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 nano-sized powders  Shock Hugoniot of nano-sized powders (either calculated or measured) currently unavailable

4. APPROACH (a) Examine applicability of McQueen’s isochoric model and Wu-Jing’s isobaric model for describing shock compression of micron-sized powders (b) Measure shock Hugoniot of 25 nm-Fe powders pre-pressed to 35% and 45% initial density; and (c) 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 (E 00 =E 00 )  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. 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 ) Correlation with Experiments: micro-Fe powder

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

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

11. Typical input and propagated stress traces 35% TMD45% TMD

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

13. Hugoniot for ~25nm-Fe powder 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. Transition Stress of Linear Segments: ~2 GPa for 35% TMD and ~6 GPa for 45% TMD Shock and Particle Velocity (D-u)Stress and Particle Velocity (σ x -u)

14. Measured Shock Velocity versus Stress (D-σ) Hugoniot for ~25nm-Fe powder D-  x calculated using jump condition: D=C 0 /2+½(C 0 2 +4S σ x V 00 ) ½ Consistent with direct measurements, suggesting steady/pseudo-steady propagation through nano- powders ~35% TMD ~45% TMD

15. Measured Hugoniot for ~25nm-Fe powder shows deviation from static curve Wu-Jing Model Correlation with Measured Hugoniot of 25 nm Fe ~35% TMD ~45% TMD V i /V o = (V oo /V o ) γ/(γ+2) Measured compression-to-expansion transition: V i /V 0 = 1.3 (for 35%) and = 1.08 (for 45% TMD) is same as obtained from calculation inflection Inflection Volume

16. Correlation of Wu-Jing Model Prediction with Experimentally Measured Hugoniot for 25 nm Fe 35% TMD (α o ≈ 2.86) 45% TMD (α o ≈ 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