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)