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Transcript of Creep Review
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7/30/2019 Creep Review
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IRRADIATION CREEP OF
NUCLEAR GRAPHITE
B. Rand
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Creep of graphite takes place under theeffects of fast neutron irradiation attemperatures where normal thermal creep isnegligible.
The effect is to act to reduce stresses that aregenerated in the graphite brick in the reactor,either internally or externally.
An ability to model the behaviour precisely is
critical to the prediction of likely stresses inthe components under operating conditionsand in response to various changes.
WHAT IS IRRADIATION CREEP IN
GRAPHITE -1 ?
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What is irradiation creep -2 ?
Irradiation creep is notcreep in the conventionalsense
It is manifest as a change
in the dimensional change
under the influence of
applied stress
Dimensional changedecreases under tension
and increases under
compression.From Kleist
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A significant, unanswered, question is
whether there different mechanisms atplay other than those involved in the
mechanism of dimensional change.
However, although irradiation creep is
very different from conventional
thermal creep of materials, the
approach to its study has been based
on the conventional approach. Thus, a
viscoelastic model, similar to thatapplied to the creep of polymers has
been the basis of the approach.
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Measurement
Measurement is difficult and expensive. Often subject to considerableerrors due to variations in temperature and stress in the reactor.
Main approaches:-
1.
Restrained shrinkage (stresses calculated)
2.
Fully instrumented strain measurement at constant stress
3.
Controlled loading of specimens with strain measured out of the
reactor after a specific fast neutron dose at known temperature.
(Usually used to determine the creep coefficient)
Many correction factors strictly required to calculate the change in
dimensional change. It is not clear that they have always been
applied to the international data that is available. The corrections
however have a small effect.
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Data normalised to initialelastic strain
Primary region ~1 elastic
strain unit
Constant strain rate insecondary region
T 300-650C
No strong dependence onneutron flux level
Early data led to the form of theCreep Law Here early UK results
(Brocklehurst
and Kelly)
0
1
Ed
d
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A portion of the creep strain is recoverable when the stress isremoved under irradiation.
This has often been taken as equal to the primary strain, but there is
strong evidence that the recoverable strain is greater than that.
Secondary creep has often been assumed to unrecoverable on stressremoval, but the above suggests differently. There is, however,
partial recovery on thermal annealing but at high temperatures,>1200C.
The UKAEA data suggested no temperature dependence in therange investigated (140-650C), but other studies suggest someincrease in creep rate at lower and higher temperatures.
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8
Creep Recovery
Dimensional recovery on load removal (UK BR-2/DFR):
> The recovery appears to be >1 initial elastic strain unit
Load removed
Taken from Bradford and Daviespresentation
+=
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The UK Creep Law A viscoelastic model
spc +=
spc +=
dEc
p )4exp()4exp(0.40=
)1(44
= eEcp
at constant stress]
dEcs
= 023.0
cs E
23.0=
at constant stress]
cc
c
E
e
E
23.0)1(4 4 +=
Ec
is the modulus corrected for structural changes and weight loss, i.e. Ec
= E0
SW
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The components of the
Linear Creep Law
-0.800
-0.600
-0.400
-0.200
0.000
0.200
0.400
0.600
0.800
1.000
0 50 100 150 200 250
Dose n/cm2
x 1020
EDND
LengthChange(mm
)
Dim change mm (inert)
Creep mm (inert)
Total Length Change mm
Creep with weight loss (no E or CTE correction)
25mm Long x 6mm diameter tensile creep Sample, stress = 6.25MPa, E=
10GPa, CTE 4.35 x 10-6
K-1
Assumed
25% weight loss at end of life
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The reducing creep coefficient (at high dose) in un-oxidisedirradiated graphite is accounted for via the structural term, S() =[E()E0
-1], accounting for the increase in Youngs modulus that takes
place.
S initially =1 but increases with dose.
Can only be tested against other graphite data that extends to highdoses, US and Petten.
Radiolytic oxidation is accounted for by a weight loss term, W, whichchanges the structurally modified Young modulus.
There is no direct experimental data (creep under simultaneousoxidation and irradiation) to validate this latter approach!
Linear Creep law and its initial UK application
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Variety of creep data
Creep rate vs TemperatureScatter due to variations in
graphite and in neutron flux
Same data normalised byinitial elastic strain, reducing
scatter and demonstrating a
temperature dependence and
perhaps a residualdependence on flux
NOTE THAT IN RANGE
UP TO 600C TEMP.
DEPENDENCE IS WEAK
(OR ABSENT)
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The general form of the creep
curve.
There is general agreement amongst all researchers that the creep curve displaysthe following characteristics:-
There is an initial transient creep region (primary creep).
The primary creep is recovered on reduction of the stress.
Primary creep is followed by a secondary creep region in which the creep rate isapproximately constant for a period after which it reduces as the graphitestructure is changed.
The primary creep and the secondary creep coefficient are proportional to theapplied stress.
The primary creep and the initial constant creep coefficient are inverselyproportional to the Young modulus of the unirradiated graphite. Thus, data for
different graphites appear to superimpose when the creep strain is normalized tothe initial elastic strain, i.e. plotting c
E0
-1
vs
.
The secondary creep is not recovered on lowering the stress but is partially
recovered by annealing at high temperature.?????
The secondary creep coefficient increases with temperature at temperaturesabove about 500C.
There are changes to the coefficient of thermal expansion (CTE) due to thecreep strain, in both compression (increases) and tension (decreases).
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Aspects on which there does not seem
to be complete agreement or which are
uncertain
Whether the primary creep fully saturates and is fully recoveredby stress removal.
The temperature dependence of the secondary creep coefficientat temperatures significantly below 500C.
The effect of creep strain on other physical properties of graphiteand the creep regime in which they occur.
The extent to which the same rules apply to different graphites inthe region where structural changes are taking place and wherethere is radiolytic oxidation.
The existence and relevance of tertiary creep.
Changes to the definition of creep strain due to so-calledinteraction effects.
Models to describe creep behaviour at high fast neutron dose.
The theory of irradiation creep in graphite.
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Tertiary Creep
From Preston and Melvin
The only evidence available at high dose is the US/PETTEN data
which are not well documented.Only available in the open literature from extended conference
abstracts.
Creep law
gives onlypartial fit
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An alternative approach to prediction was proposed by Kennedy et
al. Again not satisfactorily documented or peer reviewed.
It attempts to account for the reduced creep rate at high dose
through the change in volume as a correction factor, i.e. the effect is
a result of densification due to closure of micro-cracks
Kennedy approach gives reasonable agreement with the Petten data, Not widely used.
This was followed by Kelly and Burchell
who proposed a different
method of calculating the creep strain,
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Modelling high dose creep data Kennedy et al (US-German Approach)
Kennedy et al recognised that the structural changes involved a
densification process and proposed an alternative, empirical model,
which seemed to fit their data reasonably well.
K and
are constants; Modulus is pre-irradiated value;(V/V0
) is
volume change with dose and (V/V0
)m
is its maximum value.
=
mVV
VV
EK
d
d
)/(
/1
0
0
0sec
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What is known about the interaction between creep
strain and coefficient of thermal expansion (CTE)?
There is experimental evidence for changes in CTE with creepstrain.
The data in compression is more extensive than in tension up to4-5% strain.
Tensile data only up to strains of ~1%.
Lateral change in CTE is not known precisely, very few results.
Change in CTE during creep is fully recoverable by thermalannealing, but secondary creep strain is only partially recoverableand at much higher temperature..
Bradford and Davies recently have suggested that the change in
CTE is associated with elastic strain. This is not fully established orexplained yet.
Thus, there is experimental evidence for the correlation but poorunderstanding of creep mechanisms and of the relationship
between creep strain and CTE.
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Experimental evidence for a change in CTE
with creep strain
From Price
Higher creep strains obtained in
compression, tensile data limited in
extent.
Gilsocarbon
data
Th ti l ti di
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Theoretical assumptions regarding
interaction between creep strain, CTE
and dimensional change?
Kelly and Burchell
assumed that because CTE change and
dimensional change correlate and CTE changes with creep strainthen the dimensional change is altered by the creep strain and
should be taken into account in calculating creep strain.
They provided a method of calculating this interaction creep strain.
It was used to modify the creep law
and applied to low to medium
dose results and, for the data set studied (US data), gave better
agreement between prediction and experimental data at low tomedium dose.
Marsden
et al and recently Bradford and Davies have shown that
unrealistic creep strains are obtained at high dose.
K ll d B h ll
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Kelly and Burchell Proposed Correction to Apparent CreepStrain
True creep strain c
, is given by
Where c
= induced apparent creep strain
x
-
x
= change in CTE of crept samples as a function of dose
c
-
a
= difference in crystal thermal expansion coefficient (~ 27 x 10-6/C)
XT
= crystallite shape change parameter
= Neutron dose (1022
n/cm2
E > 50 keV)
dd
dXT
ac
xx
cc .0
''
=
The integral term in this equation corrects the apparent creep strain forcreep induced structural changes
Refs: Kelly CARBON 30 (1992) p.379 & Kelly & Burchell CARBON 32 (1994) p. 119
X is a Crystal Shape Change
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XT
is a Crystal Shape Change
Parameter
XT
= [(Xc
/Xc
)-(Xa
/Xa
)]
Where, Xc
/Xc
and Xa
/Xa
are, respectively, the dimensional changes of
the component crystallites measured parallel and perpendicular to thehexagonal planes
XT
appears to control structure factor changes, that is ,it is the
controlling
factor for structural dimensional changes
XT is independent of graphite at temperature < 450C
Above is based on early Simmons approach
Simmons explained that it is not valid when structural changes occur.
Kelly and Burchell use it in the region where structural changes take place.
HOW VALID IS THIS APPROACH?
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The procedure implicitly assumes that the change in CTE iscausative, that it automatically indicates a change in dimensional
change in the control sample and that this must be taken as thebaseline for the calculation of creep strain. This is an assumptionthat cannot easily be checked. However, it is known that the CTEis completely recovered on annealing so the interaction strainshould be reduced to zero. There is some evidence that the
secondary creep strain may be partly recovered.
Does this recovery relate to the interaction strain? This pointseems not to have been examined.
The basic Simmons treatment of CTE and dimensional change
rate assumes that the dimensional change is driven entirely bychanges to the crystal shape. This is not valid in the region wherethe so-called structural changes are taking place, which isprecisely the region where the UK creep law
requires correction.
The application of the Simmons analysis to creep assumes thatthe changes to the crystals during creep are the same as duringthermal expansion and unstressed dimensional change. This is notvalidated. The point was recognized by Kelly.
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24
Crystal strain rate and secondary creep
coefficient
Roberts/Cottrell
Crystal Strain Rate
-3
-2
-1
0
1
2
3
0 200 400 600 800 1000 1200 1400
Temperature (oC)
ln(Linear
SecondaryCreepRate)orln(A-axisC
rystalStrain
Rate)
Linear Secondary Creep Rate
A-axis Strain Rate
-3
-2
-1
0
1
2
3
0 200 400 600 800 1000 1200 1400
Temperature (oC)
ln(LinearSecondaryCreepRate
)orln(C-axisCrystalStrain
Rate)
Linear Secondary Creep Rate
C-axis Strain Rate
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25
Alternate Creep Models Recent DevelopmentsCTE Analysis
Relationships derived for
each variant from low
dose PLUTO and BR-2Data
Tested against ORNL low
dose data
Forward, i.e. predict
CTE
y = -0.080x2
- 0.426x + 1.000
0.6
0.8
1
1.2
1.4
1.6
1.8
-2.5 -2 -1.5 -1 -0.5 0 0.5 1
Primary+Recoverable Strain (%)
DeltaCTE(Relativ
e)
PLUTO 1050
PLUTO 850
BR-2 350-600
BR-2 Repeat Specimens
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 5 10 15 20 25 30
Dose (x1020
ncm-2
EDN)
CTEs/CTEu
13.8 MPa 20.7 MPa
Predict ion for 13.8 MPa Predict ion for 20.7 MPa
anomalous CTE
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Alternative Creep Model
Presented by Bradford and Davies (Cardiff Conf.2005)
( ) ( )
+
+
=
SWESWESWE
KK
c
0
)(
00
21 exp1exp1
0
2
4
6
8
10
12
14
0 10 20 30 40 50 60 70
Dose (x1020
ncm-2
EDN)
Creepstrain(
esu)
BR-2 Data
Prediction
The constants are
empirical fits
fitted to relatively low
dose data
Validated against high
dose data
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27
Alternate Creep Models Recent DevelopmentsPrediction of High Dose
Data
Revised model gives
excellent agreement
Deviations only occur
around the onset of
tertiary creep
E.g
ATR-2E 500oC
compressive and H-451
900oC tensile
WHAT IS KNOWN ABOUT THE VARIATION OF
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POISSONS RATIO IN CREEP? Transverse creep strain
Experimental data are limited..
Elastic value often used in stressmodelling
There are data that suggest itincreases with creep strain, tendstoward constant volumedeformation.
Value at low dose not so differentfrom elastic value.
BUT what about at high oxidativeweight loss and large dose whenthe creep strains might be
expected to be very muchhigher?
More information is required tounderstand the variation ofPoissons ratio in creep.
Mostly high temperature data
The variation of Poissons ratio in creep.
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Elastic Poissons ratio of previously creptmaterials
There is some evidence
that creep changes the
elastic Poissons ratio of
crept specimens
Very few studies
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Youngs Modulus
There is some evidence from high temperaturestudies in both compression and tension thatcreep leads to a reduction in the Youngs
modulus when compared with a sampleirradiated under the same conditions
unstressed.
Other studies are either ambiguous or detect nochange.
The position is unclear!
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Creep rupture
Many specimens have fractured during creep experiments.
The reasons for fracture are unknown, often attributed to
stresses developed during reactor transients.
Information is largely ignored.
There was one creep rupture experiment performed on matrix
graphite for the high temperature reactor. Simple approach
could easily have been adopted for Gilso
and PGA graphites.
If Irradiation creep is a change in dimensional change, is the
concept of creep rupture sensible?
O C O S
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Kelly and Brocklehurst
and until recently all UK researchers have
adopted a theoretical model that assumes that the creep mechanisminvolves the pinning/unpinning of basal dislocations.
An alternative approach suggested early on was based on Cottrellsstudy of irradiation creep of Uranium, in which it is proposed thatinternal stress generated by incompatible crystal dimensionalchanges bring the crystallites to the yield point and allow flow
in the
polycrystalline aggregate under an applied stress.
There are no substantive experiments to decide between these orindeed any other mechanism of creep deformation.
There is a strong case for the reappraisal of models and relevant data.
THEORETICAL MODELS
CONCLUSIONS
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CONCLUSIONS
The creep process is complexThe relationship with dimensional change needs to be re-
examined
Philosophically what exactly is irradiation creep?
How does it differ from dimensional change, which in the
absence of applied external stress must be influenced by
the local stresses generated by the differential dimensional
change in misaligned lamellar structures (crystallites).
How does the above relate to internal stress.Is the current approach (adopted internationally) really
appropriate?
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Commonality of graphite behaviour is critical to current
understanding and approach to modelling.
Is it really well established experimentally beyond the low doseregion.?
HIGH DOSE data not formally published. Perhaps it is available
in reports to certain organisations.
Only seems to be publicly available via informal contacts orfrom poorly presented graphs mostly in conferenceproceedings. Recently digitised but still poor validation
HOPEFULLY PLANNED MTR CREEP EXPERIMENTS WILLPROVIDE A MORE SATISFACTORY DATABASE ON WHICHSTRESS PREDICTIONS CAN BE BASED.
WHETHER SUCH EXPERIMENTS WILL BE DEVISED TOPROVIDE MECHANISTIC UNDERSTANDING REMAINS TO BESEEN!!!!!
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