The yield and flow of single crystals of uranium dioxide

The yield and flow of single crystals of uranium dioxide

JOURNAL OF NUCLEAR MATERIALS THE YIELD 28 (1968) 110-114. 0 NORTH-HOLLAND AND FLOW OF SINGLE CRYSTALS PUBLISHING OF URANIUM CO., AMSTERDAM D...

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JOURNAL

OF NUCLEAR

MATERIALS

THE YIELD

28 (1968) 110-114. 0 NORTH-HOLLAND

AND FLOW

OF SINGLE CRYSTALS

PUBLISHING

OF URANIUM

CO., AMSTERDAM

DIOXIDE

J. F. BYRON Departmentof Metallurgy,

University of Live~ol,

UK

Received 4 June 1968

The deformation behaviour of specimens of single crystals of uranium dioxide, tested in compression at temperatures between 600 ‘C and 1800 “C is reported. The temperature-dependence of the proportional limit was found to be dependent on the operating slip plane. The slip plane did not vary with temperature and was either (100) or { llO} depending on orientation. Le comportement a la deformation d’echantillons de monocristaux de bioxyde d’uranium soumis it la compression a des temperatures comprises entre 600 “C et 1800 “C eat report6 dans ce travail. La relation de la limite de proportionnaliteavec la

1.

Introduction

The operative slip systems for single crystals of uranium dioxide, of composition UOi.95, deformed in compression in the temperature range from 700 “C to 1900 “C have been investigated by Rapperport and Huntress 1). They found that the slip direction was (110) and the slip plane was {IOO}, (110) or (111). The latter two planes became more active at higher temperatures. Direct electron microscope evidence supporting a $(llO) Burgers vector has also been reported by Ashbee 2). No investigations of the yield and flow of single crystal uranium dioxide have been reported. In view of this it was decided to determine the yield and flow properties of single crystals of uranium dioxide, tested in compression, as a function of temperature and orientation, using the same apparatus as the previous investigation of the yield and flow of polycrystalline uranium dioxide 3). 2.

Experimental Specimens

of

crystals

Das Verformungsverhaltenvon Urandioxid wird besohrieben. Hierzu werden Einkristalle einem Druck bei Temperaturen zwischen 600 und 1800 “C ausgesetzt. Es wurde gefunden, dass die Temperaturabhlingigkeit der Proportionalitiitsgrenze von der jeweils auftretenden Gleitebene abhiingt. Die Gleitebene wechselte nicht mit der Temperatur; sie war je nach Orientierung die {lOO}- oder (llO}-Ebene.

dioxide of the three orientations shown in fig. 1 were cut on a water-cooled diamond saw. The specimens were 2.4 mm square and 4.8 mm long. The composition of the material was UOa. soi. The orientations of the specimens and the number of specimens of each orientation were limited by the size and shape of the original crystals. For this reason the deformation behaviour of specimens of orientation (1) was studied in

[iii]

COOD

procedure single

temperature depend du plan de glissement actif. Le plan de glissement ne varidt pas avec la temperature et Btait (100) ou (110) suivant l’orientation du monocristal.

of

uranium

Fig. 1. 110

COli3

Orientations of single crystals of uranium dioxide.

THE

YIELD

AND

FLOW

Denotes

Fig. 2.

OF

proportional

SINGLE

CRYSTALS

OF

URANIUM

DIOXIDE

111

limit

Stress/strain curves for single crystals of orientation (1).

greater detail than those of orientations (2) and (3). All specimens were chemically polished in a rapidly stirred bath of a solution of 10 ml glacial acetic acid, 20 ml saturated chromium trioxide solution, 5 ml 40% hydrofluoric acid and 7 ml cone nitric acid to provide a surface suitable for metallography. The specimens were compression-tested under pure argon at atmospheric pressure in the high temperature compression furnace described previously 3). The temperature of the furnace was increased at a rate of 80 “C! per minute to the testing temperature which was maintained for five minutes before starting the test. The basic strain rate used for all tests was O.OQ/min. Slip trace

become nearly horizontal (stage II). At 1000 “C and above, stage I disappeared leaving only a low rate of work-hardening similar to stage II. The stress strain curves for all three orientations up to a strain of -0.08 are shown in fig. 3. The two-stage hardening effect observed at low temperatures for orientation (1) would appear to be orientation-dependent. At 600 “C! twostage hardening was observed for orientations (1) and (2), but a smooth work-hardening curve was observed for orientation (3). At 800 “C two-stage hardening was only observed for orientation (1). The temperature-dependences of the proportional limit for specimens of all three orientations

analysis was performed on specimens strained approximately 6%. Difficulties were experienced in maintaining the surface polish at high temperatures, as had earlier been reported by Rapperport and Huntress 1). 3.

Results and discussions

Engineering stress/strain curves for single crystals of uranium dioxide of orientation (1) tested at various temperatures are shown in fig. 2. At 600 “C and 800 “C the stress strain curves showed two stages of work hardening. After the proportional limit, the flow stress first rose steeply (stage I) and then levelled off to

Fig. 3.

Stress/strain curves for single crystals of the three orientations.

112

J.

I

‘. :

. :

F.

BYRON

0

-

orientation

(1)

+

-----

orientation

(2)

orientation

(3)

A -_-

die% ide

*-..

400

800

1200 Temperature

Fig.

4.

Temperature-dependence

of

---..

the proportional

limit

1600

2000

‘C

for single

crystals

of

the three orientations.

are shown in fig. 4. The proportional limit was chosen as the parameter to describe the yield process, as it should not be affected by the orientation-dependence of the shape of the stress

single crystal specimens must be accounted for by effects due to grain boundaries. The surface morphology of yield was similar for all three orientations. At 600 “C slip was

strain curve at’ low temperatures, and also to provide a direct comparison with the previous polycrystalline work. In the temperature range from 800 “C to 1600 “C the proportional limit for orientation (1) did not vary with temperature. Below 800 “C the proportional limit rose rapidly to the value observed for polycrystalline uranium dioxide. The temperature-dependence for orientation (3) was similar to that for orientation (1). The temperature-dependence of orientation (2), near to [ill], did not show a linear part, the proportional limit increased with decreasing temperature in a manner similar to the proportional limit for polycrystalline specimens. The difference in stress between the curves for polycrystalline and

homogeneous

and no slip lines were observed.

At 800 “C fine wavy slip was observed, which became deeper ss the testing temperature was increased to 1600 “C. The operative slip planes which were determined for the three orientations are shown in table 1. The operative slip plane was either (100) or (1 lo} depending on orientation, and did not vary with temperature. The different temperature-dependence of the proportional limit for orientation (2) can be accounted for by the difference in the operative slip planes. The observed slip plane for orientation (2) was (100) but the observed slip plane for orientations (1) and (3) was (110). These results indicated that (1 IO} was a more active slip plane than {loo), whereas Rapperport and

THE

YIELD

AND

FLOW

OF

SINGLE

CRYSTALS

OF

URANIUM

113

DIOXIDE

TABLE I Operative slip planes in uranium dioxide single crystals Temperature PC) 600 800

.~ Orientation 1 = [Oil] no slip lines visible 2 systems (110)

I200

Orient&ion 3

no slip lines visible

no slip lines visible

1 system

1 system

0001

(A)

000>

(A)

0001

(A)

1110)

(AI

1 system

1 system 0%

0lOI 1 system

1 system tB)

2 systems {110)

Orientektion2 W [Ill]

0%

2 systems 0101

1600

( kerativeslip planes___...-

(A)

UlOI

(A)

Two traces were observed on faces at right angles on each specimen. In ease (A) the two traces were paired to identify ~&rnbi~o~iy one system. In case (B) the two traces belonged to two different systems.

Huntress 1) found that (100) was more active. This difference in behavionr is possibly due to the difference in s~ichiomet~ of the two materials. Assuming the rate equation for thermally activated deformation B= &Jexp ( - ~(~)~~~~,

(1)

where B is the strain rate, and do is a constant, the effective activation energy H(o) can be determined from H(a) = - ~~2(~~~~~)(~ In d/&r).

(2)

& In +a was determined by performing strain rate change experiments, using a strain rate change factor of 5, along the stress/strain curve, and extrapolating the results to the proportional limit. &r/M was obtained from the curve of the tem~rat~e dependence of the proportional limit. Fig. 5 shows the strain-rate dependence of the flow stress for single crystals of orientation (1). At 600 “C and 800 “C the change in flow stress da was almost constant at about 1 kgjmma. Between 800 “C and 1000 “C there was a discontinuity. At 1000 “C Au was only about 0.18 kg/mm2 and this increased with increasing temperature to 0.86 kg/mm2 at 1800 “C. The effective activation energv Hla)

1.2 -

*o-o-

0’ 0.B

-

$

0

y” 2

0.4

0

/ l 0

b

500 .

1

1000 Tcmpentur

1scQ

,

2oof5

c %

Fig. 5. Strain-rate dependence of the flow strese extmpolated to the proportional limit for single crystals of orientation (I), using a strain rate change factor of 5.

for crystals of orientation (1) in the temperature range from 1000 “C to 1600 “C is shown in fig, 6. In this temperature range the proportional limit was nearly athermal, the curve for the strain-rate dependence of the flow stress was continuous, and a single dislocation mechanism would be expected to be operating. For a single mechanism to be rate controlling, the. effective activation energv as a function of

114

J.

F.

BYRON

tation and depended on the operative slip plane. 2. The operative slip plane did not vary with temperature and was either (100) or (1 lo} depending on orientation. 3. An analysis of the thermally activated flow of single crystals of uranium dioxide in the

1000

1200 Temperature

Fig.

6.

Temperature-dependence

1400

1600

was operating or that the rate equation d=do exp { -H(a)/kT} did not obtain.

‘C

of

the

effective

activation energy for single crystals of orientation (1).

temperature would be a straight line passing through absolute zero. This was not the case as the effective activation energy decreased with increasing temperature, and it must be concluded that either more than one mechanism is operating or that the rate equation (1) is not valid for the deformation of single crystals of uranium dioxide in this temperature range. 4.

temperature range from 1000 “C to 1600 “C showed that either more than one mechanism

Conclusions

1. The temperature dependence of the proportional limit for single crystals of uranium dioxide tested in compression under atmospheric pressure of argon varied with orien-

Acknowledgements This work has been supported by the United Kingdom Atomic Energy Authority. The author would like to thank Mr. B. L. Eyre of the UKAEA for designing and supplying the compression furnace, Dr. W. in der Schmitten of Nukem, Hanau, West Germany for supplying the single crystals, Dr. B. L. Mordike for helpful discussions and Dr. F. W. Noble for reading the manuscript. References 1) E. H. Rapperport Report 2)

NMI-1242

USAEC

K. H. G. Ashbee, reported by B. Beagly and J. W. Edington,

3)

and A. M. Huntress, (1960)

Brit.

J. F. Byron,

J. Appl.

J. Nucl.

Phys.

Mat.

14 (1963)

27 (1968)

48

609