creep review

7/30/2019 Creep Review

1/35

IRRADIATION CREEP OF

NUCLEAR GRAPHITE

B. Rand


2/35

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 ?


3/35

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


4/35

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.


5/35

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.


6/35

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


7/35

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.


8/35

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

+=


9/35

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


10/35

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


11/35

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


12/35

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)


13/35

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).


14/35

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.


15/35

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


16/35

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,


17/35

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


18/35

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.


19/35

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


20/35

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


21/35

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


22/35

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?


23/35

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.


24/35

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


25/35

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


26/35

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


27/35

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


28/35

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.


29/35

Elastic Poissons ratio of previously creptmaterials

There is some evidence

that creep changes the

elastic Poissons ratio of

crept specimens

Very few studies


30/35

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!


31/35

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


32/35

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


33/35

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?


34/35

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!!!!!


35/35

creep review

Documents