Indent Tests for Explosive Equation of State Determination
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Transcript of Indent Tests for Explosive Equation of State Determination
Effects of explosive indent on Al plates
M. Arrigoni, S. Kerampran, ENSTA Bretagne, France
A. Desachy, M.-O. Sturtzer, ISL France
S. Barrot, Pierre Bonnet, V. Lacomère, LCPP France
2014 European ALTAIR Technology Conference, 24-26 June, München 1
2
Context
Method for characterizing the effects of an explosive
2
How to characterize explosive effects without thermodynamic data,
without heavy experimental setup ?
2014 European ALTAIR Technology Conference, 24-26 June, München
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Table of content
• Context
• Explosive plate indent test
• Metal/explosive interaction
• Detonics
• Radioss simulation of the explosive indent test
• Comparison with experiments
• Conclusion & perspectives
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Explosive plate indent
• Estimation of the metal/explosive interaction :
210g PG-2 of 43 mm diam, height 110 mm against Al 2024 : 100*100*30 mm
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detonator
Recovered sample
De
ton
atio
n p
rod
ucts
D
yn
am
ic b
eh
avio
ur
of m
ate
ria
l
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Metal/explosive interaction
• In the (P,u) plane :
2014 European ALTAIR Technology Conference, 24-26 June, München
Shock transmitted in aluminium bloc : P1=21,4 Gpa and u1= 1100 m/s
0
5E+09
1E+10
1.5E+10
2E+10
0 500 1000 1500 2000 2500 3000
Pre
ssu
re P
a
Material Velocity m/s
P HugoAL CJ
5
0
5E+09
1E+10
1.5E+10
2E+10
0 500 1000 1500 2000 2500 3000
Pre
ssu
re P
a
Material Velocity m/s
P HugoAL
Pcrussard
0
5E+09
1E+10
1.5E+10
2E+10
0 500 1000 1500 2000 2500 3000
Pre
ssu
re P
a
Material Velocity m/s
P HugoAL
Pcrussard
Rayleigh line
0
5E+09
1E+10
1.5E+10
2E+10
0 500 1000 1500 2000 2500 3000
Pre
ssu
re P
a
Material Velocity m/s
P HugoAL
Pcrussard
symCrussard
Rayleigh line
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EOS of detonation products
• The plate indent test was used by Davis, 1981 :
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W. C. Davis, Los Alamos Sci., 2
(1) (1981), 48.
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Another method : cylinder test
• EOS of prodets allows calculating the effects of an explosive.
• The most common is the JWL eos deduced from the cylinder test :
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(Esen 2005) (Davis 2001)
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EOS of detonation products
• JWL parameter set :
A, B, R1, R2 and ω are the model parameters, V is the density ratio ρ0/ρ,
E the internal energy per unit volume of explosive (E=ρ0×eint).
• Examples for TNT :
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V
Ee
VRBe
VRAP
VRVR 0
21
21 11
JWL param. A GPa B GPa w R1 R2 E0 Gpa V à CJ P à CJ
Dobratz 1985 371.21 3.23 0.3 4.15 0.95 7 0.731 19.9
Dobratz 1981 373.8 3.747 0.35 4.15 0.9 6 0.731 19.7
Kury 1997 1.a 673.1 21.988 0.3 5.4 1.8 7 0.741 18.7
Kury 1997 1.b 3394.889 63.7085 0.6 8.3 2.8 7 0.741 17.9
Kury 1997 2.a 673.1 25.1735 0.3 5.4 1.8 7 0.742 19.3
Kury 1997 2.b 3394.889 70.9736 0.6 8.3 2.8 7 0.742 18.5
Souers et kury 1993 524.4089 4.900052 0.23 4.579 0.85 7.1 0.744 20.0
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EOS of detonation products
• PG-2 (93 % RDX, 7 % HTPB) : 210 g, PCJ= 150 kBar and DCJ=6730 m/s
(By the Kamlet-Jacobs method)
2014 European ALTAIR Technology Conference, 24-26 June, München 9
JWL param. A GPa B GPa w R1 R2 E0 Gpa
PG-2 1e-20 1e-20 1.914 1e-20 1e-20 7,2
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Numerical simulation of the detonation
• 3D with sym. Planes ZX (BCS = 010 101) and ZY (BCS = 100 011)
• Mesh size about 5e-2 cm.
• Eadd=0,017 to match the CJ conditions.
• Detonator at the top center
• ALE/disp and ALE/zero and MAT/ALE/FLRD=1
2014 European ALTAIR Technology Conference, 24-26 June, München 10
P=148,4 kBar
Expected :
150,5 kBar
Error -2,8%
ρ =1,694 g/cm3
Expected :
1,755 g/cm3
Error -3,3%
11
Dynamic behaviour of materials
• « A 2024 » Aluminium blocs to indent 100*100*30 mm
• Johnson-Cook plasticity model :
A, B, C, n and m the Johnson Cook constants. T0 the reference temperature (300 K) and Tfusion the temperature of melting. [Johnson-Cook, 1981]
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m
0fusion
0
0
neq
pVM )TT
TT(1
ε
εCln1)B(εAσ
E (MPA) ν A (Mpa) B (Mpa) C n m Tfusion ( K) T0 ( K) s-1
A2024 73000 0,33 265 426 0,015 0,34 1 911 300 1e-6
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Damage model and plate EOS
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ρ0 (kg/m3) s Γ
A 2024 5328 2785 1,339 2,00
K (kBarλs) λ
A 2024 31,6e-4 16 2,02 [Tuler-Butcher, 1968]
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Numerical simulation of explosive plate indent
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• 3D with sym. Planes ZX (BCS = 010 101) and ZY (BCS = 100 011)
• Mesh size about 5e-2 cm.
• Air as perfect gas (LAW6)
• Interface 3 between Plate and Bloc
• Interface 3 inside the plate at spallation planes
• Run duration 100 ns
-2.5
-2
-1.5
-1
-0.5
0
0.5
0 20 40 60 80 100
Ind
en
t d
ep
th in
cm
Time in µs
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Simulation vs experiment
CJ conditions are well reproduced
Pressure transmitted in Al is 185,3 kBar vs 214 kBar analytically (err=-13%)
Indent depth is 19,1 mm in agreement with experiments (err=0%)
Widening is 53,2 mm in simulation vs 54,1 mm in exp (err <2%)
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5,32 cm 5,41 cm
1,9
1 c
m
1,9
1 c
m
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Simulation vs experiment
CJ conditions are well reproduced
Pressure transmitted in Al is 185,3 kBar vs 214 kBar analytically (err=-13%)
Indent depth is 19,1 mm in agreement with experiments (err=0%)
Widening is 53,2 mm in simulation vs 54,1 mm in exp (err <2%)
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5,32 cm 5,41 cm
1,9
1 c
m
1,9
1 c
m
R=9,25 cm
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• Crater shape, width and depth are well reproduced,
Simulation vs experiment
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Boundary effects Damage circle
in the crater
Experiment
Simulation
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Al indent experiment
2014 European ALTAIR Technology Conference, 24-26 June, München
• Cross section observation (only for one shot),
Poisson’s ratio for Al : ν = 0,33 Measured : h1=18 mm & R1=6,25 mm R0 = 5,48 mm
h1
h0
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ρ1= 3622 kg/m3 (experimental approach with Poisson ratio)
Vs ρ1= 3330 kg/m3 (err=8,8 %) BUT IT LEADS TO A GREAT ERR IN PRESSURE !!!
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Al indent experiment
• With AN Based emulsion explosive :
• Measured : h1=18,2 mm ± 0,3 & R1=13,87 mm ± 0,3
R0 = 12,72 mm ± 0,3
ρ1= 3120 kg/m3 ± 5%
• Analytical determination : ρ1 = ρ0D/(D-u1) ≈ 3130 kg/m3
Very good agreement < 1%
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≈18,2 ±0,3 mm
)]²1.(1[
)1(
1
0
1
0.
2
00
01
s
c
PP
13,87
P1= 15,3 GPa versus 15,5 GPa determined by shock polars
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Conclusion
• Plate indent by detonation of cylindrical cartridge :
– Some features observed on experiments are fairly well reproduced by the simulation (boundaries effects, crater depth, …).
– Computed P1 (transmitted in Al) still below what expected (=> refine the mesh ?).
– The Tuler-Butcher cumulative damage model gives some accordance with the experiments but it does not shows the same spall profile (Try Wilkins or Johnson ? Or change TB parameters ?).
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Perspectives
• Mesh refinement needed ?
• Compare computation with cross sections from the other shots on Al.
• Use another material (experiments in progress with XC38 steel).
2014 European ALTAIR Technology Conference, 24-26 June, München 20
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Any Questions ?
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About detonations
• Detonation : supersonic exothermic chemical decomposition (< 1µs) of an energetic molecule provoking a shock wave.
• Chapman-Jouget detonation : the reactive area and the shock front are merged.
• 1D case :
Conservation of mass:
Conservation of momentum:
Conservation of energy:
Where h enthalpy, u material velocity, p hydrodynamic pressure, ρ=1/v density
1100 uu
2
111
2
000 upup
22
2
11
2
00
uh
uh
2014 European ALTAIR Technology Conference, 24-26 June, München 22
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About detonations
• Combination of conservation equations :
• Thermodynamic states in the energetic material :
• The C-J state is a characteristic of the energetic material.
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1
2
1
2
0
2
0
10
01 muupp
ZND point
2014 European ALTAIR Technology Conference, 24-26 June, München 23
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Metal/explosive interaction
• PG-2 (93 % RDX, 7 % HTPB) : 210 g
• Aluminium bloc to « indent» 100*100*30
• Thermodynamical state in explosive given by the Crussard in (P,u) plane :
from JWL eos @ CJ => γ=2,68 and Q=2,52 MJ/kg
• Thermodynamical state in aluminium given by Hugoniot in the (P,u) plane :
With C0=5328 m/s and s=1,339 and ρ0=2700 kg/m3
2014 European ALTAIR Technology Conference, 24-26 June, München
)1γ(ρQ)1γ²(uρ2
1P 00
suuCP 000 ²
24
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Detonics
• Another simpler EOS is said « polytropic » :
• It is actually the JWL with A=B=0
• How to detrmine γ ?
We propose an experimental approach based on explosive plate indent (metal explosive interaction).
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eP )1(