Note: Descriptions are shown in the official language in which they were submitted.
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FABRICATION AND DESIGN OF COMPOSITES WITH ARCHITECTED LAYERS
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of and priority to U.S.
Provisional Patent
Application No. 62/593,768, filed December 1,2017 and U.S. Patent Application
16/151,186, filed October 3, 2018, all of which are hereby incorporated by
reference in
their entirety to the extent not inconsistent herewith.
STATEMENT REGARDING FEDERALLY SPONSORED
RESEARCH OR DEVELOPMENT
[0002] This invention was made with government support under Grant No.
N00014-
16-1-2431 and Grant No. N00014-16-1-2827 awarded by the Office of Naval
Research.
The government has certain rights in the invention.
BACKGROUND OF INVENTION
[0003] The present invention relates to composite material systems,
methods of
making such composite material systems, which include a structure having an
architected and monolithic three-dimensional geometry and a matrix phase. For
example, the three-dimensional geometry may include a continuous and
interconnected
network of features having any variety of shapes or configurations, including
curved and
surface features, while the matrix phase may at least partially infiltrate the
structure.
[0004] Composite materials are comprised of one or more materials which
form
.. disordered or ordered phases and combine to provide for properties or
behavior which
may be different from that of the individual materials. Usually these phases
are
classified as reinforcement phases, with high stiffness or strength
properties; or matrix
phases, which fill the remaining volume and possess inferior stiffness or
strength
properties. A composite can be broadly characterized by the volume ratio
between the
reinforcing and matrix phases, the geometry of the phases, and the
constitutive
properties of each phasel.
[0005] Composite materials with disordered phases may include short
fibers,
particles, or randomly assorted components, which do not yield a continuous
reinforcing
phase. In these materials, the only continuous phase is the matrix, which
infiltrates the
remaining volume around the reinforcement particles. The matrix phase serves
to
distribute the load between the stiffer/stronger reinforcement particles.
Alternatively,
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ordered-phase composite materials may include aligned long fibers
(discontinuous
phase) or even truss-like (continuous phase) geometries as the reinforcing
phase, which
are surrounded by a continuous matrix phase. Both ordered and unordered
composite
materials can have a mechanical response that varies from isotropic (i.e.,
behavior
.. independent of the probing direction) to anisotropic (i.e., behavior
dependent on material
orientation).
[0006] Carbon fiber composites are a form of ordered-phase composites
that have
been applied in aerospace, automotive, marine, armor, and even sporting-
equipment
applications. Their wide-spread use relies on their high stiffness-to-density
ratio, fatigue
properties, and resistance to extreme environments2. The fundamental building-
blocks
of a carbon fiber composite are the fibers, which compose the ordered
reinforcing phase
that is not continuous¨the discrete fibers are only coupled through the matrix
phase. An
arrangement of fibers impregnated by a matrix phase form a two-dimensional sub-
component of a carbon composite part; the lamina.
[0007] Discontinuity and anisotropy of the carbon phase in carbon fiber
composites is
associated with several modes of failure. To reduce the anisotropy, woven-
fiber laminae
have been made which increase contact between discrete fibers of a lamina3,
albeit
forming a reinforcing phase that is still discontinuous. Isotropy can be
attained with
unidirectional fiber laminae by forming a laminate; a collection of laminae of
varying fiber
orientations that are bonded through a matrix phase. Modifying the orientation
of the
fibers in each lamina will determine the degree of anisotropy of the laminate
as well as
the (commonly undesired) stretching-bending coupling. Due to their
construction, carbon
fiber laminates can fail through a variety of mechanisms that include fiber
buckling (in
compression), interfiber failure, and interlaminar failure. Fiber buckling is
preeminent in
compression loading of a lamina due to the high slenderness of the fibers in
the matrix,
which are otherwise unsupported in-plane. Interfiber and interlaminar failure
occurs due
to the discontinuous nature of the reinforcing phase, which relies on the
matrix phase to
distribute load both through-thickness and in-plane.
[0008] Composite materials with continuous reinforcing and matrix phases
have
been reported, the majority of which have a foam as the reinforcing pha5e5-9.
Foams are
exemplary stochastic structures, in direct contrast to deterministic
structure. Attempts at
fixing the discontinuous nature of carbon fibers include adding phases
composed of
particles, such as carbon nanotubes, to promote adhesion between fiber-matrix
and
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interlaminar interfaces10,11. While this approach may increase the strength of
these
materials, the particles do not form a continuous carbon phase, which still
results in
failure between laminae (the weakest interface). Other works report ordered
truss-like
networks as the reinforcing phase with the use of polymer waveguide processes.
The
geometry of these truss-like networks is limited to straight ray patterns that
commence
at a material edge, and a finite range of angles between connecting truss
elements12.
Functional grading of composites through these waveguide processes is subject
to the
same constraints, while decreasing the structural integrity of the reinforcing
phase13,14.
Damping materials have been reported using these waveguide patterns, requiring
one
or more viscoelastic phases as coatings to dissipate energy15,16.
[0009] In a few cases, fabrication of 3D carbon structures that are not
limited to
architectures defined by polymer waveguides has been demonstrated using
additive
manufacturing (AM) of polymer samples. Glassy carbon nanostructures with close
to
theoretical strength have been fabricated using two-photon lithography (TPL),
a process
that suffers from extremely low throughput, limiting its practical
applications17. Cellular
carbon microstructures have been produced using stereolithography (SL)18 and
printing
of graphene aer0ge1519. However, each of these lithographic structures suffer
from a
variety of disadvantages, such as failing to provide for a direct fabrication
of composite
parts with the net shape defined by a 3D carbon network, functional grading,
damping
properties, impact absorption properties, or tunability of these or other
properties.
[0010] The composite material systems, and methods of making the
systems,
provided here address these and other challenges associated with conventional
composite materials, thereby providing systems and methods that are highly
tunable for
a wide array of applications and parameter-space requirements.
SUMMARY OF THE INVENTION
[0011] Provided herein are composite material systems and methods for
making
composite material systems useful for a wide array of applications, and which
address
challenges and limitations of conventional systems and methods. Applications
for which
these systems are useful include, but certainly are not limited to, aerospace
(e.g.,
landing gear shock absorption), automotive (e.g., brake assembly vibration
mitigation),
medicine (e.g., medical devices requiring particular mechanical properties),
military (e.g,
body armor), marine devices, and sporting-equipment. For example, the systems
disclosed herein are useful for impact energy mitigation and/or vibration
damping. The
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disclosed systems and methods are highly tunable and deterministic, such that
they
may be adapted and tuned according to a desired application and set of
properties. For
example, the composite material systems disclosed herein may include
functional
grading via a plurality of three-dimensional geometries continuously
interconnected
together. For example, the composite material systems may include highly
tunable and
deterministic resonator features which provide for precise control and
tunability of
damping behavior of the composite material system.
[0012] In an aspect, a composite material system comprises: a structure
having an
architected three-dimensional geometry; wherein said three-dimensional
geometry is
monolithic and deterministic; and a matrix phase; wherein said matrix phase at
least
partially infiltrates said structure. In some embodiments, the three-
dimensional geometry
is a nano- or micro- architected three-dimensional geometry. In some
embodiments, the
structure is at least 1%, at least 2%, at least 5%, at least 10%, at least
15%, at least
20%, at least 30%, at least 50%, at least 75%, at least 90%, or preferably for
some
applications substantially 100% by-volume (vol.%) infiltrated by the matrix
phase. In
some embodiments, the structure is at least 1%, at least 2%, at least 5%, at
least 10%,
at least 15%, at least 20%, at least 30%, at least 50%, at least 75%, at least
90%, or
preferably for some applications substantially 100% by-mass (mass%)
infiltrated by the
matrix phase.
[0013] The composite material systems, structures, and/or three-dimensional
geometries disclosed herein may have a variety of physical and mechanical
properties
or embodiments, including impacting absorption and/or damping behavior,
unobtainable
or otherwise difficult to obtain in conventional material systems.
[0014] In some embodiments of the systems and methods disclosed herein,
the
structure, the composite material system, or both, is characterized by an area-
normalized impact energy mitigation metric (qJ) selected from the range of
2x104J/m2 to
4x105J/m2. In some embodiments of the systems and methods disclosed herein,
the
structure, the composite material system, or both, is by an area-normalized
impact
energy mitigation metric (qJ) that is at least 2x104J/m2, optionally at least
2.6x105J/m2,
or preferably for some applications at least 3.2x105J/m2. In some embodiments
of the
systems and methods disclosed herein, the structure, the composite material
system, or
both, is characterized by a density-normalized impact energy mitigation metric
(qJ)
selected from the range of 1.9x106 J/kg to 4x106 J/kg. In some embodiments of
the
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systems and methods disclosed herein, the structure, the composite material
system, or
both, is characterized by a density-normalized impact energy mitigation metric
(qJ)
selected from the range of 1.9x106 J/kg to 3.2x106J/kg, preferably for some
applications
selected from the range of 1x106J/kg to 5x106J/kg, preferably for some
applications
selected from the range of 1x106J/kg to 1x107J/kg, and optionally for some
applications
selected from the range of 3x106J/kg to 1x107J/kg. In some embodiments of the
systems and methods disclosed herein, the structure, the composite material
system, or
both, is characterized by mitigation of impact energy having energy selected
from the
range of 1 J to at least 900 J.
[0015] In some embodiments of the systems and methods disclosed herein, the
structure, the composite material system, or both, is characterized by a
restitution
coefficient that is selected from the range of 0.8 to 0.7. In some embodiments
of the
systems and methods disclosed herein, the structure, the composite material
system, or
both, is characterized by a restitution coefficient that is selected from the
range of 0.8 to
0.3. In some embodiments of the systems and methods disclosed herein, the
restitution
coefficient is determined when a particle is accelerated at said structure,
said particle
having a diameter that is at least 10-times greater than a physical dimension
of a unit
cell of the structure, optionally the particle size is 7 pm to 14 pm, and said
particle
having a velocity selected from the range of 500 m/s to 1100 m/s. In some
embodiments
of the systems and methods disclosed herein, the restitution coefficient
corresponds to a
structure having a relative density selected from the range of 8% to 26%.
[0016] In some embodiments of the systems and methods disclosed herein,
the
composite material system is configured to absorb impact energy substantially
via said
structure. In an embodiment, the composite material system absorbs at least
20% more
impact energy than absorbed by the structure alone under otherwise identical
conditions.
[0017] In some embodiments of the systems and methods disclosed herein,
the
structure, the composite material system, or both, is characterized by at
least one
vibrational frequency band gap. In some embodiments of the systems and methods
disclosed herein, the at least one vibrational frequency band gap is at least
one
complete vibrational frequency band gap. In some embodiments of the systems
and
methods disclosed herein, at least one vibrational frequency band gap is at
least one
partial vibrational frequency band gap. In some embodiments of the systems and
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methods disclosed herein, the structure, the composite material system, or
both, is
characterized by at least one partial vibrational frequency band gap and at
least one at
least one complete vibrational frequency band gap. In some embodiments of the
systems and methods disclosed herein, the at least one vibrational frequency
band gap
is deterministic. In some embodiments of the systems and methods disclosed
herein,
the at least one vibrational frequency band gap is within the range of 0.1 MHz
to 100
MHz, preferably for some applications within the range of 0.1 MHz to 200 MHz.
In some
embodiments of the systems and methods disclosed herein, the at least one
vibrational
frequency band gap is at least one of 52 MHz to 55 MHz, 19-26 MHz, 14-21 MHz,
46-52
MHz, 1.4 MHz to 1.5 MHz, or 2.4 0.1 MHz. In some embodiments of the systems
and
methods disclosed herein, the at least one vibrational frequency band gap
corresponds
to the structure being exposed to a continuous vibration, a pulsed vibration,
or a
combination of these. In some embodiments of the systems and methods disclosed
herein, the at least one vibrational frequency band gap is characterized by a
width
.. selected from the range of 0.1 to 200 MHz, optionally for some applications
0.1 to 100
MHz, optionally for some applications 100 Hz to 10 MHz, optionally for some
applications 0.1 to 20 MHz, preferably for some applications 0.1 to 10 MHz,
optionally
for some applications 0.1 to 5 MHz, or preferably for some applications 0.1 to
1 Hz. For
example, at least one vibrational frequency band gap corresponds to
frequencies
relevant to ultrasonic frequencies for medical applications. Broad vibrational
frequency
band gap widths (e.g., 200 MHz) may be beneficial for dissipating a wide range
of
stimuli/vibrations for various applications. Narrow vibrational frequency band
gap widths
(e.g., 1 MHz) may be beneficial for filtering certain stimuli/vibrations for
various
applications. In some embodiments, the composite material system includes
broad,
narrow, or both broad and narrow vibrational frequency band gap(s). It is also
noted that
vibrational frequency band gap (e.g., width thereof) may scale linearly with
the
characteristic length in the architecture, because the Bragg condition states
that
significant effects might occur at frequencies where AL = c/f, where AL is the
characteristic dimension of the microstructure, c is the speed of sound in the
material,
and f is the frequency. In some embodiments of the systems and methods
disclosed
herein, the structure, the composite material system, or both, is
characterized by a
damping ratio of at least 1.2%, preferably at least 3.5%, more preferably at
least 7%,
and still more preferably at least 9%. In some embodiments of the systems and
methods
disclosed herein, the structure, the composite material system, or both, is
characterized
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by a damping ratio of at least 1.2% to 3.5% in a longitudinal direction. In
some
embodiments of the systems and methods disclosed herein, the structure, the
composite material system, or both, is characterized by a damping ratio of at
least 7% to
9% in a transverse direction. In an embodiment, damping ratio corresponds to
the ratio
between energy dissipated in a cycle and the maximum energy stored in the
cycle.
[0018] In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry comprises at least one surface feature. Exemplary
surface
features include, but are not limited to, sheets, surfaces, hollow spheres,
hollow ellipses,
and shells. In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry comprises at least one surface feature, wherein at
least a
portion of said at least one surface feature is characterized by a non-zero
Gaussian
curvature. In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry comprises at least one surface feature, wherein at
least a
portion of said at least one surface feature is characterized by a non-zero
mean
curvature. In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry comprises at least one surface feature, wherein at
least a
portion of said at least one surface feature is characterized by a zero mean
curvature. In
some embodiments of the systems and methods disclosed herein, the three-
dimensional geometry comprises at least one surface feature, wherein said at
least one
.. surface feature is characterized by a non-uniform Gaussian curvature or a
non-uniform
mean curvature. In some embodiments of the systems and methods disclosed
herein,
the three-dimensional geometry comprises at least one surface feature, wherein
said at
least one surface feature is characterized by a non-uniform Gaussian
curvature. In
some embodiments of the systems and methods disclosed herein, the three-
dimensional geometry comprises at least one surface feature, wherein said at
least one
surface feature is characterized by a non-uniform mean curvature. In some
embodiments of the systems and methods disclosed herein, the three-dimensional
geometry comprises at least one surface feature, wherein said at least one
surface
feature is characterized by a uniform Gaussian curvature or a uniform mean
curvature.
In some embodiments of the systems and methods disclosed herein, the three-
dimensional geometry comprises at least one surface feature, wherein said at
least one
surface feature is characterized by a uniform Gaussian curvature. In some
embodiments
of the systems and methods disclosed herein, the three-dimensional geometry
comprises at least one surface feature, wherein said at least one surface
feature is
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characterized by a uniform mean curvature. In some embodiments of the systems
and
methods disclosed herein, the three-dimensional geometry comprises at least
one
surface feature, wherein a thickness dimension of said at least one surface
feature is
non-uniform throughout said at least one surface feature. In some embodiments
of the
systems and methods disclosed herein, the three-dimensional geometry comprises
at
least one surface feature, wherein a thickness dimension of said at least one
surface
feature is uniform throughout said at least one surface feature.
[0019] In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry is characterized as a spinodal geometry. In some
embodiments of the systems and methods disclosed herein, the structure is
characterized by a slope of normalized effective elastic modulus versus
relative density
that is selected from the range of 1 to 1.3, optionally 1 to 1.5, or
optionally 1 to 1.35.
[0020] In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry comprises a resonator. In some embodiments of the
.. systems and methods disclosed herein, the three-dimensional geometry is
characterized by a unit cell geometry, said unit cell geometry comprising a
resonator. In
some embodiments of the systems and methods disclosed herein, the resonator
comprises a micro-inertia feature connected to at least one other feature of
said three-
dimensional geometry. In some embodiments of the systems and methods disclosed
.. herein, the resonator comprises a micro-inertia feature, and wherein
another feature of
said three-dimensional geometry comprises said micro-inertia feature. In some
embodiments of the systems and methods disclosed herein, the resonator
comprises a
cantilever beam feature and a micro-inertia feature connected to an end of
said
cantilever beam feature. For example, a micro-inertia feature may be embedded
within
another feature, such as a structural member, such as a beam or a surface. For
example, a micro-inertia may be at nodes of a beam structure or at the hinges
of a
surface-based geometry.
[0021] In some embodiments of the systems and methods disclosed herein,
the
structure is characterized by deterministic anisotropic impact energy
absorption, for
example having impact energy absorption, or an impact energy absorption
metric, such
as restitution coefficient, at least 1% greater, at least 20% greater, at
least 100%
greater, preferably for some applications at least 1000% greater, or still
more preferably
for some applications at least 10000% greater along a first direction (e.g.,
X, Y, Z, or any
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direction or vector in between) than along a second direction. In some
embodiments of
the systems and methods disclosed herein, the structure is characterized by
deterministic anisotropic elasticity, for example having elasticity at least
1% greater, at
least 20% greater, at least 100% greater, preferably for some applications at
least
.. 1000% greater, or still more preferably for some applications at least
10000% greater
along a first direction (e.g., X, Y, Z, or any direction or vector in between)
than along a
second direction. In some embodiments of the systems and methods disclosed
herein,
the structure is characterized by deterministic anisotropic damping, for
example having
damping, or a damping metric, such as damping ratio, at least 1% greater, at
least 20%
.. greater, at least 100% greater, preferably for some applications at least
1000% greater,
or still more preferably for some applications at least 10000% greater along a
first
direction (e.g., X, Y, Z, or any direction or vector in between) than along a
second
direction. For example, vibrations, such as vibrations within a particular
frequency
range, such as any frequency or range described herein, may follow along a
deterministically determined pathway or component(s) of a composite material
system,
a structure thereof, or a three-dimensional geometry thereof. In some
embodiments of
the systems and methods disclosed herein, the structure exhibits vibrational
Bragg
scattering and the structure does not exhibit vibrational local resonance. In
some
embodiments of the systems and methods disclosed herein, the structure
exhibits
.. vibrational local resonance and the structure does not exhibit vibrational
Bragg
scattering. In some embodiments of the systems and methods disclosed herein,
the
structure is characterized by deterministic isotropic impact energy
absorption. In some
embodiments of the systems and methods disclosed herein, the structure is
characterized by deterministic isotropic elasticity. In some embodiments of
the systems
and methods disclosed herein, the structure is characterized by deterministic
isotropic
damping.
[0022] The systems and methods disclosed herein are compatible with a
wide variety
of materials, or combinations of materials. The structure may be formed of any
one or
more materials compared with additive manufacturing, for example.
[0023] In some embodiments of the systems and methods disclosed herein, the
structure comprises a carbon allotrope material, a polymer, a ceramic
material, a metal
material, or any combination thereof. In some embodiments of the systems and
methods disclosed herein, the structure comprises at least one of: a carbon
allotrope
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material, a polymer, a ceramic material, or any combination thereof. In some
embodiments of the systems and methods disclosed herein, the structure
comprises
one or more carbon allotrope materials. In some embodiments of the systems and
methods disclosed herein, the structure comprises at least 50% by volume of
one or
more carbon materials. In some embodiments of the systems and methods
disclosed
herein, the structure comprises a plurality of features characterized by a
core that is at
least 50% by volume of one or more carbon materials.
[0024] In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry is a node-free geometry. In some embodiments of the
systems and methods disclosed herein, the structure comprises at least one
hollow
feature. In some embodiments of the systems and methods disclosed herein, the
structure comprises at least one feature that is at least partially hollow,
such as a hollow
truss, for example. For example, a spinodal geometry may comprise at least one
hollow
portion or feature.
[0025] In some embodiments of the systems and methods disclosed herein, the
structure is formed via additive manufacturing.
[0026] In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry comprises at least one longitudinal feature,
wherein at least
a portion of said at least one longitudinal feature is characterized by a non-
zero
curvature along a longitudinal direction of said feature. In some embodiments
of the
systems and methods disclosed herein, the three-dimensional geometry comprises
at
least one longitudinal feature, wherein said at least one longitudinal feature
is
characterized by a non-uniform curvature along a longitudinal direction of
said feature.
In some embodiments of the systems and methods disclosed herein, the three-
dimensional geometry comprises at least one longitudinal feature having at
least one
cross-sectional dimension that is non-uniform along a longitudinal direction
of said
feature. In some embodiments of the systems and methods disclosed herein, the
three-
dimensional geometry comprises at least one feature having a cross-sectional
shape
that is non-uniform. In some embodiments of the systems and methods disclosed
.. herein, the said three-dimensional geometry comprises at least one
longitudinal feature
having a longitudinal axis oriented perpendicular to a thickness direction of
said
structure. For example, a thickness direction corresponds to an axis along
which each
layer is formed in a layer-by-layer additive manufacturing process.
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[0027] In some embodiments of the systems and methods disclosed herein,
the
structure defines a three-dimensional external boundary shape; and wherein
said three-
dimensional geometry comprises at least one feature that intersects said
boundary
shape at only one or zero points of intersection.
[0028] In some embodiments of the systems and methods disclosed herein, a
three-
dimensional external boundary shape defined by said structure corresponds to a
shape
of the composite material system. In some embodiments of the systems and
methods
disclosed herein, a three-dimensional external boundary shape defined by said
structure
is hollow. For example, a three-dimensional external boundary shape defined by
said
structure may be in the form of a hollow tube, a hollow cone, a hollow
ellipse, or other
configuration.
[0029] In some embodiments of the systems and methods disclosed herein,
the
three-dimensional geometry is an overall three-dimensional geometry comprising
at
least a primary three-dimensional geometry and a secondary three-dimensional
geometry, wherein said primary and said secondary three-dimensional geometries
are
different. For example, the structure may include structural functional
grading of three-
dimensional geometries, such that the structure includes a plurality of
geometries at
least two of which are directly continuous and interconnected, and all of
which are
directly or indirectly continuous and interconnected. For example, the
structure may
include compositional functional grading. Via structural functional grading
(i.e., a plurality
of three-dimensional geometries; i.e., the three-dimensional geometry
comprises at
least a primary three-dimensional geometry and a secondary three-dimensional
geometry), the structure or composite material system may have functional
grading of
impact energy absorption behavior and/or damping behavior.
[0030] In some embodiments of the systems and methods disclosed herein, the
matrix phase comprises at least a primary matrix phase and a secondary matrix
phase.
For example, a first portion of the structure may be infiltrated by a primary
matrix phase
and a second portion of the structure may be infiltrated by a secondary matrix
phase.
The primary and secondary matrix phases may be different. For example, the
primary
and secondary matrix phases may have different compositions. For example, the
primary matrix phase may be a different polymer or resin than the second
matrix phase.
In some embodiments of the systems and methods disclosed herein, the structure
comprises a closed region that is free of said matrix phase. In some
embodiments of the
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systems and methods disclosed herein, the structure is enclosed within said
matrix
phase. In some embodiments of the systems and methods disclosed herein, the
structure is enclosed within said matrix phase such that no portion of said
structure
exists beyond external boundaries of said matrix phase.
[0031] In some embodiments of the systems and methods disclosed herein, at
least
a portion of said three-dimensional geometry is characterized as a
tetrakaidecahedron,
Weaire-Phelan geometry, honeycomb geometry, auxetic geometry, an octet-truss
geometry, an octahedron, a diamond lattice, a 3D kagome geometry, a tetragonal
geometry, a cubic geometry, a tetrahedron, a space-filling polyhedron, a
periodic
minimal surface, a triply periodic minimal surface geometry, a spinodal
geometry, a
chiral geometry, or a combination of these. In some embodiments of the systems
and
methods disclosed herein, at least a portion of said three-dimensional
geometry is
characterized as a tetrakaidecahedron, auxetic geometry, an octet-truss
geometry, an
octahedron, a diamond lattice, a 3D kagome geometry, a tetragonal geometry, a
cubic
geometry, a tetrahedron, a space-filling polyhedron, a periodic minimal
surface, a triply
periodic minimal surface geometry, a spinodal geometry, a chiral geometry, or
a
combination of these when viewing the three-dimensional geometry in a beam-
based,
shell-based, open-cell-based, or closed-cell-based representation. In some
embodiments of the systems and methods disclosed herein, at least a portion of
said
three-dimensional geometry is characterized by a beam- or shell-based
geometry;
wherein said beam- or shell-based geometry is not symmetric, is not periodic,
or is not
regularly tessellated. In some embodiments of the systems and methods
disclosed
herein, features comprise one or more of struts, beams, ties, trusses, sheets,
surfaces,
spheres, ellipses, and shells.
[0032] In some embodiments of the systems and methods disclosed herein, the
three-dimensional geometry is characterized by a plurality of features
independently
having physical dimensions independently selected to a tolerance within 100
nm. In
some embodiments of the systems and methods disclosed herein, the three-
dimensional geometry is characterized by a plurality of features independently
having
physical dimensions independently selected to a tolerance within 3 pm. In some
embodiments of the systems and methods disclosed herein, the structure is
characterized by a relative density selected from the range of 5% to 99.9%,
optionally
5% to 60%, optionally 0.1% to 60%, optionally 0.1% to 99.9%, or optionally 8%
to 30%.
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In some embodiments of the systems and methods disclosed herein, the structure
is
characterized by a relative density selected from the range of 8% to 60%. In
some
embodiments of the systems and methods disclosed herein, the structure is
characterized by a plurality of features independently having at least one
physical
dimension less than or equal to 50 pm, optionally selected from the range 100
to 200
pm. In some embodiments of the systems and methods disclosed herein, the three-
dimensional geometry is characterized by a plurality of features, wherein at
least a
portion of said features independently have one or more average cross
sectional
physical dimensions (e.g., thickness, width, diameter, etc.) selected over the
range of 50
nm to 200 m, preferably for some applications 2 nm to 200 pm, preferably for
some
applications 10 nm to 200 pm, optionally 50 pm or less, optionally 200 nm or
less, or
optionally selected from the range 100 pm to 200 pm. For example, a spinodal
geometry
may be substantially hollow including walls or shells with substantially 10 nm
thickness.
For example, the structure may comprise a hollow feature, such as a hollow
beam or
truss, having an inner diameter and an outer diameter, such that a cross-
sectional
physical dimension is a thickness¨or difference between the inner and outer
radii¨or
an overall thickness or diameter of the feature, such as a beam or truss. For
example,
an inner radius may be substantially 250 nm and an outer radius may be
substantially
900 nm. In some embodiments of the systems and methods disclosed herein, at
least a
portion of said features are characterized by one or more average longitudinal
physical
dimensions selected over the range of 10 nm to 2000 pm. In some embodiments of
the
systems and methods disclosed herein, the three-dimensional geometry is
characterized by a unit cell geometry, the unit cell having at least one
overall physical
dimension selected from the range of 10 nm to 20 pm, optionally 100 nm to 20
pm,
optionally 1 pm to 20 pm, optionally 5 pm to 20 pm, or optionally 1 pm to 200
pm. For
example, the unit cell may have a tetragonal geometry with length, width, and
thickness
of 20 pm, 20 pm, and 5 pm.
[0033] In some embodiments of the systems and methods disclosed herein,
the
composite material system comprises at least one additional phase. In some
embodiments of the systems and methods disclosed herein, an additional phase
is a
void or a region free of the structure and of the matrix phase. In some
embodiments of
the systems and methods disclosed herein, the structure, the matrix phase, or
both,
comprises adhesion-promoting additive(s). In an embodiment, adhesion-promoting
additives increase adhesion between the structure and the matrix phase
compared to
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adhesion without said additives. Additives may be present during formation of
the
structure, such as being present in a precursor material during additive
manufacturing of
the structure. Additives may be deposited onto the structure after the
structure is at least
partially formed. Additives may be introduced during infiltration of the
structure with the
matrix phase. Additives may be added to a matrix phase or matrix phase
precursor prior
to infiltration.
[0034] In some embodiments of the systems and methods disclosed herein,
the
structure is characterized by an elasticity, said elasticity of said structure
being
deterministic.
[0035] In some embodiments of the systems and methods disclosed herein, the
structure is substantially undamaged by impact from an SiO2 particle having a
diameter
selected from the range of 7 pm to 14 pm and a velocity selected from the
range of 500
m/s to 1100 m/s. In some embodiments of the systems and methods disclosed
herein,
the structure is substantially undamaged by impact from an SiO2 particle
having a
diameter that is at least one order-of-magnitude (at least 10 times) larger
than an overall
dimension of the unit cell characterizing the structure's three-dimensional
geometry.
[0036] In some embodiments of the systems and methods disclosed herein,
the
structure is characterized as having a bending-dominated mode. In some
embodiments
of the systems and methods disclosed herein, the structure is characterized as
having a
stretching-dominated mode.
[0037] In some embodiments of the systems and methods disclosed herein,
the
structure is characterized by an average specific strength (strength-to-
density ratio)
selected from the range of 0.14 to 1.90 GPa g-1 cm3. In some embodiments of
the
systems and methods disclosed herein, the structure is characterized by an
average
density selected from the range of 0.24 to 1.0 g cm-3. In some embodiments of
the
systems and methods disclosed herein, the structure is characterized by an
average
Young's modulus selected from the range of 0.16 to 18.6 GPa. In some
embodiments of
the systems and methods disclosed herein, the structure is characterized by an
average
Young's modulus selected from the range of 0.16 to 440 GPa. In some
embodiments of
the systems and methods disclosed herein, the structure is characterized by a
compressive strength selected from the range of 5 MPa to 20 GPa. In some
embodiments of the systems and methods disclosed herein, the structure is
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characterized by a strain-to-failure value of greater than or equal to 20%. In
some
embodiments of the systems and methods disclosed herein, the structure is
characterized by a strength-to-failure value of greater than or equal to 1
GPa.
[0038] In some embodiments of the systems and methods disclosed herein,
the
carbon allotrope material is selected from the groups consisting of glassy
carbon,
graphitic carbon, amorphous carbon, pyrolytic carbon, graphite, carbon black,
and any
combination thereof. In some embodiments of the systems and methods disclosed
herein, the carbon allotrope material comprises pyrolytic carbon.
[0039] In some embodiments of the systems and methods disclosed herein,
the
structure comprises a coating. In some embodiments of the systems and methods
disclosed herein, the coating comprises a metal, a ceramic, or a combination
thereof.
[0040] In some embodiments of the systems and methods disclosed herein,
the
matrix phase comprises one or more material selected from the group consisting
of a
polymer, an epoxy, a carbon allotrope, a ceramic, a metal, a viscous fluid, or
any
combination thereof.
[0041] In an aspect, a method of making a composite material system,
said method
comprising steps of: preparing a structure via an additive manufacturing
process;
wherein: said structure has an architected three-dimensional geometry; and
said three-
dimensional geometry is monolithic and deterministic; and infiltrating said
structure with
a matrix phase such that said structure is at least partially infiltrated by
said matrix
phase; thereby making said composite material system. In some embodiments, the
structure is at least 1%, at least 2%, at least 5%, at least 10%, at least
15%, at least
20%, at least 30%, at least 50%, at least 75%, at least 90%, or preferably for
some
applications substantially 100% by-volume infiltrated by the matrix phase. In
some
embodiments, the structure is at least 1%, at least 2%, at least 5%, at least
10%, at
least 15%, at least 20%, at least 30%, at least 50%, at least 75%, at least
90%, or
preferably for some applications substantially 100% by-mass infiltrated by the
matrix
phase. In some embodiments of the systems and methods disclosed herein, the
three-
dimensional geometry is a nano- or micro- architected three-dimensional
geometry. In
some embodiments, the method further comprises designing said three-
dimensional
geometry using a computer-aided design technique. In some embodiments, the
step of
designing comprises determining said three-dimensional geometry based on
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computational spinodal decomposition. In some embodiments, the step of
designing
comprises determining at least one vibrational frequency band gap of said
structure,
such that said at least one vibrational frequency band gap of said structure
is
deterministic. In some embodiments, the step of designing comprises
determining an
elasticity of said structure, such that said elasticity of said structure is
deterministic. In
some embodiments, the step of designing comprises determining a restitution
coefficient
of said structure, such that said restitution coefficient of said structure is
deterministic. In
some embodiments, the step of designing comprises determining an area-
normalized
impact energy mitigation metric (qJ) of said structure, such that said area-
normalized
.. impact energy mitigation metric (qJ) of said structure is deterministic. In
some
embodiments, the additive manufacturing process is selected from the group
consisting
of: a sterolithographic (SLA) technique; a digital light processing (DLP)
technique; a
continuous liquid interface production technique; a micro- stereolithographic
(p-SLA)
technique; a two- photon polymerization lithography technique; an interference
lithography technique; a holographic lithography technique; a stimulated
emission
depletion (STED) lithography technique; other vat photopolymerization
technique; a
material extrusion technique; a powder bed fusion technique; a material
jetting
technique; and a combination of these. In some embodiments, the additive
manufacturing process is a three-dimensional lithography technique. In some
.. embodiments, the step of preparing said structure comprises forming a three-
dimensional framework; said step of preparing further comprising treating said
three-
dimensional framework to prepare said structure; said step of treating
comprising a
pyrolysis process. In some embodiments, the method further comprises applying
a
coating on said structure. In some embodiments, the method further comprises
etching
a portion of said structure such that said structure comprises at least one
hollow feature,
at least a portion of said at least one hollow feature comprising said
coating. In some
embodiments, the step of infiltrating comprises a process selected from the
group
consisting of sonication, vacuum exposure, and any combination thereof. In
some
embodiments, the method further comprises post-treating said composite
material
system, said step of post-treating comprising a cure process. In some
embodiments, the
step of preparing comprises selecting a precursor material selected from the
group
consisting of a resin, a metal, a ceramic, a polymer, and any combination of
these. In
some embodiments, the step of preparing comprises selecting a precursor
material
selected from the group consisting of an organic resin, a hybrid organic-
inorganic resin,
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a metal, a metallic alloy, a ceramic, a polymer, and any combination of these.
Useful
organic resins include, but are not limited to, acrylic-based, thiol-based,
polyurethane-
based, and epoxy-based resins. Useful hybrid organic-inorganic resins include,
but are
not limited to, siloxanes and metal alkoxide-derived precursors, such as those
described
.. in US Patent Publication 2018/0088462, which is hereby incorporated by
reference. In
some embodiments, the precursor material further comprises additives. Useful
additives
include, but are not limited to, metal and/or ceramic particles (e.g.,
nanoparticles), other
inorganic and/or organic additives, solutions of inorganic and/or organic
materials that
either form a single phase with the resin, or suspensions and emulsions
forming a
secondary phase with the resin, inorganic particles, inorganic fibers, organic
binders,
polymer powder, metal powder, ceramic powder, metal wires (e.g., micro- or
nano-
wires), metal salt solution, metal ion solution, and any combinations of
these. For
example, precursors for extrusion techniques may include thermoplastic
polymers and
low melting point metals, with additives that include inorganic particles,
fibers, etc. For
example, material feed stocks for powder bed-based techniques may include
metal,
ceramic, and polymer powders. For example, precursor for binder jet-based
techniques
use may include these powders in combination with organic binders. For
example,
precursors for direct energy deposition techniques may include metal powders
and
metal wires. As additional examples, other feedstock/precursor materials for
additive
manufacturing techniques may include metal and ceramic nanoparticle inks for
direct ink
writing and electrohydrodynamic printing, metal and polymer sheets for
lamination-
based processes, metal salt or metal ion solutions for electroplating-based
and
photoreduction-based methods, precursor gases for focused beam-based methods
(FEBID/FIBID), and droplets of molten metal for laser-induced forward transfer
and
magnetohydrodynamic printing.
[0042] In some embodiments, the pyrolysis process is carried out over a
temperature
range selected from the range of 500 C to 3000 C and for a duration selected
from the
range of 1 hour to 336 hours. In some embodiments, the pyrolysis process is
carried out
over a temperature range select from the range of 500 C to 900 C, optionally
500 to
.. 1300 C. The structure is optionally exposed to vacuum and/or an inert gas,
or any
atmosphere substantially lacking oxygen and water vapor, during pyrolysis. In
some
embodiments, the pyrolysis process provides for an isotropic shrinkage of said
three-
dimensional framework to said structure selected from the range of 15% to 80%.
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[0043] In some embodiments, the method further comprises applying an
external
stimulus to said structure to change at least one vibrational frequency band
gap of said
structure.
[0044] In some embodiments, the method does not comprise etching a
template.
[0045] In some embodiments of the systems and methods disclosed herein, the
composite material system has a density less than or equal to 1500 kg/m3, less
than or
equal to 1200 kg/m3, preferably for some applications less than or equal to
1000 kg/m3,
more preferably for some applications less than 1000 kg/m3, more preferably
for some
applications less than or equal to 900 kg/m3, more preferably for some
applications less
than or equal to 500 kg/m3, more preferably for some applications less than or
equal to
300 kg/m3, more preferably for some applications less than or equal to 150
kg/m3, or still
more preferably for some applications less than or equal to 100 kg/m3. In some
embodiments of the systems and methods disclosed herein, the composite
material
system has a density selected from the range of 100 kg/m3 to 1500 kg/m3, 100
kg/m3 to
less than 1000 kg/m3, or any subrange in between. In some embodiments of the
systems and methods disclosed herein, the composite material system or
structure is
characterized by a Young's modulus of at least 100 MPa, optionally for some
applications at least 495 MPa, preferably for some applications at least 660
MPa, more
preferably for some applications at least 1000 MPa, still more preferably for
some
applications at least 1.82 GPa, or still more preferably for some applications
at least 2.2
GPa. In some embodiments of the systems and methods disclosed herein, the
composite material system or structure is characterized by a Young's modulus
selected
from the range of 100 MPa to 5 GPa, or any subrange in between. In some
embodiments of the systems and methods disclosed herein, the composite
material
system or structure is characterized by a yield strength of at least 5 MPa,
preferably for
some applications at least 8 MPa, preferably for some applications at least 11
MPa,
more preferably for some applications at least 15 MPa, more preferably for
some
applications at least 25 MPa, still more preferably for some applications at
least 60 MPa,
or still more preferably for some applications at least 100 MPa. In some
embodiments of
the systems and methods disclosed herein, the composite material system or
structure
is characterized by a yield strength selected from the range of 5 MPa to 100
MPa, or
any subrange in between. In some embodiments of the systems and methods
disclosed
herein, the composite material system or structure is characterized by not
exhibiting
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catastrophic failure at strain (e) selected from the range of 0.1 to at least
0.5. In some
embodiments of the systems and methods disclosed herein, the composite
material
system or structure is characterized by flow stress of at least 70 MPa, or
optionally
selected from the range of 70 to 500 MPa. In some embodiments of the systems
and
methods disclosed herein, the composite material system or structure is
characterized
by a flexural strength of at least 10 MPa, preferably for some applications at
least 20
MPa, or preferably for some applications selected from the range of 10 MPa to
100
MPa, or any subrange therebetween. In some embodiments of the systems and
methods disclosed herein, the composite material system or structure is
characterized
by a bending modulus of at least 1 GPa, preferably for some applications at
least 1.4
GPa, preferably for some applications at least 2 GPa, preferably for some
applications
at least 3.3 GPa, preferably for some applications at least 3.9 GPa,
preferably for some
applications at least 5 GPa, or more preferably for some applications selected
from the
range of 100 MPa to 10 GPa, or any subrange therebetween.
[0046] Also disclosed herein are composite material systems having any one
or any
combination of embodiments of composite material systems and methods disclosed
herein. Also disclosed herein are methods for making material systems having
any one
or any combination of embodiments of composite material systems and methods
disclosed herein.
[0047] Without wishing to be bound by any particular theory, there may be
discussion
herein of beliefs or understandings of underlying principles relating to the
devices and
methods disclosed herein. It is recognized that regardless of the ultimate
correctness of
any mechanistic explanation or hypothesis, an embodiment of the invention can
nonetheless be operative and useful.
BRIEF DESCRIPTION OF THE DRAWINGS
[0048] FIG. 1. Flowchart of method to fabricate composite materials with
continuous
arbitrary phases.
[0049] FIGs. 2A-2B. Embodiment of a composite material with continuous
three-
dimensional phases with arbitrary geometries. FIG. 2A. Changing cross-sections
in a
single truss element. FIG. 2B. Non-zero curvature and horizontal truss
elements.
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[0050] FIG. 3. Embodiment of a composite material with continuous three-
dimensional phases of shell or surface geometries, with one or more matrix
phases.
[0051] FIG. 4. Embodiment of a modular three-dimensional structural
element made
a composite material described in the previous embodiments. The reinforcing
phase
.. does not require a shaping process; the geometry is defined a priori.
[0052] FIGs. 5A-5B. Embodiment of a structural element made of a
composite
material described in the previous embodiments, where the in-plane and through-
thickness geometries are functionally graded. The resulting part has
continuous three-
dimensional phases.
[0053] FIG. 6. Embodiment of a phase microarchitecture where resonators are
designed to dissipate vibration and provide damping to the material. The
resulting part
has continuous three-dimensional phases.
[0054] FIGs. 7A-7C. Sample embodiment of a composite material with
continuous
three-dimensional phases with arbitrary geometries, reduced to practice. FIG.
7A.
Structural element fabricated from a precursor resin via DLP 3D printing and
corresponding micrograph. FIG. 7B. Post-pyrolysis carbon three-dimensional
continuous reinforcing phase and corresponding micrograph. FIG. 7C. Composite
structural element with continuous three-dimensional phases and epoxy matrix
phase.
[0055] FIG. 8. Manufacturing process of continuous reinforcing phase
with arbitrary
.. geometry via additive manufacturing.
[0056] FIGs. 9A-9B. A schematic of a structure with a three-dimensional
geometry,
or unit cell thereof, that is a tetrakaidekahedron (FIG. 9A), and a composite
material
system (FIG. 9B) having the structure of FIG. 9A infiltrated by a matrix
phase.
[0057] FIGs. 10A-10B. Polymeric octet lattices. FIG. 10A. Micrograph of
full lattice
.. suspended on a bed of spring structures. FIG. 10B. Close-up showing 5 pm
octet unit
cells.
[0058] FIGs. 11A-11D. Pyrolyzed carbon lattices. FIG. 11A. Octet lattice
of 26%
relative density. FIG. 11B. Close-up showing sub-micron unit cells. FIG. 11C.
Tetrakaidecahedron lattice of 17% relative density. FIG. 11D. Close-up on
final
tetrakaidecahedron geometry.
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[0059] FIG. 12. Impact of a 7 pm SiO2 bead on an octet lattice with 27%
relative
density. The projectile and the lattice are both highlighted in red in the
initial frame, prior
to impact. Subsequent frames reveal the projectile rebounding from the
lattice, with
minor debris being ejected. The impact and rebound velocities were 1060 and
560 m/s,
respectively.
[0060] FIGs. 13A-13C. PMMA resist coating to better bond the lattice to
the
substrate. FIG. 13A. Initial carbon lattice. FIG. 13B. Carbon lattice with a
sub-micron
PMMA coating. FIG. 13C. Post-mortem confocal microscopy image showing the
impact
site and minor permanent deformation.
[0061] FIGs. 14A-14B. Approximation of impact as a planar wave through the
lattice
material. FIG. 14A. Diagram depicting a planar wave going through a lattice of
thickness
XI at and substrate thickness Xs. FIG. 14B. x-t diagram of the elastic plane
wave for a
worst-case carbon octet lattice of 60% relative density, showing that the (on-
average) 4
ns of impact time are not sufficient for elastic waves to reach the substrate
and reflect
back to the projectile.
[0062] FIGs. 15A-15D. Suspended sample fabrication process. FIG. 15A.
The
original Si substrates were patterned and etched to create stilts
approximately 50 pm in
height. FIG. 15B. The nanowires that tethered the as-pyrolyzed sampled to the
substrate were milled using a FIB. FIG. 15C. The freed sample was captured by
a nano-
manipulator. FIG. 15D. The sample was affixed to the stilts using Pt glue.
[0063] FIG. 16. Suspended sample impact experiment. The same rebounding
behavior was observed, without any through-thickness complete penetration or
catastrophic sample fracture.
[0064] FIG. 17. Summary of impact experiments. A trend between impact
energy,
a mvd , and restitution coefficient, vr/vo, can be observed. No substantial
difference was
observed across different architectures, while a decrease in restitution was
observed for
lower relative density samples. The suspended-sample experiment is shown in
yellow,
while the PMMA-coated one is shown in blue.
[0065] FIGs. 18A-18F. Tetragonal unit cell of interest. FIG. 18A.
Unmodified
tetragonal unit cell with elliptical cross-section beams in the horizontal
direction and
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circular beams in the vertical direction, (FIG. 18B) slightly buckled
geometry, (FIG. 18C)
fully buckled geometry,(FIGs. 18D-18F) top views of the unit cells in FIGs.
18A-18C.
[0066] FIGs. 19A-19D. Dispersion relations for the tetragonal unit
cells. FIG. 19A.
Unmodified unit cell, (FIG. 19B) slightly buckled unit cell, (FIG. 19C) fully
buckled unit
cell, (FIG. 19D) irreducible Brillouin zone in reciprocal space. Partial band
gaps are
shaded in green.
[0067] FIGs. 20A-20B. Auxetic unit cell. FIG. 20A. Unmodified unit cell,
(FIG. 20B)
unit cell with added resonator.
[0068] FIGs. 21A-21B. Dispersion relations of auxetic unit cells. FIG.
21A.
Unmodified unit cell with no band gaps, (FIG. 21B) unit cell with resonator
showing the
appearance of a band gap.
[0069] FIGs. 22A-22C. Custom ultrasonics setup. FIG. 22A. Image of the
transmission experiment, where one transducer drives a signal through the
material of
interest and another transducer picks up the transmitted signal, (FIG. 22B)
picture of the
vacuum chamber and the placement of the transducers, (FIG. 22C) CCD image of
the
setup in vacuum, with a rubber puck between the transducers for validation
purposes.
[0070] FIGs. 23A-23E. Frequency sweep experiment. FIG. 23A. Unmodified
unit cell,
(FIG. 23B) unit cell with resonators, (FIG. 23C) frequency sweep transmitted
signal
amplitude, (FIG. 23D) close up on sample with no contact, (FIG. 23E) close up
on
slightly strained sample due to transducer contact. A band gap centered at ¨
2.4 MHz
was found, and is highlighted in grey.
[0071] FIGs. 24A-24C. Chirp transmission experiment. FIG. 24A. Input
chirp signal
containing 1-3 MHz, (FIG. 24B) FFT on the transmitted signal through a rubber
puck,
confirming the frequency content of the chirp, (FIG. 24C) FFT of the
transmitted signal
through the resonator-containing sample, showing the same band gap as in the
sweep
experiment, centered at ¨ 2.4 MHz.
[0072] FIGs. 25A-25D. Elastic surfaces of some sample microstructures.
FIG. 25A.
Columnar structure depicting a stiff direction aligned with the z-axis, (FIG.
25B) cubic
structure showing preferential directions aligned with the x,y,and z-axes,
(FIG. 25C)
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lamellar structure showing a few orders-of-magnitude difference in stiffness
along the x-
y axes and the z-axis, (FIG. 25D) a quasi-isotropic structure.
[0073] FIG. 26. Stiffness scaling as a function of relative density.
Spinodal structures
have a higher absolute modulus and lower, more desirable, scaling exponent.
[0074] FIGs. 27A-27B. Curvature probability distributions. FIG. 27A.
Columnar
structure, (FIG. 27B) octet truss with 0.5r and r fillets at nodes, where r is
the radius of
the tubes. The absolute curvatures for the octet structure are significantly
higher than
those of the spinodal structure.
[0075] FIGs. 28A-28C. Shell-based spinodal structure at the
nano/microscale. FIG.
28A. Polymeric structure fabricated via two-photon lithog-raphy, (FIG. 28B)
coated
structure after FIB milling, exposing the polymer again, (FIG. 28C) resulting
shell-based
spinodal structure after etching the inner polymer.
[0076] FIGs. 29A-29D. Shell-based spinodal structure at the macroscale.
FIG. 29A.
Polymeric columnar spinodal structure, (FIG. 29B) top view, (FIG. 29C)
resulting carbon
.. reinforcing phase, (FIG. 29D) top view.
[0077] FIGs. 30A-30C. Arch itected plate for blast impact testing. FIG.
30A.
Polymeric precursor plate and resulting pyrolyzed plate, (FIG. 30B) micrograph
of an
octet carbon architecture, (FIG. 30C) micrograph of a tetrakaidecahedron
architecture.
[0078] FIGs. 31A-31F. Cubes of example reinforcing phases. FIG. 31A.
Polymeric
octet cube, (FIG. 31B) pyrolyzed carbon octet cube from FIG. 31A, (FIG. 31C)
pyrolyzed carbon 3D kagome beam, (FIGs. 31D-31F) close-ups of FIGs. 31A-31C.
[0079] FIGs. 32A-32F. Tubular architected component. FIG. 32A. Polymeric
tube
with tetrakaidecahedron architecture, (FIG. 32B) top view of FIG. 32A, (FIG.
32C) close
up of FIG. 32B, (FIG. 32D) pyrolyzed carbon tube with tetrakaidecahedron
architecture
prior to infiltration, (FIGs. 32E-32F) close-ups of FIG. 32D.
[0080] FIGs. 33A-33H. Fabrication and microstructurel characterization
of the
pyrolytic carbon micropillars. FIG. 33A. Schematic illustration of the
fabrication process.
This process includes the TPL DLW of cylindrical pillars from IP-Dip polymer
resin and
subsequent pyrolysis under vacuum at 900 C. FIGs. 33B-33C. SEM images of a
.. representative micropillar before and after pyrolysis, showing substantial
volumetric
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shrinkage. FIG. 33D. Bright-field TEM image of the pyrolytic carbon. The
diffraction
pattern in the inset reveals its amorphous microstructure. FIGs. 33E-33F.
HRTEM
images of the two regions outlined by solid boxes in FIG. 33D. These images
reveal the
presence of some sub-nanometer-sized voids (denoted by red arrows). FIG. 33G.
Raman spectrum of a pyrolytic carbon micropillar. The typical G and D bands at
the
energies 1359 cm-1 and 1595 cm-1 indicate 5p2-hybridization. FIG. 33H. EELS of
the
pyrolytic carbon, where the green and purple shaded areas correspond to the 1s-
7-t* and
ls-o* peaks of carbon, respectively. Quantitative analysis of the data
indicates that the
pyrolyzed carbon contains approximately 96.5% sp2 bonds.
[0081] FIGs. 34A-34F. Uniaxial compression and tension experiments on the
pyrolytic carbon micropillars. FIG. 34A. Compressive stress-strain data of
pyrolytic
carbon pillars with diameters of 4.6-12.7 pm. All of these micropillars
deformed
elastically up to -20-30% strain and exhibited marginal plastic strain (-8-
10%) before
failure. The dashed lines indicate the linear slopes. FIG. 34B. SEM images of
a typical
.. pyrolytic carbon micropillar described in FIG. 34A before and after
compression, which
reveals the occurrence of brittle fracture via multiple fragments. FIG. 34C.
Representative stress-strain data set from the in situ deformation of a 2.25
pm-diameter
pyrolytic carbon pillar, which underwent significant plastic deformation up to
33.6%
strain. The inset shows an SEM image of the micropillar before compression. A
sequence of snapshots obtained during the in situ deformation is shown above
the plot,
with numbered frames corresponding to the same-numbered red arrows in the
stress-
strain curve. The SEM images on the right of the stress-strain data show the
compressed micropillar from the front and back views. The nucleation and
propagation
of the splitting crack correspond to the strain burst indicated by the blue
arrow in the
stress-strain curve. FIG. 34D. Tensile stress-strain data of pyrolytic carbon
dog-bone-
shaped samples with gauge diameters of 0.7-2.0 pm. FIG. 34E. SEM images of a
typical
tensile specimen before and after the experiment. FIG. 34F. Statistical
distribution of
tensile fracture strengths.
[0082] FIGs. 35A-35B. Change in strength with diameter and the ultra-
large elastic
limit of pyrolytic carbon micropillars. FIG. 35A. Variation in compressive
strength with
increasing micropillar diameter. The blue dashed line represents the average
compressive strength of micropillars with diameters smaller than 2.3 pm. FIG.
35B.
Twenty-cycle force-displacement curve of a deformable pillar with a diameter
of 1.28 pm
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under a maximum compressive strain of -23%, showing nearly full recovery in
every
cycle except the first cycle. The SEM images depict the pre-deformation and
post-
deformation pillar from 20 loading cycles.
[0083] FIGs. 36A-36J. Atomistic simulations of the uniaxial compression
and tension
of pyrolytic carbon nanopillars. FIG. 36A. Atomic configurations and cross-
sectional
morphology of a simulated sample with a diameter of 20 nm. FIGs. 36B-36C.
Compressive and tensile stress-strain curves of pyrolytic carbon nanopillars.
FIGs. 36D-
36G. Snapshots of a deformed pillar at different compressive strains. FIGs.
36H-36J.
Snapshots of a deformed pillar at different tensile strains. The atoms in
FIGs. 36D-36J
are colored according to the von Mises atomic strain.
[0084] FIGs. 37A-37C. Summary of the combined ultra-high
strength/specific
strength and large deformability of the pyrolytic carbon micropillars. FIG.
37A. Ashby
chart of strength versus density for various structural materials, including
our pyrolytic
carbon micropillars. FIG. 37B. Comparison of specific tensile and compressive
strengths
between our pyrolytic carbon micropillars and other structural materials. FIG.
37C.
Summary of specific strength versus fracture strain for our pyrolytic carbon
micropillars
and other structural materials. The excellent combination of specific strength
and
deformability of our pyrolytic carbon surpasses that of almost all other
materials.
[0085] FIG. 38. Compressive stress-strain curves of simulated
nanopillars with
diameter of 10 nm and different densities.
[0086] FIG. 39. Plot of Young's modulus (GPa) versus density (g/cm3)
corresponding
to materials or structures from relevant art as well as to certain embodiments
of the
present invention.
[0087] FIGs. 40A-40E. Images corresponding to atomistic configurations
of
nanopillars formed of carbon allotrope materials. The nanopillars shown here
have
diameters of 10 nm and different densities of 1.0-1.8 g/cm3. Presence of sp
carbon, 5p2
carbon, and sp3 carbon is identified.
[0088] FIG. 41. Model for estimation of density and comparison with
densities of
pyrolytic carbon reported in recent literatures. Panels (a) and (b):
Illustration of packing
structure of curved graphene layers in pyrolytic carbon. L is the size of
curved graphene
layer, and Ls represents the interlayer distance between neighboring layers.
Panel (C):
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Illustration of a typical open-structure unit cell composed of two graphene
layers. Panel
(d): Density of pyrolytic carbon (ppc) as a function of the ratio of UL. Solid
curve is from
the prediction based on Eq. (1), while the dashed curve is from Ref. 26. The
current
extended model supplies a prediction of density of 1.0-1.8 g/cm3 for pyrolytic
carbon
micropillars.
[0089] FIG. 42. In situ compression experiment of pyrolytic micropillar
without the
residual ring. Panels (a), (b) and (c): Snapshots of in situ compressive test
on the
pyrolytic carbon pillar without the residual ring. In (c), a splitting crack
nucleated and
rapidly propagated under high compressive stress, leading to the catastrophic
fracture
of the micropillar. Panel (d): Corresponding compressive stress-strain curve.
[0090] FIG. 43. Influence of residual carbon rings on compression of
pyrolytic carbon
micropillars. Panels (a), (b), and (c): Snapshots of in situ compressive test
on the
pyrolytic carbon pillar with the residual ring. Panel (d): Corresponding
compressive
stress-strain curve. The slight burst marked by "b" is corresponding to the
bulging of the
edge of the ring due to high stress concentration. The large strain burst
marked by "c"
represents the cleavage of the pillar as well as the peeling up of the ring.
[0091] FIG. 44. Bonding structures of pyrolytic carbon pillars used for
atomistic
simulations. The sp2 bonds are much more ubiquitous than sp and sp3 bonds. The
sp
bonds are mainly localized at the edges of the curved graphene layers; the sp3
bonds
generally connect neighboring graphene layers to one another or form at the
high-
energy curved surface of graphene layers.
[0092] FIGs. 45A and 45B. Fracture mechanisms of pyrolytic carbon
nanopillars
under uniaxial tension. FIG. 45A: Snapshots of stretched nanopillars at
strains of 56.3-
60.5%. Nanoscale cavities (indicated by orange arrow) nucleated and grew up
during
stretching, and then merged with each other, leading to formation of nanoscale
cracks.
FIG. 45B: Snapshots of stretched nanopillars at strains of 61.0-61.8%. As the
tensile
strain increases, nanoscale cracks propagated along a direction normal to
tensile
direction, resulting in the smooth fracture surface. All atoms in FIG. 45A and
FIG. 45B
are colored by atomic von Mises strain.
[0093] FIG. 46. Effects of initial flaws on tensile strength of pyrolytic
carbon pillars.
Panels (a) and (b): Atomic configurations of simulated samples containing
initial cracks
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with length of 4 nm and 8 nm, respectively. All initial cracks are shown by
the white
flakes. Panels (c) and (d): A sequence of snapshots of pillars with initial
cracks with
length of 4 nm and 8 nm, respectively. The failure of both nanopillars always
initiated
from the growth and extension of pre-existing nanocracks. Both samples after
failure
have the smooth fracture surface, showing a brittle fracture mode. All atoms
in Panel (c)
and Panel (d) are colored by atomic von Mises strain.
[0094] FIG. 47. Summary plot of strength versus fracture strain for our
pyrolytic
carbon micropillars and other structural materials.
[0095] FIGs. 48A-48F. Fabrication and microstructural characterization
of pyrolytic
carbon nanolattices. FIG. 48A. Schematic illustration of the fabrication
process of
pyrolytic carbon nanolattices. CAD rendition of a (FIG. 48B) octet and (FIG.
48D) iso-
truss unit cell. SEM images of (FIG. 48C) an octet nanolattice with a strut
diameter of
d=435 nm and (FIG. 48E) an iso-truss nanolattice fabricated with a vertical
strut
diameter of d1=460 nm and a slanted strut diameter of d2=523 nm. FIG. 48F. An
HRTEM image of pyrolytic carbon extracted from the nanolattice, which
indicates the
amorphous nature of the pyrolytic carbon.
[0096] FIGs. 49A-49F. In situ uniaxial compression experiments on
pyrolytic carbon
nanolattices. FIGs. 49A-49B. Mechanical response of pyrolytic carbon octet-
and iso-
truss nanolattices with different relative densities obtained from in situ
compressions.
FIGs. 49C-49D. SEM images of an octet-truss nanolattice with d=382 nm before
and
after compression. FIGs. 49E-49F. SEM images of the iso-truss nanolattice with
d1=538
nm and d2=612 nm before and after compression, which reveal brittle failure.
Initial
detectable structural imperfections caused by fabrication process are circled
in (FIG.
49C) and (FIG. 49E).
[0097] FIGs. 50A-50B. Mechanical properties versus density maps of
pyrolytic
carbon nanolattices. FIG. 50A. Young's modulus and (FIG. 50B) compressive
strength
of pyrolytic carbon nanolattices plotted versus density on a log-log scale.
For
comparison, these charts include several micro- and nano-architected materials
reported so far, such as alumina hollow nanolattices (11), alumina-polymer
nanolattices
(16), glassy carbon nanolattices (18), carbon aerogel (22), graphene aerogel
microlattices (23), vitreous carbon nanolattice (24), cellular carbon
microstructure (25)
and SiOC microlattices (26).
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[0098] FIGs. 51A-51F. Finite-element simulations of uniaxial compression
of
pyrolytic carbon nanolattices with different unit cells. FIGs. 51A-51C.
Simulated
configurations of octet-, iso- and tetrahedron-truss nanolattices with pre-
existing defects
introduced by imposing the initial deflection of struts. The insets show the
zoom-in views
of local structures with initial deflection of struts. FIGs. 51D-51F.
Compressive stress-
strain curves of octet-truss, iso-truss and tetrahedron-truss nanolattices
with different
relative densities and initial specific deflection.
[0099] FIG. 52. Comparison of the specific strength between our
pyrolytic carbon
nanolattices and other micro- and nanolattices reported so far.
[0100] FIGs. 53A-53H. In situ compression tests on polymer nanolattices.
FIG. 53A.
Compressive stress-strain curve of octet-truss nanolattice with d=1.12 pm.
FIGs. 53B-
53D. SEM snapshots of deformed octet-truss nanolattice under different
compressive
strains. FIG. 53E. Compressive stress-strain curve of iso-truss nanolattice
with d1=1.30
pm and d2=1.49 pm. FIGs. 53F-53H. SEM snapshots of deformed iso-truss
nanolattice
under different compressive strains. The circled regions in FIG. 53C and FIG.
53G
indicate the buckling of struts during compression.
[0101] FIGs. 54A-54B. Young's modulus and compressive strength versus
density of
pyrolytic carbon nanolattices. Young's modulus and strength versus relative
density of
octet- and iso-truss pyrolytic carbon nanolattices on log-log scale. Scaling
power law
.. slopes are indicated for each architecture. Error bars represent the
standard deviations
from the average over some data of samples with comparable densities.
[0102] FIG. 55. Relative reduction in strength of nanolattice with
initial deflection as a
function of the extent of initial deflection.
[0103] FIGs. 56A-56B. Comparison between finite-element modelling and
experimental results. Modulus versus relative density and strength versus
relative
density from finite-element modelling and experiment. The dependences of
modulus
and strength of nanolattice on the relative density from finite-element
modelling are
consistent with those from experimental measurements.
[0104] FIGs. 57A-57D. Microstructure characterization of 3D architected
carbon
structure. FIG. 57A. SEM image of cross-section and energy dispersive
spectroscopy
(EDS) spectrum on the cross-section. FIG. 57B. Raman spectrum with
experimental
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data (.), fitted curves for each band (dot lines), and linear combination of
these peaks
(red line). FIG. 57C. X-ray diffraction (XRD) pattern. FIG. 57D. Transmitted
electron
microscope (TEM) high resolution image and diffraction pattern (inlet). Scale
bars are 5
pm for FIG. 57A, and 5 nm in FIG. 57D.
[0105] FIG. 58A. Line analysis of EDS on the cross-section. FIG. 58B.
Particles
crushed from the 3D architected carbon structure used for XRD analysis.
[0106] FIG. 59A. Representative stress-strain curve for compression.
Roman
numerals corresponds to distinct events shown in FIG. 59B. FIG. 59B.
Photographic
images of the compressed 3D architected carbon structure, I at the initial
contact, II-a, b,
c at local fractures shown in red doted-circle, Ill before the second stress
release IV at
the partial layer collapse shown by red line, V before the third stress
release, and VI at
the half layer collapse. Substrate and top load cell was grayed out.
[0107] FIG. 60. Stress-strain curve of five samples of the 3D
architected carbon
structure.
[0108] FIG. 61A and FIG. 61B. Images showing architected three-dimensional
structures having node-free geometries, according to certain embodiments of
the
invention. Additional exemplary node-free geometries may be found in Abueidda,
et al.
("Effective conductivities and elastic moduli of novel foams with triply
periodic minimal
surfaces", Mechanics of Materials, vol. 95, April 2016, pages 102-115), which
is
incorporated herein by reference.
[0109] FIGs. 62A-62F. Infiltration of reinforcing phases. FIG. 62A.
Shell-based
spindodal reinforcing phase, (FIG. 62B) tetrakaidecahedron-tube structure,
(FIG. 62C)
octet-cube structure, (FIGs. 62D-62F) epoxy-infiltrated composites from the
reinforcing
phases depicted in FIGs. 62A-62C.
[0110] FIGs. 63A-63D. Octet carbon material in compression. FIG. 63A.
Sample
prior to compression, (FIG. 63B) failed sample after catastrophic event, (FIG.
63C) final
geometry of a tested sample depicting fractured surfaces, (FIG. 63D) stress-
strain
response for two identical samples.
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[0111] FIGs. 64A-64C. Octet carbon-epoxy material in compression. FIG.
64A.
Sample prior to compression, (FIG. 64B) densified sample after c = 0.5, (FIG.
64C)
stress-strain response of samples.
[0112] FIGs. 65A-65D. Four-point bending of carbon octet material. FIG.
65A.
.. Sample prior to experiment, (FIG. 65B) sample after catastrophic fracture
event, (FIG.
65C) final sample morphology, (FIG. 65D) resulting stress-strain response,
corresponding to the outermost edge of the material.
[0113] FIGs. 66A-66D. Four-point bending of epoxy-infiltrated carbon
octet materials.
FIG. 66A. Sample prior to experiment, (FIG. 66B) sample at highest bending
load, (FIG.
66C) sample morphology after unload showing no visible damage, (FIG. 66D)
resulting
stress-strain response, corresponding to the outermost edge of the material.
STATEMENTS REGARDING CHEMICAL COMPOUNDS AND NOMENCLATURE
[0114] In general, the terms and phrases used herein have their art-
recognized
meaning, which can be found by reference to standard texts, journal references
and
contexts known to those skilled in the art. The following definitions are
provided to
clarify their specific use in the context of the invention.
[0115] The term "monolithic" refers to a system, structure, geometry, or
other
element that is a unitary interconnected and continuous element. In an
embodiment, a
monolithic element is formed or composed of a material without joints or
seams. In an
embodiment, the term "interconnected" refers to a system, structure, geometry,
or other
element of which every first portion or first feature is either (i) directly
connected to a
second portion or second feature of the system, structure, geometry, or other
element,
or (ii) indirectly connected to a second portion or second feature of the
system,
structure, geometry, or other element via a third portion or third feature of
the system,
structure, geometry, or other element. In an embodiment, no portion or feature
of an
interconnected system, structure, geometry, or other element is fully isolated
from the
rest of the system, structure, geometry, or other element. In an embodiment,
the term
"continuous" refers to a system, structure, geometry, or other element of
which every
first portion or first feature is directly or indirectly bonded to, fused
with, or otherwise
belongs to the same uninterrupted phase with respect to a second portion or
second
feature of system, structure, geometry, or other element. In an embodiment,
two
features which are connected merely by superficial contact (e.g., touching)
but are
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otherwise isolated with respect to each other, are not continuous. In an
embodiment,
two distinct features, such as fibers or particles, which are merely touching
or are woven
together may be interconnected but are not continuous with respect to each
other. In an
embodiment, a structure or geometry consisting of a plurality of features,
such as fibers
or particles, each of which is merely touching or woven together with another
feature,
such as a fiber or particle, may be an interconnected structure or geometry
but is not a
continuous structure or geometry.
[0116] The term "deterministic" refers a system, structure, geometry, or
other
element characterized by at least one feature and/or at least one property
(e.g.,
vibrational frequency band gap) that is known and/or controlled to be within
20%,
preferably within 10%, more preferably within 5%, more preferably within 1%,
or more
preferably within 0.1% of a determined or desired value. In an embodiment, a
deterministic geometry is characterized one or more features each
independently having
at least one physical dimension which, prior to or during formation of said
structure, is
pre-determined to be within 20%, preferably within 10%, more preferably within
5%,
more preferably within 1%, or more preferably within 0.1% of a determined or
desired
value. For example, a deterministic architected three-dimensional geometry of
a
structure comprises a plurality of features, such as trusses, having one or
more physical
dimensions (e.g., width, thickness, diameter, length) the values of which are
within 20%,
preferably within 10%, more preferably within 5%, more preferably within 1%,
or still
more preferably within 0.1% of the value(s) of the one or more physical
dimensions
designed, such as via a CAD technique, or determined prior to formation of the
structure. Stochastic geometries or structures, such as random or natural
foams, are not
deterministic.
[0117] The term "architected" refers to a system, structure, geometry, or
feature
having features that are designed and formed according to the design. In an
embodiment, an architected structure is deterministic or formed according to
deterministic process(es). In an embodiment, substantially all features, and
physical
dimensions thereof, are designed, or pre-determined, and formed according to
the
design such that the substantially all features, and physical dimensions
thereof, are
substantially equivalent to those of the design.
[0118] The term "three dimensional geometry" refers to a geometry
characterized by
a three-dimensional geometric configuration. In an embodiment, a structure has
a three
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dimensional geometry when a three-coordinate system of physical space is
required to
fully describe the physical dimensions of a unit cell of the structure. A
three dimensional
geometry may be nano-architected and/or micro-architected. In an embodiment, a
structure characterized by a nano-architected three dimensional geometry is a
structure
characterized one or more features having at least one physical size dimension
(e.g.,
length, width, diameter, or height) the value of which is in the range of
approximately 1
nm to less than 1 pm. The one or more "features" include, but are not limited
to, beams,
struts, ties, trusses, sheets, shells, and nodes. In an embodiment, a
structure
characterized by a nano-architected three dimensional geometry is a structure
characterized by a unit cell having whose at least one physical size dimension
(e.g.,
length, width, or height) the value of which is in the range of approximately
1 nm to less
than 1 pm. In an embodiment, a structure characterized by a micro-architected
three
dimensional geometry is a structure characterized one or more features having
at least
one physical size dimension (e.g., length, width, or height) the value of
which is in the
range of approximately 1 pm to 1000 pm. In an embodiment, a structure
characterized
by a micro-architected three dimensional geometry is a structure characterized
by a unit
cell having at least one physical size dimension (e.g., length, width, or
height) the value
of which is in the range of approximately 1 pm to 1000 pm.
[0119] As used herein, a "feature" of a system, such as a composite
material system
according to an embodiment, structure, or geometry, such as a three-
dimensional
geometry according to an embodiment, refers to an element such as, but not
limited to,
a beam, a strut, a tie, a truss, a sheet, a shell, a sphere, an ellipse, a
node, or a
combination of these. In an embodiment, a fillet, a bevel, a chamfer, or
similar attribute
is a portion of a feature but is not a feature itself. For example, a fillet,
or rounding of an
interior or exterior corner, is a portion of one or more features but is not a
"feature", as
used herein, itself. For example, a fillet between a first truss and a second
truss is a
portion of the first truss, of the second truss, or a portion of each of the
first and second
trusses, but the fillet is not itself a "feature", as used herein, of the
three-dimensional
geometry or structure. A "longitudinal feature" refers to an element whose
length (or,
size along its longitudinal axis) is at least 50% greater than each of its
other
characteristic size dimensions (i.e., width, height, thickness, or diameter).
Exemplary
longitudinal feature may include, but are not limited to, beams, struts, ties,
and trusses.
In an embodiment, a surface feature is a feature that may be better
characterized as a
flat and/or curved planar feature than a longitudinal feature. In an
embodiment, a
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surface feature corresponds to a feature that may be approximated or
characterized as
a mathematical two-dimensional manifold, having a uniform or non-uniform
thickness. In
an embodiment, a surface feature corresponds to a feature that may be
approximated or
characterized as a mathematical two-dimensional manifold, having a uniform or
non-
.. uniform thickness, and is an open surface. Exemplary surface features
include, but are
not limited to, sheets and shells.
[0120] A "matrix phase" refers to a material, or a combination of
materials, that may
at least partially infiltrate a structure of a composite material system. A
matrix phase
may be uniform or non-uniform. A matrix phase may be homogeneous or non-
homogeneous. At least partial infiltration of the structure refers to at least
partial filling of
void space of a structure. In an embodiment, at least partial infiltration of
the structure
refers to at least partial filling of accessible void space of a structure.
Non-accessible
void space of a structure may refer to closed void regions (e.g., hollow truss
or hollow
portion of a spinodal geometry) into a matrix phase may not penetrate without
first
.. etching or performing another destructive process on said structure. In
some
embodiments of the systems and methods disclosed herein, the matrix phase is
not a
coating, such as a coating deposited via ALD, sputtering, or electrophoretic
deposition.
In some embodiments of the systems and methods disclosed herein, the matrix
phase is
not an electrolyte, such as an electrolyte of an electrochemical cell,
including solid-state
.. electrolytes.
[0121] A "vibrational frequency band gap" refers to a frequency, or
frequency range,
corresponding to vibration (or, oscillation) of a structure, composite
material system, or
structure thereof, where the magnitude or energy of oscillation(s) at said
frequency, or
said frequency range, is at least 10 times (one order-of-magnitude), at least
20 times, at
least 50 times, preferably at least 100 times (two orders-of-magnitude),
preferably for
some applications at least 200 times, or still more preferably for some
applications at
least 500 times, less than the magnitude or energy of oscillations at
frequencies outside
of the "vibrational frequency band gap." In some embodiments, a vibrational
frequency
band gap may be characterized by a midpoint frequency and/or a frequency
width. In an
embodiment, a partial vibrational frequency band gap is a vibrational
frequency band
gap existing along one or more directions (e.g., X, Y, Z, or any direction or
vector in
between), but not existing along all directions. In an embodiment, a complete
vibrational
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frequency band gap is a vibrational frequency band gap existing along all
directions
(e.g., X, Y, Z, or any direction or vector in between).
[0122] The term "cross-sectional physical dimension" refers to a physical
dimension
of a feature measured in a transverse or cross-sectional axis. In an
embodiment, the
transverse axis is perpendicular to a longitudinal axis of the feature. In an
embodiment,
a cross-sectional physical dimension corresponds to a width or a diameter of a
feature
such as a beam, strut, or tie. In an embodiment, a longitudinal physical
dimension is a
dimension of a feature along the longitudinal axis of the feature, wherein the
longitudinal
axis is perpendicular to a cross-sectional axis. Optionally, the longitudinal
physical
dimension is measured between two nodes. Optionally, the longitudinal physical
dimensions is measured between to physical ends of a structure.
[0123] The term "unit cell" refers to the smallest arrangement,
configuration, or
geometry of a plurality of features such that an entire structure, or three-
dimensional
geometry thereof, characterized by said unit cell can be formed by repetition
of said unit
cell. For example, repetition of the unit cell in three dimensions may form a
three-
dimensional structure. The entire structure may be a three-dimensional
structure, such
as a three-dimensional porous structure.
[0124] "Young's modulus" is a mechanical property of a material, device
or layer
which refers to the ratio of stress to strain for a given substance. Young's
modulus may
be provided by the expression:
E(stress) ( Lo
=
(strain) AT, A j (I)
[0125] where E is Young's modulus, Lo is the equilibrium length, AL is
the length
change under the applied stress, F is the force applied, and A is the area
over which the
force is applied. Young's modulus may also be expressed in terms of Lame
constants
via the equation:
E= ____________
tu (II)
[0126] where A and pare Lame constants. The Young's modulus may be measured
according a method conventionally known, or not yet known, in the art. For
example, the
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Young's modulus corresponds to the slope of a linear portion of a stress-
strain curve as
described by Roylance ("Stress-Strain Curves," MIT course, August 23, 2001;
accessed
at time of filing at htt ://web. m it. edulcourse/3/3.1 1 Nvwwimodu lesiss.
df).
[0127] The term "average," when used in reference to a material or
structure
property, refers to a calculated arithmetic mean of at least two, or
preferably at least
three, identical measurements or calculations of said property. For example,
an average
density of a structure is the arithmetic mean of at least two measurements
performed
identically, of the density of said structure.
[0128] The term "density" refers to volumetric mass density. Density is
represented in
units of mass-per-volume (e.g., g/cm3). When referring to a material, the term
density
corresponds to the volumetric mass density of the material. When referring to
a
structure, the term density corresponds to the volumetric mass density of the
structure,
which is a function of the geometric configuration (geometry) of the structure
as well as
a function of the material(s) of which the structure is formed, such that an
increase in
porosity of said structure corresponds to a decrease in density of said
structure. The
density of a structure, such as a structure having a three-dimensional
geometry
according to an embodiment of the invention, may be measured according a
method
conventionally known, or not yet known, in the art. For example, the density
of a
structure may be determined by determining mass, height, and diameter for a
disk-
shape sample, and then calculating the determined mass divided by volume for
the
sample, with assuming the sample is substantially a complete circle.
[0129] The term "relative density" refers to a volume fraction of solid
material in a
composite material system, structure, or feature. In an embodiment, a relative
density
corresponds to a ratio of density of a structure to density solid material (or
the
combination of materials), of which the structure is composed. Relative
density may be
represented as a fraction (the ratio of densities) or as a percentage (the
ratio of
densities x 100%). In an embodiment, relative density of a structure, or a
three-
dimensional geometry thereof, before pyrolysis is substantially the same to
that after
pyrolysis.
[0130] The term "specific strength" refers to a ratio of strength to
density of a
material, system, structure, or feature where strength refers to force per
unit area at the
point of failure of the material, element, or structure. Specific strength may
also be
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referred to as strength-to-weight ratio. In an embodiment, "strength" refers
to
compressive strength. In an embodiment, "strength" refers to tensile strength.
In an
embodiment, compressive strength is the maximum stress a material can sustain
under
crush loading. In an embodiment, compressive strength of a material,
structure, or
element that fails by shattering fracture can be defined within fairly narrow
limits as an
independent property. In an embodiment, the compressive strength of a
material,
structure, or element that does not shatter in compression is the amount of
stress
required to distort the material an arbitrary amount. In an embodiment,
compressive
strength of a material, structure, system, feature, or element that does not
shatter in
compression can be calculated as the stress at a 0.2% strain offset from the
linear
portion in a stress-strain curve. In an embodiment, compressive strength is
calculated
by dividing the maximum load, on the material, structure, or element, by the
original
cross-sectional area of the material, structure, or element being examined.
[0131] The term "stiffness" refers to an extent to which a material,
structure, system,
or feature resists deformation in response to an applied force. Stiffness
corresponds to a
ratio of force applied to a material, structure, or element versus the
displacement
produced by the applied force along the same degree of freedom (e.g., same
axis or
direction) exhibited by the material, structure, or element. The term
"specific stiffness"
refers to a ratio of stiffness to density of the material, element, or
structure. In an
embodiment, the stiffness of a material, structure, or element is the Young's
modulus of
the material, structure, or element.
[0132] According to certain embodiments, a structure has a node-free
geometry (i.e.,
free of node features). The node-free geometry has exceptional mechanical
resilience.
Mechanical resilience may be understood, for example, in terms of strain-to-
failure and
strength-to-failure. In an embodiment, strength-to-failure of a material,
element, or
structure corresponds to compressive strength of the material, element, or
structure. In
an embodiment, a structure of the invention has a strain-to-failure of 2% to
5%,
optionally 2.9% to 3.5%. Strain-to-failure may be determined according a
method
conventionally known, or not yet known, in the art. For example, strain-to-
failure may be
determined from the strain value corresponding a linear portion, such as the
third linear
portion, of stress vs. strain data until sudden stress loss (fracture) of a
structure.
[0133] The term "additive manufacture" refers to a process for forming a
structure or
feature via deposition, or otherwise building up, of a material. The terms
"additive
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manufacture process" and "additive manufacturing process" may be used
interchangeably. An additive manufacture process may involve layer-by-layer
deposition
of a material to form a complex three-dimensional structure or element. The
deposited
material may include, but is not limited to, inorganic materials, hybrid
organic-inorganic
.. materials, polymers, metals, or combinations of these. Exemplary additive
manufacture
processes include, but are not limited to, 3D printing, stereolithography
(SLA), fused
deposit modeling (FDM), and 2-photon lithography. In some embodiments, an
additive
manufacture process does not require a subtractive manufacture to form the
structure or
element. Examples of subtractive manufacture processes include, but are not
limited to,
milling, machining, electron discharge machining, carving, shaping, grinding,
drilling,
and etching. In an embodiment, an additive manufacture process involves or is
aided by
computer-aided design (CAD).
[0134] In an embodiment, the term "defect" may refers to a fabrication-
induced
imperfection, or unintended feature or property, such as, but not limited to,
local
deformation, crack, beam junction offset, beam bulging, curvature of a strut,
and pit or
void.
[0135] The term "node" may refer to a junction or intersection of a
plurality of
features, such as beams or struts. A structure may have a three-dimensional
geometry
that is a node-free geometry.
[0136] The term "core," when referring to a feature of a structure having a
three-
dimensional geometry, according to an embodiment, refers to an inner volume of
the
feature up to and excluding the external surface of the feature. In an
embodiment, the
core of a feature corresponds to the feature's internal volume excluding that
of any
coatings, particularly coatings introduced after a pyrolysis process, present
thereon.
[0137] The term "pre-polymer" or "prepolymer" refers to a monomer or
mixture
comprising one or more monomers where the monomer(s) have been reacted to an
intermediate molecular mass state. The prepolymer is capable of undergoing
further
polymerization to a fully cured higher molecular weight state. In some
embodiments, the
terms prepolymer and monomer may be used interchangeably.
[0138] As used herein, the term "polymer" refers to a molecule composed of
repeating structural units connected by covalent chemical bonds often
characterized by
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a substantial number of repeating units (e.g., equal to or greater than 3
repeating units,
optionally, in some embodiments equal to or greater than 10 repeating units,
in some
embodiments greater or equal to 30 repeating units) and a high molecular
weight (e.g.
greater than or equal to 10,000 Da, in some embodiments greater than or equal
to
50,000 Da or greater than or equal to 100,000 Da). Polymers are commonly the
polymerization product of one or more monomer precursors. The term polymer
includes
homopolymers, or polymers consisting essentially of a single repeating monomer
subunit. The term polymer also includes copolymers which are formed when two
or
more different types of monomers are linked in the same polymer. Copolymers
may
comprise two or more monomer subunits, and include random, block, brush, brush
block, alternating, segmented, grafted, tapered and other architectures.
Useful
polymers include organic polymers or inorganic polymers that may be in
amorphous,
semi-amorphous, crystalline or semi-crystalline states. Polymer side chains
capable of
cross linking polymers (e.g., physical cross linking) may be useful for some
applications.
[0139] The term "substantially" refers to a property that is within 10%,
within 5%,
within 1%, or is equivalent to a reference property. The term "substantially
equal",
"substantially equivalent", or "substantially unchanged", when used in
conjunction with a
reference value describing a property or condition, refers to a value that is
within 10%,
optionally within 5%, optionally within 1%, optionally within 0.1%, or
optionally is
equivalent to the provided reference value. For example, a ratio is
substantially equal to
1 if it the value of the ratio is within 10%, optionally within 5%, optionally
within 1%, or
optionally equal to 1. The term "substantially greater", when used in
conjunction with a
reference value describing a property or condition, refers to a value that is
at least 2%,
optionally at least 5%, or optionally at least 10% greater than the provided
reference
.. value. The term "substantially less", when used in conjunction with a
reference value
describing a property or condition, refers to a value that is at least 2%,
optionally at least
5%, or optionally at least 10% less than the provided reference value.
[0140] In an embodiment, a composition or compound of the invention, such
as an
alloy or precursor to an alloy, is isolated or substantially purified. In an
embodiment, an
isolated or purified compound is at least partially isolated or substantially
purified as
would be understood in the art. In an embodiment, a substantially purified
composition,
compound or formulation of the invention has a chemical purity of 95%,
optionally for
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some applications 99%, optionally for some applications 99.9%, optionally for
some
applications 99.99%, and optionally for some applications 99.999% pure.
[0141] In an embodiment, the term "mitigated energy" or "energy
mitigated" refers to
the energy that is redirected from a composite system, structure, feature, or
material
and does not cause failure of the composite system, structure, feature, or
material (e.g.,
the energy of a particle before impact plus the energy of the particle after
only if the
velocity vector is different than the initial one). In an embodiment, the term
"impact
energy" refers to energy of an impactor before impact. In an embodiment, the
term
"energy absorbed" or "absorbed energy" refers to a difference between the
impact
energy and the rebound energy of an impactor (e.g., a particle). In an
embodiment, the
term "specific energy absorption" refers to the ratio of strain energy density
(W, defined
as W= f o-dE) to the material density (p). In an embodiment, the term
"specific energy
absorption" refers to the ratio of strain energy density (W, defined as W= f o-
dE) to a
composite system, structure, material, or feature density (p).
DETAILED DESCRIPTION OF THE INVENTION
[0142] In the following description, numerous specific details of the
devices, device
components and methods of the present invention are set forth in order to
provide a
thorough explanation of the precise nature of the invention. It will be
apparent, however,
to those of skill in the art that the invention can be practiced without these
specific
details.
[0143] In an embodiment, a composite material system has at least one
monolithic
structure (or, "reinforcing phase") with a three-dimensional geometry where
the
centerline of a truss element does not extend from an edge through the
entirety of the
material (as opposed to a waveguide process), but instead can initiate and
terminate at
arbitrary points within the material. In the same fashion, the centerline of
truss elements
can be placed in any orientation within the material ¨including perpendicular
to the
thickness direction ¨ as opposed to waveguide processes where this is not
possible.
Similarly, a given truss element can have arbitrary cross-section, which can
also change
throughout the truss element. Lastly, the centerline of a given truss element
is allowed
to have non-zero curvature. One or more matrix phases fill the volume around
the
reinforcing phase(s). The phases can be composed of different material
classes,
including but not limited to, polymer, ceramic, carbon, and metal.
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[0144] In an embodiment, the composite material system has a continuous
reinforcing phase with a three-dimensional shell or surface geometry, with
negative,
zero, or positive Gaussian curvature. The walls or membranes of the shell
geometry can
have varying thickness throughout the material. The surface geometry can
conform
enclosed cavities that are separated from an external matrix phase. One or
more matrix
phases fill the volume around the reinforcing phase(s). The phases can be
composed of
different material classes, including but not limited to, polymer, ceramic,
carbon, and
metal.
[0145] In an embodiment, a modular three-dimensional structural element
of an
arbitrary shape is made of the composite material described in previous
embodiments.
The reinforcing phase of the material will have the geometry of the ultimate
structural
component, as a continuous phase. The topology of the structural element can
have
zero or multiple holes (i.e., monolithic composite component or tubular
component,
respectively). The resulting holes can be infiltrated with a different matrix
phase or left
unaltered.
[0146] In an embodiment, a structural component of an arbitrary shape is
made of
the composite material described in previous embodiments, with functionally
graded
geometry of one or more of the phases. The continuous lattice architectures or
surfaces
of the reinforcing phase(s) can change through-thickness and in-plane, while
remaining
continuous. The cross-sections and thicknesses can also change without
affecting the
continuity of the phases.
[0147] In an embodiment, the microstructure of the continuous
reinforcing phase of
the composite material presented in previous embodiments can have features
that serve
as resonators and provide damping to the material. The resonators could be
surrounded
by or isolated by a matrix phase.
[0148] A method of making a three-dimensional composite material system
with
arbitrary architecture may include designing an arbitrary architecture (which
can be
periodic) through Computer Aided Design (CAD) tools, selecting a desired
precursor
resin, and exposing the resin to the desired layer-by-layer pattern
characteristic of
additive manufacturing technologies including but not limited to SLA and DLP.
Optionally, additional resin is then removed and the sample is post-cured with
UV and
heat treatments, followed by a pyrolysis process with specified temperature
profile and
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in a controlled environment. The structure is then infiltrated with one or
more materials,
aided by vacuum and sonication processes, ultimately forming the composite
material
with continuous and arbitrarily shaped phases.
[0149] The composite material systems disclosed herein provide an
improvement
from typical carbon fiber composite materials in that the weak interlaminar
interfaces are
eliminated, resulting in superior material response under bending and
compression.
Having fully interconnected reinforcing phases may also provide benefits for
impact
absorption applications, in which the in-plane properties of a thin material
can determine
the degree of damage. Additionally, the method presented above provides a
clear
advantage in manufacturing structural components by avoiding any shaping
processes
but instead fabricating the reinforcing phase in the final desired geometry.
[0150] The following is a description of exemplary, illustrative,
embodiments of the
composite material systems and methods disclosed herein.
[0151] The fabrication process embodied by FIG. 1 begins with the design
of one or
more geometries that will serve as the reinforcing phase of the composite
material. The
precursor resin may determine the constitutive properties of the resulting
reinforcing
phase, while the architecture will determine the structural response (i.e.,
stretching or
bending dominated). The structure is fabricated using additive manufacturing
technologies such as Stereolithography (SLA) or Digital Light Processing (DLP)
3D
printing, which allows arbitrary, continuous geometries to be made. The
printed structure
may then be placed in a furnace to undergo a pyrolysis process in vacuum or
inert
atmospheres. The resulting reinforcing phase can be a carbon or ceramic
material. An
optional coating process could be done prior to infiltrating the resulting
reinforcing phase
with a selected matrix phase. During the infiltration step, additional
processes such as
vacuum degassing or sonicating can help ensure complete infiltration of the
matrix
phase. Lastly, the resulting composite can be post-cured through UV or heating
processes.
[0152] In an embodiment presented in FIG. 2A, a subset of a carbon
reinforcing
phase 10 made through the process described above is embedded in an epoxy
matrix
16. In this case, a stretching-dominated architecture was chosen due to its
high
stiffness-to-density ratio ¨ unattainable by the bending-dominated
architectures
achievable via polymer waveguide patterns. A given truss element in this
structure also
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has a variable cross-section, reinforcing the lattice nodes 12 and increasing
the stiffness
compared to a constant cross-section structure. In this particular geometry,
truss
elements 14 can initiate and terminate at any point within the material, not
necessarily at
an edge, as required by waveguide processes. A modification of this embodiment
is
shown in FIG. 2B, where a given truss element is allowed to have non-zero
curvature
18, and truss elements can be oriented perpendicular to the thickness
direction 20.
[0153] An embodiment presented in FIG. 3 shows a subset of a continuous
3D
carbon phase made of shells or surfaces 22, which is infiltrated by an epoxy
matrix
phase 26. The surfaces in the reinforcing phase can have a non-zero Gaussian
curvature, which cannot be attained through waveguide processes. This geometry
was
achieved by using the surfaces of an octet-truss structure. In this geometry,
isolated
regions 28 can be fabricated to prevent infiltration from the matrix phase 26,
constituting
a gaseous phase. Lastly, the thickness of the surfaces in this structure are
designed to
be non-constant 24, which is not possible through waveguide processes.
[0154] Another embodiment, presented in FIG. 4, shows a modular structural
element made of a composite material as described in previous embodiments.
Unlike
typical fiber-based composite materials, the reinforcing phase 30 is designed
to have
the same shape as the structural component (e.g., a tube), requiring no
additional
shaping processes. In this case, a bending-dominated architecture was chosen
to add
compliance and increase the energy absorption capability of the part. The
structural
component has a primary matrix phase 32, while the inner volume of the tube
can be left
empty or it can be filled with a secondary matrix phase 34.
[0155] FIGs. 5A-5B present an embodiment in which functional grading of a
structural component (made from a composite material as described in previous
embodiments) is achieved. The structural part has one continuous reinforcing
phase
with several different geometries 36, 40, 42, and 46. A bending-dominated
tetrakaidecahedron architecture is used for the top region, in which the cross-
sectional
area of the elliptical truss elements increases from 36 to 40 to 42. The
domain transition
38 from region 36 to region 40 is continuous, and the connectivity is
unaltered (i.e., truss
elements do not end abruptly ¨ as is the case with some functional grading
attained
through waveguide processes). The bottom region 46 consists of a stretching-
dominated octet-truss architecture with circular cross-section truss elements
and
continuous transition 44 to the top region.
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[0156] In one embodiment a stiff and damping composite material is made
through
the design of resonators in the microstructure of the phases, as shown in FIG.
6. The
unit cell 48 is made of an octet-truss architecture with a resonator 50 inside
the unit cell.
The resonator consists of a cantilever beam with added micro-inertia at the
free end,
which is tuned to resonate at a given frequency w, determined by the length of
the beam
and the amount of micro-inertia at the free end. The unit cell can be made
with a
combination of truss elements and shells, which can isolate the resonator from
the
primary matrix that infiltrates the reinforcing unit cell 48. If shells are
present, the inner
volume of the octahedron within the octet 52 can be left empty to allow free
vibration of
the resonator, allowing damping properties in an otherwise stiff material.
[0157] An embodiment which has been reduced to practice is depicted in
FIGs. 7A-
70. In this embodiment, a sheet with a three-dimensional continuous octet-
truss
architecture 54, of overall dimensions 12.5 x 4 x 0.13 cm, is fabricated via
DLP 3D
printing using an Autodesk Ember printer and the PR-48 resin. The unit cell
size in the
resin structure 56 is ¨ 1.3 mm, with circular cross-section truss elements.
The resin
structure is then pyrolyzed in a furnace in an inert atmosphere at a peak
temperature of
1000 .C. The resulting carbon structure 58 undergoes isotropic shrinkage to
40% of the
original volume, with only 7% of the original mass. The resulting carbon unit
cells 60
maintain the original octet-truss geometry and a characteristic size of ¨ 500
pm. The
carbon structure is then infiltrated by an epoxy matrix phase 62, becoming the
reinforcing phase 64 of the composite structural sheet.
[0158] FIG. 8 depicts one possible method of manufacturing the
reinforcing phase of
the composite material described in previous embodiments via DLP or SLA 3D
printing.
A printer head 66 is bonded to the edge of the reinforcing phase, and pulls
the structure
vertically during the printing process. The print screen 70 has a layer of
uncured
precursor resin which polymerizes as an arbitrary exposure pattern 72 is
projected from
below. Note that this allows truss elements 68 with arbitrary cross-sections
which
commence and terminate away from the edges of the structure, in addition to
truss
elements which are perpendicular 74 to the build direction.
[0159] In general, certain illustrative embodiments of a composite material
system
with three-dimensional, arbitrarily architected, fully interconnected phases
and a method
of making the same are presented. Certain embodiments in which the reinforcing
phase
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is fully interconnected and made up of truss elements with varying cross-
sections and
non-zero curvatures ¨ infiltrated by a continuous matrix phase ¨ are
described.
Interconnected three-dimensional reinforcing phases with shells of non-zero
curvature
and varying thickness are made possible through these composite material
systems.
Modular structural parts made of the composite material described above, with
functionally graded continuous phases, are presented in some embodiments. In
addition, certain embodiments present enhanced vibrational damping in the
composite
material through the design of resonators in the microstructure, without the
need of
dissipative viscoelastic phases that affect the material's stiffness.
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[0180] The invention can be further understood by the following non-
limiting
examples.
[0181] Example 1: Impact Response of 3D Carbon Architectures
[0182] Fabrication and design of materials with high stiffness- or
strength-to-density
ratios has been studied through the use of cellular materials. In particular,
beam-based
lattice architectures have enabled the creation of lightweight-but-stiff
materials (1; 2) as
well as strong materials that approach theoretical bounds (3). Many of these
studies
have focused on the static response of these materials, while few works have
studied
the dynamic response of lattice architectures. In particular, some works have
studied the
dynamic compression of lattice structures at the pm-scale (4), while others
have studied
the impact of macro-scale structures such as lattice-core sandwich plates (5).
Due to the
length scales and tessellations associated with these studies, neither
achieves proper
separation of scales in which the length-scale of the boundary conditions is
much
greater than that of the inherent microstructure. Such separation would allow
probing of
the true material properties as opposed to the discrete structure's
properties.
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[0183] In the present Example, we describe the supersonic impact
response of
carbon lattice architectures (i.e., a form of reinforcing phase in the present
composite
materials) while maintaining proper separation of scales. Using a two-photon
lithography
manufacturing process, we fabricate three-dimensional lattice architectures
with
nanometer-scale features of different unit cell geometries and relative
densities (8 to
26%) and observe marginal damage after impacts at supersonic velocities (500
to 1100
m/s). These results show how a lightweight architected phase (prior to any
infiltration)
can provide extreme resilience to impact.
[0184] 1.1 Sample Design and Fabrication
[0185] Since architecture leads to different mechanical properties in the
static regime
(6; 7), the objective was to explore the effect of architecture on supersonic
impact of
lattice architectures. Polymeric lattices of rigid octet and non-rigid
tetrakaidecahedron
unit cells were fabricated using a two-photon lithography process
(Nanoscribe), with unit
cell sizes ranging from 5 to 10 pm (see FIGs. 10A-10B). Additionally, the beam
radii
were modified such that samples with three distinct relative densities of 8,
17, and 26%
were achieved.
[0186] A sufficiently large tessellation (approximately 60 x 60>< 15
unit cells) was
selected such that the effective sample size was much greater than the size of
a unit
cell, allowing the lattice to be approximated as an effective material. The
polymeric
samples were then subjected to a pyrolysis process in vacuum up to 900 C,
resulting in
monolithic carbon lattices with isotropic shrinkage of 80%, while retaining
the original
geometry (see FIGs. 11A-11D).
[0187] For the smallest initial unit cells (i.e., 5 pm), the resulting
carbon unit cells had
sub-micron dimensions, with beam diameters down to ¨ 200 nm. Although minor
warping takes place during pyrolysis, the final unit cell geometry corresponds
to the
original polymeric one.
[0188] 1.2 Impact Experiments
[0189] The resulting carbon architectures (i.e., the reinforcing phases)
were
subjected to supersonic impact by accelerating 5i02 particles with diameters
ranging
from 7 to 14 pm. In all cases the particle diameter was at least one order-of-
magnitude
larger than the characteristic unit cell size. The method employed is defined
as laser
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induced particle impact test (LIPIT) (8; 9), which enables controllable impact
velocities of
up to 1 km/s while capturing the impact process with high-speed cameras. FIG.
12
shows a characteristic experiment for an octet lattice with 26% relative
density, and an
impact velocity of 1060 m/s.
[0190] For all lattices tested the projectile rebounded and the impact and
rebound
velocities were measured. Due to poor adhesion between the lattices and the
substrate,
the samples delaminated a few milliseconds after impact, requiring
modifications to the
samples that would enable post-mortem characterization. To effectively tether
the
samples to the substrate, a thin layer of PMMA resist was spun onto the
substrate,
resulting in a coating of a few hundred nanometers which bonded the lattices
to the
substrate (see FIGs. 13A-130).
[0191] 1.3 Theoretical Elastic Wave Speeds
[0192] To confirm that the observed behavior is substrate-independent
(i.e.,
unaffected by the stiffness or thickness of the substrate), we propose a
simplified
problem in which a planar elastic wave emanates from the impact site through
the
thickness of the lattice, as shown in FIG. 14A. Given that the effective
Young's Modulus
of a non-slender octet lattice can be estimated (7) as
E* = Es [2.95 (92 + 103.3 (93.931, (1)
where Es is the constituent material's Young's Modulus and ril is the strut
radius-to-
length ratio, the elastic wave speed can be approximated as
Clat = (2)
P
where p is the effective lattice density. Using worst-case values such as ril
= 0.2, p =
1252 kg/m3 (corresponding to a carbon octet with 60% relative density), and a
sample
thickness of 14 pm, the elastic wave would take ¨ 12 ns to traverse the sample
twice
(i.e., roundtrip). Since the high-speed camera frames allow approximate
measurements
of impact time, an average impact time of 4 ns implies that no information
about the
substrate is transmitted to the particle prior to rebound. In other words, the
rebound
behavior is solely a function of the lattice material and not the substrate.
This is
summarized in the x-t diagram presented in FIG. 14B.
[0193] To experimentally validate this claim, we designed a suspended
sample
experiment in which an identical lattice was mounted on Si stilts, several
microns away
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from the substrate. This experiment mimicked a macro-scale drop tower impact
experiment in which a plate with fixed-fixed boundary conditions is impacted
by an
accelerated mass (see FIGs. 15A-15D). In this way, the lattice was completely
decoupled from the Si substrate it rested on previously.
[0194] Performing the same experiment on the suspended sample, at an impact
velocity of 588 m/s, resulted in the same rebounding behavior and a rebound
velocity of
320 m/s (see FIG. 16). This result confirmed that the observed response was
substrate-
independent.
[0195] 1.4 Energy Absorption Scaling Behavior
[0196] Performing impact experiments on samples of both rigid and non-rigid
architectures, at different relative densities, yielded the results in FIG.
17. The
experiments at low impact energy (i.e., mq, , where vo is the impact
velocity), yielded
the highest restitution coefficients (i.e., the restitution coefficient is the
ratio between
rebound velocity and impact velocity, yr/y0).
[0197] Although rigid and non-rigid architectures can have up to an order-
of-
magnitude difference in modulus in the static regime (7), no conclusive
difference was
observed in supersonic impact conditions. Octet and tetrakaidecahedron samples
had
similar restitution coefficients throughout the regime of kinetic energy
probed.
[0198] The trend observed in FIG. 17 seems to point to a correlation
between impact
energy and restitution coefficient, independent of architecture. Experiments
with higher
impact energies and different relative densities seemed to show a decrease in
restitution as relative density decreased, possibly due to a lower effective
material
strength and more energy being dissipated in localized damage. Despite this
slightly
localized damage at high impact energies, these results show benefits in using
an
architecture for impact mitigation, since energy can be distributed more
readily away
from the impact site and localized damage can be reduced. Given that the
impact
process does not allow time for the elastic waves to reach the projectile
before rebound
takes place, it is highly likely that this process is dominated by inertia and
not
architecture, which still requires careful design and control of material
distribution.
[0199] Additional notes: The matrix phase may increase energy dissipation
or
mitigation because the matrix phase corresponds to additional inertia (i.e.,
mass). In
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terms of damping, a viscoelastic matrix such as a polymer may further dampen
vibrations or impact energy. The strength of the material may also increase,
since the
matrix may serve to prevent cracks from opening/propagating. Specific values
of these
increases may depend heavily on the choice of architecture and materials.
[0200] One example is a 'coated sample' (covered by a thin layer of epoxy),
which
corresponds to a composite material system having a structure partially
infiltrated by a
matrix phase (e.g., epoxy). Referring to Figs. 13B and 17, adding a thin
polymeric layer
decreased the restitution coefficient to about 0.65 of that for the uncoated
sample (35%
reduction). This translates to the particle having 58% less kinetic energy
upon rebound.
The energy mitigation measure does not change since the particle still
rebounds and
structural integrity is maintained, but the energy dissipated/absorbed (i.e.,
transformed
into heat or permanent deformation) increases by 20% when compared to the
sample
with no matrix (the energy absorbed by the uncoated sample was 66% of the
impact
energy, while the coated sample absorbed 86%). Since this was a thin coating,
this may
be a lower bound of absorption increase when adding a matrix, in an
embodiment. Note
that energy absorbed corresponds to the difference between the impact energy
and the
kinetic energy of the impactor after rebound.
[0201] Generally, inclusion of a matrix may result in a reduction of the
restitution
coefficient, but an increase in energy absorption. This means less energy will
be
transferred back to the impactor to travel in the opposite direction, since
some of it is
absorbed due to the viscoelastic/plastic properties of the matrix. Having a
matrix may
enhance all damping properties compared to the structure free of the matrix
phase. For
instance, it may increase a vibrational frequency band gap width or even
decrease the
transmission intensity of vibrations at some frequencies. From a static
perspective, the
strength of the materials may significantly increase when the matrix phase is
present
compared to a structure free of the matrix phase, and the failure may go from
catastrophic/brittle to ductile-like.
[0202] Example 2: Material Damping through Architecture
[0203] Careful design of architected materials can lead to interesting
dispersive
behavior, which can translate to energetic dissipation. Works have shown large
3D-
printed effective materials that can dampen vibrations (10) as well as micro-
scale
materials that dissipate ultrasonic waves in water (11), through the use of
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mechanisms such as Bragg scattering and local resonance. Proper design of
architecture, while accounting for material density and stiffness, can lead to
effective
material damping with stiff, non-dissipative constituent materials.
[0204] In the present Example, we utilize careful design of architecture
to take
advantage of Bragg scattering and local resonance mechanisms to dissipate
vibrational
energy with stiff, non-damping constituent materials.
[0205] 2.1 Bragg Scattering: tetragonal lattice
[0206] Starting with a tetragonal unit cell such as the one depicted in
FIG. 18A,
volumetric expansion of its members would result in buckling instabilities
that change
the unit cell to the ones shown in FIGs. 18B-180, depending on the degree of
volumetric
expansion.
[0207] Introducing curvature to the beams not only changes the unit cell
geometry,
but it also changes its effective mechanical properties, particularly in the
in-plane
directions. We numerically explore the effect of this buckled geometry on the
dynamic
properties of a material made up of these tetragonal unit cells.
[0208] For this numerical study, each unit cell was assumed to have a
polymeric core
with a Si coating. The horizontal beams had a polymer minor radius of 0.25 pm,
a major
radius of 0.9 pm, and a Si coating of 0.4 pm, while the vertical beams had a
polymer
radius of 0.9 pm and an identical coating. The original tetragonal unit cell
had
dimensions 20 x 20 x 5 pm.
[0209] An eigenfrequency analysis on the three-dimensional unit cells at
each stage
of buckling was performed using the commercial finite element package COMSOL
Multiphysics. Each unit cell was divided into the horizontal- and vertical-
beam domains,
each containing an elastic material model for the corresponding homogenized
beam's
properties. The homogenized properties were obtained using a weighted volume
average from the known volumes of each material (i.e., polymer and silicon)
and the
corresponding Young's moduli, densities, and Poisson's ratios for each
material.
[0210] Using the tetragonal unit cells presented in FIGs. 18A-18F, Bloch
boundary
conditions were applied to the corresponding faces of the unit cells. Using
the
irreducible Brillouin zone depicted in FIG. 19D, the wavevector was swept
through the
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boundaries and the eigenfrequencies were calculated at each state. Tetrahedral
elements were used and mesh convergence was confirmed in all cases.
[0211] FIGs. 19A-19D show the appearance of partial band gaps in the x-
and -y
directions (due to symmetry), corresponding to frequencies that cannot
propagate
throughout a material comprised of said unit cells. Given that no band gaps
appear in
the unbuckled case in FIG. 19A, the appearance of band gaps in FIGs. 19B-190,
is
attributed to Bragg scattering enabled by the buckled geometry. The
vibrational
frequency band gap widths may scale linearly with the characteristic length in
the
architecture. Specifically, the Bragg condition states that significant
effects might occur
at frequencies where AL = c/f, where AL is the characteristic dimension of the
microstructure, c is the speed of sound in the material, and f is the
frequency (showing
the linear relation with frequency).
[0212] These results show the tunability of architected structures which
enables
dispersion mechanisms that can lead to damping. The absolute frequency and
width of
the resulting band gaps can be tuned by changing unit cell sizes and
constituent
materials. The results depicted here were achieved with a fully elastic
material model,
meaning that the same behavior can be attained with stiff materials that are
not
inherently damping, such as metals, ceramics, or carbon.
[0213] 2.2 Local Resonance: auxetic architectures with resonators
[0214] Besides Bragg scattering, local resonance can be used to enable band
gaps,
commonly at lower frequencies. In this study, we utilize the auxetic unit cell
presented
by KrOdel et al. (12), while adding a resonator (i.e., a lumped mass attached
to a
cantilever beam) to the unit cell, as shown in FIGs. 20A-20B.
[0215] We performed a numerical study as done in Section 2.1, assuming a
fully
polymeric unit cell with dimensions 60 x 60 x 210 pm. An elastic material
model was
used (i.e., no contituent material damping assumed), and the dispersion
relations in the
1--X direction (see FIG. 19D) were calculated.
[0216] The dispersion relation of the unmodified auxetic unit cell (see
FIG. 21A)
shows no band gaps in the direction of interest, while adding a resonator (see
FIG. 21B)
introduces a band gap at 1.5 MHz. Just as in Section 2.1, the width and
location of this
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band gap is fully tunable based on unit cell dimensions, materials, and
resonator
parameters.
[0217] To experimentally validate the numerical results from FIGs. 21A-
21B, we
fabricated samples of the same dimensions, materials, and parameters and
tested them
.. in a custom vibration transmission experiment in vacuum (see FIGs. 22A-
220).
[0218] Using the setup presented above, a continuous sine wave with
varying
frequencies between 1-3 MHz was transmitted through the samples (see FIGs. 23A-
23E).
[0219] Performing a frequency sweep showed a band gap centered at a
frequency of
.. approximately 2.4 MHz for the resonator unit cell, as shown in FIG. 230.
The band gap
took place at a slightly higher frequency than the one predicted by the
simulations in
FIGs. 21A-21B, since establishing proper contact with the transducer strained
the
lattices, which can change the dispersive behavior (see the difference in
strain between
FIGs. 23D-23E).
[0220] To further validate this band gap, we performed an additional
transmission
experiment where a chirp (instead of a continuous wave) was transmitted
through the
lattice. In this case, the chirp contained frequencies between 1-3 MHz, and a
Fast
Fourier Transform (FFT) was applied to the transmitted signal to analyze its
frequency
content (see FIGs. 24A-240).
[0221] These experiments and simulations on a polymeric auxetic lattice
show the
possibility of adding local resonance as a mechanism to introduce damping to a
material. Since the material properties in the simulations were fully linear
elastic, this
behavior can be extended to a variety of materials including metals, ceramics,
and
carbon.
[0222] Example 3: Fully Tunable Elasticity through Spinodal
Decomposition-
derived Architectures
[0223] Architected materials with beam-based architectures have been
shown to be
effective in achieving high stiffness-to-density ratios (1; 6), but they still
fall short from
the theoretical bounds. Additionally, their mechanical properties deviate from
the
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theoretical predictions due to the existence of nodes (7), which also serve as
stress
concentrations that can lead to failure.
[0224] In this Example, we describe the use of spinodal decomposition to
create
shell-based microstructures that lack nodes and achieve superior mechanical
properties
and higher mechanical tunability than beam-based architectures.
[0225] 3.1 Elastic Surface Tunability
[0226] Using spectral methods and an anisotropic energy functional (13),
numerical
spinodal decomposition can lead to microstructures with fully tunable
elasticity. (For
exemplary methods describing computational spinodal decomposition, see: A.
Vidyasagar, S. KrOde!, and D. M. Kochmann, "Microstructurel patterns with
tunable
mechanical anisotropy obtained by simulating anisotropic spinodal
decomposition,"
Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Science,
vol. 474, no. 2218, p. 20180535, 2018.) Using only the boundaries of the
resulting
microstructure (i.e., shells), we computed the 3D elastic surfaces using the
commercial
finite element code Abaqus and show full tunability of the effective Young's
modulus of
the microstructure (see FIGs. 25A-25D).
[0227] The elastic surfaces shown in FIGs. 25A-25D show unparalleled
elastic
tunability, which cannot be achieved with commonly studied beam-based
architectures.
Besides this highly tunable behavior, spinodal structures can exhibit Young's
moduli that
approach the theoretical bounds and are substantially greater than other
structures such
as trusses and triply-periodic minimal surfaces (14-16), as shown by numerical
simulations on these structures (see FIG. 26).
[0228] Applying periodic boundary conditions on the columnar structure,
the P-cell
minimal surface, and a hollow octet truss with equal relative densities shows
that the
spinodal structure has a superior elastic modulus when probed in the z-
direction,
coming closer to the Voigt bound. Additionally, applying a fit of the form
EVE, a#a ,
where E* is the effective Young's modulus, Es is the constituent material's
Young's
modulus, p is the relative density, and a is the scaling exponent, yields a
lower (more
desirable) scaling exponent for the spinodal structure.
[0229] As mentioned above, one clear benefit of spinodal structures is
their lack of
nodes, which reduces stress concentrations at which cracks may initiate. This
leads to
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surfaces with a quasi-constant, low curvature as opposed to trusses which have
infinite
curvature at nodes (see FIGs. 27A-27B).
[0230] The curvature distribution for the octet truss above shows a
bimodal
distribution even when applying fillets to the nodes. Although this bounds the
maximum
curvature in the structure, the absolute values are much larger than those of
the
spinodal structure.
[0231] It should be mentioned that the effective modulus of the
structures,
geometries, and/or systems disclosed herein, comes closer to the theoretical
bound
(Voigt bound) than that of typical trusses or transverse fibers (i.e., the
points will lie
closer to the black "Voigt" line in FIG. 26). In terms of elastic tunability,
it should also be
mentioned that composite material systems disclosed herein, as those having a
structure with a spinodal geometry, may be characterized by deterministic
anisotropy (or
isotropy if desired) of elasticity, damping, impact energy absorption, and/or
other
properties or features.
[0232] 3.2 Fabrication of shell-based spinodal materials
[0233] We fabricated polymeric spinodal structures at the microscale
using a two-
photon lithography process. Using deposition techniques such as atomic layer
deposition (ALD) or magnetron sputtering we then deposited anywhere from 5 nm
to 5
pm of a metal or ceramic. In this case, the resulting material is a composite
whose
reinforcing phase is shell-based. Alternatively, the polymeric core can be
removed and
left empty or replaced with another matrix. To expose the polymer under the
newly
applied coating, we used focused ion beam (FIB) milling to remove small
sections of the
coating. Lastly, introducing the structure in an etching chamber such as 02
plasma, we
removed the inner polymeric core, resulting in a shell-based spinodal
structure.
[0234] We fabricated these structures at the micro-to-centimeter scale as
well using
a DLP 3D printing method as shown in FIGs. 29A-29D. The resulting shell-based
polymeric structure was then pyrolyzed in vacuum up to 1300 C, resulting in a
shell-
based carbon reinforcing phase which can be subsequently infiltrated by a
matrix.
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[0235] Example 4: Micrographs of Pyrolyzed Plate for Blast Impact
Testing
[0236] FIGs. 30A-300. Architected plate for blast impact testing. FIG.
30A. Polymeric
precursor plate and resulting pyrolyzed plate, (FIG. 30B) micrograph of an
octet carbon
architecture, (FIG. 300) micrograph of a tetrakaidecahedron architecture.
[0237] Example 5: Reinforcing-phase Blocks of Varying Architectures
[0238] FIGs. 31A-31F. Cubes of example reinforcing phases. FIG. 31A.
Polymeric
octet cube, (FIG. 31B) pyrolyzed carbon octet cube from FIG. 31A, (FIG. 310)
pyrolyzed
carbon 3D kagome beam, (FIGs. 31D-31F) close-ups of FIGs. 31A-310.
[0239] Example 6: Direct Fabrication of Tubular Architected
Components
[0240] FIGs. 32A-32F. Tubular architected component. FIG. 32A. Polymeric
tube
with tetrakaidecahedron architecture, (FIG. 32B) top view of FIG. 32A, (FIG.
320) close
up of FIG. 32B, (FIG. 32D) pyrolyzed carbon tube with tetrakaidecahedron
architecture
prior to infiltration, (FIGs. 32E-32F) close-ups of FIG. 32D.
[0241] References corresponding to Examples 1-6
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B. Duoss,
J. D. Kuntz, M. M. Biener, Q. Ge, J. A. Jackson, S. 0. Kucheyev, N. X. Fang,
and C. M.
Spadaccini, "Ultralight, ultrastiff mechanical metamaterials," Science, vol.
344, no. 6190,
pp. 1373-1377, jun 2014. [Online]. Available:
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[0243] [2] L. R. Meza, S. Das, and J. R. Greer, "Strong, lightweight,
and recoverable
three-dimensional ceramic nanolattices," Science, vol. 5, no. 6202, pp. 1322-
1326,
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Messner, N.
Barton, B. J. Jensen, and M. Kumar, "Dynamic Behavior of Engineered Lattice
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Materials," Scientific Reports, vol. 6, p. 28094, 2016. [Online]. Available:
http://www.nature.com/articles/srep28094
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Zakraysek, and V.
S. Deshpande, "Impact response of sandwich plates with a pyramidal lattice
core,"
International Journal of Impact Engineering, vol. 35, no. 8, pp. 920-936,
2008.
[0247] [6] L. R. Meza, G. P. Phlipot, C. M. Portela, A. Maggi, L. C.
Montemayor, A.
ComeIla, D. M. Kochmann, and J. R. Greer, "Reexamining the mechanical property
space of three-dimensional lattice architectures," Acta Materialia, vol. 140,
pp. 424-432,
2017. [Online]. Available: http://dx.doi.org/10.1016/j.actamat.2017.08.052
[0248] [7] C. M. Portela, J. R. Greer, and D. M. Kochmann, "Impact of node
geometry
on the e if ective sti if ness of non-slender three-dimensional truss lattice
architectures,"
Extreme Mechanics Letters, vol. 22, pp. 110-138, 2018. [Online]. Available:
https://doi.org/10.1016/j.em1.2018.06.004
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Pezeril, K. A.
Nelson, and E. L. Thomas, "High strain rate deformation of layered
nanocomposites,"
Nature Communications, vol. 3, no. May, pp. 1164-1169, 2012. [Online].
Available:
http://dx.doi.org/10.1038/ncomms2166
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and K. A.
Nelson, "Dynamics of supersonic microparticle impact on elastomers revealed by
real
time multi frame imaging," Nature Publishing Group, pp. 1-6, 2016. [Online].
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Daraio,
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[0253] [12] S. Krodel, T. Delpero, A. Bergamini, P. Ermanni, and D. M.
Kochmann,
"3D auxetic micro-lattices with independently controllable acoustic band gaps
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2014.
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with tunable mechanical anisotropy obtained by simulating anisotropic spinodal
decomposition," Proceedings of the Royal Society A: Mathematical, Physical and
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[0258] Example 7: Energetic Calculations of Impact and Comparison to
Kevlar
[0259] The impact behavior of an octet carbon architecture fabricated
through the
two-photon lithography process described in the technical writeup (with
relative density
of = 26%) was compared to a Kevlar 170 g/m2 satin weave fabricl.
[0260] An area-normalized energy mitigation metric can be defined as
where W is the absolute energy mitigated (absorbed and/or redirected) and A is
the
area associated with the impact. Using the values for a single sheet of this
type of
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Kevlar (with areal density of o
a,Kev = 0.17 kg/m2), the obtained value was ilikev = 3.26x
105 J/m2 compared to ijiLat = 2.61 x 104 J/m2. The difference in this metric
is due largely
to the difference in scales associated with the experiments. It must also be
noted that
the Kevlar sheets were perforated by the projectile and lost physical
integrity, while the
lattice underwent minor permanent deformation and was not perforated by the
impactor.
[0261] Performing one last normalization based on the areal density of
each material
(Pa,Lat = 0.008 kg/m2 for the lattice), provides a metric of energy mitigation
per kg (or,
"density-normalized impact energy mitigation metric") of material of 1.9 x 106
and 3.2 x
106 J/kg for Kevlar and the lattice, respectively.
[0262] References corresponding to Example 7
[0263] [1] F. Figucia, US Army R&D Command (1980)
[0264] Example 8: Carbon by design through atomic-level architecture
[0265] Overview: It has been a longstanding challenge to design and
create
materials with a combination of high strength, high deformability/ductility,
large elastic
limit and low density, as these properties may be mutually exclusive. Here, we
have
created pyrolytic carbon micropillars with a specific type of atomic-level
architecture by
controlling the precursor material and conditions of pyrolysis. Nanomechanical
experiments demonstrated that the pyrolytic carbon micropillars exhibit a
tensile
strength of -2.5 GPa and a compressive strength approaching theoretical limit
of -11.0
GPa, a substantial elastic limit of 20-30%, and a low density of 1.0-1.8
g/cm3,
corresponding to a specific strength of 8.07 GPa/g cm3 which surpasses the
property of
all existing structural materials. Pyrolytic carbon micropillars with
diameters below 2.3
pm exhibited a rubber-like behavior and sustained a large compressive strain
of
approximately 50% without catastrophic failure, while larger ones exhibited
brittle
fracture at a strain of -20%. Large-scale atomistic simulations revealed that
these
excellent mechanical properties are enabled, at least in part, by the local
deformation of
1 nm curled graphene fragments within the pyrolytic carbon microstructure, the
interactions between neighboring fragments, and the presence of strong
covalent bonds
between the carbon atoms.
[0266] In modem advanced material design, the creation of high-performance
materials that combine high strength, substantial deformability, a large
elastic limit, and
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low density is a longstanding goal and challenge. Two pairs of apparent
conflicts exist
for nearly all structural materials: high strength versus high
deformability/ductility and
high strength versus low density. For example, metals and alloys are ductile
and can
sustain fracture strain beyond 10% due to accommodation of dislocation
plasticity during
.. deformationl, but their yield strengths are usually limited on the order of
-100 MPa and
their elastic limits are only around 2%. Ceramics have higher strength (up to
several
GPa), but their fracture strains are usually below 5% due to the absence of
mobile
lattice dislocations during deformationl. Metallic and ceramic materials
generally have
densities beyond 2.7 g/cm3. Polymers2 and porous materials (like foams3,
nanolattices4,
nanosponges8) are lightweight, and their densities are much lower than those
of most
metals and ceramics. These materials are significantly deformable and can
typically
sustain elastic strains beyond 50%2-8, but their strengths are only on the
order of -10
MPa.
[0267] Numerous studies8-13 have shown that mechanical properties (such
as
strength and ductility) of materials are significantly determined by their
microstructures
and intrinsic and extrinsic dimensions. Therefore, tailoring the
microstructures or
intrinsic and extrinsic dimensions is an effective way to alter the mechanical
properties
of materials. For some polycrystalline metals, reducing the grain size and
incorporating
nanotwinned microstructure8,7 at the atomic level have increased their
strengths from
.. -100 MPa to -1 GPa. High-entropy alloys (HEAs), which contain five or more
principal
elements with nearly equal atomic concentrations, exhibit high yield strengths
of 1-3
GPa and fracture strains of 10-30%8 due to solid solution, which is controlled
by the
mixture of multiple principal elements at the lattice scales8. Single
crystalline metals with
extrinsic dimensions (i.e., sample size) below -10 p.m exhibit the so-called
"smaller and
stronger" size effect9-11, examples include Au nanowires/nanopillars with
diameters of
tens of nanometers that exhibit ultra-high tensile strengths of 5.6 GPa, close
to the
theoretical limits10. This ultra-high strength is associated with a pristine
and nearly
defect-free crystalline microstructure and/or dislocation source exhaustion9
at
nanoscale. For ceramics, recent studies12 showed that micro-sized shape memory
zirconia pillars with few crystal grains along the gauge section can withstand
pseudo-
elastic strains of approximately 7% by undergoing a martensitic phase
transformation;
the compressive strengths of these ceramic pillars were up to 1.5-2.5 GPa. For
polymer,
when strong and hard phases (in forms of nanofibers or nanoparticles) are
introduced
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into polymer matrices, the resultant polymer-based composite typically have
strengths
up to -0.5 GPa13,14.
[0268] Carbon-family materials contain a large number of a110tr0pe515
due to the
unique electronic structure of the carbon atom, which allows the formation of
sp-, 5p2-
and 5p3-hybridized bonds. The mechanical and physical properties of carbon
materials
can vary widely as a result of different bonding structures. As two
representative carbon
allotropes, graphene and carbon nanotubes with 100% sp2 bonds have been
reported to
have ultra-high tensile strengths up to 100 GPa18. The mechanical properties
of these
two allotropes are extremely sensitive to defects such as vacancies, pentagon-
heptagon
pairs, and grain boundaries, which can significantly decrease their strength
due to stress
concentrations around the defect518-20. The small dimensions of individual
graphene
sheets and nanotubes render them impractical for structural applications at
larger
scales, but their three-dimensional (3D) assemblies exhibit superelastic
behavior via
buckling and bending of the basic building blocks and can be scaled up to the
macroscopic 1eve121-24. The porous microstructure of 3D graphene assemblies
makes it
possible for these architectured materials to be extremely lightweight, with
low densities
of 0.001-1.0 g/cm3 and superior elastic limits up to 50%, but strengths as low
as 10
mpa21-23. Recently, various pyrolytic carbon materia1525-28 have been
synthesized via
pyrolysis using polymeric precursors. Bulk pyrolytic carbon samples28 prepared
at 1000
C had an optimal hardness of 4 GPa and a density of 1.1-1.4 g/cm3. Micro-sized
glassy
carbon27 synthesized at a high temperature of 400-1000 C and a high pressure
of 10-
GPa exhibited a compressive strength of 9 GPa and a density of 2.0-2.5 g/cm3.
The
pyrolytic carbon materials usually have a cleavage plane with a fracture
strain below
3%27. Glassy carbon nanolattices28,28 with characteristic strut sizes of
approximately 200
25 nm and densities of 0.3-0.7 g/cm3 have been fabricated via pyrolysis
using photoresist-
based microarchitectures made via two-photon lithography, achieving a
compressive
strength of approximately 300 MPa at a fracture strain below 10%. The
microstructures
of these pyrolytic carbon materials typically consist of curved carbon layers
or fullerene-
like fragments with dimensions of a few nanometers, leading to a strong
dependence of
their mechanical properties and performance on the initial precursors, the
atomic-level
microstructure after pyrolysis, and processing temperature and pressure25,28.
These
studies suggest that multiple properties (including density, strength and
deformability) of
materials could be simultaneously improved by designing and controlling the
atomic-
level architectures and reducing the characteristic dimensions. It also
highlights both the
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promise and the challenges associated with the design and fabrication of high-
performance materials that possess a combination of high strength, substantial
ductility,
large elastic limit, and low density.
[0269] In this illustrative Example, we disclose pyrolytic carbon
micropillars with
diameters of 0.7-12.7 p.m through two-photon lithography and pyrolysis.
Characterization based on transmission electron microscopy (TEM), Raman
spectroscopy and electron energy loss spectroscopy (EELS) revealed that these
micropillars comprise 1 nm-sized curled graphene fragments, an atomic-level
architecture achieved by controlling the precursor material and conditions of
pyrolysis. In
situ nanomechanical testing showed that the pyrolytic carbon have ultra-large
elastic
limits of 20-30%, high tensile and compressive strengths of 2.5 and 11.0 GPa,
low
densities of 1.0-1.8 g/cm3, and ultra-high specific strengths up to 8.07 GPa/g
cm3, and
that samples with diameters below 2.3 p.m can undergo substantial plastic
deformation
without failure even at applied strains in excess of 40%, exhibiting a rubber-
like
behavior. We incorporated the experimentally obtained microstructures into
large-scale
atomistic simulations to investigate the deformation mechanisms underlying the
superior
mechanical properties of the pyrolytic carbon pillars under uniaxial
compression and
tension.
[0270] FIG. 33A shows a schematic of the fabrication process of
cylindrical
micropillars with diameters of 6-50 p.m and heights of 12-100 p.m, printed
using two-
photon lithography direct laser writing (TPL DLVV) from IF-Dip, a commercial
acrylate-
based photoresist. During fabrication via TPL DLW, the sample geometry and
dimension can be accurately controlled. The subsequent pyrolysis at 900 C for
5 hours
in vacuum leads to complete carbonization and 98% volume shrinkage of the
polymeric
samples29. The resulting pyrolytic carbon pillars have diameters ranging from
1.28 to
12.7 p.m (20-25% of the dimension prior to pyrolysis) (FIGs. 33B-33C). A
residual
carbon ring visible on the silicon substrate represents the footprint of the
original pillar
and the constraint posed by the substrate during pyrolysis. Some samples were
fabricated with caps to accommodate the grips for uniaxial tension
experiments. More
details on the synthesis are provided below in this Example.
[0271] FIG. 33D contains a representative high-resolution TEM (HRTEM)
image of
the pyrolytic carbon pillar, with the selected area electron diffraction
(SAED) pattern in
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the inset, revealing its amorphous microstructure. The magnified TEM images in
FIGs.
33E-33F indicate the presence of numerous 1.0-1.5 nm-sized curled atomic
fragments,
which create sub-nanometer-sized voids (indicated by red arrows in FIGs. 33E-
33F),
distributed randomly throughout the pillar volume. Both the size of the carbon
layer
fragments and spacing between neighboring layers in our pyrolytic carbon
samples are
much smaller than those (about 4-6 nm and 1.67-1.99 nm, respectively)
fabricated
previously26,27. These microstructurel features provide a useful foundation
for estimating
the density of pyrolytic carbon micropillars by augmenting a reported
geometric model
developed for non-graphitized glassy carbon26. In this geometric model, the
density is
dependent on the average size and curvature of the carbon layer and on the
spacing
between neighboring layers. Using this model, we determined the density of the
pyrolytic carbon micropillars in this work to be 1.0-1.8 g/cm3, which is close
to that of
low-density type-I glassy carbon27,30. The relevant method details are
provided later in
this Example. FIG. 33G shows the Raman spectrum of a representative pyrolytic
carbon
micropillar, which contains two prominent peaks at Raman shifts of 1359 cm-1
and 1595
cm-1 that correspond to the graphitic D and G peaks, respectively. The ratio
(/D//G) of the
integrated area under the D band to that under the G band allowed us to
calculate the
approximately characteristic crystallite size L of the curled carbon layer
fragment31
observed in the HRTEM images (FIGs. 33E-33F), as indicated by the following
equation31:
(
ID
L coli4 ¨ (1)
\IG
where a is a constant of 2.4x10-1 , and is the wavelength (in units of
nanometers) of
the laser used in the Raman experiment. Using this equation, the
characteristic
crystallite size of the carbon layer fragment was calculated to be 2.4 nm,
which is
basically consistent with the size of 1.0-1.5 nm determined from our HRTEM
observations. It should be noted that for evaluation of the crystallite size
in the carbon
layer, HRTEM observations have higher accuracy than the approximate prediction
from
Eq. (1) based on Raman spectrum. In the subsequent calculations, the
characteristic
crystallite size of the curled carbon layer were determined to be 1.0-1.5 nm,
as derived
from the HRTEM observations. EELS, as shown in FIG. 33H, revealed the presence
of
a 1s-0* peak at 292 eV and a 1s-77* peak at 285 eV, which are consistent with
the 0-and
7z-bonds characteristic of 5p2-hybridized carbon. The fraction of sp2 bonds
was estimated
by using the two-window method32 and adopting all-5p2 raw glassy carbon as a
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reference materia127. The fraction of sp2 bonds is as high as 96.5%, which
indicates the
dominance of sp2 hybridization in the pyrolytic carbon micropillars. This
result is
consistent with previous experimental observations that pyrolytic carbon
materials
treated at high temperature contain mainly disordered sp2 bonds27 because sp3-
hybridized amorphous carbon is unstable above -700 C3 . This result also
implies that
these bonds correspond to layers of graphene. More details on the estimations
and
analyses based on the Raman spectra and EELS data are supplied in the
description of
method later in this Example. The above microstructurel characterization
revealed that
our pyrolytic carbon is an assembly of nanometer-sized curled graphene
fragments
interspersed with sub-nanometer-sized voids. Overall, this specific and
delicate
microstructure was designed and created by selecting the precursor materials,
and
controlling the dimensions/geometry of the printed samples and the pyrolysis
conditions.
[0272] To characterize the mechanical properties of the pyrolytic carbon
micropillars,
we carried out a series of nanomechanical experiments. The ex situ uniaxial
compression experiments were conducted in a nanoindenter equipped with a 120
m-
diameter flat punch indenter tip. FIG. 34A shows all compressive stress-strain
data sets
for micropillars with diameters from 4.6 rn to 12.7 p.m. It appears that all
the micropillars
deformed smoothly until failure, first deforming elastically up to
approximately 20-30%
strain, then yielding and plastically deforming over an additional -8-10%
strain before
fracture. Nonlinear behaviors occurred under the first -1-3% strain due to
slight
misalignment at the top surface of the micropillars. We estimated the Young's
modulus
to be 16-26 GPa based on fitting the linear elastic portions of the stress-
strain curves in
FIG. 34A. The failure strength of these micropillars increased from 3.8 GPa to
5.6 GPa
with decreasing diameter. FIG. 34B shows SEM images of a typical micropillar
with a
diameter of 7.17 rn before and after deformation, demonstrating that it broke
into small
pieces via brittle facture.
[0273] We also carried out similar and in situ compression experiments on
micropillars with diameters of -2 rn and smaller. The in situ compression
experiments
were conducted in a custom-made in situ nanomechanical instrument (SEMentor),
which allows the precise control of deformation with simultaneous video
capture33. FIG.
340 shows the compressive stress-strain response of a 2.25 m-diameter
micropillar,
which is characterized by a linear elastic regime up to -10% strain, followed
by an
extensive plateau-like plastic region up to -25% strain, and a final stage in
which the
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stress rapidly increased from 5.48 to 12.63 GPa over a strain increase of -
18%. This
stress-strain curve is similar to that of rubber. After unloading from the
maximum stress
of 12.63 GPa, the micropillar partially recovered upon the release of
approximately 10%
elastic strain. FIG. 340 depicts a sequence of snapshots of this sample during
the
experiment, with the numbered frames corresponding to the same numbered red
arrows
in the data. We observed that the micropillar shortened and thickened
gradually, without
localization or catastrophic failure until the maximum applied strain of
43.6%. (In situ
compression of pyrolytic carbon micropillar with diameter of 2.25 pm is
performed.
During compression, the micropillar shortens and thickens gradually with
increasing of
compressive strain. A slight tilt sometimes occurrs during compression. After
unloading,
the micropillar has an elastic recovery of about 10% strain.) SEM images
obtained from
front and back views of the pillar revealed a vertically aligned splitting
microcrack, which
likely nucleated under a large applied compressive stress and led to a slight
strain burst,
indicated by the blue arrow in the stress-strain data (FIG. 340). In this
Example 1, the
.. compressive strength of such samples corresponds to the stress at the first
burst. FIG.
42 shows the detailed in situ deformation process of another micropillar with
a diameter
of 2.26 p.m under compression and captures the nucleation and propagation of
the
splitting microcrack. The corresponding stress-strain data in FIG. 42, panel
(d), show
similar features to the plot in FIG. 340. A clear difference between these two
data sets
is that a large strain burst is visible in FIG. 42, panel (d), which may be
caused by the
fast propagation of microcracks. A similar deformation and failure signature
is observed
during the compression of nearly all the 2 pm-diameter micropillars. To
eliminate the
possible influence of the residual carbon ring (FIG. 34B), we focus ion beam
(FIB)
milling to remove the ring from the samples (see FIG. 340 and FIG. 42, panel
(d),
before compression). FIG. 43 the compressive deformation of a 1.86-pm-diameter
micropillar that retained the residual carbon ring, which bulged and detached
from the
substrate during compression and led to a substantial strain burst at a strain
of -36%,
as shown in FIG. 43, panel (d). The maximum attained stresses in FIG. 43,
panel (d),
are comparable to those in FIG. 340 and FIG. 42, panel (d), which suggests a
marginal
contribution of the residual carbon ring to the strength.
[0274] Uniaxial tension experiments on dog-bone-shaped specimens
fabricated
using the same procedure were conducted in situ, inside an SEMentor, which
enables
tensile testing that cannot be accomplished in a regular nanoindenter33. FIG.
34D
summarizes the tensile stress-strain data for samples with diameters of 0.7-
2.0 m. We
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observed that all the samples failed after linear elastic loading to an
elongation of 10-
25% via brittle fracture. (In situ tension of pyrolytic carbon micropillar
with diameter of
1.5 pm is performed. The micropillar is stretched to fail with a smooth
fracture surface;
the tensile fracture strain is up to about 26%.) A typical smooth fracture
surface is
shown in FIG. 34E. A statistical distribution of the tensile strengths of all
tested pyrolytic
carbon samples is shown in FIG. 34F and fits a two-parameter Weibull
distribution,
m [af
f(0-,)=¨ -Y e . , where 0-0 and m are material parameters. This
distribution yields
0- 0-
0 \ 0 /
a characteristic strength 0-0 of 1.78 GPa and a low Weibull modulus m of 3.42,
which
indicates high variability in the failure strength. This high variability in
the failure strength
of pyrolytic carbon samples suggests that their failure likely originates from
internal
flaws.
[0275] FIG. 35A presents all experimental data obtained from the
compression
experiments, where the strength is defined as the compressive fracture stress.
This plot
reveals that for samples with diameters larger than 2.3 m, the compressive
strength ay
increases with decreasing diameter D according to a power law, oy-D- .37 (FIG.
35A).
This scaling law agrees well with the theoretical prediction of oy-D- .40,
which was
derived from the asymptotic analysis of a fracture mechanics-based mode134
describing
the compressive failure of quasi-brittle columns with characteristic diameter
D. In this
model, the columns are found to fail via the propagation of a splitting crack
with an initial
length h, similar to the experimental observations (e.g., FIG. 340 and FIG.
42). This
model also offers an expression for the theoretical limit, 0-th, of the
compressive
strength34:
E3T2 115
0-th 2.76 2 (2)
h
where E is the Young's modulus, and Tis the fracture energy. Using the modulus
E=19.5 GPa (the average modulus obtained from the compression experiments on
all
samples) and the fracture energy of glassy carbon, T=29.9-61.9 J/m2, reported
in Ref.
35, we used Eq. 2 to calculate a theoretical limit range of o-th=4.0-13.5 GPa
for the initial
length of the splitting crack, h=100 nm-1 m. This predicted range is similar
to the
experimentally acquired compressive strengths of 3.8-11.3 GPa (FIG. 35A),
which
implies that the strength of pyrolytic carbon pillars with diameters less than
2.3 pm
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approaches the theoretical limit. In the highlighted region above the average
strength
(indicated by a blue dashed line in FIG. 35A), the micropillars can sustain an
ultra-high
compressive stress of 7.2-11.3 GPa and a high compressive strain in excess of
40%.
The significant fluctuations in the compressive strength of the micropillars
with D<2.3
p.m mainly arise from the variation in the length of the initial splitting
microcrack h. The
compressive strengths of the micropillars with D<2.3 p.m are, on average,
higher by a
factor of 3.5 than the corresponding tensile strengths of 0.8-2.5 GPa. This
tension-
compression asymmetry is consistent with the theoretical prediction of an
asymmetry
factor of 2.5-4.4 that arises in high-strength, covalently bonded isotropic
materials, as
determined from a recent ellipse fracture criterion36. The compression and
tension
experiments revealed that the pyrolytic carbon micropillars with D<2.3 p.m
exhibit high
deformability, i.e., >40% compressive strain and -20% tensile strain prior to
failure. The
cyclic compression experiments on these samples exhibited nearly full recovery
after
each cycle beyond the first one. FIG. 35B shows a 20-cycle force-displacement
data set
of a 1.28 p.m-diameter micropillar with a maximum compressive strain of 23%.
These
data, in combination with the pre-/post-deformation SEM images shown in the
insets of
FIG. 35B, indicate that after 20 cycles of compression to 23% strain, the
micropillar
recovered 95% of its original height.
[0276] To reveal the underlying mechanisms that enable the observed large
deformability and ultra-high strength of the small-scale pyrolytic carbon, we
performed
large-scale molecular dynamics (MD) simulations of the uniaxial compression
and
tension of pyrolytic carbon pillars with diameters of 10-20 nm and a constant
aspect
ratio of 2 via LAMMPS37. During the simulations, nanopillars were compressed
or
stretched along the axial direction with a constant strain rate of 5x108 s-1
and a constant
temperature of 300 K. Throughout the simulations, we used the adaptive
intermolecular
reactive empirical bond order force field36 to describe the interatomic
interactions. This
force field is capable of capturing the formation and breakage of carbon
bonds36. A
complete description of the atomistic simulations is presented in Methods. The
simulated samples consist of many -1 nm-sized curled graphene layer fragments
and
possess a density of 1.4 g/cm3, which is consistent with the TEM observations
of our
experimental samples, as illustrated in FIG. 36A. These fragments were
connected by
covalent bonding or van der Weals interactions. The magnified image in FIG.
36A
shows that the spacing between neighboring graphene fragments is approximately
0.4
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nm and that several sub-nanometer-sized voids are present adjacent to them, as
in the
HRTEM images in FIGs. 33D-33F. The hybridization of carbon atoms in graphene
is
typically such that the sp bonds are mainly concentrated within the edges of
graphene
layers, and the sp3 bonds generally connect the neighboring graphene layers to
each
other or form at their high-energy curved surfaces (FIG. 36A). In certain
simulated
samples, the fraction of sp2 bonds is at least one order of magnitude higher
than the
fractions of sp and sp3 (see FIG. 44) bonds, indicating the dominance of sp2
bonds,
which is consistent with the above analyses from EELS. FIGs. 36B-360 present
the
compressive and tensile stress-strain response determined from the MD
simulations
and reveal similar trends and stresses to those in the experimental data. This
result
partially confirms the similarity of the microstructure and densities of the
simulated and
experimental samples. FIGs. 36D-36G depict several snapshots of the cross-
section of
a simulated deformed sample at different compressive strains. In the initial
elastic stage,
the curled graphene layers approached each other, and some bent significantly
(FIG.
36D). As the applied compressive strain increased, several graphene layers
slipped
relative to the neighboring ones, which led to the abrupt fracture of the
graphene layers
under shear (FIGs. 36D-36E). Such discrete failure events gave rise to stress
fluctuations in the mechanical response at a strain of 21.5%, as shown in FIG.
36B. At a
compressive strain of 50%, the sub-nanometer-sized voids collapsed and caused
densification of the nanopillars. Slight tilting occurred in the nanopillar
due to the
interlayer slipping and shear of neighboring graphene layers (FIG. 36F).
During
unloading, the nanopillar exhibited recovery associated with the release of
the stored
elastic strain energy; the distances between graphene layers increased, and
the sub-
nanometer-sized voids partially reopened (FIG. 36G). The recovered strain is
19%,
which is comparable to the experimental results (FIG. 36B). (Additionally,
atomistic
simulation of uniaxial compression on pyrolytic carbon nanopillars with
diameter of 20
nm is performed. In the initial compressive stage, the curled graphene layers
approach
each other, and some graphene layers bend significantly. As the compressive
strain
increases, a few graphene layers slip relative to the neighboring layers,
leading to the
.. abrupt fracture of the graphene layers under shear. When the compressive
strain is
50%, the sub-nanometer-sized voids tend to close, resulting in the
densification of the
pillars. Slight tilting occurs in the nanopillar due to the interlayer
slipping and shear of
neighboring graphene layers. During unloading, the nanopillar exhibits a
certain elastic
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recovery. The distances between graphene layers increases and the sub-
nanometer-
sized voids partially reopen.)
[0277] Another similarity to the experiments is that all simulated
nanopillars
subjected to tension failed after undergoing nearly linear elastic deformation
(FIG. 360).
.. FIGs. 36H-36J show a sequence of snapshots of the cross-section of a
stretched
sample at different strains. We observed that a number of nanoscale cavities
nucleated,
expanded under tension, and then coalesced, leading to the formation of
nanoscale
cracks (FIG. 361 and FIG. 45A). Eventually, these nanoscale cracks propagated
in the
direction normal to the tensile loading, resulting in a smooth fracture
surface (FIG. 36J
and FIG. 45B). This cleavage fracture is similar to the experimental
observations shown
in FIG. 34E. (Additionally, atomistic simulation of uniaxial tension on
pyrolytic carbon
nanopillars with diameter of 20 nm is performed. During tension, the curved
graphene
layers are stretched. A number of nanoscale cavities nucleate, grow up and
then
coalesce, leading to the formation of nanoscale cracks. Eventually, these
nanoscale
cracks propagate in the direction normal to the tensile direction, resulting
in a smooth
fracture surface.) FIG. 360 shows that the tensile strength of a nanopillar
without initial
cracks is above 20 GPa, which stems from the requirement for significant
forces to
break the strong covalent bonds. The strength is reduced to approximately 12
GPa after
introducing cracks into the nanopillar, which indicates that the presence of
initial
flaws/imperfections facilitates a significant reduction in the tensile
strength of pyrolytic
carbon pillars. FIG. 46 shows the deformation processes of nanopillars with
initial 4-
and 8 nm-long nanocracks. We observe that their failure always originated from
the
growth and extension of the pre-existing nanocracks, leading to a smaller
fracture strain
and a smoother fracture surface than in nanopillars without nanocracks. The
tensile
strengths of the simulated samples are much higher than those of the
experimental
samples, which is a common phenomenon caused by a difference of approximately
10-
11 orders of magnitude in the applied strain rate, a difference of
approximately 1-2
orders of magnitude in sample size and non-equivalent flaw concentrations in
the
experiments and simulations. The MD simulations also revealed some mechanistic
details regarding the compression and tension of pyrolytic carbon pillars.
During
compression, the large deformation is accommodated by the closure of sub-
nanometer-
sized voids, densification of the structures and slipping/shear of the
graphene layer
fragments. Under tension, samples with initial flaws fail via the coalescence
and
extension of pre-existing flaws. For samples without initial flaws, tensile
deformation is
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dominated by the nucleation, growth and coalescence of nanoscale cavities and
the
propagation of the resultant nanoscale cracks (FIGs. 36H-36J and FIGs. 45A-
45B).
These underlying deformation mechanisms provide reasonable explanations for
the
observed high deformability, high elastic limit and high strength of the
pyrolytic carbon
micropillars.
[0278] To
examine the properties of the pyrolytic carbon materials explored in this
work in their context, we plotted a strength-versus-density material parameter
landscape
for various structural materials in FIG. 37A, which also includes conventional
structural
materials4,26,26,39 and recently reported high-strength nanomaterials6,10,40-
43. This plot
reveals that the strengths of the pyrolytic carbon in this work are
approximately 1-3
orders of magnitude higher than those of most structural materials, including
bulk
pyrolytic carbon (PyCs) 25,26,39, graphite, carbon fiber-reinforced carbon
(C/C) 40,
graphene oxide paper (GOP)41, copper nanopillars (Cu-NPs)42, gold nanopillars
(Au-
NPs)43, and bulk nanotwinned copper (NT-Cu)6, and approaches the upper bound
for
the uniaxial strength of structural materials proposed in Ref. 28. The
strength of the
pyrolytic carbon micropillars is comparable to those of carbon microfibers44
and gold
nanowires (Au-NWs)16, but its density is approximately 79% and 7.3% of those
of
carbon fibers and Au-NWs, respectively. FIG. 47 shows an analogous property
plot of
the strength versus fracture strain for various materials, including shape
memory
zirconia12, SU-8 composites14, carbon microfibers44, GOP41, Cu-NPs42, NT-Cu6,
and Zr-
based metallic glasses (MG)46. The pyrolytic carbon micropillars in this work
exhibit a
superior combination of high strength and high deformability, which implies
that they
overcome the classical trade-off between strength and deformability that has
plagued all
materials to date. It appears that the pyrolytic carbon micropillars
simultaneously
possess high tensile and compressive strengths of 2.5 GPa and 11.0 GPa and a
low
density of 1.0-1.8 g/cm3, thereby partially overcoming the conflict between
high strength
and low density, leading to an ultra-high specific strength of 8.07 GPa/g cm3.
FIG. 37B
shows the specific tensile and compressive strengths of various materials and
reveals
that the pyrolytic carbon micropillars have at least one order of magnitude
greater
specific strength than those of GOP, NT-Cu and Au-NWs, comparable to that of
carbon
microfibers. Their specific compressive strengths exceed that of diamond,
which has the
highest specific compressive strength to date26, of common hard ceramics46
(such as
BaC, SiC, and A1203), of metallic nanopillars (Cu-NPs42 and Au-NPs43), and of
carbon
materials (PyCs25,26,39, graphite, and C/C46). FIG. 37C shows an Ashby plot of
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strength versus fracture strain for our pyrolytic carbon and other various
materials,
including titanium alloys, magnesium alloys, carbon fiber reinforced polymer
(CFRP)
and diamond. Notably, our pyrolytic carbon occupies the unexplored space in
the Ashby
diagram, where no other materials reach. Our experiments and simulations
revealed
that pyrolytic carbon micropillars exhibit a unique combination of high
deformability, an
ultra-large elastic limit, and ultra-high strength and specific strength.
These superior
mechanical properties of the pyrolytic carbon micropillars arise from their
microstructures and constituent materials. As basic building blocks, curled
graphene
layers with a size of 1 nm have high in-plane rigidity and out-of-plane
flexibility as well
as high strength. The dense assembly of these graphene layers forms pyrolytic
carbon
micropillars via covalent bonding or van der Weals interactions. As a result,
the pyrolytic
carbon micropillars can sustain large elastic distortion and resist large
compression and
stretching. These results offer a new design route of assembling nanometer-
sized curled
graphene fragments into high-performance carbon materials.
[0279] It is noted that our pyrolytic carbon micropillars exhibit 1.5-8.2
times higher
compressive strength and at least one order of magnitude larger fracture
strain than
existing bulk and micro-sized pyrolytic carbon26,27. These differences in
mechanical
properties can be attributed to differences in microstructures and sample
sizes between
these materials. First, both the crystallite size of the carbon layer
fragments and spacing
between neighboring layers in our pyrolytic carbon are much smaller than those
(about
4-6 nm and 1.67-1.99 nm) of the existing bulk and micro-sized pyrolytic
carbon26,27.
These different microstructures are induced by different pyrolysis precursor
materials
and conditions (such as temperature and duration time). Second, our pyrolytic
carbon
with high strength and large deformability are several microns in diameters,
which are 2-
4 orders of magnitude smaller than diameters (beyond hundreds of microns) of
bulk and
micro-sized pyrolytic carbon26,27. Therefore, designing/controlling atomic-
level
microstructures and sample dimension have resulted in significant enhancement
of the
mechanical properties of pyrolytic carbon.
[0280] In
summary, we have synthesized new pyrolytic carbon micropillars derived
from a polymeric photoresist via DLW and pyrolysis. These micropillars consist
of curled
graphene fragments with an average size of approximately 1.0-1.5 nm. Both
compressive and tensile tests showed that these micropillars exhibit an
exceptional
combination of large deformability, an ultra-large elastic limit, and ultra-
high strength and
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specific strength. Large-scale MD simulations provided some mechanistic
details of the
deformation of pyrolytic carbon pillars, i.e., compressive deformation was
dominated by
densification of the structure and slipping/shear of the graphene layers,
while tensile
deformation was governed by the extension of initial flaws or by the
nucleation, growth
and coalescence of nanoscale cavities. These deformation mechanisms are
responsible
for the unique combination of desirable properties such as high deformability,
a high
elastic limit and high strength. Our results reveal the critical connections
between the
microstructure, deformation mechanisms and mechanical properties of pyrolytic
carbon
materials and thereby provide potential routes for designing and synthesizing
new high-
performance carbon materials.
[0281] Methods:
[0282] Fabrication of samples: The fabrication process of pyrolytic
carbon
micropillars includes two steps: two-photon lithography and high-temperature
pyrolysis.
We first synthesized the pillars using 3D TPL DLW (Photonic Professional,
Nanoscribe
GmbH) with the dip-in laser lithography configuration, a 63x objective and
commercial
IP-Dip photoresist. For pyrolysis, the printed polymeric samples were heated
to 900 C
at a ramp rate of 7.5 C min-1 in a vacuum tube furnace, then maintained at
the target
temperature for 5 hours, and finally cooled to the room temperature at a
natural rate.
After pyrolysis, the pillar dimensions shrank to approximately 20%-25% of
their original
values, which corresponds to a 98% volumetric contraction. The diameter D of
the
pyrolytic carbon pillars for the compression experiments varied from 1.28 to
12.7 p.m.
Dog-bone shaped samples with gauge sections of 0.7 to 2.0 p.m were also
synthesized
using the same procedure for the tensile experiments. The aspect ratios (i.e.,
height to
diameter) of the pyrolytic carbon samples were 1.4-1.8 for compression and 1.5-
4.3 for
tension.
[0283] Microstructure! characterization: The microstructure of the
pyrolytic carbon
micropillars was characterized by an FEI Technai TF-30 TEM at an accelerating
voltage
of 300 kV. EELS was conducted in an FEI Technai TF-20 at an accelerating
voltage of
200 kV to estimate the relative fractions of sp2 and sp3 bonds. Samples for
TEM
analyses were prepared using a site-specific lift-out procedure, attaching the
detached
lamella to the TEM grid, and final thinning to a final thickness of 60.73 nm
using a
voltage of 15 kV and a current of 10 pA in the focused ion beam (FIB, FEI
Versa).
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Raman spectra were collected at room temperature using a Raman spectrometer
(Renishaw M1000 Micro) with a 514.5 nm laser.
[0284] Nanomechanical experiments: Uniaxial compression on samples with
diameters of 1.28-2.28 p.m and all uniaxial tension experiments were conducted
at a
constant nominal strain rate of 10-3 s-1 in a custom-made in situ
nanomechanical
instrument (SEMentor)33 with a 10 p.m-diameter flat punch indenter tip.
Samples with
larger diameters of 4.6-12.7 p.m were compressed in a nanoindenter
(Nanoindenter
G200 XP, Agilent/Keysight Technologies) with a 120 pm-diameter flat punch at a
constant loading rate of 0.02-0.2 mN s-1 because of the load limit in the in
situ
instrument. Additional compression experiments were conducted on samples with
diameters of 2.21-12.7 p.m in the G200 to independently validate the results
of the in situ
experiments.
[0285] Estimation of the density of pyrolytic carbon micropillars from
TEM analysis:
HRTEM images reveal that the pyrolytic carbon micropillars consist of
nanometer-sized,
randomly distributed curved graphene layers. FIG. 41 provides a comprehensive
set of
images that pertain to the estimation of density in these materials. FIG. 41,
panel (a),
illustrates the distribution of the curved graphene segments, and FIG. 41,
panel (b),
shows an individual representative graphene segment, where the average end-to-
end
length is L and the spacing between neighboring layers L. We built upon an
existing
geometric mode126 to estimate the density (ppc) of pyrolytic carbon. The
density of the
curved graphene layers, pcGL, can be expressed as
[0286]
PCGLLsPG (1)
where pG is the density of single crystalline graphite (pG=2 . 25 g/cm3), LG
is the interlayer
distance in single crystalline graphite (LG=0.34 nm), and p is a shape factor
that reflects
the curvature of the curved graphene layer: represents a flat graphene
layer, and
1(7.c/2 corresponds to a semi-circle. FIG. 41, panel (c), is a schematic that
represents a
reasonable stacking structure of two curved graphene layers. Using this
geometry as a
guide, the density of pyrolytic carbon can be estimated as26
(
1
Pc ¨ PCGL _____________________________________________________ (2)
* 1+ 0 5(4_0 sin Ocos
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where 8 is the orientation angle between two graphene layers in a typical unit
cell (see
FIG. 41, panel (c)), and 45 corresponds to isotropic pyrolytic carbon26,
where the
curved graphene layers are randomly distributed. Based on TEM observations
(FIGs.
33E-33F), we obtained p=1 or 7c/2, 8=7c/4, Ls=0.4 nm, and L=1.0-1.5 nm. By
substituting
these parameters into Eqs. (1-2), we obtain ppc=1.0-1.8 g/cm3. FIG. 41, panel
(d),
compares our modified model, a previous geometric model and the experimental
data
on bulk pyrolytic carbon. The predictions from this modified model agree with
the
experimental data26,39.
[0287] Estimation of carbon fragment size based on Raman spectra: Raman
spectroscopy is widely used to investigate defects and disorder in carbon
materials at
the nanoscale level, including graphene, carbon nanotubes and glassy
carbon31,47. The
ratio of the integrated area under the D peak and that under the G peak,
/D//G, in a
Raman spectrum is related to the in-plane crystallite size (L) of carbon
materials by Eq.
(1)31. We first fitted the Raman spectra of a pyrolytic carbon micropillar
using four
Lorentzian-shaped bands (G, D1, D2, Da) at the Raman shifts of -1580, 1350,
1620 and
1200 cm-1 and a Gaussian-shaped band (D3) at 1500 cm-1 in Ref. 47. The Raman
spectrum shown in FIG. 33G has /D//G=6.937 and the laser wavelength /14=514.5
nm,
which gives L=2.4 nm by Eq. (1). This result is in agreement with the
characteristic size
of 1.0-1.5 nm of curved graphene layers estimated based on HRTEM analysis.
[0288] Estimation of fraction of sp2 bonds based on EELS: EELS spectra
provide
quantitative information about the electronic structure of carbon
materials27,32. We used
the common two-window method32 to estimate the fraction of sp2 bonds in the
pyrolytic
carbon micropillars and used the EELS data of raw glassy carbon, which is
fully sp2-
hybridized, as a reference. From the EELS data of pyrolytic carbon in FIG. 33H
and raw
glassy carbon, we calculated the areas under the two windows around the 77*
and 0-*
peaks, denoted by /, and /0-, of the pyrolytic carbon and of raw glassy
carbon. A
normalized ratio Nint can then be calculated aS2732
PC 'PC
N ¨ ____________________________________________________________ (3)
jilt p:G //aRG
where the superscripts "PC" and "RG" represent pyrolytic carbon and raw glassy
carbon, respectively. The normalized ratio Nint is also a function of the
fraction of sp2
bonds f as follows27,32:
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N.=3 - (4)
Int 4 _ f
Setting Eq. (3) and Eq. (4) equal to each other, we found the fraction of sp2
bonds in the
pyrolytic carbon micropillars to be 96.5%.
[0289] Atom istic simulations: We performed a series of large-scale atom
istic
simulations that emulate the uniaxial compression and tension of pyrolytic
carbon
nanopillars using LAMMPS37. We used the adaptive intermolecular reactive
empirical
bond order force field38 in all simulations to describe the interatomic
interactions. This
force field describes the bonded interactions based on the bond order, the non-
bonded
interactions (i.e., van der Weals) and the torsional interactions, which
enables it to
capture the formation and breakage of carbon bonds38. We first constructed the
simulated samples using the microstructure determined experimentally from the
HRTEM
images, which contained many curved graphene fragments with an average size of
1
nm. These graphene fragments were extracted from 084 fullerene. A large number
of
such graphene fragments with random orientations were initially hexagonally
close-
packed in a simulation box with dimensions of 27.5x27.2x54.3 nm3. This system
was
then equilibrated by an energy minimization and a free relaxation at 300 K for
50 ps
under an NPT ensemble. After equilibration, the simulated system was
hydrostatically
compressed at a constant strain rate of 109 5-1 at 300 K for 550 ps via an NVT
ensemble
until the density of the simulated sample condensed to 1.40 g/cm3 (the
estimated
.. median density of the pyrolytic carbon micropillars based on the
microstructure!
features). After compression, the hydrostatic pressure increased to 10 GPa. We
then
performed a melting-and-quenching process while holding the volume constant by
confining all the dimensions of the simulation box. During this process, we
first gradually
increased the temperature from 300 K to 1200 K within 50 ps, then held the
temperature
at 1200 K for 300 ps to fuse the graphene flakes at high temperature and high
pressure,
and finally reduced the temperature from 1200 K to 300 K in 50 ps. We then
relaxed the
simulated sample at 300 K for 200 ps under an NPT ensemble to fully relieve
the
pressure to zero. After relaxation, the simulated sample had dimensions of
20.5x20.4x40.8 nm3 and a density of -1.40 g/cm3. Throughout these processes,
periodic boundary conditions were imposed in all three directions of the
simulated
samples.
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[0290] We then extracted the nanopillars with diameters of 10 and 20 nm
from the
above relaxed cubic sample to perform uniaxial deformation simulations. We
maintained
the aspect ratios of all nanopillars near 2 to mimic the experiments. After
equilibration,
we compressed or stretched the nanopillars along the axial direction at a
constant strain
rate of 5x108 5-1 and a constant temperature of 300 K via an NVT ensemble.
During
simulations, the stress of each atom was calculated based on the Virial stress
theorem.
The compressive and tensile stresses were obtained by averaging over the axial
stresses of all atoms in nanopillars.
[0291] We also investigated the influence of flaws, such as nanoscale
cracks, on the
tensile response of simulated samples. We introduced a few nanoscale cracks
with
lengths of 4 or 8 nm by removing some atoms from the "as-constructed" samples.
After
equilibration, we applied the same tensile loading to the samples with
nanocracks as to
the "as-constructed" ones and compared their stress-strain response and
fracture.
Throughout the simulations, periodic boundary conditions were imposed along
the axial
direction of the simulated nanopillars. We identified the sp, sp2, and sp3
bonds of the
simulated samples by counting the coordination number of each atom. We found
that
the sp bonds were mainly distributed at the edges of the curved graphene
layers, and
the sp3 bonds either connected the neighboring graphene layers to each other
or were
formed at the high-energy curved surfaces of the graphene layers (see FIG.
44). The
fractions of sp, sp2 and sp3 hybridized bonds in the "as-constructed" samples
were
8.8%, 89.1% and 1.8%, respectively, indicating that sp2 bonding was dominant
in the
simulated samples, which was consistent with the experimental results (FIG.
33H). The
remaining 0.3% of bonds were dangling bonds.
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[0293] Example 9: Lightweight, flaw tolerant and strong nano-
architected carbon
[0294] Abstract of this illustrative Example: A long-standing challenge
in modern
materials design is to create low-density materials that are robust against
defects and
can withstand extreme thermomechanical environments because these properties
typically are mutually exclusive: the lower the density, the weaker and more
fragile the
material. We developed a simple process to create nano-architected carbon that
can
attain a specific strength (strength-to-density ratio) of 1.90 GPa g-1 cm3,
which
represents greater than 1-3 orders of magnitude improvement over that of all
nano- and
micro-architected materials to date. We used two-photon lithography followed
by
pyrolysis in vacuum at 900 C to fabricate two prototype topologies of
pyrolytic carbon:
octet- and iso-truss, with unit-cell dimensions of -2 p.m, beam diameters
between 261
nm and 679 nm, and densities of 0.24 to 1.0 g/cm3. Micromechanical experiments
demonstrate a Young's modulus of 0.34-18.6 GPa, strengths of 0.05-1.9 GPa, and
an
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average strain-to-fracture of 14%-17%. Experiments and simulations demonstrate
that
for densities higher than 0.95 g/cm3, these nanolattices become insensitive to
fabrication-induced defects, which gives rise to their nearly attaining the
theoretical
strength of constitute materials and lends nano- and micro-architected carbon
to being
particularly promising candidates for structural applications under harsh
thermomechanical environments. We discuss this combination of high specific
strength,
low density, and extensive deformability prior to failure in the context of
interplay among
atomic-level microstructure of pyrolytic carbon, nano-sized beam dimensions,
and
optimized lattice topology.
[0295] Significance:
[0296] Strength and density of porous materials typically scale
together. A long-
standing challenge in modern material design has been to create porous
materials that
are simultaneously lightweight, strong and stiff. Here we demonstrated the
creation of
pyrolytic carbon nanolattices with designable topologies by a two-step
procedure: direct
laser writing and pyrolysis at high temperature. The smallest characteristic
size of the
struts in nanolattices approached the limits of resolution of the available
three-
dimensional lithograph technologies. We demonstrated that these pyrolytic
carbon
nanolattices are 1-3 orders of magnitude stronger nearly all micro-/nano-
architected
materials reported so far.
[0297] Lightweight porous materials, such as wood, bone, Euplectella
sponges,
diatoms and bamboo, are ubiquitous in nature. These natural structural
materials have
been extensively investigated (1-5) and shown to be resilient against
externally applied
loads, as well as powerful in absorbing and dissipating impact energy. Such
mechanical
resilience is enabled by two main design principles: (i) the multi-scale
hierarchy in
.. constituent materials and length scales of natural materials, which
generally consist of
complex multi-level architectures with characteristic dimensions from nano- to
macroscale (5) and (ii) their tolerance to flaws when the characteristic
material length
scale is below a critical value (4). Both principles have been applied to
engineering
advanced materials with various degrees of success (5,6).
[0298] A general guideline for a material to be considered "lightweight" is
for its
density to be less than that of water (i.e., io1.0 g/cm3) (16). Recent
breakthroughs in
material processing techniques, especially in three-dimensional (3D)
microfabrication
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and additive manufacturing provide a particularly promising pathway to
fabricate
lightweight materials, which often possess a suite of other beneficial
properties like high
specific stiffness, high specific strength and good resilience/recoverability
(7-27). The
penalty for the ultra light weight in these nano- and micro-architected
materials is a
.. severe reduction in their stiffness and strength through power law scaling:
o-y-(p/ ps)m ,
E-(p/ ps)n , where cy is the yield strength, E is the Young's modulus, p is
the density, and
Os is the density of the fully-dense constituent solid (1). The exponents m
and n are
generally greater than 1, which renders developing methodologies to create
materials
that are simultaneously lightweight and strong/stiff, while maintaining their
other
.. properties - i.e. thermal stability, electrical conductivity, magnetism,
recoverability, etc. -
a grand unsolved challenge because of the restricted material choices and
limited
architectures.
[0299] Most work on micro-/nano- architected materials to date has been
focused on
hollow-beam based architectures, which offer exceptionally light weight with a
concomitant high compliance, for example nickel-based hollow-tube
microlattices with a
modulus of 529 kPa and a compressive strength of -10 kPa at a density of -
0.010
g/cm3 (7) and ceramic hollow-tube nanolattices with Young's moduli of 0.003-
1.4 GPa,
compressive strengths of 0.07-30 MPa at densities of 0.006 to 0.25 g/cm3 (10-
14).
These micro-/nano- architected materials have a common feature of length scale
hierarchy, i.e. relevant dimensions of their structural elements span 3-5
orders of
magnitude, from tens of nanometers to hundreds of micrometers and even
greater.
Structural features of nickel-alloy hollow-tube nanolattices fabricated using
large-area
projection microstereolithography span 7 orders of magnitude in spatial
dimensions,
from tens of nanometers to tens of centimeters, and attained tensile strains
of >20%
with a low modulus of 125 kPa and a low tensile strength of -80 kPa at a
density of
-0.20 g/cm3, which corresponds to the relative density of 0.15% (17). The
deformability
of these nanolattices was attributed to a combination of bending-dominant and
stretching-dominated hierarchical architectures distributed over successive
hierarchies
and shell buckling, an elastic instability characteristic of thin-walled
hollow cylinders
(17). Among the thin-walled architectures, 3D periodic graphene aerogel
microlattices
have been synthesized via direct ink writing; these materials are
exceptionally
lightweight, with a density of 0.031-0.123 g/cm3, very compliant, with a
modulus of 1-10
MPa, and weak, with a low strength of 0.10-1.6 MPa, and exhibit nearly
complete
recovery after compression to 90% strain (23).
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[0300] Some efforts have also been dedicated to the synthesis and
mechanical
properties of micro- and nano-architected materials that are comprised of non-
hollow
beams of various materials, which offer greater stiffness and higher densities
compared
with the hollow-beam counterparts. Most of these studies have been on
architectures
comprised of core-shell types of beams, usually with an acrylic polymer core
and a thin,
from tens of nanometers to several hundred nanometers, rigid outer coating.
For
example, triangular-truss microlattices with polymer-core-alumina-shell beams
have
been synthesized by combining TPL and ALD and sustained a modulus of -30 MPa
at a
low fracture strain of -4-6% and a density of 0.42 g/cm3 (16). Octet-truss
nanolattices
made up of 262-774 nm-diameter polymer beams with sputtered 14-126 nm-thick
high-
entropy alloy (HEA)-coatings were reported to have a Young's modulus of 16-95
MPa
and a compressive strength of 1-10 MPa at densities between 0.087 and 0.865
g/cm3
(20). Samples with HEA thicknesses of less than 50 nm completely recovered
after >
50% compressions (20). Beyond core-shell-beamed nano- and micro-architected
materials, several reports exist on the fabrication and deformation of 3D
structural meta-
materials with monolithic beams. For example, nanocrystalline nickel octet-
truss
nanolattices with 300-400 nm-diameter monolithic beams and 2 p.m unit cells,
created
via TPL on custom-synthesized resins followed by pyrolisis exhibited a modulus
of -90
MPa, a compressive strength of 18 MPa, a high fracture strain of >20% at a
density of
2.5 g/cm3 (20). Reports on vitreous carbon octet-truss microlattices with beam
diameters
of -100 p.m, fabricated by pyrolyzing a UV-mask patterned polymer template,
reported a
modulus of 1.1 GPa, a compressive strength of 10.2 MPa, and a fracture strain
of only
-3% at a density of 0.19 g/cm3 (24). Glassy carbon microlattices with rhombic
dodecahedron unit cell and beam diameters of 50-150 p.m, fabricated by using
stereolithography and pyrolysis had densities of 0.03-0.05 g/cm3, moduli of 5-
25 MPa,
and compressive strengths of 0.08-0.35 MPa, and fractured at a strain of -5%
(25).
Glassy carbon nanolattices with tetrahedral unit cells created via TPL and
pyrolysis had
smaller dimensions, 0.97-2.02 p.m unit cells and beam diameters of -200 nm, a
modulus
of 3.2 GPa and a compressive strength of -280 MPa at a density of -0.35 g/cm3
(18).
This brief overview highlights the coupling between density and compliance of
architected materials, i.e. the lower the density, the softer and the weaker
the material.
[0301] We developed an approach to fabricate nano-architected pyrolytic
carbon and
demonstrate two prototype unit cell geometries, octet- and iso-truss, shown in
FIGs.
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48A-48F, using two-photon lithography and pyrolysis. The octet-truss
architecture has
cubic anisotropy and superior overall properties compared to other
conventional lattices,
such as triangular, tetrahedral, or cubic trusses and foams (28), while the
iso-truss
structure is isotropic and has been theorized to possess optimal stiffness
compared to
traditional lattice topologies (29). Uniaxial compression experiments revealed
their
Young's moduli to be 0.34-18.6 GPa, their fracture strengths to be 0.05-1.9
GPa, and
pre-failure deformability of 14-17% at density varying from 0.24 to 1.0 g/cm3.
The
highest specific strength is up to 1.90 GPa g-1 cm3, which outperforms all
other reported
mechanically robust lightweight meso-/micro-/nano-lattices (7-27). We
attribute this
distinction to optimized unit-cell geometries, reduced feature sizes, and high
quality of
pyrolytic carbon.
[0302] Results:
[0303] FIG. 48A illustrates the fabrication process, which begins with
printing 5x5x5
unit cells microlattices out of IF-Dip photoresist using TPL. We used the high-
speed
galvo mode in a layer-by-layer fashion to print 7-10 m-long struts with 0.8-
3.0 m-
diameter circular cross sections. The polymer samples were then heated in a
vacuum
furnace at a ramp rate of 7.5 C min-1 up to 900 C, pyrolyzed for 5 hours,
and cooled
down to room temperature at a natural rate (see Methods for more details).
FIGs. 48B
and 48D show CAD designs of 10 m-sized octet- and iso-truss unit cells. Strut
diameters d in the octet-truss were designed to be 0.8-2.4 p.m. In the iso-
trusses, the
vertical strut diameters d1 were 1.4-3.0 rn, and the prescribed slanted strut
diameters
d2 were maintained as d2 =V3742 , with the d2/d21 ratio of -1.14 based on
topological
optimization (29). After pyrolysis, the polymer transformed into a form of
carbon and
underwent significant volumetric shrinkage and mass loss (30). Each strut
shrunk to
-20%-25% of its initial dimensions (FIGs. 48C and 48E) with a concomitant
shrinkage in
unit-cell size from -10 rn to -2 p.m. The resulting strut diameters of -261-
679 nm after
pyrolysis are significantly below the limits of resolution of most available
3D lithographic
technologies (0,0,0). We estimated the relative density P of pyrolytic carbon
nanolattices to be between 17% to 72% by calculating the volume fraction of
solid
materials in the nanolattices based on 3D CAD models and dimensions measured
by
the scanning electron microscopy (SEM). The magnified image in FIG. 48E
reveals that
the d2/di is preserved at -1.14 after pyrolysis, which suggests uniform volume
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shrinkage. FIG. 48F shows a high-resolution transmission electron microscopy
(HRTEM) image of a typical sample extracted from the nanolattice via focused-
ion-beam
(FIB) milling and indicates its glassy/amorphous microstructure. In our
earlier work, we
estimated the density of pyrolytic carbon produced under these conditions to
be -1.40
.. g/cm3 by using a combination of atomic model and experimental measurements
(31),
which is consistent with that of type-I glassy carbon fabricated under the
pyrolysis
temperature of below 2000 C (32). We calculated the density of nanolattices
by
multiplying this absolute density by the relative density of nanolattices to
vary from 0.24
g/cm3 to 1.0 g/cm3, well within the lightweight range.
[0304] We performed uniaxial compressions on all polymer microlattices and
pyrolytic carbon nanolattices (see details in Methods). Engineering stresses
versus
strains were obtained by normalizing the load-displacement data from
compression
experiments by the cross-sectional footprint area of the overall samples and
the initial
height. FIGs. 49A and 49B convey the compressive stress-strain response of
some
.. representative octet- and iso-truss pyrolytic carbon nanolattices, which
appear to be
similar across all samples. As the relative density of the octet-truss
nanolattices ranged
from 24% to 68%, its Young's modulus increased from 2.57 GPa to 10.73 GPa, and
its
compressive strength increased from 0.21 GPa to 1.73 GPa (FIG. 49A). The
relative
density of the iso-truss nanolattices was slightly higher, from 28-72%, its
Young's
modulus increased from 2.28 GPa to 9.67 GPa, and its compressive strength rose
from
0.14 GPa to 1.90 GPa (FIG. 49B). The initial nonlinearity in the stress-strain
data arises
from the imperfect initial contact and slight initial misalignment between the
rough lattice
surfaces and the flat punch (16). Linear elastic loading persists up to a
strain of about
10-20%, after which all pyrolytic samples catastrophically failed via brittle
fracture (FIGs.
490-49F). The average fracture strains were 14.0% for octet- and 16.7% for the
iso-
truss nanolattices, which exceed -10% reported for glassy carbon nanolattices
(18) and
-3-5% for glassy carbon microlattices (24,25). This enhanced deformability is
enabled
by better mechanical stability of circular struts, which are able to transfer
load more
uniformly than the elliptical ones (33) and a longer pyrolysis time to ensure
sufficient
carbonation. FIGs. 53A-53H show the compressive stress-strain data of typical
polymer
microlattices with octet- (FIG. 53A) and iso-truss (FIG. 53E) unit cells for
comparison
and completeness. This data also has the initial nonlinear region over -2.5%
strain
caused by the slightly imperfect initial contact and misalignment between the
rough
lattice surfaces and the flat punch (16). Linear elastic loading commences
over the
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strain range of -2.5-7.5% followed by plastic deformation, followed by a
stress plateau
that extends over 5-7.5%. Such stress plateau corresponds to buckling of the
struts, as
evidenced by SEM images (FIG. 530 and 53G). Table 1 summarizes the Young's
moduli and strengths of the tested polymeric microlattices with different
relative
densities and reveals that for comparable relative densities, the Young's
modulus of iso-
truss microlattices is a factor of -2, and the strength is 1.3x higher than
those of the
octet-truss microlattices, consistent with predictions (29).
Table 1. Mechanical properties of polymer microlattices under compression
Unit cell Relative density Young's modulus Strength
geometry T.(%) E (MPa) o (MPa)
9.21 112 4.47
Iso
12.38 172 7.20
11.85 89 5.52
Octet
16.22 109 7.49
[0305] FIGs. 50A-50B show the material property space for Young's modulus
(FIG.
50A) and compressive strength (FIG. 50B) versus density of the pyrolytic
carbon
nanolattices in this work in the context of all reported micro-/nano-
architected materials
made up of carbon, ceramics or ceramics-polymer composites (11,16,18,22-26).
These
plots reveal that their moduli and strengths are -1-2 orders of magnitude
greater
compared to carbon aerogels (22), vitreous carbon microlattices (24) and
alumina-
polymer nanolattices (16) with comparable densities. The mechanical attributes
of
pyrolytic carbon nanolattices in this work span a large density range, from
0.24 to 1.0
g/cm3, and reveal a -40% higher scaling exponent between mechanical attributes
and
density, compared with glassy carbon nanolattices (18). These results imply
that at
densities greater than -0.4 g/cm3, the strength and stiffness of nano-
architected carbon
in this work surpass those of all previously reported architected materials.
The strength
of pyrolytic carbon nanolattices with iso-truss geometries at a density of 1.0
g/cm3 is
1.90 GPa, and that for the octet-truss at a density of 0.95 g/cm3 is 1.73 GPa,
which are
comparable to the theoretical strength of glassy carbon of -Es/10, i.e. 2-3
GPa, where
Es is the modulus of glassy carbon (0,0,0). FIG. 50A demarcates the
theoretical limit of
Young's modulus as a function of density, expressed as E=250p (11), and FIG.
50B
includes the theoretical limit of strength versus density, whose lower bound
is defined by
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diamond and the upper bound corresponds to graphene (18). More details about
the
determination of these theoretical limits are supplied in Methods.
[0306] FIGs. 54A and 54B show the variations of Young's modulus and
compressive
strength with the relative density, respectively. As the relative density
spans from 17% to
72%, our pyrolytic carbon nanolattices have the scaling relations of Young's
modulus as
E- )7)2 25 for the octet-truss and E- 7)1 9 for the iso-truss, and those of
compressive
strength as 0-y- 7)2 41 for the octet-truss and 0-y- 7)2 5 for the iso-truss.
These scaling
relations deviate from theoretical predictions for ideal, stretching-dominated
structures
(1), i.e., E-7, and ay-O, which is mainly attributed to the fabrication-
induced structural
imperfections and to the non-slender beams. SEM images in FIGs. 490 and 49E
show
some of the representative detectable fabrication-induced defects that we
found to be
present in virtually all samples, including beam junction offsets and bulges,
slight
curvature of the struts, and micro-pits and voids. During compression, these
imperfections induce localized deformation and micro-cracking around the
nodes, as
.. well as buckling/bending of struts, which leads to premature structural
failure (11). When
such local deformation and failure occur in stretching-dominated lattices, the
scaling
exponents for modulus and strength of lattices exceed theoretical predictions
and are
generally in the range of 1.4-2.5, as exemplified by previous studies
(8,11,12,18). The
slenderness ratio, defined as R/L, where R is the beam radius and L is the
beam length,
as well as the nodal geometry have been shown to have significant effect on
the
stiffness and strength of lattices (9,12,37). The nodes generally form solid
joints that
impede beam rotation and, to some extent, shorten the effective length of the
adjoining
beams and lead to stiffening of overall lattices (12). The recent
computational and
experimental studies found that for solid-beam octet-truss lattices, with a
beam
slenderness ratio greater than 0.06 and the corresponding relative density
beyond 10%,
the scaling relations for modulus and strength diverge from existing analytic
theories,
with the exponents of 2.20 and 1.88 instead of 1.0 (12). The beam slenderness
ratios,
R/L, of the octet-truss nanolattices in this work are 0.07-0.24, similar to
0.07-0.12 of the
monolithic polymer octet-truss nanolattices (12), as well as to 0.06-0.20 of
glassy carbon
.. nanolattices with tetrahedral unit cells (18). The scaling exponents of
2.25 (octet-truss)
and 1.90 (iso-truss) for Young's modulus and of 2.41 (octet-truss) and 2.50
(iso-truss)
for strength found for nano-architected carbon with a relative density between
15% and
80% in this work agree with these existing report (12). FIGs. 50A-50B convey
that these
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relatively high scaling exponents for the mechanical attributes of pyrolytic
carbon
nanolattices lead to highest stiffness and strength reported to date (11,18).
[0307] To further investigate the influence of the initial imperfections
on mechanical
properties of pyrolytic carbon nanolattices, we performed a series of finite-
element (FE)
simulations of compressing samples with relative densities varying from 15.9%
to 70%.
Details of FE simulations are provided in Methods. The simulated nanolattices
had three
types of unit-cell geometries: octet-truss and iso-truss for comparison with
experiments,
and tetrahedron-truss for comparison with previous literature (18), which
found that the
initial deflection of struts can reduce the compressive strength of
nanolattices at lower
relative densities. FIGs. 51A-510 show the simulated nanolattices with
different unit
cells, where pre-existing defects were created by imposing the corresponding
buckling
eigenmodes with a maximum deflection of the struts prescribed as 5%, 10% and
15% of
the edge length, similar to (18). After introducing these initial deflections,
some struts
remained pre-bent before compression, which resembles structural imperfections
in the
experimental samples (FIGs. 490 and 49E). We also simulated the compression of
a
perfect nanolattice as a reference. FIGs. 51D-51F show the compressive stress-
strain
response up to 12% strain of simulated nanolattices and reveals that the
strengths of
nanolattices with initial deflection are always lower than those of their
perfect
counterparts. FIG. 55 shows that FE simulations reveal similar trends in the
dependence
of modulus and strength on relative density as experimental measurement. FIGs.
56A-
56B quantify the variation in strength reduction as a function of initial
deflection relative
to that of a perfect nanolattice and indicates that (i) for a given relative
density and
architecture, the relative reduction in strength increases with greater
initial deflection; (ii)
for a given architecture, the nanolattices with higher densities experience
smaller
relative weakening with defects; and (iii) nanolattices with tetrahedron-truss
unit cells
are most susceptible to flaws, followed by octet-truss and iso-truss for all
densities. For
example, for the relative density of 15.9%, the relative reduction in strength
is 2% for the
iso-truss and 15% for the octet-truss architectures at a maximum deflection of
15%. The
same relative weakening for a relative density of 70% is only <1 A.
[0308] The results from our current experimental and computational studies
indicate
that carbon nanolattices with iso-truss and octet-truss architectures, which
are
intrinsically brittle, exhibit a reduced susceptibility to flaws at higher
densities. This can
be explained by the local failure in individual struts re-distributing stored
elastic energy
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among other load-bearing truss members instead of triggering catastrophic
structural
failure. This is consistent with the attainment of nearly-theoretical
strengths of carbon
nanolattices with densities higher than 0.95 g/cm3. When the struts' diameter
is reduced
by hundreds of nanometers to dimensions comparable to the critical size for
flaw
insensitivity of constitute, the struts exhibit high strength and good flaw
tolerance, which
to some extent contributes to the high strength of carbon nanolattices, which
is dictated
by local stresses and the volume fractions of the struts (4). Nanolattices
with lower
densities have thinner and more slender struts, which leads to higher local
stresses
during compression due to their smaller cross-sectional areas, and the nodal
.. contributions are negligible (12,37). In this case, the higher local
stresses lead to earlier
buckling of some struts or higher stress concertation around the nodes.
Together with
the lower volume fraction of thinner struts, the nanolattices with lower
densities (i.e.
thinner struts) might fail at lower global stresses. In contrast, nanolattices
with higher
densities (i.e. thicker struts) have lower local stresses because of the
greater cross-
sectional area in each strut, with significant contribution of the nodes to
the load-bearing
ability, which results in a relatively uniform distribution of applied load
throughout the
nanolattice (12,37). Under these conditions, the nanolattices fail when the
local stresses
in the struts approach the theoretical strength of constitute carbon. Such
local stress
and higher volume fraction of struts eventually result in high strength of
nanolattices at
higher densities. The optimized unit-cell geometries, such as octet- and iso-
truss, with
better flaw tolerance also facilitate the achievement of high strength.
[0309] FIG. 52 shows that the specific strengths of pyrolytic carbon
nanolattices
range from 0.146 to 1.90 GPa g-1 cm3, which represents 2-3 orders of magnitude
improvement over all nano- and micro-architected periodic lattices reported to
date,
including hollow-tube nickel (7) and NiP (8), copper (19), and TiAl6V4 (27)
microlattices,
as well as of hollow-beam alumina (11), alumina-polymer (16) and metallic
glass
Zr54Ni28A118 nanolattices (33). The maximum specific strength of the carbon
nanolattices
in this work, at a density of 1.0 g/cm3, is 2.4 times higher than that of 0.80
GPa g-1 cm3
reported for glassy carbon nanolattices (18), and represents 35% of fully-
dense
diamond, at 5.60 GPa g-1 cm3, which has the highest specific strength of all
bulk
materials (18). Such ultra-high specific strength of our pyrolytic carbon
nanolattices
arises from both the nano-sized beam diameters and the optimized lattice
topology.
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[0310] In this illustrative Example, we developed an additive
fabrication methodology
to create micro- and nano-architected pyrolytic carbon with densities below
1.0 g/cm3,
GPa-level strengths, and >10% deformability before failure. As a point of
departure from
all existing work on micro-/nano-lattices (11,16,18,22-26), the modulus and
strength of
nano-architected carbon in this work approach their theoretical limits.
Rational design of
lattice topologies with appropriate microstructure and nano- and micro-scale
characteristic materials dimensions enabled us to create prototype
architectures of
octet- and iso-truss pyrolytic carbon nanolattices with a Young's modulus of
0.34-18.6
GPa and strengths of 0.05-1.90 GPa at densities of 0.24-1.0 g/cm3, which
translates into
a specific strength of 0.146-1.90 GPa g-1 cm3 that has not been attained by
any carbon-
based or architected material. This nano-architected carbon also exhibited
average
fracture strains of 14.0%-16.7%, exceeding those of all other reported brittle
architected
materials. Experiments and simulations demonstrate that for densities higher
than 0.95
g/cm3, these samples become virtually insensitive to fabrication-induced
defects, which
gives rise to their attaining nearly-theoretical strength of 1.90 GPa and
lends them to
being particularly lucrative candidates for structural applications. This work
provides
insights into fundamental scientific principles that govern the design and
properties of
nano-architected materials and provides a feasible pathway for their use in
scalable
fabrication because of their emergent robustness against defects, ultra-light
weight, and
superior strength.
[0311] Materials and Methods:
[0312] Fabrication of pyrolytic carbon nanolattice. We first fabricated
polymeric
microlattices out of IF-Dip photoresist, using TPL DLW (Nanoscribe, GmbH) with
a
speed of 10,000 p.m s-1 and laser power of 17.5 mW. During the DLW process, we
printed the struts with 0.8-3.0 p.m-diameter circular cross sections via the
high-speed
galvo mode in a layer-by-layer fashion. All the printed polymeric
microlattices have two
typical unit-cell geometries: one is the octet-truss (FIG. 48B), and another
is the iso-
truss (FIG. 48D). The unit-cell size of polymeric microlattices is about 10
p.m. Then the
polymeric microlattices were pyrolized at 900 C for 5 hours in a vacuum, with
a ramp
rate of 7.5 C min-1 up to the target temperature and then cooled down to room
temperature at a natural rate. After pyrolysis, the polymeric microlattices
transformed
into pyrolytic carbon nanolattices, due to the mass-loss-induced carbonation
of the
polymers at elevated temperature (30). The diameters of all struts in
pyrolytic carbon
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nanolattices isotropically shrunk to about 261-679 nm, which is about 20%-25%
of their
initial dimensions (FIGs. 480 and 48E). The unit-cell size of all pyrolytic
carbon
nanolattices is about 2 p.m.
[0313] Mechanical testing. We conducted uniaxial compression experiments
on all
fabricated polymer microlattices and pyrolytic carbon nanolattices. Some of
these
experiments were performed in an in situ instrument (InSEM, Nanomechanics)
with a
170 p.m -diameter flat diamond punch at a constant strain rate of 10-3 5-1 to
reveal the
deformation morphology simultaneously with mechanical data acquisition. Other
experiments were carried out at a constant loading rate of 0.2 mN s-1 in a
nanoindenter
(G200, Agilent/Keysight Technologies) using a 120 p.m-diameter diamond flat
punch.
[0314] Finite element modelling. We carried out a series of FE modelling
for the
compression of pyrolytic carbon nanolattices via Abaqus. The isotropic linear
elastic
material was used for modelling. All nanolattices were modeled with beam
element. The
Young's modulus of material is 20 GPa (34) and the Poisson's ratio was 0.15
(18). The
simulated nanolattices have three types of unit-cell geometries, including
octet-truss,
iso-truss and tetrahedron-truss. For each type of nanolattice, the unit-cell
size sets to be
2 p.m, and the relative density varies from 15.9% to 70% by alternating the
diameter of
struts. Before compression, we introduce initial deflection to the struts of
simulated
nanolattices by imposing the corresponding buckling eigenmodes of nanolattices
(e.g.,
FIGs. 51A-51C). The maximum deflection of the struts is set as 5%, 10% and 15%
of
the edge length. After introducing initial deflection, some struts remain pre-
bent before
compression, which is very similar to some structural imperfections in the
experimental
samples (FIGs. 490 and 49E). During compression, the bottom of nanolattice was
fixed,
and the top is imposed by the displacement loading. We simulated the
compression of
nanolattice with perfectly straight struts as a reference to address the
influence of
imperfections/flaws on mechanical properties and response of nanolattice.
[0315] Determination of theoretical limits for Young's modulus and
strength versus
density. The modulus-density theoretical limit is taken from the literature
(11) and
determined by the bound of many data of real materials based on Granta Design,
which
is a standard software for materials selection and graphical analysis of
materials
properties. More information about Granta Design can be found in the webpage
(https.1/www.qrantadesian.corni) and relevant software documentation. The
strength-
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density limit is defined in the literature (18) and just a specific range
based on the
measurements for all materials to date. The lower bound of this range is
defined by
diamond, which has the highest specific strength of all bulk materials, while
the upper
bound is determined by graphene, which holds the highest strength in all
materials so
far.
[0316] References corresponding to Example 9:
1. Gibson LJ, Ashby MF (1999) Cellular Solids: Structure and Properties
(Cambridge
University Press, Cambridge, UK), 2nd ed.
2. Hamm CE, Merkel R, Springer 0, Jurkojc P, Maier C, Prechtel K, Smetacek V
(2003)
Architecture and material properties of diatom shells provide effective
mechanical
protection. Nature 421:841-843.
3. Weiner S, Wagner HD (1998) The material bone: structure-mechanical function
relations. Annu. Rev. Mater. Sci. 28:271-298.
4. Gao H, Ji B, Jager IL, Arzt E, Fratzl P (2003) Materials become insensitive
to flaws at
nanoscale: lessons from nature. Proc. Natl. Acad. Sci. U.S.A. 100:5597-5600.
5. Wegst UGK, Bai H, Saiz E, Tomsia AP, Ritchie RO (2015) Bioinspired
structural
materials. Nat. Mater. 14:23-36.
6. Libonati F, Gu G, Qin Z, Vergani L, Buehler MJ (2016) Bone-inspired
materials by
design: Toughness amplification observed using 3D printing and testing. Adv.
Eng.
Mater. 18:1354-1363.
7. Schaedler TA, Jacobsen AJ, Torrents A, Sorensen AE, Lian J, Greer JR,
Valdevit L,
Carter WB (2011) Ultralight metallic microlattices. Science 334:962-965.
8. Torrents A, Schaedler TA, Jacobsen AJ, Carter W B, Valdevit L (2012)
Characterization of nickel-based microlattice materials with structural
hierarchy from the
nanometer to the millimeter scale. Acta Mater. 60:3511-3523.
9. Valdevit L, Godfrey SW, Schaedler TA, Jacobsen AJ, Carter WB (2013)
Compressive
strength of hollow microlattices: Experimental characterization, modeling, and
optimal
design. J. Mater. Res. 28:2461-2473.
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10. Jang D, Meza LR, Greer F, Greer JR (2013) Fabrication and deformation of
three-
dimensional hollow ceramic nanostructures. Nat. Mater. 12:893-898.
11. Meza LR, Das S, Greer JR (2014) Strong, lightweight, and recoverable three-
dimensional ceramic nanolattices. Science 345:1322-1326.
12. Meza LR, Phlipot GP, Portela CM, Maggi A, Montemayor LC, ComeIla A,
Kochmann
DM, Greer JR (2017) Reexamining the mechanical property space of three-
dimensional
lattice architectures. Acta Mater. 140:424-432.
13. Maggi A, Li H, Greer JR (2017) Three-dimensional nano-architected
scaffolds with
tunable stiffness for efficient bone tissue growth. Acta Biomater. 63:294-305.
14. Meza LR, Zelhofera AJ, Clarke N, Mateosa AJ, Kochmanna DM, Greer JR (2015)
Resilient 3D hierarchical architected metamaterials. Proc. Natl. Acad. Sci.
U.S.A.
112:11502-11507.
15. Zheng X, Lee H, Weisgraber TH, Shusteff M, DeOtte J, Duoss EB, Kuntz JD,
Biener
MM, Ge Q, Jackson JA, Kucheyev SO, Fang NX, Spadaccini CM (2014) Ultralight,
ultrastiff mechanical metamaterials. Science 344:1373-1377.
16. Bauer J, Hengsbach S, Tesari I, Schwaiger R, Kraft 0(2014) High-strength
cellular
ceramic composites with 3D microarchitecture. Proc. Natl. Acad. Sci. U.S.A.
111:2453-
2458.
17. Zheng X, Smith W, Jackson J, Moran B, Cui H, Chen D, Ye J, Fang N,
Rodriguez N,
Weisgraber T, Spadaccini CM (2016) Multiscale metallic metamaterials. Nat.
Mater.
15:1100-1106.
18. Bauer J, Schroer A, Schwaiger R, Kraft 0(2016) Approaching theoretical
strength in
glassy carbon nanolattices. Nat. Mater. 15:438-444.
19. Gu XW, Greer JR (2015) Ultra-strong architected Cu meso-lattices. Extreme
Mech.
Lett. 2:7-14.
20. Vyatskikh A, Delalande S, Kudo A, Zhang X, Portela CM, Greer JR (2018)
Additive
manufacturing of 3D nano-architected metals. Nat. Commun. 9:593.
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21. Zhang X, Yao J, Liu B, Yan J, Lei L, Li Y, Gao H, Li X (2018) Three-
dimensional
high-entropy alloy-polymer composite nanolattices that overcome the strength-
recoverability trade-off. Nano Lett. 18:4247-4256.
22. Fairen-Jimenez D, Carrasco-Marin F, Moreno-Castilla C (2007) Adsorption of
benzene, toluene, and xylenes on monolithic carbon aerogels from dry air
flows.
Langmuir 23:10095-10101.
23. Zhu C, Han TY, Duoss EB, Golobic AM, Kuntz JD, Spadaccini CM, Worsley MA
(2015) Highly compressible 3D periodic graphene aerogel microlattices. Nat.
Commun.
6:6962.
24. Jacobsen AJ, Mahoney S, Carter WB, Nutt S (2011) Vitreous carbon micro-
lattice
structures. Carbon 49:1025-1032.
25. Chen X, Zhao G, Wu Y, Huang Y, Liu Y, He J, Wang L, Lian Q, Li D (2017)
Cellular
carbon microstructures developed by using stereolithography. Carbon 123:34-44.
26. Eckel ZC, Zhou C, Martin JH, Jacobsen AJ, Carter WB, Schaedler TA (2016).
Additive manufacturing of polymer-derived ceramics. Science 351:58-62.
27. Challis VJ, Xu X, Zhang L, Roberts AP, Grotowski JF, Sercombe TB (2014)
High
specific strength and stiffness structures produced using selective laser
melting. Mater.
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28. Deshpande VS, Fleck NA, Ashby MF (2001) Effective properties of the octet-
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lattice material. J. Mech. Phys. Solids 49:1747-1769.
29. Messner MC (2016) Optimal lattice-structured materials. J. Mech. Phys.
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30. Li X, Gao H (2016) Smaller and stronger. Nat. Mater. 15:373-374.
31. Zhang X, Zhong L, Mateos A, Kudo A, Vyatskikh A, Gao H, Greer JR, Li X
(2018)
Carbon by design through atomic-level architecture. Under submission.
32. Harris PJ (2005) New perspectives on the structure of graphitic carbons.
Crit. Rev.
Solid State 30:235-253.
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33. Liontas R, Greer JR (2017) 3D nano-architected metallic glass: Size effect
suppresses catastrophic failure. Acta Mater. 133:393-407.
34. Stein YI, Constable AJ, Morales-Medina N, Sackier CV, Devoe ME, Vincent
HM,
Wardle BL (2017) Structure-mechanical property relations of non-graphitizing
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35. Cowlard FC, Lewis JC (1967) Vitreous carbon-a new form of carbon. J.
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36. Zhao JX, Bradt RC, Walker PLJ (1985) The fracture toughness of glassy
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elevated temperatures. Carbon 23, 15-18.
37. Portela CM, Greer JR, Kochmann DM (2018) Impact of node geometry on the
effective stiffness of non-slender three-dimensional truss lattice
architectures. Extreme
Mech. Lett. 22:138-148.
[0317] Example 10: Scalable fabrication method of 3D architected
structure using
additive manufacturing and pyrolysis thereof
[0318] FIGs. 57A-57D exhibit characterizations of the microstructure of the
3D
architected carbon. A cross-section image of the 3D architected carbon, shown
in FIG.
57A, demonstrates its monolithic structure without any micropores. EDS
analysis on the
cross-section surface showed that the 3D architected carbon was composed of
98.4%
carbon in an average with minor content of oxygen. Line analysis showed
homogeneous
elemental composition across the cross-section (FIG. 58A). FIG. 57B shows XRD
patterns with three broad peaks at 23.5 , 44.3 and 79.8 in 20, corresponding
to (002),
(100)/(101) and (110) of graphite. The average interlayer spacing for graphene
sheets
and crystallite size along (002) (i.e. d002 and Lc) were estimated to be 3.78
A and 9.3 A
using the Bragg's law and Scherrer equation respectively, which suggested that
there
existed several stacked graphitic layers in average. Raman spectra, shown in
FIG. 57C,
was deconvoluted into five peaks: strong peaks of D1 (at 1355 cm-1) and G (at
1603
cm-1) and weak peaks of D2 (at 1613 cm-1), D3 (at 1539 cm-1) and D4 (1225 cm-
1). The
G peak corresponds to in-plane bond-stretching motion of pairs of C sp2 atoms
with E2g
symmetry.24 The D1 peak appears only in the presence of the disorder of
graphite and
corresponds to a graphitic lattice vibration mode with Aig symmetry.24 The D2
peak was
considered attributed to a graphitic lattice vibration, and D3 and D4 peaks
have been
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seen in amorphous or glassy carbon in other studies.25,26 The high-resolution
image of
TEM in FIG. 57D confirmed the tangled microstructure containing several
stacked
graphitic layers. Diffused diffraction rings at (002), (100)/(101) and (110)
in the inset
illustrated disordered carbon microstructure, which agreed with broad peaks of
the XRD
pattern.
[0319] Mechanical behaviors of the 3D architected carbon were evaluated
by using
uniaxial compression tests with a microcamera. FIGs. 59A-59B show
representative
mechanical response with in-situ compression side-views of a part of the
architecture
around each collapse event (full movie is accessible in Supplemental). Note
that the
bottom side of the 3D architecture was chipped when removing it from a
substrate of the
DLP 3D printer.
[0320] The first stress release was followed by the gradual decrease of
the load with
local failure events as pointed by red circles in FIG. 59B II-a, II-b, and II-
c. The second
stress release event occurred when the contact part of 3D architected carbon
on the
substrate was fractured by a half layer (FIG. 59B IV). At the third stress
release, the 3D
architected carbon was almost fully contacted on the substrate and collapsed
by a half
layer with showing the largest yield stress (29.9MPa). These two collapse
events with
small yield strength and the subsequent third collapse with high strength were
repeatedly observed (FIG. 60). Average yield strengths at each stress release
event
were tabulated in Table 2.
Table 2. Average values and standard deviations of the 1st, 2nd and 3rd yield
strength
1st yield 2nd yield 3rd yield
Average (MPa) 9.2 14.2 27.1
SD (MPa) 2.9 6.4 5.3
[0321] Example 11: Node Free Geometries
[0322] FIG. 61A and FIG. 61B. Images showing architected three-dimensional
structures having node-free geometries, according to certain embodiments of
the
invention. Additional exemplary node-free geometries may be found in Abueidda,
et al.
("Effective conductivities and elastic moduli of novel foams with triply
periodic minimal
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surfaces", Mechanics of Materials, vol. 95, April 2016, pages 102-115), which
is
incorporated herein by reference.
[0323] Example 12: Infiltration of Carbon Reinforcing Phases
[0324] The architected carbon reinforcing phases were infiltrated with a
low-viscosity
epoxy and cured at room temperature for 8 hours.
[0325] The spinodal cube depicted in FIGs. 62A and 62D underwent a
density
transition from p = 123.7 kg/m3 to 1152 kg/m3, while the octet-cube in FIGs.
62C and
62F went from 255 kg/m3 to 1160 kg/m3. The resulting composite materials had
an
average density of at least two times lower than that of light metals (i.e.,
pAi = 2700
kg/m3), and at least 40% lower than some carbon fiber reinforced polymers,
which
commonly have a density around 1600- 1800 kg/m3.
[0326] Example 13: Mechanical Testing
[0327] Uniaxial Compression of Octet Phases and Composites
[0328] We performed quasi-static uniaxial compression on octet carbon
reinforcing
phases with and without epoxy infiltration. The experiments were performed at
a strain
rate of e = 10-3 s-1. Since the underlying tessellation consisted of 17 x 17 x
17 unit cells
(with a characteristic unit cell size of - 590 pm), we assume sufficient
separation-of-
scales to discuss effective material (rather than structural) properties.
[0329] The experiments depicted in FIGs. 63A-63D were used to obtain an
effective
modulus and yield strength for this given carbon material with approximately
15%
relative density. Young's moduli of 669.7 and 495 MPa were calculated, while
the yield
strengths - defined as the stress at the initial catastrophic fracture event -
were
calculated to be 11.33 and 8.67 MPa. These carbon phases, without a matrix
phase,
were susceptible to defects in the sample.
[0330] Upon infiltration with epoxy, the mechanical behavior of these
materials
changed significantly. Most notably, the material did not undergo any
catastrophic
events and underwent significant strain hardening past c> 0.1. FIGs. 64A-64C
show the
response of the material under compression, with significant densification
after c = 0.5
but no catastrophic failure or through-sample cracks.
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[0331] These experiments resulted in Young's moduli of 1.82 and 2.24 GPa,
and
yield strengths of 59.8 and 69.6 MPa. At these strength values, this material
as strong
as some metals (e.g., copper), while having 7.7x lower density. We define the
yield
strength ay for these materials using the 0.2% strain offset from the linear
regime, and
we also define a flow stress af corresponding to the maximum stress before a
negative
tangent modulus was observed. The flow stress for these samples were
calculated to be
71.9 and 78.2 MPa. These values and comparisons to some metals are summarized
in
Table 3.
Table 3. Mechanical parameters of tested carbon octet materials including
comparison to some metals.
Material Density [kg/m3] E [MPa] 0-f
[MPa]
Carbon octets 1 291 669.7 MPa 11.33
Carbon octets 2 273 495 MPa 8.67
Composite octets 1 1157 1.82 GPa 59.8 71.9
Composite octets 2 1159 2.24 GPa 69.6 78.2
Aluminum 2700 69 GPa 95
Copper 8960 117 GPa 70
[0332] The non-catastrophic and strain-hardening response for these
composites
makes them well suited for energy absorption applications. For these quasi-
static
experiments, the specific energy absorption (SEA) can be defined as
=
where W is the strain energy density, defined as W= f 0-dE, and p is the
material
density. Calculating this metric for the experiments in FIG. 64C yielded W=
30.9 MJ/m3
and ip = 26.7 J/g, at a density of p = 1159 kg/m3. Comparing these metrics to
those of
stainless steel 316L octets (1), whose reported values were ip = 10.1 J/g and
p = 2160
kg/m3, shows that the carbon octet composites have twice the SEA capacity
while at half
the density.
[0333] 4-Point Bending of Octet Phases and Composites
[0334] We also explored the bending behavior of octet carbon materials
using a 4-
point bending setup following ASTM standard D6272.
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[0335] Bending of the carbon phase without a matrix showed catastrophic
failure, as
observed in the compression experiments. FIGs. 65A-65D show the experiment and
corresponding data, which yielded an approximate flexural strength of 10.34
MPa, and a
bending modulus of Eg = 1.4 GPa.
[0336] The same experiment was performed on epoxy-infiltrated materials,
which
resulted in bending moduli of 3.3 and 3.9 GPa. A flexural strength value was
not
calculated since no failure was observed within the allowable strain limit of
this ASTM
standard. After undergoing significant bending, the samples returned to their
original
shape with no evident permanent deformation or cracks.
[0337] References corresponding to Examples 11-12:
1. T. Tancogne-Dejean, A. B. Spierings, and D. Mohr, "Additively-manufactured
metallic
micro-lattice materials for high specific energy absorption under static and
dynamic
loading," Acta Materialia, vol. 116, pp. 14-28, 2016. [Online]. Available:
http:
//linkinghub.elsevier.com/retrieve/pii/S1359645416304153
STATEMENTS REGARDING INCORPORATION BY REFERENCE
AND VARIATIONS
[0338] All references throughout this application, for example patent
documents
including issued or granted patents or equivalents; patent application
publications; and
non-patent literature documents or other source material; are hereby
incorporated by
reference herein in their entireties, as though individually incorporated by
reference, to
the extent each reference is at least partially not inconsistent with the
disclosure in this
application (for example, a reference that is partially inconsistent is
incorporated by
reference except for the partially inconsistent portion of the reference).
[0339] The terms and expressions which have been employed herein are
used as
terms of description and not of limitation, and there is no intention in the
use of such
terms and expressions of excluding any equivalents of the features shown and
described or portions thereof, but it is recognized that various modifications
are possible
within the scope of the invention claimed. Thus, it should be understood that
although
the present invention has been specifically disclosed by preferred
embodiments,
exemplary embodiments and optional features, modification and variation of the
concepts herein disclosed may be resorted to by those skilled in the art, and
that such
modifications and variations are considered to be within the scope of this
invention as
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defined by the appended claims. The specific embodiments provided herein are
examples of useful embodiments of the present invention and it will be
apparent to one
skilled in the art that the present invention may be carried out using a large
number of
variations of the devices, device components, methods steps set forth in the
present
description. As will be obvious to one of skill in the art, methods and
devices useful for
the present methods can include a large number of optional composition and
processing
elements and steps.
[0340] As used herein and in the appended claims, the singular forms "a",
"an", and
"the" include plural reference unless the context clearly dictates otherwise.
Thus, for
example, reference to "a cell" includes a plurality of such cells and
equivalents thereof
known to those skilled in the art. As well, the terms "a" (or "an"), "one or
more" and "at
least one" can be used interchangeably herein. It is also to be noted that the
terms
"comprising", "including", and "having" can be used interchangeably. The
expression "of
any of claims XX-YY" (wherein )0( and YY refer to claim numbers) is intended
to provide
a multiple dependent claim in the alternative form, and in some embodiments is
interchangeable with the expression "as in any one of claims XX-YY."
[0341] When a group of substituents is disclosed herein, it is understood
that all
individual members of that group and all subgroups, are disclosed separately.
When a
Markush group or other grouping is used herein, all individual members of the
group and
all combinations and subcombinations possible of the group are intended to be
individually included in the disclosure. When a compound is described herein
such that
a particular isomer, enantiomer or diastereomer of the compound is not
specified, for
example, in a formula or in a chemical name, that description is intended to
include each
isomers and enantiomer of the compound described individual or in any
combination.
Additionally, unless otherwise specified, all isotopic variants of compounds
disclosed
herein are intended to be encompassed by the disclosure. For example, it will
be
understood that any one or more hydrogens in a molecule disclosed can be
replaced
with deuterium or tritium. Isotopic variants of a molecule are generally
useful as
standards in assays for the molecule and in chemical and biological research
related to
the molecule or its use. Methods for making such isotopic variants are known
in the art.
Specific names of compounds are intended to be exemplary, as it is known that
one of
ordinary skill in the art can name the same compounds differently.
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[0342] Every system, structure, geometry, feature, combination thereof,
or method
described or exemplified herein can be used to practice the invention, unless
otherwise
stated.
[0343] Whenever a range is given in the specification, for example, a
temperature
range, a time range, or a composition or concentration range, all intermediate
ranges
and subranges, as well as all individual values included in the ranges given
are intended
to be included in the disclosure. It will be understood that any subranges or
individual
values in a range or subrange that are included in the description herein can
be
excluded from the claims herein.
[0344] All patents and publications mentioned in the specification are
indicative of the
levels of skill of those skilled in the art to which the invention pertains.
References cited
herein are incorporated by reference herein in their entirety to indicate the
state of the
art as of their publication or filing date and it is intended that this
information can be
employed herein, if needed, to exclude specific embodiments that are in the
prior art.
For example, when composition of matter are claimed, it should be understood
that
compounds known and available in the art prior to Applicant's invention,
including
compounds for which an enabling disclosure is provided in the references cited
herein,
are not intended to be included in the composition of matter claims herein.
[0345] As used herein, "comprising" is synonymous with "including,"
"containing," or
"characterized by," and is inclusive or open-ended and does not exclude
additional,
unrecited elements or method steps. As used herein, "consisting of" excludes
any
element, step, or ingredient not specified in the claim element. As used
herein,
"consisting essentially of" does not exclude materials or steps that do not
materially
affect the basic and novel characteristics of the claim. In each instance
herein any of
the terms "comprising", "consisting essentially of" and "consisting of" may be
replaced
with either of the other two terms. The invention illustratively described
herein suitably
may be practiced in the absence of any element or elements, limitation or
limitations
which is not specifically disclosed herein.
[0346] One of ordinary skill in the art will appreciate that starting
materials, biological
materials, reagents, synthetic methods, purification methods, analytical
methods, assay
methods, and biological methods other than those specifically exemplified can
be
employed in the practice of the invention without resort to undue
experimentation. All
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art-known functional equivalents, of any such materials and methods are
intended to be
included in this invention. The terms and expressions which have been employed
are
used as terms of description and not of limitation, and there is no intention
that in the
use of such terms and expressions of excluding any equivalents of the features
shown
and described or portions thereof, but it is recognized that various
modifications are
possible within the scope of the invention claimed. Thus, it should be
understood that
although the present invention has been specifically disclosed by preferred
embodiments and optional features, modification and variation of the concepts
herein
disclosed may be resorted to by those skilled in the art, and that such
modifications and
variations are considered to be within the scope of this invention as defined
by the
appended claims.
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