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Chengda Dai, Daniel Eakins, Naresh Thadhani

Applicability of Analytical Models for Predicting Hugoniot of Pre-Pressed Low-Density Compacts of Iron Nano-particles. Chengda Dai, Daniel Eakins, Naresh Thadhani. School of Materials Science & Engineering Georgia Institute of Technology, Atlanta GA30332.

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Chengda Dai, Daniel Eakins, Naresh Thadhani

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  1. Applicability of Analytical Models for Predicting Hugoniot of Pre-Pressed Low-Density Compacts of Iron Nano-particles Chengda Dai, Daniel Eakins, Naresh Thadhani School of Materials Science & Engineering Georgia Institute of Technology, Atlanta GA30332 EPNM-2008, May 5-9, Lisse, Netherlands Supported by ONR/MURI under grant N00014-07-1-0740.

  2. OUTLINE • Motivation and Approach • Current Analytical Models and their Applicability to Low-density Powder Compacts • Hugoniot Measurement Experimental Procedure • Results of Measured Shock Hugoniot of Nano-Fe • Correlation of Model Predictions with Measured Shock Compressibility of Nano-Fe Powders

  3. MOTIVATION • Fabrication of bulk materials via shock compaction of powders requires reliable design of fixture geometry • Fixture design depends on availability of measured or calculated Hugoniot of pressed powders • Shock Hugoniot of low-density micro-size powders can be calculated using isobaric/isochoric models • Shock Hugoniot of nano-sized powders (either calculated or measured) currently unavailable

  4. APPROACH Examine applicability of McQueen’s isochoric model and Wu-Jing’s isobaric model for describing shock compression of micron-sized powders Measure shock Hugoniot of 25 nm-Fe powders pre-pressed to 35% and 45% initial density;and Correlate model predictions with experimental measurements on 25-nm Fe powders

  5. CURRENT ANALYTICAL MODELS  Isochoric Approach – constant volume (McQueen et al’s) • Specific internal energy for porous and solid assumed same (E00=E00) • Grüneisen parameter  assumed identical for porous and solid material

  6. CURRENT ANALYTICAL MODELS  Isobaric Approach – Constant Pressure (Wu-Jing Model) • Specific internal energy assumed same for porous and solid material • - & P-dependent parameter (R) assumed identical for porous & solid

  7. Correlation with Experiments: micro-Fe powder McQueen’s model shows correlation up to 60% TMD Wu-Jing model shows correlation up to 43% TMD

  8. Correlation with Experiments: micro-Fe powder • McQueen’s model correlates well only up to 0 = 1.66 (~60% TMD) • Wu-Jing’s method provides correlation up to 0 = 2.33 (43% TMD) • Wu-Jing model can be potentially employed to calculate Hugoniot of nanopowders (01+2/0)

  9. HUGONIOT MEASUREMENTS ON NANO-IRON STARTING NANO IRON POWDER MONO-SIZED 25 nm bcc-IRON POWDER PARTICLES

  10. 50 mm Φ x 3 mm thick powder sample Input PVDF gauge GAS-GUN IMPACT EXPERIMENTS (STRESS & SHOCK VELOCITY MEASUREMENTS) Measure:Stress profile (σ(t)), Shock velocity (D) Calculate:Particle Vel, Specific Vol D=hs/ (tA-tB) u= /(00D)  /00 = D/(D-u)

  11. Typical input and propagated stress traces 35% TMD 45% TMD

  12. Experimental data for ~25nm Fe (~35% and ~45% TMD)

  13. Hugoniot for ~25nm-Fe powder Shock and Particle Velocity (D-u) Stress and Particle Velocity (σx-u) Transition Stress of Linear Segments: • ~2 GPa for 35% TMD and • ~6 GPa for 45% TMD • Shock velocity extrapolated to ambient P: • 0.8 km/s for 35% TMD sample • 1.1 km/s for 45% TMD sample • close to measured sound speed values.

  14. Measured Shock Velocity versus Stress (D-σ) Hugoniot for ~25nm-Fe powder D-x calculated using jump condition: D=C0/2+½(C02+4S σxV00)½ Consistent with direct measurements, suggesting steady/pseudo-steady propagation through nano-powders ~45% TMD ~35% TMD

  15. Wu-Jing Model Correlation with Measured Hugoniot of 25 nm Fe ~45% TMD ~35% TMD • Measured Hugoniot for ~25nm-Fe powder shows deviation from static curve • Measured compression-to-expansion transition: Vi/V0 = 1.3 (for 35%) and = 1.08 (for 45% TMD) is same as obtained from calculation Inflection Volume Vi/Vo = (Voo/Vo) γ/(γ+2) inflection

  16. Correlation of Wu-Jing Model Prediction with Experimentally Measured Hugoniot for 25 nm Fe 35% TMD (αo ≈ 2.86) 45% TMD (αo ≈ 2.22) Wu-Jing Model with Strength Wu-Jing Model without Strength Wu-Jing model is ineffective in predicting Hugoniot of low-density nano-Fe in spite of its good correlation with micro-scale powders

  17. CONCLUDING REMARKS • McQueen’s model is insufficient for Hugoniot prediction for highly porous micro-scale powder (01+2/0). • Wu-Jing’s model capable of describing shock compression of low-density micron-powder compacts, cannot describe Hugoniot of nano-Fe powder • Wu-Jing’s and McQueen’s methods need to consider characteristic properties of high surface area of nano- particles to better predict Hugoniot of nano-particles JOURNAL OF APPLIED PHYSICS 103, 093503 2008

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