X-ray tomography observation of crack propagation in nuclear graphite

X-Ray Tomography of Crack Propagation

Hodgkins et al Manchester University

X-Ray Tomography Observation of Crack Propagation

in Nuclear Graphite1

A Hodgkins, T.J. Marrow, P. Mummery, B. Marsden and A. Fok

Materials Performance Centre, School of Materials, The University of Manchester

ABSTRACT

X-Ray Microtomography has been used to investigate the mechanisms responsible for

rising crack growth resistance with crack propagation (R-curve behaviour) in

polygranular nuclear graphite. Tomography can be used to observe changes in the

crack shape with propagation, and a side-grooved specimen has been developed to

produce the planar, straight fronted crack necessary for fracture toughness

measurement. Crack bridging from frictional contact between the fracture surfaces is

observed. A zone of reduced X-ray attenuation, attributed to microstructural damage,

is also observed around the crack tip and in its wake. These are the first, in-situ,

observations of the mechanisms of the R-curve behaviour in nuclear graphites.

1 NOTICE: this is the author’s version of a work that was accepted for publication in Materials Science

and Technology. Changes resulting from the publishing process, such as peer review, editing,

corrections, structural formatting, and other quality control mechanisms may not be reflected in this

document. Changes may have been made to this work since it was submitted for publication. A

definitive version was subsequently published in J. Mater Sci. Tech, 22, pp. 1045-1051 (2006), DOI

10.1179/174328406X114126



INTRODUCTION

Polygranular graphite is used to moderate the fast neutrons released during the fission

reaction in gas cooled nuclear reactors[1]. As a result of the combined effects of fast

neutron irradiation and radiolytic oxidation there is a gradual accumulation of damage

in the graphite[2]. This leads to changes in its dimensions and properties[3] and also to

the generation of stresses which have the potential to initiate fracture[4]. As graphite

plays a structural role within the reactor core, in addition to the role of moderator, it is

of interest to study their fracture behaviour.

Previous studies have demonstrated rising resistance to crack propagation with

increasing crack length in a variety of grades of nuclear graphite[5, 6] A common

measure of this effect is the R-curve; which describes the change in the energy

required to grow the crack, as its length increases[7]. Experimental studies have

demonstrated that variations in specimen geometry[8], the mode of loading and the

initial crack length may produce variations in the shape and magnitude of the R-

curve[9]. To generate the R-curve, test specimens may be loaded repeatedly under

displacement control then unloaded following stable crack propagation, and the data

analysed by a variety of methods[10-12]. There is, at present, no consensus as to which

is the most appropriate to apply to graphite. However both linear elastic GR methods

and elastic plastic JR methods have been used at various times.

The R curve may be defined from first principles, following each successive load

cycle, by equation 1. This is a linear elastic analysis, applied previously to graphite[7],

where W is the work input by external forces and Ue is the stored elastic strain energy.

The projected area of the crack, over which this energy is divided, is determined by

reference to ‘B’, the specimen thickness and δa, the change in crack length. There is



therefore an implicit assumption that the crack front is straight and extends

continuously from the tip.

( )aBUWR e

δδ −

= (1)

Inaccuracies in the determination of the crack length are a significant potential source

of errors in R-curves produced by this method however. Optical measurements of the

crack, made at the surface, are the simplest method of determining its length. The

most common alternatives involve measuring the elastic compliance of the

specimen[5, 7] or its electrical resistance[6].

The energy consumed in each load cycle to propagate the crack (W-UE) is determined

directly from the load v displacement curve (Figure 1).

Load

0

B

A

C

DLoadline displacement

Energy consumed by crack propagation

(W – UE) Load cycle: n-1


(W – UE) Load cycle: n


(W – UE) Load cycle: n+1

Load

0

B

A

C

DLoadline displacement


(W – UE) Load cycle: n-1






(W – UE) Load cycle: n+1

Figure 1 Schematic representation of the area beneath the load v displacement curve

used to determine the energy consumed by crack propagation. The lower edge is

defined by the load line for the subsequent load cycle.

The R-curve behaviour of AGR graphite has been reported previously[6, 13] and

compared with other brittle materials that exhibit R-curves, such as Al2O3 and BeO[14,



15]. It was deduced that micro crack formation in a deformation zone, ahead of the

crack tip, and bridging, in the wake, were together responsible for the R-curve in

graphite. Stress induced micro cracks have been observed ahead of a stationary crack

tip in isotropic graphite[16], and it has been shown by re-notching experiments[6] that

the crack wake makes the most significant contribution to fracture resistance.

In the previous reports of graphite’s R-curve in large specimens, an initial rise in

resistance is commonly observed for crack extensions of up to 10 mm (Figure 2 I - II).

The length of the bridging zone (LBr) has been estimated from the period of this rise[13,

16]. This behaviour characterises stage I of the R-curve. Stage III, the final stage of

the R-curve (Figure 2 III - IV) is commonly marked by rapidly falling resistance,

which has been suggested to occur when the length of the deformation zone (LDef) was

of comparable size to the uncracked ligament ahead of the crack tip. The R-curve

resistance is generally stable in stage II (Figure 2 II - III). The extent of crack

propagation in this stable ‘plateau’ region (Equation 2) is often limited to little more

than 10 – 15mm due to the dimensions of the specimen.

( )DefBrPl LLLL +−= (2)

These general observations of the stages of graphite’s R-curve are subject to a number

of qualifications and exceptions:

i. Significant variations are reported in the plateau region in Gilsocarbon

graphite 5 [6]

ii. Significant variations have been reported in the length of stage III of the R-

curve, in Gilsocarbon graphite[5].

iii. Continuously rising resistance has been reported in the ‘plateau’ region in

Gilsocarbon graphite [6].



iv. Sharply rising resistance has been reported in SENB specimens in stage III of

the R-curve[17].

v. Continuously falling resistance throughout the test has been observed in

compact tension specimens with a chevron notch [7].

In addition, it has been suggested that the sharp rise that characterises stage I of the R-

curve in Gilsocarbon graphite may be explained by errors in the measurement of the

crack length[18]. Differences in the way the R-curve is produced may be partially

responsible for these variations, and specimen size and configuration effects are not

fully understood, for example.

The aim of the work reported in this paper was therefore to attempt to resolve these

apparent differences in behaviour, through a detailed investigation of the crack

behaviour during fracture toughness testing of polygranular nuclear graphite. X-Ray

Microtomography has been used to look beneath the surface of the specimens, for the

first time enabling in-situ observations of the crack shape and the mechanisms

responsible for the R-curve. Virgin, non-irradiated, non-oxidised, isotropic

Gilsocarbon graphite, which is used to moderate the 2nd generation Advanced gas

reactors (AGR) in the UK, has been selected as a representative material for a coarse

grained polygranular graphite.



Ror

JR

(J/m

2 )

I

IIIII

IVRor

JR

(J/m

2 )

I

Fron

t fac

e of

the

spec

imen

Rea

r fac

e of

the

spec

imen

LBrL

LDef

Ror

JR

(J/m

2 )

I

IIIII

IVRor

JR

(J/m

2 )

I

Fron

t fac

e of

the

spec

imen

Rea

r fac

e of

the

spec

imen

LBrL

LDef

Figure 2 The relationship between R-curve behaviour and some postulated

mechanisms.

EXPERIMENTAL METHOD

The resolution of laboratory X-ray microtomography is limited by the number of

voxels (three-dimensional pixels)[19] in the 3D sample image, and is therefore

generally determined by the sample size. Modified compact tension (CT) specimens

were used to maximise the spatial resolution of X-Ray Microtomography (Figure 3)

and the thickness, B, (Figure 4) was varied between 10 mm and 50 mm. The effect of

one or two side grooves on crack behaviour was also investigated in 10 mm and 20

mm thick specimens.



Figure 3 The orientation of the specimen in the microtomography scanner showing

the part of the specimen that was imaged within the cone-shaped X-ray beam.

A

B 150

135100

90

4540

When: B = 10mm A = 1mmB = 20mm A = 2mmNotch radius ≈ 0.2mmθ = 60o

θ

X

Y 1.5 4

X YA

B 150

135100

90

4540


θ

A

B 150

135100

90

4540


θ

A

B 150

135100

90

4540


θ

X

Y 1.51.5 4

X Y

Figure 4: The Compact tension specimen configuration used.

The specimens were loaded, in tension, under displacement control, at 0.05 mm/min

until crack propagation was detected; after which the specimen was unloaded. A fall



in the measured load is the conventional method for determining crack growth in tests

of this type. In practice however this approach can be difficult to apply in graphite

owing to the noise in the load v displacement curve. . Electronic speckle pattern

interferometry (ESPI) was therefore used to monitor the crack tip as the specimen was

loaded. A change in the form of the correlation fringes produced by ESPI was

observed at loads approaching the fracture load. This significant shift in the fringes

was used to identify the load at which crack propagation had occurred (Figure 5). The

crack length a(i), was measured by four independent methods. It was firstly

determined by calculation from the unloading compliance (C(i)), using equation 3[13],

and also by direct surface measurement using a digital vernier gauge. Surface strain

mapping by Electronic Speckle Pattern Interferometry (ESPI)[20] was also used to

identify the crack tip position, and hence the surface crack length, by observing the

location of the strain concentration at the crack tip.

( ) ( )( ) ( ) ( )

( )i

iiiii C

CCaWaa 11

1 2−−

−

−×

−+= (3)

The 3D crack shape was subsequently evaluated after approximately 45 mm of stable

crack extension using X-Ray microtomography. During the observations, the

specimen was wedged open to maintain the crack opening displacement. An X-Tech

conical beam scanner with a tungsten target, filtered using a 0.1 mm thickness of pure

copper, was used with an energy of 55–75 kV and a 1024x1024 pixel CCD camera.

The sample to detector distance ranged from 480 mm to approximately 520 mm,

giving a voxel size of 0.08 - 0.12 mm. The tomography data was analysed using



AMIRA2 visualisation software to obtain two dimensional sections and three-

dimensional isosurfaces by threshold-based segmentation.

The specimens were then sectioned, perpendicular to the crack plane and parallel to

the crack propagation direction. The sections were ground and polished to a 0.25 µm

diamond finish for optical microscopy examination to investigate the crack path

through the microstructure. The optical images were directly correlated with the same

2D sections of the tomography data.

0

500

1000

1500

2000

2500

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035

Load v displacement

0

500

1000

1500

2000

2500

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035

Load line displacement (mm)

Load

(N)

(Α)

(Β)

(Α)

(Β)

Load v displacement

0

500

1000

1500

2000

2500

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035


Load

(N)

(Α)

(Β)

(Α)

(Β)

(Β)

(Α)

0

500

1000

1500

2000

2500

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035

Load v displacement

0

500

1000

1500

2000

2500

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035


Load

(N)

(Α)

(Β)

(Α)

(Β)

Load v displacement

0

500

1000

1500

2000

2500

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035


Load

(N)

(Α)

(Β)

(Α)

(Β)

(Β)

(Α)

Figure 5: The onset of a significant change in the correlation fringes obtained by ESPI

was used to identify the load at which crack propagation occurred.

RESULTS

The R curve was calculated using the method of Sakai [7] (equation 1). The data

obtained is summarised in Figure 6. The measured fracture resistance is affected by

2 Amira Ver 3.1.1 – Mercury Computer systems GmbH



the choice of crack monitoring technique. In general the stage I resistance to crack

propagation rises from below 100 Jm-2 to approximately 300 Jm-2 as the crack extends

up to 10 mm. In stage II, the resistance increases gradually to 400 Jm-2.

There was no significant effect of specimen thickness observed. However, the 3D

observations of the crack shape by X-Ray micro tomography show a tendency for

crack front curvature to develop in compact tension specimens with greater thickness

(typically above 25 mm). Typical cracks are shown in (Figure 7). The effect of this

crack bowing is apparent in the difference between the R-curve calculated from

surface measurements and bulk methods (i.e. compliance and DCPD) for the longer

crack lengths. There was also a tendency for cracks to propagate out of the plane of

the notch with decreasing thickness (typically below 20 mm). In these cases, valid R-

curve data could not be obtained beyond approximately 15 – 20mm of crack growth.

It was found that sufficiently straight, planar cracks were obtained in 20 mm thick

specimens with either one or two side grooves (Figure 8), although there was some

tendency for limited (i.e. few mm) crack propagation ahead of the main crack adjacent

to the side-grooves.



0

100

200

300

400

500

0 5 10 15 20 25 30 35 40 45 50

Crack extension (a (n) - a (0))

R (J

/m2 )

Single side grooved specimens - optical surface measurement with a vernier guage

Side grooved specimens - Compliance & DCPD

ESPI & digital surface photography

Specimens with a curved crack front - Optical measurement with a vernier guage

Figure 6: Crack propagation resistance, with increasing crack length, obtained for

compact tension of various thickness and different crack monitoring methods. The

data is for specimens without side-grooves, unless noted.

25mm25mm

Figure 7: X-Ray Microtomography isosurface image of a crack in a 50mm thick

cracked CT specimen of graphite, showing significant crack front curvature. The

direction of observation is indicated by the arrow.



(A)

20mm 20mm

(B) (C)

20mm

(A)

20mm20mm 20mm20mm

(B) (C)

20mm20mm

Figure 8: Examples of crack growth in 20 mm thick compact tension specimens

with (A) no side grooves, (B) a single side groove and (C) double side grooves. . The

direction of observation is indicated by arrows.

X-ray tomography revealed discontinuities in the resolved crack surface (Figure 9).

In the thicker specimens (30 mm ≤ B ≤ 50 mm) these are concentrated in a region

approximately 10 mm from the observed perimeter of the crack (Figure 9A). In the

thinner specimens (B ≤ 20 mm) isolated discontinuities were also observed, over the

whole crack length (Figure 9B).

The optical examination did not find any of these discontinuities in the crack, but in

some cases the fracture surfaces were observed to be in contact at the same location as

the tomographically observed discontinuities (Figure 10B & C). A zone containing



features with reduced X-ray attenuation both in the crack tip region and in the crack

wake was also observed (Figure 11).

(B)

(A)

10mm10mm

‘Discontinuities’ in the surface of the crack which may represent the location of bridging particles

10mm(B)

(A)

10mm10mm

‘Discontinuities’ in the surface of the crack which may represent the location of bridging particles

10mm

Figure 9: Discontinuities in the crack surface observed by tomography. Specimen

‘A’ is 50mm thick and ‘B’ is a 20mm thick specimen with a single side groove.

(Voxel dimension A = 120µm, B = 78µm). . The direction of observation is

indicated by the arrow.



0.5mm

(C) (D)

5mm20mm

(A) (B)

10mm 0.5mm

(C) (D)

5mm5mm20mm

(A) (B)

10mm

Figure 10: Discontinuities in the tomography image are observed over the crack

path (A). A 2D section of the tomography data is shown in B, with an optical

microscopy image within the same region in C. The same location is circled in each

image. Section A is orthogonal to B and C, which are in the same plane.

10mm10mm

Figure 11: A 2 dimensional image from a tomography scan of a 20mm thick

specimen of Gilsocarbon graphite. The primary crack is observed to be surrounded



by zone of features with low attenuation. . The direction of observation is indicated

by the arrow.

DISCUSSION

The R curve for isotropic Gilsocarbon graphite is characterised by sharply rising

resistance in the first 10 – 15 mm of crack growth (Figure 6). This is followed by a

further, shallower, rise with crack extension. The highest resistance to fracture,

calculated using the observed crack length at the specimen surface, was observed in

thicker specimens. X-ray microtomography was used to determine the crack size and

shape, and agreed with the surface measurements of crack length (Figure 7 & Figure

8). However, the observations also showed that for thicker specimens (>25mm), the

surface measurements of the crack length underestimated the true crack extension due

to crack front curvature (Figure 7). This had the effect of increasing the calculated

apparent resistance for thick specimens in comparison to the thin specimens, which

had a straighter crack front.

Side-grooving in 25 mm thick specimens gave comparable fracture resistance to the

thin specimens (Figure 6). This implies that the actual fracture resistance is not

sensitive to specimen thickness in this range. The discrepancies in the reported

fracture resistance in similar nuclear graphites[5, 6] may therefore be due to differences

in the crack shape, particularly in thicker specimens, which were not observable

without tomography. The results reported here also show that side-grooves to control

the crack shape may be recommended, although further work is required to determine

the maximum specimen thickness to which they could be successfully applied.

X-ray micro tomography provides a 3D map of the variation in X-ray attenuation in

the sample during the fracture test. To the authors’ knowledge, these are the first in-



situ observations of crack propagation in graphite. The crack is clearly observed

when the crack opening displacement approaches that of the voxel dimension, which

was typically 80 to 120 µm. Optical microscopy found no discontinuities in the crack,

but some of the discontinuities that were identified by tomography (Figure 10) were

found to correspond to frictional contacts between the crack faces. This is consistent

with the tomography observation of an increase in the density of discontinuities close

to the crack tip where the crack opening displacement is reduced (Figure 9). The

apparent lack of discontinuities at greater distances from the crack tip in the thicker

specimens may be a result of the lower resolution achieved in the tomography scans

of these larger samples, or a difference in the crack opening profile.

Frictional contact mechanisms for R-curve behaviour have been observed in other

materials, such as polycrystalline alumina[21]. Crack bridging by frictional contact is

consistent with previous observations, using re-notching, that crack wake processes

were responsible for a significant fraction of the R-curve behaviour in nuclear

graphite[16]. The observations reported here are consistent with this mechanism,

which is expected to be sensitive to specimen geometry effects on the crack opening.

X-ray tomography also observed a region of reduced attenuation at the crack tip

region and in the wake of the crack (Figure 11). It is suggested that this represents

microcracking, due to heterogeneous deformation in the polygranular microstructure

of the nuclear graphite. Microcracking is a toughening mechanism in some

materials[22, 23], and may therefore also be responsible for significant part of the R-

curve behaviour in nuclear graphite. Further work is in progress, using optical strain

mapping (ESPI) to determine the crack tip strain distribution and X-ray tomography

to determine the crack shape, to confirm the relative contributions of wake and tip

processes.



CONCLUSIONS

• Tomography has been used to observe changes in the crack shape with

propagation, and the mechanisms responsible for R-curve behaviour in

polygranular nuclear graphite.

• Bowed cracks develop in CT specimens thicker than 25 mm. The crack tends

to propagate out of the notch plane in specimens thinner than 20 mm. A side-

grooved specimen has been developed to produce the planar, straight fronted

crack necessary for fracture toughness measurement.

• Crack bridging from frictional contact between the fracture surfaces is

observed. A zone of reduced X-ray attenuation, attributed to microstructural

damage, is also observed around the crack tip and in its wake.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support of the Health and Safety Executive,

BNFL, Magnox Electric and British Energy Plc. The opinions expressed in this paper

are those of the authors, and do not necessarily reflect those of the research sponsors.

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X-ray tomography observation of crack propagation in nuclear graphite

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