Effects of Material Properties on Cratering

Kevin HousenThe Boeing Co.MS 2T-50P.O. Box 3999Seattle, WA 98124

Impact Cratering: Bridging the Gap between Modeling and ObservationLunar & Planetary Institute, Houston, TX Feb. 7-9, 2003

Which properties?

• There are many more material properties to consider than we can address.

• Constitutive behavior of geological materials is complex– rate-dependent brittle fracture– pressure dependent yield– dilatation– pore space compaction

• We need to pare the list down to a manageable number of dominant properties, e.g.– a measure of target strength– density– porosity

Sources of information

• Laboratory experiments– impact cratering– material property characterization

• Field explosion tests• Code calculations

– CSQ, CTH, SOVA, SALE, SPH, DYNA• Scaling

Simple scaling model

Crater size = F [ {impactor prop}, {target prop}, {env. prop.} ]

V = F [ aU, , Y, g ]

Strength-regime:

1-3 -3/2) ( )Y

U2(Vm

Vm

ga/U2

Gravity-regime:

-3/(2+)) ( )ga

U2(2+-6

2+Vm

Cratering in metals

Ref: Holsapple and Schmidt (1982) JGR, 87, 1849-1870.

Regression gives =0.4, =0.5

Simple scaling model

Crater size = F [ {impactor prop}, {target prop}, {env. prop.} ]

V = F [ aU, , Y, g ]

Strength-regime:

1-3 -3/2) ( )Y

U2(Vm

Vm

ga/U2

Gravity-regime:

-3/(2+)) ( )ga

U2(2+-6

2+Vm

Strength of geological materials

• Unlike metals, many geologic materials are not “simple”.

• The strength of rock, ice and some soils is known to be rate- and scale-dependent.

Rock at small scale

Crater somewhat larger than joint spacing

10 m

Crater is large compared to joint spacing

70 m

Dynamic strength measurements

Lange & Ahrens (1983)

Rate dependent Mohr-Coulomb model

Normal stress, N

She

ar s

tres

stan()

0

Friction angle insensitive to loading rate

Cohesion is rate dependent for wet soils, but not for dry.

c = c0 3/m. cohesionc

= c + N tan()

Porosity

• For highly porous materials (rubble piles), pore-space compaction is an important part of crater formation.

Max Pressure

2 km/s impact

0.0

0.2

0.4

0.6

0.8

1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10

Pressure (cgs)

PorosityDense sand

Loose sand

70% porosity

Rate-dependent Mohr-Coulomb model with porosity

V

gravity-regime:

Simple material:

V constant

2

Rate dependent:

V 29/(2m-1-)

Evidence of size effects in rock

Ref: Schmidt (1980)

Evidence for rate effects in soils

Sand

Alluvium

PlayaSilty Clay

v

2

1 gm 103 gm 106 gm 109 gm

Gravity scaling

10

100

1000

1.0E-08 1.0E-07 1.0E-06 1.0E-05 1.0E-04

charge

Strength-gravity transition

Rate-dependent strength:

c = c0 3/m.

Transition occurs when:

c0

g1-3/2m D1+3/2m= constant

D g(3-2m)/(3+2m)

m is in the range of ~6 to 12 for rockgravity exponent ranges from -0.6 to -0.78

Strength-gravity transition

Hard rock

Ice

Weak soil

Damage from impact on Gaspra-size body

Grady-Kipp H&H (2002)

V

2

Rate-dependent Mohr-Coulomb model with porosity

Gravity-regime:

-3/(2+)) ( )ga

U2(2+-6

2+Vm f (, n)

Friction angle, porosity and density

porosity = 1 -bulk densitygrain density

How to determine effect of target density

• Vary the density and grain density such that porosity etc are about constant:– porosity = 1 -

• A better way. In the gravity regime-– πV = f( π2 , /porosity, friction angle)– Dependence on can be found by varying ,

while holding all else constant.

bulk densitygrain density

Expected dependence on target density

• Impact data for metals: =0.4

• For sand, =0.4

• Density exponent = (2 + 0.4 - 2.4)/2.4 = 0

• Cratering efficiency is independent of target density (and projectile density) at fixed 2

Gravity-regime:

-3/(2+)) ( )ga

U2(2+-6

2+Vm f (, n)

Impacts in sand (Schmidt, 1980)

Tungsten Carb. (=14.8)

Lead --> sand (=11.4)

Al --> “Hevi-sand” (=3.1)

Schultz & Gault (1985)

Target density/projectile density has been varied from 0.12 to 138, or a factor of 1200!

• The good news. Cratering efficiency is independent of the target/impactor density ratio. Differences among materials must be due to friction angle or porosity.

• The not so bad news. It’s not easy to separate these two effects, but we may not need to for most practical applications

Friction angle effects for sand

#24 sand =28°

Flintshot sand =35°

Cohesionless material with a “small” friction angle

Flintshot sand (=35°)

Spherical grains =21-22° (Albert et al, 1997)

=45°? (e.g. JSC-1)

Cohesionless material with a large friction angle

v

2

Flintshot sand

Glass plates

Shot 2nd time

3rd shot

CTH calculations

• Series of calculations of a shallow-buried explosion (modeled Piekutowski’s experiments)– porous p- model

– pressure-dependent yield surface, zero cohesion

– varied effective friction angle, all else constant

-12

-10

-8

-6

-4

-2

0

2

4

-15 -10 -5 0 5 10 15

cm

cm

phi=87 (C53)

C63

phi=9 (C67)

phi=35 (C50)

phi=43 (C57)

~10°

25-35°

30-44°>44°

CTH models with and without friction

Sailor Hat

Effect of variations in friction angle

=20°

=28°=35°

Water =0°CTH

Frac. glass

πV

=45°?

π2

1

10

100

1,000

10,000

100,000

1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04

Friction angles for various materials

RockGabbro 10°-30°Shale 15°-30°Limestone 35°-50°Basalt 50°-55°Granite 45°-60°

“Soils”Mica powder (ordered) 16°Smooth spheres 21°-22°Lunar soil 25°-50°Sand 26°-46°Gravel 40°-50°Crushed glass 51°-53°Sand (low confining stress) ~70°

Ice

Ref: Fish and Zaretsky (1997) “Ice strength as a function of hydrostatic pressure and temperature”, CRREL Report 97-6.

Friction angleCohesion

Practical range of friction angles

1

10

100

1,000

10,000

1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03

pi2

piVV

2

Water impactDry soil impact

Field data for shallow explosions

Water impactDry soil impact

MPict, MScale

1

10

100

1,000

10,000

1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03

pi2

piV

Dry (d/a<=1.5)

V

2

Effect of porosity

1

10

100

1,000

10,000

100,000

1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04

pi2

piV

Water

πV

π2

20°

28°35°

45°?

44% porosity

1

10

100

1,000

10,000

100,000

1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04

pi2

piV

Effect of porosity

Water

πV

π2

20°

28°35°

45°?

44% porosity72% porosity

1

10

100

1,000

10,000

100,000

1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04

pi2

piV

Effect of porosity

Water

πV

π2

20°

28°35°

45°?

44% porosity72% porosity

Vermiculite (0.09 g/cm3)Schultz et al. 2002

Porosity is important

• Permanent compaction of target material• Increased heating/melting of target• Rapid decay of the shock pressure• Affects penetration and geometry of flow field• Increased crater depth/diameter ratio• Reduction or complete suppression of ejecta

Kieffer (1975); Cintala et al (1979); Love et al (1993); Asphaug et al (1998); Housen et al (1999); Stewart & Ahrens (1999); O’Keefe et al (2001); Schultz et al (2002).

Effect of porosity on cratering flow field

Effect of porosity on cratering flow field

Low porositytargets

High   porosity      targets

Shock propagation in rubble-piles

To what degree does the heterogeniety of the target (e.g. grain size) affect shock propagation, crater formation, ejecta?

Petr V., et al. (2002)

QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.

Menikoff (2001)Barnouin-Jha, Cintala and Crawford (2002)

QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.

Solid aluminum Aluminum balls

Effect of grain size on crater radius

π2

πR

Flintshot: di/dg = 6-37

Blasting sand: (Cintala et al, 1999)

di/dg = 1.2 - 4.8

Banding sand: di/dg = 70

F-140 sand: di/dg = 186

Three ways to help narrow the gap

1. Codes should be benchmarked– O’Keefe and Ahrens (1981): “The comparison of

impact cratering experiments with detailed calculations has to date, surprisingly, only been carried out in the case of metals and composite structures.”

Sources of benchmark data

• Large database of lab experiments– final crater size, shape– ejection velocities

• Quarter-space experiments– detailed motions of tracer particles– kinematics of crater growth

• Field tests– HE yields up to 4.4 kt, 90m crater dia.

Fracture of rockPolansky & Ahrens (1990)

Ahrens & Rubin (1993)

Fracture of rock100 ton HE near surface explosion in rock

Three ways to help narrow the gap

1. Codes should be benchmarked– O’Keefe and Ahrens (1981): “The comparison of impact

cratering experiments with detailed calculations has to date, surprisingly, only been carried out in the case of metals and composite structures.”

2. We need measurements of material properties– Triaxial or direct shear tests– Crushup curves (e.g. porosity vs pressure)– Unconfined compression/tension

3. Identify a standard suite of experimental data for benchmark calculations.