CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
MODELING AND SIMULATION OF EXPLOSIVELY DRIVEN
ELECTROMECHANICAL DEVICES
Paul N. Demmie
Sandia National Laboratories* Box 5800, MS0820, Albuquerque, NM871S5
Abstract. Components that store electrical energy in ferroelectric materials and produce currents
when their permittivity is explosively reduced are used in a variety of applications. The modeling and
simulation of such devices is a challenging problem since one has to represent the coupled physics of
detonation, shock propagation, and electromagnetic field generation. The high fidelity modeling and
simulation of complicated electromechanical devices was not feasible prior to having the Accelerated
Strategic Computing Initiative (ASCI) computers and the ASCI developed codes at Sandia National
Laboratories (SNL). The EMMA computer code is used to model such devices and simulate their
operation. In this paper, I discuss the capabilities of the EMMA code for the modeling and simulation
of one such electromechanical device, a slim-loop ferroelectric (SFE) firing set.
INTRODUCTION
WHAT IS A FIRING SET?
In this paper, I discuss the capabilities of the
EMMA computer code (1) for modeling an SFE
firing set and simulating its operation with the
added complexity of assessing its performance with
aged materials.
A firing set is a device whose purpose is to
remain in an inactive state and initiate detonators in
a safe and reliable manner only when intended. The
type of firing set discussed here stores electrical
energy in the SFE material, PBZT (2) when a
voltage is applied and releases this energy into
circuits when the permittivity of the PBZT is
explosively reduced. This material is desirable
since its low remanent polarization renders the
device safe when the charging voltage is removed.
Figure 1 is an exterior view of an SFE filing set.
THE EMMA COMPUTER CODE
Figure 1. Exterior view of an SFE firing set.
EMMA was used to model the firing set shown
in Fig. 1 and to simulate its operation. EMMA is
based on the ALEGRA computer code (1) that is an
arbitrary Lagrangian-Eulerian, material-dynamics
code that accommodates large deformations and
In the following sections I address: what is a
firing set, the EMMA computer code, the EMMA
computational model, verification of the model,
summary of the validation process, and conclusions
and discussion.
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of
Energy under Contract DE-AC04-94AL85000
311
strong shock physics. EMMA adds to ALEGRA
the capabilities to perform electromagnetic field
calculations based on a quasi-static approximation
to Maxwell's equations and to model circuits.
Electromechanical models were developed and
implemented in the EMMA code to represent
materials such as the ferroelectric material PBZT.
The programmed-burn model is used to model
the explosive. The CHEETA computer code (3)
was used to determine all input required by EMMA
for the explosive.
CHEETA determines all
reaction-state parameters for a given explosive with
a specified unreacted density under the assumption
of one-dimensional, perfect detonation. Aging
effects in the explosive can be incorporated into the
programmed-burn model through measurements of
unreacted density or detonation velocity (DV).
Two types of experiments were performed to
determine the DV for the explosive, DV-block
experiments and rheology-block experiments. The
difference between these experiments is that the
tracks are straight in the DV-block experiments and
are curved in the rheology-block experiments. The
average DV obtained from these experiments is
7272 km/s. CHEETA showed that this velocity
corresponds to an unreacted density of 1490 kg/m3.
The explosive lens includes a cover plate, track
plate, isolation plate, and output plate. The plates
are made of chemically inert Lexan and have welldefined geometry. The tracks in the track plate are
filled with explosive. The detonation propagates
along the tracks in the track plate shown in Fig. 3,
down holes in the plate, and to explosive pellets in
the output plate. It also propagates along timing
tracks to locations of switches that close when the
pressure wave reaches them. The effect of this
configuration is to produce a nearly plane wave in
the SFE stack. No aging effects are known or
expected for the Lexan in the explosive lens,
THE EMMA COMPUTATIONAL MODEL
Figure 2 is an exploded view of the SFE firing
set shown in Fig. 1.
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Figure 2. Exploded view of an SFE firing set.
We developed a comprehensive, high fidelity,
three-dimensional model of a firing set from the
cover plate through the ceramic backup plate with
attached test circuits and without the detonator. The
elements of the EMMA computational model are:
• Explosive
• Explosive Lens
• Buffer Plate
• SFE Ceramic Elements
• Mylar Layer and Electrode Interfaces
• Transducer and Output Circuits
• Explosively Inert Regions (everything
else)
Values for material properties were found in
the literature or data from experiments.
This model is the best-estimate representation
of the firing set with attached test circuits and
without the detonator. It contains 9,021,601 nodes
and 8,878,535 elements, A typical simulation
requires about 36 hours on the ASCI Red computer.
Figure 3. Track plate.
The buffer plate is made of alumina and has
well-defined geometry and material properties. No
aging effects are known or expected.
The SFE elements are made of PBZT. The
dynamic properties of a charged PBZT element
being shattered by a shock wave were the biggest
unknowns. No aging effects are known or expected
312
for this element, but can be incorporated through the
many parameters in the model.
Experimental data were used to calibrate the
electromechanical model for PBZT. In this model,
the stress and dielectric tensors are coupled under
the assumption of uniaxial strain by the electrostrictive coupling parameters. The coupling parameters
specify a function that is proportional to the
reciprocal of the relative permittivity. Experiments
using a gas gun to shatter PBZT elements were
performed at SNL to determine these parameters.
The Mylar layer between the buffer plate and
the SFE stack is an important feature of this firing
set and is designed to reduce the pressures in the
SFE stack so that electrical conduction does not
occur in the PBZT elements. Inclusion of this thin
but necessary feature, as well as the electrodes with
a rubberized material on each surface, is part of the
present work. Results of simulations using this
higher-fidelity model are not available at this time.
Test firings of the device used known circuits.
Transducer and output circuits were modeled using
resistances and inductances listed in the diagrams
for these circuits. We also included values for
resistance and inductance of the attached wiring and
internal to the firing set. Estimates of the internal
resistances and inductances were obtained using the
DAKOTA (4) and Spice (5) computer codes and
data from test firings.
SFE ceramic stack. Figure 5 compares calculated
and measured output currents in the two circuits.
These figures imply that the features listed are
present in an EMMA simulation.
VERIFICATION OF THE MODEL
SUMMARY OF THE VALIDATION PROCESS
Verification is the process of determining that a
computer simulation correctly represents the
conceptual model and its solution. The features
expected for a correct representation of the
performance of an SFE firing set are
• A detonation propagates in the track
plate,
• detonates the explosive pellets in the
output plate,
• produces pressures waves that propagate through the buffer plate and into
the SFE ceramic stack,
• shatters the SFE ceramics, and
• produces currents in the circuits
Figure 4 shows propagation of a detonation in a
section of the track plate and propagation of
pressure waves and electric field production in the
Validation is the process of determining the
degree to which a computer simulation is an
accurate representation of the real world. Five types
of experiments were performed at SNL that
provided data for the validation process.
The first type of experiment is a test firing of
the device. Features of interest include peak
current, difference in closure time of switches,
width at half height (time difference at halfmaximum current), and pulse length. We have data
for 29 experiments for this SFE firing set. Figure 5
shows the calculated and measured currents for one
test firing. This figure shows that the calculated
peak values of current and the width at half height
agree very well with the measured values.
However, the pulse lengths do not agree as well.
Finally, the calculated value for difference in
Figure 4. Propagation of detonation in track plate, pressure
waves in buffer plate, and electromagnetic field in SFE stack.
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Figure 5. Calculated and measured currents. (This figure is in
color on the CD.)
switch-closure time differs significantly from the
measured value.
In the second type of experiment, the buffer
plate and ceramic stack were removed and replaced
by a Lexan block with holes where sensors could
determine time of arrival of a detonation. In the
third type of experiment, material below the track
plate was removed and sensors were placed to
measure time of arrival of a detonation at locations
in the track plate. From these data and calculated
distances, average velocities could be determined.
In both types of experiments the difference between
DVs determined from calculations and measurements differed by less than 1%. This agreement
indicates that the programmed-burn model works
extremely well.
The fourth type of experiment was designed
specifically for validation. In these experiments,
locations in the track plate were blocked so that the
detonation would not propagate past these
blockages and 50%, 25%, 72.5%, and 6.25% of the
explosive pellets could not be detonated. For both
circuits, the calculated fractions of peak current
differ from the measured values by less than 2%.
In the fifth type of experiment, material below
the SFE stack was removed and replaced with
polymethylmethacrylate (PMMA). VISAR (velocity interferometer system for any reflecting surface)
measurements were made to determine pressures
just below the SFE stack. We are waiting for results
to compare with EMMA simulation results. These
experiments are very important to determine how
well the computational model is an accurate
representation of the real world.
CONCLUSIONS AND DISCUSSION
EMMA is a viable analytic tool for modeling
an SFE firing set and simulating its operation. A
verification process shows that the EMMA
computational model correctly represents the
conceptual model of an SFE firing set and its
solution.
A validation process indicates that, while many
features of the EMMA model represent reality well,
there is room for improvement. Experiments
indicate that PBZT is conductive at the fields and
pressures currently calculated by EMMA. Since the
device was designed so that conduction does not
occur in the SFE stack, present work focuses on a
higher-fidelity model that includes the Mylar layer
and all coated-electrode interlaces to improve
pressure prediction. We have data for validating
this model.
Experiments also indicate the
electrostrictive coupling parameters are functions of
strain and electric field strength. Therefore, a new
electromechanical model for the PBZT is being
developed and implemented in EMMA.
There is uncertainty in the modeling of any
physical system and in simulating its performance.
Therefore, an important part of this work is to
perform sensitivity studies to determine the effects
of variations in selected input parameters and
modeling features. Simulation results and results
from sensitivity studies that are not discussed here
support the position that this filing set is a robust
device and is expected to perform its intended
function as it ages.
REFERENCES
1. Computational Physics R&D Department, ALEGRA
User Input and Physics Descriptions Version 4, Draft
SAND document, SNL, Albuquerque, NM (2001).
2. Samara, G. V., and Hansen, L. V., The Properties and
Physics of the Slim-Loop Ferroelectric (SFE)
(Pb71Ba,29).99(Zr7o7Ti,293).98B(o203) SAND98-2275, SNL,
Albuquerque, NM (1998).
3.
Fried, L. E., CHEETA 139 User's Manual,
UCRLOMA0116541, Rev. 3, Lawrence Livermore
National Laboratory, Livermore, CA (1996).
4. Eldred, M. S., Bohnhoff, W. I, Hart, W. E., DAKOTA,
A Multilevel Parallel Object-Oriented Framework for
Design Optimization, Parameter Estimation, Sensitivity
Analysis, and Uncertainty Quantification, SAND99-QOOO,
SNL Albuquerque, NM (1999).
5. Johnson, B. T., SPICES Version 3f Users Manual,
University of California, Berkeley, CA (1992).