notch sensitivity measurements of gilsocarbon graphite

Notch Sensitivity Measurements of

Gilsocarbon Graphite Small

SpecimensMatthew S.L. Jordan

S.M. Barhli, G. Copeland, J. Dinsdale-Potter, A. Tzelepi, A.G. Steer, D. Nowell, T.J. Marrow

INGSM – September 2019

MSL Jordan, Notch Sensitivity Measurements of Gilsocarbon Graphite Small Specimens

Outline

Research question:Can small sample tests (cm scale) monitor nuclear graphite notch sensitivity behaviour at the component-scale?

1. Background

2. Flexural Testing

3. Elastic properties


Axial cracking

• AGR graphite bricks are keyed together, with keyways cut down the outer surface

• Keyways were designed with corner (root) radii of around 2 mm

• Turn around results in a tensile hoop stress across the keyways

• Expected that axial cracks would initiate from the keyway root

3

Figure: [1]


Notch sensitivity

• Insensitivity may result from process/damage zone development

▫ Accommodates greater strain to fracture and strain energy

• Measuring notch sensitivity probes the evolving failure behaviour.

Notch sensitivity: How much a material responds to stress raiser like an ideal solid

Ductile–Large and well-developed shape

Notch

Brittle –very small process zone

Notch

4


Designing with notch sensitivity

• Notch strengthening factor (k) is the ratio by which the stress is overestimated

𝑘(𝑅) =𝜎𝑛𝑜𝑡𝑐ℎ𝑒𝑑(𝑅)

𝜎𝑢𝑛𝑛𝑜𝑡𝑐ℎ𝑒𝑑(𝑅)

• Used for design to estimate the additional apparent strength of a component

eg

▫ 0.1 mm radius notch in Gilsocarbon: k = 1.6

▫ If strength 𝜎𝑛 = 16 MPa

▫ Highest global stress that could be applied 𝜎𝑢 = 10 MPa

5

Notch radius (mm)N

otc

h S

tren

gth

enin

g F

act

or

PGA

Gilsocarbon (sleeve)

POCO

Theory

UK AGR Graphite

0.01 0.1 1 10

1

2

4

3

Non-irradiated

From Brocklehurst and Brown, Fatigue, Notch Sensitivity and Work of Fracture Studies on Isotropic Graphite. 1973, Springfields.


Designing with notch sensitivity

• Notch sensitivity (λ) measures how closely the material notch strengthening resembles linear elasticity

𝜆(𝑅) =𝑘𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙(𝑅)

𝑘𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙(𝑅)

• Predict strength based on a linear elastic model▫ Detailed knowledge of the damage

processes is not required

• Historical tests used large beams (>12 mm) or feature tests

6

From Brown, et al., A study of the notch sensitivity and the effect of specimen size on the strength of a wide range of graphites. 1986, Springfields Nuclear Power


Challenges for AGR PIE

• Notched strength only measured in virgin material▫ No recognised test geometry exists

• Unclear if size effect down to 6 mm▫ Current AGR PIE uses slices or beams 6 mm thick

▫ Historical measurements on beams/components >12 mm

• Effect of radiolytic oxidation and fast neutron irradiation unknown▫ Shrinkage

▫ Pore shape and volume evolution

7

1 mm

9 % wl

22 % wl

40 % wl

Increa

sing

do

se


Small specimen notch sensitivity

• Over 100 notched beamsfractured ▫ Beam dimensions: 6 x 6 x

19 mm

• Notches with different tip geometries and depths▫ Notch depths: 0, 1.0, 3.0

and 4.5 mm

• Quasi-static 4-point bending

• In situ imaging withmultiple cameras

8

Sample

Blunt Sharp

6 mm

MSL Jordan, Notch Sensitivity Measurements of Gilsocarbon Graphite Small Specimens 9

Detect crack

initiation

Analysis (1)

Load distributions

Displacement distributions


Stress:

Linear elastic vs reduced ligament• Linear elastic theory assumes a perfect

stress raising effect

• Notches ‘act as they look’

• Reduced ligament theory assumes a perfect blunting effect

• Notches ‘act as though they don’t exist’

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𝜎𝑅𝐿 =3𝑃𝐿

𝑏(𝑊 − 𝑎)2

W

a

P

L

b = breadth


Notch strengthening

• Notch strengthening factor (k) is the ratio by which the stress is overestimated

𝑘 =𝜎𝑛𝑜𝑡𝑐ℎ𝑒𝑑𝜎𝑢𝑛𝑛𝑜𝑡𝑐ℎ𝑒𝑑

11

Error bars at 1.96 St. Dev.


Notch sensitivity

• Notch sensitivity (λ)measures how closely the material notch strengthening resembles linear elastic

𝜆 =𝑘𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙

𝑘𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙

12

Error bars at 1.96 St. Dev.


Ex-reactor material

• Installed sets from Hinkley Point B▫ Dose: 18-22 x1020

n.cm-2 EDN

▫ Weight loss: 3-8%

• Beams of two sizes▫ 6 x 6 x 19 mm

▫ 8 x 8 x 38 mm

▫ U-notched

▫ R = 2 mm

▫ a/W = 0.25

• Tested in 3-point bend

13

Ex-reactor (RL)

6x6x19 mm

8x8x38 mm


Analysis (2)

14

FE with fitted Modulus

In situ imaging of fracture

3D surface digital image correlation


Linear elasticity?

• Modelling for notch strengthening factor did not need accurate stiffness

▫ Strains not known

• Apparent stiffness derived by fitting both strain and load

▫ Strains known from the in situ imaging

▫ FE model iteratively fitted to strain, then modulus

• Response is non-linear stiffness (as expected)

15

Using tensile modulus

At crack initiation, tensile modulus overestimates

Apparent stiffness seen to degrade with strain


User-MATerial (UMAT) stiffness

• Graphite has non-linear stress-strainproperties

▫ Tensile stiffness depends on tensile extension

• Measure the change in stiffness by performing a dog-bone tensile test with DIC

• Considering only the axial component (= Young’s Modulus, E), stiffness decays exponentially

16

𝐸 = 𝐸0(1 − 𝑎(𝑃0 + 𝐴𝜀 + 𝐵))𝑛

Where P0 is porous fractionε is strainE0, α, A, B and n are fitted constants

E0 28.3 GPaA 36.34B 6.8×10-7P0 0.18n 4.12a 1

Proposed by Barhli et al, Carbon, 2017. 124: p. 357-371


Notch strengthening with UMAT

17


Notch Sensitivity with UMAT

18


Summary

• No standardised method exists for measuring notch sensitivity in small graphite samples, such as those extracted from an AGR

• A ‘statistically-valid’ campaign has been conducted to determine if notch sensitivity is observable in such samples▫ Testing in 4PB, over 100 samples were tested▫ 6x6x19 mm beams appear to be under-sensitive

• Notch sensitivity of ex-reactor material measured▫ Indication of size effect▫ Comparable to virgin test

• Multi-camera in situ imaging was employed to inform stress-strain comparisons of the test geometries

• Non-linear behaviour demonstrated and a non-linear elastic model trialled.

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Thank you for listening.

Any questions?With thanks to:• S.M. Barhli, M. Molteno, P. Earp, C. Farrar, N. Tzelepi, S. Wilkinson, M. Haverty, A.

Qaisar and J. Bradley• EDF Energy for useful discussions, providing test material and sponsorship of this

project. The views presented here are not necessarily those of EDF Energy.• EPSRC, Oxford Materials, St Edmund Hall and the University of Oxford for

supporting the DPhil. Funded by EPSRC Industrial CASE Studentship 11220486.• Innovate UK and University of Manchester for supporting the irradiated

measurements

[email protected]

[1] Timothy D. Burchell, Carbon, 1996, 34(3), pp. 297-316[2] J.V. Best et al., Prog. in Nuc. En., 1985 16(2), pp. 127-178.

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MSL Jordan, Notch Sensitivity Measurements of Gilsocarbon Graphite Small Specimens 21


Limitations of the UMAT

22

For the sharp notch tips, numerical instabilities caused nonphysical distortion in the elements along the notch centre line.

Model cannot be run to correct distortion


Short-beam notched FlexureNotched bend samples in five non-standard geometries

23

Sharp, half depth

Sharp, shallow

Unnotched

Blunt, half depth

Blunt, shallow

After drying, the samples were tested to failure (quasi-static loading)

Based beam dimensions of post

irradiation examination (PIE) flexure specimens:

6 x 6 x 19 mm

Notches with different tip geometries (blunt

and sharp) and depths


Set-up

24

1 mm

Loading systemArticulated flexure fixture on table top

load frame

Lighting:- Diffuse LED pair

- Annular halogen fibre

Stereo pairCapture full sample

movement for stereo out of plane correction

Mono cameraSurface microstructure

deformation at high resolution


Analysis route

1. Load-displacement data

▫ Detect fracture loads

2. Calculate apparent notch stresses

1. Upper bound stats

2. Lower bound stats

3. Measure actual strains

▫ Infer stress distributions

25

Sample

Blunt Sharp

6 mm


Finite Element

Modelling• Peak stress-strain behaviour

derived from a DIC-FE analysis

• Model parameters are fitted in model▫ Stereo DIC gives the

displacements

▫ Young’s modulus is fitted (linear elastic)

• Stresses and strains are then extracted▫ Can be linearly scaled to

create statistical distribution

26


Notch strengthening inc UMAT

27


Notch sensitivity inc UMAT

28


ResultsDVC (experimental) Deviation (between DVC and elastic FE simulation)

0.00

0.50

1.00

1.50

> 1.75

-0.50

-1.00

-1.50

< -1.75

Ho

rizo

nta

l D

isp

lace

men

t D

evia

tio

n /

µm

29

85 N

Notch deformation

before fracture is effectively

linear elastic


FEM BCs

30

BCs now applied on 3 DOF, so all deformation mode

accounted for

Limited tomography field of view, favours notch BCs over

support rollers

BC nodes

Roller position


FEM vs DVC

31

(110N)


Where does all the stress go?

• Why is Gilsocarbon insensitive to sharp notches?

• How does Gilsocarbon absorb so much concentrated strain energy without fracture?

• Why does the modulus relax?

• What happens prior to crack initiation?

32


I

H

G

Tomographic

examination

33

10 mm

Notch radius of 1 or 2 mm


Internal displacements • Displacements measured by DVC

34

concentration

I

G

HI

G

H1 mm notch

Sample at load


Internal strains • Strains are displacements differentiated

35

concentration

I

G

HI

G

H

Estimated strain concentration zone locus, notch tip centredRC = 1.28 mm

1.5 mStrain

Sample at load

1 mm notch


Internal strains (2) • Strains are displacements differentiated

36

concentration

I

G

H

Sample fractured

1 mm notch


Internal strains (3) • Strains are displacements differentiated

37

concentration

Sample at loadSample at unload

I

G

H

The same locus, notch tip centredRC = 1.28 mm

2 mm notch


Theoretical LE strains • Linear elastic simulation using experimental boundary conditions

38

concentration

ϵYY[-] I

G

H

Experimental locus, notch tip centred, RC = 1.28 mm

Boundary for 1.5 mStrainApprox simulated locus for notch radius = 2 mm,

Centre: (0, -0.3), locus radii (1.3 mm, 1.1 mm)

2 mm notch


Implications

• Gilsocarbon is relatively notch insensitive

• Sharp notch tips behave like blunt tips

39

notch sensitivity measurements of gilsocarbon graphite

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