Small-Scale Approaches to Evaluate the Mechanical Properties of Quasi-Brittle Reactor Core Graphite

Dong Liu,1 Peter J. Heard,2 Soheil Nakhodchi,3

and Peter E. J. Flewitt2,4

Small-Scale Approachesto Evaluate the MechanicalProperties of Quasi-BrittleReactor Core Graphite

Reference

Liu, Dong, Heard, Peter J., Nakhodchi, Soheil, and Flewitt, Peter E. J., “Small-Scale

Approaches to Evaluate the Mechanical Properties of Quasi-Brittle Reactor Core Graphite,”

Graphite Testing for Nuclear Applications: The Significance of Test Specimen Volume and

Geometry and the Statistical Significance of Test Specimen Population, STP 1578, Nassia

Tzelepi and Mark Carroll, Eds., pp. 1–21, doi:10.1520/STP157820130127, ASTM International,

West Conshohocken, PA 2014.5

ABSTRACT

A range of small scale, from centimetre scale to micrometre scale, mechanical

testing techniques have been used to measure the properties of nuclear reactor

core graphite, including Pile Grade A (PGA) graphite and Gilsocarbon graphite.

These testing methods include four-point bending (centimetre scale), diametral

compression (millimetre scale), micro-scale cantilever bending (micrometre

scale) and nano-indentation (micrometre scale). These methods provide both a

measure of mechanical properties including elastic modulus and fracture

strength and detailed information concerning the deformation and fracture

mechanisms. For each test, an example using a particular specimen geometry is

given and discussed with respect to the particular mechanical property

evaluated and compared with macro-scale data. Nano-indentation was carried

Manuscript received August 31, 2013; accepted for publication June 6, 2014; published online July 18, 2014.1Interface Analysis Centre, School of Physics, Univ. of Bristol, Bristol, BS8 1TL, UK (Corresponding author),

e-mail: [email protected] Analysis Centre, School of Physics, Univ. of Bristol, Bristol, BS8 1TL, UK.3Department of Engineering, Univ. of Bristol, Bristol, BS8 1TR, UK.4HH Wills Physics Laboratory, Univ. of Bristol, Bristol, BS8 1TL, UK.5ASTM Symposium on Graphite Testing for Nuclear Applications: The Significance of Test Specimen Volume

and Geometry and the Statistical Significance of Test Specimen Population on Sept 19–20, 2013 in Seattle,

WA.

Copyright VC 2014 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959.

GRAPHITE TESTING FOR NUCLEAR APPLICATIONS: THE SIGNIFICANCE OF TEST SPECIMEN VOLUME

AND GEOMETRYAND THE STATISTICAL SIGNIFICANCE OF TEST SPECIMEN POPULATION 1

STP 1578, 2014 / available online at www.astm.org / doi: 10.1520/STP157820130127

out as a conventional approach to validate and assist the understanding of the

mechanical properties obtained via other small scale tests. The use of small scale

test specimens offers benefits when handling irradiated reactor core graphite.

The results are discussed with respect to the potential benefits, difficulties and

value of small scale mechanical tests for this particular application.

Keywords

reactor core graphite, millimetre scale testing, micrometre scale testing,

mechanical properties

Introduction

Pile Grade A (PGA) and Gilsocarbon graphites are used in the UK nuclear powerstation gas cooled reactor cores. These graphites are often cited as a classic exampleof a quasi-brittle material where failure, in tension, is associated with small strains.PGA was manufactured for use in the early Magnox gas-cooled reactors, and usedfiller particles derived from the petroleum industry. These coke particles have anelongated, needle-like shape where the long axis aligns with the extrusion axis ofthe reactor core bricks (Fig. 1(a)) [1]. These particles are embedded in a matrix offine flour particles of micrometre dimensions and graphitised pitch. As the crystalli-tes within the filler particle are also preferentially aligned, the bulk material has ani-sotropic material properties. Graphite components manufactured from Gilsonitecoke, which is usually referred to as Gilsocarbon, have been used as moderators inthe Advanced Gas Cooled Reactors (AGR) in the UK, the THTR in Germany, andas fuel supports in some French Magnox reactors. Gilsocarbon was a later class ofgraphite where the filler was obtained from naturally occurring asphalt mined inthe USA called Gilsonite. The coke manufactured from Gilsonite produced spheri-cal, “onion-like” filler particles that had no preferential alignment from the manu-facturing process (Fig. 1(b)) [1]. Again, these filler particles are embedded in amatrix of fine particles and graphitised pitch. As the crystallites within the particlestended to align circumferentially, the bulk material has near-isotropic behaviour.

These graphites have polygranular aggregate microstructures and features simi-lar to other aggregate materials such as concrete. A typical example is shown by theload–displacement response for bend geometry specimens (Fig. 2). There is noevidence that polygranular aggregate graphites can be plastically deformed. Hence,the change in compliance together with any deviation from an initial linearresponse of the load-displacement curve, Region II in Fig. 2, can be attributed tomicro-cracking. Progressive softening is also observed in some specimens post thepeak load, Region III. This type of load–displacement behaviour is a characteristicof quasi-brittle materials [2].

A wide range of standardised macro-scale test methods have been adopted toevaluate the mechanical properties of these materials both in the as-fabricated vir-gin condition and following exposure to the service environment [3,4]. These data

2 STP 1578 On Graphite Testing for Nuclear Applications

are used as inputs to the structural integrity assessment of the reactor cores andprovide information about the underlying mechanisms leading to failure of thematerial. However, there are potential advantages for testing material at the micro-scale since the use of smaller volumes of irradiated material requires less substantialshielding for the test facilities. For this class of quasi-brittle material, failure involvesmicro-scale crack initiation at microstructural defects or weakly bonded sites, thepropagation and coalescence of micro-scale cracks to form long macro-scale cracks,and the eventual failure of the materials [2,5]. Hence, for quasi-brittle materialswith complex microstructure, multi-scale tests have to be adopted. However, it isimportant to understand the difference in the derived mechanical propertiesobtained using various size and geometry test specimens.

In this paper, we summarise the range of small scale graphite mechanical test-ing carried out at the University of Bristol across the centimetre to micrometre scale

FIG. 1 Image taken by scanning electron microscopy for graphite grades (a) PGA and

(b) Gilsocarbon [1].

LIU ET AL., DOI 10.1520/STP157820130127 3

range. In particular, we compare the load–displacement characteristics and thederived mechanical properties such as elastic modulus and tensile strength.

Experiments

In this section, we describe the mechanical test methods adopted and the specificsize and geometry of graphite specimens.

FOUR-POINT BEND TEST (PGA GRAPHITE)

Rectangular beams of virgin and irradiated PGA graphite 25 by 25 by 200mm weresupplied by Magnox Electric Ltd. These beams were cut parallel to the long axis ofthe direction of extrusion of the original graphite brick. Hence the flexural strengthmeasured would be parallel to the oriented grains. The irradiated PGA has a poros-ity of� 48 %. The beams were subjected to quasi-static four-point bend loading(150mm support span and 50mm loading span). This arrangement ensured thatthe region between the two middle rollers was subjected to a pure bending moment.The load applied to the two inner rollers generates a tensile stress at the bottom sur-face and a compressive stress at the top surface of the beam specimen. Prior to test-ing, a uniaxial strain gauge (06-240LZ) 6mm long was bonded using M bond 200adhesive (Vishay Precision Group). The strain gauge was bonded to the top surfaceof each graphite specimen to measure compressive strains. A 25 kN Roell AmslerMJ6273 servo-hydraulic test machine was used to load the specimens. Tests were

FIG. 2 A schematic characteristic bend geometry load–displacement curve for a

quasi-brittle material, region I is linear, region II is non-linear, region III is post

peak softening.

4 STP 1578 On Graphite Testing for Nuclear Applications

performed with a controlled displacement rate of 0.05mm/min. To measure verticaldisplacement of the beams, a linear variable displacement transducer (LVDT) wasmounted on the test machine at the mid-position between the two lower rollers andat the bottom of the test specimens. Test specimens were subjected to severalloading–unloading cycles prior to failure and load-displacement signals wereextracted from the data files.

DIAMETRAL COMPRESSION TEST (PGA AND GILSOCARBON GRAPHITES)

The diametral compression test, the Brazilian test, and the indirect tensile test arethree names used to describe one test method for measuring the tensile strength ofbrittle materials proposed by Hondros in 1959 [6]. Cylindrical graphite test speci-mens were made by trepanning 12mm diameter rods extracted from bulk virginGilsocarbon graphite reactor core bricks provided by EDF Energy Ltd. These weresliced into 6 and 4mm thick cylinders using a South Bay Technology Inc. Model650 low speed diamond wheel saw with deionised water as coolant (Fig. 3(a)). Thediamond saw produced smooth high-quality surfaces suitable for subsequentmicroscopic examination [1]. Additional 6mm thick discs of unirradiated and irra-diated PGA graphite were cut parallel to the extrusion direction for testing.

Compression testing of the cylindrical graphite specimens was undertakenusing a Deben compression/tensile stage (MicroTest 2000 model, Gatan Ltd.,Abingdon, Oxon, UK) can be seen in Fig. 3(b). The unit is capable of operationexternally or within a scanning electron microscope or focused ion beam (FIB)workstation. The stage has curved anvils to match the geometry of the test specimento ensure the applied load is correctly distributed. Under the distributed compres-sion loading, failure occurs close to the centre of the disc specimen where a tensilestress is generated [7]. It can be operated at compression speeds of between 0.033and 0.4mm/min, with a load cell giving force measurements up to a maximum of2 kN. The cylindrical graphite specimens were loaded into the compression testersuch that the direction of the compressive load was along a diameter of the flat faceof the cylinders. Load–displacement curves were recorded whilst observing the sur-face of the specimen by either optical microscopy or focused ion beam imaging.

MICRO-SCALE CANTILEVER BEAMS (GILSOCARBON GRAPHITE)

At the micro-scale, a novel technique for in situ testing cantilever beam specimenshas been developed [8,9]. This approach combines a dualbeam workstation (FEIHelios NanoLab 600i Workstation) and a force measurement system (FMS) fromKleindiek Nanotechnik. In an extension to the specimen preparation proceduredescribed by Liu et al. [8,9], as shown in Figs. 5(a) and 5(b), two steps are requiredto produce the specimens. Step 1 is to mill two rectangular slots, 5lm apart, with a45� ion beam incident angle to the sample surface. This leaves a 5lm thick wall ofgraphite sandwiched by two empty trenches, each with the size of 15 lm in widthby 10 lm in height and more than 10lm in depth (Fig. 4(a)). Step 2 requires repeat-ing the milling at 45� from the other direction. This allows the formation of a

LIU ET AL., DOI 10.1520/STP157820130127 5

square sectioned cantilever beam with the dimension of 5 by 5 by 10 lm (Fig. 4(b)).Repeating the two steps with a reduced beam current of 2.7 nA using the “cleaningcross-section” approach to produce a thinner cantilever beam, 2 by 2 by 10lm,with minimum surface ion damage. When loaded in situ, the stage in the dualbeamunder the sample holder has to be tilted by 45� about the axis of the beam to allowthe side surfaces to be loaded by a force measurement probe (Fig. 4(b)). The millingdepth for the test specimen in Step 1 and 2 is flexible; usually a depth of 10 to20 lm is selected.

FIG. 3 (a) Optical image of the surface of a typical Gilsocarbon graphite disc (12 mm

diameter, 6 mm thickness); (b) the loading jig use circular grips with the

diameter of 12 mm to ensure full contact when the disc is loaded.

6 STP 1578 On Graphite Testing for Nuclear Applications

FIG. 4 Schematic of the milling sequence for cantilever creation (a) Step 1 is to mill two

square patterns into the material at an incident beam angle of 45�, which leaves a

5lm thick wall in the middle; (b) Step 2 is to rotate the stage 180� to incident the

ion beam 45� from the opposite side to mill another two rectangular trenches 5lm

apart on the residual wall material from the first step. (c) The loading configuration

showing a typical cantilever beam, 1.4 by 1.4 by 10lm, under bending by the force

measurement probe observed under scanning electron microscope.

LIU ET AL., DOI 10.1520/STP157820130127 7

Specimens are usually created at the edge of the bulk material to allow accessfor the loading probe. A typical arrangement for the loading probe and a cantileverbeam specimen is shown in Fig. 4(c). The details of the loading system and calibra-tion of the technique can be found in Refs. [8,9]. For all the tests, the system is cali-brated against single crystal silicon. The force measurement system instantlyoutputs the applied load (with the resolution of 0.01 lN) on the cantilever, whereasthe displacement at the loading point is measured on the secondary electron mi-croscopy images recorded during the test (with the resolution of 0.5 pixels). Severalmicro-cantilevers were created and loaded to fracture. The loading curves togetherwith elastic modulus are obtained and compared with those data derived frommacro-scale testing.

NANO-INDENTATION (GILSOCARBON GRAPHITE)

Nano-indentation was undertaken on Gilsocarbon graphite with the surface cutby a South Bay Technology Inc. Model 650 low speed diamond wheel saw withdeionised water as coolant. An Agilent Nano Indenter G200, housed at the CulhamCentre for Fusion Energy, Materials Research Laboratory, was used and the testsfollowing the ISO 14577-4:2007 [10] standard procedure. Nano-indentationhardness tests are generally made with either spherical or pyramidal indenters. TheBerkovich indenter is generally used in small-scale indentation studies and has theadvantage that the edges of the pyramid are more easily constructed to meet at a

FIG. 5 A typical load–displacement curve obtained for PGA graphite beam under

four-point loading [11].

8 STP 1578 On Graphite Testing for Nuclear Applications

single point rather than the inevitable line that occurs in the four-sided Vickerspyramid [11]. Hence, a standard Berkovich diamond tip with a tip diameter of�50 nm was adopted. Each measurement comprises of a square array of 5 by 5 dis-tributed indents with a separation of 100 lm. The tests were conducted under loadcontrol with the maximum load of 100mN and peak hold time of 10 s. Theindenter was pre-calibrated on fused silica and a drift correction carried out aftereach indent.

Results

FOUR-POINT BENDING PGA GRAPHITE BEAM

A typical load–displacement curve is shown in Fig. 5. Four-loading and unload-ing cycles are included prior to achieving peak load. In general, this loadingcurve showed the characteristics of a quasi-brittle material with three distinctregions, linear, non-linear to peak load, and post peak softening (compare Fig. 5

with Fig. 2). From zero to 400N, the loading curve is linear (Fig. 5). Between400 N and point A (600N), there is a small departure from linearity; hence atpoint A upon unloading, hysteresis is present and non-linearity was found to-gether with a residual permanent displacement. This permanent displacementincreases with the number of increasing loading cycles, and reached 0.08mm,point E in Fig. 5, after the fourth unloading from point C. The reloading curveexhibited linear behaviour prior to the point at which it was unloaded, beyondthis point, non-linearity occurred with further loading. The peak load was1370N and post-peak softening occurred due to the propagation of macro-cracks [12].

The measured strains and loads up to 400N in Fig. 5 were used to determinethe elastic modulus, E, using simple beam bending theory

E ¼ My=Ie(1)

where:M¼ the bending moment,y¼ the distance between the strain gauge and the neutral axis,I¼ the moment of area (¼ bh3/12) with b the width and h the depth of the rec-

tangular beam cross-section, ande¼ the measured strain.Compressive strain gauge readings were used to determine an average bulk

elastic modulus of 7.56 0.4GPa. This value is comparable with 7.96 0.4 GPaderived by Ouagne [13] from the initial slope of stress–strain curves for PGAgraphite.

Given that for this test specimen geometry, the loading span is a third of thesupporting span in the loading jig, and the section of the beam is square, theflexural strength, rf, can be derived from

LIU ET AL., DOI 10.1520/STP157820130127 9

rf ¼ FL=a3(2)

where:F¼ the peak load, which is 1370N in this case,L¼ the supporting span of the four-point bending jig, which is 150mm, anda¼ the width and height for the square cross-section of the loaded beam.Hence rf is determined to be 13.2MPa. In the same batch of PGA beams, a

higher peak load was observed at 1500N giving a higher rf value of 14.4MPa.The same procedure was adopted for the neutron irradiated PGA beams. The

load–displacement curve had the same general form as virgin material, but the peakload reduced to 700N. Thus, the tensile strength was 6.5MPa, about half the valuefor the virgin PGA graphite beam. No strain gauges were applied to the irradiatedgraphite, but a reduced gradient in the linear elastic range of the load–displacementindicated a smaller elastic modulus after irradiation.

DIAMETRAL COMPRESSION TEST ON PGA AND GILSOCARBON GRAPHITE

As mentioned in the Diametral Compression Test subsection, optical images wererecorded during the whole test for the observation of crack initiation. It was con-firmed that fracture occurred at the centre of the specimen. The load–displacementcurves for the PGA and Gilsocarbon graphite discs are shown in Fig. 6(a). Theupper limit of the loading jig, 2 kN, was reached before the Gilsocarbon graphitedisc reached the non-linear range. Hence, the thickness of the Gilsocarbon disc wasreduced from 6 to 4mm to allow a full range displacement curve to be achieved(Fig. 6(b)).

Brazilian disc compression was standardised by the International Society forRock Mechanics in 1978 [14] as a method for determination of the tensile strengthof rock materials, and subsequently by the American Society for Testing and Mea-surement for obtaining the tensile strength of concrete materials [15]. It has beenwidely adopted in the application for testing quasi-brittle materials with low tensilestrength. However, it worth noting that the tensile elastic modulus determinationfrom the conventional Brazilian disc test is not straightforward as there is not ananalytical solution for the stress at the curved loading point/area. Strain gaugeshave to be applied to the specimen surface to record the strain during loading[6,16], or alternatively, other strain capture techniques such as digital image corre-lation [17] are required to measure the strain at the surface. In the present work, asthe specimen is relatively small, the penetration of the glue for strain gauges intothe specimen would influence the measured property hence no strain gauges wereapplied. No digital image correlation was adopted in the present paper; hence thetensile elastic modulus cannot be accurately derived. Wang et al. [18] proposed aflat-end Brazilian disc method to obtain the elastic modulus; unfortunately, it is notimplemented in the current paper, but is to be evaluated for future tests. However,for the data acquired from the present test, an approximate tensile elastic modulus,E, is derived by adopting the relation proposed by Wang et al. [19]:

10 STP 1578 On Graphite Testing for Nuclear Applications

E ¼ 2Pp � DL � t 1� �ð Þ � ln 1þ 4

sin2 a

� �� �a

sin a(3)

where:P¼ the applied force,DL¼ the displacement applied on the disc,t¼ thickness of the disc,�¼ the Poisson ratio of graphite, anda¼ the distribution angle over which the force is applied.Using this equation, E can be determined from the slope of the linear section of

the load–displacement curve before the maximum load. Here for both the PGA andGilsocarbon graphite, a Poisson ratio of 0.25 is used.

For PGA graphite, from the load–displacement curve in Fig. 6(a), a linear fit forthe section prior to the peak load of 1314N gives a slope of 30126 80N mm�1. For

FIG. 6 The load–displacement curves for (a) the 6 mm thick PGA and Gilsocarbon

graphite discs and (b) the 4 mm thick Gilsocarbon graphite. The asterisks mark

the linear range.

LIU ET AL., DOI 10.1520/STP157820130127 11

the testing geometry, 2a is 30� and t is 6mm, then E is determined to be 5.1GPawith associated errors 65 %. Another two specimens with the same dimensionwere tested and using the same algorithm procedure, the tensile elastic moduli areapproximately 6.1 and 5.7GPa with associated error about 5 %. This gives an aver-age of 5.6 GPa with an standard deviation of 0.5 GPa. It is emphasized that the PGAdisc was trepanned from a brick along the extrusion direction hence the tensilemodulus is perpendicular to the aligned grains.

For Gilsocarbon graphite with the thickness of 4mm, Fig. 6(b), the slope of theload–displacement curve before the peak load is fitted to be 31966 130N mm�1.With a value for 2a of 30� and t of 6mm, the tensile elastic modulus of this speci-men is 8.08GPa with an error of 5 %. The other two specimens gave an E of 8.4and 7.3GPa with errors of 5 %. The three specimens tested provided an average Eof 7.9 GPa with a standard deviation of 0.5 GPa.

The tensile strength was calculated according to the analytical solution devel-oped by Hondros [6] when a distributed load is applied to the specimen. It can beseen in Fig. 6(a) that the PGA graphite disc failed at a peak load of 1314N. Anothertwo disc specimens were tested and the average tensile strength obtained was8.5MPa with a standard deviation of 1.3MPa. For Gilsocarbon graphite, threespecimens with the dimension of 12mm diameter by 4mm thickness were testedand gave tensile strength values of 13.6, 16.9, and 16.5MPa; an average value of15.7MPa with standard deviation of 1.8MPa.

MICRO-SCALE CANTILEVER GILSOCARBON GRAPHITE BEAMS

When preparing the micro-scale cantilever specimens the selection of the regionwithin the sample is crucial because of the heterogeneity of the microstructure.Essentially, some specimens have no strength because of the presence of either sig-nificant micro-cracks or large pores. The loading system has the capability to loadspecimens from various directions and for multiple cycles. Typically, the beam sizesare 2 by 2 by 10 lm, and elastic modulus could be derived from the linear range ofthe load–displacement curve; the flexural strength could be derived from the peakload according to cantilever bending theory [8]. One typical example of the loadingand unloading of a cantilever beam is shown in Fig. 7(a). This cantilever beam had across-section of 2.3 by 2.3 lm and the loading arm length was 13 lm.

For the first load cycle, the load curve was linear (max load was 14.80 lN) andunloading was performed before any non-linearity occurred (Fig. 7(b)). The slope ofthe linear loading curve was 24.26 0.13N m�1; hence the elastic modulus is calcu-lated to be 7.76 0.05GPa. During the second loading cycle (max load reached27.45 lN), Fig. 7(c), the fitting of the initial linear part of the curve gives a maximumgradient of 28.16 1.2N m�1, and an elastic modulus value of 8.96 0.4 GPa. Uponremoval of load, a permanent displacement of 0.057 lm was observed. There wasenergy dissipated during the second loading cycle according to the hysteresis areabetween the load and unload curves. For the third loading cycle, Fig. 7(d), a hystere-sis similar to that observed for load cycle 2 occurred together with a final residual

12 STP 1578 On Graphite Testing for Nuclear Applications

displacement of 0.086 lN when unloaded. The elastic modulus was calculated to be8.46 0.5 GPa. The cantilever was loaded to fracture during the fourth cycle. Elasticmodulus was derived from the initial linear range up to 8 lN to be 9.56 0.1 GPa.Non-linearity was observed between� 8lN and the peak load. Failure of the canti-lever commenced at a maximum load of 48.15 lN with a displacement of� 3.0 lmat the loading point. The flexural strength of this cantilever was determined to be308MPa.

FIG. 7 (a) SEM image of the micro-cantilever beam under load; (b)–(e) the

load–displacement curve for four loading cycles using the loading geometry

shown in (a).

LIU ET AL., DOI 10.1520/STP157820130127 13

As pointed out at the beginning of this section, the mechanical propertiesobtained from the cantilever beams tested will depend on the pores/defects sampledwithin the specimen volume. Several other cantilevers with a size of 2 by 2 by10 lm were tested, and a range of elastic moduli/flexural strengths were obtained.So far, from the tests performed, the maximum flexural strength reached was979MPa and the highest elastic modulus was 36GPa. In general, at the micro-scale,the graphite showed very large elastic deformation and much higher values for theelastic modulus and flexural strength compared with larger-scale specimens.

NANO-INDENTATION OF GILSOCARBON GRAPHITE

Nano-indentation is a conventional test approach; it was applied on Gilsocarbongraphite to explore the variability within the data when sampling small areas fromthe overall complex microstructure. Figure 8 shows the load–displacement curvesobtained from nano-indentation. All the curves exhibited incomplete recovery withsignificant hysteresis between loading and unloading. This hysteresis was attributedto inter-layer friction in the graphite microstructure [20]. The variation of themicrostructure leads to the scatter of the loading curve because every indent sam-ples a relatively small area (several micrometres). The elastic modulus calculatedfrom the slope of the unloading curve was 9.36 3.5GPa.

In theory, high resolution imaging in a SEM could be combined with the nano-indentation to locate and identify the indents left by the test, and thereby loadingcurves and measured elastic modulus could be assigned to a particular constituentin the graphite (particle, matrix, pores, etc.). However, in the current graphite,the indents were found to be very difficult to identify. Hence it is unclear if

FIG. 8 Load–displacement curves for a square array of nano-indentation tests

undertaken on the surface of Gilsocarbon graphite.

14 STP 1578 On Graphite Testing for Nuclear Applications

micro-cracking is present or absent under a given indent. Since the penetrationdepth of the indenter reached 5 lm, the sampled volume was estimated to be largerthan for the micro-cantilever tests. The elastic modulus calculated from the gradientof the unloading curve is not directly comparable to the elastic modulus derivedfrom the bending of a cantilever beam.

Discussion

Both PGA and Gilsocarbon reactor core graphites have a porous, polygranularaggregate microstructure so that changes in relative proportions of materialssampled by the particular test specimen cause modifications in the measuredmechanical properties. The inherent strength of reactor core graphite is governedby the pore size, the pore distribution and other major factors such as the formingoperation, the baking, and graphitization processing. The testing techniques that wehave described sample the material at different length-scales. It is important tounderstand if there is a critical length-scale or test geometry where the resultsbecome non-representative of macro-scale data.

The mechanical properties obtained for the graphites are summarised in Table 1

for the various tests conducted and the specimen types. Data extracted from litera-ture for similar types of graphites are included in Table 2. The data are arranged interms of the properties and specimen types. PGA graphite is highly anisotropic due

TABLE 1 Measured mechanical properties of virgin PGA and Gilsocarbon graphites at a

length-scale range.

Data Acquired in the Present Work

PGA (Para) PGA (Perp) Gilsocarbon Graphite

FPB Tens. E 7.5 6 0.4 GPa — —

Flexural strength 13.2 MPa — —

14.4 MPa

BD Tens. E — 5.6 6 0.5 GPa 7.9 6 0.5 GPa

Tensile strength — 8.5 6 1.3 MPa 15.7 6 1.8 MPa

MC Tens. E — — 7.7 6 0.05 GPa (load 1)

8.9 6 0.4 GPa (load 2)

8.4 6 0.5 GPa (load 3)

9.5 6 0.1 GPa (load 4)

Max Tens. E¼ 36 GPa

Flexural strength — — 308 MPa

Max value: 979 MPa

IDT Comp. E — — 9.3 6 3.5 GPa

Note: FPB¼ four point bending; BD¼Brizallian disc; Micro-scale cantilever¼MC;Indentation¼ IDT; Paralell to PGA oriented grains¼PGA (para); Perpendicular to PGA orientedgrans¼PGA (Perp); Tensile elastic modulus¼Tens. E; Compressive elastic modulus¼Comp. E.

LIU ET AL., DOI 10.1520/STP157820130127 15

to the alignment of the petroleum-coke filler particles parallel to the direction ofextrusion process during manufacture. The typical elastic modulus found in litera-ture for virgin PGA graphite similar to the material tested in the current work inthe parallel direction is� 11GPa and is� 6GPa along the perpendicular direction[4]. Certainly, the measurements obtained in the present work using four-pointbending and Brazilian disc tests are consistent with these literature values. In gen-eral, the flexural strengths for PGA graphite measured in the perpendicular direc-tion obtained from literature and the present work fall within the range of 10 to20MPa. Specifically, Payne [24] undertook a series of Brazilian disc compressionson PGA and Gilsocarbon graphites with similar dimensions to those investigated inthe present work. This gave a tensile strength of 6.376 0.42MPa for PGA in theparallel direction and 5.756 0.43MPa in the perpendicular direction, which areconsistent with the value of 8.56 1.3MPa given in Table 1. For Gilsocarbon graph-ite, an average strength value of 15.76 1.8MPa was derived from the current work,which falls within the range of 14 to 18MPa obtained by Payne [24] from a largenumber of Brazilian disc tests.

In terms of the mechanical properties derived from the indentation technique,Manika et al. [25] tested an isotropic polycrystalline graphite R6650 (SGL Carbon)with 10 % porosity using an MTS G200 nano-indenter with a Berkovich diamondtip. This gave an elastic modulus of� 13GPa, slightly higher than the average of9.3 GPa obtained for the present Gilsocarbon graphite, which has a higher level ofporosity (20 %). Micro-indentation tests were conducted by Oku et al. [26] onGilsocarbon graphite. In this case, two loads were applied, one at 19.6mN and theother at 147mN, to give penetration depths of 2 and 5 lm, respectively. Theseworkers also found large variations of measured elastic modulus and hardness withlocation on the test specimens. The elastic modulus value obtained was around10GPa with standard deviation of� 4GPa, which is consistent with the valuederived from the present work, Table 1.

The elastic modulus of Gilsocarbon graphite has been measured using manytechniques. Frequently, the dynamic elastic modulus is determined by measuring

TABLE 2 Measured bulk mechanical properties of virgin PGA and Gilsocarbon graphites in the

literature [13,21–23].

(Comp.¼Compression; Tens.¼ Tension)

PGA (Perp) PGA (Para) Gilsocarbon Graphite

E (GPa) 7.9 6 0.4 (comp.) 7.6 6 2.1 (comp.) 10.8 6 0.5 (comp.)

3.74 6 0.4 (comp.) 11.3 6 0.4 (comp.)

4.1 6 1.4 (comp.)

4.8 6 1.4 (tens.) 11.0 6 3.4 (tens.) —

Tensile Strength (MPa) 7.6 6 2.8 9.6 6 3.4 19.6

Flexural Strength (MPa) 12 18.3 27.2

16 STP 1578 On Graphite Testing for Nuclear Applications

the density and the velocity of sound in the specimen. Marsden et al. [3] measuredthe dynamic elastic modulus in 8mm diameter Gilsocarbon graphite specimens inthree directions, and confirmed that there is no obvious directionality associatedwith determined value. The three directions all gave a value of� 10GPa with mea-surement errors. Although dynamic moduli in quasi-brittle materials may differ sig-nificantly from each other, the static elastic modulus measured in Gilsocarbongraphite is also measured to be about 10GPa [27].

Polygranular reactor core graphite is well-known for the large scatter in themeasured properties [28]. Hence, as long as the measured data are within the rangeof reported values, they can be considered to be valid. Certainly there will be batchto batch variability as well as within batch variability for a particular type of graph-ite. However, this is considered to be exacerbated by variability when making meas-urements at the micro-scale. Hence, for these data there, is both a size effect for thetest specimens and their geometry which is combined with contributions arisingfrom the microstructure. For example, Virgil’ev and Makarchenko [29] found thatthe tensile strength from round specimens, 8.36 1MPa, is 20 % higher than thatobtained from rectangular beams, 5.16 1.2MPa; unfortunately, the author referredto the material as “reactor graphite” without specifying the type.

In reality, components being assessed may have sizes considerably larger thanboth the specimen size specified in the measurement standard and the specimen onwhich the property measurement is performed. However, within some limitedrange of specimen sizes for a particular test method, the size effect is not significant.This understanding would provide a basis for making use of the available small vol-ume of material to derive quantitative data that is consistent with that obtainedfrom test specimens with much larger dimensions. For example, Yoon et al. [30]measured the uniaxial tensile strength of NBG-18 using subsize specimens (4, 8,and 12mm rods) and the tensile strength was found to be between 21 and 23MPawith a standard deviation from 2 to 3.1MPa. The tensile strength of a 4mm diame-ter rod is at the higher end of this range. This indicates that the measurements froma 4mm specimen can be readily extrapolated to larger specimens of similar loadingand geometry. These values are generally higher than the tensile strength(15.76 1.8MPa) measured by Brazilian disc compression in this work; however,just as Brocklehurst [31] suggested, a higher gradient of stress during the loadingconfiguration (three-point and four-point bending) results in a higher nominalstrength of the material. Of course, these discrepancies could well be caused by thevaried graphite manufacture and microstructure. Thus the emphasis of the currentpaper is that the same material evaluated using various techniques across a length-scale in the same laboratory can provide a higher confidence in the data. In addi-tion, the extraordinary mechanical behaviour of graphite at the micro-scale is high-lighted by comparing with larger specimens.

From the results presented in Table 1 for the four-point bend and the Brazilliandisc test, it is clear that they are of a size that accommodates the overall microstruc-ture associated with the two reactor core graphites evaluated. However, there is a

LIU ET AL., DOI 10.1520/STP157820130127 17

need to accommodate the inherent inhomogeneity within the graphite microstruc-ture that varies over a significant greater length-scale. Thus a statistically designedtest programme would be required to achieve a mean representative measure of aspecific mechanical property.

The small length-scale associated with both nano-indentation and micro-scalecantilever beams means that the properties of the individual features of themicrostructure can be determined—for example the property of filler particles.These data may not be appropriate for evaluation of components, but are prob-ably a necessary requirement for input to computer models such as the finite ele-ment beam models described by Schlangen et al. [32]. However, there are otherreasons why micro-scale cantilever tests are of benefit: (i) the testing of nucleargraphite that has undergone reactor irradiation remains a challenge. The micro-scale cantilever beams allow the role of irradiation damage to be addressed; (ii)one of the ultimate aims of experimental investigation of nuclear graphite is to es-tablish an understanding and models for integrity and durability prediction andevaluation. As such, the input of mechanical properties into the model have to bethe intrinsic properties of the individual components in the graphite, i.e., matrix,particles. Cantilever tests are capable of providing these measurements; (iii) it wasfound that for both PGA and Gilsocarbon graphite, apart from the macro-poresthat are discernible under optical microscopy, there are nano-size pores embed-ded in the matrix and the particles. The cantilever beams sample these nano-sized pores and evaluate the compliance of the matrix/particles independently.Various sizes of micro-cantilever beams with sections in the range 0.5 by 0.5 by20 by 20lm have been created and tested in tested in Bristol, and it has beenobserved that there is also a size effect at this micro-scale.

Nuclear graphite has a complex microstructure; hence the measured propertieschange with the size of specimens tested and the loading configuration adopted. Tointerpret this scenario, fundamental investigation based on the constituents con-tained in the material is considered to be key. The micro-cantilever beam tests havethe capability to provide insights into these factors and hence develop physicallybased prediction models to provide integrity and durability assessment criteria.

Concluding Comments

The work presented includes a range of small scale tests and there is scatter in themeasured elastic modulus (compliance) and fracture strength, but this is within therange of data reported in literature (Tables 1 and 2). Overall, there are potential ben-efits to be obtained from testing small scale specimens to acquire a measure of themechanical properties of reactor core graphite, particularly in the irradiated condi-tion. However, our work indicates that these data need to be treated with caution.

• Change from centimetre scale to millimetre scale does not change the meas-ured properties significantly, which indicates that the volume of microstruc-ture sampled is sufficient to yield a representative average value.

18 STP 1578 On Graphite Testing for Nuclear Applications

• Reducing sampling volume results in larger scatter and it is necessary to havestatistically designed programmes to provide mean data for comparison withdata obtained from larger specimens.

At the micro-scale, the cantilever beam tests show that the mechanical proper-ties of specific microstructural features of the reactor core graphite can bemeasured.

ACKNOWLEDGMENTS

The writers acknowledge the financial support from EPSRC funded project, QUBE

(QUasi-Brittle fracture: a 3D Experimentally-validated approach). Grant number: EP/

J019801/1. The Materials Research Laboratory at the Culham Centre for Fusion

Energy was used for the nano-indentation on Gilsocarbon graphite.

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