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Impact Calculations A Review and Assessment

Impact Calculations A Review and Assessment. K. A. Holsapple University of Washington, 352400 Seattle, WA 98195 holsapple@aa.washington.edu. Part 1: Introduction. Rocks: A Modeling Challenge. Part 1: Introduction.

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Impact Calculations A Review and Assessment

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  1. Impact Calculations A Review and Assessment K. A. Holsapple University of Washington, 352400 Seattle, WA 98195 holsapple@aa.washington.edu

  2. Part 1: Introduction Rocks:A Modeling Challenge

  3. Part 1: Introduction The modeling of material behavior is the biggest shortcoming in code calculations, and the primary reason for bad results..

  4. Part 1: Introduction What I won’t talk about, but are important: Eulerian v. Lagangian codes Handling Mixtures in Eulerian codes Boundaries in Eulerian codes Grid distortion in Lagrangian N-body codes: Limited material behavior: simple coefficient of restitution Large-scale macro-porosity: cannot smear into a continuum

  5. Part 1: Introduction Energy Limit Water Wet sand and rocks Dry Sand But, there is lots of data, and it is consistent if organized in appropriate ways..

  6. Part 1: Introduction And, while much of it is for explosions, Impacts and Explosions are (almost) the same…

  7. Part 1: Introduction The Siren of CPU Power!

  8. Part 1: Introduction Understanding the processes:Regions of Impact Processes r ~0-> a: Coupling of the energy and momentum of the impactor into the asteroid 2. r ~ a -> 2a: Transition into point source solution, shock breakaway. 3a. r ~ 2a ->†¥ : Shock decays with distance, strength (and gravity) become important 3b. r ~ 5a -> 15a: Crater boundary, depending on problem

  9. Part 1: Introduction What do we need? • Balance Laws (easy: continuum mechanics: balance of mass, momentum, energy) • Material behavior (very hard: 100 Mbar down to partial bars!) • Robust computer codes

  10. Part 1: Introduction Single species EOS e(P, r) Single species EOS e(P, r) Mixture Theory (including porosity) Stress-Strain Equations Yield Flow & Failure Fracture Yield surface, Flow rule Fracture Criteria Material Behavior: Three regimes EOS P>>r c2 Solids P~r c2 Flow, fracture, failure P<<r c2

  11. Part 2: Source region, EOS Region 1: Source Coupling • Other Names: • Penetration region • Contact and Compression region • Coupling region • Early-time region • Isobaric Core region • Characteristics • High Pressure >> c^2 • => Hydrodynamic • => Primarily determined by EOS In this regime, the energy and momentum of the impactor are transferred into the target.

  12. Single species EOS e(P, r) Single species EOS e(P, r) Mixture Theory (including porosity) This is the bailiwick of the EOS.. EOS P>>r c2

  13. Part 2: Source region, EOS • It is the EOS that determines the initial high-pressure response, including: • The Maximum Initial Pressure • The Transition into the Point-Source field • The exponent m of that point source • The source effect on all subsequent scaling

  14. Part 2: Source region, EOS 1. Max Pressure=r0[(c0 /2)U+(s/4)U2] 2. Transition to a Point-Source Solution 3. If P>>r0c2, The Point-Source is Self-Similar and Power-Law Stress Waves: Pressure Decay PROPERTIES: 4. But every impact velocity case approaches a Point-Source Solution (but not self-similar)

  15. Part 2: Source region, EOS And, pressure decay is problem dependent:Pressures decay much faster in a porous material, the point source has m~1/3, P~r-6

  16. Part 2: Source region, EOS Point-Source Impacts • Initially, the flow field depends on all three of the impactor measures: • radius a, velocity U and mass density r • However, soon all signatures of those disappear, and there remains but a single measure of the impactor: • aUmdn Then all aspects of the process can depend only on aUmdn and not separately on the three measures..

  17. Part 2: Source region, EOS Scaled Pressure Decay All Velocity Cases in a given material approach the same Point-Source Solution after a few impactor radii Thus, there is no signature of the impact velocity except in the source region r<2a

  18. Part 2: Source region, EOS EOS => EOS • Different sources have the same far-field results whenever the point-source property holds! • The EOS determines the EOS: The Equation Of State determines Equivalence Of Sources

  19. Part 2: Source region, EOS Depends on: U=5 km/s Mass=1010 kg U=30 km/s Mass=5 108 kg U=50 km/s Mass=2.2 108 kg TNT Q=4.2 1010 Mass=2.4 1010 (24 Mtons) “Equivalent” Sources: mass x Q0.82

  20. Part 2: Source region, EOS So, what do we need to define the EOS? • 1. Equations of State for solid • 2. + modified by mixtures • 3. + modified by Porosity

  21. Part 2: Source region, EOS Analytical Single-phase EOS Models • Murnaghan: Non-linear elastic, no thermodynamics, limited uses. • Tillotson (1962): Powers in density + thermal component~E + vapor interpolation • Mie-Gruneisen: Linear Us-up + thermalcomponent~E + vapor interpolation • Puff (1966): vapor Simple algebraic descriptions, no phase changes

  22. Part 2: Source region, EOS Analytical, Explicit Three-Phase • Gray (1971), ESA, Philco-Ford (1969), Barnes et al. (1967 and on) • Aneos (1970) solid, liquid, vapor • No molecules, no mixture theory, limited solid phase changes • Panda (1981+) Various combinations of cold, thermal, electron and multi-phase models • Allows mixtures of molecular species, multiple phases

  23. Part 2: Source region, EOS Complete Equations of State E(r,P)(Cold+Thermal+Electron components) Electrons T h e r m a l C o m p o n e n t| <<--Cold Component-->>

  24. Part 2: Source region, EOS Loading along the Hugoniot from shock measurements, but usually not energy or temperature directly. U<10km/s. 2. Maybe some data on adiabats from shock unloading. 3. Static melt and vapor points at atmospheric pressure. 5. The critical point. What properties are sometimes available for calibration?? 4. Other data at one bar such as specific heat, thermal expansion.

  25. Part 2: Source region, EOS Porosity Addition..solid + voids • Herrmann’s P-alpha (1969) • Carroll-Holt (1972) • Seaman and Linde POREQST (1969) • Holt et al. (1971)

  26. Part 2: Source region, EOS Herrmann’s P-alpha • Distension ratioa=rsolid/rtotal • ranges from r0 (initial) to (fully crushed) • A crush curve defines crushing: decrease of the void volume: • a=f(P,Pe,Ps) • Instantaneous state variable • P(r, T,a)= Psolid(rsolid,T)/a • e(r,T,a)= esolid(rsolid,T) Ps Pe

  27. Part 2: Source region, EOS Crush curves for porous Sands: Crush begins at Pe, complete at Ps (From Kevin Housen)

  28. Part 2: Source region, EOS The P-Alpha model Pe=1e7 Ps=2e9: Crush is limited to one decade! You don’t always get what you think!!

  29. Part 2: Source region, EOS Furthermore: The actual path followed in CTH with Ps=20 mpa P=85 mpa You don’t always get even what you think you didn’t get!!

  30. Part 2: Source region, EOS Finally, supposing we have a reasonable EOS, how do we use it in Wave Codes? • Direct analytical evaluation, or.. • Tabular Data Tables (Sesame) • We have Sesame tables from Panda, Aneos, Seslan (Los Alamos) and others

  31. Part 2: Source region, EOS Summary of EOS • The model choice will fix the scaling and other important features of a solution • The tools are there for complex models, but it is very hard to get the data to calibrate the models, even for “simple” ones like Aneos (24 constants) • I think many users are unaware of the major uncertainties: the very existence of a pre-existing model gives it unwarranted credibility • It is Extremely complex to construct a multiple-species model using Panda.

  32. Part 2: Source region, EOS But wait, there’s more… • Porosity adds yet another large uncertainty • Phase changes • Kinetic Effects • Multiple Species And all of that assumes we know the actual material, which we don’t in most or our applications!

  33. Part 3, Stress-Strain Single species EOS e(P, r) Single species EOS e(P, r) EOS P>>r c2 Mixture Theory (including porosity) Solids P~r c2 Stress-Strain Equations Stress-Strain

  34. Part 3, Stress-Strain Stress-Strain behavior • When P≈rc2 the material no longer behaves as a fluid. • Then we need a constitutive equation for the stress-strain behavior • Almost always, in wave codes that is simply an isotropic linear elastic relation (which is undoubtedly extremely crude).

  35. Part 4, Strength Single species EOS e(P, r) Single species EOS e(P, r) Mixture Theory (including porosity) Stress-Strain Equations Yield Flow & Failure Fracture Yield surface, Flow rule Fracture Criteria Which brings us to the strength parts.. EOS P>>r c2 Solids P~r c2 Flow, fracture, failure P<<r c2

  36. Part 4, Strength The “F” words: Flow, Fracture and Failure • Models for these fall into three groups: • “Degraded Stiffness”, no explicit flow or fracture. • “Flow” including plasticity and damage, used to model microscopic voids and cracks leading to an inability to resist stress. • “Fracture”, involving actual macroscopic cracks and voids which are tracked, leading to an inability to resist stress.

  37. Part 4, Strength In a continuum theory, the first two can be included directly, the latter is difficult, unless some statistical approach is used to smear them out.

  38. Part 4, Strength Some Real Data

  39. Part 4, Strength ANGLE OF FRICTION Cohesion Tensile strength Yield depends on pressure

  40. Part 4, Strength Damage and degradation leading to ultimate failure occur at some limiting strain

  41. Part 4, Strength Pressure-Dependent Ductility:Failure Strain depends on pressure..

  42. Part 4, Strength Pressure Dependent Yield and Ductility

  43. Part 4, Strength Bulking: increase in volume at failure

  44. Part 4, Strength Damaged material: Cohesionless,but not Fluid. Grady Kipp, failed

  45. Part 4, Strength Tensile fracture depends strongly on strain rate Codes

  46. Part 4, Strength • Degradation with strain over failure (damage) • Pressure dependent ductility: Failure strain increases with pressure • Rate dependent, especially in tension • Pressure dependent Yield envelope and Permanent strains • Pressure dependent failure envelope even when fully failed Flow and Fracture Models should include:

  47. Part 4, Strength We can do all of that using: • An Explicit Yield Envelope • Envelope is pressure dependent • A damage measure • Envelope changes with damage • Damage accumulation depends on pressure

  48. Part 4, Strength Flow and Fracture: Yielding and CrackingLets put it all together; Start with the yield envelope: Initial Yield=F(stresses) or G(strains) • Isotropic=> s1, s2, s3 • (Or three stress invariants) • Commonly only 2, e.g. • J2=F(P) • Or max shear=f(pressure)

  49. Part 4, Strength Special Case: VonMises (metals)

  50. Part 4, Strength Special Case: Mohr-Coloumb & Drucker-Prager

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