Crush Curve Measurements of Porous Materials Used for...
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Crush Curve Measurements of Porous Materials Used for Laboratory Impact Experiments
Kensuke Hiraoka and Akiko M. Nakamura
(Kobe University)
VII WORKSHOP ON CATASTROPHIC DISRUPTION IN THE SOLAR SYSTEM
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Introduction
• powders (sands, glass beads etc.) --- no tensile strength
• porous solids (sintered materials, gypsum, pumice etc.) ---�������These objects have tensile strength. �������Sintered materials are maybe good analogues for the icy bodies.
Various porous materials are used in laboratory impact experiments.
JAXA/ISAS
Porous structure has been found to be common among small bodies in the solar system.
Itokawa: porosity = ~ 40% (Abe et al., 2006)
Wild 2: 30~60% (lower limit)(Davidsson & Gutiérrez, 2005)
Tempel 1: 50~88%(Davidsson et al., 2006)
asteroids: 0~70% (Britt et al., 2002)
porosity:
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Previous impact experiments on porous materialLaboratory impact experiments at elevated acceleration (500g)
to simulate large impact cratering in low gravity
(Housen et al., 1999; Housen & Holsapple, 2003)
Crater made by compactionrather than ejection
Compaction is a main process of the cratering on highly porous materials
(target initial porosity�60%)
The response of highly porous materials to compaction should be quantitatively investigated.
Introduction
Housen et al. (1999)
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Hugoniot of porous material
The approximation by Mie-Grüneisen equationvalid only for high pressure
Dynamic compaction of porous silica powder (Borg et al., 2005)
porosity: ~60%
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To study the response of porous materialsto the compaction
Purpose of this work
�crush curve measurements of porous materials which used for impact experiments��� measure stress-strain curves��� dependence of crush curves on the target properties
�crush curve is well studied for porous metal, ceramics powders and SiO2 powders��� Is there any difference between powders and solids?
P-α model (Herrmann, 1969)Simple model describes a compaction of porous materials
ρ s : solid material density ρ : porous material densityP : pressurePs : solid pressurePe : elastic pressure
1 ( )1
s F Pporosity
ραρ
= = =−
F(P) is the parameter for modeling of impacts in porous materials (Juzti, 2004)
Herrmann, 1969
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Samples
pumiceporosity = 79+/-2%compressive strength = 5.1MPa
sintered soda lime glass beadsporosity = 39 +/- 2%compressive strength = 10MPa
gypsumporosity = 42 +/- 1%compressive strength = 14MPa
hollow glass beads (boro silica glass)macro porosity = 87 +/- 2%micro porosity ~ 82%
aluminaporosity = 91+/-1%particle strength ~ GPa
soda lime glass beadsporosity = 39+/-2%particle strength ~ 850MPa
~50µm
10~80µm ~50µm
~µm“porous solids”
“powders”
maximum particle size: 0.1µm
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Measurements
• by compression testing machine (Maximum=10 kN)
• loading rate =0.06 mm/min (or 6 mm/min)
• sample diameter=9.95 mm, height=6~12 mm
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Results
head speed=0.06mm/min
0.1
1
10
100
1000
1 10
pumicegypsumsintered glass beadsglass beadshollow beadsalumina
Pres
sure
in M
Pa
α (= solid density/porous density)
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Normalized by initial α
Pres
sure
in M
Pa
α/α0
pumicegypsumsintered glass beadsglass beadshollow beadsalumina
0.1
1
10
100
0.1 1
The crush curve depends on initial target porosity, and the component strength.
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Normalized by uniaxial compressive strength
pumicegypsumsintered glass beads
Pres
sure
/com
pres
sive
stre
ngth
α (= solid density/porous density)
0.01
0.1
1
10
100
1 2 3 4 5
almost elastic deformation
plastic deformation
pumicegypsumsintered glass beads
Pres
sure
/com
pres
sive
stre
ngth
α (= solid density/porous density)
0.01
0.1
1
10
100
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
almost elastic deformation
plastic deformation
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Effect of the strain rate
red���~ 106s-1
blue���~ 10-5s-1
Compaction of ceramics powder(Vogler et al., 2007)
The strength of brittle material increases with a strain rate.
• Strain rate dependence of crush curve
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Results (pumice and glass beads)Pr
essu
re in
MPa
α (= solid density/porous density)
1
10
100
1 2 3 4 5 6
6mm/min6mm/min0.06mm/min0.06mm/min
No apparent rate dependence effect.
1
10
100
1000
1.4 1.5 1.6 1.7
Pres
sure
in M
Paα (= solid density/porous density)
sintered glass beads (0.06mm/min)glass beads (0.06mm/min)sintered glass beads (6mm/min)glass beads (6mm/min)
There is no distinguished difference between each loading rate.Relocation is probably a dominant process.
pumice glass beads
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Results (gypsum)
After the first disruption, the pressure of higher strain rate is larger than that of lower strain rate.�These difference probably show the strain rate dependence of the gypsum sample.
Pres
sure
in M
Pa
α (= solid density/porous density)
1
10
100
1.2 1.3 1.4 1.5 1.6 1.7 1.8
6mm/min6mm/min0.06mm/min0.06mm/min
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Summary and future work
We measured crush curves of porous materials.
� Crush curve highly depends on the initial porosity of sample.� There is the strain rate dependence for gypsum.
• quantitatively discussion about the dependence of crush curve on the target property
• to describe the path from the compression state
• discussion about the difference between static and dynamic compression
• to measure the lateral pressure and describe the stress state accurately
Future Work
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( )( )VV
VVPP H −−
−−= *
0
0
22
ργργ
E: internal energy of porous material EH: internal energy of dense materialP: pressure of porous material PH: pressure of dense materialV0: initial specific volume of dense materialV0*: initial specific volume of porous materialV: compacted specific volume (=1/ρ)γ: Grüneisen parameter
(McQueen et al., 1970)
From Mie-Grüneisen equation,
Mie-Grüneisen equation,
Mie-Grüneisen equation
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Hugoniot of porous material
( )( )VV
VVPP H −−
−−= *
0
0
22
ργργ
P: pressure of porous material PH: pressure of dense materialV0: initial specific volume of dense materialV0*: initial specific volume of porous materialV: compacted specific volume (=1/ρ)γ: Grüneisen parameter(McQueen et al., 1970)
From Mie-Grüneisen equation,
Dynamic compaction of porous silica powder (Borg et al., 2005)
porosity = 65%
�This approximation is only valid for high pressure.
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0.1
1
10
100
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pres
sure
/com
pres
sive
stre
ngth
α/α0
pumicegypsumsintered glass beads
Normalized by uniaxial compressive strength
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Plastic deformation starts over 1 of vertical axis.(This plastic deformation is caused by a disruption of sintering neck, not of glass bead particles.)
↓Porosity is only slightly decreasing with pressure. The change of the slope is similar to that of gypsum.
Normalized by uniaxial compressive strength
pumicegypsumsintered glass beads
Pres
sure
/com
pres
sive
stre
ngth
α (= solid density/porous density)
0.01
0.1
1
10
100
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
elastic deformation
plastic deformation
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○0.06mm/min�8~16×10-5s-1
pumice: 5.1±0.2MPagypsum: 20.1±0.6MPas-glass beads: 12.0±0.1MPa
pumice: 4.1±2.0MPagypsum: 19±2MPas-glass beads: 12±2MPa
○6mm/min�8~16×10-3s-1
Uniaxial compressive strength
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0.01
0.1
1
10
100
1000
2 4 6 8 10
0.06mm/min6mm/min
Pres
sure
in M
Pa
α (= solid density/porous density)
Results (hollow beads)
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�GPa91±1%0.1µmpowderalumina
�850MPa39±2%�50µmpowdersoda lime glass beads
10MPa39±2%�50µmsolidsintered soda lime glass beads
5.1MPa79±2%solidpumice
87±2%10�80µmpowderhollow glass beads(boro silica glass)
uniaxial compressive
strength
initial porositygrain sizeconditionsample
14MPa50±1%�µmsolidgypsum
Experiments
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Future work
�quantitatively discussion about the dependence of crush curve on the target property
�to describe the path from the compression state
�discussion about the difference between static and dynamic compression
�to measure the lateral pressure and describe the stress state accurately
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Results (sintered glass beads)
1
10
100
1000
1.4 1.5 1.6 1.7
Pres
sure
in M
Pa
α (= solid density/porous density)
sintered glass beads (0.06mm/min)glass beads (0.06mm/min)sintered glass beads (6mm/min)glass beads (6mm/min)
There is no distinguished difference between each loading rate.
↓This shows that a relocation is probably a dominant process.
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α
compressivestrength
plastic deformation
elastic deformation
Pres
sure
α0
α
compressivestrength
plastic deformati
elastic deforma
Pres
sure
1
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0.1
1
10
100
1000
104
105
1 10
BD
Density (g/cm3)
Pres
sure
in M
Pa
sintered glass beads
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0.1
1
10
100
1000
104
105
0.1 1 10 100
pumice
BDF
Pres
sure
in M
Pa
Density (g/cm3)