Effects of Material Properties on Cratering Kevin Housen The Boeing Co. MS 2T-50 P.O. Box 3999 Seattle, WA 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 [ aU  , , Y, g ]  Strength-regime:     /2 ) ( ) Y U2U2 ( VV m VV m ga/U 2 Gravity-regime:    -3  /(2+  ) ) ( ) ga U2U2 ( 2+   VV m

Cratering in metals Ref: Holsapple and Schmidt (1982) JGR, 87, 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:     /2 ) ( ) Y U2U2 ( VV m VV m ga/U 2 Gravity-regime:    -3  /(2+  ) ) ( ) ga U2U2 ( 2+   VV m

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 Shear stress tan(  ) 0 Friction angle insensitive to loading rate Cohesion is rate dependent for wet soils, but not for dry. c = c 0  3/m. cohesion c  = 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 Dense sand Loose sand 70% porosity

Rate-dependent Mohr-Coulomb model with porosity VV gravity-regime: Simple material:  V  constant 22 Rate dependent:  V   2 9  /(2m-1-  )

Evidence of size effects in rock Ref: Schmidt (1980)

Evidence for rate effects in soils Sand Alluvium Playa Silty Clay vv 22 1 gm 10 3 gm 10 6 gm10 9 gm Gravity scaling charge

Strength-gravity transition Rate-dependent strength: c = c 0  3/m. Transition occurs when: c0c0  g 1-3/2m D 1+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 Hard rock Ice Weak soil

Damage from impact on Gaspra-size body Grady-Kipp H&H (2002)

VV 22 Rate-dependent Mohr-Coulomb model with porosity Gravity-regime:    -3  /(2+  ) ) ( ) ga U2U2 ( 2+   VV m f ( , n)

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: –porosity = 1 - A better way. In the gravity regime- –π V = f( π 2,  /  porosity, friction angle) –Dependence on  can be found by varying , while holding all else constant. bulk density grain density

Expected dependence on target density Impact data for metals: =0.4 For sand,  =0.4 Density exponent = ( )/2.4 = 0 Cratering efficiency is independent of target density (and projectile density) at fixed  2 Gravity-regime:    -3  /(2+  ) ) ( ) ga U2U2 ( 2+   VV m 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v 22 Flintshot sand Glass plates Shot 2 nd time 3 rd 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 ~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 πVπV  =45°? π2π2

Friction angles for various materials Rock Gabbro10°-30° Shale15°-30° Limestone35°-50° Basalt50°-55° Granite45°-60° “Soils” Mica powder (ordered)16° Smooth spheres21°-22° Lunar soil25°-50° Sand 26°-46° Gravel40°-50° Crushed glass51°-53° Sand (low confining stress)~70°

Ice Ref: Fish and Zaretsky (1997) “Ice strength as a function of hydrostatic pressure and temperature”, CRREL Report Friction angle Cohesion

Practical range of friction angles VV 22 Water impact Dry soil impact

Field data for shallow explosions Water impact Dry soil impact VV 22

Effect of porosity Water πVπV π2π2 20° 28° 35° 45°? 44% porosity

Effect of porosity Water πVπV π2π2 20° 28° 35° 45°? 44% porosity 72% porosity

Effect of porosity Water πVπV π2π2 20° 28° 35° 45°? 44% porosity 72% porosity Vermiculite (0.09 g/cm 3 ) 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

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) Solid aluminum Aluminum balls

Effect of grain size on crater radius π2π2 πRπR Flintshot: d i /d g = 6-37 Blasting sand: (Cintala et al, 1999) d i /d g = Banding sand: d i /d g = 70 F-140 sand: d i /d g = 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 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.