Ballistic Response of
Pyramidal Lattice
Truss Structures
A Thesis
Presented to
the faculty of the School of Engineering and Applied Science
University of Virginia
In Partial Fulfillment
of the requirements for the Degree
Master of Science (Engineering Physics)
By
Christian Joseph Yungwirth
May 2006
APPROVAL SHEET
The thesis is submitted in partial fulfillment of the
Requirements for the degree of
Master of Science (Engineering Physics)
_______________________________
Author, Christian J. Yungwirth
This thesis has been read and approved by the examining committee:
_______________________________
Thesis advisor, Haydn N.G. Wadley
_______________________________
Committee Chairperson, Dana M. Elzey
_______________________________
Stuart A. Wolf
Accepted for the School of Engineering and Applied Science:
_______________________________
Dean, School of Engineering
Applied Science
May 2006
Abstract
Cellular metal structures with periodic “lattice truss” topologies are being utilized for an
expanding variety of multifunctional applications including mitigation of the high
intensity dynamic loads created by nearby explosions. In these situations, the panels are
also exposed to high velocity projectiles and their ballistic response is then pertinent.
This thesis explores the ballistic resistance of a cellular pyramidal lattice truss structure
fabricated from both a high ductility, high work hardening rate 304 stainless steel and an
age hardened 6061 aluminum alloy with similar yield strength, but lower ductility and
significantly smaller work hardening rate.
Projectiles made of 1020 carbon steel,
measuring 12.5 mm in diameter, made normal impact with these sandwich structures.
The pyramidal lattice truss core sandwich panels had a core relative density of
approximately 3% with cell sizes of approximately 2.54 cm x 2.54 cm x 2.54 cm and 1.5
mm thick faces that were 25.4 mm apart.
The stainless steel structures were first
penetrated at an impact velocity of approximately 450 m/s. Above this critical velocity,
the exit velocity of the projectile was between 55 and 70% of the impact velocity. The
sandwich structure outperformed a solid plate of similar composition, with an equivalent
areal density of 28 kg/m2, exhibiting an exit velocity of the projectile that was between 67
and 70%. The aluminum alloy structures were penetrated at the lowest test velocity of
approximately 200 m/s. The exit velocity of the projectile was between 60 and 92% of
the impact velocity. The stainless steel lattice structures were then infiltrated with a
polyurethane that had a Tg of -56 °C, a low tensile modulus of 2.76 MPa and a high
elongation to yield of approximately 700%. Infiltration of the stainless steel lattice with
this low Tg polyurethane exhibited a similar critical velocity of approximately 450 m/s,
similar to the empty structure. Above the critical velocity, the exit velocity of the
projectile was between 50 to 55% of the impact velocity at the expense of doubling the
mass per unit area. Energy was mainly dissipated from the associated strain fields as the
polymer was transiently displaced outwardly from the projectile.
Methods were
developed to fabricate other “hybrid” lattice truss structures with various materials
infiltrated into the sandwich panel. These systems contained ballistic fabrics, a different
polymer system and metal encased ceramics. Two of the systems prevented penetration
by projectiles with velocities in the 600 m/s range. The first system was a polyurethane
infiltrated lattice that had a Tg of 49 °C. The significantly higher Tg material had a higher
tensile modulus of 1120 MPa and a lower elongation to fracture of 16%. A second
system containing 304 stainless steel encased alumina prisms, with the surrounding space
infiltrated with a high Tg polyurethane, also resisted penetration but at the expense of a
four fold increase in mass per unit area. The success of the system can be attributed to
the degree of energy absorption of the alumina prisms and the confinement of the
fragments. After fracturing, the ceramic fragments were contained in steel tubes and
frictionally dissipated a majority of the remaining kinetic energy while fracturing the
projectile.
The remainder of the kinetic energy appeared to be dissipated by the
polyurethane and plastic dishing of the rear metal facesheet. These “hybrid” lattice
systems show significant promise as multifunctional load-bearing structures that also
possess high ballistic performance.
Acknowledgements
I want to express my gratitude to my advisor Professor Haydn N.G. Wadley. He has
been instrumental in sharpening my analytical tools and assisting me in accomplishing
my goals. Allowing a large degree of latitude, he gave me the opportunity to explore my
ideas and provided the resources to see them until their conclusion. Along the journey, I
gained an immense professional respect for him and forged a personal friendship that will
continue after my graduate education.
I want to extend my appreciation to the members of the IPM Laboratory, in particular
Mrs. Sherri S. Thompson, Dr. Doug T. Queheillalt, Dr. Kumar P. Dharmasena and Mr.
Rich T. Gregory. Without Sherri’s connection to the group members or her “greasing the
wheels”, the IPM Laboratory would cease to function. I am indebted to Doug and Kumar
for their tolerance of my innumerable questions and curiosities.
Their breadth of
knowledge was an invaluable resource that was not taken for granted. I owe Rich thanks
for keeping the computers operating smoothly and maintaining my lifeline to the group
over distances despite my occasional indoor headwear.
Additionally, I would like to express my sincere gratitude to Dr. Mark T. Aronson and his
group at the University of Virginia for conducting chemical characterizations, Dr. Alan
M. Zakraysek at the Naval Surface Warfare Center for conducting ballistic testing, Dr.
Steve G. Fishman at the Office of Naval Research for providing funding for my research
and my other committee members Dr. Dana M. Elzey and Dr. Stuart A. Wolf.
Dedication
I would like to dedicate my efforts to my grandmother Agnes V. Sands, my deceased
grandfather Joseph E. Sands, my mother Katherine M. Yungwirth, my aunt Joann M.
Sands and my aunt Anne M. Sands. My accomplishments are a testimonial to the abyss
of love and affection they have provided me from the day I was brought into this world.
Every one of them has provided a safe haven where I could venture into the farthest
expanses of my imagination and explore each crevice thoroughly. These explorations
and their support have forged the man that stands today.
Through the trials and
tribulations, they have remained steadfast in their support even with the occasional mild
opposition. Therefore, I extend my deepest, sincerest gratitude to each of them and wish
that happiness and prosperity finds them on their continued journey through life.
Additionally, I would like to make a dedication to all of my friends and the beloved
people for who I care deeply, particularly Janet and the Conterelli’s. Janet has been a
pillar of support that I have come to depend and I look forward to a future rich with
joyous memories shared with her. She is an amazing woman that epitomizes beauty,
intelligence and loyalty. The Conterelli’s have lovingly embraced me into their lives and
their hearth, a deed that has earned my eternal gratitude and appreciation.
Quotations
Ad astra per aspera (A rough road leads to the stars)
- Plaque dedicated to the crew of Apollo 1 at Launch Complex 34, Kennedy
Space Center
Γνώθι Σεαυτόν (Gnothi Seauton): “know thyself”
Μηδέν Άγαν (Meden Agan): "nothing in excess"
- Inscribed in golden letters at the lintel of the entrance to the Temple of Apollo at
Delphi
He who fights with monsters might take care lest he thereby become a monster. And if
you gaze for long into an abyss, the abyss gazes also into you.
- Friedrich Nietzsche, Beyond Good and Evil
If you aspire to the highest place, it is no disgrace to stop at the second, or even the third,
place.
- Cicero
i
Table of Contents
Table of Contents ............................................................................................................... i
List of Figures................................................................................................................... iii
List of Tables .................................................................................................................. viii
List of Symbols ................................................................................................................. ix
Chapter
1. Introduction........................................................................................................1
1.1
1.2
1.3
1.4
Multifunctional Cellular Materials ........................................................1
Ballistic Properties of Cellular Metals...................................................4
Goals of this Thesis................................................................................6
Thesis Outline ........................................................................................6
2. Impact and Plate Penetration Mechanics ........................................................7
2.1
2.2
Impact Mechanics ..................................................................................7
Plate Impact Mechanics .......................................................................11
3. Materials and Structures.................................................................................19
3.1
3.2
3.3
3.4
3.5
Sandwich Panel Fabrication.................................................................19
Relative Density Relations...................................................................22
Alloy Mechanical Properties................................................................23
3.3.1
304 Stainless Steel .......................................................23
3.3.2
Age Hardened 6061-T6 Aluminum Alloy ...................24
Polymer Infiltrated ...............................................................................25
3.4.1
Hybrid Lattice Fabrication...........................................25
3.4.2
Polymer ........................................................................26
Polymer Characterization.....................................................................28
3.5.1
DSC Analysis...............................................................28
3.5.2
DMA Analysis .............................................................29
4. Ballistic Testing ................................................................................................33
4.1
4.2
4.3
Stage One Powder Gun........................................................................33
Sabot and Projectile .............................................................................34
Test Fixture ..........................................................................................35
ii
5. Empty Lattice Resistance ................................................................................38
5.1
5.2
5.3
5.4
304 Stainless Steel Panel Response .....................................................38
304 Stainless Steel Plate Response ......................................................44
AA6061 Panel Response......................................................................49
Discussion ............................................................................................55
6. Polymer Infiltration Study ..............................................................................57
6.1
6.2
Ballistic Response................................................................................57
Discussion ............................................................................................63
7. Enhanced Ballistic Lattice Fabrication ...........................................................65
7.1
7.2
7.3
7.4
7.5
7.6
Concept Systems..................................................................................65
Lattice Structure Fabrication................................................................66
Double Layer Lattice Relative Density................................................67
Infiltration Materials and Methods ......................................................69
7.4.1
Polymers ......................................................................69
7.4.2
Fabric ...........................................................................70
7.4.3
Metal Encased Ceramic Prisms ...................................70
Hybrid Lattice Relative Density ..........................................................71
Material Properties...............................................................................71
7.6.1
Brazed 304 Stainless Steel ...........................................73
7.6.2
PU 2 .............................................................................74
7.6.2.1
DSC Analysis....................................74
7.6.2.2
DMA Analysis ..................................75
8. Ballistic Testing ................................................................................................78
8.1
8.2
8.3
Test Setup.............................................................................................78
Results..................................................................................................80
8.2.1
Single Layer Empty System............................................80
8.2.2
Soft Polymer Filled System ............................................82
8.2.3
Double Layer Filled with PU 1.......................................84
8.2.4
Hard Polymer Filled System...........................................85
8.2.5
Single layer filled with PU 1 plus Fabric........................87
8.2.6
Ceramic plus PU 2 Filled System ...................................88
Discussion ............................................................................................89
9. Discussion..........................................................................................................91
10. Conclusions.....................................................................................................96
References
iii
List of Figures
Figure 1. a) Photograph and illustration of Alporas®, a stochastic closed cell aluminum
foam manufactured by Foam Tech Co. Ltd. via titanium hydride particle decomposition.
b) Photograph and illustration of Duocel®, a stochastic open cell aluminum foam
manufactured by ERG Materials and Aerospace Corp. via pressure casting.
Figure 2. Isometric view of a) Hexagonal honeycomb b) Square honeycomb c)
Triangular honeycomb d) Triangular corrugation e) Diamond corrugation f) navtruss
corrugation g) Tetrahedral lattice truss h) Pyramidal lattice truss and i) 3-D Kagomé
lattice truss structures between solid face sheets. The tetrahedral lattice truss has three
sets of triangular, prismatic voids (0°/60°/120°). The pyramidal lattice truss possesses
similar geometrical voids running orthogonally (0°/90°) through the lattice. The 3-D
Kagomé lattice truss possesses two sets of similar geometrical void orientations
(0°/60°/120° and 30°/90°/150°).
Figure 3.
Bonded-interface test result showing section view with subsurface
accumulated damage beneath the indentation (Left). Finite-element result showing extent
of the plastic zone in terms of contours of maximum shear stress at τ Max / Y = 0.5 for
indenter load P = 1000 N (Right). Distances are expressed in terms of the contact radius,
a0 = 0.326mm , for the elastic case of P = 1000 N . The bold black line indicates the
radius of the circle of contact, a0 = 0.437mm , as determined from the finite-element
calculation [393H57].
Figure 4. Illustration of a thin target showing a) bulging b) dishing and c) cratering
[407H69].
Figure 5. Perforation mechanisms [421H69].
Figure 6. Manufacturing process for making pyramidal lattice truss cored sandwich
panels [465H3].
Figure 7. Illustration of the laser welding process for bonding the truss lattice to
proximal and distal facesheet.
Figure 8. Cross section of the single layer empty pyramidal truss lattice along a nodal
line.
Figure 9. Unit cell geometry used to derive the relative density for single layer
pyramidal topology.
Figure 10. Uniaxial tension data for as-received 304 stainless steel.
Figure 11. Uniaxial tension data for the age hardened 6061-T6 aluminum alloy.
Figure 12. Heat capacity (Rev Cp) of PU 1 as a function of temperature (°C).
iv
Figure 13. Storage modulus at a frequency of 1 Hz for PU 1 as a function of
temperature.
Figure 14. Predicted values for the storage and loss modulus of PU 1 at a reference
temperature of 25 °C as a function of frequency.
Figure 15. Tan δ ( E ′′ / E ′ ) of PU 1 as a function of frequency.
Figure 16. Illustration of the single stage powder gun used for ballistic studies. The
sabot carried a 12.5 mm spherical projectile.
Figure 17. Illustration of the sabot used to carry the projectile.
Figure 18. Illustration of setup used in the blast chamber to mount the samples, measure
velocities and record via high-speed photography.
Figure 19. Plot of exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 stainless steel pyramidal truss lattice.
Figure 20. Plot of energy absorbed (J) as a function of the impact velocity (m/s) for the
304 stainless steel pyramidal truss lattice system.
Figure 21. a) Cross section of the 304 stainless steel sample that was impacted at 339.2
m/s and was not fully penetrated, shot 1 b) Cross section of the entry hole of shot 1 c)
Cross section of the exit hole of shot 1.
Figure 22. a) Cross section of the 304 stainless steel sample that was impacted at 810.8
m/s, shot 3 b) Cross section of the entry hole of shot 3 c) Cross section of the exit hole of
shot 3.
Figure 23. a) Cross section of the 304 stainless steel sample that was impacted at 1206.1
m/s, shot 54 b) Cross section of the entry hole of shot 54 c) Cross section of the exit hole
of shot 54.
Figure 24. Plot of exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 stainless steel monolithic plate compared to the 304 stainless
steel pyramidal truss lattice.
Figure 25. Plot of energy absorbed (J) as a function of the impact velocity (m/s) for the
304 stainless steel pyramidal truss lattice system and solid plate.
Figure 26. Cross section of the monolithic 304 stainless steel plate that was shot at 341.7
m/s, shot 58.
Figure 27. Cross section of the monolithic 304 stainless steel plate that was shot at 509.6
m/s, shot 105.
v
Figure 28. Cross section of the monolithic 304 stainless steel plate that was shot at
1226.5 m/s, shot 108.
Figure 29. Plot of exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the age hardened AA6061 aluminum alloy pyramidal truss lattice
compared to the 304 stainless steel pyramidal truss lattice system.
Figure 30. Plot of the energy absorbed (J) as a function of the impact velocity (m/s) for
the 304 stainless steel sandwich panel and AA6061 aluminum alloy sandwich panel.
Figure 31. a) Cross section of the AA6061 sample that was impacted at 280.1 m/s, shot
114 b) Cross section of the entry hole of shot 114 c) Cross section of the exit hole of shot
114.
Figure 32. a) Cross section of the AA6061 sample that was impacted at 493.3 m/s, shot
81 b) Cross section of the entry hole of shot 81 c) Cross section of the exit hole of shot
81.
Figure 33. a) Cross section of the AA6061 sample that was impacted at 1222.2 m/, shot
55 b) b) Cross section of the entry hole of shot 55 c) Cross section of the exit hole of shot
55.
Figure 34. Plot of exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 hybrid stainless steel pyramidal truss and the empty 304
stainless pyramidal truss lattice.
Figure 35. Plot of projectile the energy absorbed (J) as a function of the impact velocity
(m/s) for the 304 stainless steel pyramidal truss lattice infiltrated with PU 1 and the
empty 304 stainless pyramidal truss lattice.
Figure 36. a) Cross section of the 304 stainless steel sample infiltrated with PU 1 that
was impacted at 370.9 m/s, shot 70 b) Cross section of the entry hole of shot 70 c) Cross
section of the exit hole of shot 70.
Figure 37. a) Cross section of the 304 stainless steel pyramidal truss lattice filled with
PU 1 that was impacted at 515.7 m/s, shot 110 b) Cross section of the entry hole of shot
110 c) Cross section of the exit hole of shot 110.
Figure 38. a) Cross section of the 304 stainless steel pyramidal truss lattice filled with
PU 1 that was impacted at 984.5 m/s, shot 112 b) Cross section of the entry hole of shot
112 c) Cross section of the exit hole of shot 112.
Figure 39. Schematic illustrations of pyramidal lattice truss concepts evaluated in the
study. a) Empty pyramidal truss lattice b) Polymer filled in truss lattice c) Ballistic fabric
interwoven between trusses with polymer filling remaining air space d) 304 SS encased
alumina inserted in triangular prismatic voids and remaining air space filled with polymer
vi
Figure 40. Unit cell geometry used to derive the relative density for a double layer
pyramidal topology.
Figure 41. Uniaxial tension data for brazed 304 stainless steel.
Figure 42. Heat capacity (Rev Cp) PU 2 as a function of temperature (°C).
Figure 43. Storage modulus at a frequency of 1 Hz for PU 2 as a function of
temperature.
Figure 44. Predicted values for the storage and loss modulus of PU 2 at a reference
temperature of 25 °C as a function of frequency.
Figure 45. Tan δ ( E ′′ / E ′ ) of PU 2 as a function of frequency.
Figure 46. Ballistic testing configuration. Ball bearing projectiles with a radius of 6 mm
and weight of 6.9 g were used. An impact velocity of approximately 600 m/s was used
for all the tests.
Figure 47. Projectile impact location for a) Single and b) Double layer pyramidal lattice
truss sandwich panels.
Figure 48. Test 1: a) Cross section of the single layer empty pyramidal truss lattice
along a nodal line b) Cross section of the single layer empty pyramidal truss lattice after a
projectile impact of 598 m/s.
Figure 49. High-speed photography of a projectile impact with the empty single layer
pyramidal lattice (system 1). Each figure (a)-(h) depicts a frame of the high-speed
photography. The time in microseconds (μs) is labeled from the initial impact of the
projectile with the proximal facesheet.
Figure 50. Position of a spherical projectile from the proximal facesheet of the empty
single layer pyramidal lattice truss as a function of time. To the left of the time of impact
is before the impact of the projectile and the right of the time of impact is after impact of
the projectile.
Figure 51. Test 2: a) Cross section of the single layer pyramidal truss lattice filled with
PU 1 b) Cross section of the single layer pyramidal truss lattice filled with PU 1 after a
projectile impact of 616 m/s. Notice the brass breech rupture disk (b) remaining in the
polymer while the projectiles path resealed.
Figure 52. Test 7: a) Cross section of the double layer pyramidal truss lattice filled with
PU 1 b) Cross section of the double layer pyramidal truss lattice filled with PU 1 after an
impact of 613 m/s.
vii
Figure 53. Test 4: a) Cross section of the single layer pyramidal truss lattice filled with
PU 2 b) Cross section of the single layer pyramidal truss lattice filled with PU 2 after a
projectile impact of 632 m/s showing approximately 8.5 mm deflection of the rear face
panel. Note that the projectile is visibly arrested in (b).
Figure 54. X-ray tomography of specimen 4. Side profile (Left). Elevated view above
proximal face sheet (Right).
Figure 55. Test 5: a) Cross section of the single layer pyramidal truss lattice filled with
the interwoven fabric and the PU 1 b) Cross section of the single layer pyramidal truss
lattice filled with interwoven fabric and the PU 1 after a projectile impact of 613 m/s.
Figure 56. Test 6: a) Cross section of the single layer pyramidal truss lattice filled with
304 stainless steel prisms and PU 2 b) Cross section of the single layer pyramidal truss
lattice filled with 304 stainless steel prisms and PU 2 after an impact of 613 m/s.
viii
List of Tables
Table 1. Manufacturer reported properties for the polyurethane system.
Table 2. The impact and exit velocities of the projectile, nodal disbonding of the distal
facesheet and whether the projectile penetrated the distal facesheet for the 304 stainless
steel pyramidal truss lattice sandwich structure.
Table 3. The impact and exit velocities of the projectile for a 3 mm thick 304 stainless
steel monolithic plate.
Table 4. The impact and exit velocities of the projectile, nodal disbonding of the distal
facesheet and whether the projectile penetrated the distal facesheet for the age hardened
AA6061-T6 aluminum alloy pyramidal truss lattice sandwich structure.
Table 5. The impact and exit velocities of the projectile, nodal disbonding of the distal
facesheet and whether the projectile penetrated the distal facesheet for the 304 stainless
steel pyramidal truss lattice sandwich structure with polyurethane.
Table 6. Physical descriptions of composite lattice truss systems fabricated.
Table 7. Manufacturer reported properties for the polyurethane system.
Table 8. Physical properties of AD-94 Al2O3 triangular prisms.
ix
List of Symbols
Δ
δ
ν
π
ρ
ρ
θ
σ
τ
υ0
υr
ω
a
b
cp
cpr
ct
d
h
h0
k
l
m
pm
p0
r
t
w
x⎫
⎪
y⎬
z ⎪⎭
E
Ec
Ed
E*
E′
E ′′
P
R
Tg
V
W
distance of mutual approach between indenter and specimen
parameter used to assess dissipative energy efficiency
Poisson’s ratio
pi
mass density
relative density
petal rotation angle at the end of stages
stress
shear stress
initial velocity of projectile
residual velocity of projectile
angle between truss and facesheet
indenter contact area radius
triangle base height
heat capacity
wave velocity of projectile
dilatational wave velocity of target
diameter
height
plate thickness
mass ratio
length
mass
mean contact pressure
maximum contact pressure (Hertz stress)
radial distance
thickness
width
Cartesian coordinates
Young’s modulus
perforation energy of plate
energy absorbed through plate dishing
contact modulus
storage modulus
loss modulus
indenter load force
(reduced) radius of sphere
glass transition temperature
volume
work
x
Subscripts
θ
a
c
cr
f
i
m
p
pu
r
t
tr
u
y
z
angular cylindrical coordinate
aluminum oxide
unit cell
crack
fabric
intermediate plate
base metal
projectile
polyurethane
radial cylindrical coordinate
target
truss
ultimate
yield
height cylindrical coordinate
xi
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1
Chapter 1
Introduction
Cellular metals are a relatively new class of materials [1-2]. Using foaming or foam
derived methods, various groups developed stochastic topology structures in the 1980’s
[1]. Examples of closed and open cell systems are shown in Figure 1. More recently,
methods have begun to be developed to create open cell topology structures with
periodic, or lattice cells [3] and compliment closed cell periodic systems (e.g.
honeycombs) that have been developed for weight sensitive structural applications [3-4].
1.1
Multifunctional Cellular Materials
Cellular metal structures with both stochastic (metal foams) [2-6], Figure 1, and periodic
topologies [5,6], Figure 2, are being utilized for an expanding variety of structural [3-12],
thermal [13-15], and acoustic damping [2] applications.
a) Closed-cell Metal Foam
b) Open-cell Metal Foam
Figure 1. a) Photograph and illustration of Alporas®, a stochastic closed cell aluminum
foam manufactured by Foam Tech Co. Ltd. via titanium hydride particle decomposition.
b) Photograph and illustration of Duocel®, a stochastic open cell aluminum foam
manufactured by ERG Materials and Aerospace Corp. via pressure casting.
2
Figure 2. Isometric view of a) Hexagonal honeycomb b) Square honeycomb c)
Triangular honeycomb d) Triangular corrugation e) Diamond corrugation f) navtruss
corrugation g) Tetrahedral lattice truss h) Pyramidal lattice truss and i) 3-D Kagomé
lattice truss structures between solid face sheets. The tetrahedral lattice truss has three
sets of triangular, prismatic voids (0°/60°/120°). The pyramidal lattice truss possesses
similar geometrical voids running orthogonally (0°/90°) through the lattice. The 3-D
Kagomé lattice truss possesses two sets of similar geometrical void orientations
(0°/60°/120° and 30°/90°/150°).
The periodic structures show significant promise as multifunctional structures when
configured as the cores of sandwich panel structures. In these scenarios, functions such
as structural load support and thermal management can be simultaneously exploited
[11,13,15].
Periodic structures consisting of 3-D space filling unit cells with honeycomb [3,16-17],
corrugation [18] or lattice truss topologies [3,7] are significantly more structurally
efficient than equivalent relative density metal foams. The fabrication routes developed
3
for these periodic cellular systems [19] also enable much higher strength alloys to be
used. As a result, periodic topology structures can be an order of magnitude, or more,
stronger than metal foams of the same mass [12].
As the relative density decreases, lattice topologies have been shown to have higher
strengths than honeycombs and simple corrugations [20]. The first proposed lattice
structure was lattice block material [21-23]. More recently, structures based on the octet
truss (i.e. a tetrahedral structure) [24], a pyramidal truss [25-26], the 3-D Kagomé [27-28]
and various lattices created by weaving or laying up metal wires and tubes have all been
developed [7]. Figure 2 showed examples. The cell size of these structures can be varied
from several hundreds of micrometers to several centimeters using metal folding and
either brazing or spot welding fabrication methods [29,16].
All cellular metals have been shown to possess excellent impact energy absorption
characteristics [11,30-33]. Typically, these materials exhibit three regions of deformation
[1]. The first region is an elastic region followed by a plateau stress region persisting to
plastic strains of around 60-70%. It corresponds to a region where buckling and plastic
collapse of the cell walls occurs. Finally, after the collapse of the cells, sufficient
densification of the structure has occurred that cell wall/truss impingement causes a sharp
rise in stress. This arises because of their very extensive crush strains at near constant
flow stress. The mechanics of foam deformation and associated energy absorption have
been reviewed by M. Ashby et al. [2], and includes expressions for foam elastic modulus,
elastic collapse stress, plastic collapse, strength and densification strain etc.
Recent experimental and numerical modeling studies indicate that periodic lattice truss
and honeycomb core sandwich panels enable significant mitigation of explosion created
shock waves [31-34]. These studies indicate that sandwich panels fabricated from high
ductility metals (e.g. stainless steels and some aluminum alloys) with honeycomb, lattice
truss or corrugated cores could provide multifunctional static load support and blast
protection in air and underwater [36]. If cellular metal structures of this type were used
for air blast mitigation applications, they would also be exposed to impact by high
4
velocity projectiles.
Very little is known about the penetration resistance of these
structures or ways to enhance it.
1.2
Ballistic Properties of Cellular Metals
A study conducted by B. Gama et al. [37] has explored the ballistic characteristics of a
cellular metal. It investigated metal foams made from low strength aluminum alloys in
the context of integral armor concepts and reported only modest system performance
enhancements. In this application, closed-cell aluminum foam delayed and attenuated
stress wave propagation throughout the composite integral armor system. The cellular
structure of the metal foam acted as small waveguides and a geometric dispersion of the
stress waves occurred leading to propagation delays. Damping in these systems has been
studied by D. Radford et al. at the University of Cambridge [31-34] and is associated
with thermo-elastic effects. These studies provided little illumination of the performance
of periodic lattice truss topologies, or sandwich panels constructed from them when
exposed to high velocity projectiles.
It is to be expected that the two solid faces of a sandwich panel will each individually
provide some level of projectile propagation resistance. The penetration of a metal sheet
such as rolled homogenous armor (RHA) [35] by a normal incidence projectile has been
widely studied [38].
The critical velocity (i.e. the velocity at which the projectile
penetrates the target) increases linearly with target thickness [32,35]. The depth of
penetration (DOP) also increases linearly as the projectile velocity is increased [32, 35].
Experimental studies by A. Almohandes et al. [39] indicated that distributing the mass of
a plate amongst a pair of plates of equivalent areal density resulted in a slight lowering of
the ballistic resistance. Theoretical studies by G. Ben-Dor et al. [40] and experimental
studies by J. Radin and W. Goldsmith [41] indicate that the distance between such a pair
of plates has little or no effect upon the ballistic resistance of such systems. Other work
conducted by R. Corran et al. [42] found that two plates in tight contact had a slightly
higher ballistic limit than an identical pair that was not in contact. They tentatively
attribute this small effect to a frictional interaction between layers.
5
The lattice truss structure itself might be anticipated to have some effect upon the
propagation of a projectile provided the projectile impacts the lattice during penetration
(i.e. the cell spacing is small compared to the projectile diameter). For example, it might
increase the ballistic performance by deflecting (tipping) the projectile or causing some
of its energy to be dissipated by plastic deformation/fracture of the trusses.
Projectile kinetic energy losses during penetration of the face sheets and the truss
structures are likely to be increased by utilizing metals with high strength, high fracture
toughness (ductility) and high strain and strain rate hardening coefficients.
Many
austenitic and super austenitic stainless steels [43] have medium strength levels but high
toughness and strain rate hardening coefficients. Analytical and experimental results
from a study conducted by S. Shun-cheng et al. [44] showed that for 304 stainless steel,
the yield stress increased with increasing strain rate until an upper limit of approximately
2500 s-1. Other materials, such as AA6061-T6 aluminum alloy, exhibit a decrease in
strength as the strain rate is increased [45]. Recent developments in the fabrication of
lattice structures from such alloys using perforated metal folding and brazing techniques
[3,29] now enable an experimental assessment of the ballistic behavior of sandwich
panels with lattice truss cores to be investigated.
The voids in lattice truss structures provide easy access to the interior of the sandwich
panel and enable materials to be added that might improve ballistic resistance. For
example, the voids could be infiltrated with polymers to dissipate a projectiles kinetic
energy [46], or with ballistic fabrics to arrest fragments [47,48] or with hard ceramics that
fragment projectiles and impede their penetration [49,50]. The merits of these are also
presently unclear and no experimental assessments of the ballistic properties and
deformation mechanisms of these “hybrid” lattice truss structures have ever been
reported.
6
1.3
Goals of this Thesis
This thesis experimentally investigates the ballistic response of stainless steel and 6061
aluminum alloy pyramidal lattice truss core sandwich structures using spherical
projectiles with impact velocities up to approximately 1200 m/s. The stainless steel
sandwich panel structures response is compared to that of a monolithic plate of
equivalent areal density (mass per unit area). The effects of filling the lattice void space
with an elastomer are then investigated and the feasibility of fabricating more
sophisticated “hybrid” sandwich structures containing ceramics and ballistic fabrics is
added. The study finds significantly enhanced ballistic resistance can be achieved by this
approach.
1.4
Thesis Outline
The thesis is organized as follows: Chapter 2 presents the mechanisms of impact and
plate penetration mechanics. Chapter 3 presents the materials and the fabrication
methodology for the lattice truss sandwich structure. Chapter 4 describes the ballistic
facility used to conduct the experiments and the sabot-projectile system. Chapter 5
presents the initial impact study of the 304 stainless steel and the age hardened AA6061T6 aluminum alloy mono-layer pyramidal lattice truss sandwich structures. Chapter 6
presents a study infiltrating the 304 stainless steel pyramidal lattice truss sandwich
structure with an elastomer. Chapter 7 presents the fabrication of hybrid systems where
various materials were infiltrated into the structure and Chapter 8 presents the results of
the study. Chapter 9 summarizes the findings from the studies while Chapter 10 briefly
lists the conclusions obtained.
7
Chapter 2
2.1
Impact and Plate Penetration Mechanics
Impact Mechanics
The impact of a hard projectile with a softer target causes local deformation (i.e. indent of
both objects). The first attempt to develop a theory of the local indentation at the contact
between two solid bodies was by Hertz [51], who likened the problem to an equivalent
one in electrostatics. Hertzian contact mechanics is based on three key assumptions:
i.
The surfaces of the contacting bodies are both continuous, smooth,
nonconforming and form a frictionless contact.
ii.
The strains associated with the deformations are small.
iii.
Each solid behaves as an elastic half-space in the vicinity of the contact
zone. The size of the contact area (extent of the deformation field) is
therefore small compared to the size of the bodies.
According to Hertz, if two elastic spheres with radii R1 and R2 are pressed into contact
with a force P, the resultant circular contact area has a radius, a, such that:
1
⎛ 3PR ⎞ 3
a=⎜ * ⎟
⎝ 4E ⎠
(1),
where E* is the contact modulus defined by:
1 − ν 12 1 − ν 22
E =
+
E1
E2
*
(2).
In equation (2), E and ν are the Young’s modulus and elastic Poisson’s ratio of each
sphere, respectively. In equation (1), R is the reduced radius of curvature and is related to
those of the individual components by the relation:
R=
1
1
+
R1 R2
(3).
Convex surfaces are taken as positive radii of curvature (concave surfaces are therefore
taken as negative radii of curvature). If one of the solids is a plane surface then its
effective radius is infinite so that the reduced radius of the contact is numerically equal to
8
that of the opposing sphere. This is then reduced to the half-space problem [52]. If we
place a cylindrical coordinate system at the initial point of contact, the resulting radial
pressure distribution, p(r), is axisymmetric and dependent only upon the radial distance
from the initial point of contact.
The pressure distribution is semi-elliptical, and of the form
1
⎛
r2 ⎞2
p( r ) = p0 ⎜⎜1 − 2 ⎟⎟
⎝ a ⎠
(4),
where r 2 = x 2 + y 2 is the radial distance from the initial point of contact. The maximum
pressure, p0, occurs on the axis of symmetry. This and the mean pressure, pm, are related:
1
⎛ 6 PE *2 ⎞ 3
3
3P
⎟
⎜
p0 = p m =
=
2
2πa 2 ⎜⎝ π 3 R 2 ⎟⎠
(5).
The maximum pressure, p0, is also sometimes known as the Hertz contact stress.
Under this loading, the two spheres move together by a small displacement, Δ, given by:
Δ=
aπp0 ⎛ 9 P ⎞
a
⎟
=
=⎜
2 E * ⎜⎝ 16 RE *2 ⎟⎠
R
2
2
1
3
(6).
Equation (6) is a quasi-static derivation of a sphere making contact with a sphere or plane
3
with a load placed on the axis of symmetry to cause a displacement in the direction of
mutual approach.
In a dynamical derivation of a sphere impacting a flat plane specimen in the elastic region
[53], the second derivative of the displacement of the plane is related to the mass of the
projectile, mp, and the force of the projectile impact, P:
mp
d 2 Δ (t )
= −P
dt 2
where Δ is the displacement from the flat plane specimen.
(7),
9
By rearranging equation (6) to give an expression for P(Δ) and equating it to equation (7),
we obtain the indentation velocity:
1
3
dυ
4 R 2 Δ2
mp
=−
dt
3E *
where υ =
(8),
dΔ
. Multiplying both sides of equation (8) by velocity and integrating from
dt
the impact velocity of the projectile, υ 0 , to the final velocity, υ f = 0 , we obtain:
1
5
1
8
m pυ 02 = R 2 E * Δ2
2
15
(9).
The left hand side of equation (9) equates the kinetic energy of the projectile to the strain
energy stored in the specimen.
Equation (9) can be arranged to give an expression for the depth of penetration, Δ, as a
function of the mass, mp, and the impact velocity, υ 0 , of the projectile:
2
⎛ 15m υ 2 ⎞ 5
p 0 ⎟
Δ = ⎜⎜
1
⎟⎟
⎜
⎝ 16 R 2 E * ⎠
(10).
This relationship is limited to elastic impacts (i.e. when the impact velocity is low) and
both objects are made of materials of high strength. It does not address the plasticity and
fracture that can accompany projectile penetration [52, 53].
An elastic-plastic material will reach the limit of its elastic behavior at the point beneath
the surface where the maximum contact pressure p0 at the instant of maximum
compression has reached the von Mises flow criterion. The von Mises yield criterion for
ductile materials can be written [53]:
σ
1
(σ 1 − σ 2 )2 + (σ 2 − σ 3 )2 + (σ 3 − σ 1 )2 = k 2 = y
6
3
[
]
2
(11),
where σ y is the yield stress of the impacted (usually softer) material and σ i are the
principal stress components (i.e. the stress components along the principal axes) [52].
For the axisymmetrical problem of a sphere impacting a flat plane, the principal axes are
10
with the cylindrical coordinate axes, and thus the principal stresses are σ z , σ r and σ θ
with σ r = σ θ . Given the relation between the maximum contact pressure, p0, and the
principal stress components [53], and assuming an elastic Poisson’s ratio, ν = 0.3 , the
maximum value of stress in a thick plate, 0.62 p0 , and occurs at a depth (z-direction)
below the surface of 0.48a . Thus by the von Mises yield criterion the value of p0 for
the onset of plastic yield is given by
p0 = 2.8k = 1.6σ y
(12).
Now by equating equation (6) and (10), we can obtain an expression for the maximum
contact stress of an elastic impact:
4
1
⎛
⎞5
5
3 ⎜ 4E * ⎟ ⎛ 5
2⎞
p0 =
m
υ
⎜
⎟
0
in
3
2π ⎜⎜ 4 ⎟⎟ ⎝ 4
⎠
⎝ 3R ⎠
(13).
By equating (13) to the von Mises critical contact pressure, equation (12), it is possible to
obtain an expression relating the kinetic energy of the projectile to target materials
mechanical properties [53]:
53R 3σ 5y
1
minυ 02 ≈
2
E *4
(14).
In the case of a rigid sphere impacting the planar surface of a large softer body, equation
(14) reduces to
υ0 =
26σ 5y
ρE *
4
(15),
where ρ is the density of the softer (target) material [53].
Analytical treatments of the stress indentation field for elastic-plastic contact are made
complex by the plasticity zone underneath the impact. The analysis of the elastic-plastic
stress field of a spherical impact with the surface of a half-space therefore requires the
use of finite element analysis [54-56]. The actual size and shape of the plasticity zone
depend on the mechanical properties of the target material, particularly the ratio of its
Young’s modulus to yield strength, E/σy [57]. A section view of the subsurface damage
for the Macor® glass-cermamic material is shown in Figure 3 together with the
11
corresponding finite-element solution. The residual impression in the surface made by
the indenter is clearly visible as is the shear-driven accumulated subsurface damage
resulting from the indentation.
Figure 3.
Bonded-interface test result showing section view with subsurface
accumulated damage beneath the indentation (Left). Finite-element result showing extent
of the plastic zone in terms of contours of maximum shear stress at τ Max / Y = 0.5 for
indenter load P = 1000 N (Right). Distances are expressed in terms of the contact radius,
a0 = 0.326mm , for the elastic case of P = 1000 N . The bold black line indicates the
radius of the circle of contact, a0 = 0.437mm , as determined from the finite-element
calculation [57].
2.2
Plate Impact Mechanics
In the 1960’s and early 1970’s, H. Hopkins and H. Kolsky [59], W. Goldsmith [60-63],
M. Cook [64], A. Olshaker and R. Bjork [65], J. Rinehart and J. Pearson [66], L. Fugelso
and F. Bloedow [67] and R. Sedgwick [68] conducted experimental studies to explore the
impact processes and penetration mechanisms in plates. A compendium on the study of
the mechanics of projectile penetration was published in 1978 by M. Backman and W.
12
Goldsmith [69]. A more recent review by G. Corbett et al. in 1996 [70] has incorporated
copious amounts of experimental data and analytical interpretations that enable important
penetration mechanisms to be identified.
The analysis of failure mechanisms in finite thickness plates can be found in the
aforementioned studies of M. Backman and W. Goldsmith and G. Corbett et al. [69,70].
Permanent deformations, possibly a convolution of two or more mechanisms, occur for
both the non-penetrated and the penetrated cases. In the non-penetrated case, there are
two failure modes that can be attributed to the transverse displacement of a thin1 target
due to plastic deformation, Figure 4 (a) and (b).
Figure 4. Illustration of a thin target showing a) bulging b) dishing and c) cratering [69].
1
A plate is defined as ‘thin’ if stress and deformation gradients throughout its thickness do not exist [69]
13
The first mode is known as bulging in which the plate deforms to conform to the nose of
the projectile. Bulging may be considered by the static and quasi-static methods of
analysis used in metal processing problems [80]. The second failure mode is induced by
bending, called dishing, and can extend far from the contact zone. Dishing, unlike
bulging, requires a dynamical explanation of plastic bending, plastic hinge propagation
and shear banding and/or other fracture modes [70,81-82]. As the target thickness and
impact velocity increases, these two modes decrease and the deformation involves
displacement that tends to involve the proximal and distal side of the target so as to
thicken it with little or no deflection. This process is called cratering, Figure 4 (c),
common in thick plates, and appropriately describes the effects of highly local
deformations in targets of any thickness.
As the velocity of the projectile increases, the ductile limit of target is approached, and
penetration can begin to occur. In the penetrated regime, failure involving fracture
occurs in plates of thin or intermediate 2 thickness.
The fracture occurs from a
combination of mechanisms with one often dominating the others depending on
projectile/target material characteristics, geometry, velocity and angle of impact, etc.
[69]. Figure 5 depicts the most common types of failure modes including that due to the
initial compression wave, fracture in the radial direction, spalling, scabbing, plugging,
front/rear petaling or fragmentation in the case of brittle targets and ductile hole
enlargement [63-66, 69-70, 83-93].
2
A plate is defined as ‘intermediate’ if the rear surface exerts considerable influence on the deformation
process during all (or nearly all) of the penetrator motion [69].
14
Figure 5. Perforation mechanisms [69].
15
Fracture due to the initial stress wave can be caused by two different mechanisms
depending on whether the tensile strength or compressive strength of the target is greater
than the other. If the tensile strength of the target is greater than its compressive strength
then failure occurs on the distal side, back side, of the plate from the dilatational wave,
Figure 5 (a). Spalling, similar to the fracture on the distal side from the initial stress
wave in Figure 5 (a), is a tensile material failure resulting from the reflection of the initial
compressive transient off the distal side of the target, Figure 5 (c). Reflection of the wave
changes the sign of the pulse thereby placing the target in tension from compression. The
dilatational wave, produced by the impact, creates a fracture when the maximum shear
stress of the reflected wave begins to exceed the materials yield stress [83]. A rough
approximation for the velocity limit, the limit at which the projectile penetrates the distal
side of the target, of fracture from compressive failure of the distal side due to impact is
given by [69]:
1
υ Lim
2 2
⎡
⎤
⎛ 1 − ν ⎞ ⎢ ⎛⎜ 2h0 ⎞⎟ ⎥ ⎛⎜ ρ t cd + ρ p c pr
+
= σY ⎜
1
⎟
⎝ 1 − 2ν ⎠ ⎢ ⎜⎝ d p ⎟⎠ ⎥ ⎜⎝ ρ t cd ρ p c pr
⎣
⎦
⎞
⎟
⎟
⎠
(16).
where cd is the dilatational wave velocity of the target, cpr is the extensional wave
velocity in the projectile, ρt is the target density, ρp is the projectile density, dp is the
diameter of the projectile, h0 is the target thickness, σy is the yield stress of the target and
ν is the Poisson’s ratio of the target.
If the tensile strength of the target is lower than its compressive strength, then a radial
fracture behind the initial stress wave will result, Figure 5 (b), based on the assumption
that radial stress has exceeded the yield value in tension. A rough approximation for the
velocity limit of this type of fracture is given by [69]:
υ Lim =
⎛ ⎛ 2h
2σ y (1 − ν )⎜1 + ⎜ 0
⎜ ⎜ dp
⎝ ⎝
⎞
⎟
⎟
⎠
2
⎞
⎟
⎟
⎠
⎛ ρ t c d + ρ p c pr
⎜
1
⎜ ρc ρ c
⎧
⎫
2 2
⎝ t d p pr
⎡
⎤
⎛ 2h0 ⎞
⎪
⎪
⎟ ⎥ ⎬
⎨(1 − ν ) + 2ν ⎢1 + ⎜⎜
⎟ ⎥
d
⎢
p
⎪
⎠ ⎦ ⎪
⎣ ⎝
⎩
⎭
⎞
⎟
⎟
⎠
(17).
16
In the ductile separation, voids nucleate through particle-matrix debonding or through
particle cracking, then they grow by local plastic deformation, and finally coalesce by the
onset of local instabilities or inhomogeneities [84,85]. A rough approximation for the
velocity limit of this type of fracture is given by [69]
υ Lim =
⎛ ⎛ 2h
σ y ⎜1 + ⎜⎜ 0
⎜
d
⎝ ⎝ p
⎞
⎟
⎟
⎠
1
⎧
2 2
⎡
⎤
⎛ 2h0 ⎞
⎪
⎟ ⎥
⎨ ⎢1 + ⎜⎜
⎟
d
⎢
⎪ ⎣ ⎝ p ⎠ ⎥⎦
⎩
2
⎞
⎟
⎟
⎠
⎛ ρ t c d + ρ p c pr
⎜
⎫ ⎜⎝ ρ t c d ρ p c pr
⎪
− 1⎬
⎪
⎭
⎞
⎟
⎟
⎠
(18).
Plugging results as a cylindrical slug, nearly the size of the projectile is sheared from the
target, Figure 5 (d). The failure occurs due to large shears around the moving slug.
Generated heat is restricted to an annulus surrounding the slug and causes a reduction in
material strength, resulting in instability; this is called an adiabatic shearing process [69].
This catastrophic shear results from interplay between thermal softening and the low
work, and strain hardening rate of the plate material within the shear bands [86,87].
Plugging is most common for blunt projectiles impacting thin or intermediate, hard plates
due to material being geometrically constrained to move ahead of the projectile.
Analytical models describing the failure mechanism have been difficult to develop and
tend to be complex, reaching five stages to adequately model the event [88]. Again,
observed empirical relations have given a rough approximation for the velocity limit of
this type of fracture [69] given by:
υ Lim
⎡σ y
=⎢
⎢⎣ ρ t
1
1
⎛ 2ρ h ⎞
⎤2
⎛ 2h0 ⎞⎤ 2 ⎡ ⎜⎜⎝ ρ Pt l 0 ⎟⎟⎠
⎜
⎟ ⎢e
− 1⎥
⎜ d ⎟⎥ ⎢
⎥
⎝ p ⎠⎥⎦ ⎣
⎦
(19).
where l is the length of the projectile.
Petaling, both frontal and rear, is produced by high radial and circumferential tensile
stresses after passage of the initial wave near the lip of the penetration [69,89], Figure 5
(e) and (f). This deformation is the result of bending moments created by the forward
motion of the plate material being pushed ahead of the projectile and by inhomogeneities
or weaknesses in the target. Petaling is usually accompanied by large plastic flows
17
and/or permanent flexure. As the material on the distal side of the plate is further
deformed, the tensile stresses are exceeded and a star-shaped crack is initiated by the tip
of the projectile [70]. Finally, the sectors are rotated back by the ensuing motion of the
projectile, forming, often symmetric, petals. Petaling commonly occurs from ogival or
conical shaped noses on projectiles penetrating thin ductile plates (h0 / dp < 1). B.
Landkof and W. Goldsmith [91] expanding upon a study conducted by C. Calder and W.
Goldsmith [93], carried out an experimental and theoretical investigation of petaling. In
the study, they used an energy balance through multiple stages of impact to establish an
expression for the final velocity of the projectile given by
υ Lim
⎡ 2+k
πσ y lcr h02 (θ1 − θ 2 ) 2 E d
2
−
−
υ
⎢
2 0
m
mp
(
)
+
2
1
k
p
=⎢
2
2
⎢
πl h ρ cos θ 2
1 + cr 0
⎢
6m p
⎣⎢
1
⎤2
⎥
⎥
⎥
⎥
⎦⎥
(20),
where Ed is the energy absorbed through plate dishing [70], k is a mass ratio parameter, θ1
and θ2 are the petal rotation angles at the ends of the stages and lcr is the crack length.
Fragmentation of the projectile and target occur in situations similar to radial fracture
where the stress wave of the impact creates tensile and compressive stresses which
exceed those of the projectile and target, Figure 5 (b). A study conducted by M. Kipp et
al. [92] explores the effect of high-velocity impact fragmentation, both numerically and
experimentally.
Ductile hole enlargement seems to be a common failure of thick 3 plates of medium to
low hardness common from ogival or small-angle conical shaped projectiles [69], Figure
5 (h). At the beginning of contact, the tip of the projectile begins displacing material
radially and continues so that a hole in the target is enlarged along the trajectory of the
projectile.
Heavily dependent on projectile shape and projectile diameter to target
thickness ratio, ductile hole enlargement is favorable instead of plugging if the following
condition is satisfied with a ogival or small-angle conical shaped projectile [87]
3
A plate is defined as ‘thick’ if there is an influence of the distal boundary on the penetration process only
after substantial travel into the target element [69].
18
h0 >
3
dp
2
(21).
A quasi-static analysis of the completely symmetrical enlargement of the hole that
develops at the moving point of the sharp projectile was given in a classical paper for a
thin infinite elastic-perfectly plastic sheet [69, 94]. This description was improved by G.
Taylor [95] providing a more precise stress analysis in the region of significant target
thickening. The work required to expand such a hole to a given radius R1 is
W = 1.33πR12 h0σ y
(22).
A complex analytical solution to the radial stresses at the hole and the total resistance to
penetration were formulated by W. Herrmann and A. Jones [96] and H. Bethe [94]. A
rough approximation for the velocity limit can be found by equation (23).
Several models describing impact upon plates with a finite thickness have been proposed
[71-76] but the complexity of the impact event has limited general closed-form analytical
solutions [77].
To supplement the lack of analytical solutions, empirical relations,
neglecting plate bending, stretching or dynamic effects beyond the impact zone, have
been proposed but are of limited utility. These relations are only applicable in a narrow
set of velocity ranges for a particular type of projectile geometry. For example, the
Standard Research Institute Formula (SRI) [70] proposes that for a cylindrical geometry
the critical projectile impact energy, Ec, to penetrate a sample is given by:
Ec =
σ u d p3
13
(42.7h
2
0
+ l p h0 )
(23),
where σu is the ultimate stress, dp is the diameter of the projectile and h0 is the thickness
of the target. This empirical expression is valid only for 0.1 < h0/dp < 0.6; 0.002 < h0/lp <
0.005; 10 < lp /dp < 50; 5 < lp /dp < 8; lp /h0 < 100 and 21 < v0 < 122 m/s. Other empirical
formulas only make accurate predictions significantly greater than the target’s ballistic
limit. For example the study conducted by W. Thomson [78,79] found
υ r2 = υ 02 −
16πd p2 h0 ⎛ σ y ρυ 02
⎜
+
m p ⎜⎝ 2
3
where and υr is the residual velocity of the projectile.
⎞
⎟⎟
⎠
(24),
19
Chapter 3
3.1
Materials and Structures
Sandwich Panel Fabrication
A perforated sheet folding process [29] was used to create pyramidal truss sandwich
panel structures with a core relative density ( ρ ) between 5 and 6%.
A diamond
perforation pattern was die stamped into a 1.9 mm thick (14 gauge) 304 stainless steel
sheet, Figure 6. A similar thickness, 6061-T6 aluminum alloy was annealed to the Ocondition also die stamped in a similar manner to the 304 stainless steel. The Ocondition annealing was achieved by placing the assembly in a furnace at 500 °C for 30
minutes and allowed to furnace cool. Afterwards, the sheets were perforated to create a
2-D array of diamond perforations that were each 5.46 cm in length and 3.15 cm wide.
Adjacent perforations were separated by 4.0 mm of metal. The patterned sheets were
then bent as schematically illustrated in Figure 6, to create a single layer pyramidal truss
lattice with trusses that were 31.75 mm in length and 1.9 x 4.0 mm2 in cross section.
After bending, the annealed O-condition AA6061 trusses were artificially aged at 165 °C
for 19 hours and then water quenched from the solutionizing temperature to return them
to their peak strength condition (T6).
20
Figure 6. Manufacturing process for making pyramidal lattice truss cored sandwich
panels [3].
The lattice truss panels were trimmed to form 3x3 pyramidal cell arrays. The 304
stainless steel structures were placed between a pair of 1.5 mm thick (16 gauge) 304
stainless steel (12.07 cm x 12.70 cm) facesheets and laser welded at the nodes, Figure 7.
The AA6061 lattices were sandwich between 1.5 mm thick (14 gauge) AA6061 face
sheets with similar dimensions 12.07 cm x 12.70 cm and laser welded, Figure 7. The 7axis CO2 laser was manufactured by LaserDyne (Champlin, MN), and used 600-1300 W
to control the depth and size of the welds which were conducted on both alloys.
21
Figure 7. Illustration of the laser welding process for bonding the truss lattice to
proximal and distal facesheet.
Figure 8 shows a cross section of the single layer empty pyramidal truss lattice along a
nodal line.
Figure 8. Cross section of the single layer empty pyramidal truss lattice along a nodal
line.
22
3.2
Relative Density Relations
The relative density, ρ , is non-dimensional ratio defined as the volume fraction of truss
members occupying a prescribed unit cell. Ignoring the detailed geometry located at the
nodes, the relative density of the pyramidal lattice truss core can be calculated from a unit
cell analysis of the single layer pyramidal unit cell, Figure 9.
Figure 9. Unit cell geometry used to derive the relative density for single layer
pyramidal topology.
°
where ω = 54.7 is the included angle (the angle between the truss members and the base
of the pyramid), w is the truss width, t is the truss thickness and l is the truss length.
Based upon these considerations, the volume, Vtr , of the truss members occupying the
single layer pyramidal unit cell shown in Figure 9 is:
Vtr = 4lwt
(25).
The volume, Vc , of the single layer pyramidal unit cell is:
Vc =
(
2l cos ω
)(
)
2l cos ω (l sin ω ) = 2l 3 cos 2 ω sin ω
(26),
23
Taking the ratio between the volume of the trusses, equation (25), and volume of the unit
cell, equation (26), we obtain the single layer pyramidal relative density ( ρ ) expression:
ρ=
Vtr
2 wt
= 2
Vc l cos 2 ω sin ω
(27).
14 gauge thick 304 stainless steel and 12 gauge thick age hardened AA6061-T6
aluminum alloy panels are used here, with t = 1.9 mm, w = 4.0 mm, l = 31.75 mm and
ω = 54.7° . Substituting these values into equation (27) yields a ρ = 5.5 ± 0.3% . The
304 stainless steel sandwich panel had an areal density of approximately 28 kg/m2 while
that of the age hardened 6061-T6 aluminum alloy was approximately 10 kg/m2.
3.3
Alloy Mechanical Properties
3.3.1 304 Stainless Steel
Uniaxial tension specimens were machined from 304 stainless steel with a 0.61 mm plate
thickness, according to ASTM E-8 guidelines [97]. A servo-electric universal testing
machine (Model 4208, Instron Corp., Canton, MA) with self-aligning grips was used to
test each specimen at ambient temperature, approximately 25 °C. The applied nominal
strain rate for the stainless steel was 0.3 mm/min (10-3 s-1), and the strain measurements
were made using a linear variable differential transformer (LVDT) clip-on extensometer
with an accuracy of ±0.5% of the gage length of 50 mm. The stress as a function of
strain for the as received alloy is plotted in Figure 10. The elastic modulus measured
approximately 200 GPa, the yield strength measured approximately 255 MPa, the
ultimate yield strength measured approximately 1000 MPa and the strain to fracture
measured approximately 0.39. The test results approximately agree with referenced
values [98].
24
Figure 10. Uniaxial tension data for as-received 304 stainless steel.
3.3.2 Age Hardened 6061-T6 Aluminum Alloy
Uniaxial tension specimens were machined age hardened 6061-T6 aluminum alloy with a
6.35 mm plate thickness, according to ASTM E-8 guidelines [97]. The equivalent servoelectric universal testing machine as described in Chapter 3.4.1 was used for testing the
mechanical properties of the alloy. The applied nominal strain rate for age hardened
6061-T6 aluminum alloy was 0.2 mm/min (10-3 s-1). The stress as a function strain
response is plotted in Figure 11. The elastic modulus measured approximately 68 GPa,
the yield strength measured approximately 268 MPa respectively, the ultimate yield
strength measured approximately 310 MPa and the strain to fracture measured
approximately 0.15. The test results approximately agree with referenced values [98].
25
Figure 11. Uniaxial tension data for the age hardened 6061-T6 aluminum alloy.
3.4
Polymer Infiltrated Sandwich Panels
In an attempt to add ballistic resistance to the sandwich panels, a low Tg polyurethane,
designated PU 1, was infiltrated into the structure to create a hybrid lattice. This
polyurethane was chosen due to its wide availability and customizable mechanical
properties allowing a polymer with a high elongation to yield to be chosen easily.
3.4.1 Hybrid Lattice Fabrication
Twenty five 304 stainless steel mono-layer pyramidal lattice truss structures, with
equivalent dimensions as described in Chapter 3.1, were fabricated and assembled. The
samples were taped on three sides. PU 1 was poured into the sandwich structure and the
samples were allowed to cure for twenty four hours at ambient temperature,
approximately 25 °C.
26
The relative density of the system can be calculated using a similar unit cell analysis,
described in Chapter 3.2. Equation (28) shows the relative density for the 304 stainless
steel pyramidal truss lattice with infiltrated PU 1, incorporating the different densities of
the metal and the PU 1,
ρ pu (2l 3 cos 2 ω sin ω − 4lwt ) + ρ tr (4lwt )
ρ=
ρ m (2l 3 cos 2 ω sin ω )
(28),
where ρ pu is the density of the polyurethane, ρ tr is the density of the trusses and ρ m is
the density of the base metal system. With polyurethane density of ρ p = 1.3 g/cc, a truss
density of ρ tr = 7.97 g/cc and a base metal density of ρ m = 7.97 . Compared to an all
steel plate, the relative density of the system is approximately ρ = 27%. The areal
density of the 304 stainless steel pyramidal truss lattice infiltrated with PU 1 is 55 kg/m2.
3.4.2 Polymer
The PU 1 polymer chosen for the study was a type of polyurethane, designated PMC-780
Dry [100], formulated by Smooth-On (Easton, PA). PU 1 is a two component, pliable,
castable elastomer with an approximate twenty-four hour cure time at room temperature.
Part A is composed mostly of polyurethane prepolymer and a trace amount of toluene
diisocyanate. Part B is composed of polyol, a proprietary chemical (NJ Trade Secret
#221290880-5020P), di(methylthio)toluene diamine and phenylmercuric neodecanoate.
This polyurethane has a low elastic modulus and tensile strength but a very high
elongation to failure. The term elastomer is loosely applied to polymers that at room
temperature can be stretched repeatedly to at least twice their original length and,
immediately upon release of the stress, return with force to their approximate original
length [101]. Table 1 lists the manufacturer’s specifications for the polyurethane.
27
Property
PU 1
Manufacturer
Product Name
Tensile Modulus (MPa)
Tensile Strength (MPa)
Elongation to Break (%)
Shore Hardness
Smooth-On (Easton, PA)
PMC-780 Dry
2.76
6.21
700
80 A
Table 1. Manufacturer reported properties for the polyurethane system.
The hardness testing of plastics is most commonly measured by the Shore (Durometer)
test or Rockwell hardness test. Both methods measure the resistance of the plastic toward
indentation by a spring-loader. Both scales provide an empirical hardness value that
doesn't correlate to other physical properties or fundamental characteristics such as
strength or resistance to abrasion. Shore hardness, either the Shore A or Shore D scale, is
the preferred method for rubbers/elastomers and is also commonly used for 'softer'
plastics such as polyolefins, fluoropolymers, and vinyls. The Shore A scale is used for
'softer' rubbers while the Shore D scale is used for 'harder' ones. The Shore A hardness is
the relative hardness of elastic materials such as elastomers or soft plastics can be
determined with an instrument called a Shore A Durometer. If the indenter completely
penetrates the sample, a reading of 0 is obtained, and if no penetration occurs, a reading
of 100 results. Shore hardness is a dimensionless quantity. A full description of the test
method can be found in ASTM D2240, or the analogous ISO test method is ISO 868.
28
3.5
Polymer Characterization
A characterization of the dynamical properties of the polymer is necessary due to their
effect on the ballistic response. Three properties were characterized, the glass transition
temperature, the storage modulus and the loss modulus. The glass transition temperature
indicates the amount of crosslinking in the polymer and affects the elongation to yield.
This property can be ascertained by measuring the heat capacity as a function of
temperature with a differential scanning calorimeter (DSC). The storage modulus and
loss modulus are related to a parameter, Tanδ , that indicates a materials ability to
absorb and dissipate energy. These rheological properties can be ascertained by the use
of a dynamic mechanical analyzer (DMA).
3.5.1 DSC Analysis
A DSC analysis of PU 1 was conducted by M. Aronson et al. of the University of
Virginia. The glass transition temperature, Tg, of the polyurethane was determined with
modulated differential scanning calorimetry (MDSC®) using a Q1000 Modulated DSC
(TA Instruments-Waters, LLC). The polymer was heated over a temperature range of -80
to 240 °C with a heating rate of 3 °C/min and a modulation of ± 0.5 °C/60 sec period.
With traditional DSC, the heat flow curve is a superimposition of the Tg, endotherms and
exotherms. Due to this superimposition, it is difficult to make an accurate determination
of the Tg with traditional DSC. With modulated DSC, the reversing heat flow curve
associated with the Tg is separated from the non-reversing heat flow curve associated
with endotherms and/or exotherms, thus enabling an accurate determination of the Tg
[103].
Figure 12 is a plot of the heat capacity, Rev Cp, of PU 1 as a function of temperature.
The Cp of the polyurethane was determined by dividing its reversing heat flow value,
J/(sec·g), by the heating rate, °C/sec.
29
Figure 12. Heat capacity (Rev Cp) of PU 1 as a function of temperature (°C).
The Tg of each sample was taken to be the inflection point of the step-change in Cp.
Based on this definition, and the information included in Figure 12, the Tg of PU 1 was
-56 °C. The small step-change in Cp, around 70 °C, is believed to be an experimental
artifact and not associated with a second Tg of this sample.
3.5.2 DMA Analysis
A DMA analysis of PU 1 was also conducted by M. Aronson et al. of the University of
Virginia.
The rheological properties of PU 1 were characterized with dynamic
mechanical analysis (DMA) using a Q800 DMA (TA Instruments-Waters, LLC).
Measurements were made on each sample at three different frequencies, 1, 10 and 100
Hz, over a temperature range of -100 to 40 °C in 5 °C increments. The data over the
entire temperature range were transformed using time-temperature superposition (TTS)
with a reference temperature of 25 °C [106,107]. The result of this data manipulation is a
491H
master curve of predicted storage modulus, E ′ , and loss modulus, E ′′ , values over a
frequency range of 10-1 to 1010 Hz for each sample at the reference temperature.
30
Figure 13 is a plot of the storage modulus of PU 1 at a frequency of 1 Hz over a
temperature range of -100 to 40 °C. As the temperature is increased from -70 to 0 °C, the
storage modulus of PU 1 decreases by three orders of magnitude. This difference is due
to the fact that the Tg of PU 1 is -56 °C, Figure 12.
Figure 13. Storage modulus at a frequency of 1 Hz for PU 1 as a function of
temperature.
The predicted storage and loss modulus values for PU 1 over a frequency range of 1 to
106 Hz at a reference temperature of 25 °C was computed, Figure 14. As previously
discussed, these predicted values were obtained by transforming the measured E’ and E”
values obtained over the temperature range of -100 to 40 °C at the three different
frequencies using TTS (data obtained at low temperatures corresponds to the high
frequency data in Figure 14, while data obtained at high temperatures corresponds to the
low frequency data).
31
Figure 14. Predicted values for the storage and loss modulus of PU 1 at a reference
temperature of 25 °C as a function of frequency.
The ratio of E ′ to E ′′ , which is referred to as Tan δ, is a parameter that is often used to
assess the ability of a material to absorb and dissipate energy.
For materials with
comparable storage moduli, the greater the Tan δ value, the more efficient the material is
able to absorb and dissipate energy. Figure 15 is a plot of Tan δ of PU 1 over the same
frequency range covered in Figure 14.
32
Figure 15. Tan δ ( E ′′ / E ′ ) of PU 1 as a function of frequency.
33
Chapter 4
Ballistic Testing
Fifteen pyramidal lattice truss structures of each alloy, with contrasting mechanical
properties, were tested using impact velocities between approximately 225 m/s and 1225
m/s. Eleven 304 stainless steel monolithic plates, 3 mm thick, with an equivalent areal
density to 304 stainless steel lattice truss sandwich panels, were tested as a comparison
to evaluate the ballistic resistance of the lattice truss sandwich system. Both stainless
steel systems had the same (as-received) mechanical properties and neither underwent
heat treatment prior to testing.
4.1
Stage One Powder Gun
Ballistic testing was conducted by A. Zakraysek et al. at the Indian Head Division, Naval
Surface Warfare Center, MD, using a powder gun shown schematically in Figure 16.
Figure 16. Illustration of the single stage powder gun used for ballistic studies. The
sabot carried a 12.5 mm spherical projectile.
34
A cable connected the firing switch to an electric solenoid, Figure 16. Upon closing the
circuit, the electric solenoid activated a firing pin. The firing pin then struck a 0.38
caliber blank cartridge supplied by Western Cartridge Company (East Alton, IL) which
ignited a gun powder charge whose mass determined the projectile velocity. Gun powder
3031, manufactured by IMR (Shawnee Mission, KS), and cotton, placed in front of the
gun powder, was contained in the middle region of the breech in Figure 16. The purpose
of the cotton was to ensure the initiated shock wave remained uniform throughout
propagation of the detonation. A sabot was located within the 2.54 cm bore gun barrel,
Figure 16. A series of holes placed along the gun barrel were used to dissipate the shock
wave and maintain a smooth acceleration of the sabot until it exited the barrel.
4.2
Sabot and Projectile
The plastic sabot was composed of four quarters that, upon mating, surrounded a 12.5
mm diameter spherical projectile. The sabot plugs had an inner diameter of 1.25 cm, an
outer diameter of 2.54 cm, a height of 3.50 cm and weighed 18.60±0.12 g. A 40° bevel at
the sabot opening facilitated separation of the sabot from the projectile by air drag,
shortly after initiation of free flight. Figure 17 shows a photograph of both the fully
assembled and separated sabot. The projectiles had a diameter of 1.25 cm and weighed
8.42±0.02 g. The spherical projectiles were manufactured by National Precision Ball
(Preston, WA). They were made from 1020 plain carbon steel with an ultimate tensile
strength of 365 to 380 MPa [99].
35
Figure 17. Illustration of the sabot used to carry the projectile.
4.3
Test Fixture
The test sample fixture was located within a blast chamber, Figure 18.
36
Figure 18. Illustration of setup used in the blast chamber to mount the samples, measure
velocities and record via high-speed photography.
A square steel plate 41.28 cm long, 2.86 cm thick, was located one meter from the end of
the barrel with a 3.8 cm diameter hole located in the center. A square wood plate 41.28
cm long, 2.22 cm thick, with a 6.35 cm diameter hole, was located 30.48 cm successively
after the steel plate. On the back of the wood plate, covering the hole, was the first of
four brake screens to measure entry and exit velocities. A brake screen is a piece of
paper with a thin, silver mask that is connected into a circuit. These circuits were
connected into a four channel oscilloscope. Upon penetration by the projectile, the
circuit is broken. Using four brake screens, two for entry and two for exit, velocities can
be calculated by knowing the distance between and the time difference between circuit
closures. The oscilloscope was precise to ±1 μs therefore causing decreasing error in the
velocity measurement as the projectile velocity was increased (i.e. time is inversely
37
proportional to length in velocity). The mounting steel plate, 2.86 cm thick, was located
30.86 cm after the wood plate. In the center of plate, was a 13.34 cm square aperture to
house the sample. On each side of the sample, a brake screen was attached. An iron
angle bracket 17.78 cm long, with 1.19 cm overlap over the top and bottom was used to
clamp the sample into the fixture with bolts. Adjacent to the fixture, a Fresnel lens was
used to collimate the light onto the sample to provide adequate contrast for the highspeed photography located on the opposing side. Located 30.48 cm, successively after
the mounting steel plate, was another square wood plate 41.28 cm long, 2.22 cm thick,
with a 12.7 cm diameter hole located in the center. On the back of this plate was the final
brake screen in the series. A final square steel plate 41.28 long, 2.86 cm thick, was
located 28.21 cm successively after the second wood plate. This plate was used as
backstop to catch any fragments from the sample or remaining projectile remnants.
38
Chapter 5
Empty Lattice Resistance
Both alloy systems, 304 stainless steel and AA6061 aluminum alloy, were fixtured as
described in Chapter 4.3 and impacted using the aforementioned projectiles as described
in Chapter 4.2. Exit velocity of the projectile through the target was recorded and the
impact velocity was gradually increased from 200-1200 m/s. Fifteen sandwich structure
samples of both alloy systems and eleven 304 stainless steel plate samples were tested.
5.1
304 Stainless Steel Panel Response
Table 2 displays the data acquired for the 304 stainless steel pyramidal truss lattice
sandwich structure. The mass of each 304 stainless steel sample was 432.2±1.1 g.
Shot
#
Impact
Velocity
(m/s)
Exit
Velocity
(m/s)
Nodal
Disbond of
Distal FS
Penetration
of Distal FS
1
46
56
2
48
133
3
50
134
4
52
135
54
136
137
339.2±0.1
290.8±0.1
227.1±0.1
506.9±0.3
481.3±0.3
493.8±0.3
810.8±0.8
768.4±0.8
812.3±0.9
1029.9±1.4
992.4±1.3
1001.0±1.3
1206.1±1.9
1214.9±1.9
1221.9±1.9
N/A
N/A
N/A
310.0±0.1
266.1±0.1
276.5±0.1
551.1±0.4
491.9±0.3
653.5±0.6
721.5±0.7
744.0±0.7
653.5±0.6
868.4±1.0
882.7±1.0
851.9±0.9
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Table 2. The impact and exit velocities of the projectile, nodal disbonding of the distal
facesheet and whether the projectile penetrated the distal facesheet for the 304 stainless
steel pyramidal truss lattice sandwich structure.
Figure 19 depicts the exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 stainless steel pyramidal truss lattice sandwich structure. The
error bars for the impact and exit velocities are not illustrated on the graph because they
are smaller than the size of the plotted data points.
39
Figure 19. Plot of exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 stainless steel pyramidal truss lattice.
The results for the system can be fitted to a linear equation after the critical velocity
region (i.e. the velocity at which penetration begins to occurs), R2 = 0.98,
y = −100.8 + 0.81x
(29).
Figure 20 depicts the energy absorbed (J) as a function of the impact velocity (m/s) for
the 304 stainless steel pyramidal truss lattice system. As described previously, the error
bars for the impact and exit velocities are not illustrated on the graph because they are
smaller than the size of the plotted data points.
40
Figure 20. Plot of energy absorbed (J) as a function of the impact velocity (m/s) for the
304 stainless steel pyramidal truss lattice system.
The left parabaloid in Figure 20 represents the target preventing penetration of the
projectile. After the critical velocity, the energy absorbed begins to decrease until it
reaches a minimum, and then begins to increase monotonically with the initial velocity.
The first 304 stainless steel pyramidal truss lattice sandwich structure sample to be
penetrated occurred with an impact velocity of 481.3 m/s. The projectile exited the
lattice structure at 266.1 m/s, approximately 55% of the impact velocity. The critical
velocity is approximately 400±25 m/s.
Figure 21 shows a cross sectional view of a 304 stainless steel sample that was impacted
by a spherical projectile at 339.2 m/s.
41
Figure 21. a) Cross section of the 304 stainless steel sample that was impacted at 339.2
m/s and was not fully penetrated, shot 1 b) Cross section of the entry hole of shot 1 c)
Cross section of the exit hole of shot 1. Bulging and dishing are apparent on the distal
facesheet and a crack began to initiate petaling as the energy from the impact was fully
absorbed.
Physical examination after the test indicated a center-cell impact (i.e. equidistant from
four nodes), Figure 21. The projectile impacted a truss/distal facesheet node causing a
truss to separate and plastically deform. Penetration of the proximal facesheet resulted in
an entry hole of 12.5 mm wide and deflected 4.5 mm. Dishing was approximately 3 cm
in diameter. Full penetration of the distal facesheet did not occur and fully arrested the
projectile resulting in a deflection of 12.5 mm. A star-shaped crack began to initiate
forming sectors, but no petaling occurred. There was no nodal disbonding of the trusses
and facesheets except for the impact location.
42
Figure 22. a) Cross section of the 304 stainless steel sample that was impacted at 810.8
m/s, shot 3 b) Cross section of the entry hole of shot 3 c) Cross section of the exit hole of
shot 3. A small amount of ductile hole enlargement occurred on the proximal facesheet
and bending/dishing exceeded the ductile limit of the 304 stainless steel to form petaling.
Figure 22 shows a center-cell impact on shot 3 of 810.8 m/s and brake screens recorded
an exit velocity 551.1 m/s, approximately 68% of the impact velocity. The projectile
impacted a truss/distal facesheet node causing trusses to separate and plastically deform.
Penetration of the proximal facesheet resulted in an entry hole of 12.5 mm wide and
deflected 1.5 mm displaying ductile hole enlargement in the immediate impact location.
Penetration of the distal facesheet resulted in an exit hole of 22.0 mm wide and deflected
11.0 mm exhibiting three separate petals. There was no nodal disbonding of the trusses
and facesheets except for the impact location.
43
Figure 23. a) Cross section of the 304 stainless steel sample that was impacted at 1206.1
m/s, shot 54 b) Cross section of the entry hole of shot 54 c) Cross section of the exit hole
of shot 54. A small amount of ductile hole enlargement occurred on the proximal
facesheet and bending/dishing exceeded the ductile limit of the 304 stainless steel to form
petaling.
Figure 23 shows a center-cell impact on shot 54 of 1206.1 m/s and an exit velocity of
868.4 m/s, approximately 72% of the impact velocity.
The projectile impacted a
truss/distal facesheet node causing trusses to separate and plastically deform. Penetration
of the proximal facesheet resulted in an entry hole of 12.5 mm wide and deflected 0 mm.
Similar to shot 3, ductile hole enlargement was evident surrounding the impact location.
Penetration of the distal facesheet resulted in an exit hole of 26.0 mm wide and deflected
44
12.5 mm exhibiting four distinct petals. There was no nodal disbonding of the trusses
and facesheets except for the impact location.
5.2
304 Stainless Steel Plate Response
Table 3 displays the data acquired for the 3 mm thick 304 stainless steel monolithic plate.
The mass of each plate was 367.2±13.8 g, an approximate areal density of 28 kg/m2.
Shot #
Impact
Velocity
(m/s)
Exit
Velocity
(m/s)
104
57
58
59
105
60
106
61
107
62
108
177.4±0.0
377.0±0.2
341.7±0.2
477.3±0.3
509.6±0.3
805.0±0.8
806.2±0.8
989.4±1.3
985.7±1.3
1191.8±1.8
1226.5±1.9
N/A
N/A
N/A
323.1±0.1
302.4±0.1
617.8±0.5
574.9±0.4
794.0±0.8
725.7±0.7
1000.0±1.3
874.8±1.0
Table 3. The impact and exit velocities of the projectile for a 3 mm thick 304 stainless
steel monolithic plate.
Figure 24 depicts the exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 stainless steel monolithic plate compared to the 304 stainless
steel pyramidal truss lattice. As described in Chapter 5.1, the error bars for the impact
and exit velocities are not illustrated on the graph because they are smaller than the size
of the plotted data points.
45
Figure 24. Plot of exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 stainless steel monolithic plate compared to the 304 stainless
steel pyramidal truss lattice.
The results for the systems can be fitted to a linear equation after the critical velocity
region. Equation (29) gives the relation for the pyramidal truss lattice sandwich structure
and the 304 stainless steel solid plate is given by, R2 = 0.98,
y = −109.1 + 0.87 x
(30).
Figure 25 depicts the energy absorbed (J) as a function of the impact velocity (m/s) for
the 304 stainless steel pyramidal truss lattice system and solid plate. As described in
Chapter 5.1, the error bars for the impact and exit velocities are not illustrated on the
graph because they are smaller than the size of the plotted data points.
46
Figure 25. Plot of energy absorbed (J) as a function of the impact velocity (m/s) for the
304 stainless steel pyramidal truss lattice system and solid plate.
Similar to the sandwich panel, after the critical velocity of the solid plate, the energy
absorbed begins to decrease until it reaches a minimum, and then begins to increase
monotonically with the initial velocity.
The first 304 stainless steel monolithic plate sample to be penetrated occurred at an
impact velocity of 477.3 m/s. The projectile exited the plate at 323.1 m/s, approximately
68% of the impact velocity.
Figure 26 shows a cross sectional view of the monolithic 304 stainless steel plate that was
impacted by a spherical projectile at 341.7 m/s.
There was no penetration of the
projectile and plate was only deflected 9.5 mm. The bulging zone had a diameter of 12.5
mm and the dishing zone extended 4.5 cm in diameter.
47
Figure 26. Cross section of the monolithic 304 stainless steel plate that was shot at 341.7
m/s, shot 58. Significant bulging and dishing occurred without penetration.
Figure 27 shows a cross sectional view of the monolithic 304 stainless steel plate that was
impacted by the spherical projectile at 509.6 m/s. The exit velocity of the projectile was
302.4 m/s, approximately 59% of the impact velocity. The projectile penetrated the steel
plate with a hole 12.5 mm in diameter and a deflection of 6.5 mm. Adiabatic shearing is
apparent from the cross-sectional view and the dishing zone extended approximately 3.5
cm.
Figure 27. Cross section of the monolithic 304 stainless steel plate that was shot at 509.6
m/s, shot 105. Significant bulging and dishing occurred reaching the ductile limit and
penetrated the plate.
Figure 28 shows a cross sectional view of the monolithic 304 stainless steel plate that was
impacted by the spherical projectile at 1226.5 m/s. The exit velocity of the projectile was
874.8 m/s, approximately 71% of the impact velocity. The projectile penetrated the steel
plate with a hole 15.9 mm in diameter and a deflection of 0 mm. The sample exhibited a
high degree of ductile hole enlargement and displayed little or zero dishing.
48
Figure 28. Cross section of the monolithic 304 stainless steel plate that was shot at
1226.5 m/s, shot 108. No bulging or dishing occurred but significant ductile hole
enlargement occurred.
As can be seen from Figure 21-Figure 23 and Figure 26-Figure 28, the penetration
mechanisms of the sandwich panel are different from those of the monolithic plate with a
few similarities. Large amounts of deformation, bulging and dishing, occurred at the
slower speeds in both the plate and the proximal and distal sides of the sandwich
structure. In the sandwich structure, the trusses stretched and assisted in restraining the
bending of the facesheets. But as the impact speeds increased, bulging and dishing began
to diminish. The plate transitioned to larger degrees of ductile hole enlargement whereas
the sandwich structure displayed this phenomenon transition only on the proximal face
sheet. The distal side exhibited large degrees of petaling deformation, with the petals still
attached to truss members, whereas the plate never exhibited signs of petaling.
49
5.3
AA6061 Panel Response
Table 4 displays the data acquired for the AA6061-T6 pyramidal truss lattice sandwich
structure. The mass of each AA6061-T6 sample was 155.0±0.3 g.
Shot
#
Impact
Velocity
(m/s)
Exit
Velocity
(m/s)
Nodal
Disbond of
Distal FS
Penetration
of Distal FS
47
80
114
49
81
115
51
82
116
53
83
117
55
84
118
232.1±0.1
370.4±0.2
280.1±0.1
506.5±0.3
493.3±0.3
545.9±0.4
756.5±0.7
739.0±0.7
795.5±0.8
997.8±1.3
1006.2±1.3
1020.7±1.3
1222.2±1.9
1222.0±1.9
1209.5±1.9
144.7±0.0
270.8±0.1
196.4±0.0
411.1±0.2
395.4±0.2
433.0±0.2
670.7±0.6
639.1±0.5
685.3±0.6
922.2±1.1
889.0±1.0
898.1±1.0
1125.5±1.6
1102.4±1.6
1045.5±1.4
No
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Table 4. The impact and exit velocities of the projectile, nodal disbonding of the distal
facesheet and whether the projectile penetrated the distal facesheet for the age hardened
AA6061-T6 aluminum alloy pyramidal truss lattice sandwich structure.
Figure 29 depicts the exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the AA6061 pyramidal truss lattice compared to the 304 stainless steel
pyramidal truss lattice sandwich structure. As described in Chapter 5.1, the error bars for
the impact and exit velocities are not illustrated on the graph because they are smaller
than the size of the plotted data points.
50
Figure 29. Plot of exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the age hardened AA6061 aluminum alloy pyramidal truss lattice
compared to the 304 stainless steel pyramidal truss lattice system.
The results for the systems can be fitted to a linear equation after the critical velocity
region. Equation (29) gives the relation for the pyramidal truss lattice sandwich structure
and the AA6061-T6 truss lattice sandwich structure is given by, R2 = 0.99,
y = −79.7 + 0.97 x
(31).
Figure 30 depicts the energy absorbed (J) as a function of the impact velocity (m/s) for
the 304 stainless steel and AA6061 aluminum alloy sandwich panel. As described in
Chapter 5.1, the error bars for the impact and exit velocities are not illustrated on the
graph because they are smaller than the size of the plotted data points.
51
Figure 30. Plot of the energy absorbed (J) as a function of the impact velocity (m/s) for
the 304 stainless steel sandwich panel and AA6061 aluminum alloy sandwich panel.
Unlike the stainless steel, the critical velocity for the aluminum alloy could not be
ascertained.
The energy absorbed by the age hardened AA6061 aluminum alloy
increased marginally as the entry velocity was increased.
Penetration of the distal facesheet for the AA6061 empty pyramidal truss lattice occurred
with an impact velocity of 232.1 m/s, the slowest projectile speed possible with the stage
one powder gun. The exit velocity of the projectile was 144.7 m/s, approximately 62% of
the impact velocity. The critical velocity of the structure is at some velocity less than
232.1 m/s but speeds below this were unattainable due to technical constraints.
Figure 31 shows a cross sectional view of the AA6061 sample that was impacted by the
spherical projectile at 280.1 m/s.
52
Figure 31. a) Cross section of the AA6061 sample that was impacted at 280.1 m/s, shot
114 b) Cross section of the entry hole of shot 114 c) Cross section of the exit hole of shot
114. Significant amount of bulging and dishing occurred on the proximal facesheet and
petaling occurred as a result of penetration.
Break screens indicated an exit velocity of 196.4 m/s, approximately 70% of the impact
velocity.
Post impact observation revealed a center-cell impact on the proximal
facesheet, with an entry hole 12.5 mm in diameter and deflected 6.5 mm, and dishing
approximately 3 mm in diameter. The projectile impacted a node-facesheet contact on
the distal facesheet separating and plastically deforming two pairs of the trusses. The exit
hole on the distal facesheet was 12.5 mm in diameter and deflected 8.0 mm.
Additionally, the energy absorbed by the impact of the projectile fractured all of the
nodal contacts on the distal facesheet and separated it from the truss structure.
53
Figure 32. a) Cross section of the AA6061 sample that was impacted at 493.3 m/s, shot
81 b) Cross section of the entry hole of shot 81 c) Cross section of the exit hole of shot
81. Significant amount of bulging and dishing occurred on the proximal facesheet and
petaling occurred resulting in penetration.
Figure 32 shows a slightly off center-cell impact on shot 81 of 493.3 m/s and brake
screens recorded an exit velocity 395.4 m/s, approximately 80% of the impact velocity.
The projectile only impacted one truss upon penetration as a result of the impact being
slightly off the center of the cell. The truss did not separate upon impact but did
plastically deform. Penetration of the proximal facesheet resulted in an entry hole of 12.5
mm wide and deflected 2.5 mm. Penetration of the distal facesheet resulted in an exit
54
hole of 14.5 mm wide and deflected 8.0 mm. There was nodal disbonding of two contact
points on the distal facesheet adjacent to impact cell.
Figure 33. a) Cross section of the AA6061 sample that was impacted at 1222.2 m/, shot
55 b) b) Cross section of the entry hole of shot 55 c) Cross section of the exit hole of shot
55. A significant amount of ductile hole enlargement occurred on the proximal facesheet
with little to no bulging/dishing and petaling occurred on the distal facesheet.
Figure 33 shows a center-cell impact on shot 55 of 1222.2 m/s and brake screens
recorded an exit velocity 1125.5 m/s, approximately 92% of the impact velocity. The
projectile impacted the trusses and plastically deformed them to adjacent cells.
55
Penetration of the proximal facesheet resulted in an entry hole of 12.5 mm wide and
deflected 0 mm with a high degree of ductile hole enlargement. Penetration of the distal
facesheet resulted in an exit hole of 17.5 mm wide and deflected 8.0 mm with three
distinct petals. The impact energy completely fractured all nodal contacts on the distal
facesheet, separating it from the truss lattice.
5.4
Discussion
The 304 stainless steel lattice truss system and the 304 stainless steel plate both had
approximately equivalent critical velocities of approximately 450 m/s. Both systems
shared similar performance, with the lattice truss exhibiting greater success at higher
speeds. Although Almohandes [39] found poorer performance of distributing a mass
equally over a given distance compared to the solid plate; our increased performance can
most likely be attributed to the lattice truss in the sandwich structure. As can be seen in
Figure 21-Figure 23 and Figure 26-Figure 28, large amounts of deformation, bulging and
dishing, occurred at the slower speeds in both the plate and the proximal and distal sides
of the sandwich structure.
The trusses occasionally separated and deformed thus
absorbing the remainder of the kinetic energy accounting for the approximate equal
ballistic performance. Additionally, the lattice truss core restrained the facesheets from
bending and dishing absorbing additional energy. But as the impact speeds increased, the
plate transitioned to larger degrees of ductile hole enlargement whereas the sandwich
structure displayed this phenomenon transition only on the proximal face sheet because
of reduced projectile velocity. The distal side did not exhibit any phenomenon transition
and continued displaying larger degrees of petaling deformation, with the petals still
attached to truss members. The projectile would be forced to deform the distal face sheet
to the point of fracture, maximal bulging, and then push each of the sectors out thus
forming the petals. This additional deformation, in addition to the plastic deformation of
the trusses, most likely accounts for greater energy absorption and thus lower exit speeds
than the solid plate.
56
The AA6061 aluminum alloy structures were penetrated at the slowest possible speeds
attainable at the facility, approximately 200 m/s. Similar to the 304 stainless steel, the
aluminum alloy exhibited a large degree of bulging and dishing on the proximal and
distal facesheets at the lower velocities. Petaling was prominent on the distal facesheet in
addition to the bulging and dishing. As the velocity was increased, bulging and dishing
diminished, transitioning to ductile hole enlargement on the proximal facesheet. On the
distal facesheet, the degree of petaling became more pronounced with larger sectors.
The vast difference in critical velocity and reduction in impact velocity between the
AA6061 aluminum alloy and the 304 stainless steel can most likely be attributed to the
aluminum alloy having lower ductility and a significantly lower work hardening rate.
Given that these two materials have similar yields strengths, it is a possibility that
lowering these properties drastically reduces the amount of energy absorbed through
plastic deformation. Additionally, the density of the stainless steel is approximately two
and a half times that of the aluminum alloy. Given the projectile diameter and cell size
ratio (i.e. approximately 0.5), this drastic difference in density reduces the amount of
momentum transfer from the projectile to the structure, thereby decreasing the amount of
energy transferred to the system. All of these properties enable the 304 stainless steel to
absorb more energy than the AA6061 aluminum alloy lattice truss sandwich structure.
Therefore, the 304 stainless steel has a superior ballistic resistance compared to the age
hardened AA6061 aluminum alloy with the same dimensions and relative density.
57
Chapter 6
6.1
Polymer Infiltration Study
Ballistic Response
Table 5 displays the data acquired for the 304 stainless steel pyramidal truss lattice
sandwich structure filled with PU 1. The mass of each hybrid, polymer and 304 stainless
steel sample was 857.1±6.4 g.
Shot
#
Impact
Velocity
(m/s)
Exit
Velocity
(m/s)
Nodal
Disbond of
Distal FS
Penetration
of Distal FS
6
26
70
109
128
7
27
71
110
129
8
28
72
111
130
29
63
73
112
131
10
30
74
113
132
364.8±0.2
341.4±0.2
370.9±0.2
299.0±0.1
340.2±0.1
545.3±0.4
530.4±0.4
540.7±0.4
515.7±0.3
571.5±0.4
781.2±0.8
791.0±0.8
804.7±0.8
819.0±0.9
746.5±0.7
999.7±1.3
1057.7±1.4
1006.1±1.3
984.5±1.3
986.9±1.3
1316.7±2.2
1197.6±1.8
1229.6±1.9
1220.4±1.9
1232.0±2.0
N/A
N/A
N/A
N/A
N/A
273.7±0.1
245.7±0.1
213.7±0.1
275.8±0.1
251.8±0.1
466.3±0.3
467.6±0.3
473.4±0.3
468.2±0.3
456.0±0.3
622.1±0.5
573.3±0.4
670.6±0.6
557.5±0.4
589.2±0.4
779.1±0.8
719.3±0.7
692.2±0.6
680.0±0.6
675.1±0.6
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Table 5. The impact and exit velocities of the projectile, nodal disbonding of the distal
facesheet and whether the projectile penetrated the distal facesheet for the 304 stainless
steel pyramidal truss lattice sandwich structure with polyurethane.
Figure 34 depicts the exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 stainless steel pyramidal truss lattice infiltrated with PU 1 and
the empty 304 stainless pyramidal truss lattice. As described in Chapter 5.1, the error
58
bars for the impact and exit velocities are not illustrated on the graph because they are
smaller than the size of the plotted data points.
Figure 34. Plot of exit velocity of the projectile (m/s) as a function of the impact
velocity (m/s) for the 304 hybrid stainless steel pyramidal truss and the empty 304
stainless pyramidal truss lattice.
The results for the systems can be fitted to a linear equation after the critical velocity
region. Equation (29) gives the relation for the pyramidal truss lattice sandwich structure
and 304 stainless steel truss lattice sandwich structure infiltrated with PU 1 is given by,
R2 = 0.97,
y = −72.2 + 0.65 x
(32).
Figure 35 depicts the energy absorbed (J) as a function of the impact velocity (m/s) for
the 304 stainless steel pyramidal truss lattice infiltrated with PU 1 and the empty 304
stainless pyramidal truss lattice. As described in Chapter 5.1, the error bars for the
59
impact and exit velocities are not illustrated on the graph because they are smaller than
the size of the plotted data points.
Figure 35. Plot of projectile the energy absorbed (J) as a function of the impact velocity
(m/s) for the 304 stainless steel pyramidal truss lattice infiltrated with PU 1 and the
empty 304 stainless pyramidal truss lattice.
Similar to the empty truss lattice sandwich structure, the energy absorbed by the PU 1
infiltrated sandwich structure decreases after the critical velocity until it reached a
minimum and then increased monotonically with the impact velocity.
The first sample of the 304 stainless steel pyramidal truss lattice filled with PU 1 to be
penetrated occurred with an impact velocity of 530.4 m/s. The projectile exited the distal
face sheet with an exit velocity of 245.7 m/s, approximately 46% of the impact velocity.
Figure 36 shows a cross sectional view of a 304 stainless steel sample filled with PU 1
that was impacted by the spherical projectile at 370.9 m/s, shot 70.
60
Figure 36. a) Cross section of the 304 stainless steel sample infiltrated with PU 1 that
was impacted at 370.9 m/s, shot 70 b) Cross section of the entry hole of shot 70 c) Cross
section of the exit hole of shot 70.
Physical examination after the test indicated a center-cell impact (i.e. equidistant from
four nodes), Figure 36. The projectile impacted a truss/distal facesheet node causing a
truss to separate and plastically deform. Penetration of the proximal facesheet resulted in
an entry hole of 12.5 mm wide and deflected 3.0 mm with significant bulging.
Penetration of the distal facesheet did not occur but displayed significant bulging and
dishing. The projectile was fully arrested resulting in a deflection of 10.0 mm in the
61
bulge zone. The projectile’s path through the polyurethane resealed after penetration
leaving no air space. The dishing zone diameter was approximately 65.0 mm and the
impact caused a separation of the polyurethane/distal facesheet. There was no nodal
disbonding of the trusses and facesheets except for the exit location.
Figure 37. a) Cross section of the 304 stainless steel pyramidal truss lattice filled with
PU 1 that was impacted at 515.7 m/s, shot 110 b) Cross section of the entry hole of shot
110 c) Cross section of the exit hole of shot 110.
Figure 37 shows an impact that was approximately 12.5 mm off of the center of the cell,
shot 110. The projectile impacted at 515.7 m/s and brake screens recorded an exit
62
velocity 275.8 m/s, approximately 53% of the impact velocity. The projectile did not
impact any truss or nodal contact due to the off axis impact. Penetration of the proximal
facesheet resulted in an entry hole of 12.5 mm wide and deflected 3.0 mm, displaying
only minor bulging. Penetration of the distal facesheet resulted in an exit hole of 12.5
mm wide and deflected 8.0 mm. No petaling occurred on the distal facesheet, but
significant dishing and bulging were observed. Similar to the rest of the shots infiltrated
with polyurethane, there was separation of the polyurethane/distal facesheet interface
with a diameter of 54.0 mm and a resealing of the projectile’s path through the
polyurethane. There was only one nodal contact that began to disbond and separate, but
that was adjacent to the exit location of the projectile.
63
Figure 38. a) Cross section of the 304 stainless steel pyramidal truss lattice filled with
PU 1 that was impacted at 984.5 m/s, shot 112 b) Cross section of the entry hole of shot
112 c) Cross section of the exit hole of shot 112.
Figure 38 shows a center-cell impact on shot 112 of 984.5 m/s and an exit velocity of
557.7 m/s, approximately 57% of the impact velocity.
The projectile impacted a
truss/distal facesheet node causing trusses to separate and plastically deform. Penetration
of the proximal facesheet resulted in an entry hole of 12.5 mm wide and deflected 1.0
mm. The proximal face sheet separated from the polyurethane in the center of the entry
hole by approximately 3.0 mm and the diameter of any separation of the interface was
74.0 mm.
There was minor ductile hole enlargement of the proximal facesheet.
Penetration of the distal facesheet resulted in a petaling exit hole of 27.5 mm wide and a
deflection of 16.0 mm. The distal facesheet exhibited three distinct petals that terminated
at each adjacent node.
Similar to previously impacted polyurethane samples, the
projectiles path resealed after penetration but showed signs of tearing due to the plastic
deformation of the trusses. There was no nodal disbonding of the trusses and facesheets.
6.2
Discussion
The 304 stainless steel lattice truss sandwich structure infiltrated with PU 1 and the 304
stainless steel empty sandwich structure both share approximate critical velocity regions
64
of 400 to 500 m/s. Although, the addition of the PU 1 to the 304 stainless steel truss
lattice system marginally increased the first penetrated sample impact velocity by
approximately 10%, from 481.3 m/s to 530.4 m/s. It also reduced the slope of the linear
fit of the exit velocity by approximately 13%. Improvement of the ballistic resistance for
the PU 1 infiltrated system compared to the empty truss lattice system was seen in Figure
34 as the entry velocity increased.
This increase in performance was most likely
attributed to the energy dissipated in the associated strain fields as the polymer was
transiently displaced outward from the projectile. Additionally, reduction of the proximal
facesheet deflection occurred at the lower speeds because of the physical restraint of the
PU 1 inside the structure. The onset of petaling did not appear to change as the transition
from dishing/bulging to fracture occurred. Another consideration for the improvement in
ballistic efficiency was the constraint of the trusses and the energy absorbed through
frictional dissipation as the trusses were plastically deformed from impact.
With the 304 stainless steel empty truss lattice system possessing an areal density of 28
kg/m2 and the 304 stainless steel truss lattice infiltrated with PU 1 possessing an areal
density of 54 kg/m2, a direct comparison between the normalized, first penetrated sample
impact velocity yields 17 m3/kg·s and 10 m3/kg·s (first penetrated sample impact velocity
divided by the areal density), respectively. The higher the normalized velocity indicates
greater ballistic resistance efficiency. Therefore, accounting for areal density, the 304
stainless steel system has a higher ballistic efficiency than the PU 1 infiltrated system.
Further improvement might have been attained if there was greater adhesion between the
facesheet-PU 1 interfaces. The elastomeric properties of PU 1 allowing a large degree of
elastic spring back, in addition with high velocities generating highly localized heat, may
account for the resealing of the projectile path through the test samples.
65
Chapter 7
Enhanced Ballistic Lattice Fabrication
Although the PU 1 did not increase the ballistic efficiency of the sandwich structure,
there exists the possibility that other materials could be infiltrated or inserted into the
structure to improve its resistance to penetration. This chapter conducts a preliminary
investigation of several possibilities including a different polymer, ballistic fibers and
metal encased ceramics with a polymer. Also investigated is the utility of a double layer
pyramidal truss lattice. This preliminary investigation is a simple survey of six “hybrid”
lattice truss systems at a fixed impact velocity of approximately 600 m/s with no
recording capability of exit velocity. The investigation provides an insight for possible
materials, with a high ballistic resistance, to be introduced into the truss lattice structure
which future studies can explore.
7.1
Concept Systems
Seven system concepts were constructed and evaluated. Six utilized a single layer system
and one the double layer concept. Various materials were introduced into the structures
void space.
Table 6 summarizes the concepts evaluated.
Figure 39 schematically
illustrates these basic concepts.
System
Layer
Polymer
Fabric
Encased
Ceramic
1
2
3
4
5
6
7
Single
Single
Single
Single
Single
Single
Double
None
PU 1
PU 1
PU 2
PU 1
PU 2
PU 1
None
None
None
None
Yes
None
None
None
None
None
None
None
Yes
None
Areal
Density
(kg/m2)
27.7
54.8
54.6
55.9
53.7
105.1
53.1
Table 6. Physical descriptions of composite lattice truss systems fabricated.
66
Figure 39. Schematic illustrations of pyramidal lattice truss concepts evaluated in the
study. a) Empty pyramidal truss lattice b) Polymer filled in truss lattice c) Ballistic fabric
interwoven between trusses with polymer filling remaining air space d) 304 SS encased
alumina inserted in triangular prismatic voids and remaining air space filled with polymer
e) Double layer pyramidal truss lattice filled with PU 1.
7.2
Lattice Structure Fabrication
Single layer pyramidal truss lattice sandwich structures were constructed according to the
procedures described in Chapter 3.1.
Double layer pyramidal truss lattice sandwich structures were created by stacking two
layers of the lattice truss structure made from a 1.5 mm thick (16 gauge) 304 stainless
67
steel using an intermediate solid sheet of 0.5 mm thick (20 gauge) 304 stainless steel.
The diamond perforation punch for the double layer lattice was 2.65 cm in length and
1.53 cm wide. The bent perforated sheets were then assembled to make nodal line
contacts as shown in Figure 6.
The double layer samples were cut to a 5x7 pyramidal cell array and also placed between
identical 16 gauge thick 304 stainless steel facesheets 11.09 cm x 12.70 cm. In both
systems, the lattice truss layer(s) were bonded to these facesheets using a transient liquid
phase bonding process [111,112].
This involved spray coating the face and the
intermediate solid sheets with a NICROBRAZ® alloy 51 (Wall Colmonoy, Dayton OH).
This alloy is composed of 25 Cr, 10 P, 0.03 C (wt. %) with the balance consisting of Ni.
The powder was contained in a polymer binder. These brazing alloys contain melting
point depressants (e.g. boron, phosphorous, silicon) to achieve desirable liquid flow and
adequate wetting behavior. The sandwich structure was placed in a high-temperature
vacuum oven for brazing at 10 °C/min up to 550 °C, held for 20 minutes to remove any
residual polymer binder, then heated to 1050 °C, for 60 minutes at 1.3 x 10-2 Pa before
furnace cooling to ambient temperature at 25 °C/min.
7.3
Double Layer Lattice Relative Density
Similar to the single layer pyramidal unit cell in Chapter 3.2, the relative density of the
double layer pyramidal lattice truss core can be simply calculated from a unit cell
analysis. Figure 40 shows the double layer pyramidal unit cell,
68
Figure 40. Unit cell geometry used to derive the relative density for a double layer
pyramidal topology.
where wi is the intermediate plate width, ti is the intermediate plate thickness and li is the
intermediate plate length.
We may write the volume of the truss members, in addition to the intermediate plate,
occupying the double layer pyramidal unit cell shown in Figure 40 as
Vtr = 8lwt + l i wi t i
(33),
where t is truss thickness, l is the truss length, w is the truss width, li is the intermediate
plate length, wi is the intermediate plate width and ti is the intermediate plate thickness.
From the unit cell geometry the volume of the double layer pyramidal unit cell, it can be
shown that:
Vc =
(
2l cos ω
)(
)
2l cos ω (2l sin ω ) + l i wi t i = 4l 3 cos 2 ω sin ω + l i wi t i
(34),
Taking the ratio between the truss volume (33) and cell volume (34) we obtain the double
layer pyramidal relative density expression:
69
ρ=
Vtr
8lwt + l i wi t i
= 3
V c 4l cos 2 ω sin ω + l i wi t i
(35),
with a truss length l = 14.7 mm, a truss width w = 1.5 mm, a truss thickness t = 1.5 mm,
an intermediate length li = 25.4 mm, an intermediate width wi = 25.4 mm, an
intermediate thickness of ti = 0.9 mm, yields a ρ = 10.2% (including the 20 gauge
intermediate layer). The areal density of the double layer pyramidal truss lattice structure
is 53.1 kg/m2.
7.4
Infiltration Materials and Methods
7.4.1 Polymers
Two polyurethanes, PU 1 described in Chapter 3.4, and another polyurethane, designated
PU 2, were inserted into six of the seven concept cellular sandwich systems. PU 2 was
chosen to complement PU 1’s material characteristics. PU 2, model name CLC-1D078
[102], supplied by Crosslink Tech, Inc. (Mississauga, ON Canada), was chosen due to a
high elastic modulus and high tensile strength but low elongation to failure. PU 2 is a
two component, rigid, rapid prototyping polyurethane system with cure time of
approximately five minutes at room temperature. Part A is composed of polyether
polyol. Part B is composed of diphenylmethane-4,4’-diisocyanate. Table 7 shows the
manufacture’s reported mechanical properties for the PU 2 system.
Property
Manufacturer
Product Name
Tensile Modulus (MPa)
Tensile Strength (MPa)
Elongation to Break (%)
Shore Hardness
PU 2
Crosslink Technology Inc.
(Mississauga, ON Canada)
CLC-1D078
1,120
68.9
16
78 D
Table 7. Manufacturer reported properties for the polyurethane system.
70
7.4.2 Fabric
A ballistic fabric was integrated into the one of cellular sandwich systems to investigate if
it provided additional resistance to projectile penetration and fragment protection. The
ballistic fabric chosen was a high strength ribbon composed of woven Spectra®,
approximately 2.54 cm wide, and interwoven between every other cell in a 0-90°
orientation. The ribbon was a 1200 denier 4 with a 21 x 21 plain weave impregnated with
a 20 ± 2% resin. A single layer of interwoven ribbon was located inside the sandwich
structure proximal to the distal face sheet.
7.4.3 Metal Encased Ceramic Prisms
Metal encased alumina prisms were inserted in one of the single layer samples. The AD94 alumina rods were manufactured by CoorsTek (Golden, CO). They were equilateral
triangular prisms with a base length of 2.54 cm, 12.07 cm long. The apexes of the prisms
were ground to remove 0.32 cm of material so they could be slipped into 0.05 cm thick
(20 gauge) 304 stainless steel triangular tubes.
The 304 stainless steel equilateral
triangular tubes had an interior base length of 2.54 cm. The AD-94 grade of alumina
consists of 93.3 Al2O3, 4.1 SiO2, 0.8 BaO, 0.7 MgO, 0.7 ZrO2, 0.3 CaO, 0.2 Fe2O3 and
0.1 Na2O (wt. %). The mechanical properties for AD-94 alumina reported by CoorsTek
are summarized in Table 8.
Elastic
Density
Material
Modulus
(g/cc)
(GPa)
AD-94
3.97
303
Tensile
Strength
(MPa)
221
Comp.
Strength
(MPa)
2068
Fracture
Toughness
(MPa·m1/2)
4-5
Hardness
(GPa)
11.5
Table 8. Physical properties of AD-94 Al2O3 triangular prisms.
4
Denier is a system of measuring the weight of a continuous fiber, numerically equivalent to the weight in
grams of 9,000 m of a continuous fiber. Plain weave is one of the basic weaves utilizing a simple alternate
interlacing of the fill and warp yarn, seriatim.
71
The 304 stainless steel tubes were then capped with 304 stainless steel plugs and sealed
by brazing utilizing the NICROBRAZ® alloy 51 and an identical process to that used to
fabricate the truss structures.
7.5
Hybrid Lattice Relative Density
A unit cell analysis for polymer infiltration into the metal sandwich structure can be
found in Chapter 3.4.1, with both polymer densities approximately equal, ρ = 1.3 g/cc.
The relative densities of the systems are approximately ρ = 27-27.5%. The areal density
of the 304 stainless steel pyramidal truss lattice infiltrated with PU 1 is approximately 55
kg/m2 and the truss lattice infiltrated with PU 2 is approximately 56 kg/m2.
The relative density for the 304 stainless steel truss lattice infiltrated with PU 1 and
ballistic fabric is given by:
ρ=
ρ pu (2l 3 cos 2 ω sin ω − 4lwt − l f w f t f ) + ρ tr (4lwt ) + ρ f (l f w f t f )
ρ m (2l 3 cos 2 ω sin ω )
(36).
where ρ pu is the density of the polyurethane, ρ tr is the density of the trusses, ρ f is the
density of the fabric and ρ m is the density of the base metal system. With a polyurethane
density of ρ pu = 1.3 g/cc, a truss length of l = 31.75 mm, truss width of w = 1.9 mm, a
truss thickness of t = 1.9 mm, an included angle of ω = 54.7° , a fabric length of l = 25.4
mm, a fabric width of w = 25.4 mm, a fabric thickness of t = 1.6 mm, a truss density of
ρ tr = 7.97 g/cc, a fabric density of ρ t = 1.4 g/cc and a base metal density of ρ m = 7.97 ,
the relative density of the system is approximately ρ = 26.5%. The areal density of the
304 stainless steel pyramidal truss lattice infiltrated with PU 1 and fabric is
approximately 54 kg/m2.
The relative density for the 304 stainless steel truss lattice infiltrated with PU 1 and Al2O3
encased in 304 stainless steel tubes is given by:
72
ρ=
⎛
⎝
1
2
⎞
⎛1
[bo ho − bi hi ]⎞⎟ + ρ a ⎛⎜ 1 [bi hi ]⎞⎟
⎠
⎝2
⎠
⎝2
⎠
ρ m (4l 3 cos 2 ω sin ω )
ρ pu ⎜ 2l 3 cos 2 ω sin ω − 4lwt − bo ho ⎟ + ρ tr (4lwt ) + ρ m ⎜
(37),
where ρ pu is the density of the polyurethane, bo and bi are the bases of the triangle for the
outer and inner tube respectively, ho and hi are the heights of the triangle for the outer and
inner tube respectively ρ tr is the density of the trusses, ρ m is the density of the base
metal system and ρ a is the density of the aluminum oxide. With a polyurethane density
of ρ pu = 1.3 g/cc, a truss length of l = 31.75 mm, truss width of w = 1.9 mm, a truss
thickness of t = 1.9 mm, an included angle of ω = 54.7° , triangle bases of bo = 2.54 cm
and bi = 2.49 cm, triangle heights of ho = 2.20 cm and hi = 2.15 cm, a truss density of
ρ tr = 7.97 g/cc, an aluminum oxide density of ρ a = 3.97 g/cc and a base metal density
of ρ m = 7.97 , the relative density of the system is approximately ρ = 52%. The areal
density of the 304 stainless steel pyramidal truss lattice infiltrated with PU 1 and fabric is
approximately 105 kg/m2.
Extending the cell analysis used to derive the relative density of the double layer truss
lattice system in Chapter 7.3, the relative density for the double layer 304 stainless steel
truss lattice infiltrated with PU 1 is given by:
ρ=
ρ pu (4l 3 cos 2 ω sin ω − 8lwt ) + ρ m (8lwt + li wi ti )
ρ m (4l 3 cos 2 ω sin ω + li wi ti )
(38),
with a truss length l = 14.7 mm, a truss width w = 1.5 mm, a truss thickness t = 1.5 mm,
an intermediate length li = 25.4 mm, an intermediate width wi = 25.4 mm, an
intermediate thickness of ti = 0.9 mm, yields a relative density, compared to an all steel
plate, of approximately ρ = 26% (including the 20 gauge intermediate layer). The areal
density of the double layer pyramidal truss lattice structure is approximately 53 kg/m2.
73
7.6
Material Properties
7.6.1 Brazed 304 Stainless Steel
The uniaxial tensile response of 304 stainless steel subjected to the same thermal history
as the lattice truss structures has been previously measured and reported [7], Figure 41.
The elastic modulus and 0.2% yield strength were 203 GPa and 176 MPa, respectively.
Significant work hardening occurred in the plastic region.
Figure 41. Uniaxial tension data for brazed 304 stainless steel.
74
7.6.2 PU 2
To contrast PU 1, another polyurethane system was chosen with a significantly higher
glass transition temperature thus a higher elastic modulus and lower elongation to
fracture. DSC analysis and DMA analysis were performed to characterize the
mechanical properties of the polyurethane.
7.6.2.1
DSC Analysis
The glass transition temperature, Tg, of PU 2 was determined with a similar modulated
differential scanning calorimetry (MDSC®) technique using a similar Q1000 Modulated
DSC described in Chapter 3.5.1. The polymer was heated over a temperature range of 80 to 240 °C with a heating rate of 3 °C/min and a modulation of ± 0.5 °C/60 sec period.
Figure 42 is a plot of the heat capacity, Rev Cp, of PU 2 as a function of temperature
revealing an approximate Tg of 49 °C. The Cp of each sample was determined by dividing
its reversing heat flow value, J/(sec·g), by the heating rate, °C/sec.
Figure 42. Heat capacity (Rev Cp) PU 2 as a function of temperature (°C).
75
7.6.2.2
DMA Analysis
The rheological properties of PU 2 were characterized with dynamic mechanical analysis
(DMA) using a similar Q800 DMA described in Chapter 3.5.2. Measurements were
made at three different frequencies, 1, 10 and 100 Hz, over a temperature range of -100 to
40 °C in 5 °C increments. The data over the entire temperature range were transformed
using time-temperature superposition (TTS) with a reference temperature of 25 °C
[106,107]. The result of this data manipulation is a master curve of predicted storage
modulus, E ′ , and loss modulus, E ′′ , values over a frequency range of 10-1 to 1010 Hz at
the reference temperature.
Figure 43 is a plot of the storage modulus of PU 2 at a frequency of 1 Hz over a
temperature range of -100 to 40 °C.
Figure 43. Storage modulus at a frequency of 1 Hz for PU 2 as a function of
temperature.
76
The storage modulus of PU 2 did decrease by more than one order of magnitude as the
temperature is increased to 40 °C. The observation that there was such a large decrease in
the storage modulus of PU 2 more than 10 °C below its Tg was consistent with the
observation that the temperature range over which the glass transition of this sample
occurs was very large.
Next, the predicted storage and loss modulus values for PU 2 over a frequency range of 1
to 106 Hz at a reference temperature of 25 °C were computed, Figure 14. As previously
discussed, these predicted values were obtained by transforming the measured E’ and E”
values obtained over the temperature range of -100 to 40 °C at the three different
frequencies using TTS (data obtained at low temperatures corresponds to the high
frequency data in Figure 14, while data obtained at high temperatures corresponds to the
low frequency data).
Figure 44. Predicted values for the storage and loss modulus of PU 2 at a reference
temperature of 25 °C as a function of frequency.
Figure 15 is a plot of Tan δ of PU 2 over the same frequency range covered in Figure 14.
77
Figure 45. Tan δ ( E ′′ / E ′ ) of PU 2 as a function of frequency.
78
Chapter 8
Ballistic Testing
A preliminary study was conducted that initiates an exploration of 304 stainless steel
hybrid pyramidal truss lattice structures ballistic response to moderate velocity impact
by a spherical projectile. A full ballistic evaluation of each concept was not conducted;
instead a comparison of relative performance was conducted against the impact of a
spherical projectile 12 mm in diameter and constant velocity of approximately 600 m/s.
8.1
Test Setup
A series of ballistics experiments with spherical projectiles were conducted using the
University of Cambridge gas gun facility with samples whose fabrication was described
in Chapter 7 [31]. Compressed nitrogen was used to accelerate the projectile which then
impacted the samples normal to their surface, Figure 46. The gas gun fired 12 mm
diameter, 6.9 g, 420 stainless steel ball bearings at the specimens at impact velocities of
approximately 600 m/s. For these experiments, the gas gun was fitted with a 12 mm
bore, 4.5 m long barrel designed for ballistic testing.
The loading configuration,
illustrated in Figure 46, shows that the projectile impacted the center of the panels, which
were simply supported over an approximate 60 mm diameter hole located in a rigid
backing plate (25 mm thick).
A Hadland Imacon-790 image-converter high speed camera was used to monitor the
responses of the (empty) system 1. It enabled observation of the projectile impact with
the sandwich panel and the sequence of subsequent deformation. An inter-frame time of
10 µs and an exposure time of 2 µs was used. Additionally, x-ray tomography was
performed on system concept 4.
79
Figure 46. Ballistic testing configuration. Ball bearing projectiles with a radius of 6 mm
and weight of 6.9 g were used. An impact velocity of approximately 600 m/s was used
for all the tests.
The specimens were adhesively attached to a backing plate with double-sided tape as
shown in Figure 46.
Specimens used in evaluations of systems 1 through 6 were
orientated such that impact occurred at the center of the proximal faceplate, which was
supported centrally by the pyramidal core, as sketched in Figure 47 (a). The specimen
used in evaluation of system 7, which consisted of the double-layered pyramidal core,
was loaded in the configuration illustrated in Figure 47 (b).
Figure 47. Projectile impact location for a) Single and b) Double layer pyramidal lattice
truss sandwich panels.
80
8.2
Results
8.2.1 Single Layer Empty System
Figure 48 shows cross sectional views of a truss sandwich panel (system 1) before and
after impact by a spherical projectile with an incident velocity of 598 m/s.
Figure 48. Test 1: a) Cross section of the single layer empty pyramidal truss lattice
along a nodal line b) Cross section of the single layer empty pyramidal truss lattice after a
projectile impact of 598 m/s.
Examination after impact indicated buckling and plastic deformation of the trusses was
limited to one cell in the lattice, as seen in Figure 48 (b). A fracturing of the nodes
occurred at all four truss/facesheet contact points of the impacted cell, two of these
contact points are shown in Figure 48 (b). The entry hole on the proximal facesheet was
15 mm in diameter and deflected 5 mm. The exit hole on the distal facesheet was
approximately 18 mm in diameter and deflected 11 mm. The plastic deformation of both
81
facesheets is known as petaling, a phenomenon common among impacted thin, ductile
metals.
A time sequence of high-speed photographs was taken during the test and these are
shown in Figure 49 (a)-(h). The time after impact is indicated for each frame, and it is
seen that impact occurred between Figure 49 (b) and (c). Subsequent frames, Figure 49
(d)-(h), show the projectile penetrating the proximal face and propagating towards the
distal face.
Estimating the distance traveled from frames, Figure 49 (c)-(h), to be
approximately 22.5 mm and knowing the time between these frames was 50 µs, the
velocity of the projectile was approximately 450 m/s as it propagated between the
proximal and distal faces. As the impact velocity was measured to be 598 m/s, the
reduction due to penetrating the proximal face was approximately 148 m/s.
Figure 49. High-speed photography of a projectile impact with the empty single layer
pyramidal lattice (system 1). Each figure (a)-(h) depicts a frame of the high-speed
photography. The time in microseconds (μs) is labeled from the initial impact of the
projectile with the proximal facesheet.
As indicated in Figure 49, the projectile impacted at a node-facesheet contact. There was
no observable deflection of the projectile and no core compression could be detected.
82
The lack of core compression in the ballistic experiments is considerably different than
that observed in beams [31,32] and plates [33,34] with pyramidal lattice cores, which
were loaded with metal foam projectiles. Figure 50 shows the position of the projectile
from the proximal facesheet as a function of time. As described in Chapter 5.1, the error
bars for the graph are smaller than the plotted data points.
Figure 50. Position of a spherical projectile from the proximal facesheet of the empty
single layer pyramidal lattice truss as a function of time. To the left of the time of impact
is before the impact of the projectile and the right of the time of impact is after impact of
the projectile.
8.2.2 Soft Polymer Filled System
Figure 51 shows the cross section of the single layer pyramidal truss lattice filled with PU
1 before and after impact with a spherical projectile whose contact velocity was 616 m/s.
83
Figure 51. Test 2: a) Cross section of the single layer pyramidal truss lattice filled with
PU 1 b) Cross section of the single layer pyramidal truss lattice filled with PU 1 after a
projectile impact of 616 m/s. Notice the brass breech rupture disk (b) remaining in the
polymer while the projectiles path resealed.
Examination after impact showed an entry hole on the proximal facesheet 12 mm in
diameter and deflected 2 mm. The exit hole on the distal facesheet measured 15 mm in
diameter and deflected 12 mm. Displaying less deflection of the proximal facesheet than
the empty pyramidal lattice truss system indicates that the polymer constrained the
movement of the structure. Approximately equal deflections and exit holes of the distal
facesheets, with system 1, indicate similar exit velocities.
A remnant of the brass breech rupture disk impacted the specimen also but did not
penetrate the PU 1. The PU 1 resealed the remainder of the void space from the
84
projectiles penetration. These results further corroborated the data obtained in Chapter 6
which showed a penetration at approximately 600 m/s and a resealing of the projectile
path.
8.2.3 Double Layer Filled with PU 1
The projectile impacted the double layer pyramidal truss lattice filled with PU 1 at 613
m/s. Figure 52 shows cross sections before testing (a), and after impact (b).
Figure 52. Test 7: a) Cross section of the double layer pyramidal truss lattice filled with
PU 1 b) Cross section of the double layer pyramidal truss lattice filled with PU 1 after an
impact of 613 m/s.
Examination after impact showed an entry hole 12 mm in diameter and a deflection of 2
mm. The exit hole was 16 mm in diameter and a deflection of 14 mm. The soft polymer,
85
at its apex, was displaced 5 mm. On the proximal facesheet, nodal failure was limited to
the adjacent cells. On the distal facesheet, nodal failure extended to a radius of two to
three cells in all directions. Differing from the other soft polymer infiltrations, only
partial resealing of the PU 1 occurred due to the smaller dimensions of the cell size.
Reducing the pyramidal unit cell size did not seem to improve ballistic efficiency given
that penetration still occurred and approximately the same degree of deformation on the
distal facesheet was exhibited.
8.2.4 Hard Polymer Filled System
The projectile impacted the single layer pyramidal truss lattice filled with PU 2 at 632
m/s. Figure 53 shows cross sections before testing (a), and after impact (b).
Figure 53. Test 4: a) Cross section of the single layer pyramidal truss lattice filled with
PU 2 b) Cross section of the single layer pyramidal truss lattice filled with PU 2 after a
projectile impact of 632 m/s showing approximately 8.5 mm deflection of the rear face
panel. Note that the projectile is visibly arrested in (b).
86
Examination after impact showed the entry hole 12 mm in diameter and deflected by 1
mm, similar in performance to the soft polymer filled system. The rear facesheet was
deflected by 8.5 mm and arrested the projectile. The projectile itself was intact with
gashes equal in thickness to the trusses, shown in Figure 53 (b). Nodal failure occurred
in multiple cells, including the impacted and adjacent cells.
X-ray tomography was performed on this test specimen 4. Figure 54 depicts the sample
after projectile impact.
Figure 54. X-ray tomography of specimen 4. Side profile (Left). Elevated view above
proximal face sheet (Right).
The x-ray tomography reveals one of the pyramidal trusses severed and plastically
deformed, without fragmentation. The projectile penetrated the PU 2/rear facesheet
interface and the rear facesheet, in conjunction with complete nodal failure, absorbed the
remaining kinetic energy.
87
8.2.5 Single layer filled with PU 1 plus Fabric
The projectile impacted the single layer pyramidal truss lattice filled with fabric and PU 1
at 613 m/s. Figure 55 shows cross sections before testing (a), and after impact (b).
Figure 55. Test 5: a) Cross section of the single layer pyramidal truss lattice filled with
the interwoven fabric and the PU 1 b) Cross section of the single layer pyramidal truss
lattice filled with interwoven fabric and the PU 1 after a projectile impact of 613 m/s.
Examination after impact showed the entry hole 12 mm and deflected 2 mm. The exit
hole was 12 mm in diameter and deflected 8 mm. Similar to the single layer pyramidal
truss lattice filled with PU 1 only, the PU 1 resealed the void space left by the projectile.
Additionally, there was complete nodal failure of the proximal facesheet but only partial
nodal failure on the distal facesheet, limited to the impact cell. The addition of the fabric
to the soft filled polymer system did alter its performance.
88
8.2.6 Ceramic plus PU 2 Filled System
The projectile impacted the single layer pyramidal truss lattice filled with fabric and PU 1
at 613 m/s. Figure 56 shows cross sections before testing (a), and after impact (b).
Figure 56. Test 6: a) Cross section of the single layer pyramidal truss lattice filled with
304 stainless steel prisms and PU 2 b) Cross section of the single layer pyramidal truss
lattice filled with 304 stainless steel prisms and PU 2 after an impact of 613 m/s.
Examination after impact showed the entry hole 12 mm in diameter and deflected by 3
mm. The projectile was arrested and fractured, as seen in Figure 56 (b), by the center 304
stainless steel tube containing the alumina. The tube was breeched and the alumina was
fragmented. Damage was limited to the center tube with minimal fracturing of the
surrounding hard polymer.
There was no observable nodal disbonding.
The rear
facesheet was deflected by 3.5 mm, absorbing the remaining impact energy.
Due to the large amount of 304 stainless steel in the specimen, an accurate x-ray
tomographical analysis was unable to be performed.
89
8.3
Discussion
The empty pyramidal lattice truss structure did not prevent the penetration of the
projectile as expected from results obtained in Chapter 5. A fraction of the kinetic
energy was absorbed in the plastic deformation of the trusses and the petaling of the face
sheets, accounting for approximately a 25% reduction of the incoming velocity. There
appeared to be no observable deflection of the projectile by the truss as previously
theorized.
The sample infiltrated with polyurethane, designated PU 2, was the only one of the four
infiltrated with polymer, three single layer and one double layer, that successfully
defeated the projectile.
The possibility exists that the high tensile modulus and/or
strength of the PU 2 facilitated the prevention of penetration. Additionally, the failure of
all contact nodes with the rear face sheet may have also provided the necessary
absorption of energy to prevent the projectile from penetrating and only deflecting the
rear face sheet approximately 8.5 mm. All three samples infiltrated with PU 1 failed to
prevent penetration of the projectile. A double layer pyramidal truss lattice with PU 1
infiltrated in the structure seems to offer no advantage to ballistic performance. Reducing
the cell size and increasing the amount of layers offered an increased probability of an
interaction with a truss thus deflecting the projectile but the evidence did not substantiate
this assertion. As with the single layered samples, the PU 1 contributed minimally to the
ballistic performance of the sample. Serendipitously, the elastomeric properties of PU 1
provided a unique side effect, a resealing of the projectiles path through the sample.
Further studies could exploit this effect for maritime armoring.
The addition of the ballistic fabric to the PU 1 system had no observable effect. This can
most likely be attributed to the constraint of the fabric by the PU 1. A composite and/or
ballistic fiber will absorb higher energy by either breaking a larger number of fibers or
involving a larger area/volume of fibers. However, the fiber cannot fulfill its highest
capability because of the constraints imposed by the matrix. Essentially, only a portion
of the fibers is plastically deformed and fractured; a large portion of the fibers is not
90
stressed to their ultimate capability [113]. Penetration of the sample occurred with no
deflection of the projectile.
The sample containing the metal encased Al2O3 prisms was not penetrated by the
projectile. Possessing the highest areal density, it outperformed all of the samples within
the study by resisting penetration and having the smallest deflection of the distal
facesheet. Not unexpected, the Al2O3 prisms were designed for ballistic impact and
encasing them within 304 stainless steel prisms confined the fragmented ceramic pieces
thus providing further resistance to penetration. Although an interior analysis of the
sample was not conducted due to technical constraints, physical observation of the cross
section revealed that the projectile breached the metal tubing and fractured the encased
alumina. Also, the projectile fractured and remnants were visible in the cross sectioned
sample. Plastic deformation was restricted by the back mounting, a 60 mm diameter
circle cut from a sheet, thus allowing a permanent plastic deflection of 3.5 mm.
91
Chapter 9
Discussion
Distributing the mass into the trusses and separate facesheets did not change the critical
velocity of the 304 stainless steel system. The 304 stainless steel lattice truss system and
the 304 stainless steel plate both had approximately equal critical velocities of 450 m/s
based upon an extrapolation of the ballistic data. As the velocity was increased beyond
the critical velocity, the sandwich structure exhibited superior performance to the plate by
reducing the exit velocity to 55-70% of the impact velocity compared to the plate of 6770%. In the solid plate, the energy was absorbed through the dishing and bulging of the
solid plate, with shear bands being created during the impact process. In the sandwich
structure, the energy was absorbed through the dishing and bulging of the proximal
facesheet, debonding of the truss-facesheet node, plastic deformation and bending of the
trusses and minor petaling of the distal facesheet.
At velocities significantly higher than the critical velocity (i.e. three times), the lattice
truss system displayed an approximate 12% reduction in the exit velocity of the projectile
and/or its fragments. As the projectile velocity increased, the failure mechanisms of the
target altered. In the solid plate, dishing and bulging diminished, eliminating large shear
band zones, and larger degrees of ductile hole enlargement began to dominate. In the
lattice truss system, the proximal facesheet exhibited a similar transition between bulging
and dishing to ductile hole enlargement. Additionally, a large degree of petaling still
occurred on the distal facesheet but the size of the petals increased beyond the impacted
unit cell thus causing further plastic deformation to the surrounding trusses still attached
to the petals. This additional deformation could possibly explain the slight improvement
of ballistic resistance for the lattice truss system compared to the solid plate.
By comparing equivalent lattice truss systems composed of 304 stainless steel and age
hardened 6061 aluminum alloy, we were able to gain an insight as to the role of the base
metal’s effectiveness in ballistic resistance. These two systems were chosen due to their
varied mechanical properties and their differing areal densities, 304 stainless steel truss
92
lattice panels having an areal density of 28 kg/m2 and AA6061 being 10 kg/m2. Although
the critical velocity of AA6061 could not be ascertained directly due to technical
constraints, it was linearly extrapolated to be approximately 60 m/s. By dividing the
critical velocity of the system by the areal density, we can directly compare the systems.
This normalization yields AA6061 being approximately 6 m3/kg·s compared to the 304
stainless steel being approximately 16 m3/kg·s. The higher the normalized velocity
indicates greater ballistic resistance efficiency. Also, the AA6061 system exhibited
similar failure mechanisms and similar transitions between mechanisms as the 304
stainless steel lattice truss system. The noticeable difference was the AA6061 petals
formed at high velocities were considerably smaller. The lower performance of the
ballistic resistance of the AA6061 compared to the 304 stainless steel can be attributed to
the significantly lower work hardening rate, lower ductility and lower density of the
former.
The lower work hardening rate decreases the amount of energy dissipated
through plastic deformation and therefore less bulging and dishing. Also, the lower
density reduced the amount of energy absorbed through the momentum transfer of the
projectile to the structure. The combination of these factors allowed fracture to initiate
earlier and less energy to be absorbed causing penetration at lower speeds and higher exit
velocities.
The addition of the low Tg elastomer (PU 1) to the 304 stainless steel truss lattice system
marginally increased the first penetrated sample impact velocity by approximately 10%
(from 481.3 m/s to 530.4 m/s) and reduced the slope of the linear fit to the exit velocity
by approximately 13%.
This additional energy being absorbed can most likely be
attributed to the associated strain fields dissipating energy as the polymer was transiently
displaced outward from the projectile. The critical velocity was similar to the empty
truss lattice sandwich structure of approximately 450 m/s.
Another consideration for the improvement in ballistic efficiency was the physical
constraint of the trusses by the surrounding polymer and the energy absorbed through
frictional dissipation by the trusses as they were plastically deformed from impact. A
possible improvement in ballistic performance might have been attained if there was
93
greater adhesion between the facesheet-PU 1 interfaces. The elastomeric properties of
PU 1, in addition with high velocities generating highly localized heat, possibly account
for the resealing of the projectile path through test samples. Similar failure mechanisms
and trends were exhibited between the empty truss lattice system and the PU 1 infiltrated
system with only one minor difference; the PU 1 physically restricted the proximal
facesheet from bulging and dishing. The PU 1 infiltrated system exhibited the same
progression to larger degrees of ductile hole enlargement on the proximal facesheet and
larger degrees of petaling on the distal facesheet as the impact velocity of the projectile
increased.
With the 304 stainless steel empty truss lattice system possessing an areal density of 28
kg/m2 and the 304 stainless steel truss lattice infiltrated with PU 1 possessing an areal
density of 54 kg/m2, normalizing the PU 1 infiltrated system yields 8 m3/kg·s compared
to the empty truss lattice sandwich structure of 16 m3/kg·s (both systems having a critical
velocity of 450 m/s). Therefore, accounting for areal density, the 304 stainless steel
system has a higher ballistic efficiency than the PU 1 infiltrated system. The infiltration
of polymers is only beneficial if their application exploits some other feature such as
damping, leak plugging, thermal insulation, etc.
The study investigating various hybrid truss lattice systems displayed some insight into
the importance of polymer selection, in addition to other infiltrated materials. The
sample infiltrated with PU 2 was the only one of the four infiltrated with polymer, three
single layer and one double layer, that successfully defeated the projectile. The Tg of PU
2 was above room temperature therefore at ambient temperature (i.e. test conditions) the
polyurethane was hard and brittle. Because of the differences in Tg, the possibility exists
that the high tensile modulus and/or strength of the PU 2 facilitated the prevention of
penetration as compared to the PU 1. This claim is substantiated by the fact that the
temperature range over which the glass transition takes place is much larger with PU 2
than with PU 1, as can be seen from Figure 12 and Figure 42. This probably indicates
that PU 2 has a greater molecular weight distribution and is more cross-linked and/or
crystalline than PU 1 [104,105]. Additionally, the failure of all contact nodes with the
94
rear face sheet may have also provided the necessary absorption of energy to prevent the
projectile from penetrating and only deflecting the rear face sheet approximately 8.5 mm.
A double layer pyramidal truss lattice with PU 1 infiltrated in the structure seems to offer
no advantage to ballistic performance. Reducing the cell size and increasing the amount
of layers offered an increased probability of an interaction with a truss thus deflecting the
projectile but the evidence did not substantiate this assertion. As with the single layered
samples, the PU 1 contributed minimally to the ballistic performance of the sample.
Increasing the projectile diameter to cell size ratio above 0.5 could possibly alter the
intensity and extent of the damage zone. Further study is necessary to ascertain the
relationship between the projectile diameter and cell size ratio to damage and/or
penetration.
It was anticipated that the addition of a ballistic fabric would delocalize the impact zone
and lessen the degree of deformation by spreading it over a larger area. Unfortunately,
the addition of the ballistic fabric to the PU 1 system had no observable effect.
Penetration of the sample occurred with no deflection of the projectile. By containing the
ballistic fabric within the PU 1 system, it was unable to bend and flex freely thus
inhibiting it from absorbing the incoming energy of the projectile/fragments over a large
area. To properly utilize the ballistic fabric in future studies, it would be beneficial to
place the fabric on the distal side outside of the structure. In this situation, structural and
projectile fragments would eject out of the structure and the fabric would be free to
absorb energy without constraint.
Additionally, a weak adhesion between the
fabric/metal interface would allow the fabric to disbond upon structural failure.
The sample containing the metal encased Al2O3 prisms was not penetrated by the
projectile.
Possessing the highest areal density of approximately 105 kg/m2, it
outperformed all of the samples within the hybrid study by resisting penetration and
having the smallest deflection of the distal facesheet. Not unexpected, the Al2O3 prisms
were designed for ballistic impact and encasing them within 304 stainless steel prisms
confined the fragmented ceramic pieces thus providing further resistance to penetration.
Although an interior analysis of the sample was not conducted due to technical
95
constraints, physical observation of the cross section revealed that the projectile breached
the metal tubing and fractured the encased alumina. Also, the projectile fractured and
remnants were visible in the cross sectioned sample, Figure 56. The elastic bending of
the samples motion was restricted by the back mounting, a 60 mm diameter circle cut
from a sheet, thus allowing a permanent plastic deflection of 3.5 mm. With only one data
point for this system, we are unable to linearly extrapolate a critical velocity to obtain a
direct comparison between other systems. Further studies will have to be conducted to
evaluate its ballistic efficiency, incorporating its high areal density.
96
Chapter 10
Conclusions
This thesis attempted to experimentally investigate the ballistic response of stainless steel
and 6061 aluminum alloy pyramidal lattice truss core sandwich structures using spherical
projectiles with impact velocities up to approximately 1200 m/s. We compared the
stainless steel sandwich panel structures response to that of a monolithic plate of
equivalent areal density (mass per unit area).
We then explore the effect of filling the
lattice void space with an elastomer. Finally, we investigate the feasibility of fabricating
more sophisticated “hybrid” sandwich structures containing ceramics and ballistic fabrics
and find significantly enhanced ballistic resistance can be achieved by this approach.
•
The failure mechanisms for the 304 stainless steel monolithic plate and the truss
lattice system transitioned as impact velocity increased. In the solid plate, dishing
and bulging diminished, while ductile hole enlargement began to dominate. In the
truss lattice, a similar transition occurred for the proximal facesheet and the
degree/size of the petaling on the distal facesheet increased.
•
The 304 stainless steel monolithic plate and the truss lattice system both had
similar extrapolated critical velocities but as impact velocity increased, the truss
lattice exhibited better ballistic performance by reducing to the exit velocity of the
projectile from 55-70% of impact velocity rather than 67-70%.
•
The 304 stainless steel truss lattice and the age hardened 6061 aluminum alloy
truss lattice exhibited similar failure mechanisms and transitions with varying
degrees, ductile hole enlargement and petaling.
•
The 304 stainless steel truss lattice system has a better ballistic efficiency than the
age hardened 6061 aluminum alloy truss lattice system based on the normalized
critical velocities of 16 m3/kg·s and 6 m3/kg·s, respectively.
•
The failure mechanisms for the 304 stainless steel empty truss lattice and the PU 1
infiltrated truss lattice system are similar, ductile hole enlargement and petaling,
except for the PU 1 physically restricted the proximal facesheet from bulging and
dishing.
97
•
The 304 stainless steel truss lattice has a better ballistic efficiency than the PU 1
infiltrated into the 304 stainless steel truss lattice system based on the normalized,
first penetrated sample impact velocities of 16 m3/kg·s and 10 m3/kg·s,
respectively.
•
PU 2 outperformed PU 1 by preventing penetration at an approximate velocity of
600 m/s which can possibly be attributed to either and/or both: the PU 2 has a
high tensile modulus and strength compared to the PU 1, the PU 2 has a storage
modulus of approximately 100 times than PU 1.
•
Decreasing cell size and increasing the amount of pyramidal truss lattice layers in
the 304 stainless steel system did not prevent penetration indicated by a single
data point.
•
The addition of a ballistic fabric into the PU 1 infiltrated truss lattice system did
not prevent penetration indicated by a single data point.
•
The addition of metal encased Al2O3 tubes into 304 stainless steel truss lattice
system prevented penetration in a single data point but at a cost of increasing the
areal density from 28 kg/m2 to 105 kg/m2.
98
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