Effects of Material Properties on Cratering

1. 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

2. 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

4. Gravity-regime: rV rV m m -3m/(2+m) r ga ( ) ( ) µ d U2 rV m 2+m-6n 2+m 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 n=0.4, m=0.5 Ref: Holsapple and Schmidt (1982) JGR, 87, 1849-1870.

6. Gravity-regime: rV rV m m -3m/(2+m) r ga ( ) ( ) µ d U2 rV m 2+m-6n 2+m 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 †

7. 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

9. Crater somewhat larger than joint spacing 10 m

10. Crater is large compared to joint spacing 70 m

11. Dynamic strength measurements Lange & Ahrens (1983)

12. . c = c0 e3/m 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 c cohesion 0 Normal stress, sN

13. 2 km/s impact Max Pressure Porosity • For highly porous materials (rubble piles), pore-space compaction is an important part of crater formation. 70% porosity Loose sand Dense sand

14. Rate-dependent Mohr-Coulomb model with porosity Simple material: pV= constant gravity-regime: pV Rate dependent: pVµp29m/(2m-1-m) p2

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

16. Evidence for rate effects in soils 1 gm 103 gm 106 gm 109 gm charge Sand pv Gravity scaling Alluvium Playa Silty Clay p2

17. Rate-dependent strength: . c = c0 e3/m Transition occurs when: c0 = constant r g1-3/2m D1+3/2m D µg(3-2m)/(3+2m) Strength-gravity transition m is in the range of ~6 to 12 for rock gravity exponent ranges from -0.6 to -0.78

18. Weak soil Strength-gravity transition Hard rock Ice

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

20. Gravity-regime: rV -3m/(2+m) m r ga ( ) ( ) f (f, n) = d U2 2+m-6n 2+m Rate-dependent Mohr-Coulomb model with porosity pV p2

21. bulk density grain density Friction angle, porosity and density porosity = 1 -

22. 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- • πV = f( π2 , r/d , porosity, friction angle) • Dependence on r can be found by varying d, while holding all else constant.

23. Gravity-regime: rV -3m/(2+m) m r ga ( ) ( ) f (f, n) = d U2 2+m-6n 2+m Expected dependence on target density • 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

24. Al --> “Hevi-sand” (r=3.1) Lead --> sand (d=11.4) Impacts in sand (Schmidt, 1980) Tungsten Carb. (d=14.8)

25. Schultz & Gault (1985) Target density/projectile density has been varied from 0.12 to 138, or a factor of 1200!

26. 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

27. Friction angle effects for sand #24 sand f=28° Flintshot sand f=35°

28. Cohesionless material with a “small” friction angle Spherical grains f=21-22° (Albert et al, 1997) Flintshot sand (f=35°) f=45°? (e.g. JSC-1)

29. Cohesionless material with a large friction angle Flintshot sand Shot 2nd time pv 3rd shot Glass plates p2

30. 30-44° >44° 25-35° ~10° 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

31. CTH models with and without friction Sailor Hat

32. Effect of variations in friction angle f=20° CTH Water f=0° f=28° πV f=35° f=45°? Frac. glass π2

33. 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°

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

35. Practical range of friction angles Water impact Dry soil impact pV p2

36. Field data for shallow explosions Water impact Dry soil impact pV p2

37. Effect of porosity 28° 35° 20° Water 45°? πV 44% porosity π2

38. Effect of porosity 28° 35° 20° Water 45°? πV 44% porosity 72% porosity π2

39. Effect of porosity 28° 35° 20° Water 45°? Vermiculite (0.09 g/cm3) Schultz et al. 2002 πV 44% porosity 72% porosity π2

40. 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).

41. Effect of porosity on cratering flow field

42. Effect of porosity on cratering flow field Low porositytargets High   porosity      targets

43. To what degree does the heterogeniety of the target (e.g. grain size) affect shock propagation, crater formation, ejecta? Menikoff (2001) Barnouin-Jha, Cintala and Crawford (2002) Aluminum balls Solid aluminum Shock propagation in rubble-piles Petr V., et al. (2002)

44. Effect of grain size on crater radius Blasting sand: (Cintala et al, 1999) di/dg = 1.2 - 4.8 πR Flintshot: di/dg = 6-37 F-140 sand: di/dg = 186 Banding sand: di/dg = 70 π2

45. 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.”

46. 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.

47. Fracture of rock Polansky & Ahrens (1990) Ahrens & Rubin (1993)

48. Fracture of rock 100 ton HE near surface explosion in rock

49. 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.