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
Bestämning av emulsionssprängämnens egenskaper med cylinderexpansionsprov och FEM-simulering
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
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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.
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Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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.
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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
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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
Figure 2.10. Cylinder wall expansions for tests with emulsion E682-b and E682 with 6% aluminium.
........................................................................................................................................ 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
Figure 3.5. Model geometry for simulation with half wall 100 mm cylinders for PETN simulations.
........................................................................................................................................ 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
Figure 3.8. Model geometry for simulation with half wall 100 mm cylinders for emulsion
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
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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
Figure 3.14. Model geometry for simulation with half wall 40 mm cylinders for emulsion
simulations. ..................................................................................................................... 43
Figure 3.15. Model geometry for simulation with half wall 100 mm cylinders for emulsion
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
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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
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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.
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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)
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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.
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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.
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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
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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.
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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.
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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.
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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)
Note: (1) Average cylinder thickness at measurement locations. The two values are for measurement data sets (a) and (b), respectively.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Density 1197 kg/m3 1205 kg/m3
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)
Note: (1) Average cylinder thickness at measurement locations. The two values are for measurement data sets (a) and (b), respectively.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Note: (1) Average cylinder thickness at measurement locations. The two values are for measurement data sets (a) and (b), respectively.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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-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
Figure 2.9. Cylinder wall expansions for tests with emulsion E682-b and E682 with 6% aluminium.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
E682-b 2005, t=5.03 mm: Average r,m
Figure 2.10. Cylinder wall expansions for tests with emulsion E682-b and E682 with 6% aluminium.
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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).
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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Table 3.2. Cheetah output for the pure emulsion explosives.
Emulsion E682-a
Emulsion E682-a
Emulsion E682-b
Emulsion E682-b
Density 1129 kg/m3 1169 kg/m3 1180 kg/m3 1203 kg/m3
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
dE at 20 MPa pressure 2.51 MJ/kg 2.54 MJ/kg 2.58 MJ/kg 2.60 MJ/kg
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
dE at 20 MPa pressure 3.04 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).
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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).
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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Table 3.5. Vixen-I output for the pure emulsion explosives.
Emulsion E682-a
Emulsion E682-a
Emulsion E682-b
Emulsion E682-b
Density 1129 kg/m3 1169 kg/m3 1180 kg/m3 1203 kg/m3
Shock velocity 5664 m/s 5840 m/s 5929 m/s 6028 m/s
JWL fit from Vixen-I ------------------- ------------------- ------------------- -------------------
0E = )(vEd 3.137 kJ/cc 3.261 kJ/cc 3.317 kJ/cc 3.387 kJ/cc
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
dE at 100 MPa pressure 1.98 MJ/kg 2.03 MJ/kg 2.07 MJ/kg 2.11 MJ/kg
dE at 20 MPa pressure 2.31 MJ/kg 2.35 MJ/kg 2.38 MJ/kg 2.41 MJ/kg
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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Table 3.6. Vixen-I output for the aluminized emulsion explosive.
Aluminized E682 with 6% aluminium
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
dE at 100 MPa pressure 2.36 MJ/kg
dE at 20 MPa pressure 2.76 MJ/kg
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Density 1766 kg/m3 1766 kg/m3
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Values plotted to a cut off pressure of 20 MPa
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
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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 3.3. Model geometry for simulation with half wall 60 mm cylinders for PETN simulations.
Figure 3.4. Model geometry for simulation with full wall 60 mm cylinders for PETN simulations.
Figure 3.5. Model geometry for simulation with half wall 100 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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Velocity at v =4.1 (1) 2217 m/s 2283 m/s 2286 m/s 1710 m/s 1730 m/s
Velocity at v =6.5 (1) 2292 m/s 2376 m/s 2377 m/s 1780 m/s 1770 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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
StreakV at v =4.1 (1) 2.37×10³ m/s 2.36×10³ m/s 1.72×10³ m/s
StreakV at v =6.5 (1) 2.44×10³ m/s 2.44×10³ m/s 1.78×10³ 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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Figure 3.8. Model geometry for simulation with half wall 100 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
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
dE at 20 MPa pressure 2.38 MJ/kg 2.27 MJ/kg 2.41 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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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-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
Values plotted to a cut off pressure of 20 MPa
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 2005, t=5.03 mm: Average r,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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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)
Density 1129 kg/m3 1129 kg/m3 1169 kg/m3 1169 kg/m3
Shock velocity 5664 m/s 5635 m/s (2) 5840 m/s 5712 m/s
0E = )(vEd 3.137 kJ/cc 3.057 kJ/cc 3.261 kJ/cc 3.155 kJ/cc
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
dE at 100 MPa pressure 1.98 MJ/kg 1.91 MJ/kg 2.03 MJ/kg 1.94 MJ/kg
dE at 20 MPa pressure 2.31 MJ/kg 2.24 MJ/kg 2.35 MJ/kg 2.26 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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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-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-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
E682-a, Data set A-16, density=1.129 g/cc
Values plotted to a cut off pressure of 20 MPa
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Sim. E682-a 1.129 g/cc D100 t 5.0 mm Ideal
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
Sim. E682-a 1.169 g/cc D100 t 5.0 mm Ideal
Sim. E682-a 1.169 g/cc D100 t 5.0 mm Set A-11
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Figure 3.14. Model geometry for simulation with half wall 40 mm cylinders for emulsion simulations.
Figure 3.15. Model geometry for simulation with half wall 100 mm cylinders for emulsion simulations.
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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Table 3.17. Compiled experimental data for the aluminized emulsion explosives E682.
Aluminized E682 with 6% aluminium
Aluminized E682 with 6% aluminium
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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Table 3.18. Input data for the aluminized emulsion explosives E682.
Aluminized E682 with 6% aluminium
Aluminized E682 with 6% aluminium
Aluminized E682 with 6% aluminium
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
dE at 100 MPa pressure 2.36 MJ/kg 2.31 MJ/kg 2.28 MJ/kg
dE at 20 MPa pressure 2.76 MJ/kg 2.71 MJ/kg 2.68 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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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-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 Al 6%, Vixen set C-01, density=1.180 g/cc
E682 Al 6%, Data set C-11, density=1.180 g/cc
E682 Al 6%, Data set C-14, density=1.180 g/cc
Values plotted to a cut off pressure of 20 MPa
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Sim. E682-a 1.169 g/cc D100 t 5.0 mm Ideal
Sim. E682-a 1.169 g/cc D100 t 5.0 mm Set A-11
Figure 3.18. Cylinder wall expansions for tests and simulations with aluminized E682 using 40 mm cylinders.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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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
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
53
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 5 10 15 20Relative volume (-)
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
Values plotted to a cut off pressure of 20 MPa
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
54
a)
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 Al 6%, Data set C-11, density=1.180 g/cc
E682 Al 6%, Data set C-14, density=1.180 g/cc
E682-b, Data set B-11, density=1.180 g/cc
E682-a, Data set A-11, density=1.169 g/cc
E682-a, Data set A-16, density=1.129 g/cc
Values plotted to a cut off pressure of 20 MPa
b)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 5 10 15 20Relative volume (-)
Det
onat
ion
ener
gy (M
J/kg
)
E682 Al 6%, Data set C-11, density=1.180 g/cc
E682 Al 6%, Data set C-14, density=1.180 g/cc
E682-b, Data set B-11, density=1.180 g/cc
E682-a, Data set A-11, density=1.169 g/cc
E682-a, Data set A-16, density=1.129 g/cc
Values plotted to a cut off pressure of 20 MPa
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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.
Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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Determination of properties for emulsion explosives......... Swebrec Report 2009:1
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References
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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.
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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.
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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