crush curve measurements of porous materials used for...
TRANSCRIPT
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
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:
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)
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%
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
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
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
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)
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.
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
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
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
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
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
( )( )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
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.
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
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
○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
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)
�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
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
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.
α
compressivestrength
plastic deformation
elastic deformation
Pres
sure
α0
α
compressivestrength
plastic deformati
elastic deforma
Pres
sure
1
0.1
1
10
100
1000
104
105
1 10
BD
Density (g/cm3)
Pres
sure
in M
Pa
sintered glass beads
0.1
1
10
100
1000
104
105
0.1 1 10 100
pumice
BDF
Pres
sure
in M
Pa
Density (g/cm3)