Strain'mapping'the'fracture'process'zone'in'a'heterogeneous'bri4le'material'

(polygranular'graphite)'by'synchrotron'X:ray'diffrac=on,'computed'

tomography'and'image'correla=on'

Luis'Saucedo'Mora,'Selim'Barhli,'David'Collins,'Mahmoud'Mostafavi,'Chris=na'Reinhard*,'

Yelena'Vertyagina,'James'Marrow'

'

*'Beamline'I12,'Diamond'Light'Source,'UK'Characterisa*on-of-Crack-Tip-Fields-Urbino,-Italy,-20<22-April-2015-

Overview'•  Key'techniques'–  Computed'Tomography'– Digital'Volume'Correla=on'– Diffrac=on'

•  The'Engineering'Problem'–  Keyway'cracking'in'AGR'Graphite'– Notch'sensi=vity'in'a'heterogeneous,'bri4le'material'

•  Strain,'Damage'and'Cracking''–  Experimental'observa=ons'in'fracture'process'zone''

•  Mul=scale'modelling'of'deforma=on'and'damage'

2'

Research(Ques+ons:((•  What'is'the'notched'strength'of'irradiated'and'oxidised'nuclear'graphite?'•  What'is'the'criteria'for'fracture'propaga=on'in'nuclear'graphite?'-

Radiograph'of'a'crack'in'graphite'

COMBINED(TOMOGRAPHY(AND(DIGITAL(VOLUME(CORRELATION((

Observing'and'Measuring'in'3D'

3'

Tomography'and'Image'Correla=on'

4'

Mathematical, Physical and Life Sciences Division

Quasi-Brittle Materials

Studies of Quasi-Brittle Materials by X-ray Tomography and Digital Volume Correlation Mahmoud Mostafavi1, Christina Reinhard2, Robert C. Atwood2 and James Marrow1

1 Oxford University, Department of Materials and Oxford Martin School

2 Diamond Light Source, Beamline I12

The three-dimensional tomography images are analysed by Digital Volume Correlation. This highly sensitive technique measures displacement vectors between successive images. Differentiation of the displacement field produces an effective strain field, which can be used to visualise and quantify the crack opening behaviour as well as the elastic and inelastic strains around the crack. These data validate and tune material-dependent models for damage propagation, such as the cohesive zone model. The models may be used to design miniature test specimens to reliably measure the properties of degraded materials, extracted from engineering components.

Our work aims to understand the interaction between microstructure and damage in quasi-brittle materials, of which nuclear graphite in an example. The techniques are also applicable to feature-rich, heterogeneous brittle materials such as ceramic-matrix composites, thermal barrier coatings and concretes, which are key structural materials in current and next generation nuclear power. Engineers assure the safety of structures containing defects by Structural Integrity Assessment (SIA). For instance, the SIA of nuclear graphite is critical to the continued safe operation of the UK’s Advanced Gas Reactors (AGR). Radiolytic oxidation degrades its strength (amongst other properties), while neutron irradiation causes dimensional change, which develops tensile stress at critical locations. Ultimately, this would cause the moderator bricks in the reactor core to fracture; this is a major limit to reactor lifetime as they also act as channels for fuel and control rods. Confidence in graphite integrity is a major challenge to AGR lifetime extension and over-conservative assessments that end the lifetime prematurely will be detrimental to the UK economy. Detailed observations of fracture processes, using three-dimensional characterisation techniques, are being used in our work to validate models for the effects of microstructure degradation on fracture behaviour in nuclear materials.

Ceramic matrix composites (e.g. Silicon Carbide – Silicon Carbide fibre) are candidate materials for the fuel clad of some Generation IV nuclear fission reactors and also for the tritium breeding components in nuclear fusion power. Their high temperature structural properties are critical for safe operation; tolerance is needed to fast neutron irradiation that may cause damage to fibre-matrix interfaces and swelling. Techniques are needed that can study damage, in situ and at elevated temperatures. Initial studies at room temperature show that deformation within the material can be mapped by digital volume correlation of high resolution tomographic images. Future work will investigate elevated temperature deformation and the relation between damage and microstructure. 1 mm

Awards of X-ray beam time at the Diamond Light Source (JEEP I12) are gratefully acknowledged (Experiments EE7119 & EE7730).

Wedge-loading of the short chevron-notch specimen

Digital volume correlation to measure the relative crack opening displacements between two successive tomography scans. Image slices in the plane orthogonal to the Z-axis are shown; left - prior to loading (no crack) and right - under load (cracked).

0

-1

-2

-3

-4

-5

-6

Log(ε1)

3 mm

Visualisation of deformation caused by Hertzian indentation of a SiC-SiCfibre composite

Displacements measured beneath the Hertzian indentation by digital volume correlation of the tomography data. The maximum principal strains from the displacement field are also shown, and are compared with finite element simulation (left).

The propagated crack within the chevron-notch specimen (crack opening displacement visualised as nominal opening strain). The crack has diverted around a strong “filler” particle.

Crack opening displacement (along middle of the crack), compared with linear elastic and cohesive zone models. The measured opening ahead of the elastic crack tip is due to damage in the fracture process zone.

Selected Publications: Observation and quantification of three-dimensional crack propagation in poly-granular graphite, , M. Mostafavi, S.A. McDonald, P.M. Mummery, T.J. Marrow Engineering Fracture Mechanics 2013 Flexural strength and defect behaviour of polygranular graphite under different states of stress, M. Mostafavi, S.A. McDonald, H. Çetinel, P.M. Mummery, T.J. Marrow Carbon 2013

Sample diameter: 25 mm

Contact details: Prof. James Marrow

Tel.: +44 (0)1865 273938

E-Mail: james.marrow@materials.ox.ac.uk

Website: oxford.academia.edu/JamesMarrow

500'µm'

Loaded' Unloaded'

Sub:indenta=on'cracking'in'alumina'

50'µm'

'1'mm'

Damage'in'SiC:SiC'composite'

Fa=gue'in'Magnesium'

3D'deforma=on'mapping'provides'new'insights'into'materials'deforma=on'doi:-10.1016/j.ijfa*gue.2014.04.003-Int.-J.-Fa*gue,-66,-(2014),-183<193-

doi:-10.1016/j.mspro.2014.06.251-Procedia-Mat.-Sci.,-3,-(2014),-1554<1559-

doi:-10.1016/j.jeurceramsoc.2014.04.002-J.-Eur.-Ceram.-Soc.,-34,-(2014),-3127<3232-

Ver*cal-Displacement-Maps-

Diamond'Air'

Alumina'Crack'

THE(ENGINEERING(PROBLEM:(FRACTURE(AND(DEFORMATION(IN(A(QUASIBBRITTLE(MATERIAL(

How'does'nuclear'graphite'deform'and'fracture'from'stress'concentra=ons?'

5'

174

Figure 5:25 Examples of filler particle porosity.

5.2 Evaluation of Young’s modulus in virgin Gilsocarbon IM1-24 Accurate measurement of Young’s modulus represents an essential precursor to

determining fracture properties in elastic media using the techniques prescribed

by both ASTM E1820 and BS7448 Pt4. The most common method for

measuring static Young’s modulus is to load tensile test specimens below the

elastic limit using an extensometer, or strain gauge, to measure the

displacements throughout the test.

Porous'microstructure'of'graphite'

6'

1'mm' Graphite'has'pores'at'many'length'scales.''This'structure'changes'with'oxida=on'during'reactor'life'

158

few microns distributed, apparently at random, throughout the structure (Figure

5:13). The grains observed in this image are likely to consist of both the flour

and the binder[97]; the regions between them are commonly referred to as flour.

This is fine graphite powder that forms the interface between the grains. Far

higher resolution is needed to study the matrix in any significant manner.

Figure 5:13 Progressive magnification of a surface of a graphite specimen to highlight a region within the binder that contains unconnected particles (Mosaics).

50µm

A B

50µm

A B

Figure 5:14 Optical microscopy of the matrix. A region within the binder where the

orientation of the Basal planes extends to approx 50µm is shown in ‘A’. Highlighted in ‘B’ are some of the smallest binder particles, measuring only a few microns in length. The latter forms a mosaic region as defined above. Both of these images are from a specimen of Gilsocarbon graphite.

500'µm'

100'µm'

50'µm'

UK'AGR'Gilsocarbon'Graphite' Matrix'

“Filler”'par=cle'

Open'Porosity' 11

����QP ����QP

a

Fig. 2

100 nm

H

b

Keyway'Failure'Condi=on'Crack'ini=a=on'at'keyway'predicted'when'stress'exceeds'strength'With'irradia=on,'tensile'stress'develops'at'the'keyways'due'to'dimensional'change'Strength'and's=ffness'reduce'with'radioly=c'oxida=on'

Time'or'Burn:up'

Keyw

ay'Stress'a

nd'Stren

gth'

Strength'

Stress'

Oxida=on'Stress'

The'aim'is'to'predict'how'the'number'of'bricks'in'the'core'will'increase'as'the'core'ages'

Keyway-

Fast-neutrons-ini*ally-increase-strength-and-elas*c-modulus-Oxida*on-via-gamma-irradia*on-reduces-strength-and-modulus-

Graphite'Property'Measurement'

8'

Trepanning'Tool'

The'effects'of'irradia=on'and'oxida=on'are'measured'using'small'test'specimens,'cut'from'trepanned'cores'

Trepanning'Tool'

10 10

•Large variability in irradiated graphite properties due to: •variability in manufactured graphite •operating conditions (dose, temperature, oxidation)

•Measurements have to be done on very small samples: •because there is a size limitation on the material that can be trepanned from the reactor •because there is a large density gradient in a trepanned sample •in order to obtain as much information as possible on each trepanned sample

Challenges in measuring irradiated graphite

Trepanned'Core'Sample'(NNL)'

~20'mm'

~6'x'6'mm'

Flexural'strength'specimen'

26'cm'

Trepanning'Instrument'

keyway'

9'

Graphite'Notch'Sensi=vity'

Notch'radius'(mm)'

Stress'Con

centra=o

n'Factor'

Coarse'grained'graphites'have'low'notch'sensi=vity'

€

PGA'

Gilsocarbon'(sleeve)'

POCO'

Theory'(linear'elas=c,'bri4le)'

This'is'a4ributed'to'the'inherent'large'defects'in'the'microstructure'

Crack'nuclea=ng'defect'in'AGR'graphite,'observed'in-situ'by'digital'volume'correla=on'of'tomographs'

UK'AGR'Graphite'

0.01' 0.1' 1' 10'1'

2'

4'

3'

Non<irradiated-

Stress'Concentra=on'Factor'

Un:notched'strength''Notched'strength''

='

measured-through-life---

measured-only-at-start-of-life---doi:-10.1016/j.carbon.2013.03.025-Carbon-(2013)-

Graphite'Notch'Sensi=vity'

10'

Distance'

Stress'

Linear'elas=c'

Non:irradiated'graphite'

Irradiated-graphite?-

Inelas*c-or-nonlinear-elas*c-behaviour-may-affect-notch-sensi*vity,-par*cularly-in-small-specimens-

Can-a-“small-specimen-test”-measure-the-notch-sensi*vity-in-irradiated-graphite-to-sufficiently-describe-large-component-behaviour?-

We'need'to'measure'the'notch'stress/strain'field'to'validate'damage'models'

In-metals,-size-effects-are-due-to-inelas*c-behaviour-in-fracture-process-zone-(i.e.-plas*c-zone)-that-affects-constraint-

What(is(the(Notch(Sensi+vity(of(Irradiated(Graphite?(

Crack'Nuclea=on'at'a'Stress'Concentra=on'

11'

6'mm'

5'mm'

Microstructure'effects'and'damage'examined'as'the'difference'between'predicted'FE'linear'elas=c'and'measured'displacement'fields''

Tomographed'region'

Wedge:loaded,'blunt:notched'specimen'

50'N'75'N'85'N'

Horizontal'displacement'(µm)'

:''3.5'

:':3.5'

:''0.0'

In'situ'DVC'study'of'notch'strain'field'

Mabhew-Jordan-(PhD-at-Oxford)-

~1'mm'

GRAPHITE(DEFORMATION(

12'

An'examina=on'of'strain'during'tensile'deforma=on'

X:ray'Strain'Mapping'on'I12'(JEEP)'

13'

XBray(Beam((80(ke

V)( 250'cm'

42'cm'

Diffrac=on'Image'Plate'

Loading'Rig'

Radiography'Camera'and'

Op=cs'

Specimen'

:1000'

:500'

0'

500'

1000'

:500' 0' 500' 1000'1500'2000'2500'

Tran

sverse(Bulk(Strain((µε)(

Tensile(Bulk(Strain((µε)(

14'

Strain'Measurement'in'Graphite'Vy Vx

Raw

dat

aC

orre

cted

Load 450N: step 4

Tensile'Displacements'(µm)'

Bulk'strain'measurement'by'digital'image'correla=on'of'radiographs''

Just'aner'

fracture'

Tungsten'Carbide'fiducial'markers'

Poisson’s'ra=o'of'0.20'±'0.03'

15'

Strain'Measurement'in'Graphite'

0"

1000"

2000"

3000"

4000"

5000"

6000"

7000"

8000"

0" 500" 1000" 1500" 2000" 2500" 3000"

Intensity

((32b

its)(

Posi0on(in(profile((pixels)(

(002)'

(100)'(101)'(102)'

Intensity

'(rela=

ve)'

Posi=on'(Pixels)'

Diffrac=on'

d(002)-peak-shics-measured-to-obtain-crystal-strains.-

Diffrac=on'

Azimuth'

Load'

Crystal'strain'measurement'by'diffrac=on' :0.00025'

0.00000'

0.00025'

0.00050'

0.00075'

0.00100'

0' 30' 60' 90' 120' 150' 180'

Chan

ge(in(d

(00.2)((Å

)(

Azimuth(Angle((°)(

Diffrac=on'

0.0001-Å-=-30-µε-

Strain'Measurement'in'Graphite'

16'

!0.0005%

0.0000%

0.0005%

0.0010%

!1000% 0% 1000% 2000% 3000%

Chan

ge'in'd

(0002)'(Å

)'

Tensile'Bulk'Strain'(µε)'

H1%(0°):%Loaded%

H1%(0°):%Unloaded%

H1%(90°):%Loaded%

H1%(90°):%Unloaded%

H2%(0°):%Loaded%

H2%(0°):%Unloaded%

H2%(90°):%Loaded%

H2%(90°):%Unloaded%

Compressive'“strain”'aner'first'loading'(relaxa=on'of'residual'stress?)'

H1'

H2'

Loaded( Unloaded(

Tensile'Deforma=on:'Summary'•  Image'correla=on'of'radiographs'(and'

tomographs)'measures'displacement'field'within'the'test'specimen'–  Bulk'and'local'total'strains'can'be'

determined'–  Deforma=on'reduces'the'Young’s'elas=c'

modulus'–  Deforma=on'is'inelas=c'and'

heterogeneous'•  Diffrac=on'can'measure'the'crystalline'

response'to'bulk'strain'–  Elas=c'strains'can'be'determined'

•  Evidence'for'micro:cracking''–  Tensile'strain'relieves'residual'stress'

•  Residual'stress'expected'from'thermal'strains'aner'graphi=sa=on'

–  Reduc=on'in'Elas=c'modulus'17'

8'

10'

12'

14'

0' 5' 10' 15' 20'

Unloa

ding((M

odulus((G

Pa)((

Peak(Stress((MPa)(

0'

500'

1000'

1500'

0' 5' 10' 15'

Tensile(Bulk(Strain(

(µe)(

Tensile(Stress((MPa)(

cycle'5'(load)'

cycle'5'(unload)'

CRACK(PROPAGATION(An'examina=on'of'crack'strain'fields'

18'

Crack%Propaga>on%

Wedge'Loaded'Notched'Specimen'

Radiograph'

1'mm'

Inside'the'Fracture'Process'Zone..'

19'

Crack%Propaga>on%

Tomograph'

Crack'propaga=on'from'notch'with'periodic'tomography'and'diffrac=on'mapping'

Wedge:loaded'specimen'with'straight'notch'

Tomography'and'DVC:'Bulk'Strains'

Data-from-4th-loading-cycle-

Crack%Propaga>on% Cycle%4%(example)%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

Loaded% Unloaded%

Bulk%

Crystal%

Ver>cal%Horizontal% Ver>cal%Horizontal%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

0.04%

40.04%

0.0004%

40.0004%

Cycle%4%(example)%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

Loaded% Unloaded%

Bulk%

Crystal%

Ver>cal%Horizontal% Ver>cal%Horizontal%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

0.04%

40.04%

0.0004%

40.0004%

Horizontal'

Horizontal'

15'm

m'

8'mm'

Unloaded'

Loaded'

Opening'Displacement'across'the'crack' 20'

Crack'opening'and'sample'deforma=on'measured''

Strain'

Cycle%4%(example)%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

Loaded% Unloaded%

Bulk%

Crystal%

Ver>cal%Horizontal% Ver>cal%Horizontal%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

0.04%

40.04%

0.0004%

40.0004%

0.04'

:0.04'

Reference dataset: Tomo 4 (#28990)

Deformed dataset: Tomo 7 (#29024)

Volume size: 6.48 x 3.96 x 4.68 mm (3600x2200x2600 pixels)

DaVis parameters:

256 × 256 × 256 voxel interrogation window, with 50% overlap and 2 passes, followed by a 128 × 128 × 128 interrogation window, with 75% overlap and 3 passes

Output displacement matrix size: 112x69x81 voxels

Crack opening displacement (notch area was removed at z=0.52 mm, average COD-value and errors were calculated across all y-coordinates):

0

1

2

3

4

5

6

4

3

2

1

0

-0 .04

-0.02

0.00

0.02x-displacement,

Pm

depth, mm

x-dis

place

men

t, m

m

x-distance, mm

-40.6

-30.7

-20.9

-11.0

-1.1

8.7

18.6

0 1 2 3 4 5

0.01

0.02

0.03

0.04

0.05

0.06

0.07

CO

D, m

m

crack length, mm

4

3

2

1

00 1 2 3 4 5 6

x-displacement, Pm

XZ-plane, y=middle

dept

h, m

m

-40.0

-29.2

-18.3

-7.5

3.3

14.2

25.0

z=0.52 mm

Crack'visualised'using'phase'congruency'of'displacement'field'

Diffrac=on:'Crystal'Strains'

21'

Cycle%4%(example)%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

Loaded% Unloaded%

Bulk%

Crystal%

Ver>cal%Horizontal% Ver>cal%Horizontal%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

0.04%

40.04%

0.0004%

40.0004%

Cycle%4%(example)%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

Loaded% Unloaded%

Bulk%

Crystal%

Ver>cal%Horizontal% Ver>cal%Horizontal%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

0.04%

40.04%

0.0004%

40.0004%Data-from-4th-loading-cycle-

Crack%Propaga>on%

Horizontal'

Horizontal'

19'm

m'

10'mm'

Strain'

0.0004'

:0.0004'

Unloaded'

Loaded'

Horizontal%Strains%

Bulk%

Bulk%

Crystal%

Crystal%

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

Horizontal%Strains%

Bulk%

Bulk%

Crystal%

Crystal%

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

Horizontal%Strains%

Bulk%

Bulk%

Crystal%

Crystal%

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

Horizontal%Strains%

Bulk%

Bulk%

Crystal%

Crystal%

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

Horizontal%Strains%

Bulk%

Bulk%

Crystal%

Crystal%

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded1' 2' 3' 4' 5'

Strain'field'of'a'propaga=ng'crack'measured'(2D)'Cycle%4%(example)%

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

strain z DVC

inc d0 at 90º

Loaded

strain z DVC

inc d0 at 90º

Unloaded

Loaded% Unloaded%

Bulk%

Crystal%

Ver>cal%Horizontal% Ver>cal%Horizontal%strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

0.04%

40.04%

0.0004%

40.0004%

Stress'Intensity'Factor:'R:Curve'

22'

0'

1'

2'

3'

0' 5' 10'

Stress(In

tensity

(Factor,(K((M

Pa(m

1/2 )(

Crack(Length((mm)(

Full'3D'deforma=on'field'provides'boundary'condi=ons'to'calculate'the'stress'intensity'factor'

3D'FE:model'(elas=c)'

3D'Displacement'Field'

Wedge:loaded'specimen:'Applied'load'is'NOT'used'to'calculate'K'

Crack'Tip'Strain'Field'

23'

Crack%Propaga>on%

:0.001'

0.000'

0.001'

0.002'

0' 5' 10' 15' 20'

Chan

ge(in(d

(00.2)((Å

)(

Distance((mm)(

Cycle'1'

Cycle'2'

Cycle'3'

Cycle'4'

Maximum-change-in-d(00.2)-measured-in-tensile-test-

:0.001'

0.000'

0.001'

0.002'

0' 5' 10' 15' 20'K(no

rmalised

(Cha

nge(in(d

(00.2)((Å

/MPa

m1/2 )(

Distance((mm)(

Cycle'1'

Cycle'2'

Cycle'3'

Cycle'4'

Normalised'by'applied'stress'intensity'factor'

Crack'=p'posi=ons'

Notch'

:0.0002'

:0.0001'

0.0000'

0.0001'

0.0002'

0.0003'

0.0004'

0.0005'

:10' 0' 10' 20'K(no

rmalised

(Cha

nge(in(d

(00.2)((Å

/MPa

m1/2 )(

Distance(from(Crack(Tip((mm)(

Cycle'1'

Cycle'2'

Cycle'3'

Cycle'4'

Rela=ve'to'crack'=p'

Magnitude'of'strain'field'depends'on'the'applied'stress'intensity'factor'

:0.0002'

:0.0001'

0.0000'

0.0001'

0.0002'

0.0003'

0.0004'

0.0005'

:5.0' :2.5' 0.0' 2.5' 5.0'K(no

rmalised

(Cha

nge(in(d

(00.2)((Å

/MPa

m1/2 )(

(Distance(from(Crack(Tip)1/2((mm1/2)(

Cycle'1'

Cycle'2'

Cycle'3'

Cycle'4'

•  Peak'strain'at'the'crack'=p'•  Strains'in'the'crack'wake'•  Crack'wake'length'increases'with'crack'propaga=on'

r:1/2'field'

Crack'Propaga=on:'Summary'

•  Crack:bridging'zone'observed'– Elas=c'strains'are'measured'in'the'crack'wake'– Expected'to'cause'crack'=p'shielding'

•  Rising'crack'resistance'with'crack'growth'–  (R:curve)'measured'

•  Crack'=p'strain'field'depends'on'the'applied'stress'intensity'factor'– The'crack'propaga=on'criteria'is'not'a'cri=cal'stress'intensity'factor'

24'

These'data'are'being'used'to'test'and'validate'models'for'damage'nuclea=on'and'fracture'propaga=on'

Concluding'Comments'•  Non<irradiated'graphite'deforma=on'is'accompanied'by'microcracking'– Techniques'developed'to'measure'deforma=on'and'strains'in'small'test'specimens'

– Used'to'validate'models'to'simulate'behaviour'of'engineering'components'

•  Effects'of'distributed'cracking'on'notch'sensi=vity'and'size'effects'are'being'examined'

25'

Deforma=on'and'notch'sensi=vity'in'irradiated'graphite'could'be'examined'and'is-being-simulated'to'es=mate'size'effects'

Acknowledgements'

26'

Mathew-Jordan,-Ahmet-Cinar-Alan-Steer,-David-Nowell-

Dr(James(Mar+n'(1933<2013)-Founder'of'the'Oxford'Mar=n'School'

Experiments:-EE7119,-EE8519,-EE9036,-EE9478-

MICROSTRUCTUREBBASED(DAMAGE(MODEL(

Mul=:scale'modeling'of'damage'development'and'crack'propaga=on'

27'

28'

Filler-Pore'Damage'

Matrix-1'mm'

CA'model'

Fracture'Criterion:'Strain'energy'release'rate'Failure'Stress'(MPa)'

Cumula=

ve'Probability'

Filler'

Matrix'Stochas=c'proper=es'provide'input'to'Cellular'FE'model'

Fracture'Criterion:'Strain'

Modelling'of'microstructural'effects:'at'the'microstructure'scale'

Microstructure'provides'the'heterogeneity'in'simula=on'of'specimen'fracture'

Model/inputs:-3D-pore-geometry,-pore<free-modulus,-local-work-of-fracture-(0.6-Jm<2)-

NumericalExperimental

Tensile test, decay of the stiffness

Experimental range

Tensile test, peak load for different microstructures

Modelling'of'microstructural'effects:'at'the'test'specimen'scale'

Large'Pores''''Filler''

6'mm'Tensile'Test'

Matrix''

Increasing'applied'stress...'

Simula=on'of'•  the'effect'of'

damage'on'elas=c'modulus'

•  stochas=c'effect'of'microstructure'on'strength'

Modulus' Tensile'Strength'

doi:-10.1016/j.mspro.2014.06.186-Procedia-Mat.-Sci.,-3,-(2014),-1143<1148-

Finite'Element'Microstructure'MEshfree'fracture'model'(FEMME)''

Cellular'Automata'(CA'Model)'

Modelling'of'microstructural'effects;'at'the'test'specimen'scale'

30'

Simula*ons-for-different-distribu*ons-of-microstructure-

Simula=on'of'microstructure'effects'on'damage'nuclea=on'

10'mm'

Modelling'of'microstructural'effects:'at'the'test'specimen'scale'

Simula=on'of'crack'propaga=on'

Input:'notch'opening'displacement'

Crack%Propaga>on%

0"

0.02"

0.04"

0.06"

0" 5" 10" 15"

Strain:(ε

Distance((mm)(

Cycle"2"(Model)"Cycle"3"(Model)"Cycle"4"(Model)"Cycle"5"(Model)"Cycle"2"(Experiment)"Cycle"3"(Experiment)"Cycle"4"(Experiment)"Cycle"5"(Experiment)"

Modelling'of'microstructural'effects:'at'the'test'specimen'scale'

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

Load 2 Load 3 Load 4 Load 5

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

UnloadedExperimental Numerical Experimental Numerical Experimental Numerical NumericalExperimental

wedge compression test, crack tip position

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

Unloaded

Load 2 Load 3 Load 4 Load 5

strain x DVC

inc d0 at 0º

Loaded

strain x DVC

inc d0 at 0º

UnloadedExperimental Numerical Experimental Numerical Experimental Numerical NumericalExperimental

wedge compression test, crack tip position

Cycle'2' Cycle'3'

Cycle'4' Cycle'5'

32'

:0.001'

0.000'

0.001'

0.002'

0' 5' 10' 15' 20'

Chan

ge(in(d

(00.2)((Å

)(

Distance((mm)(

Cycle'1'

Cycle'2'

Cycle'3'

Cycle'4'

Cycle'5'

:50'

0'

50'

100'

:0.001'

0.000'

0.001'

0.002'

0' 5' 10' 15' 20'

Stress((M

Pa)(

Chan

ge(in(d

(00.2)((Å

)(

Distance((mm)(

Cycle'1'

Cycle'2'

Cycle'3'

Cycle'4'

Cycle'5'

Model'(Cycle'2)'

Model'(Cycle'3)'

Model'(Cycle'4)'

Model'(Cycle'5)'

Model'simulates'key'features'of'experimental'data'

Modelling'of'microstructural'effects:'at'the'component'scale'

“Brick'Slice'Test”'

26'cm'

Keyway'root'damage'

5'mm'

20'mm'

33'

Keyway'root'damage'and'component'strength'simulated'Agreement'with'measured'strengths'

Concluding'Comments'•  Microstructure:sensi=ve'modelling'aims'to'predict'the'sensi=vity'of'notch'strength'to'neutron'irradia=on'and'radioly=c'oxida=on'–  Porosity'distribu=on'is'measured'–  Local'proper=es'of'microstructure'are'simulated'– Global'proper=es'of'component,'and'the'variability'of'strength,'are'simulated'

'•  Mul=:scale'modelling'approach'is'being'further'developed'and'validated'by'experiment'

34'

K'field:'1/√r'

35/50'

:0.0002'

:0.0001'

0.0000'

0.0001'

0.0002'

0.0003'

0.0004'

0.0005'

:5.0' :2.5' 0.0' 2.5' 5.0'K(no

rmalised

(Cha

nge(in(d

(00.2)((Å

/MPa

m1/2 )(

(Distance(from(Crack(Tip)1/2((mm1/2)(

Cycle'1'

Cycle'2'

Cycle'3'

Cycle'4'