyed (Table 4) and highly irradiated graphite does have a compressive/ tensile strength ratio of N 8 (Table 2).

However, unirradiated graphite exhibits a compressive/tensile strength ratio less than 8. The data obtained in triaxial compression, certainly in the unirradiated graphite, does not obey the parabolic GRIFFITH criterion. It is found that the COULOMB-

NAVIER theory (cf. ref. 21) describes the unirradiated triaxial results very well and is a good repre- sentation of the irradiation results. This theory postulates that the shear strength S, is increased by ,u times the normal pressure (a) across the fracture plane where p is the coefficient of internal friction. If c and r are the normal and shear stresses across a plane, fracture will occur in that plane when

r=S,-/Xr . (8)

Resolving cri and 02 into normal and shear stress components acting on the crack, and following usual practice where tensile stresses are positive (ai is thus the hydrostatic pressure, 02 is the axial stress) gives

C,[P + (P2 + I>“1 + g2b - (P2 + 1>*1= 2so (9)

where p= l/tan 2 0. 8 defines the fracture plane as before. The results in Fig. 6 show very good agreement

with equation (9) for four unirradiated graphites having very different microstructures. It is interesting to note that the coefficients of friction determined from the slope of the plot of axial stress vs. hydrostatic pressure are roughly the same for all graphites, in fact three have the same value. The fracture angle 8 was found to be independent of hydrostatic pressure and agrees very well with the calculated angle (Table 5) although the values of 0 are higher than those obtained from &axial tests (Table 3).

H

For irradiated graphite the same linear dependence between axial stress and hydrostatic pressure is observed at low doses, although at higher doses the results show considerable scatter. Values of CL and 8 calculated from the slope of ~1 vs. 62 are listed in Fig. 7 and suggest a trend to an increasing coefficient of friction and a decreasing fracture angle with increasing dose. Thii could not be checked since the inaccuracies in measuring fracture angles were too great to enable the small changes at low doses to be measured contidently. At the two highest doses the specimens generally fragmented; but from a few specimens the fracture angle was assessed at 30 & 4”, in agreement with the calculated value for specimens irradiated to 7.5 x 102* n.cm2. At the highest doses however, there is considerable scatter in the results and these could just as readily be fitted by a parabolic law as predicted by the Griffith relation.

MCCLINTOCK and WALSH(“) derived equations 8 and 9 from the Grifhth model by assuming the critical cracks to be closed in compression, and this model has been shown by HOEK and BIENIAWSKI(~~) to apply to a wide range of rock materials. However, unless the cracks are initially closed, this predicts a compressive/tensile strength ratio between 8 and 10; moreover, this model merely predicts the critical angle of the crack(s) from which fracture is initiated. This need not necessarily be the macroscopic fracture angle. In fact, the observations of BRACE and BQMBOLAKIS(~~) on glass show that the crack, which is initiated at a point near to, but not at, the crack tip(25) runs out by following a curved path, and having gone out of critical orientation the crack ceases to grow.

Although the COULOMB-NAVIER relation pro- vides a good qualitative picture of the uniaxial results, it does not explain why the observed fracture angle coincides with the critical crack orientation. Whilst in tension a single crack can produce failure it is extremely unlikely that graphite in compression will fail by the propagation of a single crack. Rock failure due to natural faults has been observed to occur from an echelon system of cracks (MCKINSTRY 1941,‘26’ BRACE 1963’27’), and it seems possible that graphite fails in similar fashion. Ultimate failure will occur by the shear of thin slabs of graphite still connecting cracks which have ceased to grow. Since the maximum shear stress acts along this plane of critical orientation,

530 R. TAYLOR, R. G. BROWN, K. GILCHRIST, Ft. HALL, A. T. HODDS, B. T. KELLY and F. MORRIS

which is moreover weakened by these cracks, one would expect shear along this plane and the macroscopic fracture angle to correspond to the critical crack angle. The failure of graphite in two stages is substantiated by:

1. The observation that certain triaxial specimens had not broken even though the drop in stress corresponding to crack propagation, and usually failure, has occurred.

2. The high speed tine photography of compression tests which showed a visible surface crack for a significant time before failure occurred.

Additional evidence is that a specimen subjected to a large irradiation creep strain has been found with large surface cracks even though the specimen as a whole was still intact.(“)

In order to explain the effects of irradiation using a crack concept the strain energy associated with the cracks must be entirely associated with crystal shear. This limits the cracks to either macroscopic flaws sufficiently large to sample the average modulus of the polycrystal, which depends upon crystal shear almost entirely, or to micro- scopic cracks inside crystals which propagate under shear stresses. REYNOLDS(~) considers the GIUFFITH flaws in graphite are the microcracks while MASON suggests that the larger flaws are appropriate. The microscope observations of tensile fracture suggest that the large pores are the sources of weakness. Our metallographic observations of tensile fracture of a limited number of Type 1 graphite specimens suggests pore sizes up to a maximum of 0.6 mm, but detailed visual examination indicates that the largest pores have dimensions as high as 2 mm. If values of crack length (2c) lying in this range are inserted in the Griffith equation :

(11)

using for E the Young’s modulus of the polycrystal, values of y lying in the range 06-2.4 x 10’ ergs.cms2 are deduced.

We have determined the work required to initiate fracture of Type 1 graphite specimens having artificially induced cracks about 0@04 in. wide using GILMAN’s technique and determined this to lie in the range 0.7-2.5 x lo4 ergs.cmb2. Substituting the mean value ~-1.5~

lo4 ergscm” and c=O*l cm in equation (11) yields a value for o+r2/2E=4*8 x IO4 dynes.cm-2 which is in good agreement with the value of strain energy derived from our tensile stress strain curves (see Table 2). The calculated and observed surface energy values show very good agreement but are considerably higher than the energy expended by the propagation of cracks along the basal plane of the graphite crystal (119 ergs.cm-2(30) and 150 ergs.cm-2(31)) and less than work of fracture values obtained from controlled crack growth in polycrystalline graphites (N 105(32’ and l-5 x lOS(33’).

The former value is not applicable to polycrystalline graphites since a basal plane crack can only propagate for one grain diameter. After that more energy must be expended to cross a grain which is not suitably oriented.

The work of fracture determination from controlled crack growth experiments are derived from measurements of the nominal fracture surface area and are not applicable to tensile failure for the following reasons :

The true surface area may be many times the nominal fracture area. LOSTY has estimated this difference from fractographic analysis to be a factor of S-10.

Our observation of crack growth show that many minor cracks are opened up. These are not allowed for.

Crack growth in u&radiated graphite is modi- fied by plastic flow around the crack tip.

Crack interaction occurs.

For these reasons we feel that our work of fracture which measures the energy required to initiate complete fracture from a crack is more directly applicable and it seems therefore that the large pores constitute the GRIFFITH cracks in graphite. Since the pores themselves are often blunt it is entirely probable that the effective crack comprises the pore plus the microcracks radiating from it and that an effective c is frac- tionally greater than the values we have quoted.

The assumption that one can use the bulk modulus of the aggregate in equation (11) is open to question and it may be argued that a crystal modulus such as Css may be more applicable. If the large cracks are indeed the sources of weakness, then the change in tensile strength on irradiition is


due in part to the change in crystal moduli. The modulus of the polycrystal reflects the effective crystal C44 which increases whereas other crystal moduli decrease or remain unchanged.(lO) Thus, since these larger pores persist after irradiation and c is relatively unchanged, it is more appropriate to use the measured modulus.

After neutron irradiation the strain energy to failure of these graphites shows an initial increase followed by a subsequent fall. The increase may be caused by an increase in y or a reduction in c. Our hypothesis suggests that c will be relatively unchanged by neutron irradiation at low doses; therefore we postulate that y must increase. An increase in 2’ is most probably due to the fact that, due to the decrease in plasticity, the crack is propagating in an elastic stress field. At high doses crack generation(‘) is known to occur and the subsequent decrease in strain energy is probably due to an increase in c.

The increase in hardness of graphite on irradiation is, we believe, due to two effects, the first the decrease in permanent set or plastic flow on irradiation and the second, the reduction in microporosity into which deformation can take place.

7. BROC~BHUR~T J. B. and LYNAM J. T., U.K.A.E.A. Report TRG Report 901(C) (1965).

8. PRICE N. J., Mechanical Properties of No-n-Met&c Materiak (editor W. H. Watton), p. 106. Butter- worth (1958).

9. MURRBLL S. A. F. Ibid. p. 123. 10. S~MMERB L., WALKER D. C. B. and KELLY B. T,,

Phil. Msg. 14, 317 (1966). 11. WOOLLW R. W.,Phil. Mag. 11,475 (1965). 12. GOC~IN P., Second International Conference on

Industrial Carbons and Graphite, S.C.I., London (1965).

13. JENKINS G. M., Phil. Mug. 8, 903 (1963). 14. HALL E., J. Nucl. Mat. 15, 137-139 (1965). 15. LOSTY H. H. W. and ORCHARD J. S., Proceedings of

the Fifth Carbon Conference, p. 519. Pergamon (1961).

16. MAsON I. B. Ibid. p. 597. 17. SELDIN E. J., Carbon 4, 177 (1966). 18. GRIFFITH A. A., Proceedings of the First Int. Congress

Appl. Mech. p. 5.5 (1924). 19. YOKOBORI T., Strength Fracture ond Fat&e of

Materials, p. 127. Noordhof, Groningen (1964). 20. OROWAN E.. R&orts on Promess in Phwics 12, 485

(1949). ’ - - - 21. JAEGER J. C., Elasticity, Fracture and Flow (3rd

edition). Methuen. 22. MCCLINTOCK F. E. and WALSH J. B., Proceedings

of the Fourth U.S. Congress Appl. Mech., Berkeley, 1962. Aw. Sot. Mech. Engs. New York, 1015 (1963).

23. HOEK E. and BIENIA~SKI 2. T.. Int. 7. Fruct. Mech. , ”

Acknowle&men~The authors wish to acknowledge the 1, 137 (1965).

assistance of the reactor operators, rig technicians and 24. BRACE W. F. and BOMBOLAKIS E. G., J. Geophy S.

R.M.L. site staff at A.E.R.E. HarweII. Res. 68, 3709 (1963).

25. ODE H., Geol. Sot. Am. Me-m. 79,293-321 (1960).

REFERENCES 26. MCKINSTRY H. E., Am. Inst. Mining Met. Eng.

Techn. Pub. No. 1267 (1941). 1. KELLY B. T., MARTIN W. H. and Nrrnxrrv P. T., 27. BRACE W. P., Proc. Symposium Stress in Crust.

Phil. Trans. Roy. Sot. A260, 37 (1966). Santa Monica, June 1963. 2. MARTIN W. H. Private communication. 28. GRAY B. S. Private communication. 3. REYNOLDS W. H., Phil. Meg. 11, 357 (1965). 4. HIJTCHE~N J. M. and THORNE R. P. Second Inter-

29. GILMAN J. J., J. Appl. Phys. 31, 2208 (1960). 30. GOOD R. J., GIRIFALCO L. A. and Kwus G.. 7. P&S. _”

national Conference on Industrial Carbons and Graphite, S.C.I., London (1965). 31. BJXLL J. C., BRIDGE J., CO~LL A. M., G~JXNOUGH G. B., REYNOLDS W. N. and SIMMONS J. H. W., 32. Phil. Trans. Roy. Sot. A254, 361 (1962). MARTINW.H.~~~CLARED.M.,NUCZ.S~~.E~~.~~, 33. 468 (1964).

5.

6.

Chem. 62, 1418 (1958). BRUCE R. H., J. of Metals. Club R.C.S. Glasgow No. lo., p. 41 (1958-9). LOC~DAIL D. H., KNIBBS R. H. and TATTERSALL H. C. Unpublished data. BLAKELOCK H. D. and LOS= H. H. W. Unpublished data.

THE MECHANICAL PROPERTIES OF REACTOR … CAES...using a 5 mm Huggenberger extensometer mounted on...

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