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

3

Table of content

• Context

• Explosive plate indent test

• Metal/explosive interaction

• Detonics

• Radioss simulation of the explosive indent test

• Comparison with experiments

• Conclusion & perspectives

3 2014 European ALTAIR Technology Conference, 24-26 June, München

4

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


detonator

Recovered sample

De

ton

atio

n p

rod

ucts

D

yn

am

ic b

eh

avio

ur

of m

ate

ria

l

5

Metal/explosive interaction

• In the (P,u) plane :


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


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


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


P HugoAL

Pcrussard

symCrussard

Rayleigh line

6

EOS of detonation products

• The plate indent test was used by Davis, 1981 :


W. C. Davis, Los Alamos Sci., 2

(1) (1981), 48.

7

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 :


(Esen 2005) (Davis 2001)

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• 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 :


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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• PG-2 (93 % RDX, 7 % HTPB) : 210 g, PCJ= 150 kBar and DCJ=6730 m/s

(By the Kamlet-Jacobs method)


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


P=148,4 kBar

Expected :

150,5 kBar

Error -2,8%

ρ =1,694 g/cm3

Expected :

1,755 g/cm3

Error -3,3%

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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]


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


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


• 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%)


5,32 cm 5,41 cm

1,9

1 c

m

1,9

1 c

m

15


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%)


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,



Boundary effects Damage circle

in the crater

Experiment

Simulation

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Al indent experiment


• 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

17

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%


≈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 ?).


20

Perspectives

• Mesh refinement needed ?

• Compare computation with cross sections from the other shots on Al.

• Use another material (experiments in progress with XC38 steel).


21

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


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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.

22

1

2

1

2

0

2

0

10

01 muupp

ZND point


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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


)1γ(ρQ)1γ²(uρ2

1P 00

suuCP 000 ²

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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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Engineering

Indent Tests for Explosive Equation of State Determination