thermomechanical behaviour of ceramic breeder and beryllium pebble beds

Fusion Engineering and Design 49–50 (2000) 643–649

Thermomechanical behaviour of ceramic breeder andberyllium pebble beds

J. Reimann *, E. Arbogast, M. Behnke, S. Muller, K. ThomauskeAssociation FZK-EURATOM, Forschungszentrum Karlsruhe, Postfach 3640, D-76021 Karlsruhe, Germany

Abstract

In order to describe the interaction between ceramic breeder and beryllium pebble beds and the structural materialin ceramic breeder blankets, the characteristic properties of these pebble beds in the relevant temperature and pressureranges must be known. Uniaxial compression tests with Li4SiO4 pebble beds were performed in temperatures betweenambient and 900°C and pressures up to 8 MPa. Corresponding experiments with a smaller parameter variation werecarried out with Li2TiO3, Li2ZrO3, and Li2O pebble beds. Empirical correlations for the moduli of deformation arepresented for the different materials and first relationships for thermal creep of Li4SiO4 pebble beds are given. Usinga different test facility, uniaxial tests were carried out with monosized and binary beryllium pebble beds in atemperature range between ambient and 480°C and pressures up to 8 MPa. Again, relationships for the deformationmodulus are presented. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Thermomechanical behaviour; Ceramic breeder pebble beds; Beryllium pebble beds

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1. Introduction

Ceramic breeder blankets consist of ceramicbreeder and beryllium pebble beds; the latter areneeded for neutron multiplication. During opera-tion, the blanket structure restrains the expansionof the pebble beds and, therefore, causes stresses.These stresses jeopardise the safe blanket opera-tion if the mechanical integrity of the blanketelement is endangered or if heat and tritium re-moval is significantly deteriorated due to pebblebreakage or melting.

The stresses arise from different thermal expan-sions of the structural and the pebble bed materi-als, pebble bed swelling and thermal creep. Inorder to describe the thermomechanical behaviourof a blanket element, appropriate finite elementcodes are used with appropriate modules for thedescription of pebble beds. As input, these mod-ules require data on characteristic pebble bedproperties determined in standard-type tests. Ofprime importance are uniaxial compression tests(UCT) for the determination of uniaxial stress-strain relationships and thermal creep for blanketrelevant temperature and pressure ranges. For thedescription of the macroscopic movement of peb-bles in blanket elements, further experiments arerequired such as triaxial compression tests (TCTs)

* Corresponding author. Tel.: +49-7247-823498; fax: +49-7247-824837.

E-mail address: [email protected] (J. Reimann).

0920-3796/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S0 920 -3796 (00 )00357 -4

J. Reimann et al. / Fusion Engineering and Design 49–50 (2000) 643–649644

and measurements of the friction coefficient be-tween structural materials and pebble beds.

In a previous paper [1], stress/strain data fromUCTs for different ceramic breeder materials werepresented, see also Refs. [2,3] and first measure-ments on thermal creep. For beryllium pebblebeds, no data existed at all. An overview on thestatus of the pebble bed work is given in [4].

In this article, further results from UCTs arepresented for different ceramics. Additionally,stress/strain and thermal creep data for berylliumpebble beds are reported, obtained in a separateUCT facility. Results from investigations on themacroscopic movement of pebbles in a blanketrelevant geometry are reported elsewhere [5].

2. Experimental

2.1. UCT set-ups

In a UCT, the pebble bed in a cylindricalcontainer is compressed in the axial direction andboth the axial pressure on the bed (identical to theaxial stress) and the axial displacement aremeasured.

Fig. 1 shows the experimental set-up used forceramic breeder material tests. The granular mate-rial is filled densely in a container (inner diameter:60 mm) with Al2O3 top and bottom discs enablingbed heights up to 14 mm. A small ratio of bedheight to diameter was chosen in order to keepthe wall friction influence small. The equipment ispositioned in an electrical three-zone INSTRONfurnace with maximum temperatures of about900°C. The bed was loaded axially by a hydraulicpress (SCHENCK hydraulic stress/strain test fa-cility); the force is measured by a load cell.

The bed height strains are measured by fourinductive displacement transducers connected tothe test container by quartz rods and tubes. Thismeasurement system is superior to the previouslyused system [1] where only one displacementtransducer was used which was unsatisfactory ifthe upper Al2O3 disk did not stay parallel duringoperation. Furthermore, the piston design waschanged in order to allow the pebble bed toexpand freely (without a minimum axial force aspreviously) during the heating-up phase. Espe-cially the creep strain measurements are sensi-tively influenced by this effect. Therefore, in thisarticle only results obtained with the new systemare reported.

For the Be pebble bed experiments, a separatetest facility was built up in a glove box, fordetails, see Ref. [6]. Fig. 2 shows that the design

Fig. 1. UCT set up for ceramic pebble beds.

Fig. 2. UCT set-up for Be pebble beds.

J. Reimann et al. / Fusion Engineering and Design 49–50 (2000) 643–649 645

Table 1Pebble bed characteristics

rth (g/cm3) gp (%) Size (mm) PackingPebble Test conditionsHeatGranularmaterial factors gpb (%)pretreatmentgeometry

T (°C) pmax (MPa)

Li4SiO4 2.39 97 0.25–0.63 Spherical Therm. 60–63.5Ta−900 6.3condit.;annealed

93 1–1.4Li2TiO3a Potato-shaped3.45 As received Ta−700 6.3 56–58

90 0.8–1.2 Potato-shapedLi2TiO3b Annealed3.45 Ta−700 6.3 56–58

86 1–1.4 Potato-shapedLi2ZrO3 As received4.18 Ta−700 6.3 59–6186 1–1.4 Potato-shapedLi2ZrO3 Annealed4.18 Ta−700 6.3 59–61

80 1 Pot. shap.Li2O As received2.013 Ta 6.3 57Be 1.86 0.98 2 Pot. shap. As received Ta−480 8 63Be/Be 0.98/0.961.86 2/0.1–0.2 Pot. As received Ta−480 8 63+18

shap./irregular

a Extrusion process.b Aglomeration process.

of both the test container and the measurementsystem are very similar to those used in thepresent ceramic pebble bed tests. Bed heights were:30 mm. The maximum temperature was re-stricted to :480°C. UCTs with Li4SiO4 pebblebeds in this test facility agreed very well withresults from the facility shown in Fig. 1.

2.2. Characteristics of in6estigated materials

Table 1 contains characteristic data of the in-vestigated pebble beds. In order to achieve a largefilling factor gpb, the pebbles are filled into the bedcontainer by appropriate tapping and vibrating.For ‘monodisperse pebble beds’ (pebbles of uni-form shape and size) the maximum filling factor isabout 65% for a face centred cubic array. Inpractice, maximum values of :62% are achievedfor smooth pebbles. In technical applications‘polydisperse pebble’ beds are often used consist-ing of pebbles of uniform shape but with a certainsize distribution. Maximum observed filling fac-tors are again some percents below the maximumvalue of :65%. Significantly larger filling factors(:80%) are reached by pouring small particles in

a bed consisting of larger particles (diameter ratioof small to large pebbles50.2). The Be-beds inblankets consist often of such ‘binary beds’.

The investigated ceramic breeder pebble bedsconsist of polydiperse beds as reflected in Table 1.The surface of all pebbles can be characterised as‘slightly rough’.

The Li4SiO4 pebbles, originating from a meltingprocess, are characterised by a high pebble den-sity, spherical shapes, and diameter distributionsbetween 0.25 and 0.63 mm. This material has beeninvestigated the most intensively. Details on heatpre-treatment and thermal annealing are given in[7]. The Li2TiO3 pebbles consisted of two chargesmanufactured by either the extrusion-sinteringprocess (gp:93%, characteristic diameters 1–1.4mm) or the agglomeration process (gp:90%,characteristic diameters 0.8–1.2 mm). In bothcases the pebble shapes were characterised as‘potato-shaped’.

The metazirconate Li2ZrO3 pebbles were manu-factured by the extrusion-sintering process andthe geometric properties were similar to those ofthe corresponding Li2TiO3

The Be pebbles, fabricated by Brush Wellman,consisted of pebbles with nominal diameters of 2


and 0.2-mm diameters. The 2-mm pebbles werequite spherical in shape, however, with indenta-tions on the surface. The shapes of the smallpebbles were more irregular, see Ref. [8].

3. Experimental results

3.1. Uniaxial compression tests

Fig. 3 (from Ref. [6]) shows a characteristicresult of an UCT at high temperatures. The axialcompressive stress (calculated as applied forcedivided by the bed cross section) is plotted as afunction of the a. The characteristic parts of anUTC are:� ‘The first pressure increase, (curve ‘1st pi’)’: this

curve is caused by the irreversible displacementof particles forming a denser configuration andthe plastic deformation of particles. For thedescription of the thermomechanical interac-tion between pebble beds and structural mate-rial knowledge of this curve is of primeimportance because it determines the pressurebuild-up during the first blanket operation.

� ‘The first pressure decrease (curve ‘1st pd’), andsecond pressure increase (curve ‘2nd pi’)’: the

slope of the curve ‘1st pd’, and the subsequentstress increase are much steeper than the slopeof curve ‘1st pi’ because these curves are causedmainly by elastic deformations. The hysteresisis characteristic for the influence of internalfriction. For further cycles, these curves do notdiffer significantly. The difference between thecurves ‘1st pi’ and ‘1st pd’ is relevant for theformation of gaps, which might form duringblanket operation.

� Creep strain: keeping the stress constant at agiven value, the strain increases with time dueto thermal creep. The knowledge of thermalcreep is important for the relaxation of stressesduring the first days of blanket operation andfor the compensation of swelling due to irradi-ation which occurs during long operationaltime periods.

� Cycling at the end of the creep period mightshow that the bed stiffness has increasedslightly due to the enlarged contact areas be-tween individual particles because of creep.This effect is not expressed in the present ex-periments due to the small creep ratesexperienced.The first compression to a given value (curve ‘i’)

is mainly caused by the irreversible displacementof particles forming a denser configuration. Theslopes of the curves for the first decompression(curve ‘d’) and the subsequent compression (curve‘si’) are much steeper than the slope of curve ‘i’because the relevant mechanism is primarily elas-tic pebble deformation with an additional influ-ence of internal friction. Keeping the stressconstant, the strain increases with time due tothermal creep. Cycling at the end of the creepperiod shows that the bed stiffness increases dueto the enlarged contact areas because of creep.

For the description of the thermomechanicalinteraction between pebble beds and structuralmaterial the knowledge of curve ‘i’ is of primeimportance because it determines the pressurebuild-up during the first blanket operation. Curve‘d’ in combination with curve ‘i’ is relevant for theformation of gaps which might form during theblanket cool-down phase. The knowledge on ther-mal creep (curve ‘c’) is important in order tocompensate swelling due to irradiation.Fig. 3. UCT of binary Be bed at 480°C.


Fig. 4. UCT at Ta for ceramic pebble beds.

Fig. 5 shows corresponding results for Be.Characteristically, the first compression of thebinary bed shows a softer behaviour than the bedconsisting of large pebbles only. This might bedue to two mechanisms: (i) the small pebbles actas ball bearings for the large ones and displace-ments require smaller forces; and (ii) small peb-bles separating large pebbles exhibit a softerelastic/plastic deformation behaviour.

The steeper slope of the Be beds during decom-pression compared to the ceramic beds indicatesplastic deformation of the Be pebbles during thecompression phase.

3.2. E6aluation of moduli of deformation

From the measured stress(s)/strain(o) curve theuniaxial modulus of deformation is evaluated,defined by:

E=s/o or: E*=Ds/Do

For a power law dependence of the type:

E=Csm (1)

E* differs from E by the factor (1−m)−1:

E*=Csm/(1−m) (2)

These moduli of deformation are evaluatedboth for the first compression and decompressionas shown in Table 2. The values are fairly inde-pendent of temperature up to values of about600°C. Presently, only for Li4SiO4 the tempera-ture dependence for the 1st stress increase wasinvestigated in more detail, see Fig. 6. The datacan be well described by

C=130(1–5.5×10−10 T(°C)3) (3)

3.3. Measurement of thermal creep strains

Creep strain ocreep is more complicated to beevaluated for pebble beds than for homogeneousmaterials because the contact zones between peb-bles change with time t. Therefore, ocreep= f(mate-rial, T, p, t).

In order to reduce the number of requiredexperiments to generate a sufficiently large data

Fig. 5. UCT at Ta for Be pebble beds.

Fig. 4 shows UCT results at ambient tempera-ture with the new measurement system. The re-sults agree very well with previous ones [1]; Li2Owas not investigated before. The Li2O pebble bedexhibits the largest strains for a given stress; at theend of the experiments, a significant portion ofbroken particles were observed, in contrast to theother materials.


base, a relationship of the type

ocreep=A(T) pm tn (4)

would be desirable with m and n being tempera-ture independent.

Fig. 7 shows new thermal creep results forLi4SiO4 beds performed at pressures of :6.3MPa. The data can be well fitted by the exponentn=0.26. The temperature dependence, see Fig. 8,can be expressed as

A(T)=55 exp(−11 000/T(K)) (5)

Fig. 7. Creep strains for Li4SiO4.

Table 2Moduli of deformation

Material 1st compression 1st decompression

m C m C

0.47 130 0.60 170Li4SiO4

0.47 174Extr. Li2TiO3 0.61 2672250.6100Aggl. Li2TiO3 0.43

0.48 102Li2ZrO3 0.6 2180.38Li2O 73 0.67 277

4400.651400.47Monos. BeBinary Be 0.52 4400.6590

Fig. 8. Temperature dependence of Li4SiO4 creep strain.

Fig. 6. Temperature dependence of modulus of deformation Efor Li4SiO4.

More experiments are required in order to de-scribe the pressure dependence.

First results on thermal creep of Be beds arepresented in [6].

4. Conclusions

As two prerequisites for the description of theinteraction between ceramic breeder and beryl-


lium pebble beds and the structural material inceramic breeder blankets, the modulus of deforma-tion for the first compression and decompressionand the creep strain were measured in uniaxialcompression tests with different ceramic pebblebeds and with beryllium. The results are presentedas functions of temperature. At present, the re-quired database for detailed calculations is by farnot complete and more experiments are required.

Acknowledgements

This work was supported by the European Com-munities within the European Fusion TechnologyProgramme.

References

[1] J. Reimann, E. Arbogast, S. Muller, K. Thomauske, Ther-momechanical behaviour of ceramic breeder pebble beds,7th Int. Workshop on Ceramic Breeder Blanket Interac-tion, Petten, The Netherlands, Sept. 14–16, 1998.

[2] A.Y. Ying, Z. Lu, M. Abdou, Mechanical Behavior andDesign Data Base of Packed Beds for Blanket Designs,ICFRM-8, Dendai, Japan, October 26–31, 1997.

[3] J. Reimann, J.S. Muller, First experiments on the ther-momechanical behaviour of Li4SiO4 pebble beds, Proc.20th SOFT, Marseille, F, 7–11 Sept. 1998.

[4] A.Y. Ying, M.A. Abdou, L. Buhler, M. Enoeda, S.Malang, Y. Ohara, J. Reimann, Summary of laboratoryexperiments and modelling for thermomechanical proper-ties and interactions of solid breeder pebble bed materials,this conference.

[5] L. Buhler, J. Reimann, E. Arbogast, K. Thomauske, Me-chanical behaviour of Li4SiO4 pebble beds in a blankettypical geometry, this conference.

[6] J. Reimann, M. Behnke, Experiments on the thermome-chanical characterization of beryllium pebble beds, 4thIEA Int. Workshop on Beryllium Techn. for Fusion,Forschungszentrum Karlsruhe, Karlsruhe, Germany, Sept15–17, 1999.

[7] G. Piazza, M. Dalle Donne, H. Werle, E. Gunther, R.Knitter, N. Roux, J.D. Lulewics, Long term Annealing ofceramic Breeder pebbles for the HCPB DEMO Blanket,ICBBI-7.

[8] F. Scaffidi-Argentina, M. Dalle Donne, H. Werle, ‘Me-chanical Performance of Irradiated Beryllium Pebbles,’Proc. Third IEA Int. Workshop on Beryllium Techn. forFusion, Oct. 22–24, 1997, Mito, Japan, JAERI-Conf 98-001.

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thermomechanical behaviour of ceramic breeder and beryllium pebble beds

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