Determination of properties for emulsion explosives using ...998065/FULLTEXT01.pdf · These explosives have relative short reaction zones, and as a result the equation of state can

Report 2009:1 ISSN 1653-5006

Swedish Blasting Research CentreMejerivägen 4, SE-117 43 Stockholm

Luleå University of TechnologySE-971 87 Luleå www.ltu.se

Determination of properties for emulsion explosives using cylinder expansion tests and numerical simulation

Bestämning av emulsionssprängämnens egenskaper med cylinderexpansionsprov och FEM-simulering

Håkan Hansson

Universitetstryckeriet, L

uleå

Swebrec Report 2009:1

Determination of properties for emulsion explosives using cylinder expansion tests and FEM simulation


Håkan Hansson, Swebrec

Stockholm August 2009 Swebrec - Swedish Blasting Research Centre

Luleå University of Technology Department of Civil and Environmental Engineering • Division of Rock Engineering

Determination of properties for emulsion explosives......... Swebrec Report 2009:1

i

Summary

Earlier performed cylinder expansion tests at Swebrec/SveBeFo are analysed with the aid of FEM

simulations. This results in an increased accuracy for the parameters describing the resulting material

behaviour.

The analytical approach earlier used at Swebrec/SveBeFo uses several simplifications that are not

necessary to apply when FEM simulations are used. The main advantages FEM simulations are that

the kinetic energy for explosive and copper are calculated independent of each other, and that the gas

expansion is calculated without the restriction of no axial flow.

The ideal detonation code Vixen-I is used to obtain initial sets of parameters for the JWL equation of

state for the emulsion explosives used. These initial sets of parameters are then used as starting points

for simulations of the cylinder expansion tests with the explicit FEM code LS-DYNA. The input

parameter sets are then modified until rough agreements are obtained between cylinder wall

displacements from tests and simulations. This was considered adequate due to the limited accuracy

for the test measurements, and the variations of the properties for the emulsions between different

manufactured batches of the explosives.

Keywords Explosives, emulsion explosives, cylinder tests, detonation energy, numerical simulations, equation of

state, LS-DYNA.

ii


Sammanfattning

Tidigare genomförda cylinderexpansionsförsök vid Swebrec/SveBeFo har utvärderats med stöd av

FEM-simuleringar. Detta resulterar i en ökad noggrannhet för beskrivningen av explosivämnets

egenskaper.

De analytiska uttrycken tidigare använda vid Swebrec/SveBeFo förutsätter ett flertal förenklingar som

inte längre är nödvändiga vid användande av FEM-simuleringar. De största fördelarna med FEM-

simuleringar är att rörelseenergin för explosivämne och kopparrör beräknas oberoende av varandra,

samt att spränggasernas expansion beräknas utan antagandet att axiellt flöde försummas.

Programmet Vixen-I används för att erhålla initiala parametervärden till en JWL-tillståndsekvation för

en ideal detonation av emulsionssprängämnena. Dessa initiala materialparametrar används sedan som

startpunkt för simuleringar av cylinderexpansionsförsöken med det explicita FEM-programmet LS-

DYNA. Indata anpassas sedan tills en hyfsad överensstämmelse har erhållits mellan kopparrörets

väggförskjutningar i försöken och i simuleringarna. Detta bedömdes som en acceptabel nivå för denna

inledande studie, detta då försöksresultatens spridningen är betydande. Det finns även avvikelser i

egenskaper mellan de olika tillverkade satserna av emulsionssprängämne.

NyckelordExplosivämnen, emulsioner, cylinderförsök, detonationsenergi, numerisk simulering, tillståndsdata,

LS-DYNA.


iii

Content

1. Introduction .................................................................................................................................. 1

2. Cylinder expansion tests .............................................................................................................. 3

2.1. JWL equation of state ............................................................................................................ 3

2.2. Theoretical background for cylinder expansion tests............................................................. 4

2.3. Selected tests performed at Swebrec and SveBeFo ............................................................... 5

2.3.1. Tests performed with pure emulsion E682-b ................................................................ 7

2.3.2. Tests performed with aluminized emulsion E682....................................................... 10

2.3.3. Tests performed with pure emulsion E682-a .............................................................. 12

2.4. Discussion of earlier performed tests................................................................................... 16

3. Numerical simulation of cylinder expansion tests ................................................................... 21

3.1. Ideal detonations runs using Cheetah................................................................................... 21

3.2. Ideal detonations runs using Vixen-I ................................................................................... 24

3.3. Simulation of reference cylinder test using PETN............................................................... 27

3.4. Simulation of cylinder tests performed with pure emulsion E682....................................... 35

3.4.1. Simulation of tests with emulsion E682-b .................................................................. 36

3.4.2. Simulation of tests with emulsion E682-a................................................................... 39

3.5. Simulation of cylinder tests performed with aluminized emulsion ..................................... 43

4. Discussion of simulation results................................................................................................. 49

4.1. Simulation of reference case with PETN............................................................................. 49

4.2. Simulation of pure emulsion explosives .............................................................................. 49

4.3. Simulation of an aluminized emulsion explosive ................................................................ 50

5. Summary ..................................................................................................................................... 51

5.1. Cylinder expansion tests ...................................................................................................... 51

5.2. Evaluation methodology using ideal detonation codes and FEM analysis .......................... 52

5.3. Suggested parameters for the JWL EOS for emulsion explosives....................................... 52

6. Future research and development............................................................................................. 55

References ............................................................................................................................................ 57

iv



v

Figure list

Figure 2.1. Cylinder test set up with double pin sets (Esen et al., 2005). ........................................... 7

Figure 2.2. Cylinder wall expansions for tests with emulsion E682-b................................................ 9

Figure 2.3. Cylinder wall expansions for tests with emulsion E682-b, averaged values. ................... 9

Figure 2.4. Cylinder wall expansions for tests with aluminized E682 and 100 mm cylinders. ........ 11

Figure 2.5. Cylinder wall expansions for tests with aluminized E682 and 40 mm cylinders. .......... 12

Figure 2.6. Cylinder wall expansions for tests with emulsion E682-a and 100 mm cylinders. ........ 14

Figure 2.7. Cylinder wall expansions for tests with emulsion E682-a and 60 mm cylinders. .......... 14

Figure 2.8. Cylinder wall expansions for tests with emulsion E682-a and E682-b. ......................... 17

Figure 2.9. Cylinder wall expansions for tests with emulsion E682-b and E682 with 6% aluminium.

........................................................................................................................................ 17


........................................................................................................................................ 18

Figure 2.11. Cylinder wall expansions for tests with aluminized emulsion E682. Data from the

40 mm cylinder tests are scaled to displacements of a 100 mm cylinder. ...................... 19

Figure 2.12. Cylinder wall expansions for tests with emulsion E682-a. Data from the 60 mm cylinder

tests are scaled to displacements of a 100 mm cylinder. ................................................ 20

Figure 3.1. Comparison between pressure for JWL data set from cylinder tests and Vixen-I run. .. 28

Figure 3.2. Comparison between detonation energy for JWL data set from cylinder tests and Vixen-

I run................................................................................................................................. 29

Figure 3.3. Model geometry for simulation with half wall 60 mm cylinders for PETN simulations.

........................................................................................................................................ 31

Figure 3.4. Model geometry for simulation with full wall 60 mm cylinders for PETN simulations.31


........................................................................................................................................ 31

Figure 3.6. Cylinder wall expansions for simulations with PETN using the Vixen-I and cylinder test

JWL data sets. JWL data from cylinder tests results in the lowest velocity in each set. 35

Figure 3.7. Model geometry for simulation with half wall 60 mm cylinders for emulsion

simulations. ..................................................................................................................... 36


simulations. ..................................................................................................................... 36

Figure 3.9. Detonation energy from JWL EOS data sets for simulations with emulsion E682-b..... 38

Figure 3.10. Cylinder wall expansions for tests and simulations with emulsion E682-b using 100 mm

cylinders.......................................................................................................................... 38

Figure 3.11. Detonation energy from JWL EOS data sets for simulations with emulsion E682-a. .... 41

vi


Figure 3.12. Cylinder wall expansions for tests and simulations with emulsion E682-a using 60 mm

cylinders.......................................................................................................................... 41

Figure 3.13. Cylinder wall expansions for tests and simulations with emulsion E682-a using 100 mm

cylinders. The diagrams (a) and (b) refer to blends with different densities for the

emulsion explosive. ........................................................................................................ 42


simulations. ..................................................................................................................... 43


simulations. ..................................................................................................................... 43

Figure 3.16. Detonation energy from JWL EOS data sets for simulations with aluminized emulsion

E682................................................................................................................................ 46

Figure 3.17. Cylinder wall expansions for tests and simulations with aluminized E682 using 100 mm

cylinders.......................................................................................................................... 46

Figure 3.18. Cylinder wall expansions for tests and simulations with aluminized E682 using 40 mm

cylinders.......................................................................................................................... 47

Figure 5.1. Estimated detonation energy during expansion for the used of emulsion explosives

according to Esen et al. (2005). Average values for cylinder tests with 100 mm copper

cylinders.......................................................................................................................... 53

Figure 5.2. Estimated detonation energy during expansion for the used of emulsion explosives. The

diagrams (a) and (b) uses the units kJ/cc and MJ/kg for the detonation energy,

respectively. .................................................................................................................... 54


vii

Table list

Table 2.1. Composition of the emulsions E682-a (Arvanitidis et al., 2004) and E682-b (Esen et al.,

2005). ................................................................................................................................ 6

Table 2.2. Composition of the aluminized emulsion E682, with an additive of 6% aluminium (Esen

et al., 2005). ...................................................................................................................... 6

Table 2.3. Data for cylinder tests with emulsion E682-b performed in 2007 (Nyberg, 2009). ......... 8

Table 2.4. Data for cylinder tests performed with emulsion E682-b in 2005 (Esen et al., 2005)...... 8

Table 2.5. Data for 100 mm cylinder tests performed with aluminized emulsion E682 (Esen et al.,

2005). .............................................................................................................................. 10

Table 2.6. Data for 40 mm cylinder tests performed with aluminized emulsion E682 (Esen et al.,

2005). .............................................................................................................................. 11

Table 2.7. Data for cylinder tests performed with emulsion E682-a (Arvanitidis et al., 2004)....... 13

Table 2.8. Data for cylinder test performed with emulsion E682-a (Esen et al., 2005)................... 13

Table 2.9. Detonation velocity measurements performed with emulsion E682-a in PVC tubes (Nie

et al., 2000). The rows with double detonation velocities values are for identical test set-

ups................................................................................................................................... 15

Table 2.10. Detonation velocity measurement performed with emulsion E682-a in steel cylinder

(Nie et al., 2000). ............................................................................................................ 16

Table 3.1. Properties of the ingredients for the explosive used for Cheetah runs............................ 22

Table 3.2. Cheetah output for the pure emulsion explosives. .......................................................... 23

Table 3.3. Cheetah output for the aluminized emulsion explosive. ................................................. 24

Table 3.4. Properties of the ingredients for the explosive used for Vixen-I runs. ........................... 25

Table 3.5. Vixen-I output for the pure emulsion explosives............................................................ 26

Table 3.6. Vixen-I output for the aluminized emulsion explosive................................................... 27

Table 3.7. JWL fit to PETN cylinder tests and ideal detonation data from Vixen-I........................ 28

Table 3.8. Shock data for copper (Marsh, 1980). ............................................................................ 29

Table 3.9. Elastic and strength data used for copper (Johnson and Cook, 1985). ........................... 30

Table 3.10. Cylinder tests data for PETN (Souers et al., 1996)......................................................... 32

Table 3.11. Results from simulations of cylinder tests for PETN using cylinder test JWL. ............. 33

Table 3.12. Results from simulations of cylinder tests for PETN using Vixen-I data....................... 34

Table 3.13. Compiled experimental data for the pure emulsion explosives E682-b. ........................ 36

Table 3.14. Input data for the pure emulsion explosives E682-b. ..................................................... 37

Table 3.15. Compiled experimental data for the pure emulsion explosives E682-a.......................... 39

Table 3.16. Input data for the pure emulsion explosives E682-a....................................................... 40

Table 3.17. Compiled experimental data for the aluminized emulsion explosives E682. ................. 44

Table 3.18. Input data for the aluminized emulsion explosives E682. .............................................. 45

viii



1

1. Introduction

Cylinder expansion tests have been used at Swebrec/SveBeFo to investigate the properties of mainly

emulsion explosives. These tests were conducted with explosives intended for rock blasting, while the

methodology initially was indented to determine the properties of high explosive military explosives,

e.g. PETN, RDX, and Comp B. These explosives have relative short reaction zones, and as a result the

equation of state can be determined almost independently of the burning rate or kinetic law for the

explosive. Equation of state data for these explosives are easily available from the literature, e.g.

Souers et al. (1996) published data for several military explosives. Even though the method also is

used for military non-ideal explosives, e.g. different types of PBX (plastic bonded explosives), the use

of this method to characterize explosives used in rock blasting may not be that straight forward. Due to

the increased reaction zone for these explosives, the use of the simplified analytical methodology

sometimes used for military explosives may not be good enough to determine the properties of

explosives used in rock blasting. However, it is quite common to use numerical simulation to obtain

more accurate description of the behaviour of military explosives, e.g. with the use of an explicit FEM

code or hydrocode. Simplified analytical evaluations were earlier performed by Esen et al. (2005) for

the majority of these data. These earlier results showed considerable differences between the equation

of state determined for a ideal detonation using Vixen-I (Cunningham, 2001 and Cunningham et al.,

2006), and the data obtained from the analytical evaluation of the cylinder test. On the other hand, the

velocity of detonation measurements from the tests indicates that the detonation of pure and

aluminized emulsions should be close the ideal for the used dimensions of copper cylinders. This

discrepancy needed to be further investigated.

This study is an attempt to use this later methodology with explicit FEM simulation to obtain

parameter sets for emulsion explosives to the JWL (Jones-Wilkins-Lee) equation of state (EOS). This

gives a possibility to estimate the pressure for the expanding gases during blasting, and in the future

also study the interaction between expanding gases and solid material, e.g. rock.

Initial parameter sets for the JWL equation of state are calculated with the ideal detonation code

Vixen-I, these are initial parameters are then used as input for the simulation of the earlier performed

cylinder tests. The input parameters are then changed until acceptable agreements between cylinder

expansion for the tests and simulations are obtained for the tested cases. However, unique fits to the

parameters to the JWL equation of state for the explosives are not likely to be obtained.


2


3

2. Cylinder expansion tests

This chapter is only intended as a short introduction, for further details regarding evaluation of

cylinder tests it is recommended that the reader study the following references: Souers and Haselman

(1994), Souers et al. (1996), and Fickett & Davis (2000). Also a short summary of the earlier

performed tests are given, for further details it is recommended that the reader study the earlier reports

by Arvanitidis et al. (2004) and Esen et al. (2005). Tests and evaluation of cylinder tests using NSP 71

plastic explosive is reported by Helte et al. (2006).

2.1. JWL equation of state

The cylinder test has long been a tool to obtain equation of state (EOS) data for high explosives, e.g.

for the JWL (Jones-Wilkins-Lee) equation of state. The pressure of the expanding gases according to

the JWL equation of state is given by equation 2.1 below (Souers and Haselman, 1994).

121 expexp)( CvvRBvRAvPs (Eq. 2.1)

where 21,,, RRBA , and are material input to be determined

0VVv where V is the specific volume

0V is the initial specific volume.

If equation 2.1 above describes an adiabat with constant entropy, then it may be integrated to give the

total internal energy (Souers et al., 1996), see equation 2.2 below. sE is always positive, and

decreases from the detonation point, )( js vE , to zero at an infinite volume for the detonation products.

vCvR

RBvR

RAdvPvE ss 2

21

2

expexp)( (Eq. 2.2)

Further, to obtain the energy of detonation at volume v , it is necessary to subtract the energy of

compression for the explosive ( )( jc vE ) from the energy of the adiabatic expansion (Souers and

Haselman, 1994), see equation 2.3 below.

)()()()( jcsjsd vEvEvEvE (Eq. 2.3)


4

The detonation energy is zero where the adiabatic energy output equals the energy put in by the

compression. Further, the energy of detonation at infinite volume ( 0E ) has a positive value according

to equation 2.4 below.

)()(0 jcjs vEvEE (Eq. 2.4)

This gives the detonation energy according to equation 2.5 below.

)()( 0 vEEvE sd (Eq. 2.5)

Further, )( jc vE may be estimated according to equation 2.6 below (Souers and Haselman, 1994).

2

222

221

)(D

PvDvE jj

jc (Eq. 2.6)

where jv is the relative volume at the detonation point

jP is the detonation pressure

is the initial density of the explosive

D is the detonation velocity of the explosive.

2.2. Theoretical background for cylinder expansion tests

A cylinder test is a relatively simple setup. However, the evaluation and determination of material

parameters are more complicated and requires several simplifications. In short, a copper pipe, or

hollow cylinder, is filled with explosive. The explosive is then detonated, and the movement of the

cylinder wall and detonation velocity of the explosive are registered. The volume of the expanding

gases and the pressure required accelerate the copper cylinder are then determined. Also the kinetic

energy for the expanding gases and copper cylinder needs to be determined. Finally, the relationship

between pressure and volume of the expanding gases is calculated.

The copper for the cylinder should be of OFHC copper, and two wall thicknesses are standardised, the

so called full wall and half wall tests. The full wall cylinder test uses a wall thickness equal to 1/10th of

the cylinders inner diameter, and the half wall cylinder test uses a thinner wall dimension equal to

1/20th of the cylinders inner diameter. Further, the copper cylinder may be replaced with a cylinder of

another metal, e.g. tantalum cylinders are sometimes used for testing of high density military

explosives.


5

The velocity of the outer surface is normally measured with streak cameras or Fabry-Perot

interferometers, although other measurement techniques also exist. The used measurement technique

needs to be considered during the evaluation, due to the difference in velocity measurement. A streak

camera measure perpendicular to the initial cylinder wall and a Fabry-Perot interferometer is normally

used to measure in the direction of the material movement of the cylinder.

The displacement or velocity of the copper pipe should be calculated at the centre radius of the tube,

this can be estimated under the assumption of incompressible deformation and no material flow in the

length direction of the copper tube (Hornberg and Volk, 1989). The mid-wall radius is then calculated

from the half cross sectional surface area according to equation 2.7.

222222

21

ioommo RRrrrr (Eq. 2.7)

where mr is the mid-wall radius

or is the outer radius

ir is the inner radius

oR is the initial outer radius

iR is the initial inner radius.

The radial change of the centre radius ( mr ) is then given by equation 2.8.

22

222

222 oi

ooi

ommmRRRRRrRrr (Eq. 2.8)

The obtained values for the radial expansion of the centre radius are then used for comparison with the

results from the numerical simulations.

2.3. Selected tests performed at Swebrec and SveBeFo

Cylinder expansion tests of emulsions were earlier performed at Swebrec and SveBeFo (Arvanitidis et

al., 2004, Esen et al., 2005 and Nyberg, 2009). The tests were performed with commercial available

explosives, and with variations of an emulsion developed earlier for research purposes. This research

emulsion is named E682, and this emulsion was tested with additives of aluminium, prilled AN or

ANFO, and in pure form. The cylinder tests that later are used as a basis for the simulations are shortly

described in this chapter, with the latest performed tests described first. The cylinder wall

displacement data are later used for comparison against data obtained from the simulations.


6

The composition for the emulsion E682 was changed for the tests performed in 2005 and later (Esen et

al., 2005), resulting in an increased nominal density. To distinguish between the different

compositions, this later composition will be named E682-b, with the earlier composition used by e.g.

Arvanitidis et al. (2004) named E682-a. The compositions of the pure emulsions are given in Table

2.1, and the composition of the aluminized emulsion in Table 2.2.

Table 2.1. Composition of the emulsions E682-a (Arvanitidis et al., 2004) and E682-b (Esen et al., 2005).

Pure emulsion E682-a Pure emulsion E682-b Component Ingredient

Composition (wt %) Composition (wt %)

Ammonium Nitrate 65.31 65.80

Sodium Nitrate 10.88 10.97 Salt solution

Water 14.52 14.62

Emulsifier Lubrizol 2724 1.50 1.46

Mineral oil Whiterex E309 4.51 4.37

Micro-balloon 3M K20 3.28 2.79

Table 2.2. Composition of the aluminized emulsion E682, with an additive of 6% aluminium (Esen et al., 2005).

Aluminized E682 Al 6%Component Ingredient

Composition (wt %)

Ammonium Nitrate 61.49

Sodium Nitrate 10.25 Salt solution

Water 13.67

Emulsifier Lubrizol 2724 1.36

Mineral oil Whiterex E309 4.09

Microballoon 3M K20 3.15

Aluminium A80 5.99

The displacements of the wall of the copper pipes are measured during the cylinder expansion test as

discussed earlier. For these tests, the displacement of the pipe was measured with contact pins giving

the time of arrival at each gauge location. The setup of a test with two sets of contact pins is shown in


7

Figure 2.1. However, a test setup with only one set of contact pins was used for several of the tests.

For further descriptions of the tests and results, see Arvanitidis et al. (2004) and Esen et al. (2005).

Observe that the times are shifted for the registrations to obtain a common starting point for the

deformation, i.e. the measurement data are shifted so that the first measurement points for each

registrations falls on a typical deformation history curve for the initial displacement for the midpoint

of the cylinder wall. This was done since no common time reference is used for the tests. The method

accounts for the varying distance between the cylinders outer surface and the contact pins for the tests.

However, no attempt is made to verify the location of the individual contact pins or the time

registrations for each contact pin.

Figure 2.1. Cylinder test set up with double pin sets (Esen et al., 2005).

2.3.1. Tests performed with pure emulsion E682-b

Three cylinder test were performed in 2007 with 100 mm copper pipes and the explosive E682-b.

Only one set of contact pins for wall displacement measurements was used for these tests. However,

the registration for one of the tests was unsuccessful. The data for the tests with successful

registrations are given in Table 2.3. The cylinder wall expansion results for these tests are shown in

Figure 2.2 and 2.3.


8

Table 2.3. Data for cylinder tests with emulsion E682-b performed in 2007 (Nyberg, 2009).

Test no. R22 Test no. R22

Density 1203 kg/m3 1205 kg/m3

Detonation velocity 5688 m/s 5838 m/s

Cylinder type and material Half wall, copper Half wall, copper

Cylinder inner diameter 100 mm 100 mm

Cylinder thickness at measurement location 5.14 mm 5.18 mm

Three cylinder tests were performed in 2005 with 100 mm copper pipes and the explosive E682-b. The

data for the tests are given in Table 2.4. The set up with double sets of contact pins for wall

displacement measurements was used for these tests. The cylinder wall expansion results for these

tests are shown in Figure 2.2 and 2.3. Observe that the times are shifted for the registrations to obtain a

common starting point for the deformation; this was done since no common time reference was used

for the tests.

Table 2.4. Data for cylinder tests performed with emulsion E682-b in 2005 (Esen et al., 2005).

Test no. 200 Test no. 203 Test no. 204 Test no. 207

Density 1169 kg/m3 1185 kg/m3 1179 kg/m3 1178 kg/m3

Detonationvelocity 5856 m/s 5784 m/s 5959 m/s 5836 m/s

Cylinder type and material Half wall, copper Half wall, copper Half wall, copper Half wall, copper

Cylinder inner diameter 100 mm 100 mm 100 mm 100 mm

Cylinder thickness (1)

5.085 mm (a) 5.013 mm (b)

4.993 mm (a) 5.048 mm (b)

4.996 mm (a) 5.034 mm (b)

4.804 mm (a) 5.202 mm (b)

Note: (1) Average cylinder thickness at measurement locations. The two values are for measurement data sets (a) and (b), respectively.


9

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682-b, R22, t=5.14 mmE682-b, R28, t=5.18 mmE682-b, 200a, t=5.09 mmE682-b, 200b, t=5.01 mmE682-b, 203a, t=4.99 mmE682-b, 203b, t=5.05 mmE682-b, 204a, t=5.00 mmE682-b, 204b, t=5.03 mm

Figure 2.2. Cylinder wall expansions for tests with emulsion E682-b.

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682-b 2005, t=5.03 mm: Average r,m

E682-b, R22 and R28, t=5.16 mm: Average r,m

Figure 2.3. Cylinder wall expansions for tests with emulsion E682-b, averaged values.


10

2.3.2. Tests performed with aluminized emulsion E682

Three cylinder tests were performed in 2005 with 100 mm copper cylinders and aluminized E682

explosive, and the another batch was used for two tests using 40 mm copper cylinders. The set up with

double sets of contact pins for wall displacement measurements was used for these tests. The data for

the tests are given in Tables 2.5 and 2.6. The cylinder wall expansion results for these tests are shown

in Figures 2.4 and 2.5. The contact pins placed furthest from the 40 mm cylinders are located at a point

relating to a greater relative expansion ( 0,/ mm rr ), than for the 100 mm cylinder tests. Therefore, these

measurement points may be subjected to influence of breakage of the copper cylinder. Observe that

the times are shifted for the registrations to obtain a common starting point for the deformation; this

was done since no common time reference was used for the tests.

Table 2.5. Data for 100 mm cylinder tests performed with aluminized emulsion E682 (Esen et al., 2005).

Test no. 201 Test no. 202 Test no. 205

Density 1178 kg/m3 1182 kg/m3 1180 kg/m3

Detonation velocity 5690 m/s 5606 m/s 5610 m/s

Cylinder type and material Half wall, copper Half wall, copper Half wall, copper

Cylinder inner diameter 100 mm 100 mm 100 mm

Cylinder thickness (1) 5.014 mm (a) 5.050 mm (b)

5.014 mm (a) 5.013 mm (b)

5.016 mm (a) 5.030 mm (b)



11

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682 6% Al, 201a, t=5.01 mm

E682 6% Al, 201b, t=5.05 mm

E682 6% Al, 202a, t=5.01 mm

E682 6% Al, 202b, t=5.01 mm

E682 6% Al, 205a, t=5.02 mm

E682 6% Al, 205b, t=5.03 mm

Figure 2.4. Cylinder wall expansions for tests with aluminized E682 and 100 mm cylinders.

Table 2.6. Data for 40 mm cylinder tests performed with aluminized emulsion E682 (Esen et al., 2005).

Test no. 208 Test no. 209


Detonation velocity 5565 m/s 5484 m/s

Cylinder type and material Half wall, copper Half wall, copper

Cylinder inner diameter 40 mm 40 mm

Cylinder thickness (1) 2.01 mm (a) 1.96 mm (b)

1.97 mm (a) 1.98 mm (b)



12

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18Time (ms)

r,m (m

)

E682 6% Al, 208a, t=2.01 mm

E682 6% Al, 208b, t=1.96 mm

E682 6% Al, 209a, t=1.97 mm

E682 6% Al, 209b, t=1.98 mm

E682 Al 6%, 40 mm, t=1.98 mm:Average r,m

Figure 2.5. Cylinder wall expansions for tests with aluminized E682 and 40 mm cylinders.

2.3.3. Tests performed with pure emulsion E682-a

Seven cylinder tests were performed using copper pipes with 40 to 100 mm diameters, and the

explosive E682-a (Arvanitidis et al., 2004). The test set up used one set of contact pins to measure the

cylinder wall displacements. The data for these tests are given in Table 2.7. However, the thickness

variation of the 80 mm copper cylinders increases the uncertainties regarding the cylinder expansion

measurement of tests no. 139 and 142. Further, for the cylinder tests with 40 and 100 mm diameters

there was only one test performed for each diameter. This strongly reduces the use of data from tests

no. 140 and 144, since later tests have shown relative large differences for the measurements between

tests with the same test set up (Esen et al., 2005). The cylinder wall expansion results for test no. 140

is shown in Figure 2.6, and the cylinder wall expansion results for the tests with 60 mm cylinders are

shown in Figure 2.7.


13

Table 2.7. Data for cylinder tests performed with emulsion E682-a (Arvanitidis et al., 2004).

Test no. Cylinder inner diameter

Nominal cylinder thickness Charge density Detonation velocity

139 80 mm 4.0 ± 0.4 mm 1148 kg/m3 5699 m/s

140 100 mm 5.0 ± 0.1 mm 1130 kg/m3 5697 m/s

141 60 mm 3.0 ± 0.1 mm 1120 kg/m3 5609 m/s

142 80 mm 4.0 ± 0.4 mm 1140 kg/m3 ----

143 60 mm 3.0 ± 0.1 mm 1137 kg/m3 5660 m/s

144 40 mm 2.0 ± 0.1 mm 1120 kg/m3 5662 m/s

145 60 mm 3.0 ± 0.1 mm 1130 kg/m3 5700 m/s (1)

Note: (1) Low quality detonation velocity measurement.

Testing with the emulsion explosive E682-a was also conducted earlier in 2004, these tests are

reported by Esen et al. (2005). However, both the densities for these batches and the thicknesses of the

copper cylinder at the pin location vary for these tests. The data for the 100 mm cylinder tests are

shown in Table 2.8, with the cylinder wall expansion results shown in Figure 2.6. Other tests with the

use of the additives ANFO or 3.5% aluminium to the explosive were also performed.

Table 2.8. Data for cylinder test performed with emulsion E682-a (Esen et al., 2005).

Test no. Cylinder inner diameter

Cylinder wall thickness

Cylinder thickness at pin location (1)

Charge density

Detonationvelocity

154 100 mm Nominal value equal to 5.0 mm

5.4 mm (a) 4.7 mm (b) 1179 kg/m3 5779 m/s

157 100 mm 4.97 - 5.03 mm ---- 1126 kg/m3 5717 m/s

160 100 mm 4.92 - 5.05 mm ---- 1169 kg/m3 5712 m/s



14

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682-a, 140, t 5.0 mm

E682-a, 157, t 5.0 mm

E682-a, 160, t 5.0 mm

E682-a, 154a, t 5.4 mm

E682-a, 154b, t 4.7 mm

E682-a, 140, 157 and 160, t 5.0 mm:Average r,m

Figure 2.6. Cylinder wall expansions for tests with emulsion E682-a and 100 mm cylinders.

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20Time (ms)

r,m (m

)

E682-a, 141, t 3.0 mm

E682-a, 143, t 3.0 mm

E682-a, 145, t 3.0 mm

E682-a 1.129 g/cc D60, t 3.0 mm: Average r,m

Figure 2.7. Cylinder wall expansions for tests with emulsion E682-a and 60 mm cylinders.


15

Detonation velocities for emulsion explosive E682-a with the nominal density 1169 kg/m3 were earlier

determined by Nie et al. (2000). These data are compiled in Tables 2.9 and 2.10. The data were

obtained by MREL MiniTrap registrations using measurement probes inside the charges. A detonation

velocity of 6078 m/s is given by Nie et al. (2001) for this explosive and an infinite charge diameter.

Table 2.9. Detonation velocity measurements performed with emulsion E682-a in PVC tubes (Nie et al., 2000). The rows with double detonation velocities values are for identical test set-ups.

Charge diameter Charge length PVC thickness Detonation velocity

13.6 mm 246 mm 1.25 mm 3896 m/s

17.0 mm 245 mm 1.5 mm 4418 m/s

17.0 mm 207 mm 1.5 mm 4242 m/s

20.5 mm 497 mm 2.25 mm 4606 m/s 4497 m/s

27.0 mm 500 mm 2.5 mm 4916 m/s

27.2 mm 582 mm 2.5 mm 4921 m/s

33.8 mm 495 mm 3.1 mm 5167 m/s

34.6 mm 497 mm 2.7 mm 5166 m/s

45.2 mm 495 mm 2.4 mm 5479 m/s 5405 m/s

56.8 mm 495 mm 3.1 mm 5655 m/s 5532 m/s

67.5 mm 495 mm 3.75 mm 5731 m/s

67.8 mm 495 mm 3.6 mm 5751 m/s

81.4 mm 805 mm 4.3 mm 5707 m/s

84.0 mm 1150 mm 4.5 mm 5734 m/s

84.0 mm 1200 mm 4.5 mm 5748 m/s

105.6 mm 770 mm 2.2 mm 5762 m/s


16

Table 2.10. Detonation velocity measurement performed with emulsion E682-a in steel cylinder (Nie et al., 2000).

Charge diameter Charge length Steel thickness Detonation velocity

68.6 mm 740 mm 3.6 mm 5798 m/s

2.4. Discussion of earlier performed tests

The quality of the experimental data were enhanced during the performed test period, resulting in

more reliable measurement data of the wall displacements for the last test series than for the earlier

test series. The quality of the detonation velocity measurement also varies between the test series.

Further, due to the change of the composition for the explosive, it is not possible to compare results

obtained for different test series directly. Several tests were performed with an identical setup in 2005

but using double pin sets (Esen et al., 2005), these tests showed that there were relatively large

differences between the displacement measurements of the cylinder wall.

It is difficult to obtain the nominal density when the explosive is manufactured, and the density is also

likely to change during the handling of the explosive. This adds to the problems described above when

it comes to the comparisons between different tests and test series.

The cylinder wall displacements from tests with E682-b in 2005 are compared with the earlier tests

with E682-a in Figure 2.8. All these tests are for 100 mm cylinders. The tests with E682-b explosive

show a minor increase in wall displacement vs. time compared to the tests with E682-a explosive.

The results from the tests performed in 2005 using 100 mm cylinders, and emulsion with and without

the additive of aluminium are shown in Figures 2.9 and 2.10. The tests with the additive of aluminium

explosive show a minor increase in wall displacement vs. time compared to the tests with E682-b

explosive. However, there is a large variation between the individual tests, and the changes in wall

displacements are not obvious until average wall displacements are calculated for the different

explosives.


17

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)


E682-a, 140, 157 and 160, t 5 mm: Average r,m

Figure 2.8. Cylinder wall expansions for tests with emulsion E682-a and E682-b.

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

) E682-b, 200a, t=5.09 mmE682-b, 200b, t=5.01 mmE682-b, 203a, t=4.99 mmE682-b, 203b, t=5.05 mmE682-b, 204a, t=5.00 mmE682-b, 204b, t=5.03 mmE682 6% Al, 201a, t=5.01 mmE682 6% Al, 201b, t=5.05 mmE682 6% Al, 202a, t=5.01 mmE682 6% Al, 202b, t=5.01 mmE682 6% Al, 205a, t=5.02 mmE682 6% Al, 205b, t=5.03 mm



18

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682 Al 6%, t=5.02 mm: Average r,m



The obtained wall displacements for the tests performed in 2005 using 40 mm cylinders and

aluminised emulsion are scaled up to be comparable to the 100 mm cylinder tests. An arbitrary time

shift is therefore applied to the data sets obtained for the 40 mm cylinder size, since a common

timescale is missing. For the aluminized emulsion there seems to be no significant change of the

recorded displacements and velocities between the scaled 40 mm data seta and the one obtained for the

100 mm cylinder tests, see Figure 2.11. However, the data for the 40 mm cylinder test were obtained

with an explosive with a slightly greater density. See Table 2.6 earlier. The 100 mm cylinder tests that

used the aluminized emulsion showed relative large experimental variations. Fortunately, these data

were obtained for three tests using the double pin set up. According to this only very small variations

of the behaviour of the aluminised emulsion are likely to occur with the change of the diameter of the

copper cylinder from 40 mm to 100 mm.


19

0.05

0.07

0.09

0.11

0.13

0.15

0.17

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682 Al 6%, t=5.02 mm: Average r,m

E682 Al 6%, 208 and 209, D40 t=1.98 mm:Scaled r,m

Figure 2.11. Cylinder wall expansions for tests with aluminized emulsion E682. Data from the 40 mm cylinder tests are scaled to displacements of a 100 mm cylinder.

In a further attempt to evaluate the diameter effect on the wall velocity, also the two test series with

60 mm and 100 mm cylinders using emulsion E682-a is compared. As for the aluminised emulsion,

this is done by up scaling of the smaller diameter test to 100 mm cylinder test displacements. An

arbitrary time shift is therefore applied to the data sets obtained for the 60 mm cylinder size, since a

common timescale is missing. For the pure emulsions E682-a it seems that there are a small reduction

of the recorded displacements and velocities for the tests using 60 mm cylinders when compared to the

100 mm cylinder tests, see Figure 3.12. However, the experimental variations for the cylinder tests

using this emulsion are relative large, and this experimental uncertainty makes it difficult to draw any

valid conclusions. Further, these data sets are also from early test series, and therefore of lower

quality.


20

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682-a, 140, 157 and 160, t 5.0 mm: Average r,m

E682-a, 141, 143 and 145, D60 t 3.0 mm: Scaled r,m

Figure 2.12. Cylinder wall expansions for tests with emulsion E682-a. Data from the 60 mm cylinder tests are scaled to displacements of a 100 mm cylinder.


21

3. Numerical simulation of cylinder expansion tests

Ideal detonation codes are used to estimate the equation of state for the used emulsion explosives.

These data are then used as a basis for numerical simulations of the earlier discussed cylinder with the

use of an explicit FEM code.

The use of detonation theories to compute the detonation properties of explosives is potentially an

effective method of predicting the performance of explosives. Detonation runs were performed with

the use of Cheetah 2.0 (Fried et al., 1998), and also with Vixen-I developed by AEL (African

Explosives Limited) (Cunningham, 2001 and Cunningham et al., 2006), see chapter 3.2. The later data

sets obtained with Vixen-I were used for the initial numerical simulations of the cylinder tests.

However, the data from Cheetah 2.0 are also included in the report for comparison.

3.1. Ideal detonations runs using Cheetah

The code Cheetah 2.0 was developed by LLNL (Lawrence Livermore National Laboratory), and it is

commonly used for calculation of ideal detonation properties of explosives.

Input data for the Cheetah runs are the composition of the explosive, and the properties of each

ingredient. See Tables 2.1, 2.2 and 3.1. The BKWS library was used for the runs with a freezing

temperature at 2145 K, and with a maximum expansion of 50 times. The BKW equation of state was

used with it's default parameters. A JWL fit was also obtained from Cheetah. However, note that the

JWL fit will depend on the calculated relative volumes for the runs. The output data, incl. the JWL fit,

from Cheetah runs are compiled in Tables 3.2 and 3.3 for the used emulsion explosives.


22

Table 3.1. Properties of the ingredients for the explosive used for Cheetah runs.

Component Ingredient Chemical formula Heat of formation Density

Ammonium Nitrate NH4NO3 -365.14 kJ/mol 1.73 g/cc

Sodium Nitrate NaNO3 -424.84 kJ/mol 2.26 g/cc Salt solution

Water H20 -285.83 kJ/mol 1.00 g/cc

Emulsifier Lubrizol 2724 (1) C6,8H13.9N0.5O2(1) -336.56 kJ/mol (1) 0.916 g/cc (1)

Mineral oil Whiterex E309 (2) C12H26(3) -673.88 kJ/mol (3) 0.850 g/cc (2)

Micro-balloons 3M K20 SiO2 Noncrystalline

form (glass) -910.86 kJ/mol (4) 2.20 g/cc (5)

Aluminium A80 Al N/A 2.70 g/cc

Notes: (1) Data from the manufacturer Lubrizol Lim.: Density at 15.6 °C is equal to 916 kg/m3 and heat of formation at liquid state is -2500 kJ/kg (Arvanitidis et al., 2004). (2) Data from the manufacturer Mobil Oil: density at 20.0 °C is equal to 850 kg/m3 and heat of combustion is 45.6 MJ/kg (Arvanitidis et al., 2004). (3) Chemical formula and heat of formation according to Nie et al. (2000). (4) Heat of formation according to Nie et al. (2000). (5) Density equal to 2.204 g/cc for fused quarts (Marsh, 1980).


23

Table 3.2. Cheetah output for the pure emulsion explosives.

Emulsion E682-a

Emulsion E682-a

Emulsion E682-b

Emulsion E682-b


Shock velocity 5970 m/s 6056 m/s 6136 m/s 6246 m/s

Mechanical energy at 0.1013 MPa pressure 3.215 kJ/cc 3.330 kJ/cc 3.404 kJ/cc 3.470 kJ/cc

JWL fit from Cheetah -------------------- -------------------- -------------------- --------------------

0E = )(vEd 3.458 kJ/cc 3.582 kJ/cc 3.657 kJ/cc 3.730 kJ/cc

A 470.05 GPa 544.75 GPa 569.72 GPa 620.97 GPa

1R 5.561 5.606 5.613 5.644

B 3.792 GPa 4.173 GPa 4.319 GPa 4.581 GPa

2R 1.209 1.221 1.223 1.231

C 0.788 GPa 0.802 GPa 0.817 GPa 0.823 GPa

0.422 0.430 0.434 0.438

CJ condition: Calculated P 8.736 GPa 9.485 GPa 9.797 GPa 10.26 GPa

CJ condition: Fit P 8.916 GPa 9.681 GPa 10.001 GPa 10.474 GPa

dE at 100 MPa pressure 2.19 MJ/kg 2.24 MJ/kg 2.28 MJ/kg 2.30 MJ/kg



24

Table 3.3. Cheetah output for the aluminized emulsion explosive.

Aluminized E682 with 6% aluminium

Density 1180 kg/m3

Shock velocity 6071 m/s

Mechanical energy at 0.1013 MPa pressure 4.421 kJ/cc

JWL fit from Cheetah --------------------

0E = )(vEd 5.680 kJ/cc

A 363.01 GPa

1R 4.878

B 2.431 GPa

2R 0.805

C 0.546 GPa

0.164

CJ condition: Calculated P 9.990 GPa

CJ condition: Fit P 10.518 GPa

dE at 100 MPa pressure 2.66 MJ/kg


3.2. Ideal detonations runs using Vixen-I

The detonations runs that are used to get initial input for the JWL (Jones-Wilkinson-Lee) equation of

state (EOS) were performed with the use of Vixen-I version 5.1 developed by AEL (African

Explosives Limited) (Cunningham, 2001 and Cunningham et al., 2006).


25

Input data for the Vixen-I runs are the composition of the explosive, and the properties of each

ingredient. However, the densities of the ingredients are not used as input for this code. See Tables

2.1, 2.2 and 3.4. The default properties of the ingredients in Vixen-I are used if the ingredient exists in

the database. The obtained JWL data are given in Tables 3.5 and 3.6.

Table 3.4. Properties of the ingredients for the explosive used for Vixen-I runs.

Component Ingredient Chemical formula Heat of formation (1)

Dissolved Ammonium Nitrate NH4NO3 -4561.4 kJ/kg

Sodium Nitrate NaNO3(2) -5502.0 kJ/kg Salt solution

Water H20 -15865.3 kJ/kg

Emulsifier Lubrizol 2724 (3) C6,8H13.9N0.5O2(3) -2500 kJ/kg (3)

Mineral oil Whiterex E309 (4) C12H26(5) -3955 kJ/kg (5)

Micro-balloons 3M K20 SiO2 Noncrystalline

form (glass) -14301.7 kJ/kg

Aluminium A80 Al N/A

Notes: (1) Heat of formation are default values for Vixen-I if not another source is specified. (2) Small amounts of hydrogen and chlorine are accounted for in the Vixen-I default input.

(3) Data from the manufacturer Lubrizol Lim.: Density at 15.6 °C is equal to 916 kg/m3 and heat of formation at liquid state is -2500 kJ/kg (Arvanitidis et al., 2004). (4) Data from the manufacturer Mobil Oil: density at 20.0 °C is equal to 850 kg/m3 and heat of combustion is 45.6 MJ/kg (Arvanitidis et al., 2004). (5) Chemical formula and heat of formation according to Nie et al. (2000).


26

Table 3.5. Vixen-I output for the pure emulsion explosives.

Emulsion E682-a

Emulsion E682-a

Emulsion E682-b

Emulsion E682-b


Shock velocity 5664 m/s 5840 m/s 5929 m/s 6028 m/s

JWL fit from Vixen-I ------------------- ------------------- ------------------- -------------------


A 243.214 GPa 261.314 GPa 272.118 GPa 282.472 GPa

1R 4.991 4.933 4.933 4.910

B 7.671 GPa 8.366 GPa 8.676 GPa 9.097 GPa

2R 1.967 1.958 1.962 1.962

C 0.963 GPa 0.979 GPa 1.000 GPa 1.004 GPa

0.499 0.512 0.520 0.529

CJ condition: Calculated P 8.821 GPa 9.713 GPa 10.016 GPa 10.688 GPa

CJ condition: Fit P 8.750 GPa 9.636 GPa 9.223 GPa 10.624 GPa




27

Table 3.6. Vixen-I output for the aluminized emulsion explosive.


Density 1180 kg/m3

Shock velocity 5586 m/s

JWL fit from Vixen-I --------------------

0E = )(vEd 3.928 kJ/cc

A 251.094 GPa

1R 5.215

B 9.861 GPa

2R 2.112

C 1.370 GPa

0.501

CJ condition: Calculated P 9.279 GPa

CJ condition: Fit P 9.223 GPa



3.3. Simulation of reference cylinder test using PETN

Simulations are performed of cylinder tests to justify the numerical assumptions made for the

modelling. The simulations are performed with the JWL equation of state described earlier and with

the programmed burn algorithm. Simulations using both the data based on the ideal detonation code

Vixen-I and the equation of state from the cylinder test are used for the simulations. The used data sets

for the PETN are given in Table 3.7. The Figures 3.1 and 3.2 show plots of pressure and detonation

energy vs. relative volume for both these data sets, respectively. The used material model for copper is

also described later in this chapter.


28

Table 3.7. JWL fit to PETN cylinder tests and ideal detonation data from Vixen-I.

PETN PETN

Source Cylinder JWL Vixen-I output

Reference Souers et al., 1996 N/A


Shock velocity 8283 m/s 8197 m/s

)(vEd 11.2 kJ/cc 9.932 kJ/cc

A 622.045 GPa 424.255 GPa

1R 4.5 4.147

B 21.465 GPa 21.462 GPa

2R 1.5 1.776

C 1.4966 GPa 3.264 GPa

0.29 0.674

CJ condition: P 33.31 GPa 32.28 GPa

dE at 100 MPa pressure 4.75 MJ/kg 4.95 MJ/kg

dE at 20 MPa pressure 5.23 MJ/kg 5.27 MJ/kg

10

100

1000

10000

100000

0 5 10 15 20 25 30Relative volume (-)

Pre

ssur

e (M

Pa)

PETN, Cylinder test JWL, density=1.766 g/cc

PETN, Vixen data set, density=1.766 g/cc

Values plotted to a cut off pressure of 20 MPa

Figure 3.1. Comparison between pressure for JWL data set from cylinder tests and Vixen-I run.


29

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0 5 10 15 20 25 30Relative volume (-)

Det

onat

ion

ener

gy (k

J/cc

)

PETN, Cylinder test JWL, density=1.766 g/cc

PETN, Vixen data set, density=1.766 g/cc


Figure 3.2. Comparison between detonation energy for JWL data set from cylinder tests and Vixen-I run.

The Gr neisen shock equation of state in combination with the Johnson and Cook (1985) strength

model are used for the copper cylinder. The input data for these material models are described by

equations 3.1 and 3.2, with values given in Tables 3.8 and 3.9.

PS USCU (Eq. 3.1)

where SU is the shock velocity

PU is the particle velocity

C and S are material parameters.

Table 3.8. Shock data for copper (Marsh, 1980).

Value

Density 8924 kg/m3

C 3.91×103 m/s

S 1.51


30

m

roommelt

roomn

TTTTCBA 1ln1

0

(Eq. 3.2)

where A , B , n ,C , m are strength constants T is the current temperature

roomT is the initial temperature

meltT is the melting temperature

0 is equal to 1.0 s-1.

Table 3.9. Elastic and strength data used for copper (Johnson and Cook, 1985).

Value

G 46 GPa

E 124 GPa

Poisson's ratio 0.34

A 90 MPa

B 292 MPa

n 0.31

C 0.025

m 1.09

Tmelt 1356 K

Troom 293 K

Cp 383 J/KgK

The simulations are performed using a 2D axial-symmetric Eulerian formulation. The use of an

Eulerian description with a stationary mesh avoids the heavily distorted elements associated with

simulations of contact detonations using Lagrangian elements. The use of the rotational symmetry

reduces the computational resources needed for the simulations considerably, when compared to

running 3D simulations of the same cases. All simulation geometries use a copper cylinder with

1.00 m length, and for the PETN simulations the explosive is extended one radius outside the copper

cylinder in the end of the detonation point. The initial detonation point is located 30 mm from the end

of the copper cylinder, i.e. outside the cylinder. The geometries for 60 mm and 100 mm simulations of

cylinder tests are shown in Figures 3.3 to 3.5. The geometries for the simulations were chosen to be


31

representative for the later simulations of emulsion explosives. The used element size for the explosive

and copper cylinder is 0.5 mm × 0.5 mm for all PETN simulations.


Figure 3.4. Model geometry for simulation with full wall 60 mm cylinders for PETN simulations.


Data from cylinder tests with PETN are compiled in Table 3.10 (Souers et al., 1996). The Fabry-Perot

interferometer measurement results in a lower velocity than the streak camera registration. This is due

to the different measurement directions that are used. The ratio between the interferometer and streak

camera registrations was approximately 0.97 for a test with RX-48-AA explosive using full wall

cylinders (Souers and Haselman, 1994). This value is close to the ratio between interferometer and

streak camera measurements for the half wall PETN shot no. 586 in Table 3.10. The angle of the

Fabry-Perot interferometer is chosen to obtain a registration of the velocity approximately in the

direction of the particle movement of the cylinder wall. Typical angles for the Fabry-Perot

interferometer measurements of cylinder tests of military high density explosives are between 7° and

9°, measured from a normal to the cylinder wall. This angle needs to be increased for explosives with

lower detonation velocities, e.g. 4000 to 5000 m/s. Accordingly, the ratio between particle velocity

and radial expansion velocity are also changed for both tests and simulations for explosives with lower

detonation velocities.


32

Table 3.10. Cylinder tests data for PETN (Souers et al., 1996).

PETN PETN PETN PETN PETN

Density 1766 kg/m³ 1766 kg/m³ 1761 kg/m³ 1765 kg/m³ 1765 kg/m³

Shock velocity 8.28×10³ m/s 8.28×10³ m/s 8.32×10³ m/s -------- 8.28×10³ m/s

Cylinder type and material Half wall, Cu Half wall, Cu Half wall, Cu Full wall, Cu Full wall, Cu

Measurement type Fabry-Perot interferometer

Streakcamera

Streakcamera

Streakcamera

Streakcamera

Shot No. 586 586 511 187 209

Cylinder diameter 25.4 mm 25.4 mm 25.4 mm 25.4 mm 25.4 mm

Velocity at v =2.2 (1) 2040 m/s 2080 m/s 2086 m/s 1570 m/s 1580 m/s



Note: (1) The given relative volumes are determined for 6.0, 12.5 and 19.0 mm radial expansion for the 25.4 mm diameter cylinders (Souers et al., 1996).

Simulations of cylinder tests with the JWL data set from independent cylinder tests according to

Souers et al. (1996) show a good agreement when the scaled results from the simulations compiled in

Table 3.11 are compared with the tests results shown earlier in Table 3.10. The errors are typically in

the order of a few percent, and given that all input are material properties obtained from literature this

seems reasonable. The particle velocity vs. radial expansion curves from the simulations are shown in

Figure 3.6. The use of the Vixen-I data set for PETN increases the expansion velocity of the cylinder

wall, see Table 3.11 and Figure 3.6.


33

Table 3.11. Results from simulations of cylinder tests for PETN using cylinder test JWL.

PETN PETN PETN

Density 1766 kg/m³ 1766 kg/m³ 1766 kg/m³

Shock velocity 8.28×10³ m/s 8.28×10³ m/s 8.28×10³ m/s

Cylinder type and material Half wall, Cu Half wall, Cu Full wall, Cu

Cylinder diameter 100.0 mm 60.0 mm 60.0 mm

ParticleV at v =2.2 (1) 2.12×10³ m/s 2.10 ×10³ m/s 1.56×10³ m/s

ParticleV at v =4.1 (1) 2.28×10³ m/s 2.28×10³ m/s 1.68×10³ m/s

ParticleV at v =6.5 (1) 2.35×10³ m/s 2.35×10³ m/s 1.74×10³ m/s

StreakV at v =2.2 (1) 2.20×10³ m/s 2.19×10³ m/s 1.61×10³ m/s



StreakParticle VV 0.96 0.96 0.98

(2) 7.9° ±0.2° 7.9° ±0.1° 6.2° ±0.3°

Note: (1) The given relative volumes are determined for scaled distances equal to 6.0, 12.5 and 19.0 mm radial expansion for the standardised 25.4 mm cylinders. (2) The angle is measured between the vector for the particle velocity and a normal to the cylinder wall.


34

Table 3.12. Results from simulations of cylinder tests for PETN using Vixen-I data.

PETN PETN

Density 1766 kg/m³ 1766 kg/m³

Shock velocity 8.197×10³ m/s 8.197×10³ m/s

Cylinder type and material Half wall, Cu Full wall, Cu

Cylinder diameter 60.0 mm 60.0 mm

ParticleV at v =2.2 (1) 2. 14×10³ m/s 1.59×10³ m/s

ParticleV at v =4.1 (1) 2.32×10³ m/s 1.71×10³ m/s

ParticleV at v =6.5 (1) 2.40×10³ m/s 1.78×10³ m/s

StreakV at v =2.2 (1) 2.32×10³ m/s 1.64×10³ m/s

StreakV at v =4.1 (1) 2.42×10³ m/s 1.75×10³ m/s

StreakV at v =6.5 (1) 2.50×10³ m/s 1.83×10³ m/s

StreakParticle VV 0.96 0.98

(2) 8.1° ±0.2° 6.4° ±0.3°

Note: (1) The given relative volumes are determined for scaled distances equal to 6.0, 12.5 and 19.0 mm radial expansion for the standardised 25.4 mm cylinders. (2) The angle is measured between the vector for the particle velocity and a normal to the cylinder wall.


35

0

500

1000

1500

2000

2500

-0.005 0.000 0.005 0.010 0.015 0.020 0.025Radial expansion normalized to deformation for a 25.4 mm cylinder (m)

Parti

cle

velo

city

at o

uter

sur

face

(m/s

) .

PETN 1.766 g/cc D=60 mm t=3.00 mm, Cyl. test JWLPETN 1.766 g/cc D=60 mm t=6.00 mm, Cyl. test JWLPETN 1.766 g/cc D=60 mm t=3.00 mm, Vixen data setPETN 1.766 g/cc D=60 mm t=6.00 mm, Vixen data set

Figure 3.6. Cylinder wall expansions for simulations with PETN using the Vixen-I and cylinder test JWL data sets. JWL data from cylinder tests results in the lowest velocity in each set.

3.4. Simulation of cylinder tests performed with pure emulsion E682

These simulations use the same set up as the earlier models for the cylinder tests with PETN, but with

changes to the element meshes and with the material data for the explosive changed to describe

emulsions. Further, the small variations in the thickness for the walls for the different tests are

accounted for by changes of the density of the copper. This is to obtain the right masses of the cylinder

wall at the measurement location without applying changes to the element mesh.

Simulations with input data for the emulsion explosive according to the Vixen-I runs are used as

references, and later to estimate the error for the detonation energy calculated with Vixen-I for ideal

detonation of emulsion explosives. Modified data sets are constructed with the use of 1R , 2R and

from Vixen-I, and with the experimentally determined velocity of detonation. The energy is then

reduced to obtain a fit to the cylinder tests by changes of the values for A, B and C. The improved, but

still very rough, estimates of the detonation energies are obtained by a fit of the expansion of the

cylinder obtained in the simulations to the measured wall expansion from the cylinder tests. However,

since the measurement variations for the major part of the earlier discussed tests are substantial, this

methodology was considered to be adequate for this preliminary study.

All simulation geometries use a copper cylinder with 1.00 m length, and for the emulsion simulations

the explosive is extended 50 mm outside the copper cylinder in the end of the detonation point. The


36

initial detonation point is located 30 mm from the end of the copper cylinder, i.e. outside the cylinder.

The geometries for 60 and 100 mm cylinder test simulations are shown in Figures 3.7 and 3.8,

respectively.

The used element size for the explosive and copper cylinder is 0.5 mm × 0.5 mm for the simulations

with the 100 mm cylinder and 0.5 mm × 0.3 mm for the simulations with the 60 mm cylinder. The

shortest distance is in the radial direction.

Figure 3.7. Model geometry for simulation with half wall 60 mm cylinders for emulsion simulations.


3.4.1. Simulation of tests with emulsion E682-b

Simulations of cylinder tests using the explosive E682-b are performed. A modified data set for the

JWL equation of state is determined to improve the agreement between the simulations and the earlier

discussed tests. The experimental data for the cylinder tests of interest for the emulsion E682-b are

compiled in Table 3.13 below.

Table 3.13. Compiled experimental data for the pure emulsion explosives E682-b.

Emulsion E682-b Emulsion E682-b

Test no. 200, 203, 204 R22, R28

Cylinder diameter 100 mm 100 mm

Average density 1180 kg/m3 1203 kg/m3

Average detonation velocity 5866 m/s 5763 m/s

Average wall thickness at measurement location 5.03 mm 5.16 mm


37

The used JWL equation of state data sets for emulsion E682-b are given in Table 3.14 and shown in

Figure 3.9. The modified data set B-11 for emulsion E682-b with a density of 1180 kg/m³ reduces the

detonation energy with 5.8% at the pressure 100 MPa and with 4.6% at the pressure 20 MPa, when

compared to the ideal detonation calculation set obtained by Vixen-I. This change of detonation

energies results in a good fit of the simulation data to the experimental cylinder wall displacements

using 100 mm cylinders, see Figure 3.10.

Table 3.14. Input data for the pure emulsion explosives E682-b.

Emulsion E682-b Emulsion E682-b Emulsion E682-b

Data set no. B-01 B-11 B-02

Type of data Vixen-I output Modified data (1) Vixen-I output

Density 1180 kg/m3 1180 kg/m3 1203 kg/m3

Shock velocity 5929 m/s 5866 m/s (2) 6028 m/s

0E = )(vEd 3.317 kJ/cc 3.176 kJ/cc 3.387 kJ/cc

A 272.12 GPa 285.73 GPa 282.47 GPa

1R 4.933 4.933 4.910

B 8.676 GPa 6.715 GPa 8.676 GPa

2R 1.962 1.962 1.962

C 1.000 GPa 0.997 GPa 1.004 GPa

0.520 0.520 0.529

Detonation pressure 9.223 GPa 10.064 GPa 10.624 GPa

dE at 100 MPa pressure 2.07 MJ/kg 1.95 MJ/kg 2.11 MJ/kg


Note: (1) Modified data sets with 1R , 2R and from Vixen-I, and with the experimentally determined velocity of detonation. The energy is reduced to obtain a fit to the cylinder tests by changes of the values for A, B and C, and thereby is also 0E determined. (2) Experimentally determined velocity of detonation.


38

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 5 10 15 20Relative volume (-)

Det

onat

ion

ener

gy (k

J/cc

)

E682-b, Vixen set B-02, density=1.203 g/cc

E682-b, Vixen set B-01, density=1.180 g/cc

E682-b, Data set B-11, density=1.180 g/cc


Figure 3.9. Detonation energy from JWL EOS data sets for simulations with emulsion E682-b.

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)


E682-b, R22 and R28, t=5.16 mm: Average r,m

Sim. E682-b 1.180 g/cc D100 t=5.03 mm Ideal

Sim. E682-b 1.203 g/cc D100 t=5.16 mm Ideal

Sim. E682-b 1.180 g/cc D100 t=5.03 mm Set B-11

Figure 3.10. Cylinder wall expansions for tests and simulations with emulsion E682-b using 100 mm cylinders.


39

3.4.2. Simulation of tests with emulsion E682-a

Simulations of cylinder tests are performed using the emulsion explosive E682-a with the same set up

as the earlier models for the cylinder tests with emulsion E682-b. Two modified data set to the JWL

equation of state are determined to improve the agreement between the simulations and earlier

discussed cylinder tests. The experimental data for the cylinder tests of interest for the emulsion E682-

b are compiled in Table 3.15 below.

Table 3.15. Compiled experimental data for the pure emulsion explosives E682-a.

Emulsion E682-a Emulsion E682-a Emulsion E682-a

Test no. 140, 157 160 141, 143, 145

Cylinder diameter 100 mm 100 mm 60 mm

Average density 1128 kg/m3 1169 kg/m3 1129 kg/m3

Average detonation velocity 5706 m/s 5712 m/s 5635 m/s (1)

Average wall thickness at measurement location 5.0 mm 5.0 mm 3.0 mm

Note: (1) Detonation velocity for test no. 145 not considered in the calculation of average value.

The used JWL equation of state data sets for emulsion E682-a are given in Table 3.16 and shown in

Figure 3.11. The modified data set A-16 for emulsion E682-a with a density of 1129 kg/m³ reduces the

detonation energy with 3.5% at the pressure 100 MPa and with 3.0% at the pressure 20 MPa, when

compared to the ideal detonation calculation set obtained by Vixen-I. This change of detonation

energies results in a fair fit of the simulation data to the experimental cylinder wall displacements

using 60 mm cylinders, see Figure 3.12. A reduction of the detonation energy with approximately 4%

instead might improve the fit to experimental data. A modified JWL data set was not determined for

the emulsion E682-a with the density 1129 kg/m³ in 100 mm cylinders due to uncertainties of the data

obtained from these cylinder tests. However, the base data set from the Vixen-I run was used for a

simulation and the result is shown in Figure 3.13a.

The modified data set A-11 for emulsion E682-a with a density of 1169 kg/m³ reduces the detonation

energy with 4.4% at the pressure 100 MPa and with 3.8% at the pressure 20 MPa, when compared to

the ideal detonation calculation set obtained by Vixen-I. This change of detonation energies results in

a good fit of the simulation data to the experimental cylinder wall displacements using a 100 mm

cylinder, see Figure 3.13b.


40

Table 3.16. Input data for the pure emulsion explosives E682-a.

Emulsion E682-a

Emulsion E682-a

Emulsion E682-a

Emulsion E682-a

Data set no. A-01 A-16 A-02 A-11

Type of data Vixen-I output Modified data (1) Vixen-I output Modified data (1)


Shock velocity 5664 m/s 5635 m/s (2) 5840 m/s 5712 m/s


A 243.21 GPa 253.49 GPa 261.31 GPa 258.87 GPa

1R 4.991 4.991 4.933 4.933

B 7.671 GPa 6.481 GPa 8.366 GPa 7.075 GPa

2R 1.967 1.967 1.958 1.958

C 0.963 GPa 0.960 GPa 0.979 GPa 0.982 GPa

0.499 0.499 0.512 0.512

Detonation pressure 8.750 GPa 8.967 GPa 9.636 GPa 9.601 GPa





41

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


Det

onat

ion

ener

gy (k

J/cc

)

E682-a, Vixen set A-02, density=1.169 g/cc

E682-a, Vixen set A-01, density=1.129 g/cc

E682-a, Data set A-11, density=1.169 g/cc



Figure 3.11. Detonation energy from JWL EOS data sets for simulations with emulsion E682-a.

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20Time (ms)

r,m (m

)

E682-a, 141, t 3.0 mm

E682-a, 143, t 3.0 mm

E682-a, 145, t 3.0 mm

Sim. E682-a 1.129 g/cc D60 t 3.0 mm Ideal

Sim. E682-a 1.129 g/cc D60 t 3.0 mm Set A-16

E682-a 1.129 g/cc D60, t 3.0 mm: Average r,m

Figure 3.12. Cylinder wall expansions for tests and simulations with emulsion E682-a using 60 mm cylinders.


42

a)

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682-a, 140, t 5.0 mm

E682-a, 157, t 5.0 mm


b)

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682-a, 160, t 5.0 mm



Figure 3.13. Cylinder wall expansions for tests and simulations with emulsion E682-a using 100 mm cylinders. The diagrams (a) and (b) refer to blends with different densities for the emulsion explosive.


43

3.5. Simulation of cylinder tests performed with aluminized emulsion

These simulations use the same set up as the earlier models for the cylinder tests with pure emulsion

explosives, but with the material data for the explosive changed to describe the emulsion with 6%

aluminium. Instead of 60 mm cylinder tests, a set of 40 mm cylinder tests are simulated. Further, as for

the simulations of pure emulsions, the small variations in the thickness for the walls for the different

tests are accounted for by changes of the density of the copper.

All simulation geometries use a copper cylinder with 1.00 m length, and the emulsion explosive is

extended 50 mm outside the copper cylinder in the end of the detonation point. The initial detonation

point is located 30 mm from the end of the copper cylinder, i.e. outside the cylinder. The geometries

for 40 and 100 mm simulations of cylinder tests are shown in Figures 3.14 and 3.15, respectively.

The used element size for the explosive and copper cylinder is 0.5 mm × 0.5 mm for the simulations

with the 100 mm cylinder, and 0.5 mm × 0.2 mm for the simulations with the 40 mm cylinder. The

shortest distance is in the radial direction.



In the same way as for the pure emulsions, simulations with input data for the aluminized explosive

according to the Vixen-I run are used as references, and later to estimate the error for the detonation

energy calculated with Vixen-I for ideal detonation of aluminized emulsions.

Two modified data set to the JWL equation of state are determined to improve the agreement between

the simulations and earlier discussed cylinder tests. The used methodology is the same that earlier was

used the pure emulsion explosives. The experimental data for the cylinder tests of interest for the

aluminized emulsion are compiled in Table 3.17 below.


44

Table 3.17. Compiled experimental data for the aluminized emulsion explosives E682.



Test no. 201, 202, 205 208, 209

Cylinder diameter 100 mm 40 mm

Average density 1180 kg/m3 1201 kg/m3

Average detonation velocity 5635 m/s 5525 m/s

Average wall thickness at measurement location 5.02 mm 1.98 mm

The used JWL equation of state data sets for aluminized emulsion E682 are given in Table 3.18 and

shown in Figure 3.16. The modified data set C-11 for the aluminized emulsion E682 with a density of

1180 kg/m³ reduces the detonation energy with 2.1% at the pressure 100 MPa and with 1.9% at the

pressure 20 MPa, when compared to the ideal detonation calculation set obtained by Vixen-I. This

change of detonation energies results in a fair fit of the simulation data to the experimental cylinder

wall displacements using 100 mm cylinders, see Figure 3.17. A reduction of the detonation energy

with approximately 3% instead might further improve the fit to experimental data.

The simulations of the tests performed with 40 mm cylinders used data sets for an aluminized

emulsion with the nominal density of 1180 kg/m³, although the density of the explosive for the tests

had average density of 1201 kg/m³. The modified data set C-14 for the aluminized emulsion E682 with

a density of 1180 kg/m³ reduces the detonation energy with 3.4% at the pressure 100 MPa and with

2.9% at the pressure 20 MPa, when compared to the ideal detonation calculation set obtained by

Vixen-I. These changes of detonation energies results in a fair fit of the simulation data to the

experimental cylinder wall displacements using 40 mm cylinders, see Figure 3.18. A reduction of the

detonation energy with approximately 3% instead might further improve the fit to experimental data.


45

Table 3.18. Input data for the aluminized emulsion explosives E682.




Data set no. C-01 C-11 C-14

Type of data Vixen-I output Modified data (1) Modified data (1)

Density 1180 kg/m³ 1180 kg/m³ 1180 kg/m³

Shock velocity 5586 m/s 5635 m/s (2) 5525 m/s (2)

0E = )(vEd 3.928 kJ/cc 3.868 kJ/cc 3.833 kJ/cc

A 251.09 GPa 276.20 GPa 262.78 GPa

1R 5.215 5.215 5.215

B 9.861 GPa 8.436 GPa 7.911 GPa

2R 2.112 2.112 2.112

C 1.370 GPa 1.371 GPa 1.380 GPa

0.501 0.501 0.501

Detonation Pressure 9.223 GPa 9.531 GPa 9.202 GPa





46

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


Det

onat

ion

ener

gy (k

J/cc

)

E682 Al 6%, Vixen set C-01, density=1.180 g/cc

E682 Al 6%, Data set C-11, density=1.180 g/cc



Figure 3.16. Detonation energy from JWL EOS data sets for simulations with aluminized emulsion E682.

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682 Al 6%, D100 mm, t=5.02 mm: Average r,m

Sim. E682 Al 6% 1.180 g/cc D100 t=5.02 mm Ideal

Sim. E682 Al 6% 1.180 g/cc D100 t=5.02 mm Set C-11

Figure 3.17. Cylinder wall expansions for tests and simulations with aluminized E682 using 100 mm cylinders.


47

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.10 0.12 0.14 0.16 0.18 0.20 0.22Time (ms)

r,m (m

)

E682-a, 160, t 5.0 mm



Figure 3.18. Cylinder wall expansions for tests and simulations with aluminized E682 using 40 mm cylinders.


48


49

4. Discussion of simulation results

Unique fits to the parameters to the JWL equation of state for explosives are not likely to be obtained,

several sets of parameters can be determined. Further, the obtained parameter sets are only valid for

the tested diameter of the explosive and the used confinement for the explosive, this is due to the use

of non-ideal emulsion explosives.

4.1. Simulation of reference case with PETN

The used numerical methodology reproduces the expected behaviour of the cylinder test with PETN

explosive to an acceptable degree. Even for this well known and ideal explosive that is considered to

be well described by the JWL equation of state, there exist several different parameter sets for this

equation of state. Different parameter sets can be chosen to obtain an improved fit of the pressure

within a certain volume expansion interval. Further, more complicated equations of state exist.

However, these equations of state are more difficult to derive material parameters for, although data is

likely to be available for several types of military explosives. The data sets obtained from cylinder

tests (Souers et al., 1996) and the data set obtained with the ideal detonation code Vixen-I, do not

result in simulations results with same cylinder wall velocities. A homogenous and well defined

explosive, and with a short reaction zone, should be relatively easy to determine equation of state data

for by using an ideal detonation code. Even though the same energy vs. volume relationships are not

determined from cylinder tests and ideal detonation codes.

4.2. Simulation of pure emulsion explosives

The parameter sets for the JWL equation of state from Vixen-I together with a programmed burn

algorithm result in a relatively fair agreement when used as input FEM analysis of cylinder tests to

simulate pure emulsion explosives. To obtain a fair to good fit, only small changes of the parameters

are needed. The detonation energy for the pure emulsion needed to be reduced with somewhere

between 3% and 5%, at the pressure 20 MPa, to obtain a fair fit to the wall displacements from the

cylinder tests with FEM simulations. The actual value depends on the used composition, density of the

explosive and diameter of the used cylinder. Theses changes in detonation energies may be smaller

than the error of an ideal detonation code to determine detonation energies at a given pressure. As a

consequence of this, an ideal detonation code can not be used on its own to give an accurate

description of detonation energies of emulsion explosives.


50

4.3. Simulation of an aluminized emulsion explosive

One major problem is to simulate the behaviour of aluminized explosive is the slow burning rate for

the aluminium. Due to the slow energy release of the aluminium, only a fraction of this material is

likely to be burned within the detonation driving zone. The particle size of the aluminium is likely to

influence the burning rate of the aluminium. To simulate this type of behaviour, it is necessary to use a

kinetic law to describe the reaction rate of the explosive. However, reasonable results for the cylinder

wall displacement were obtained by reducing the detonation energy for the JWL equation of state.

The detonation energy for the aluminized emulsion needed to be reduced with somewhere between 2%

and 4% from the value calculated by an ideal detonation code, at the pressure 20 MPa, to obtain a fair

fit to the wall displacements from the cylinder tests with FEM simulations. As for the pure emulsions,

theses changes in detonation energies may be smaller than the error of an ideal detonation code to

determine detonation energies at a given pressure. Further, the reaction rate of the aluminium particles

is lower than for the emulsion part of the explosive. The reaction rate for the aluminium also depends

on the size of the particles. This is not considered within an ideal detonation code, and the uncertainty

of the energy vs. pressure relationship is therefore likely to be further increased.

It is also known that the expansion of gases from aluminized explosive is not well described by the

JWL equation of state. Other equation of states may be bore suitable to use for this type of explosive.

However, the use of a more advanced equation of state may not be of any real advantage at the time

being since there are large uncertainties regarding the experimental data.


51

5. Summary

Although, many explosives are non-ideal, there are great differences in the length of both the

detonation driving zone and the reaction zone, and also curvature of the detonation front. In general,

short detonation driving and reaction zones are likely to result in a more accurate description of the

evaluated equation of state for the explosive by the used methodology. Even though the cylinder

expansion test is considered to give reliable equation of state data for high density military explosives,

e.g. PETN, this might not be the case for an emulsion explosive. For the later case, the width of the

reaction zone and curvature of the detonation front are likely to influence the acceleration of the

cylinder wall, thereby reducing the possibility to determine pure equation of state data from the

cylinder test even with the use of numerical simulation. However, a rough estimate of the detonation

energy of the used explosive may be determined. This estimate of the detonation energy is likely to be

a better estimate than the values obtained directly from an ideal detonation code. The use of this

methodology may be limited to emulsion without additives of coarse aluminium particles, prilled AN

or ANFO, since these additives tend to reduce the burning rate and extend the reaction zone

5.1. Cylinder expansion tests

The quality of the cylinder expansion tests was enhanced during the testing period, giving more

reliable data for the later test series. Further, since the composition of the emulsion was changed in

2005 with an increased density as a result, the earlier data are not directly comparable with the later

tests. The use of a streak camera for the registration of cylinder wall displacements enhances the time

resolution since a continues registration is obtained, and an absolute time reference is also obtained.

The use of continues displacement data gives additional information that are valuable for the

evaluation of the parameters for the explosives by numerical simulation. The use of copper cylinders

for tests with a non-ideal emulsion explosive is likely to result in an increased initial confinement

compared to a rock material. Thereby, the detonation reaction is likely to be influenced, e.g. the

detonation velocity is likely to be increased. This is caused by the higher impedance of the

surrounding material. Other materials may be better suitable to use for this type of explosives if the

behaviour of the explosive in a rock of primary interest.

The cylinder expansion tests only showed a minor increase of the wall displacement vs. time for the

emulsion with 6% aluminium, compared with the pure emulsion. Further, the aluminised emulsion

showed very small changes in behaviour when the diameter of the cylinder was reduced from 100 mm

to 40 mm. Earlier tests showed a greater influence on the wall displacements for the pure emulsion

E682 when the diameter of the cylinder was reduced from 100 mm to 60 mm, even though it is still

small effects that are discussed. It is not determined if this is an effect caused by the uncertainties of


52

the performed cylinder tests, or that the influence from the diameter effect actually is greater for this

emulsion.

5.2. Evaluation methodology using ideal detonation codes and FEM analysis

An ideal detonation code to obtain input data for the JWL equation of state can not be used on it's own

for emulsion explosives in these cylinder dimensions. The initial parameters values that were input to

LS-DYNA did not result in an acceptable agreement between the cylinder wall displacements from

tests and simulations The output from an ideal detonation code for the emulsions results in

overestimated pressures of the expanding gases, resulting in an increased cylinder wall velocity. This

is what would be expected with the use of an ideal code to determine the parameters of a non-ideal

emulsion in the used dimensions. The detonation energies at the pressure 20 MPa needed to be

reduced by somewhere between two and five percent for both the aluminized and pure emulsions.

However, the calculated pressures during expansion of the gases from the obtained equation of state

are likely to show greater errors. The introduction of non-ideal detonation codes is likely to enhance

the possibility to describe the behaviour of explosives used for rock blasting.

5.3. Suggested parameters for the JWL EOS for emulsion explosives

It is suggested that the earlier evaluated detonation energies and equation of states according to Esen et

al. (2005) should not be used for the tested explosives, instead the input data for the JWL equation of

state given in this report should be used. The later data sets give a more realistic behaviour of the

behaviour of the used explosives. The average detonation energies for the tests with emulsion E682

and aluminised emulsion according to Esen et al. (2005) are shown below in Figure 5.1. Compare this

data with the later equation of state data shown Figure 5.2 with the newly developed JWL data sets. It

is clear that the new data sets describe a much slower pressure decrease than Esen’s data does and that

the new detonation energies are substantially higher. The earlier analytical results according to Esen et

al. (2005) showed considerable differences between the equation of state determined for a ideal

detonation using Vixen-I, and the data obtained from the analytical evaluation of the cylinder test. The

detonation energies also varied considerably between different tests with the same explosive. Further,

the velocity of detonation measurements from the cylinder tests indicates that the detonation of pure

and aluminized emulsions should be close the ideal for the used dimensions of copper cylinders. The

FEM simulations performed with LS-DYNA of cylinder tests in this study show that the data from

Vixen-I ideal detonation runs results in cylinder wall displacements that are relatively close to the

velocities measured during the cylinder tests. This is taken as further evidence that the detonation of

the used emulsions under these conditions are close to ideal.


53

0.0

0.5

1.0

1.5

2.0

2.5

3.0


Det

onat

ion

ener

gy (M

J/kg

)

E682-b, Esen data set, nominal density= 1.180 g/cc

E682 Al 6%, Esen data set, nominal density= 1.180 g/cc


Figure 5.1. Estimated detonation energy during expansion for the used of emulsion explosives according to Esen et al. (2005). Average values for cylinder tests with 100 mm copper cylinders.

The data indicate that the performance of the explosives is close to the calculated ideal performance by

Vixen-I, which can be used as a first approximation for the properties of the explosives. A better

approximation of the behaviour of the explosives can be obtained by using the cylinder test data for

comparison with FEM analysis. However, the used data for the JWL equation of state are dependent

on both the diameter and confinement of the explosive. In these cases, the equation of state data are

also influenced by the reaction rate of the explosive and the data are not likely to give accurate

descriptions of the equation of states of the expanding explosive gases. Further, there are relatively

large variations of the measured wall velocities for the tests and for some test set ups only one test

may be considered to representative. According to these uncertainties, the user of the given data

should be aware of its limitations, and also the simplifications made to be able to use an JWL equation

of state and a programmed burn algorithm for emulsions. The estimated detonation energies for the

used emulsion explosives are plotted in Figure 5.2, observe that the data sets are tested for different

cylinder diameters. The data sets A-11, B-11 and C-11 are tested versus 100 mm cylinder test data.

The data sets A-16 and C-14 are tested versus 60 mm cylinder test data and 40 mm cylinder test data,

respectively.


54

a)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


Det

onat

ion

ener

gy (k

J/cc

)







b)

0.0

0.5

1.0

1.5

2.0

2.5

3.0


Det

onat

ion

ener

gy (M

J/kg

)







Figure 5.2. Estimated detonation energy during expansion for the used of emulsion explosives. The diagrams (a) and (b) uses the units kJ/cc and MJ/kg for the detonation energy, respectively.


55

6. Future research and development

It is of great interest to model non-ideal behaviour of commercial explosives. Unfortunate, to directly

perform this type of simulations in e.g. an explicit FEM code in 3D, requires substantial computational

resources. The combination of non-ideal detonation codes to determine the behaviour of the

explosives, and codes suitable for calculating the fluid structure interaction and behaviour of solid

material, may give reasonable results. It is therefore recommended that existing material models for

non-ideal behaviour are used for e.g. FEM analysis, with input parameters determined by the use of

non-ideal detonation codes. The use of a kinetic law, instead of the programmed burn algorithm, to

describe the burning rate of the explosive enhances the possibility to describe the reactions within the

reaction zone. However, the necessary resolution of the model is likely to be increased since the

detonation driving zone needs to have an adequate resolution. This increases both run times and

memory requirements for the computer. Therefore, for a 3D simulation of an explosive charge in a

borehole, this may be to stretch the limit too far for the time being. The use of a modified equation of

state, or modified programmed burn algorithm, may be used to describe the energy release within 3D

simulations to obtain reasonable run times. This still requires that the release rate of the energy is

known for the explosive in the specific case. There is also a possibility to use data from non-ideal

detonation codes as input to FEM analysis. However, this requires the implementation of specialised

material models to import and use the data that can be obtained from non-ideal detonation codes

within a FEM code. This is likely to enhance the possibility to numerically simulate the behaviour of

the interaction of explosive and rock in a borehole.

The cylinder expansion test can not alone supply the data that are needed to describe an explosive.

However, to obtain a better understanding of the used emulsion explosives, it is possible to perform

additional testing. Complementary testing, e.g. to determine the detonation pressures, are likely to

enhance the possibility to accurately model the used emulsion explosives, especially for emulsions

with additives of aluminium. The cylinder expansion tests can then be used as one of the means to

establish a verified material model for a non-ideal explosive.

The modified data sets based on FEM simulations may be used as first approximations of the

behaviour of these emulsion explosives in rock or concrete. These data sets are intended to be used for

numerical simulations of the blasting experiments that are planned to be performed by Swebrec during

the autumn of 2009. The aim for these tests is to determine the energy loss close to boreholes, and a

verified data set for the expansion work of the explosive is therefore essential for the numerical

evaluation of the tests.


56


57

References

Arvanitidis, I., Nyberg, U., and Ouchterlony F., The diameter effect on detonation properties of cylinder test experiments with Emulsion 682. SveBeFo report 66, SveBeFo, ISSN 1104-1773, Stockholm, 2004.

Cunningham, C. V. B., The energy of detonation: A fresh look at pressure in the blasthole, Pro. of EXPL 2001, Hunter valley, NSW, Australia, 2001, pp. 105-110.

Cunningham, C., Braithwaite, M. and Parker, I., Vixen detonation codes: Energy input for the HSBM, Pro. of the 8th Int. Sym. on rock fragmentation by blasting (FRAGBLAST 8), 2006, pp. 169-174.

Esen, S., Nyberg, U., Hiroyuki, A. and Ouchterlony, F., Determination of energetic characteristic of commercial explosives using the cylinder expansion test technique, Swebrec report 2005:1, Luleå Technical University, ISSN 1653-5006, Stockholm, December 2005.

Fickett, W. and Davis, W. C., Detonation: Theory and Experiment. Dover Publications: Mineola, USA, 2000 (reprint of 1979 edition).

Fried, L. E., Howard, W. M. and Souers, P. C., Cheetah 2.0 User's manual, UCRL-MA-117541 Rev. 5, Lawrence Livermore National Laboratory, Livermore, California, August 1998.

Helte, A., Lundgren, J., Örnhed, H. and Norrefeldt, M., Evaluation of the performance of m/46, FOI-R--2051--SE, FOI, ISSN 1650-1942, September 2006. (In Swedish)

Hornberg, H. and Volk, F., The cylinder test in the context of physical detonation measurement methods. Propellants, Explosives, Pyrotechnics 14: 199-211, 1989.

Johnson, G. R. and Cook, W. H., Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fracture Mechanics, Vol. 21, No. 1, 1985, pp. 31-48.

Marsh, S. P., ed., LASL shock Hugoniot data, University of California press, ISBN 0-520-04008-2, California, 1980.

Nie, S., Deng, J., and Ouchterlony, F., Expansion work of an emulsion explosive in blast hole – measurement and simulation. SveBeFo report 48, SveBeFo, ISSN 1104-1773, Stockholm, May 2000. (In Swedish)

Nyberg, U., Cylinder tests 2007- 2008, Swebrec, Stockholm, 2009. Personal communication.

Souers, P. C. and Haselman, Jr., L. C., Detonation equation of state at LLNL, 1993, UCRL-ID-116113, Lawrence Livermore National Laboratory, Livermore, California, Mars 1994.

Souers, P. C. Wu, B, and Haselman, Jr., L. C., Detonation equation of state at LLNL, 1995, UCRL-ID-119262 Rev 3, Lawrence Livermore National Laboratory, Livermore, California, February 1996.

Report 2009:1 ISSN 1653-5006

Swedish Blasting Research CentreMejerivägen 4, SE-117 43 Stockholm

Luleå University of TechnologySE-971 87 Luleå www.ltu.se

Determination of properties for emulsion explosives using cylinder expansion tests and numerical simulation


Håkan Hansson

Universitetstryckeriet, L

uleå

Determination of properties for emulsion explosives using ...998065/FULLTEXT01.pdf · These explosives have relative short reaction zones, and as a result the equation of state can

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