effects of material properties on cratering kevin housen the boeing co. ms 2t-50 p.o. box 3999...
TRANSCRIPT
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.