AN ANALYSIS OF IRRADIATION AN ANALYSIS OF IRRADIATION CREEP IN - - PowerPoint PPT Presentation

AN ANALYSIS OF IRRADIATION AN ANALYSIS OF IRRADIATION CREEP IN NUCLEAR GRAPHITE CREEP IN NUCLEAR GRAPHITE

• G. B. Neighbour1 and P. J. Hacker2
• 1. Department of Engineering, University of Hull, UK.
• 2. British Energy Generation Ltd, Barnwood, Gloucester, UK.

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INTRODUCTION

• Nuclear Graphite

– High creep ductility under load with neutron fluence – Additional to dimensional changes – Important property - compensates other irradiation effects – Complex and often neglected Mechanical Properties, e.g. strength Elastic Properties Irradiation Creep Thermal Properties Irradiation Dimensional Change

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OBJECTIVES

• Review the UK Creep Law

– High neutron fluence, applied stress and radiolytic oxidation

• Better understanding of creep data

– Historically, data obtained under very different conditions – Improved predictions of irradiation creep, particularly for simultaneous neutron fluence and radiolytic oxidation

• The output!

– Alternative analysis of irradiation creep applicable to most situations, including HTR systems, using AGR moderator graphite as an example.

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EARLY CREEP EXPERIMENTS (1)

• First “real” irradiation creep experiments undertaken in

1963 by C. R. Kennedy

– cantilever beams under constant load – transient creep and steady-state creep detected

• Three main experimental methods
• “Real” creep experiment where samples are subjected to a

constant stress under irradiation with continuous strain measurement

– High complexity and cost – Large number of specimens impractical

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EARLY CREEP EXPERIMENTS (2)

• “Restrained Shrinkage” experiments

– Dimensional change rates differ markedly between graphites – E.G. graphite tensile specimen restrained by split sleeves made of a graphite that exhibits a smaller shrinkage rate – Induced creep strain calculated knowing the various differences in shrinkage rates of the various components (stress deduced from established creep laws) – Disadvantage - no measurements during the irradiation. – Advantage - many results (less accurate)

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EARLY CREEP EXPERIMENTS (3)

• Combination of stress relaxation and

restrained shrinkage experiment

– Large block of graphite irradiated under a temperature and neutron flux density gradient – Strips cut from block and their curvatures measured – Results only meaningful if a stress calculation can be performed (used in Dragon experiments)

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A SUITE OF TECHNIQUES?

• Complementary
• Real irradiation experiments derive the creep laws
• Restrained shrinkage experiments provide information on

different material, temperatures and flux gradients

• Larger block experiments provides a test of the data and

stress models under more realistic conditions

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IRRADIATION CREEP DATA

• All studies support the view that any nuclear graphite

irradiated under constant stress, the tensile and compressive creep strains, plotted as creep strain/initial elastic strain (εcE0/σ) are directly proportional to the fluence and independent of temperature in the range 140-650°C

• At >600 °C, creep strain/initial elastic strain is the same for

all graphites over a wide range of stresses, but the gradient

• f the line is proportional to irradiation temperature. Only

at very high stresses (~30 MN/m2) is there a deviation from linearity

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UK Creep Law

Creep strain/initial elastic strain (E0εc/σ) Fast neutron fluence (γ)

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CT C

E ε γ σ ε + × =

− 20

10 23 . )] 10 4 exp( 1 [

20

γ σ ε

−

× − − = E

CT

UK Creep Law

IRRADIATION CREEP OF GRAPHITE

• At fluence > 60 x 1020 n cm-2 EDN

– Steady state creep rate deviates from linearity (decreases with increasing fluence – Often attributed to structural changes, i.e. E0 replaced by SE0 (ignoring any weight loss term)

• =

γ

γ σ ε ' 1 d S k

II

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• UK Creep Model

– Assumes that the properties measured on a control sample exposed unstressed apply to the stressed sample. – CTE is known to change with irradiation creep and so other properties may also be affected.

RECENT DEVELOPMENTS

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• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 3

• 5
• 4
• 3
• 2
• 1

1

Apparent Irradiation Creep Strain (%) Changes in CTE (20-120 degC) (α α α α'x - α α α αx) (x 10-6 K-1)

Data taken from Kelly and Brocklehurst, 1994

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y = -0.6101x R2 = 0.7116

• 2
• 1

1 2 3 4 5

• 6
• 5
• 4
• 3
• 2
• 1

1 2

Apparent Irradiation Creep Strain (%) Changes in CTE (20-120 degC) (α α α α'x - α α α αx)(x 10-6 K-1)

AGR Graphite Price Mobasheran Linear (AGR Graphite)

Data points taken from Kelly and Brocklehurst, 1994

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RECAP

• UK Creep Law represents data well up to ~60 x 1020 n.cm-2 EDN
• At higher fluence, the UK creep law progressively

underestimates the measured creep strain, εc’, i.e. mismatch between the true creep strain εc and the measured creep strain εc’

• Structure term added to account for any discrepancy between the

measured and predicted creep strain, however this term has limited success, no real physical meaning and cannot be measured directly

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A NEW ANALYSIS

• Without reference to a structure term
• Generate a relationship between the apparent creep strain εc’

and fluence γ

• Evidence to suggest that CTE variance with irradiation

creep is LINEAR

• For UK AGR graphite

(αx'-αx) = -0.6106εc'

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IRRADIATION CREEP OF GRAPHITE

γ γ α α α α

γ

d d dX e e

T a c x x c c

⋅

• −

− − =

• 1

1

[ ]

2 6 2 1

10 7803 . 2 10 1864 . γ γ α α α α

ε − −

× + ×

• −

− =

a c x x

C

( )

' '

6106 .

c x x

ε α α − = −

( ) ( ) ( )

( ) ( )

2 6 2 '

10 0316 . 6 10 4043 . 1 23 . 4 exp 1 γ γ γ γ ε

− −

× + × + + − − = esu

c

dXT - crystal shape change parameter (HAPG data) ec is true creep strain ec’ is apparent creep strain

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0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 50 100 150 200

Neutron Fluence (x1020 n cm-2 EDN) Irradiation Creep Strain (esu)

UK Creep Law Expected Apparent Creep Strain

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STRESS

• Deviation from linear

creep rate does not become apparent until samples experience stress above ~30MN/m2

Effect of applied stress on compressive creep strain of different graphites after ~1021 n/cm2 (EDN) (taken from Kelly and Brocklehurst, 1977).

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WEIGHT LOSS(1)

• Young’s modulus is known to decrease exponentially with

thermal or radiolytic oxidation to high levels of weight loss (Eox = E0 exp(-bx) where b=3.4).

• It seems intuitive that irradiation creep can continue to be

predicted by correcting Ec by Eox. At present, there is no evidence to suggest that these relationships will not continue to hold at high weight losses.

• Effects of simultaneous oxidation and irradiation appear not

to have been addressed either experimentally or theoretically.

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WEIGHT LOSS(2)

• =

γ

γ σ ε ' 23 . d EC

II

• −

= ab ab E

II

1 ) exp( 23 . γ σ ε If the relationship to include simultaneous weight loss is considered it can be shown that

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10 20 30 40 50 60 70 80 50 100 150 200

Neutron Fluence (x1020 n cm-2 EDN) Irradiation (True) Creep (esu)

Simultaneous Ox and Irr Irradiation only Pre-oxidation (15%) Simultaneous Ox and Irr (x1.5)

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10 20 30 40 50 60 70 80 50 100 150 200

Neutron Fluence (x1020 n cm-2 EDN) Irradiation (Apparent) Creep (esu)

Simultaneous Ox and Irr Irradiation only Pre-oxidation (15%) Simultaneous Ox and Irr (x1.5)

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SUMMARY AND CONCLUSIONS (1)

• The UK Creep Law is semi-empirical and indicates

Young’s modulus is the controlling parameter.

• Steady-state creep progressively deviates from linearity

and an apparent reduction in creep strain is observed.

• The “Structure” term does not this explain this

phenomenon satisfactorily.

• The effects of radiolytic oxidation on creep strain is

predictable, BUT simultaneous oxidation and irradiation does not appear to have been addressed.

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SUMMARY AND CONCLUSIONS (2)

• A more physically satisfying explanation - modification of

CTE, and consequently dimensional change, by creep strain.

• The analysis presented showed that steady-state creep rate

should remain constant without reference to a structure factor (excluding simultaneous radiolytic oxidation), i.e. the approach provided a more physically satisfying explanation for the decrease in the apparent creep strain observed at high fluence.

• The approach allowed the prediction of irradiation creep of

graphite subject to simultaneous oxidation and irradiation.

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POSTSCRIPT

• Recommendations

– There is a clear need for new creep experiments with the improvement in the measurement of stress, fluence and temperature.

• Real stress experiments
• High stress, fluence and temperature
• Studies on biaxial/triaxial systems
• CTE (and particularly (αx'-αx) vs εc'), Young’s

modulus and Poisson’s ratio

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FURTHER INFORMATION

See Our Web Pages at

–http://www.eng.hull.ac.uk

Write to

–g.b.neighbour@hull.ac.uk

Department of Department of Engineering Engineering