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Shock Physics Simulation of Pressure, Temperature, and Combustion within
an Aerospace Carbon Fiber Panel Fastener Assembly due to Direct Lightning
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2017 International Conference on Lightning and Static Electricity (Nagoya, Japan)
Shock Physics Simulation of Pressure, Temperature, and Combustion
within an Aerospace Carbon Fiber Panel Fastener Assembly due to
Direct Lightning Attachment
Trenton Kirchdoerfer1 , Andreas Liebscher2 , Hasim Mulazimoglu2 , and Michael Ortiz∗1
1
2
California Institute of Technology
Arconic Fastening Systems and Rings
Keywords: Composite materials, Fastener, Shock physics,
Joule heating, Combustion
Cu Mesh
CFRP
Abstract
CFRP
In this study we examine detailed CTH simulation results of
a carbon fiber composite panel assembly where the binding
titanium fastener joint is the attachment point of a direct lightning strike. A refined COMSOL Multiphysics electromagnetics
calculation is performed on the undeformed installed fastener
geometry to obtain the spatial distribution of the current and electric field solutions in time using SAE ARP5412B lightning test
waveforms. Electro-mechanical coupling is achieved through
the use of Joule heating to simulate non-chemical effects on
structural components using J · E, the power per unit volume
dispersed throughout the structure due to the lightning energy
transport. The shock physics code CTH is used to model the
fluid-structure calculations in conjunction with combustion effects introduced by fuel tank sealant. These reactions involve
highly non-linear and high temperature material effects. Specifically, synthetic resin is used as the sealant surrogate around
the fastener shank region in an attempt to understand chemical combustion contributions to the formation of large internal
pressures that frequently result in hot particle ejection (HPE).
Previously, experimental test panel coupon images of lightning
strike material effects have been used for verification of material
and equation of state selections. Here we make use of these
selections, along with dynamic pressure measurements and observations of char patterns, to select properties of the affected
combustion. The effects of the lightning energy depositions in
the inner spaces surrounding the fastener, as well as affected
local geometrical changes are discussed. The spatiotemporal
pressure evolution within the fastener assembly cavities are compared with experimental results and importance of the modeled
chemistry changes is discussed.
1
Air
Shank Gap
Titanium
(Nut)
Titanium
(Fastener)
Figure 1: Composite panel fastener assembly with detail views.
acterizing these structures’ responses to lightning strike events
becomes ever more important. Within these designs composite
panels are frequently joined using titanium fasteners. The high
conductivity of the metal fastener, relative to the composite panels, makes these fasteners likely attachment points for lightning
strike. Once struck these fastener assemblies can exhibit outgasing events, also known as hot particle ejections (HPE), into the
interior spaces of the aircraft[10].
Figure 1 contains a diagram detailing the panel-fastener assembly used in this analysis, which represents a typical example of
a CFRP fastener installation. Here two panels are joined though
the use of a fastener-nut assembly, with an intimate electrical
connection across the bearing surfaces in the countersunk region.
Along the top of the panel an expanded copper mesh provides
greater conductivity to the outward face of the assembly. Along
the shank of the fastener there exists a narrow clearance gap
which is occupied by air and fuel tank sealant. This gap sees
significant heating and arcing once lightning attaches to the fastener head. The open volume in the nut acts as a relief chamber
for the exhaust products from the clearance gap. Numerical
analysis of this system can provide estimates of both structural
and thermodynamic properties that are difficult or impossible to
probe experimentally.
Introduction
As the number of aircraft that make significant use of carbon The focus of this paper is to simulate the significant material
fiber reinforced polymer composites (CFRP) increases, char- effects observed in both the gasses and solids during an applied
∗ 1200 E. California Blvd., MC 105-50, Pasadena, Ca, USA, 91125
lightning strike. We first describe our generation of a transient
E-mail: ortiz@caltech.edu
electrodynamic solution which will provide the electric field (E)
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2017 International Conference on Lightning and Static Electricity (Nagoya, Japan)
and current density (J). With these field values as inputs J · E is
used to calculate the Joule heating power term. We then discuss
our use of these fields as inputs to a shock physics code, which
then simulates the thermal and material effects of the strike.
Chemical effects are then addressed through the combustion of
a defined surrogate material for tank sealant. Our simulation
results include visualized fields of stress and temperature along
with time-history plots of temperature, pressure, velocity and
displacement during the lightning strike. We conclude with
a discussion on the CTH results in comparison with test data,
along with the broader implications for such events.
2
fiber-aligned electrical conductivity of CFRP remains
relatively constant [4], significant reductions in copper[5] and
titanium[9] conductivity occur over the simulated temperature
ranges. These reductions in conductivity, along with material
erosion, would most strongly affect the structural solution in
regions of extreme heating. As such, analysis will not focus
heavily on solid materials that are subject to extensive amounts
of heating. The use of Joule heating to inform material analysis
explicitly omits the direct resolution of arcing effects, which
are particularly important to the simulation of gas and sealant
materials. We seek to estimate such effects through two mechanisms, the Joule heating of gas components and the chemical
combustion of tank sealant. While the internal spaces in the
assembly are treated using the initial electrical conductivity of
air, it merits mention how significant arcing would be expected
to affect temperature and pressure rises in these environments.
Arcing causes the formation of plasma that would create new
conductive pathways across the shank gap of the fastener assembly. Excluding these effects means that more energy is deposited
in the gas than would be expected if the arcing phenomena were
modeled. The chemical effects are then affected directly through
a defined combustion of the tank sealant. Thus, the calculated
temperatures and pressures for the gap and chamber would act
as upper bound estimates of a simulated system response which
includes arc heating.
Background
Previous work has been done to determine that the composite
panel damage response to lightning strike is strongly related to
Joule heating [7]. Others have made use of this finding to provide an electro-mechanical coupling capable of predicting composite panel damage [11, 4]. Subsequent work [8] then extended
analysis from a uniform panel to a panel-fastener assembly,
adding significant complexity to the simulated mechanical processes. Simulated panel lightning strikes can be handled within
the confines of commercial software packages (e.g. Abaqus,
COMSOL) that allow a direct coupling of the electrical, thermal,
and deformation fields. Fastener strikes require the resolution
of responses and interactions of the Titanium fastening components, the CFRP panel, and the substances enclosed by the
assembly. The need to resolve fluid effects and their interaction
with solid assembly components in the presence of extensive
heating has motivated [8] the selection of Sandia’s shock physic
code CTH [6]. This shock physics code makes use of a coupled
multi-material Euler-Lagrange scheme which admits materials
both with and without significant shear stress response to deformation. CTH also makes use of a library of tabulated equations
of state (EOS), which are based on the SESAME database [1]
developed by the Los Alamos National Laboratory. These equations of state have been characterized across extensive temperature and pressure ranges, including phase changes, which make
them well suited to the extreme environments expected during
a lightning strike. This work extends the previous use of this
code to include its ability to make use of composite equations
of state, which are capapble of modeling the irreversible
phase changes associated with chemical combustion.
3
3.1
Setup
Electrodynamics
Figure 2 shows the cross-sectional geometry shown earlier in
Figure 1, now with a more complete accounting of materials and
with fine details enlarged for clarity. The fastener is a quarter
inch aerospace flush head type fastener with accompanying
containment nut holding together two quarter inch (0.635 cm)
carbon fiber reinforced polymer (CFRP) panels. The top face of
the outer composite panel has an expanded copper mesh 0.005
cm thick with an increased bolt-line mesh thickness of 0.0127
cm in the region adjacent to the fastener head. The clearance
gap of 0.0025 cm between the shank of the fastener and the
hole walls connects directly to the relief cavity created by the
Current Channel
Expanded Copper
Mesh
Presently, there is no direct way link CTH to a solver
capable of providing the electric and current fields necUpper Panel
essary for full electro-mechanical coupling. Instead a
detailed electrodynamic COMSOL[3] solution is used
Lower Panel
Sealant
to generate current and electric field values to determine
Joule heating, which is used in the material calculations.
Paint Layer
This one-directional coupling ignores the changes in the
Nut
electrical solution that would result from thermal, deforAir
mation and errosion effects. CFRP has directionally deFastener
pendent electrical properties, where conductivity values
aligned with fiber directions are significantly higher than Figure 2: Simulation material and geometry, components annotated with leadthose seen without fiber alignment. Further, while the ers have thin features thickened
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2017 International Conference on Lightning and Static Electricity (Nagoya, Japan)
is then averaged to calculate an effective heating
power for each element for use in CTH. As this
process spatially smears the solution between neighboring cells, this naturally affects a phenomenon
frequently referred to as “edge glow.” Heating induced by this form of numerical edge glow arises
from the low heat capacity of the gasses that lie adjacent to solution zones with greater amounts of Joule
heating.
For the purposes of energy injection, CTH requires
the definition of geometric zones, here referred to
as phantom parts, which are spatially static and material dependent. These injection forms only apply
power to specific materials which overlap a defined
spatial domain. Coupling is then achieved by first
using the nodal Joule heating values to calculate the
Figure 3: Meshed domain with details showing resolution of critical features
mean heating power of each element from the COMSOL solution. This Joule heating rate can then be
containment nut. Fastener installation holes bored in composite combined with the element’s geometry and material to fully
materials have significant surface irregularities [10] not resolved describe a given phantom part. However, as will be shown, this
in these models or the subsequent analyses. The panel-panel form of coupling requires additional corrections in both spatial
interface has an insulating sealant layer 0.005 cm thick, while and temporal domains.
the back face of the bottom panel has a 0.002 cm thick paint
layer. Figure 2 also annotates the location of the arc root current
injection location. Taking this location for the arc channel of
the lightning and this work then makes use of a 40 kA SAE
ARP5412B lightning test waveform [2] run over 250 µs. An
additonal 225 µs is simulated, post-strike, to allow pressures and
temperatures to equilibrate. Simulations were performed with
polar symmetry about the fastener axis to affect a significant
reduction in the computational cost and complexity. The top
panel and lower panels are being used to model a face panel and
stringer with an impedance balanced electrical configuration
typically used in aerospace lightning tests.
The direct electrical effects were simulated using COMSOL
Multiphysics software. Shown in Figure 3 is the mesh geometry
where the full domain includes an air region 10 cm in radius from
the center of the fastener head. For fine features, a single layer
of triangle elements combines with interface elements to provide
sufficient resolution of the electro-dynamics while larger shapes
were resolved using coarser meshes. The full model constitutes
70,371 triangle elements resolving the swept volumes, while
4,120 line elements are used to resolve the revolved interfaces
and boundaries. Solution outputs included all electric field
and current density components for each mesh node at discrete
time intervals that could be used to calculate the power input
associated with Joule heating.
3.2
(a)
(b)
Figure 4: The lightning waveform as
R approximated by steps shown for
(a) the normalized action integral I 2 dt and (b) the normalized I 2
waveform.
The static geometry of the injection domains naturally cause
a form mismatch as materials deform and translate. For small
deformations, the effects of this mismatch become problematic
in the context of fine features. Small amounts of radial gap
translation along the fastener clearance gap could significantly
affect the amount of overlap between phantom and material
components. Such issues are handled through the creation of
material specific buffer zones, which are populated with additional phantom parts. These zones are used to provide extensions to a material’s energy injection domain using the nearest,
COMSOL element heating rate for the matching material. By
making use of these material heating extensions, the translation of small features is prevented from significantly affecting the amount of defined material heating in critical regions.
Energy Coupling
Once the Joule heating per unit volume is calculated from the
fields supplied by the COMSOL model for each time step, they
are used to set power levels for energy injection. Both J and E
are solved at element centers and output from COMSOL at the
element nodes. The Joule heating of each node of an element
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2017 International Conference on Lightning and Static Electricity (Nagoya, Japan)
Symmetry
Symmetry
While spatial buffer zones mitigate the use of static
shapes, more extensive measures are required to set the
rate of heating. CTH’s phantom parts are capable of
time dependent heating rates, however, for the large
number used to characterize our electro-mechanical
coupling, the capability incurs prohibitive computational costs. To compensate for the resulting need
for constant rates, the time interval is split into nine
sub-simulations in which each phantom part has an
independent but constant heating rate. These nine temporally chained simulations then make use of heating
rates re-calculated for each COMSOL element using
the expression
Figure 5: Full domain with details showing mesh resolution of critical features.
R ti+1
J · E dt
(Q̇equiv )i = ti
,
(1) preserving the bulk validity of the static power injection geometi+1 − ti
tries used for the electro-mechanical coupling. The remaining
outflow boundary was selected to allow materials ejected by
where ti and ti+1 represent the time interval bounds of the regions with significant surface erosion to exit the simulation.
sub-simulation associated with the approximating heating rate These reductions in geometric and material complexity were
(Q̇equiv )i . The use of equation (1) maintains energy equiva- necessary to reduce the solution complexity and computational
lence to the COMSOL solution at the time interval transitions. cost.
The duration of these time subdomains is selected by using an
equivalent methodology to approximate the action integral while
minimizing the intermediate errors. Figure 4a shows how action 3.3.2 Mesh Resolution
is approximated in time, while the I 2 waveform approximation
Unlike material computations that make use of the standard
is shown in figure 4b.
finite element (FEA) analysis methods, CTH tracks materials on
a fixed grid. The large deformations, or flows, associated with
3.3 Material Dynamics
fluid motion are easily handled by this eulerian frame, but at the
cost of significant refinement requirements for detailed features.
3.3.1 Geometry and Boundary Conditions
Because elements are fixed in space, deformations are resolved
through the advection of material between cells. When multiple
The material diversity within materials occupy a single cell, as occurs in the presence of
Outflow
structural sections joined by material interfaces, calculated responses use a volume weighted
fasteners, coupled with the average to combine the properties of the constituent materials.
non-local nature of electrody- Fine features need to be resolved with multiple cells across their
namics solutions, require the span in order for the code to prevent mixed cell properties from
inclusion of both an expan- dominating the measured response. For these calculations the
sive spatial domain and an resolution in the air filled gap channel is such that a minimum
extensive level of feature de- of three cells are always contained within the channel as seen in
tail. Material effects are com- Figure 5. Further refinement of these channels would not result
paratively local, and fine fea- in resolving boundary effects as materials modeled without
tures, such as paint, sealant shear deformation resistance, such as air, exhibit no viscous
or copper layers, are much effects. Resolution of fine features was achieved though the use
less likely to affect the gen- of adaptive mesh refinement (AMR), allowing this system to
eral material response. Fig- be resolved with 170,000 to 230,000 cells. The full calculation
ure 6 shows a new smaller discussed in the results section required 1,833,847 time steps to
(Support)
Symmetry
domain, which is radially 1.1 complete the 475 µs of simulated time.
Figure 6: The domain, boundary cm from origin to boundary.
conditions, and boundary supports The copper mesh, inter-panel
used to resolve material response. sealant and paint layer were 3.3.3 Material Erosion
modeled as parts of the composite panels, while the air outside the assembly was simulated Even with sufficient resolution, mixed material cells can cause
using a void material that incurs little computational cost. Also spurious thermodynamic states to develop which both contamipictured in Figure 6 are the fixed boundary conditions and added nate subsequent results and severely restrict the time step. Such
boundary supports which hold the assembly in position, thus occurrences are especially common when gases interact with
(Support)
4
2017 International Conference on Lightning and Static Electricity (Nagoya, Japan)
the void material used to resolve external air. To prevent these
effects both the CFRP and titanium materials are discarded following significant drops in density or achieving temperatures
in excess of their gas transition values. It has been found previously [8] that discarding air in excess of 22,000 K stabilizes
such calculations without contaminating solution results.
Gap Channel:
Tracer 1
Tracer 2
Tracer 3
Tracer 4
Nut Chamber
3.3.4
Material Modeling
Most equations of state (EOS) used for the simulation were
selected from the tabular SESAME models available within the
CTH equation of state library. Air and titanium models were
directly available, and previous work [8] has found that CFRP
Figure 7: Locations of tracers used for time history plots.
panels were best able to match surface damage using CTH’s
carbon equation of state. The panels’ material strength was
modeled using an elastic perfectly plastic formulation while
titanium was modeled using a characterized Steinberg-Guinan- can calculate the local changes in the gap,
Lund plastic flow model.
d − (dinit. − wg )
Gap Change(%) = 100 ×
− 1 , (2)
The CTH library offers a limited number of combustion modwg
els for plastics, from these the Arrhenius composite EOS for
PMMA was selected. The chemical effects modeled by CTH to analyze the percent-change in the gap geometry. The third
have been developed explicitly to model detonation effects, thus tracer of the set is geometrically static and provides information
the available chemical effects are fast acting. It is unlikely that on temperature, pressure, velocity, and sound speed. Finally, the
chemical detonations would propogate continuously through last tracer was placed concurrently with the third but left free
the narrow, irregular domain of the panel-shank gap, however to move with the fluid, providing a massless particle to track
the combined arcing-combustion events would likely propogate gas migration. The mean temperature and pressure response in
quickly from the initial arc points via the fast expanding ionized the nut chamber was characterized using the mean values from
products of these reactions. Burn detonation speed was defined three locations to provide aggregate time histories.
to travel at 7 km/s, from the middle of the bottom pannel. This
location exhibits significantly stronger electric fields due the
the semi-isolation of the lower pannel. Detonation was initi- 4 Results
ated at 1.2 µs, the time that the electric-field adjacent to the
lower panel exceeded the dielectric strength of air, 3 MV/m [12].
Preliminary spherical calculations, which were volumetrically
equivalent to the gap/chamber system, were used to estimate final chamber pressures of a sealant filled gap. Pressures of 1,100
atm were higher than the highest pressures seen for this system
in testing (700 atm) and 3 times the more typical pressures seen
in testing (300 atm)[8]. Inspection of tested fastener shanks for
such systems typically see char patterns covering approximately
50% of the shank surface area. These observations, combined
with the estimated high pressures, led to the gap being modeled
as half full of fuel tank sealant.
3.3.5
Tracer Locations
Figure 8: Material (left) and temperature (right) plots at 475 µs
.
The focus of this work is to characterize the fastener system
response to the significant energy loading that takes place during
the attachment of a lightning strike to the fastener head. Of
interest are the system responses along the shank-panel gap
and in the nut chamber. Tracer locations 1 to 4 each have 4
tracers which are used to calculate physical properties in the
gap channel. On either side of the gap lie two tracers that are
free to move with the material. Using the radial locations of
these tracers (d = r2 − r1 ) and the initial gap width (wg ) we
Figure 8 shows the material erosion and temperature plots
225 µs after the end of the 250 µs simulated lightning attachment. Responses to these energy inputs naturally segregate
themselves into a discussion of structural and fluid effects. Solid
materials showed significant heating and erosion along the top
surface of the assembly, with a ringing response dominating the
final stresses. Fluid responses are characterized by chemical and
heating effects causing temperature and pressure rises within
5
2017 International Conference on Lightning and Static Electricity (Nagoya, Japan)
in Subsection 4.2, and likely represent high estimates due to
the assumed form of chemical effects. Aside from having significant effects on the flow properties of contained fluids, the
energy injection zone extensions discussed in Subsection 3.2
would combine with these gap expansions to effect the energy
depositions applied in the gap spaces.
the clearance gap surrounding the shank region of the fastener,
causing the air to vent into the nut chamber. Ultimately, the
combustion driven pressure increases in the assembly’s internal
spaces caused significant deformations in the panel along the
shank of the fastener.
4.1
Structural Response
4.2
Fluid Effects
Figure 9: Stress field components σzz and σrr after 475 µs of simulated time.
Figure 11: Axial(z-direction) coordinate evolution of massless particles initiated at tracer locations 1 to 4.
Figure 9 shows a snapshot of the final stresses of calculation
which are dominated by a transient ringing of the system. This is
a significant contrast with previous work that excluded chemical
effects in the chamber dynamics[8] where thermal expansion
was the primary driver of the final stress states.
The fluid temperature effects most visible in Figure 8 are the
hot gases in the nut’s containment chamber. All combustion and
most of the gas heating takes place in the clearance gap which is
then vented out to the cavity. Figure 11 shows the time evolution
of material points initialized at the four tracer locations. The
motion path of the massless particle initiated at Tracers 2 to 4
demonstrates that most of the initial mass contained within the
clearance-gap channel is vented into the cavity within 50 µs.
Figure 10: Gap width change as a function of time, moving averages
were used to plot trend
Specific changes in the gap width, shown in Figure 10, were
analyzed to understand their time evolution. Since the noise in
these signals was significant, the labeled series in the shown
plot were generated using a centered moving average. The area
between the highest and lowest measured gap values was colored white to indicate the extent of the measurement noise. Any
future work to resolve small-scale internal flows might have
difficulties introduced by the vibration of fluid-solid interfaces.
As can be seen in Figure 10, structural changes along the channel gap were significant and severe (> 100%). The amount of
deformation arises from the detonation pressures next discussed
Figure 12: Pressure time histories measured in the channel gap.
Initial pressures within the gap are extreme, reaching peak values of 16,000 atm (1.6 GPa) as shown in Figure 12, but decay
quickly enough that the time axis is shown with a log scale. After 50 µs the detonation effects disperse enough that the chamber
pressures seen in Figure 13 initially equilibrate to 300 atm (30
MPa). After the completion of these initial dynamic processes,
additional heating and significant mixing cause the final system
pressure to approach 550 atm (55 MPa).
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2017 International Conference on Lightning and Static Electricity (Nagoya, Japan)
Figure 13: Pressure time histories measured in the nut chamber.
Figure 16: Temperature mixing evolution of nut chamber flows as
shown with visualizations at marked times.
The velocity plots in Figure 14 indicate a similar division of
early-late responses at the annotated tracer locations. Downward
flow velocities reached speeds as high as 200 m/s to 600 m/s
with higher speeds reached by tracers closer to the nut chamber,
similar to speeds seen without combustion [8]. None of the
velocities for these flows significantly exceeded Mach 0.5. After
75 µs speeds decay into oscillations driven by chamber mixing
which roughly center on 0 m/s.
arc attachment. Final temperature and pressure values are affected by the amount of mixing taking place in the nut chamber.
Figure 16 shows several field plots of temperature at various
times during the simulation. Some of the visualized temperature
discontinuities arise because of material differences between
the combustion products and the air and the non-resolution of
thermal conduction. The images show hot gases injected by the
initial jet at 2.2 µs, the initial temperature equilibration at 25
µs, some localized high temperature zones 250 µs, and a mixed
chamber approaching conformity at 475 µs. Beyond the initial combustion, observed mixing and heating within the gases
drives the system’s pressure rise from 300 atm (30 MPa) at 100
µs to 550 atm (50 MPa) at 475 µs.
Figure 14: Axial velocity (Vz ) time histories in the channel gap.
Figure 17: Temperature progression within the nut chamber.
The chamber temperature evolution seen in Figure 17 similarly
shows sudden injections of hot gases followed by slower injection and mixing processes within the nut chamber.
Figure 15: Temperature time histories measured in the channel gap.
5
Figure 15 shows the temperature time histories of Tracers 1 to 4
within the gap channel. Following combustion, temperatures
initially rise to 2000 K which then stabilize to 1500 K by 75
µs. Subsequent heating in the channel generates high postcombustion temperature peaks from 5500 K to 11000 K, after
which, values subside following the termination of simulated
Two distinct simulation codes were employed for the purposes
of multiphysics coupling, which provided the ability to make
use of advanced capabilities of both COMSOL and CTH within
their respective ranges of applicability. COMSOL provided
high fidelity electrodynamic currents and electric fields which
accounted for small but important features needed for resolving
7
Conclusion
2017 International Conference on Lightning and Static Electricity (Nagoya, Japan)
References
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solutions in both spatial and temporal domains. With these coupling methods developed, the CTH model was configured to
provide the material response to the direct lightning strike. The
combustion of fuel tank sealant was modeled through the detonation of a surrogate material defined by a PMMA composite
equation of state. With Joule heating and combustion effects
being fully defined, the model could then be used to characterize
properties that would be difficult to measure experimentally.
Table 1 summarizes the peak and steady state properties that
best summarize the responses seen in the gap channel and nut
chamber.
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Peak Pressure
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Acknowledgements
T.K. and M. O. are grateful to Arconic Fastening Systems and
Rings for both technical and financial support.
8
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