Univesity f Pisa - ITALY - Depatment f Mechanical, Nuclea and Pductin Engineeing Them-Mechanical Behaviu f Li 4 SO 4 and Li TiO 3 N. Zaccai, D. Aqua
Cntents f Pesentatin This pesentatin descibes the them-mechanical test n ceamics Pebble bed mateials candidate as ceamic beede mateials in a Fusin eacts Li 4 SiO 4 φ.435 -.5 mm Ppeties Li TiO 3 Li 4 SiO 4 Li TiO 3 φ.8 - mm Density (g/cm 3 ) Psity % E yung (GPa) Ceff. Pissn ν Stenght Raptue (MPa) Yielding stess (MPa) Cnductiv ity (W/mK) at 98 K 3.89.35 8.6 9.7.5 39 3 88 3.8.8 This eseach aims t veify the pssibility f simulate the them-mechanical behaviu f this mateials with a theetical mdel develped by the auths Them-Mechanical Behaviu f
Cntents f Pesentatin Desciptin f a epeimental set-up t investigate the Them-mechanical behavi f pebble bed Desciptin f a new instumentatin t measue the lcal packing fact f pebble bed Desciptin f the theetical mdel Results f the epeiments and cmpaisn with the theetical mdel Cnclusin Them-Mechanical Behaviu f 3
Epeimental Set-up Hydaulic pistn Unaial defmatin test Cnductivity test vesus aial defmatin with and withut gas Lad Cell Tns N. Zaccai, D. Aqua Epeimental and numeical analysis n Pebble beds used in an ITER Test Mdule Blanket, ISFTN-7, Tky, Japan, May -6, 5 Them-Mechanical Behaviu f 4
Epeimental Set-up Cppe plate Themcuples Cylinde that cntain the pebble bed Guaded Themal Resistance Cental Themal Resistance Them-Mechanical Behaviu f Blanket Themal Resistance 5
Epeimental Equipment Themcuples Gas Cnduct Them-Mechanical Behaviu f 6
Epeimental Equipment Filling f cylinde that cntains the bed Bed vib-cmpactin The themal cnductivity f Pebble-bed is detemined by cmpaisn with a efeence mateial (in this test alumina ALUBIT 9) LabView Cntl Panel ) The lad was inceased deceased step by step. ) Each lading step was held f the time inteval needed t each a steady state heat tansfe cnditin, in de t detemine the themal cnductivity vesus aial defmatin. TEST CONDITION: - Packing fact.635 f Li TiO 3 and.68 f Li 4 SiO 4 -ma Pessue 6.6 MPa -Aveage temp. In the bed 3 K -Ai atm and vacuum 6.5e-3 atm Them-Mechanical Behaviu f 7
Peliminay gamma ay densimete This device is made up f : ) a lead cylinde ) the scintillat detect (Na I) 3) the gamma suce The lead cylinde is put in psitin n the pebble bed by means f a cicula plate (with a buttnhle) cnnected t the cntaine f the pebble bed Them-Mechanical Behaviu f 8
Peliminay gamma ay densimete T measue the density f mateial, we take in accunt nly the gamma backscatte peak (.8,4 Mev) This instumentatin supply, in the field pints, the aveage density f pebble bed thickness Calibatin cuve Field pints Them-Mechanical Behaviu f 9
Theetical elastic-plastic D mdel f a tw half sphees Theetical Mdel f them-mechanical mechanical behaviu f pebble bed stiffness cnductivity Etensin t 3D mdel Simple lattices cmpsed f sphees The develped mdel has been cmpaed with the epeimental esults btained by eseach n the slid beeding blanket f Fusin Nuclea React. [] D. Aqua, Themal Mechanical Analysis f a Slid Beeding Blanket, Fusin Eng. Des., 69 (3) 5-58. [] D. Aqua, N. Zaccai, Mitigatin f a Ce Meltdwn Scenai by Means f a Ce Catche Lcated Inside The React Pessue Vessel, th ICONE, Alingtn, Viginia (Washingtn, D.C.), USA, Apil 5-9, 4. [3] D. Aqua, N. Zaccai, Themal Analysis f a Ce Catche Made f Pebble Bed Lcated Inside The React Pessue Vessel, Int. Junal f Heat and Technlgy, vl., Januay 5, -9. [4] D. Aqua, N. Zaccai, Pebble Bed Themal-Mechanical Theetical Mdel: Applicatin at The Gemety f Test Blanket Mdule f ITER-FEAT Nuclea Fusin React, Fusin Engineeing and Design, in pess, 5. Them-Mechanical Behaviu f
Them-Mechanical Behaviu f Theetical Mdel Theetical Mdel Effective stiffness f tw half sphee Effective stiffness f tw half sphee σ σ E E σ σ ε E u / / ln σ 3.5 E P y e σ X p (MPa); q (W/m ) Effective stiffness ( ) E P u P K / ) / ) /( / ( ln ) ( / σ E E P u P K y p σ σ ε ln ) ( Elastic egimen Plastic egimen Sphee stess tend (ο) ο σ σy ο The main hyptheses f the them-mechanical theetical mdel ae the fllwing: the mateial behaviu is elastic-pefectly plastic the sphee is cnsideed a mn dimensinal beam with a vaiable css-sectin the mateial cnductivity is cnstant with the tempeatue
Them-Mechanical Behaviu f Theetical Mdel Theetical Mdel Effective cnductivity f tw half sphees cmpessed by a fce Effective cnductivity f tw half sphees cmpessed by a fce P in elastic P in elastic-plastic egimen plastic egimen T dv q V H V eq Δ & λ The effective cnductivity f tw half sphees cmpessed by a fce P, can be given by the fllwing fmula: X p (MPa); q (W/m ) sf sf c c eq eq R V V R V V R * * λ The ttal themal esistance is btained by additining f the sphee themal esistance and the cntact themal esistance P E R eq λ ν λ π ln 3 ) 9 ( 4 3 3 7 R eq λ λ ln 3 3 4 Themal esistance f tw half sphee Elastic egimen Plastic egimen The plastic zne is simulated by a cylinde that it have the same vlume f a the plastic sphee sect
Theetical Mdel Effective stiffness and cnductibility f cubic simple lattice We cnsideed the bed made f egula lattices which ae chaacteized by diffeent values f packing fact γ, in paticula : simple cubic lattice: γ.536; bdy cented cubic lattice : γ.68; face cented cubic lattice : γ.74 λ CS π R 3R CS S eq λ CC.94 π R.987 CC S Req λ FC.88 π R.486 R FC S eq K R Z 8 K K K csα. 44 K 4 R R SS KY K X 4 Keq Keq Z X Y SS K K Y K K 4( K ). 47 K X Z Y eq Them-Mechanical Behaviu f 3
Theetical Mdel Cack Ppagatin In de t simulate the cacking and cushing effect f ceamics mateials, we have cnsideed that the adius f sphees decease when the cmpessin lad incease because a pat f mateial (afte the cacking) desn t cntibute t the mechanical esistance. The plastic mateial is simulated like a fluid which pduces a tensile stess nmally t the applied lad. This tensile can cack the sphee mateial. Vn Mises Stess (ma MPa) Analisi tem-meccanica di letti di sfee D.Aqua, N. Zaccai, 5 R.L. n 78 DIMNP Univ. Di Pisa- Italy. Radial cack ppagatin aund the cntact zne Them-Mechanical Behaviu f 4
Results Li TiO 3 Pessue vesus aial defmatin cuve Cuve f themal cnductivity vesus pessue Pessue (MPa) 7 6 5 4 3.5.5.5 defmatin, ε % Cnductivity (W/mK).5.45.4.35.3.5..5..5 4 6 Pessue (MPa) ai atm at T3K vacuum 6.5e-3 atm at 3K I Cycle Ma Pessue: 6.6 MPa Ma defmatin:.73 % II Cycle Ma Pessue: 6.5 MPa Ma defmatin:.9 % Ma cnductivity (ai):.38 W/mK Min cnductivity (ai):.6 W/mK Ma cnductivity (vacuum):.3 W/mK Ma cnductivity (vacuum):.9 W/mK Them-Mechanical Behaviu f 5
Distibutin paametes Packing fact Aveage Befe the test γ.63 Results Li TiO 3 Befe the test 5 Radial distibutin f the packing fact 5 Afte the test 6 Afte the test γ. 64 Pecentage f the pebble bed vlume which has a paticula value f packing fact 4.695 3.69.685.68.675.67.665.66.655.65.645.64.635.63.65 -.6.65.6 -.65.6.595.59-3.585.58-4 4 3 - - -3-4 % in vlume 5 4 3 Befe the test Afte the test -5-5 -4-3 - - 3 4 5-5 -5-4 -3 - - 3 4 5.68-.69.5.67-.68.66-.67.64-.66.6-.64 ange f Packing Fact.6-.6.58-.6 Them-Mechanical Behaviu f 6
Results Li 4 SiO 4 Pessue vesus aial defmatin cuve Cuve f themal cnductivity vesus pessue Pessue (MPa) 7 6 5 4 3.5.5.5 3 defmatin ε % Cnductivity (W/mK).4.35.3.5..5..5 ai atm at T3K vacuum 6.5e-3 atm at T3K 3 4 5 6 7 Pessue (MPa) I Cycle Ma Pessue: 6.45 MPa Ma defmatin:.55 % II Cycle Ma Pessue: 6.6 MPa Ma defmatin:.83 % Ma cnductivity (ai):.3 W/mK Min cnductivity (ai):.4 W/mK Ma cnductivity (vacuum):.6 W/mK Ma cnductivity (vacuum):. W/mK Them-Mechanical Behaviu f 7
Distibutin paametes Packing fact Aveage Befe the test γ.65 Results Li 4 SiO 4 Radial distibutin f the packing fact Befe the test 5 4 5 4 Afte the test.65 Afte the test γ. 635.65.648.646.644.64.64.638 3 3.636.634.63 Pecentage f the pebble bed vlume which has a paticula value f packing fact.63.68.66.64.6.6.68.66 - - -3 - - -3 6-4 -4-5 -5 % in vlum e 5 4 3 Befe the test Afte the test -5-4 -3 - - 3 4 5-5 -4-3 - - 3 4 5.68-.69.5.65-.66.64-.65.63-.64.6-.63.6-.6 Range f Packing Fact.59-.6 Them-Mechanical Behaviu f 8
S.E.M. pht n cacked Pebble bed Cntact zne Cushed sphees Them-Mechanical Behaviu f 9
S.E.M. pht n cacked Pebble bed Seveal pebbles agglmeated themselves abve all in the cental pat f the bed. The cntact aea lks like a cylinde cacked The cacks ae due t tensile esidual stesses which develp duing the unlading. The mateial f the cntact cylinde was analysed and it pved have the same cmpsitin f the pebble mateial. Them-Mechanical Behaviu f
Pessue (MPa) 8 7 6 5 4 3 Results Cmpaisn between Theetical mdel and Epeimental esults Li 4 SiO 4 φ.435 -.5 mm Li TiO 3 φ.8 - mm Theetical Epeimental ( cycle)..4.6.8 Defmatin ε (%) Pessue (Mpa) 7 6 5 4 3 Theetical Epeimental ( cycle).5.5 Defmatin ε (%).7.6 Cnductivity (W/mK).6.5.4.3.. Epeimental, mean T3K Theetical Cnductivity (W/mK).5.4.3.. Epeimental (mean T3 K) Theetical 3 4 5 6 7 Pessue (MPa) Them-Mechanical Behaviu f 4 6 8 Pessue (MPa)
FUTURE DEVELOPMENT Discete Mdel f Pebble bed Them-Mechanical Behaviu f
CONCLUSION The tests have pemitted t detemine the effective stiffness and cnductivity f the pebble beds vesus aial defmatin; The adial distibutin f the packing fact has been detemined by means f a peliminay gamma ay device. We can pint ut that bed cmpessin pduces a me unifm distibutin f the packing fact. The cmpaisn with the theetical mdel shws a gd ageement f the epeimental effective cnductivity and stiffness f the bed abve all in the elasticplastic defmatin; Develpment f the mdel ae being pefmed in de t simulate the aangement phase. Them-Mechanical Behaviu f 3