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Joseph E. Backofen
4192 Hales Ford Rd.
Moneta, VA 24121
Shaped Charge Jet Initiation of Explosives:
a Different View into the Processes of
Penetration and Initiation
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Dedicated to Prof. Dr. Manfred Held
To whom I promised this work for many years…..
guiding-concepts for students to consider
so as to continue our research work
Goal
“If somebody wants to get deeper in a topic, one
should prepare a presentation first. To explain the
fundamentals in more detail, the relating chapters in
books and the important papers have to be studied.
In this way somebody has to enforce oneself to study
the fundamental references.” *
* M. Held, Review -- Contributions along 40 Years of ICT’s
Annual Conferences, 40th Int. Annual Conf. of ICT, 2009
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Three Major Issues have driven
Jet-Initiation of Explosives Research:
• Initiation of munitions (safety) − particularly
ammunition inside armored vehicles
• Disruption / destruction of mines, unexploded
ordnance (UXO) and terrorist devices (IEDs)
• Invention of dynamic, plate-moving,
explosive reactive armor
Also fundamental technology for non-nuclear
interception and destruction of rockets, missile
warheads, and mortar and artillery shells
Held published a photograph of an artillery shell in-flight with
“machine-gun stitching” of small holes made by jet particles
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“Held’s Criteria” for bare explosive
Explosivstoffe 1968; ICT 1970
Explosive equivalent to Composition B
Vj
2 dj = Constant1
As most jets were Copper, then later modeling and analysis:
ρj Vj
2 dj = Constant2
Dimensions:
(g [mm/µs] 2 / cm3) mm (energy density) length
or pressure length
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“Held’s Criteria”
Data expanded to include threshold or impact velocity for more
explosives as well as impact by projectiles and “flyer foils”
M. Held, 9th Det.Symp., 1989
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“Held’s Criteria” − also acquired using other tests
M. Held, 9th Det.Symp., 1989
Explosive equivalent to Composition B

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∆s, ∆t, ti = f (vj)
Held’s experiments revealed that different tests
produced significantly different initiation results
∆s = run-up distance, ∆t = run-up time
ti = run-up time − time (TD) for detonation to travel
from the axis to the charge surface
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Held’s data expressed as ∆s, ∆t, ti = f (vj
2 • dj)
Detonation
Initiation
Location
∆s
Explosive equivalent to Comp B
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Held’s experiments revealed some parameters also
produced significantly different initiation results
Spaced Barrier on HE
∆s = f (Thickness of Cover)∆s = f (Width of Air Gap)
Air Gap to Bare HE
Region where plate is bulging and
“Kernel” is accelerated by jet
“Kernel” affects penetration rate
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Images in Plexiglas behind Mild Steel Barrier
Figures are not to the same scale
Held, KB44Los Alamos, Viper
Bow Shock
Kernel within bulging plate
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Held‘s Model for Time − Distance − Actions
Caused by a Cover Plate in Contact with HE
ρj UHE
2 dj = Constant3
where Vj = UHE (1+[ρHE /ρj]1/2)
Penetration Criteria
Incompressible
Hydrodynamic
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Shaped Charges do not
have a Virtual Origin
J. Backofen, The Use of
Analytical Computer Models
in Shaped Charge Design,
Prop. Expl. Pyro. 18(5), 1993

3. 3
Radiographs Showing Jet Tip Erosion and
the Air Crater Boundary
300-kV radiography
Liner implosion locus measured
using double-image radiography
Also note jet’s “nail head” shape in radiographs
BRIGS 1989 International Symposium on Ballistics
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BRIGS 1989 International Symposium on Ballistics
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K
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Are BRIGS “Kernels” real ?
Plaster of Paris
Aluminum
Alloys
Tungsten
Alloy
Plasticine
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Photographs courtesy of Dr. M. Held, 1993 - 1994
High-Speed Streak Photography Showing:
• Interaction Between Jet Particles and Air,
• Lack of such Interaction within the Crater
Photographs for copper
jets from three experiments
Brilliant bow shock light emissions
indicate air temperatures much
higher than Copper jet-particle and
jet-particle-debris temperatures.
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7.5
Penetration of a Cover Plate and
Acceleration of the “Kernel” behind the Plate
ISL experiment

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BRIGS 1989 International Symposium on Ballistics
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BRIGS 1989 International Symposium on Ballistics
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K
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ρj Vj
2 dj = Constant2 ρj UHE
2 dj = Constant3
What / Which Initiation Criteria “Constant” ?
• Impact mode for initiation a few millimeters into
“bare” or “thinly”-covered explosive ?
• Bow-wave / penetration mode occurring deep
within explosive covered by a plate of higher
density and sound speed ?
• Increased sensitivity for “bare” explosive
after an air gap behind a plate ?
Why such different “constants” ?
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A “Kernel”-based Explanation
Let Uk be “Kernel” penetration rate into explosive
from initial contact to steady-state penetration
“Kernel” diameter Dk is a function of:
Dk = f (ρj, dj, Vj as well as ρt, Hj, Ht
and jet and target compressibility)
Uk
2 Dk = Constant4 / ρj
Assuming ρj is constant, then
Providing a criteria model that changes as
a “Kernel” is formed moving into explosive
“Kernel” angle in target Tan αk = (Dk/2) / heightk
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What might these describe ?
ρj Uk
2 Dk = C4
as Dk = 2 hk tan αk
ρj Uk
2 hk tan αk = C5or
Suggest a critical energy density* or a
critical pressure within the penetrated explosive:
* Kinetic Energy per unit Volume
(g [mm/µs] 2 / cm 3)
• on a cumulating critically-sloped surface, or
• on sloped surface area divided by a circumference
[ Acritical = f(tan αk and Dk
2) ] / πDk
• along a linear length (a circumference ?),
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Which can reveal ….. What ?
As distance x and time t are related by
Uk = dx/dt
then
d/dx [Uk
2 Dk] = d/dx [C4 / ρj]
assuming C4 and ρj are constant
[2 Uk dUk/dx Dk + Uk
2 dDk/dx] = 0
as long as Uk and Dk are not zero
dUk/dx = -- [Uk / 2 Dk] dDk/dx
[dUk/dx] / [dDk/dx] = -- [Uk / 2 Dk]
or

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dUk/dx = -- [Uk / 2 Dk] dDk/dx
[dUk/dx] / [dDk/dx] = -- [Uk / 2 Dk]
or
And ….. ?
Appear to define a deceleration of the “Kernel”
as it forms while penetrating into explosive*
*Note: the derivative could have been taken
replacing Dk with (hk tan αk) to find their effect as
they may be more affected by explosive viscosity
For a constant-diameter constant-velocity jet,
Dk should be increasing during penetration while
Uk is decreasing until Usteady-state is reached
Then αk, hk and Dk will describe the surface of
stagnating explosive where other explosive will
shear and slide due to the jet’s driving pressure
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Implications …. So What !
Initiation delay to an initiation-at-depth of penetration
implies dependency on “Kernel”
Size … diameter may represent a circumference
containing a critical quantity of “hot spots”
Shape … hk and αk may represent a critical height
defining a sloped surface on which a critical quantity
of explosive grains are sheared to create “hot spots”
Uk / 2 Dk …. may represent a time-for-initiation criterion
based on a critical shearing flow along a “Kernel”
driven by the jet’s dynamic pressure
and
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As Held observed ...
An air gap results in a larger diameter jet-tip
impacting onto bare explosive
And, … ISL experiments also showed that a jet
“accelerates” behind a plate … meaning that “Kernel”
impact occurs at Vj rather than a penetration rate
And, … a cover plate results in shock and pressure
sent into the explosive to induce motion and
compression ahead of the penetration front which
moves into the moving explosive at lower pressure
Thus, … “Kernel” formation and penetration
processes provide reasonable rationales for
different “constants” for different conditions
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Is any of this useful …. ?
Having a “feel” for “Kernel” formation and
penetration processes … in union with …
an understanding of shaped charge jets …
Provides rationales for varying jet and target
parameters in order to study and control the
initiation of explosives ….. as well as a basis
for developing prototype hardware:
• insensitive explosives / munitions
• reactive armors
• IED disrupters / UXO destruction
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Held’s version of Battelle scientific-research
shocked-water-driven disrupter charge
Battelle Institute - Columbus
Summer 1982
Design principles:
• low-velocity jet capable of
perforating metal plates but
still below “Held’s criteria”
for explosive initiation
• smooth small-diameter
continuous-rod jet
• easy-to-build easy-to-use
[ frangible-tamper wall also used ]
• water follow-through disruption
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Explosives
Water-Based or
Organic Material
LIFT Charge
(1980-1981)
Plastic Liner

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Kinetic Energy of Fluid Converts Water into Steam Explosion
or Organic Material into Fuel-Air Explosion Upon Impact
with Materiel / Surfaces within an Air-Filled Target
Plastic Liner
Plastic Jet shocks up to
penetrate metallic plates
Fluid Fill
Detonation-Driven Shock
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“Gedanken” Principles of LIFT Design
• Jet shocking-up to higher density as compressible
penetrator during impact with metal plates
(consuming penetrator length to increase density)
• Slow subsonic penetration through metal cover
plates to maximize time for shock transmission
and in-contact-explosive compression
• Jet dropping back in density to provide lower
acceleration of plate’s “Kernel” fragment as it is
accelerated through air gap or in-contact-explosive
• Low-density low-velocity continuous jet capable of
non-initiating penetration of explosives
[ Water or other driving material forms shaped charge
“slug” and acts as follow-through penetrator ]
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Summary and Recommendations
• Material viscosity affecting “Kernel” formation
particularly the explosive-target portion
• Binder thickness, viscosity and “softness”
effects should be studied with respect to
explosive grain size in flow along the “Kernel”
• Susceptibility of explosive crystal initiation
by combinations of pressure and shear as
functions of crystal size, imperfections, and
shear-driven grain rotation and deformation
Key research areas needing study include the interface regions
between the jet, the “Kernel” and the target explosive:
Viscosity-stagnated jet and target materials form a “Kernel”
providing a reasonable rationale for experimental observations
of where and when an explosive initiates due to jet attack
Hypothesis
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Additional Information
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Radiograph and High-Speed Photograph Showing
Jet Tip Erosion Debris Along the Air Crater Boundary
From Figure 8(b) 450-kV sequential pulsed radiographs
of a VIPER experiment in L. Shaw, et al., “Electro-Optic
Frame Photography with Pulsed Ruby Illumination”,
UCRL-JC-112232, preprint, for 20th Int’l Cong. on High-
Speed Photography and Photonics, Victoria, B.C., 1992
Figure caption noted material around the jet tip
that was also shown in Figure 9(a) which
included the photograph shown to the right.
Note the shape and size of
the very fine solid particles
Also note the “nail head” shape in radiograph.
]})1/{}1({}/{1[/VU jet1jet1 λλρρ +++=
)/(1 211 ρρλ −=
]2M1)[(/]M1)[( 2
1
2
112 +−+= γγρρ
airerjetjetcrater X/R2.05R ρρ=
L/P/(V/U)R2.5738R airjetjetcrater ρρ=
Air Cratering (Model 1)
J. E. Backofen, “Shaped Charge Jet Aerodynamics, Particulation, and
Blast Field Modeling”, Proc. 10th Int. Symp. Ballistics, 1987 (BR 92-7)
Where the penetration rate (U) and jet velocity( V)
have comparable units (km/s), ρ1 and ρjet are the
density of free-stream air and the jet, respectively
in comparable units (g/cm3), and λ1 and
(λjet = 0, incompressible) are the compressibility
of air and the jet, respectively.
With the increased density (ρ2) after
the shock front provided by:
Where the free-stream Mach number (M1 = V/Co)
uses Co = 0.335 km/s for air’s speed of sound;
and the effective adiabatic exponent γ is 1.25 or
obtained from an equation of state.
Where Xer is the distance within which
1-mm of jet length (L) is consumed; and
penetration is: P = [ U / (V – U) ] L“Air Blast” model from 1987
“Classical” model
1987 Model

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Flash Radiograph and High-Speed Streak
Photographs of Copper Jets Penetrating Air
Note: small copper particles
traveling alongside the jet
Photographs courtesy of Dr. M. Held, 1986, 1994
Note: crater boundary defined by
bow-shock light emissions as well as
radiation from and the combustion
of jet debris dissipating the debris
mass along crater wall
Near its melting temperature, Copper’s
radiation appears orange to light yellow.