Applicability of Analytical Models for Applicability of Analytical Models for Predicting Predicting Hugoniot of Pre-Pressed Low- Hugoniot of Pre-Pressed Low- Density Compacts of Iron Nano-particles Density Compacts of Iron Nano-particles Chengda Dai, Daniel Eakins, Naresh Thadhani School of Materials Science & Engineering School of Materials Science & Engineering Georgia Institute of Technology, Atlanta GA30332 Georgia Institute of Technology, Atlanta GA30332 EPNM-2008, May 5-9, Lisse, Netherlands Supported by ONR/MURI under grant N00014-07-1- 0740.
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Applicability of Analytical Models for Predicting Hugoniot of Pre-Pressed Low- Density Compacts of Iron Nano-particles Chengda Dai, Daniel Eakins, Naresh.
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Applicability of Analytical Models for Applicability of Analytical Models for Predicting Predicting Hugoniot of Pre-Pressed Low-Hugoniot of Pre-Pressed Low-Density Compacts of Iron Nano-particlesDensity Compacts of Iron Nano-particles
Chengda Dai, Daniel Eakins, Naresh Thadhani
School of Materials Science & Engineering School of Materials Science & Engineering Georgia Institute of Technology, Atlanta GA30332Georgia Institute of Technology, Atlanta GA30332
EPNM-2008, May 5-9, Lisse, Netherlands
Supported by ONR/MURI under grant N00014-07-1-0740.
OUTLINEOUTLINE
• 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
MOTIVATIONMOTIVATION
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 powdersnano-sized powders (either calculated
or measured) currently unavailable
APPROACHAPPROACH
(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
CURRENT ANALYTICAL MODELSCURRENT ANALYTICAL MODELS
Isochoric Approach – constant volume (McQueen et al’s)
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Specific internal energy for porous and solid assumed same (E00=E00)
Grüneisen parameter assumed identical for porous and solid material
CURRENT ANALYTICAL MODELSCURRENT ANALYTICAL MODELS
50 mm Φ x 3 mm thick powder sampleInput PVDF gauge
Typical input and propagated stress tracesTypical input and propagated stress traces
35% TMD 45% TMD
Experimental data for ~25nm Fe (~35% and ~45% TMD)
Hugoniot for ~25nm-Fe powderHugoniot 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 (σx-u)
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
~35% TMD
~45% TMD
• Measured Hugoniot for ~25nm-Fe powder shows deviation from static curve
Wu-Jing Model Correlation with Wu-Jing Model Correlation with Measured Hugoniot of 25 nm FeMeasured Hugoniot of 25 nm Fe
~35% TMD ~45% TMD
Vi/Vo = (Voo/Vo) γ/(γ+2)
• Measured compression-to-expansion transition: Vi/V0 = 1.3 (for 35%) and = 1.08 (for 45% TMD) is same as obtained from calculation inflection
Inflection Volume
Correlation of Wu-Jing Model Prediction with Correlation of Wu-Jing Model Prediction with Experimentally Measured Hugoniot for 25 nm FeExperimentally Measured Hugoniot for 25 nm Fe
35% TMD (αo ≈ 2.86)
45% TMD (αo ≈ 2.22)
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Wu-Jing Model with StrengthWu-Jing Model with Strength
Wu-Jing Model without StrengthWu-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
CONCLUDING REMARKSCONCLUDING 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