1. No category

Paper
Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015)
http://dx.doi.org/10.5139/IJASS.2015.16.1.50
A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes
Juho Lee* and Jae-Hung Han**
Department of Aerospace Engineering, KAIST, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic
of Korea
YeungJo Lee***
The 4th R&D Institute, Agency for Defense Development, Daejeon 305-600, Republic of Korea
Hyoungjin Lee****
PGM R&D Lab., LIG NEX1 Co. Ltd., Seongnam 463-400, Republic of Korea
Abstract
Explosive bolts are one of pyrotechnic release devices, which are highly reliable and efficient for a built-in release. Among
them, ridge-cut explosive bolts which utilize shock wave generated by detonation to separate bolt body produce minimal
fragments, little swelling and clean breaks. In this study, separation phenomena of ridge-cut explosive bolts or ridge-cut
mechanism are computationally analyzed using Hydrocodes. To analyze separation mechanism of ridge-cut explosive
bolts, fluid-structure interactions with complex material modeling are essential. For modeling of high explosives (RDX and
PETN), Euler elements with Jones-Wilkins-Lee E.O.S. are utilized. For Lagrange elements of bolt body structures, shock
E.O.S., Johnson-Cook strength model, and principal stress failure criteria are used. From the computational analysis of the
author’s explosive bolt model, computational analysis framework is verified and perfected with tuned failure criteria. Practical
design improvements are also suggested based on a parametric study. Some design parameters, such as explosive weights,
ridge angle, and ridge position, are chosen that might affect the separation reliability; and analysis is carried out for several
designs. The results of this study provide useful information to avoid unnecessary separation experiments related with design
parameters.
Key words: Pyrotechnics, Ridge-Cut Explosive Bolts, Hydrocodes, Separation Behavior Analysis.
1. Introduction
one of the high-explosive types, utilize shock wave generated
by detonation to separate bolt bodies. Furthermore, it is well
known that the ridge-cut explosive bolt produces minimal
shrapnel, little swelling, and a clean break [3].
While the usage of explosive bolts is quite prevalent,
designing procedures still rely on heritage with repetitive
experiments. To overcome this limitation, the computational
analysis method for the explosive bolts is needed. Based
on the computational analysis, separation reliability of the
explosive bolts can be evaluated without time-consuming
and costly experiments. Furthermore, complex separation
phenomena and characteristics can be studied. In many
Explosive bolts are reliable and efficient pyrotechnic
release devices that can be used for diverse applications
including launcher operation, stage separation, release of
external tanks, and thrust termination [1, 2]. The explosive
bolt, which has a form of a bolt body with the cavity filled
with a removable cartridge or an explosive charge, is more
reliable and robust than other types of release devices, due to
its simplicity. Most of the explosive bolts can be categorized
as high-explosive type and pressure type, based on their
separation mechanism. Ridge-cut explosive bolts, which are
* Ph. D Student
Professor, Corresponding author: [email protected]
**
***Principal Researcher
****Principal Researcher
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: January 21, 2015 Revised: March 5, 2015 Accepted: March 5, 2015
Copyright ⓒ The Korean Society for Aeronautical & Space Sciences
(50~63)15-012.indd 50
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2015-03-31 오후 1:53:57
Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes
A 17-4PH stainless steel is used for the bolt body and the
fixtures of the ridge-cut explosive bolts. A removable initiator
and the priming material (Lead Azide, LA) are utilized to
initiate the high explosives. For the high explosives, PETN
and RDX are utilized. The separation reliability of the
ridge-cut explosive bolts is verified by repetitive separation
experiments. The separation plane observed by separation
experiments is shown in Fig. 1. However, the pyroshock
generated by the exploding bolts exceeded 10,000 g above
4,000 Hz at near field. If the explosive weight can be reduced
without compromising the separation reliability, the
probability of malfunctions in nearby electrical components
can be significantly reduced.
Unlike other types of explosive bolts, the separation
mechanism of ridge-cut explosive bolts cannot be
understood by classical fracture mechanics, but it can
be explained by ridge-cut mechanism (Fig. 2). Ridge-cut
technique or mechanism can be explainable by the fracture
mechanism, when a metal structure has ridge on one side
and high explosives detonate on the other side. At first, shock
waves generated by detonation of high explosives are emitted
cases, complex separation characteristics cannot be fully
understood based on simple theories and experimental
results. Based on the computational method regarding the
blast loading on structures [4-10], the authors proposed the
computational analysis method for the separation behaviors
of the ridge-cut explosive bolts [11]. Previous study clearly
showed the separation mechanism of the ridge-cut explosive
bolts from the computation analysis, and the computation
scheme was verified by comparing with the experimental
results. From the separation characteristics study regarding
the confinement conditions, design improvements were
proposed [11]. However, previous study focused only on
the specific confinement condition. To widely apply the
computation analysis method for the designing procedures,
it still requires further studies by applying computation
analysis method to general design parameters of explosive
bolts.
In this study, computational analysis methodology for
ridge-cut explosive bolts separation behavior is revised
and improved in some aspects. By utilizing this numerical
analysis framework, a parametric study with design
parameters of ridge-cut explosive bolts is performed, and
meaningful analysis results are obtained to apply design
procedures.
2. Separation mechanism of ridge-cut explosive bolts
In this study, the ridge-cut explosive bolts as depicted in
Fig. 1, which are designed by the author’s previous experience
[12, 13], are computationally analyzed to understand the
separation characteristics. The ridge-cut explosive bolts are
designed based on the theory of ridge-cut mechanism [11].
Fig. 2. Ridge-cut mechanism
Fig. 2. Ridge-cut mechanism
Fig. 1. Cross-sectional diagram of ridge-cut explosive bolts
Fig. 1. Cross-sectional diagram of ridge-cut explosive bolts
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Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015)
3.1 Summary of computational analysis method
the connections between the bolt body and the fixtures are
modeled as mesh connections, allowing the joining of the
meshes of topologically disconnected bodies. In ANSYS
AUTODYN, the mesh connections are recognized as bonded
connections.
The remaining modeling steps, including Eulerian
modeling and materials modeling, are performed in
ANSYS AUTODYN. Materials modeling, definition of
initial conditions, Euler parts, Euler boundary conditions,
structural boundary condition, Euler-Lagrange interaction,
detonation, and solution controls are necessary in
AUTODYN. In the ridge-cut explosive bolts, the removable
initiator and the priming material are utilized merely to
initiate detonation of PETN and RDX. Therefore, initiator
and LA that generate negligible blast loading on bolt body
are neglected in computational analysis. For high explosives,
RDX and PETN, Jones-Wilkins-Lee (JWL) E.O.S. are used.
For 17-4PH stainless steel (material of the bolt body and the
fixtures), the Shock E.O.S., the Johnson-Cook strength model,
and the principal stress failure model are used. Surrounding
air is defined as the ideal gas with material properties at 1
atmosphere.
Initial density and internal energy of each material are
defined as initial conditions. The air, PETN, and RDX are
constructed as the Euler parts. The size of Euler elements for
air and high explosives is 0.1 mm, which is half of Lagrange
elements (Fig. 4). To model the spread-out of detonation
products, flow out Euler boundary condition is applied to
Due to geometric complexity of ridge-cut explosive
bolts, geometric modeling including structure meshing,
the connections and body interaction are performed in
ANSYS Workbench Explicit Dynamics. The structural
mesh is constructed via a quadrilateral dominant method
with Lagrange elements 0.2 mm in size, as shown in Fig. 3.
Smaller element sizes generally induce accurate analysis
results, but they require high computational costs. Therefore,
optimal mesh size is determined to guarantee converged
numerical results and fast computation time. In this study,
Fig. 4. Elements size comparison between Lagrange and Euler.
Fig. 4. Elements size comparison between Lagrange and Euler.
into the metal structure. When the shock waves encounter
the free surface of metal structure, they reflect back as the
rarefaction waves (or release waves). When the rarefaction
waves collide at the meeting site of rarefaction waves,
particles at the meeting site move in opposite directions.
These movements create high tensile stress at the meeting
site, resulting in the separation.
3. Improvements of computational analysis
methodology
Ridge-cut explosive bolts and their separation mechanism
can be computationally analyzed in AUTODYN (one of
commercial Hydrocodes), due to necessity of Euler-Lagrange
interactions and complex material models. Computational
analysis of ridge-cut explosive bolts are performed in
2-D axisymmetric to minimize computational costs. The
computational analysis method for the ridge-cut explosive
bolts was well developed in previous study [11]. The
analysis method is summarized and the improvements are
introduced here. The improvements include the structural
boundary condition and the parameter values of the Shock
E.O.S. (the Gruneisen constant and the U-u Hugoniot). The
estimation method for the material properties of the high
explosives with slightly different density is also proposed.
Fig. 3. Structure geometric modeling and meshing of the ridge-cut explosive bolts.
Fig. 3. Structure geometric modeling and meshing of the ridge-cut explosive bolts.
DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50
(50~63)15-012.indd 52
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2015-03-31 오후 1:53:58
strength model, and the principal stress failure model are used. Surrounding air is defined as the ideal
gas with material properties at 1 atmosphere.
Initial density and internal energy of each material are defined as initial conditions. The air, PETN,
and RDX are constructed as the Euler parts. The size of Euler elements for air and high explosives is
Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes
0.1 mm, which is half of Lagrange elements (Fig. 4). To model the spread-out of detonation products,
flow out Euler boundary condition is applied to the boundary of the Euler parts, excluding the
the boundary of the Euler parts, excluding the axisymmetric
Here, V is the relative volume ν/ν0; E is the internal energy;
axis. In this study,
a transmit
utilized is utilized
and A,
R1, R2, ωboundary
are empirical parameters determined
axisymmetric
axis. In
this study,boundary
a transmitcondition
boundaryiscondition
as aB,structural
as a structural boundary condition, as shown in Fig. 5. The
by detonation experiments. The detonation velocity and
condition,
shown in condition
Fig. 5. The ensures
transmit boundary
condition
the stress waves
to transmit
transmit as
boundary
the stress
wavesensuresinformation
regarding
the Chapman-Jouguet (C-J) point as
to
transmit
out
without
reflection
at
the
boundary.
It
is
the
reference
state
of
JWL
out without reflection at the boundary. It is modeled as infinite structures are attached at the boundaryE.O.S. are also required. The C-J
modeled as infinite structures are attached at the boundary
point is the position where the reaction (or detonation) is
with
value
(the(the
density
multiplied
by the
velocity). It is defined that
with identical
identicalimpedance
impedance
value
density
multiplied
by soundcomplete.
the sound velocity). It is defined that detonation is initiated
Material properties of RDX and PETN for computational
detonation is initiated at the left bottom point of PETN in 2-D model. A single time step is determined
at the left bottom point of PETN in 2-D model. A single
analysis are given in Table 1. The density of RDX and PETN for
3 3
by
CFL
(Courant-Friedrichs-Lewy)
which guarantees stabilityof
and
accuracy
of the
solution.
time
step
is determined by CFL condition
(Courant-Friedrichs-Lewy)
reference
isfor1.65
g/cm3 model
and 1.50
g/cm
, respectively.
RDX
andmodel
PETN
reference
is 1.65
g/cm
and 1.50 g/cm3, respectively. Material
condition which guarantees stability and accuracy of the
Material properties of COMP A-3 and PETN 1.50 supplied by
The computational analysis is performed up to 0.01 ms.
of
COMP A-3
and
PETN for
1.50RDX
supplied
by AUTODYN
solution. The computational analysis is performed up to 0.01
AUTODYN
are
utilized
1.65 and
PETN 1.50.are utilized for RDX 1.65 and PETN
ms.
Inthis
thisstudy,
study,
material
properties
of explosive
high explosive
In
thethe
material
properties
of high
for different explosive density ar
for different explosive density are needed. The estimation
3.2 Modeling of high explosives
The
estimation
method
derived
for the
material with
properties
with slightly different densit
method
is derived
foristhe
material
properties
slightly
3.2 Modeling of high explosives
different density of up
to 10%. The linear dependence of
For
from
E.O.S.
Formodeling
modelingofofdetonation
detonationproducts
products
fromhigh
highexplosives,
explosives,the Jones-Wilkins-Lee
10%. The linear(JWL)
dependence
of detonation velocity D upon initial density  0 can b
detonation velocity D upon initial density ρ0 can be used to
the
Jones-Wilkins-Lee
(JWL)
E.O.S.
[14]
are
widely
used.
[14] are widely used. It can evaluate experimental geometries of detonation
products
from
initiationvelocity.
to
estimate
thedetonation
detonation
explosives,
the
estimate
the
velocity. For For
mostmost
explosives,
the following
relationships are quit
It can evaluate experimental geometries of detonation
following
relationships
are
quite
accurate
for
a
broad
range
large
expansions.
products
from initiation to large expansions.
for
a broad [15]:
range of density [15]:
of density
P  A(1 

R1V
)e  R1V  B (1 

R2V
)e  R2V 
E
D j  k 0
(1)
V
(1)
(2)
(2
For RDX, j is 2.56 and k is 3.47. For PETN, j is 1.82 and k is 3.7 when the
Here, V is the relative volume v / v0 ; E is the internal energy; and A , B , R1 , R2 ,  are
between 0.37 g/cm3 and 1.65 g/cm3.
empirical parameters determined by detonation experiments. The detonation velocity and information
Also, accurate estimation of the C-J pressure from the detonation velocity and the initial
regarding the Chapman-Jouguet (C-J) point as the reference state of JWL E.O.S. are also required.
as follows [15]:
The C-J point is the position where the reaction (or detonation) is complete.

P
 D 2 (1  0.7215  0.04 )
(3
0
0
CJ in Table
Material properties of RDX and PETN for computational analysis are given
1. The density
Fig. 5. Euler parts including air, RDX, PETNItand
transmit
boundary
is not
unreasonable
tocondition.
assume that the C-J energy per unit volume E0 is proportional
Fig. 5. Euler parts including air, RDX, PETN and transmit
7 boundary condition.
[14]. Within 10% variation of density, parameters R1 , R2 ,  can be retained [14]. To
Table 1. Revised Material Properties
Explosive
with different
density
Tableof1.High
Revised
Material
Properties
of High Explosive with different density
Parameter of JWL E.O.S.
Density  0
(g/cm3)
PETN 1.77
A andRDX
B , following
system
of equations
should be solved [14]. Even though
PETN 1.50parameters
PETN 1.26
1.815 RDX
1.65
RDX 1.485
1.77
1.50
8
it is not necessary
modeling.
C will
1.26be calculated,
1.815
1.65 for our Hydrocodes
1.485
8
Parameter A
(kPa)
6.1705×10
6.253×10
Parameter B
(kPa)
1.6926×107
2.329×107
Parameter R1
(none)
4.4
5.25
Parameter R2
(none)
1.2
1.6
Parameter 
(none)
0.25
0.28
3
3
8
5.731×108 7.826×108 6.113×10
1
PCJ  Ae  R17VCJ  Be  R2VCJ 7 C  1
7
2.016×10
1.335×10 V1.065×10
CJ
4.634×108
6.0
4.4
4.4  R2VCJ
4.4
1
e R1VCJ
e
1
E0  PCJ (1  VCJ
) A
B
C
R1 1.2 R2
VCJ
1.8 2
1.2
1.2
(5
0.28
0.32
0.32
0.32
PCJ
1
 3AR1e  R1VCJ  BR23e  R2VCJ  C (
3  1) (  2)
3
8.858×10
8.3×10
V7.713×10
 VCJ
16.54×10
CJ
(6
Detonation velocity D
(m/s)
8.30×10
7.45×10
C-J Energy
volume E0
(kJ/m3)
1.01×107
8.56×106
VCJ 6 is the9.79×10
v / v06 at C-J8.01×10
Here,
relative 6volume
point: 6
7.19×10
8.9×10
(kPa)
3.35×107
2.2×107
7 P
7
CJ 3.718×10
V1.4×10
)
CJ (1 
2
D
C-J Pressure
per
unit
53
(50~63)15-012.indd 53
(4
8.049×106
3×107
2.359×107
(7
8http://ijass.org
2015-03-31 오후 1:53:59
 can
be used
to the Shock E.O.S. are utilized, which is the Mie-Gruneise
10%. The linear dependence of detonation velocity D upon initial density
For 17-4PH
stainless
steel,
D upon
0000 can
upon initial
initial density
density
can
be
be used
used
to
to
10%.
10%. The
The linear
linear dependence
dependence of
of detonation
detonation velocity
velocity D
E.O.S. [16] that
shock Hugoniot as reference.
estimate the detonation velocity. For most explosives, the following relationships
are uses
quitethe
accurate
estimate
estimate the
the detonation
detonation velocity.
velocity. For
For most
most explosives,
explosives, the
the following
following relationships
relationships are
are quite
quite accurate
accurate
for a broad range of density [15]:
for
for aa broad
broad range
range of
of density
density [15]:
[15]:
P  PH 
D j  k 0
D
D jj kk000

v
(e  eH )
(8
(2)
(2)
(2)
Here, P is the pressure,  is the Gruneisen constant,  is the specific volume, and
Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015)
For RDX, j is 2.56 and k is 3.47. For PETN, j is 1.82 and k is 3.7 when the density is
For
For RDX,
RDX, jj is
is 2.56
2.56 and
and kk is
is 3.47.
3.47. For
For PETN,
PETN, jj is
is 1.82
1.82 and
and kk is
is 3.7
3.7 when
when the
the density
density is
is
specific internal energy. Subscript H denotes the shock Hugoniot, which is defined as th
between
0.37 jg/cm3
and
1.65
g/cm3.
Subscript H denotes the shock Hugoniot, which is defined
For RDX,
is 2.56and
and
k isg/cm3.
3.47. For PETN, j is 1.82 and k is
between
between
0.37
0.37 g/cm3
g/cm3
and
1.65
1.65
g/cm3.
all
shocked
states
each material. Here, we need the P  v Hugoniot for the Shock E.
3
3
as the
locus
allfor
shocked
3.7Also,
when
the density
is between
0.37pressure
g/cm and
1.65
.
accurate
estimation
of the C-J
from
theg/cm
detonation
velocity
and
theof
initial
density isstates for each material. Here, we
Also,
Also,
accurate
estimation
estimation
of
of the
the
C-J
pressure
from
from the
the
detonation
detonation
velocity
and the
the initial
initial
density
density is
isthe Shock E.O.S.. This Hugoniot
need and
the
P-ν
Hugoniot
Also,accurate
accurate
estimation
of C-J
thepressure
C-J pressure
from
the velocity
Hugoniot
can
be
obtained for
from
the U  u Hugoniot or the relationship between shock an
as
follows
[15]:
can be obtained from the U-u Hugoniot or the relationship
detonation
velocity and the initial density is as follows [15]:
as
as
follows
follows [15]:
[15]:
velocities.
between shock and particle velocities.
0.04
(3)

PCJ  0 D2222(1  0.7215  00.04
(3)
0.04
0.04)
(3)
(3)


PPCJ


D
D
(1
(1


0.7215
0.7215


)
)
CJ
000
000
CJ
(9)
U
 C0  su
(9
notunreasonable
unreasonable
to assume
thatC-J
theenergy
C-J energy
ItItisisnot
to assume
that the
per unitper
volume E0 is proportional to density
It is not unreasonable to assume that the C-J energy per unit volume E000 is proportional to density
Here, C
C0 and
s are empirical parameters obtained from
unit volume E0 is proportional to density [14]. Within 10%
Here,
0 and s are empirical parameters obtained from the least-square fits to the exp
theretained
least-square
fitscalculate
to the experimental results [17, 18]. For
variation
of 10%
density,
parameters
R1, parameters
R1, ω can be
R1 ,retained
R2 ,  can be
[14].
Within
variation
of density,
[14]. To
R111,, RR222 ,, 
 can
[14].
[14]. Within
Within 10%
10% variation
variation of
of density,
density, parameters
parameters R
can be
be retained
retained [14].
[14]. To
To calculate
calculate
results
[17,
18].
For
the
shockstainless
E.O.S. ofsteel,
17-4PH
the
shock
E.O.S.
of
17-4PH
the stainless
density, steel,
the the density, the specific
[14]. To calculate parameters A and B, following system of
A
B
parameters
and
,
following
system
of
equations
should
be
solved
[14].
Even
though
parameter
specific heat, the Gruneisen constant, and the U-u Hugoniot
equations should
solved
[14].
Even
AA and
BB,, following
parameters
parameters
and be
following
system
system
of
of though
equations
equationsparameter
should
should be
be solved
solved
[14].
[14]. Even
Even though
though parameter
parameter
C0 and s ) are
Hugoniot
(empirical
Gruneisen
and C
the and
U s)u are
(empiricalconstant,
parameters
necessary.
Only parameters
the
C will be calculated, it is not necessary for our Hydrocodes
0
C will be calculated, it is not necessary for our Hydrocodes modeling.
will be
be calculated,
calculated, itit is
is not
not necessary
necessary for
for our
our Hydrocodes
Hydrocodes modeling.
modeling. density and the specific heat are known [19].
C
C will
modeling.
Only the density and the specific heat are known [19].
In this study, the Gruneisen constant is theoretically
1
 R1VCJ
 R2VCJ
(4)
1
1
P

Ae

Be

C

R
V

R
V
CJ
CJ
CJ  AeRR111VVCJ
CJ  BeRR222VVCJ
CJ  C
 1
(4)Gruneisen
PCJ
estimated
[16] the
from
the volumetric
expansion
In this study,
constant is thermal
theoretically
estimated [16] from the volumetr
(4)
CJ
V

CJ

111
CJ
VCJ
CJ
CJ
coefficient, the specific heat Cν, and the bulk modulus:
expansion coefficient, the specific heat Cv , and the bulk modulus:
1
eRRRR1VVVVCJ
eRRRR2VVVVCJ
1
PP
E0  11 PCJ (1  VCJ
) A ee 111 CJCJCJ  B ee 222 CJCJCJ  C 11
((VV //VV ))
11
(5)
(1
EE000  2 PPCJ
(1VVCJ
)) AA R1  BB R2 1C
C VCJP


(5)
(1
(10)
1 (( (5)
P )()(  (V / V000 )))PP00
CJ
CJ
CJ (1
CJ
(5)
(V / V0 )   
(1

(
)(
C
V
V

(
/
)

22
RR111
R
R
V
V


298
C
V
V

(
/
)
TT )TTP298

0 KK
CJ
(10)
( CJ
)(
)
  222
CJ
00 vv
00
P 0
T
 0Cv  (V / V0 )
T  298 K
T
 0Cv  (V / V0 )
T  298 K
PCJ
1
 R1VCJ
 R2VCJ
The
volumetric
thermal
expansion
coefficient
three
times of
of the
the linear
linear thermal
thermal
The
thermal
expansion
coefficient
isis three
times
The volumetric
volumetric
thermal
expansion
coefficient
is three
(6)
PPCJ
11
C


CJ
CJ
9 is three
(6)
AR1111eeRRR111VVVCJCJCJ 
BR2222eeRRR222VVVCJCJCJ 
C ((
 AR
 BR
The
volumetric
 1)
1) V ((((2)2)2)2)thermal (6)
The
volumetric
thermal
coefficient
times of the linear thermal
11 
expansion
coefficient
is three
timesexpansion
of
the linear
thermal
expansion
CJ
CJ
VCJ
V
V
times
of
the
linear
thermal
expansion
coefficient.
All
the
CJ
CJ
CJ
CJ
CJ
coefficient.All
All the
the parameters
parameters for
for the
the theoretical
theoretical calculation
calculation are
are known
known [19].
[19].
coefficient.
coefficient.
forcalculation
the
theoretical
are known [19].
forthe
theparameters
theoretical
are calculation
known [19].
coefficient.
All
parameters for theparameters
theoretical All
calculation
are known
[19].
Here, VCJ is the relative volume v / v0 at C-J the
point:
v /0vat
Here,
therelative
relative volume
volume ν/ν
at C-J
point:
C-J
point:
Here, V
VCJ
CJ isisthe
Becausethe
theU
of17-4PH
17-4PHstainless
stainless
steel
is
CJ
Because
the
Hugoniot of
of
17-4PH
stainless
steel
unknown,
the relationship
relationship per
pe
UU-u
CJ
000
Because
Hugoniot
steel
isis unknown,
the
uu Hugoniot
Because
the Usteel
ofthe
17-4PH
stainless
steel is unknown,
the relationship pe
 u isHugoniot
Because the U  u Hugoniot of 17-4PH
stainless
unknown,
relationship
pertaining
to
unknown,
the
relationship
pertaining
to
PH13-8MO
stainless
PCJ
PH13-8MO stainless
stainless
steel [20],
[20], which
which isis the
the material
material most
most similar
similar in
in terms
terms of
of this
this relati
relat
PH13-8MO
steel
(7)the
VCJ (1  PCJ
CJ
(7)
CJ )
steel
[20], which
is
material
most similar
in terms
of this
PH13-8MO
stainless
steel
[20], in
which
thethis
material
most
similar
in terms of this relat
(7)
(7)
VVCJ


(1
(1


CJ
 D2222 ))
CJ
PH13-8MO stainless steel [20], which
is the material
most
similar
termsis of
relationship,
is
D
D
relationship,
utilized
in thisstainless
study. PH13-8MO
utilized
in this
this is
study.
PH13-8MO
stainless
steel isis also
also astainless
a precipitation-hardening
precipitation-hardening martensitic
martensiti
utilized
in
study.
PH13-8MO
steel
utilized
in
this
study.
PH13-8MO stainlessmartensitic
steel
is also stainless
astainless
precipitation-hardening martensiti
in this study.
PH13-8MO stainless
isaalso
a precipitation-hardening
martensitic
steel
issteel
also
precipitation-hardening
Obviously, if we apply thisutilized
calculation
for reference
steel,
like
17-4PH
stainless
steel.
steel,
like
steel.
8
steel,
like17-4PH
17-4PHstainless
stainless
steel.
density, for which the parameters of JWL E.O.S.
known,
88 are
steel, like
17-4PH
stainless
steel.
steel, like for
17-4PH
stainless
steel.for which
Obviously, if we apply this calculation
reference
density,
the
parameters
of
JWL
For
modeling
of
the
high-strain-rate
plastic
deformation
the calculated parameters A and B are exactly the same as
For modeling
modeling of
of the
the high-strain-rate
high-strain-rate plastic
plastic
deformation
or flow
flow stress,
stress, Johnson-Cook
Johnson-Coo
For
deformation
or
For
modeling
of
the
high-strain-rate
plastic
deformation
or flow stress, Johnson-Coo
or
flow
stress,
Johnson-Cook
strength
model
is
used.
The
the
known
values.
For
modeling
of
the
high-strain-rate
plastic
deformation
or
flow
stress,
Johnson-Cook
strength
E.O.S. are known, the calculated parameters A and B are exactly the same as the known values.
model
used. The
The
Johnson-Cook
equation
[21] isis constitutive
an empirical
empirical constitutive
constitutive equation
equation rega
reg
model
isis used.
Johnson-Cook
[21]
an
Johnson-Cook
equation
[21] is equation
an empirical
For the material properties of PETN with different
model is[21]
used.
The
Johnson-Cook
equation
[21] isregarding
an empirical
constitutive equation reg
model
is
used.
The
Johnson-Cook
equation
is
an
empirical
constitutive
equation
the
For the material
properties
of PETN
with different
material regarding
properties of
equation
thePETN
plastic deformation of metals with
explosive
densities,
material
properties
of PETNexplosive
1.26 anddensities,
plastic deformation
deformation of
of metals
metals with
with large
large strains,
strains, high
high strain
strain rates,
rates, and
and high
high temperatures.
temperatures.
plastic
plastic
deformation
of
metals
with
large
strains,
high strain rates, and high temperatures.
large
strains,
high
strain
rates,
and
high
temperatures.
PETN 1.77 are utilized, which plastic
is supplied
by AUTODYN.
metals with However,
large strains,
strainproperties
rates, and
high
temperatures.
1.26 and PETN 1.77 are utilized, which
isdeformation
supplied byofAUTODYN.
thehigh
material
However, the material properties of RDX with different

TT TT
n
(1
 T
)(1CCln
ln  )[1
)[1(( T  Trrr ))mmm]]

(1
((00  BBnn)(1

T 
n
m properties
(1
of
RDX withdensities
different explosive
are
not
available.
Therefore,
the
material
of
RDX


)(1
ln
)[1
(

B

C

r (


T
T ) ]

explosive
are notdensities
available.
Therefore,
the
(11)

T
0
(11)

( 0  B )(1  C ln )[1  (
) ]
00
mm  Trr
0
Tm  Tr
0
Tm  Tr
material properties of RDX with 10% variations in density
with 10% variations in density are estimated. Material properties of high explosives with different
B isis the
Here,  isis the
the yield
yield stress
stress or
or flow
flow stress,
stress, 00 isis the
the static
static yield
yield stress,
stress, B
the
Here,
are estimated. Material properties of high explosives
the
Here,
yield
stress
or flow
stress,
ishardening
theyield
static yield stress, B is the
Here,
σisis
thethe
yield
stress
oryield
flow
stress,
σB0 isisthe
0 static
Here,  is the yield stress or flow
stress,
is
the
static
stress,
0
with different
explosive
are
in
explosive
densities
are also densities
summarized
inalso
Tablesummarized
1.
stress, B is
hardening
ε is the strain,
n isCCtheisis the
 the
the
strain, nnconstant,
the hardening
hardening
exponent,
the strain
strain rate
rate constant,
constant,
constant,
isis the
strain,
isis the
exponent,
constant,
Table 1.
is the strain,
isstrain
the hardening
exponent,
constant,
C isisnthe
rate
hardening exponent,
exponent,
the
strain
rate constant,
constant,
theis the strain rate constant,
constant,  is the strain, n is thehardening
 isisCthe
T the
strain
rate,
thereference
referencestrain
strainrate,
rate,T T
the temperature,
temperature, TTrr isis the
the reference
reference tem
tem
strainrate,
rate, 00 isisisthe
is
strain
the
reference
strain
rate,
isis temperature,
the
strain
rate,
the reference Tstrain
rate, T is the
temperature, Tr is the reference te
3.3
of17-4PH
17-4PH
stainless
steel
0 is the reference strain
3.3Modeling
Modeling of
stainless
steelrate,
strain
rate,
is0theis temperature,
temperature,
T is the T
reference
temperature,Tr isis the
the reference
melting point,
and m
r
m
Tmmthe
m isis the
the melting
melting
point, and
and
the thermal
thermal softening
softening exponent.
exponent.
m
isis the
point,
is
thermal
softening
exponent.
For 17-4PH
17-4PH stainless
stainlesssteel,
steel,the
theShock
Shock E.O.S.are
areutilized,
utilized,which T
For
is
form
Tmthe
is Mie-Gruneisen
the melting
point,
andofm is the thermal softening exponent.
T is theE.O.S.
melting point, and m is the
thermal
softening
exponent.
For 17-4PH stainless steel (H1025, HRC38), only the
which is the Mie-Gruneisen formmof E.O.S. [16] that uses the
For 17-4PH
17-4PH stainless
stainless steel
steel (H1025,
(H1025, HRC38),
HRC38), only
only the
the static
static yield
yield stress isis known
known [1
[1
For
E.O.S.
[16]
that
uses
the
shock
Hugoniot
as
reference.
static 17-4PH
yield stress
is known
[19]. Other
parameters
are yield stress
stainless
steelyield
(H1025,
only
theOther
static
stress is known [1
shock Hugoniot as reference.
For 17-4PH stainless steel (H1025,For
HRC38), only
the static
stressHRC38),
is known
[19].
assumed by
of 4340
andsteel
S-7 and
toolS-7
parameters
are averaging
assumed by
bythose
averaging
thosesteel
of 4340
4340
steel
and
S-7 tool
tool steel,
steel, which
which have
have
parameters
are
assumed
averaging
those
of

parameters
arehave
assumed
byS-7
averaging
those
ofspecific
4340
and
parameters are assumed by(8)
averaging
those
of 4340
steel
tool steel,
which
havesteel
the
same
P  PH 
(e  eH )
(8)
steel,
which
the and
same
density
and
the
heat
asS-7 tool steel, which have
v
density
and
the specific
specific
heat
as 17-4PH
17-4PHthe
stainless
steel.
In
addition, the
the static
static yield
yield stres
stre
density
and
the
as
stainless
In
addition,
17-4PH
stainless
steel.heat
In addition,
static steel.
yield
stress
density
and
thesteel.
specific
heat
as 17-4PH
steel.and
In
addition,
the static yield stre
density and the specific heat as 17-4PH
stainless
In addition,
the staticstainless
yield stress
the
and thevolume,
Rockwell
of 17-4PH
stainless
are
Here, P
P isisthe
e17-4PH
Here,
the pressure,
pressure, γ isisthe
theGruneisen
Gruneisen constant,
constant, ν isis the specific
and
is thestainless
Rockwell
hardness
ofhardness
stainless
steel are
are similar
similarsteel
with the
the average
average values
values of
of 4340
4340 ste
ste
Rockwell
hardness
of
17-4PH
steel
with
Rockwell
hardness
of 17-4PH
stainless
steelofsteel
are
similar
with
the
similar
with
the average
of
4340
and
the specific volume, and e is the
specific
internal
energy. stainless
Rockwell
hardness
of 17-4PH
steel are
similar
with
the values
average
values
4340
steelS-7
andtool
S-7 average values of 4340 ste
tool steel.
steel.
tool
specific internal energy. Subscript H denotes the shock Hugoniot, which
is defined as the locus of
tool steel.
tool steel.
To
model
ridge-cut
mechanism,
the principal
principal stress
stress failure
failure criteria
criteria are
are utilized.
utilized. With
With the
the
ridge-cut
mechanism,
the
all shocked states for each material. Here, we need the P  v HugoniotTo
formodel
the Shock
E.O.S..
This
modelstress
ridge-cut
mechanism,
principal
stress
criteria are utilized. With the
DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50
To model ridge-cut mechanism,
principal
failure
criteria aretheutilized.
With
the failure
principal
54 the To
stress
failureshock
model,
failure
of each
each element
element isis initiated
initiated ifif the
the maximum
maximum principal
principal ten
ten
stress
failure
model,
Hugoniot can be obtained from the U  u Hugoniot or the relationship
between
andfailure
particleof
failure
model,
failure
each element
is initiated
if the maximum principal ten
stress failure model, failure of eachstress
element
is initiated
if the of
maximum
principal
tensile stress
exceeds aa critical
critical value
value of
of normal
normal tensile
tensile stress.
stress. The
The appropriate
appropriate failure
failure criteria
criteria for
for the
the
exceeds
velocities.
exceedsstress.
a critical
of normal
tensile
stress.
appropriate failure criteria for the
exceeds a critical value of normal tensile
The value
appropriate
failure
criteria
for The
the ridge-cut
U
 C0  su
(50~63)15-012.indd 54
explosive bolts
bolts are
are determined
determined from previous
previous study
study [11].
[11]. Revised
Revised material
material properties
properties oo
explosive
(9)determined from
previous
studyof[11].
Revised material properties o
explosive bolts are determined fromexplosive
previousbolts
studyare[11].
Revised from
material
properties
17-4PH
2015-03-31 오후 1:53:59
stainless steel
steel for
for computational
computational analysis
analysis are
are summarized
summarized in
in Table
Table 2.
2.
stainless
Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes
waves from detonation are emitted into the bolt body and
encounter the free surface near the ridge around 2.1 μs
(Fig. 6(b)). At the free surface, shock waves reflect back as
rarefaction waves, and these reflected rarefaction waves
collide at the meeting site of rarefaction waves at around
2.5 μs (Fig. 6(c)). From this computational analysis, the
ridge-cut explosive bolts are expected to be separated at
around 2.5 μs.
From the previous study [11], the appropriate principal
stress failure criteria are determined as 2.8 GPa critical
value of normal tensile stress. For comparison, material
statuses at 5.0 μs are given in Fig. 7, which use different
critical values of normal tensile stress ranging from 2.4
GPa to 3.2 GPa. If low failure criteria are used, widespread
failures are observable as shown in Fig. 7(a) and (b),
and these are unlike the separation experiments. In
the experiments, clean ridge breaks were observed.
Furthermore, this makes the separation analysis results
insensitive to parameter variations. If high failure criteria
are applied, localized failures will be observed as shown
in Fig. 7(d) and (e), which imply no separation of the
explosive bolts. This makes it difficult to evaluate the
separation reliability.
steel.
To model ridge-cut mechanism, the principal stress
failure criteria are utilized. With the principal stress
failure model, failure of each element is initiated if the
maximum principal tensile stress exceeds a critical value
of normal tensile stress. The appropriate failure criteria
for the ridge-cut explosive bolts are determined from
previous study [11]. Revised material properties of 17-4PH
stainless steel for computational analysis are summarized
in Table 2.
4. Computational analysis results of ridgecut explosive bolts
By utilizing developed numerical analysis framework,
separation behavior of the ridge-cut explosive bolts is
computationally analyzed. At first, the principal stress
failure model is not used to clearly observe propagation,
reflection of shock waves, and collision of reflected
rarefaction waves. Detonation is initiated at the left bottom
point of PETN as analysis starts (0 ms). Detonation of PETN
and RDX is finished at around 1.7 μs (Fig. 6(a)). Shock
Table 2. Revised Material Properties Table
of 17-4PH
2. Stainless
RevisedSteel
Material
Properties of 17-4PH Stainless Steel
Parameter of Shock E.O.S.
Density  0
17-4PH Stainless Steel
7.81 g/cm3
Gruneisen coefficient 
Empirical parameter C0
1.36
4550 m/s
Empirical parameter s
Reference temperature Tr
1.41
Specific Heat Cv
460 J/kgK
Parameter of Johnson Cook strength model
Shear modulus
Static yield stress  0
7.7437×107 kPa
1.172×106 kPa
300 K
Hardening constant B
Hardening exponent n
Strain rate constant C
Thermal softening exponent m
Melting point Tm
4.935×105 kPa
0.22
0.013
1.015
Reference strain rate 0
1.0
Parameter of principal stress failure model
Critical value of normal tensile stress  c
2.8×106 kPa
Parameter of geometric strain erosion model
Erosion strain
Type of geometric strain
1.5
Instantaneous
1778 K
55
http://ijass.org
2
(50~63)15-012.indd 55
2015-03-31 오후 1:53:59
Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015)
for various ridge-cut explosive bolt designs. Some
design parameters are chosen that might affect the
separation reliability, and behavior analysis is carried
out for several designs.
From the computational analysis results of ridge-cut
explosive bolts, separation reliability can be estimated.
Number, position, direction, and density of failed
Lagrangian elements can be considered for the evaluation.
Through comparison with computational results of
the reference ridge-cut explosive bolts, the separation
reliability can be evaluated for diverse designs of ridge-cut
explosive bolts.
5.1 Explosive weight
In the reference ridge-cut explosive bolts, 47 mg of PETN
and 50 mg of RDX are used to break the bolt body. When
the explosive weight is increased or decreased, shock
propagation and the separation reliability are affected. In
this study, to observe the effect of the explosive weight on
the separation reliability, only the densities of explosives
are varied, and the dimensions of the ridge and the fixture
are unchanged. Here, four cases are considered as follows:
5. Parametric study of ridge-cut explosive bolts
In this study, a separation-behavior analysis method
is developed for ridge-cut explosive bolts, and this
method allows evaluation of the separation reliability
(a)
(b)
(c)
Fig. 6. Pressure contours without failure modeling: (a) at 1.7 μs; (b) at 2.1 μs; (c) at 2.5 μs.
Fig. 6. Pressure contours without failure modeling: (a) at 1.7 μs; (b) at 2.1 μs; (c) at 2.5 μs.
DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50
56
6
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Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes
(a)
(b)
(c)
7
(d)
(e)
Fig. 7. Material statuses at 5.0 μs for different principal stress failure criteria: (a) 2.4 GPa; (b) 2.6 GPa;
(c) 2.8
GPa;criteria:
(d) 3.0 GPa;
(e) 3.2
GPa.
Fig. 7. Material statuses at 5.0 μs for different principal stress
failure
(a) 2.4
GPa;
(b) 2.6 GPa; (c) 2.8 GPa; (d) 3.0 GPa; (e) 3.2 GPa.
57
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2015-03-31 오후 1:54:02
Int’l J. of Aeronautical & Space Sci. 16(1), 50–63 (2015)
status at 5.0 μs is shown in Fig. 8. According to the
comparison with the results for the reference model (Fig.
7 (c)), it is easily inferred that the separation reliability
increases as the explosive weight increases. However, this
inference is not always correct, due to the side effects of
excess explosive. Furthermore, it is quite clear that the
separation reliability is affected by the explosive weight
1) the explosive densities of RDX and PETN are increased
(RDX 1.815 and PETN 1.77), 2) the explosive density of RDX
is increased (RDX 1.815 and PETN 1.50), 3) the explosive
densities of RDX and PETN are decreased (RDX 1.485
and PETN 1.26), and 4) the explosive density of PETN is
decreased (RDX 1.65 and PETN 1.26).
To demonstrate the separation reliability, the material
(a)
(b)
(c)
9
(d)
Fig. 8. Material statuses at 5.0 μs for different explosive weight (a) High density RDX and PETN; (b)
High density
RDX;weight
(c) Low (a)
density
RDX
and PETN;
Low
density
Fig. 8. Material statuses at 5.0 μs for different
explosive
High
density
RDX(d)
and
PETN;
(b)RDX.
High density RDX; (c) Low density RDX and
PETN; (d) Low density RDX.
DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.50
(50~63)15-012.indd 58
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2015-03-31 오후 1:54:03
Juho Lee A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes
elements (i.e., a smaller portion of the bolt) must fail to
induce bolt separation, which implies higher separation
reliability for the same explosive weight. On the other
hand, in the decreased ridge-angle model, the bisection
line of the ridge rotates clockwise with respect to the
vertex of the ridge, which implies a length increment of
the line, as shown in Fig. 9(b). Therefore, more elements
(i.e., a larger portion of the bolt) must fail to induce bolt
separation, which implies lower separation reliability for
the same explosive weight.
of RDX, rather than the explosive weight of PETN. This is
because PETN is utilized to initiate RDX, and the shock
waves mainly generated by the RDX break the bolt body.
5.2 Ridge angle
For the reference ridge-cut explosive bolts, the ridge
angle of the bolt body is 120°. When the ridge angle is
increased or decreased, the reflection of shock waves,
the superposition of release waves, and the separation
reliability are affected. In this study, the ridge angle
(which affects the reflection of shock waves) is increased
and decreased by 10°. The meshes used for the increased
and decreased ridge angle models are shown in Fig.
9(a) and Fig. 9(b), respectively, with a dashed outline
of the reference model. The bisection line of the ridge
is indicated by a dotted red line in the reference model
and by a dashed black line in the models, with increased
and decreased ridge angles. To determine the separation
reliability, the material status at 5.0 μs is shown in
Fig. 10. Even though the increased ridge-angle model
has a larger volume around the ridge of the explosive
bolt, it has higher separation reliability than either the
decreased ridge angle model or the reference model.
These phenomena can be explained by the rotation of the
bisection line of the ridge. In the increased ridge-angle
model, this line rotates counterclockwise with respect to
the vertex of the ridge, which implies a length decrement
of the line, as shown in Fig. 9(a). Therefore, fewer
5.3 Ridge position
As with the other parameters, ridge position can be
adjusted. When the ridge position is shifted to the left or
right, the reflection of shock waves, the superposition of
release waves, and the separation reliability are affected.
In this study, the ridge position is shifted to the left
and to the right by 5 mm. To observe the effect of ridge
position on the separation reliability, the dimensions of
the ridge and the fixture are uniformly varied, as shown
in Fig. 11(a) and Fig. 11(b). To illustrate the separation
reliability, the material status at 5.0 μs is shown in Fig.
12. Even though the left-shifted ridge-position model has
a smaller volume around the ridge of the explosive bolt,
it has lower separation reliability than either the rightshifted ridge-position model or the reference model.
These phenomena can be explained by the cancellation
of the propagating shock waves and reflected release
(a)
(b)
Fig. 9. Mesh with dashed reference outline for different ridge angle (a) Increased ridge angle model;
Fig. 9. Mesh with dashed reference outline for different ridge
angle (a) Increased
angle model; (b) Decreased ridge angle model.
(b) Decreased
ridge angleridge
model.
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encounter trailing shock waves that are not sufficiently
dissipated. Therefore, the tensile stress induced by the
superposition of release waves is inadequate for failure,
waves. In the left-shifted ridge-position model, the
distance from the RDX to the free surface of the ridge is
reduced, which implies that the reflected release waves
(a)
(b)
Fig. 10. Material statuses at 5.0 μs for different ridge angle (a) Increased ridge angle model; (b)
Decreased
ridge
angle
model.
Fig. 10. Material statuses at 5.0 μs for different ridge angle (a)
Increased
ridge
angle
model; (b) Decreased ridge angle model.
(a)
12
(b)
Fig. 11. Mesh with dashed reference outline for different ridge position (a) Left-shifted ridge-position
model; (b)
Right-shifted
model.
Fig. 11. Mesh with dashed reference outline for different
ridge
position ridge-position
(a) Left-shifted
ridge-position model; (b) Right-shifted ridge-position
model.
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5.4 Summary of parametric study and design improvements
which implies lower separation reliability. On the other
hand, in the right-shifted ridge-position model, the
distance from the RDX to the free surface of the ridge
is increased, which implies that the reflected release
waves encounter trailing shock waves that are already
dissipated. Therefore, the tensile stress induced by the
superposition of release waves is greater than that for
the reference model. However, the right-shifted ridgeposition model has a larger volume around the ridge
of the explosive bolt; and more elements (i.e., a larger
portion of the bolt) must fail to induce bolt separation.
Due to both effects, the separation reliability will be
similar to the reference model.
Based on this parametric study, practical design
improvements are suggested for the reference explosive
bolts. When the explosive weights of the high explosives are
increased, the ridge angle is increased; and the separation
reliability is increased. Therefore, with an increased ridge
angle, the explosive weight can be reduced so that the
side effects, such as pyroshock, are reduced even as the
separation reliability similar to that of the reference model
is maintained.
To determine the separation reliability of the increased
(a)
(b)
Fig. 12. Material statuses at 5.0 μs for different ridge angle (a) Left-shifted ridge-position model; (b)
ridge-position
model.
Fig. 12. Material statuses at 5.0 μs for different ridge angleRight-shifted
(a) Left-shifted
ridge-position
model; (b) Right-shifted ridge-position model.
Fig. 13. Material statuses at 5.0 μs of increased ridge angle with decreased explosive weight model.
Fig. 13. Material statuses at 5.0 μs of increased ridge angle with decreased explosive weight model.
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Meeting of the Pyrotechnics and Explosives Applications
Section on the American Defense Preparedness Association,
1983.
[4] Balden, V. H. and Nurick, G. N., “Numerical simulation
of the post-failure motion of steel plates subjected to blast
loading”, International Journal of Impact Engineering, Vol.
32, 2005, pp. 14-34.
[5] Bonorchis, D. and Nurick, G. N., “The influence
of boundary conditions on the loading of rectangular
plates subjected to localised blast loading - Importance
in numerical simulations”, International Journal of Impact
Engineering, Vol. 36, No. 1, 2009, pp. 40-52.
[6] Bonorchis, D. and Nurick, G. N., “The analysis and
simulation of welded stiffener plates subjected to localised
blast loading”, International Journal of Impact Engineering,
Vol. 37, No. 3, 2010, pp. 260-273.
[7] Katayama, M. and Kibe, S., “Numerical study of
the conical shaped charge for space debris impact”,
International Journal of Impact Engineering, Vol. 26, 2001,
pp. 357-368.
[8] Katayama, M., Itoh, M., Tamura, S., Beppu, M.
and Ohno, T., “Numerical analysis method for the RC
and geological structures subjected to extreme loading
by energetic materials”, International Journal of Impact
Engineering, Vol. 34, No. 9, 2007, pp. 1546-1561.
[9] Trelat, S., Sochet, I., Autrusson, B., Cheval, K. and
Loiseau, O., “Impact of a shock wave on a structure on
explosion at altitude”, Journal of Loss Prevention in the
Process Industries, Vol. 20, 2007, pp. 509-516.
[10] Trelat, S., Sochet, I., Autrusson, B., Loiseau, O.
and Cheval, K., “Strong explosion near a parallelepipedic
structure”, Shock Waves, Vol. 16, 2007, pp. 349-357.
[11] Lee, J., Han, J.-H., Lee, Y. and Lee, H., “Separation
characteristics study of ridge-cut explosive bolts”, Aerospace
Science and Technology, Vol. 39, 2014, pp. 153-168.
[12] Lee, Y. J., The Study of Development of Ridge-Cut
Explosive Bolt (I), Agency for Defense Development, 2000.
[13] Lee, Y. J., The Study of Devlopment of Ridge-Cut
Explosive Bolt (II), Agency for Defense Development, 2001.
[14] Lee, E. L., Hornig, H. C. and Kury, J. W., Adiabatic
Expansion of High Explosive Detonation Products, Lawrence
Radiation Laboratory, UCRL-50422, 1968.
[15] Zukas, J. A. and Walters, W. P., Explosive effects and
applications, Springer, New York, 1998.
[16] Meyers, M. A., Dynamic behavior of materials, Wiley,
New York, 1994.
[17] Cooper, P. W., Explosives engineering, VCH, New
York, N.Y., 1996.
[18] Zukas, J. A., Introduction to hydrocodes, Elsevier,
Amsterdam, 2004.
ridge angle with decreased explosive weight model, the
material status at 5.0 μs is shown in Fig. 13. Comparison
between the results for the decreased explosive weight
model (Fig. 8(c)), and the increased ridge angle with
decreased explosive weight model (Fig. 13) shows that
the separation reliability is slightly increased due to the
effect of ridge angle increment. However, the separation
reliability is lower than the reference model (Fig. 7(c)). From
this observation, it is easily inferred that the separation
reliability are mainly influenced by the explosive weight,
rather than by the slight modification of ridge shape.
However, the parametric study with design parameters of
explosive bolts clearly shows that the separation reliability
of ridge-cut explosive bolts are affected by the slight
changes in ridge angle and position.
6. Conclusion
This study established the separation behavior analysis
environments for ridge-cut explosive bolts, based on the
ridge-cut mechanism. By using this analysis scheme, a
parametric study of ridge-cut explosive bolts was carried
out. Some design parameters were chosen that might affect
the separation reliability, and the behavior analysis was
carried out for several designs. Based on this parametric
study, practical design improvements were suggested for
the reference explosive bolts. When the explosive weights of
the high explosives were increased, followed by an increase
in the ridge angle the separation reliability was increased.
Especially, the separation reliability was mainly influenced
by the explosive weight, rather than by the slight modification
of ridge shape.
Acknowledgement
This work was supported by the LIG Nex1 under the
contract YD11-3242.
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NASA Technical Memorandum 110172, 1995.
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“Ridge-Cut” Technique Used in Explosive Bolts”, Annual
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