Transcript Document

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
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 [ aUmdn,
r, Y,
Strength-regime:
g ]
Gravity-regime:
r 2+m-6n
rV
ga -3m/(2+m)
2+m
m  (d )
U2
r 1-3n Y -3m/2
rV
(rU2)
m  d
( )
( )
rV
m
ga/U2
Cratering in metals
Regression gives n=0.4, m=0.5
Ref: Holsapple and Schmidt (1982) JGR, 87, 1849-1870.
Simple scaling model
Crater size = F [ {impactor prop}, {target prop}, {env. prop.} ]
V = F [ aUmdn,
r, Y,
Strength-regime:
g ]
Gravity-regime:
r 2+m-6n
rV
ga -3m/(2+m)
2+m
m  (d )
U2
r 1-3n Y -3m/2
rV
(rU2)
m  d
( )
( )
rV
m
ga/U2
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
Cohesion is rate
dependent for
wet soils, but
not for dry.
.
c = c0 e3/m
Shear stress
s = c + sN tan(f)
c cohesion
0
Friction angle
insensitive to
loading rate
Normal stress, sN
Porosity
• For highly porous materials (rubble piles),
pore-space compaction is an important part
of crater formation.
0.8
2 km/s impact
70% porosity
Porosity
0.6
Loose sand
0.4
Dense sand
0.2
Max Pressure
0.0
1.E+05
1.E+06
1.E+07
1.E+08
Pressure (cgs)
1.E+09
1.E+10
Rate-dependent Mohr-Coulomb model with porosity
Simple material:
pV = constant
gravity-regime:
pV
Rate dependent:
pV  p29m/(2m-1-m)
p2
Evidence of size effects in rock
Ref: Schmidt (1980)
Evidence for rate effects in soils
1000
1 gm
103 gm
106 gm
109 gm
charge
Sand
pv
100
Gravity
scaling
Alluvium
Playa
Silty Clay
10
1.0E-08
1.0E-07
1.0E-06
p2
1.0E-05
1.0E-04
Strength-gravity transition
Rate-dependent strength:
.
c = c0 e3/m
Transition occurs when:
c0
r g1-3/2m D1+3/2m
= constant
D  g(3-2m)/(3+2m)
m is in the range of ~6 to 12 for rock
gravity exponent ranges from -0.6 to -0.78
Strength-gravity transition
Damage from impact on Gaspra-size body
Grady-Kipp
H&H (2002)
Rate-dependent Mohr-Coulomb model with porosity
Gravity-regime:
rV
m =
pV
p2
r 2+m-6n
ga -3m/(2+m)
2+m
f (f, n)
( d ) ( U2
)
Friction angle, porosity and density
porosity = 1 -
bulk density
grain density
How to determine effect of target density
• Vary the density and grain density such that
porosity etc are about constant:
bulk density
– porosity = 1 - grain
density
• A better way. In the gravity regime– πV = f( π2 , r/d , porosity, friction angle)
– Dependence on r can be found by varying d,
while holding all else constant.
Expected dependence on target density
Gravity-regime:
rV
m =
r 2+m-6n
ga -3m/(2+m)
2+m
f (f, n)
( d ) ( U2 )
• Impact data for metals: n=0.4
• For sand, m=0.4
• Density exponent = (2 + 0.4 - 2.4)/2.4 = 0
• Cratering efficiency is independent of target
density (and projectile density) at fixed p2
Impacts in sand (Schmidt, 1980)
Al --> “Hevi-sand”
(r=3.1)
Tungsten Carb.
(d=14.8)
Lead --> sand
(d=11.4)
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
f=28°
Flintshot sand
f=35°
Cohesionless material with a “small” friction angle
Spherical grains
f=21-22° (Albert et al, 1997)
f=45°? (e.g. JSC-1)
Cohesionless material with a large friction angle
10000
1000
Shot 2nd time
pv
100
3rd shot
10
Glass plates
1
1.0E-09
1.0E-08
1.0E-07
p2
1.0E-06
1.0E-05
1.0E-04
CTH calculations
• Series of calculations of a shallow-buried explosion
(modeled Piekutowski’s experiments)
– porous p-a model
– pressure-dependent yield surface, zero cohesion
– varied effective friction angle, all else constant
4
2
0
-10
cm
-15
-5
-2
30-44°
>44°
0
5
10
-4
25-35°
-6
phi=87 (C53)
C63
phi=9 (C67)
phi=35 (C50)
phi=43 (C57)
-8
~10°
-10
-12
cm
15
CTH models with and without friction
Sailor Hat
Effect of variations in friction angle
100,000
CTH
10,000
1,000
πV
100
Frac.
glass
10
1
1.E-11
1.E-10
1.E-09
1.E-08
π2
1.E-07
1.E-06
1.E-05
1.E-04
Friction angles for various materials
Rock
Gabbro
Shale
Limestone
Basalt
Granite
“Soils”
Mica powder (ordered)
Smooth spheres
Lunar soil
Sand
Gravel
Crushed glass
Sand (low confining stress)
10°-30°
15°-30°
35°-50°
50°-55°
45°-60°
16°
21°-22°
25°-50°
26°-46°
40°-50°
51°-53°
~70°
Ice
Cohesion
Friction angle
Ref: Fish and Zaretsky (1997) “Ice strength as a function of hydrostatic pressure
and temperature”, CRREL Report 97-6.
Practical range of friction angles
10,000
1,000
piV
pV
100
10
1
1.E-08
1.E-07
1.E-06
ppi2
2
1.E-05
1.E-04
1.E-03
Field data for shallow explosions
10,000
1,000
piV
pV
100
MPict,
MScale
10
Dry (d/a<=1.5)
1
1.E-08
1.E-07
1.E-06
ppi2
2
1.E-05
1.E-04
1.E-03
Effect of porosity
100,000
10,000
1,000
piV
πV
44% porosity
100
10
1
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
πpi22
1.E-06
1.E-05
1.E-04
Effect of porosity
100,000
10,000
1,000
piV
πV
44% porosity
72% porosity
100
10
1
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
πpi22
1.E-06
1.E-05
1.E-04
Effect of porosity
100,000
10,000
1,000
piV
πV
Vermiculite
(0.09 g/cm3)
Schultz et al. 2002
44% porosity
72% porosity
100
10
1
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
πpi22
1.E-06
1.E-05
1.E-04
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
porosity
targets
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)
Menikoff (2001)
Barnouin-Jha, Cintala and Crawford (2002)
Quic kT ime™ and a T IFF (LZW) decompress or are needed to see this pic ture.
Solid aluminum
QuickTime™ and a TIFF (LZW) decompressor are needed to see this pi cture.
Quic kT ime™ and a T IFF (LZW) decompress or are needed to see this pic ture.
Aluminum balls
Effect of grain size on crater radius
100
Blasting sand:
(Cintala et al, 1999)
di/dg = 1.2 - 4.8
πR
10
Flintshot:
di/dg = 6-37
F-140 sand:
di/dg = 186
Banding sand:
di/dg = 70
1
1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04
π2
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 rock
Polansky & Ahrens (1990)
Ahrens & Rubin (1993)
Fracture of rock
100 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.