An analysis of creep ductility of magnox Al80 and its implications

JOURNAL

OF NUCLEAR

15,3 (1965) 201-207 0, NORTH-HOLLAND

MATERIALS

AN ANALYSIS

OF CREEP DUCTILITY

OF MAGNOX

PUBLISHING

CO., AMSTERDAM

AL80 AND ITS IMPLICATIONS

J. E. HARRIS Berkeley

Nuclear

Laboratories

of he

Received

The

ductility-temperature

crystalline wt

%

relationships

magnesium-O.8

beryllium

alloy

relationship

based

on heterogeneous

and theories

growth

casts are made

by

La

nucleation

l’alliage

entre

polycristallin

cavit&

de Stroh

de lacunes.

at particles of this alloy

ductilitb

et

under

ult&ieure

Des p&visions

en sent

alliage

possibles

sent

Die

Beziehungen

ratur

fiir

eine

alliage

dans

les

et les diverses

les propri&%

zwischen

en utilisant de

sur des

par condensation du point

(1)

where y is the surface energy and G the shear modulus. This equation, which strictly only applies for an elastic body, has been used successfully by McLean 2) to determine the

Dehnbarkeit

polykristalline

Al+0,005

de cet

Gew.-%

und die Theorie

erkllirt

Diese Theorie

werden.

kondensation. macht,

um

werden

Reaktorbedingungen MBglichkeiten werden

die

basiert

auf der heteroPartikeln

durch

Planungsvorschliige dieser

zu priifen.

zur Verbesserung

Legierung

Mehrere ihrer

und

Hohlraumgeunter

verschiedene Eigenschaften

diskutiert.

transition and

iiber

der Hohlraumbildung

Wachstum

Betragen

aus Mgf

Be kijnnen

an verschiedenen

Es das

und Tempe-

Legierung

Stroh-Gleichung

nachfolgenden

deduites

cet

reacteur

d’ambliorer

einem

h&&og&ne

de

d’un

discuthes.

% Al en poids-

The Stroh 1) condition for fracture at the head of a sliding interface of length L under an applied shear stress os is: 12yG 1/ 7CL

m&hodes

comportement d’utilisation

Keimbildung

Cracking

q>

du

genen

The purpose of this paper is to examine if modern theories of nucleation and propagation of creep fracture can account for the tensile ductility-temperature relationships of a magnesium-0.80 wt oh aluminium-0.005 wt oh beryllium alloy (Magnox ALBO). This alloy is used as a canning material in the UK nuclear reactors and some comments are made on creep failure under service conditions. 1.

vue

conditions

pour

6tre expliqube

UK

1964

0,8 Gew.-%

et les thPiories de formation

et la croissance

Glos.,

and

temperature

magn&ium-0,8

de

Berkeley,

Fore-

are discussed.

bashes sur la germination

particules

the

formation

and various possible methods

0,005 % Be en poids peut la relation

poly-

using

condensation.

on the behaviour

its properties

relation

for

30 October

aluminium-0.005

of cavity

vacancy

reactor service conditions of improving

oh

can be explained

Stroh

subsequent

wt

CEGB,

stress

cavitation

between of

a

triple

Nimonic

point alloy.

cracking For

this

L an estimate of the maximum length of sliding grain boundary. For a given tensile strain rate, the maximum stress maintained during a test will fall as the temperature is raised and it is thus possible to calculation

he

used

for

define a maximum temperature above which triple-point cracking does not occur. Such a theoretical transition temperature has been found 3) to be in reasonable agreement with experimental observations on polycrystalline magnesium deformed rapidly. Taking y = 600 ergs/cm2 and G= 1.3 x 1011 dynes/cmz, this temperature, called here the S&-oh-McLean transition, has now been determined for the 1 %/h tests on Magnox AL80 carried out by Brookes et aZ.4) (see fig. la). During this type of deformation in the cracking range, fracture is rarely achieved by the nucleation and propagation of a single crack but rather by the 201

202

5.

E.

HARRIS

(as) has been assumed to be half the applied tensile stress and this may have led to a slight overestimate 2.

of the transition

temperature.

Cavity Nucleation In

argued

in a review

1961,

convincingly

nucleated

paper,

that

heterogeneously

creep

Co&e11 5) has cavities

at particles.

are

There

is some evidence for an association of creep cavities with particles in Magnox AL80 6) and recently it has been demonstrated are sufficient

second

phase

3)

that there

particles

in this

material to nucleate all the cavities observed in typical creep specimens (fig. 2). Vacancies will condense onto non-wetting particles in grain boundaries orientated normal to an applied tensile stress G if the particles are larger than a critical diameter d, given by 7) :

dr

2n

dt

t 3 ”

-

62 un

kTmr

given by 3) :

‘-lp m-lop

l-09 r-0

Ogb

In fig. lb, the critical diameter for the 1 %/h tests on Magnox AL80 is plotted as a function of temperature. Particles slightly smaller than the critical diameter may act as cavity nuclei if the grain boundary sliding rate B exceeds the longitudinal sintering rate and if intersecting slip spreads the void laterally faster than axial sintering. The critical grain boundary sliding velocity is

1’ ,

, 100

,

, 200

,

, 300

TEMPERATURE

,

, 400

,

, 500

B

_

D&Z rzlnf

2YQ

-exp kTr ’1

(3)

*C

Fig.

1. 1 %/h tensile test on Magnox AL80 4): (a) ductility-temperature plot showing the StrohMcLean transition and the Hull and Rimmer predictions; (b) critical diameter for cavity nucleation versus temperature; (c) radial rate of sintering versus temperature; (d) cavity growth rate by vacancy condensation versus temperature.

nucleation and impingement of many. Thus, in order to isolate the “general cracking” range from cavitation, the length of sliding interface has been taken here as equal to the mean grain diameter (0.18 mm). The maximum shear stress

where &b is the atomic grain boundary diffusion coefficient, 6z the grain boundary width, Q the atomic volume, r the particle radius, a the radius of the annular sink and k and T have their usual meaning. In fig. lc, the rate of radial sintering for a 500 J%diameter particle has been plotted again& temperature. For these calculations the following values have been used ; Bz = 10-T cm, y= 600 ergs cm-z, Q= 2.3 x lo-23 cm3 and a= 10-3 cm. It has been assumed that the activat,ion energy for grain boundary diffusion is 19 200 cal/mole, i.e. 0.6 times the activation

CREEP

Fig.

DUCTILITY

OF

AL80

203

2. Electron transmission photograph of Magnox AL80 specimen quenched from 600” C. The nume1‘OUS x8000 particles within the foil can be distinguished by the dislocations generated around them.

energy for lattice diffusion s), the frequency factor remaining unchanged at 1 cm2/sec. 3.

MAGNOX

Cavity

Using Rimmer ship for diffusion

Growth

as their starting point eq. (2), Hull and 9) have derived the following relationthe rate of growth by grain boundary of a cavity of radius r and spacing m: dr

2nDgbBzuQ

z-

lcTmr

(4)

’

By assuming that failure eventually occurs by the growth and impingement of the voids, an expression derived :

for

the

time

to

tr -

a%T 167KrSZD,b6x *

rupture

was

(5)

There are valid objections to Hull and Rimmer’s analysis and it is wrong to apply their model too literally. For example if most of the strain during creep is attributed to the opening-up of voids 5) then the objection of Feltham 10) that the analysis is inconsistent with the stress exponent and activation energy determined experimentally, would apply. In addition, during the final stages of tertiary

creep the inter-void areas would become highly stressed leading to necking and cracking between the cavities. Furthermore Greenwood 11) has pointed out that the analysis predicts a change in specimen density with time, at variance with the careful experimental measurements of Boettner and Robertson 12). The discrepancy can be resolved if it is postulated ii) that the voids are not all nucleated at the beginning of the test, but form progressively during the course of the deformation. Hull and Rimmer 9) admit the possibility of stressnucleated cavitation but this process is difficult to incorporate into a simple analytical expression for the time to rupture. However the basic assumptions of the Hull and Rimmer analysis, heterogeneous nucleation of cavities at particles 51s) and their subsequent growth by vacancy condensation sJs), now seem to be well established and the refinements in theory do not invalidate order-of-magnitude calculations. For example, Brookes et aZ.4) have illustrated the structure of a Magnox AL80 specimen which fractured in 1700 hours at 225’ C under a stress of 142 kg/cm2. The theoretical cavity spacing for this test calculated from eq. (5) is 17 pm and this is in reasonable

204

J.

agreement with a spacing of 25 to deduced from their photomicrograph. During a constant to failure is directly elongation, calculate

E.

50 ,um

strain rate test the time proportional to the final

Thus, from eq. (5) it is possible to the theoretical

elongation

at fracture

HARRIS

growth would be rapid (fig. Id) leading to lowductility failure (fig. la). If cavities could be nucleated at temperatures > 300” C then they would grow rapidly enough to give brittle failure (fig. la). However, at these high temperatures

the critical

diameters

as a function of temperature. These “Null & Rimmer” predictions for 1 %jh tests have been

become large and sintering rates are extremely fast, nueleation is thus inhibited and the material

superimposed

fails in a ductile manner by localised to almost 100 o/o reduction in area.

onto

ature-ductility growth

rate

the experimental

plot in fig. la. (eq.

temper-

In fig.

Id the

(4)) has been plotted

as a

function of temperature. For these calculations, which will be used here simply to illustrate the temperature dependence of fracture and growth, an arbitrary void spacing of 10 pm has been chosen.

4.

Ducti~ty-Temperature

Relationship

icant size. On this interpretation, optimum conditions for cavitational failure occurs only in the narrow temperature range 250 + to 300” C. Here, although the stress is too low for Stroh-McLean cracking, the critical diameters are still smaller than particles seen quite frequexltly in electron transmission specimens a). In addition, although sintering rates are fairly rapid, local bursts of grain boundary sliding should be capable of forming stable void nuclei from particles slightly smaller than the critical size. Subsequent void 7 In practice,

true

cavitation

failures

occur

as low as 190’ C in 1 Oh/h tests.

at

influence

of

primary

and

secondary

recrystallisation on fracture characteristics has been discussed elsewhere 14-17).These effects are important, for example the fall in ductility above 400” C is probably due to excessive grain growth which results in the deformation concentrated into only a few grains. 5,

An explanation of the temperature-ductility relationships of the 1 %/h tests illustrated in fig. la, is now possible. At low temperatures ( < N ‘200” C) the stresses maintained during the tests are high and the critical diameters correspondingly small (< N 700 A). Moreover, even particles smaller than the critical diameter can act as nuclei in sliding grain boundaries, since the sintering rate is low (fig. 1~). However, the cavity growth rates by vacancy condensation are also low (fig. Id) and as these temperatures are below the Stroh-McLean transition, failure occurs by cracking before the voids can grow to a signif-

temperatures

The

necking

being

App~ca~on of Theories to Reactor Operating Conditions

A large number of creep tests have been carried out on Magnox ALSO in the temperature range of interest for reactor applications (200 to 450” c). Recently these data have been analysed 18) and the following relationships established : d= 3.8 x lo-15 d-0.5 ~7 exp for stresses

(- 32 OOO/RT), > “r’ 2240 psi

2=5*g x IO-4 d-0.8 03.5 exp ( - 32 000~~~)~ for stresses > N 80 and -: N 2240 psi d--90

d-2

oT-1 exp (-32

(6)

(7)

OOO/RT),

for stresses

< N 80 psi

(8)

where d is the steady state creep rate and d is the mean grain diameter in inches. The fuel elements remain in the reactor for a maximum period of five years and a suitable design criterion is that the can must not deform more than 1 O/Oin 40 000 hours. If, as is reasonable for these slow rates of deformation, primary strain is ignored, this corresponds to a secondary creep rate of 2.5 x 10-‘/h. Using this criterion, it is possible to calculate from eqs. (6) to (8) for a given temperature, the maximum stress generated in a can as a function of its grain size.

These

relationships,

for

the

grain

size

CREEP

‘DUCTILITY

range 0.25 to 0.0025 cm (0.1 to 0.001 inches) at 450, 300 and 200’ C are given in figs. 3a, b and c respectively and designated “design” curves. Similar curves are presented for an arbitrary “fault” condition of 1 O/Jdeformation in 400 hours (i.e. a creep rate of 2.5 x 10-5/h). 6.

Cracking

As described earlier, using eq. (1), the minimum stress necessary for triple point cracking can be calculated for each grain size. Such “cracking” curves have been compared with the corresponding “design” and “fault” curves in fig. 3. The average as-charged grain size of high STRESS

(Kg.

CM-2)

0.1

OF

ERAGE AS- CHARGED. .-*-.-.-.-.-. GRAIN SIZE. 0.01

Fig. 3. Stress generated in a Nagnox ALSO can at imposed defo~tion rates of 1 o/0in 40 000 hours (Design) and 1 o/oin 400 hours (Fault) as a function of grain size. From the Stroh relationship the minimum stress for triple point cracking (Cracking) hes also been plotted against grain size; only where the cnrves cross is such cracking possible. The horizontal dotted lines oorrespond to the average as-charged gain sizes in UX reactors.

AL80

205

temperature fuel element cans (> - 390'C) is 0.038 cm (0.015 inches) and for low temperature cans is 0.018 cm (0.007 inches). From fig. 3 it is clear that even if considerable grain coarsening occurred, there is no possibility of the material reaching the theoretical cracking stress at 300 and 450” C. Cracki~lg should also be avoided at 200"C even under the specified fault condition for here no grain growth should occur. However, the analysis indicates that it would probably be unsafe to use material with grain size > 0.02inches at 200” C and thus trouble may be experienced with “shuffled” + oans at this temperature. The implication, so far, is that in normal circumstances triple point cracking should not occur in reactor cans. It follows that the most likely fracture mode is cavitation and there have been reports of this type of can failure rs,z*). 7.

0.01

NAGNOX

Cavitation

Again using eqs. (6) to (S), it is possible to calculate the stress correspon~ng to the 1 o/O in 40 000 hours criterion as a function of temperature for a fixed grain size of 0.018 cm (0.007 inches). Then, using equation (2) a plot of critical particle diameter versus temperatnre can be prepared (fig. 4). Also included is another arbitrary fault condition of a 1 o/oin 400 hours creep rate for material with an average grain size of 0.051 cm (0.02 inches). The “design” curve in fig. 4 demonstrates that even at the minimum reactor temperatures the critical diameter is as large as 0.5to 1 ,um. Such particles would just be visible in the optical microscope and in fact, are not seen frequently enough in reactor Magnox to account for a significant cavity nucleation rate (a relatively large number of nuclei would be needed to cause failure owing to the low cavity growth rates at these low temperatures, see fig. 1). In addition, at this slow rate of deformation, the average grain boundary sliding rate (- 4 x IO-9 cm/h) is much slower than rates of t “Shuffling” consists of moving fuel elements from hot regions to cooler parts of the reactor core (and vice versa) t#qobta& qveq bqrg-up qf the fuel,

206

J.

E.

HARRIS

cavitation range of temperatures may be due simply to the lower creep resistance of the finer grained material. This leads to a lower stress for a given imposed deformation rate and a correspondingly larger critical diameter. This effect is illustrated in fig. 5 where the critical diameter for a 1 y0 in 40 000 hours (2.5 x 10-7/h) strain rate at 200” C is plotted

against grain

size. Another effect which could lead to a lower cavity nucleation rate is that the average grain boundary

sliding rate is decreased as the grain

size is decreased (fig. 5). Grain boundary sliding may be important during the early stages of cavity formation at sub-critical particles. An alternative method of improving creep ductility would be to remove the second phase particles or at least keep their maximum size

250

200 I CRITICAL

Fig. 4.

DIAMETER

Critical particle diameter for cavity nucleation

versus temperature

for Magnox

size 0.018

cm deformed

in 40 000

hours

0.051

(CM)

(Design)

cm deformed

AL80

of mean gram

at an imposed and

of mean

at an imposed

MEAN

rate of 1 y0 grain

rate of

size

1 y0 in

GRAIN

DIAMETER

0.01

(CMS) 0.1

9t

400 hours (Fault).

radial sintering (- 4x 10-4 cm/h for a 0.1 ,um particle at 200” C) making it improbable that particles much smaller than the critical size can act as nuclei. It follows that, if no part of the can is strained at a rate faster than the design criterion (2.5 x 10-‘/h), then few cavities will be nucleated and brittle failure will not occur. condition the specified fault Under (2.5 x lo-s/h),

particles

in the range

1000 to

2000 A could act as cavity nuclei at the lower reactor temperatures and such particles occur in reactor Magnox 3).

8.

Production

of Ductile Magnox 1

It is well known that refining the grain structure increases creep ductility and this is exploited in the production of ductile cans 2s). In the cracking range this effect is easy to understand, for a reduction in grain size leads to a reduction in the length of grain boundary sliding interface. An improved ductility in the

0.01

0.001 MEAN

Fig. 5.

GRAIN

DIAMETER

(INCHES)

Critical particle diameter for cavity nucleation

versus average grain size of Magnox deformation

in 40 000

hours

at

average rates of grain boundary plotted

against

grain size for deformation.

AL80

for 1 o/0

200” C. Estimated

sliding has also been the

same

rate

of

CREEP

below about 500 A. However

DUOTILITY

the high vapour

pressure of magnesium would make, for example, zone-reining

operations

carry out and may preclude prove possible addition of a that

the

ductility

extremely

difficult

to

the low density of magnesium centrifugal separation. It may to clean up the material by the scavenging element: it is likely

observed

improvement

in

tensile

on adding beryllium 4) is due to some

such effect.

0%’ %XAaNOX

Acknowledgements A

number

of

of the Central Electricity

There have been examples in UK reactors of small leaks in the end welds of the can resulting in the build-up of uranium oxide at the fuel/can interface and the volume changes being accommodated by local deformation of the can wall. Where the original leak has been too small to be detected by the Burst Cartridge Detection Gear, the first warning of the fault has been the final rupture of the can wall which has only occurred after extensive deformation, following the build up of a large oxide mound 21-23). The large radial dimensional changes in the fuel elements lead to difficulties during discharge and an ultimate danger here is that of blocking the coolant gas flow in the channel. The ideal can material in these circumstances may be envisaged to be one which is ductile at very slow rates of strain, but which fails in a brittle manner when the deformation rate is increased during the build-up of the oxide mound and thus gives an early warning of the fault. At low temperatures ( < 250” C) this may be achieved with a coarse-grained inclusion-free alloy, for such material would not cavitate at slow strain rates, but at high rates of deformation the cracking stress would be exceeded and brittle failure occur (fig. 3). At higher temperatures it would be necessary to control the size of the inclusions such that they are smaller than the critical size for cavity nucleation at low rates of deformation yet Iarger than the critical size when the stress rises under the fault condition.

discussions

with

Generating

Board.

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McLean,

J. E.

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Metals

85

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Brookes,

J. Inst. A.

J.

Harris,

I?. E.

Fast Burst Failures

valuable

Dr. G. W. Greenwood are gratefully acknowledged, This paper is published by permission

submitted

9.

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