experimental and theoretical characterization of li2 tio3 and ......n) i cycle ii cycle iii cycle...

1

Experimental and theoretical characterization of

Li2 TiO3 and Li4 SiO4 pebbles

Donato Aquaro - Nicola Zaccari

Dipartimento di Ingegneria Meccanica , Nucleare e della Produzione

Universita' di Pisa (Italy)

2

Experimental and theoretical characterization of Li2 TiO3 and Li4 SiO4 pebbles Aquaro - Zaccari

• Content• experimental tests on single pebbles of Li2 TiO3

and Li4 SiO4 (compression tests)• numerical simulation of the pebble compression• comparison between numerical and experimental

results (assessment of the numerical model )• numerical simulation of a oedometer test on a

Li4 SiO4 pebble bed using the Cam-clay model. comparison with the experimental results

• conclusions

3


• Experimental set up

INSTRON Press

4


Pebble tested

Li2 TiO3 pebbles

maximum variation of the average diameter 4%

- 1.1-1.3 mm of diameter

Li4 SiO4 pebbles

- maximum variation of the average diameter 7.8%

0.55-0.6 mm of diameter

The tests were carried out at room temperature and atmospheric pressure

5


Some pebbles were loaded until they broke - other pebbles were subjected at several cycles of loading and unloading without reaching the failure.

Before the test

After the test

0

2

4

6

8

10

12

14

16

0 0.01 0.02 0.03 0.04 0.05 0.06

Piston Displacemnt (mm)

Load

(N) I cycle

II cycle

III cycle

Com

pres

sive

load

(N)

Before the test

After the test

0

5

10

15

20

25

30

35

40

45

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Piston Displacement (mm)

Com

pres

sive

Loa

d (N

)Collapse

Loading phase

Li2 TiO3

6


Before the test

After the test

0

2

4

6

8

10

12

0 0.01 0.02 0.03 0.04 0.05

Piston displacement (mm)

Com

pres

sive

Loa

d (N

)

I cycle

II cycle

III cycle

0

2

4

6

8

10

12

14

16

0 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (mm)

Com

pres

sive

Loa

d (N

)

I cycle

II cycle

Collapse

Before the test

After the test

Li4 SiO4

7


0

10

20

30

40

50

60

0 0.02 0.04 0.06 0.08

displacement (mm)

load

(N)

t37 t23t22 t28t17 t34t27 regression curve

0

10

20

30

40

50

60

70

0 0.05 0.1 0.15

displacem ent (m m )

load

(N)

t37t23t22t28t11t12t15t34t27regression curve

Li2 TiO3

loading unloadingRegression curvesP=687.55 s 1.257

r2=0.9917

P=-3.287 + 733.62 s

r2=0.9854

8


0

2

4

6

8

10

12

14

0 0.02 0.04 0.06

displacement (mm)

load

( N)

t412 t45t43 t48regression curve

0

2

4

6

8

10

12

0 0.01 0.02 0.03 0.04

displacement (mm)lo

ad (N

)

t44 t43t45 t412regression curve

Li4 SiO4

loading unloadingRegression curve

P=3613 s 1.9027

r2=0.927

P=7657 s 1.8922

r2=0.974

9


0

0.1

0.2

0.3

0.4

0.5

0.6

11 17 24 26 31 31 35 36 37 39 40 51fracture load (N)

colla

psed

peb

ble

frac

tion

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1.06 6.97 7.29 7.67 9.77 10.16

load (N)

colla

psed

peb

ble

frac

tion

Collapsed fraction of Lithium- Metatitanate pebble

Collapsed fraction of Lithium- Orthosilicate pebble

No Li2 TiO3 pebbles collapsed under 25 N

1 N is the maximum load supported by the Li4 SiO4 pebbles without any rupture

10


NUMERICAL SIMULATION OF THE PEBBLE COMPRESSION

FEM code MSC-MARC

aim of the simulations: to understand the main phenomena which occur during the pebble compression

- Mesh: axial symmetric elements. - load applied by means of a rigid upper plate- pebble located on a rigid lower plate.

- constraints pebble - plates : unilateral contacts (reacting only to compression loads) without friction.

11


Material model : low tension material

ε+

σ+σtu

εcr

softening

Traction

Compression

E0

Es

σy

- linear elastic behaviour under tensile stress

- elastic- plastic behaviour under compressive stress

Failure: - if tensile stress overcomes the cracking stress value (σcr ) - if the plastic strain (under compressive stresses) reaches the crushing strain value (εu ).

Other parameters:softening module ( Es), - the shear retention (τ),

12


The material data for the lithium metatitanate and Lithium Ortosilicate are reported in:

- Lithium-Metatitanate : E= 200.6 GPa - ν= 0.27 - σu = 1113 MPa- Lithium-ortosilicate : E= 90 GPa - ν= 0.25 - σu = 880 MPa

1] W. Dienst, H. Zimmermann, Mechanical properties of ceramics breeder materials, J. of Nucl. Mat., 155-157 (1998) 476-479.[2] P. Gierszewski, Review of properties of lithium metatitanate, Fusion Engineering and Design 39–40 (1998) 739–743.[3] G. Schumacher at alii, Properties of Lithium Ortosilicate, J. of Nuclear Materials, 155-157 (1998) 451-454.

E Young module, ν

Poisson coefficient, σu ultimate compression stress.

13


If we use the previous data for obtaining the material parameters,

the numerical results do not fit the experimental results.

Considering the experimental results of oedometer tests or single pebble compression tests we can conclude that the Young module must

be two or three order of magnitude lower than the previous data.

The previous data could not refer to the tested pebbles

for the ceramic material, the thermal mechanical characteristics are strongly dependent on the production technology

14


This problem was overcame performing a parametric analyses varying the model parameters in manner that the load- displacement curves fitted

the experimental ones.

0

10

20

30

40

50

60

0 0.05 0.1 0.15

displacement (mm)

load

(N)

t22

regression curve

sy=200Mpa-E=3.5GPa-eu=0.3-sc=100MPa

sy=200MPa-E=5GPa-eu=0.15-sc=100MPa

0

2

4

6

8

10

12

0 0.02 0.04 0.06

displacement (mm)

load

(N)

t44

sy=250MPa-E=5.5GPa-eu=0.15-sc=139MPa

Li4 SiO4 pebble Li2 TiO3 pebble

15


9.5 N 19 N 28 N 47N

Lithium Metatitanate pebble- Plastic strain

16


9.5 N 19 N 28 N 47N

Lithium Metatitanate pebble- Von Mises stress

17


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.00 0.05 0.10 0.15 0.20

strain

vert

ical

str

ess

(- M

Pa)

d=0.5 mm

d=0.1 mm

d=0.0125 mm

18


Collapse of the pebble

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006

pebble

cracking in 1st princ. direction

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006

pebble

cracking in 2d princ. direction

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006

pebble

crushed point

Cracking in the 1st principal direction

Cracking in the 2nd principal direction

Integration points in which the plastic strain reaches the crushing strain

19


NUMERICAL SIMULATION OF AN OEDOMETER TEST ON LITHIUM ORTOSILICATE PEBBLE BED WITH AN

HOMOGENEOUS MODEL

Material model : Modified Cam-clay model of Roscoe and Burland

The main parameters of the Cam-clay model are the following:

- - M, the slope of the critical state line

- - pc , preconsolidation pressure ( a stress-like hardening variable)

- - K, the slope of the over consolidation lines

- λ, the slope of the normal consolidation line.

20


Modified Cam-clay model of Roscoe and Burland

Main relations :-elastic stress-strain law: non linear elastic law - bulk modulus function of the hydrostatic pressure, p : K=pν/k

- f(σ,pc )=q2/M2+p(p-pc)=0

- Yield criterion

q=Mp

-isotropic compression constitutive relations- elastic range : ν= νp -kln(p/po)

-elasto-plastic range: ν= νco - λln(p/pco )

ν=V/Vs specific volume

V=current soil volume, Vs, volume of the solid phase

21


A good agreement between the experimental curve and numerical one was obtained assuming the following values for the four parameters :

M=0.5; K=0.002; λ=0.006; pc = 0.9 MPa.Sensitivity analysis for the four parameters

M=0.5 - k=2e-3 - pc=0.9 MPa

0.E+00

1.E+04

2.E+04

3.E+04

4.E+04

5.E+04

6.E+04

0.00 0.10 0.20 0.30 0.40

displacement (mm)

load

(N)

lbd=5e-3

lbd=6e-3

exp.results

lbd=6.5e-3

– Influence of the parameter λ

M=0.5 - k=2e-3 lbd=6e-3

0.E+00

1.E+04

2.E+04

3.E+04

4.E+04

5.E+04

6.E+04

0.00 0.10 0.20 0.30 0.40

displacement (mm)

load

(N)

pc=0.9MPa

exp.results

pc=2 MPa

pc=0.7 MPa

Influence of the parameter pc

22


lambda=6e-3 - k=1e-3 - pc=0.9 MPa

0

10000

20000

30000

40000

50000

60000

0 0.1 0.2 0.3 0.4

displacement (mm)

load

(N)

exper. results

M=0.5

M=0.8

M=1.5

M=0.5 -lbd=6e-3-pc=0.9 MPa

0

10000

20000

30000

40000

50000

60000

0.00 0.10 0.20 0.30 0.40

displacement (mm)

load

(N)

exp.results

k=3e-3

k=2e-3

k=0.5e-3

Sensitivity analysis for the four parameters

Influence of the parameter k Influence of the parameter M

23


Conclusion

- The compression tests on single pebbles permitted to estimate the fracture load of Lithium-Metatitanate pebbles (1.1-1.3 mm of diameter) and of Lithium-Orthosilicate pebbles (0.55-0.6 mm of diameter).

- The numerical simulations of the pebble compression give results which agree very well with the experimental ones assuming values of the material characteristics different from those found in the technical literature for these materials. the mechanical characteristics of ceramic materials depend strongly on the production technology.

24


Conclusion

- with an homogeneous model developed for soil , choosing appropriate values for the several constants it is possible to fit the experimental curves,

- the physical meaning of the parameter values are not immediately extrapolate to the pebble bed

.

experimental and theoretical characterization of li2 tio3 and ......n) i cycle ii cycle iii cycle...

Documents