Effects of Material Properties on Cratering

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Effects of Material Properties on Cratering
Kevin Housen The Boeing Co. MS 2T-50 P.O. Box
3999 Seattle, WA 98124
Impact Cratering Bridging the Gap between
Modeling and Observation Lunar Planetary
Institute, Houston, TX Feb. 7-9, 2003
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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

3
Sources of information

• Laboratory experiments
• impact cratering
• material property characterization
• Field explosion tests
• Code calculations
• CSQ, CTH, SOVA, SALE, SPH, DYNA
• Scaling

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Simple scaling model
Crater size F impactor prop, target
prop, env. prop.
V F aUmdn, r, Y, g
Strength-regime
-3m/2
r
1-3n
(
)
Y
)
(

µ
d
rU2
ga/U2

5
Cratering in metals
Regression gives n0.4, m0.5
Ref Holsapple and Schmidt (1982) JGR, 87,
1849-1870.
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Simple scaling model
Crater size F impactor prop, target
prop, env. prop.
V F aUmdn, r, Y, g
Strength-regime
-3m/2
r
1-3n
(
)
Y
)
(

µ
d
rU2
ga/U2

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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.

8
Rock at small scale
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Crater somewhat larger than joint spacing
10 m
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Crater is large compared to joint spacing
70 m
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Dynamic strength measurements
Lange Ahrens (1983)
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Rate dependent Mohr-Coulomb model
s c sN tan(f)
Cohesion is rate dependent for wet soils, but not
for dry.
tan(f)
Shear stress
Friction angle insensitive to loading rate
cohesion
c
0
Normal stress, sN
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Porosity

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

70 porosity
Loose sand
Dense sand
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Rate-dependent Mohr-Coulomb model with porosity
Simple material pV constant
gravity-regime
pV
Rate dependent pV µ p29m/(2m-1-m)
p2
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Evidence of size effects in rock
Ref Schmidt (1980)
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Evidence for rate effects in soils
1 gm
103 gm
106 gm
109 gm
charge
Sand
pv
Gravity scaling
Alluvium
Playa Silty Clay
p2
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Strength-gravity transition
m is in the range of 6 to 12 for rock gravity
exponent ranges from -0.6 to -0.78
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Strength-gravity transition
Hard rock
Ice
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Damage from impact on Gaspra-size body
Grady-Kipp
HH (2002)
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Rate-dependent Mohr-Coulomb model with porosity
pV
p2
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Friction angle, porosity and density
porosity 1 -
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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-
• pV f( p2 , r/d , porosity, friction angle)
• Dependence on r can be found by varying d, while
  holding all else constant.

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Expected dependence on target density

• Impact data for metals n0.4
• For sand, m0.4
• Density exponent (2 0.4 - 2.4)/2.4 0
• Cratering efficiency is independent of target
  density (and projectile density) at fixed p2

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Impacts in sand (Schmidt, 1980)
Tungsten Carb. (d14.8)
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Schultz Gault (1985)
Target density/projectile density has been varied
from 0.12 to 138, or a factor of 1200!
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• 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. Its not easy to separate
  these two effects, but we may not need to for
  most practical applications

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Friction angle effects for sand
24 sand f28
Flintshot sand f35
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Cohesionless material with a small friction
angle
Spherical grains f21-22 (Albert et
al, 1997)
Flintshot sand (f35)
f45? (e.g. JSC-1)
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Cohesionless material with a large friction angle
Flintshot sand
Shot 2nd time
pv
3rd shot
Glass plates
p2
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CTH calculations

• Series of calculations of a shallow-buried
  explosion (modeled Piekutowskis experiments)
• porous p-a model
• pressure-dependent yield surface, zero cohesion
• varied effective friction angle, all else constant

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CTH models with and without friction
Sailor Hat
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Effect of variations in friction angle
f20
CTH
Water f0
f28
pV
f35
f45?
Frac. glass
p2
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Friction angles for various materials

• Rock
• Gabbro 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

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Ice
Cohesion
Friction angle
Ref Fish and Zaretsky (1997) Ice strength as
a function of hydrostatic pressure and
temperature, CRREL Report 97-6.
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Practical range of friction angles
Water impact
Dry soil impact
pV
p2
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Field data for shallow explosions
Water impact
Dry soil impact
pV
p2
37
Effect of porosity
28
35
20
Water
45?
pV
44 porosity
p2
38
Effect of porosity
28
35
20
Water
45?
pV
44 porosity
72 porosity
p2
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Effect of porosity
28
35
20
Water
45?
Vermiculite (0.09 g/cm3) Schultz et al. 2002
pV
44 porosity
72 porosity
p2
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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) OKeefe et
  al (2001) Schultz et al (2002).

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Effect of porosity on cratering flow field
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Effect of porosity on cratering flow field
Low porositytargets
High   porosity      targets
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Shock propagation in rubble-piles
Petr V., et al. (2002)
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Effect of grain size on crater radius
Blasting sand (Cintala et al, 1999) di/dg
1.2 - 4.8
pR
Flintshot di/dg 6-37
F-140 sand di/dg 186
Banding sand di/dg 70
p2
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Three ways to help narrow the gap

• 1. Codes should be benchmarked
• OKeefe 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.

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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.

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Fracture of rock
Polansky Ahrens (1990)
Ahrens Rubin (1993)
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Fracture of rock
100 ton HE near surface explosion in rock
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Three ways to help narrow the gap

• 1. Codes should be benchmarked
• OKeefe 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.