Note: Descriptions are shown in the official language in which they were submitted.
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AUXETIC STRUCTURES WITH DISTORTED PROJECTION SLOTS IN
ENGINEERED PATTERNS TO PROVIDE NPR BEHAVIOR AND IMPROVED
STRESS PERFORMANCE
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the right of priority to U.S. Provisional
Patent Application No.
62/118,830, filed on February 20, 2015, and U.S. Provisional Patent
Application No.
62/101,852, filed on January 9, 2015, both of which are incorporated herein by
reference in
their respective entireties.
TECHNICAL FIELD
[0002] The present disclosure relates generally to porous materials and
cellular solids with
tailored isotropic and anisotropic Poisson's ratios. More particularly,
aspects of this
disclosure relate to auxetic structures with engineered patterns that exhibit
negative Poisson's
Ratio (NPR) behavior, as well as systems, methods and devices using such
structures.
BACKGROUND
[0003] When materials are compressed along a particular axis, they are most
commonly
observed to expand in directions transverse to the applied axial load.
Conversely, most
materials contract along a particular axis when a tensile load is applied
along an axis
transverse to the axis of contraction. The material property that
characterizes this behavior is
known as the Poisson's Ratio, which can be defined as the negative of the
ratio of
transverse/lateral strain to axial/longitudinal strain under axial loading
conditions. The
majority of materials are characterized by a positive Poisson's Ratio, which
is approximately
0.5 for rubber, approximately 0.3 for aluminum, brass and steel, and
approximately 0.2 for
glass.
[0004] Materials with a negative Poisson's Ratio (NPR), on the other hand,
will contract (or
expand) in the transverse direction when compressed (or stretched) in the
axial direction.
Materials that exhibit negative Poisson's Ratio behavior are oftentimes
referred to as
"auxetic" materials. The results of many investigations suggest that auxetic
behavior
involves an interplay between the microstructure of the material and its
deformation.
Examples of this are provided by the discovery that metals with a cubic
lattice, natural
layered ceramics, ferroelectric polycrystalline ceramics, and zeolites may all
exhibit negative
Poisson's Ratio behavior. Moreover, several geometries and mechanisms have
been proposed
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to achieve negative values for the Poisson's Ratio, including foams with
reentrant structures,
hierarchical laminates, polymeric and metallic foams. Negative Poisson's Ratio
effects have
also been demonstrated at the micrometer scale using complex materials which
were
fabricated using soft lithography and at the nanoscale with sheet assemblies
of carbon
nanotub es.
[0005] A significant challenge in the fabrication of auxetic materials is that
it usually
involves embedding structures with intricate geometries within a host matrix.
As such, the
manufacturing process has been a bottleneck in the practical development
towards
applications. A structure which forms the basis of many auxetic materials is
that of a cellular
solid. Research into the deformation of these materials is a relatively mature
field with
primary emphasis on the role of buckling phenomena, on load carrying capacity,
and energy
absorption under compressive loading. Very recently, the results of a combined
experimental
and numerical investigation demonstrated that mechanical instabilities in 2D
periodic porous
structures can trigger dramatic transformations of the original geometry.
Specifically,
uniaxial loading of a square array of circular holes in an elastomeric matrix
is found to lead to
a pattern of alternating mutually orthogonal ellipses while the array is under
load. This
results from an elastic instability above a critical value of the applied
strain. The geometric
reorganization observed at the instability is both reversible and repeatable
and it occurs over a
narrow range of the applied load. Moreover, it has been shown that the pattern
transformation leads to unidirectional negative Poisson's Ratio behavior for
the 2D structure,
i.e., it only occurs under compression.
[0006] U.S. Patent No. 5,233,828 ("828 Patent") shows an example of an
engineered void
structure - a combustor liner or "heat shield" - utilized in high temperature
applications.
Combustor liners are typically used in the combustion section of a gas
turbine. Combustor
liners can also be used in the exhaust section or in other sections or
components of the gas
turbine, such as the turbine blades. In operation, combustors burn gas at
intensely high
temperatures, such as around 3,000 F or higher. To prevent this intense heat
from damaging
the combustor before it exits to a turbine, the combustor liner is provided in
the interior of the
combustor to insulate the surrounding engine. To minimize temperature and
pressure
differentials across a combustor liner, cooling feature have conventionally
been provided,
such as is shown in the '828 Patent, in the form of spaced cooling holes
disposed in a
continuous pattern. As another example, U.S. Patent No. 8,066,482 B2 presents
an
engineered structural member having elliptically-shaped cooling holes to
enhance the cooling
of a desired region of a gas turbine while reducing stress levels in and
around the cooling
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holes. European Patent No. EP 0971172 Al likewise shows another example of a
perforated
liner used in a combustion zone of a gas turbine. None of the above patent
documents,
however, provide examples disclosed as exhibiting auxetic behavior or being
engineered to
provide NPR effects.
[0007] U.S. Patent Application Pub. No. 2010/0009120 Al discloses various
transformative
periodic structures which include elastomeric or elasto-plastic periodic
solids that experience
transformation in the structural configuration upon application of a critical
macroscopic stress
or strain. Said transformation alters the geometric pattern, changing the
spacing and the shape
of the features within the transformative periodic structure. Upon removal of
the critical
macroscopic stress or strain, these elastomeric periodic solids recover their
original form. By
way of comparison, U.S. Patent Application Pub. No. 2011/0059291 Al discloses
structured
porous materials, where the porous structure provides a tailored Poisson's
ratio behavior.
These porous structures consist of a pattern of elliptical or elliptical-like
voids in an elastomeric
sheet which is tailored, via the mechanics of the deformation of the voids and
the mechanics of
the deformation of the material, to provide a negative or a zero Poisson's
ratio. All of the
foregoing patent documents are incorporated herein by reference in their
respective entireties
and for all purposes.
SUMMARY
[0008] Aspects of the present disclosure are directed towards auxetic
structures with
repeating patterns of elongated apertures (also referred to herein as "voids"
or "slots") that
are engineered to provide a desired negative Poisson's Ratio (NPR) behavior
and enhanced
stress performance. Unlike prior art NPR void shapes that extend through the
structure
material, traversing the material's thickness with a constant three-
dimensional (3D) geometry
and in a direction normal to the material's plane, NPR voids disclosed herein
traverse the
material's thickness with a variable 3D-geometry (e.g., a distorted shape
projected through
the material at an oblique angle). These void configurations enhance the
stress performance
of the structure while retaining a low porosity and providing a desired NPR
behavior. Other
aspects of the present disclosure are directed to multi-functional NPR
structures with variable
3D-geometry air passages in the hot section of a gas turbine. Additional
aspects are directed
towards gas turbine combustors that are made with walls from a material with
engineered
variable 3D-geometry void features that provide particular thermal, damping
and/or acoustic
functionalities. Such functionalities include, for example, acoustic
attenuation (or noise
damping), stress reduction (or load damping), and thermal cooling (or heat
damping).
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[0009] According to aspects of the present disclosure, auxetic structures with
distorted NPR
slots are disclosed. In an example, an auxetic structure includes an
elastically rigid body,
such as a metallic sheet or other sufficiently elastic solid material, with
opposing top and
bottom surfaces. First and second pluralities of elongated apertures extend
through the
elastically rigid body from the top surface to the bottom surface. The first
plurality of
elongated apertures extends transversely (e.g., orthogonally) with respect to
the second
plurality of elongated apertures. The first and/or second pluralities of
elongated apertures
have distorted shapes projected through the elastically rigid body at an
oblique angle. In an
example, the profile of each angled NPR slot that appears on an outer (top or
bottom) surface
can be a distorted projection of an original, unadulterated image. Moreover,
each slot
traverses the thickness of a sheet material at an angle that is oblique (e.g.,
approximately 40-
75 degrees) to the material's plane. The elongated apertures are cooperatively
configured to
provide a desired stress performance while exhibiting a negative Poisson's
Ratio (NPR)
behavior under macroscopic planar loading conditions. By way of example, the
elongated
apertures are engineered with a predefined porosity, a predetermined pattern,
and/or a
predetermined aspect ratio to achieve the desired NPR behavior. The auxetic
structure may
exhibit a reduction in stress concentration proximate the longitudinal ends of
one or more or
all of the elongated apertures, a porosity of about 0.3 to about 9%, and a
Poisson's Ratio of
about -0.0001 to about -0.9%.
[0010] In accordance with other aspects of this disclosure, effusion-cooling
auxetic sheet
structures are featured. In an example, an effusion-cooling auxetic sheet
structure is presented
which includes a metallic sheet with opposing top and bottom surfaces. First
and second
pluralities of elongated apertures extend through the metallic sheet from the
top surface to the
bottom surface. The first plurality of elongated apertures has a first set of
geometric
characteristics and is arranged in a first pattern. Likewise, the second
plurality of elongated
apertures has a second set of geometric characteristics and is arranged in a
second pattern. The
elongated apertures of the first plurality are orthogonally oriented with
respect to the elongated
apertures of the second plurality. The elongated apertures have distorted
shapes projected
through the elastically rigid body at an oblique angle. The geometric
characteristics and
pattern of the first plurality of elongated apertures are cooperatively
configured with the
geometric characteristics and pattern of the second plurality of elongated
apertures to provide a
desired stress performance while exhibiting negative Poisson's Ratio (NPR)
behavior under
macroscopic planar loading conditions.
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[0011] Other aspects of the present disclosure are directed to methods of
manufacturing and
methods of using auxetic structures. In an example, a method is presented for
manufacturing
an auxetic structure. Said method includes: providing an elastically rigid
body with opposing
top and bottom surfaces; adding to the elastically rigid body a first
plurality of apertures
extending through the elastically rigid body from the top surface to the
bottom surface, the
first plurality of apertures being arranged in rows and columns; and, adding
to the elastically
rigid body a second plurality of apertures extending through the elastically
rigid body from
the top surface to the bottom surface, the second plurality of apertures being
arranged in rows
and columns. Each aperture of the first and/or second pluralities of elongated
apertures has a
distorted shape that is projected through the elastically rigid body at an
oblique angle. The
first and second pluralities of apertures are cooperatively configured to
provide a desired
stress performance while exhibiting a negative Poisson's Ratio (NPR) behavior
under
macroscopic planar loading conditions. By way of example, the elongated
apertures are
engineered with a predefined porosity, a predetermined pattern, and/or a
predetermined
aspect ratio to achieve the desired NPR behavior. The auxetic structure may
exhibit a
reduction in stress concentration proximate one or more or all of elongated
apertures and a
Poisson's Ratio of about -0.0001 to about -0.9%. The elastically rigid body
may take on
various forms, such as a metallic sheet or other sufficiently elastic solid
material.
[0012] The above summary is not intended to represent every embodiment or
every aspect of
the present disclosure. Rather, the foregoing summary merely provides an
exemplification of
some of the novel aspects and features set forth herein. The above features
and advantages,
and other features and advantages of the present disclosure, which are
considered to be
inventive singly and in any combination, will be readily apparent from the
following detailed
description of representative embodiments and modes for carrying out the
present disclosure
when taken in connection with the accompanying drawings and the appended
claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] FIG. 1 is a graph of Nominal Strain vs. Poisson's Ratio illustrating
the Poisson's Ratio
behavior of representative structures with elongated through holes according
to aspects of the
present disclosure.
[0014] FIGS. 2A-2C are illustrations of the representative structures of FIG.
1 corresponding
to specific data points from the graph.
[0015] FIGS. 3A and 3B are side-view and perspective-view illustrations,
respectively, of a
distorted projection NPR slot according to aspects of the present disclosure.
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[0016] FIGS. 4A and 4B are plan-view illustrations of a distorted NPR S-shaped
through slot
and a distorted NPR Z-slot, respectively, with variable cap rotation in
accordance with
aspects of the present disclosure.
[0017] FIGS. 5A-5D are plan-view illustrations of an NPR S-shaped through slot
exhibiting a
0-degree angle, a distorted projection NPR S-shaped through slot exhibiting a
45-degree
angle, a distorted projection NPR S-shaped through slot exhibiting a 55-degree
angle, and a
distorted projection NPR S-shaped through slot exhibiting a 65-degree angle,
respectively, in
accordance with aspects of the present disclosure.
[0018] FIG. 6A-6C are finite element (FE) models illustrating radial
displacement under axial
tension of a cylindrical structure with S-shaped through slots in accordance
with aspects of
the present disclosure.
[0019] FIGS. 7A-7C are finite element (FE) models illustrating radial
displacement under
axial tension of a cylindrical auxetic structure with distorted NPR S-shaped
through slots in
accordance with aspects of the present disclosure.
[0020] The present disclosure is susceptible to various modifications and
alternative forms,
and some representative embodiments have been shown by way of example in the
drawings
and will be described in detail herein. It should be understood, however, that
the inventive
aspects of this disclosure are not limited to the particular forms illustrated
in the drawings.
Rather, the disclosure is to cover all modifications, equivalents,
combinations and
subcombinations, and alternatives falling within the spirit and scope of the
invention as
defined by the appended claims.
DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS
[0021] This disclosure is susceptible of embodiment in many different forms.
There are
shown in the drawings, and will herein be described in detail, representative
embodiments
with the understanding that the present disclosure is to be considered as an
exemplification of
the principles of the present disclosure and is not intended to limit the
broad aspects of the
disclosure to the embodiments illustrated. To that extent, elements and
limitations that are
disclosed, for example, in the Abstract, Summary, and Detailed Description
sections, but not
explicitly set forth in the claims, should not be incorporated into the
claims, singly or
collectively, by implication, inference or otherwise. For purposes of the
present detailed
description, unless specifically disclaimed or logically prohibited: the
singular includes the
plural and vice versa; and the words "including" or "comprising" or "having"
means
"including without limitation." Moreover, words of approximation, such as
"about,"
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"almost," "substantially," "approximately," and the like, can be used herein
in the sense of
"at, near, or nearly at," or "within 3-5% of," or "within acceptable
manufacturing tolerances,"
or any logical combination thereof, for example.
[0022] Aspects of the present disclosure are directed towards auxetic
structures which
include repeating patterns of angled slots that provide negative Poisson's
Ratio (NPR)
behavior when macroscopically loaded. Poisson's Ratio (or "Poisson
coefficient") can be
generally typified as the ratio of transverse contraction strain to
longitudinal extension strain
in a stretched object. Poisson's Ratio is typically positive for most
materials, including many
alloys, polymers, polymer foams and cellular solids, which become thinner in
cross section
when stretched. The auxetic structures disclosed herein exhibit a negative
Poisson's Ratio
behavior.
[0023] According to aspects of the disclosed concepts, when an auxetic
structure is
compressed along one axis (e.g., in the Y-direction), coaxial strain results
in a moment
around the center of each cell because of the way the adjacent apertures are
arranged. This,
in turn, causes the cells to rotate. Each cell rotates in a direction opposite
to that of its
immediate neighbors. This rotation results in a reduction in the transverse
axis (X-direction)
distance between horizontally adjacent cells. In other words, compressing the
structure in the
Y-direction causes it to contract in the X-direction. Conversely, tension in
the Y-direction
results in expansion in the X-direction. At the scale of the entire structure,
this mimics the
behavior of an auxetic material. But many of the structures disclosed herein
are composed of
conventional materials. Thus, the unadulterated material itself may have a
positive Poisson's
Ratio, but by modifying the structure with the introduction of the distorted-
NPR-slot patterns
disclosed herein, the structure behaves as having a negative Poisson's Ratio.
[0024] FIG. 1 is a graph of Poisson's Ratio (PR) against Nominal Strain
illustrating the
Poisson's Ratio behavior of three representative void structures shown in
FIGS. 2A-2C. The
chart of FIG. 1 shows the Poisson's Ratio of each test piece under load. At a
certain level of
deformation, the "instantaneous" PR can be determined and plotted against a
parameter (e.g.,
nominal strain) representing the level of deformation. When a designer has a
desired NPR
for an intended application, the level of deformation corresponding to that PR
can be
determined and the geometry of the holes at that condition determined. This
hole shape
pattern can then be machined (manufactured) on an unstressed part to achieve a
component
with the desired PR.
[0025] As seen in FIGS. 2B and 2C, the NPR aperture patterns can consist of
horizontally
and vertically oriented, elongated holes (also referred to as "apertures" or
"voids" or "slots"),
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shown as elliptical through slots. These elongated holes are arranged on
horizontal and
vertical lines (e.g., rows and columns of a square array in FIG. 2B) in a way
that the vertical
lines are equally spaced and the horizontal in both dimensions lines are
equally spaced (also
Ax=Ay). The center of each slot is on the crossing point of two of the lines.
Horizontally
oriented and vertically oriented slots alternate on the vertical and
horizontal lines such that
any vertically oriented slot is surrounded by horizontally oriented slots (and
vice versa),
while the next vertically oriented slots are found on both diagonals. These
voids can also act
as cooling and/or damping holes and, due to their arrangement, also as stress
reduction
features. One or more of the slots shown herein can be replaced by elongated
NPR
protrusions or semispherical NPR dimples.
[0026] Also disclosed are gas turbine combustors that are made with one or
more walls from a
material with any of the specific auxetic structure configurations disclosed
herein. In some
embodiments, the NPR slots are generated in a metal body directly in a stress-
free state such
that the apertures are equivalent in shape to collapsed void shapes found in
rubber under
external load in order to get NPR behavior in the metal body without
collapsing the metallic
structure in manufacturing. Various manufacturing routes can be used to
replicate the void
patterns in the metallic component. The manufacturing does not necessarily
contain buckling
as one of the process steps. The auxetic structures disclosed herein are not
limited to the
combustor wall; rather, these features can be incorporated into other sections
of a turbine (e.g.,
a blade, a vain, etc.).
[0027] In a conventional combustor wall, holes used for cooling air flow and
damping also
act as stress risers. In some of the disclosed embodiments, as the wall
material at a hot spot
presses against its surrounding material, e.g., in a vertical direction, the
negative Poisson's
Ratio (NPR) behavior will make the wall material contract in the horizontal
direction, and
vice versa. This behavior will reduce the stresses at the hotspot
significantly. This effect is
stronger than just the impact of the reduced stiffness. Stress at hot spot
gets reduced, for
example, by 50% which, in turn, leads to an increase in stress fatigue life by
several orders of
magnitude. The stress reduction by the NPR behavior does not increase the air
consumption
of the combustor wall. The longer life could be used as such or the wall
material could be
replaced by a cheaper one in order to reduce raw material costs.
[0028] It has also been demonstrated that the replacement of circular
combustor cooling holes
with a fraction of elongated and angled air passages of 2-3% reduces thermo-
mechanical
stress by a factor of at least five, while maintaining cooling and damping
performance. For
example, elliptical cooling holes in the combustor have been predicted to
result in a five-fold
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decrease in the worst principal stress. Inducing NPR behavior, thus, adds
further
functionality to the cooling holes of the combustor in that the NPR behavior
generates a five-
fold reduction in worst principal stress as compared to traditional cooling
holes. In stress
fatigue of a combustor-specific superalloy, halving the component stress
increases the fatigue
life by more than an order of magnitude. In some embodiments, the superalloy
may be a
nickel-based superalloy, such as Inconel (e.g. IN100, IN600, IN713), Waspaloy,
Rene alloys
(e.g. Rene 41, Rene 80, Rene 95, Rene N5), Haynes alloys, Incoloy, MP98T, TMS
alloys,
and CMSX (e.g. CMSX-4) single crystal alloys.
[0029] It has been shown that optimized porosity offers increased cooling
function. As used
herein, "porosity" can be defined to mean the surface area of the apertures,
AA, divided by
the surface area of the structure, AS, or Porosity = AA / AS. It may be
desirable, in some
embodiments, that the porosity of a given void structure be approximately 0.3-
9.0% or, in
some embodiments, approximately 1-4% or, in some embodiments, approximately
2%. By
comparison, many prior art arrangements require a porosity of 40-50%.
[0030] There may be a predetermined optimal aspect ratio for the elongated
apertures to
provide a desired NPR behavior. As used herein, "aspect ratio" of the
apertures can be
defined to mean the length divided by the width of the apertures, or the
length of the major
axis divided by the length of the minor axis of the apertures. It may be
desirable, in some
embodiments, that the aspect ratio of the apertures be approximately 5-40 or,
in some
embodiments, approximately 20-30. An optimal NPR may comprise, for example, a
PR of
about 0 to about -0.9 or, for some embodiments, about -0.5. Aspects of the
disclosed
concepts can be demonstrated on structural patterns created with a pattern
lengthscale at the
millimeter, and are equally applicable to structures possessing the same
periodic patterns at a
smaller lengthscale (e.g., micrometer, submicrometer, and nanometer
lengthscales) or larger
lengthscales so far as the unit cells fit in the structure.
[0031] Turning next to FIGS. 3-5, there are shown various examples of
distorted-slot auxetic
structures which exhibit desired NPR behaviors and enhanced stress-mitigating
performance
in accordance with the present disclosure. FIGS. 3A and 3B, for example,
illustrate an
auxetic structure, designated generally at 300, which utilizes an alternating
pattern of
elongated asymmetrical slots. The foregoing slots are elongated in that each
has a major axis
(e.g., a length) that is larger than and perpendicular to a minor axis (e.g.,
a width). As shown,
the auxetic structure 300 comprises an elastically rigid body 310, which may
be in the form
of a metallic sheet or other solid material with adequate elasticity to return
substantially or
completely to its original form once macroscopic loading conditions are
sufficiently reduced
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or eliminated. Elastically rigid body 310 has a first (top) surface 314 in
opposing spaced
relation to a second (bottom) surface 316. Fabricated into the elastically
rigid body 310 is a
first plurality of S-shaped through slots (also referred to herein as
"apertures" or "voids" or
"slots"), represented herein by slot 312, which extend through the body 310
from the top
surface 314 to the bottom surface 316. A
second plurality of S-shaped through
slots/apertures, represented herein by slots 318, also extends through the
elastically rigid
body 310 from the top surface 314 to the bottom surface 316. The pattern of
elongated
apertures present in the elastically rigid body 310 may be similar in
arrangement to what is
seen in FIGS. 2B and 2C.
[0032] S-shaped through slots 312, 318 are arranged in an array or matrix of
rows and
columns, with the first plurality of elongated apertures 312 extending
transversely with
respect to the second plurality of elongated apertures 318. Note that hidden
lines indicating
the internal structural configuration of slots 318 have been omitted from
FIGS. 3A and 3B for
clarity to better show the internal structural configuration of slots 312. For
at least some
embodiments, the rows are equally spaced from each other and, likewise, the
columns are
equally spaced from each other. According to the illustrated embodiment of
FIGS. 3A and
3B, for example, each row and each column comprises vertically oriented S-
shaped through
slots 312 interleaved with horizontally oriented S-shaped through slots 318.
In effect, each
vertically oriented through slot 312 is neighbored on four sides by
horizontally oriented
through slots 318, while each horizontally oriented through slot 318 is
neighbored on four
sides by vertically oriented through slots 312. With this arrangement, the
minor axes of the
first plurality of S-shaped through slots 312 are parallel to the rows of the
array, whereas the
minor axes of the second plurality of S-shaped through slots 318 are parallel
to the columns
of the array. Thus, the major axes of the through slots 318, which are
parallel to the rows of
the array, are perpendicular to the major axes of the through slots 312, which
are parallel to
the columns of the array. It is also envisioned that other patterns and
arrangements for
achieving NPR behavior are within the scope and spirit of the present
disclosure.
[0033] The illustrated pattern of elongated, angled slots provides a specific
porosity (e.g., a
porosity of about 0.3 to about 9.0%) and a desired stress performance (e.g.,
lower stress
concentration factors) while exhibiting a desired negative Poisson's Ratio
behavior (e.g., a
PR of about -0.0001 to about -0.9) under macroscopic planar loading conditions
(e.g., when
tension or compression is applied in the plane of the sheet). When the auxetic
structure 300
is stretched, for example via tensile force FT along a vertical axis Y, axial
strain in the vertical
direction results in a moment around the center of each cell, which causes the
cells to rotate.
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A cell may consist of two laterally adjacent vertical slots aligned with two
vertically adjacent
horizontal slots to form a square-shaped unit. Each cell rotates in a
direction opposite to that
of its immediate neighboring cells. This rotation increases the X-direction
distance between
horizontally adjacent cells such that stretching the structure in the Y-
direction causes it to
stretch in the X-direction. The first plurality of S-shaped through slots 312
have (first)
engineered geometric characteristics, including a predefined geometry and a
predefined
aspect ratio, while the second plurality of S-shaped through slots 318 have
(second)
engineered geometric characteristics, including a predefined geometry and a
predefined
aspect ratio, that are cooperatively configured with (third) engineered
geometric
characteristics of the aperture pattern, including NPR-slot density and cell
arrangement, to
achieve a desired NPR behavior under macroscopic loading conditions.
[0034] Each slot of the first and/or second pluralities of elongated S-shaped
through slots
312, 318 has a distorted shape that is projected through the elastically rigid
body at an
oblique angle. By way of explanation, the profile of each angled NPR slot that
appears on an
outer surface of the auxetic structure's body can be a distorted projection of
an original,
unadulterated image. According to the illustrated example, top-surface and
bottom-surface
profiles 312A and 312B, respectively, of S-shaped through slot 312 are
generated by
projecting a standard "S" shape 320 at a desired oblique angle through the
thickness of the
elastically rigid body 310. In so doing, the profiles 312A, 312B of the NPR
slot 312 that
appear on the top and bottom surfaces 314, 316 of the body 310 are distorted
from the
original image 320. The degree of distortion can be varied depending, for
example, on the
desired angle and/or the desired orientation of the slot, e.g., to provide a
desired cooling
performance or a desired stress-mitigation. Top-surface and bottom-surface
profiles of S-
shaped through slots 318 can be generated in a similar manner. It is
envisioned that the
surface profiles of S-shaped through slots 312 are identical to the surface
profiles of S-shaped
through slots 318, e.g., for applications where the body 310 of the auxetic
structure is
relatively flat and the angle of projection is common for both sets of through
slots.
Contrastingly, the surface profiles of S-shaped through slots 312 can be
distinct from the
surface profiles of S-shaped through slots 318, e.g., for implementations
where the body 310
of the auxetic structure is curved and/or the angle of projection of S-shaped
through slots 312
is distinct from the angle of projection of S-shaped through slots 318.
[0035] Slot 312 is shown in FIG. 3A traversing the entire thickness of the
body 310 at an
angle that is oblique to the material's horizontal plane. For at least some
embodiments, each
aperture has an angle 0 of approximately 20-80 degrees or, in some
embodiments,
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approximately 45-75 degrees with the top and bottom surfaces 314, 316 of the
auxetic
structure's body 310. These macroscopically patterned NPR voids ¨ i.e., S-
shaped angled
slots (or, equivalently, I-shaped angled slots, barbell-shaped angled slots,
elliptical angled
slots, Z-shaped angled slots, C-shaped angled slots, etc.) ¨ serve as effusion
cooling holes
which allow a cooling fluid FL to traverse one surface of the auxetic
structure, pass through
the body at an inclination angle a, as shown in FIG. 3A, and traverse the
opposing surface of
the auxetic structure. This configuration enhances film cooling performance as
compared to
traditional cooling slots/holes that are normal to the thickness of the body
and, thus, more
restrictive of cooling fluid flow. Inclination angle a can be defined as the
angle between the
injection vector and its projection on the material plane. This inclination
angle a can be
varied in a 360 rotational angle of freedom using three rotational axis to
achieve numerous
desired combinations of auxetic behavior and film cooling performance.
Inclination angle a
can be varied with respect to any plane, or the compound of any two planes,
giving the
transverse direction of the shape three rotational degrees of freedom.
Patterned angled NPR-
slot features have been shown to cool significantly better than conventional
right-angled
(normal) circular holes and cooling slots as the internal surface area of the
slots is larger than
that of normal circular holes or slots. Adiabatic film cooling effectiveness
is also increased
compared to traditional normal cooling holes and slots, for example, due to a
more even
distribution of cooling air over the surface and reduced coolant jet
penetration into the
mainstream flow.
[0036] Auxetic structure 300 provides a reduction in stress concentration
proximate one or
more of all of the elongated apertures 312, 318. Patterned angled S-shaped
slot structures
provide significantly better effusion cooling characteristics than
conventional circular holes
while providing lower stress concentration factors. Projecting cooling holes
onto a surface of
an auxetic structure forms elongated through slots (e.g., ellipses or s-shaped
slots), which can
result in high stress concentrations at the opposing tips of the slots.
Macroscopic patterned
voids, such as those illustrated in FIGS. 3A and 3B, have smoother curvature
when projected,
and hence lower stress concentration factors. To reduce the stress
concentration caused by
the distorted shape when projecting onto an outer surface of an elastically
rigid body, such as
a cylindrical surface of a tubular component, a projection vector 322 of each
aperture can be
substantially or completely parallel to a direction of loading of the
elastically rigid body.
FIGS. 5A-5D illustrate slot distortion on an outer surface of a tubular
auxetic structure. FIG.
5A, for example, illustrates normal NPR S-shaped through slots exhibiting a 0-
degree
projection angle. By comparison, FIG. 5B illustrates angled NPR S-shaped
through slots
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exhibiting a 45-degree projection angle with the projection vector placed
parallel to the
loading direction, while FIG. 5C illustrates angled NPR S-shaped through slots
exhibiting a
55-degree projection angle with the projection vector placed parallel to the
loading direction,
and FIG. 5D illustrates angled NPR S-shaped through slots exhibiting a 65-
degree projection
angle with the projection vector placed parallel to the loading direction.
Since tensile loading
acts to separate the through holes, projecting along the loading direction
acts to keep the
voids interacting throughout deformation of the rigid body.
[0037] Projecting the distorted slots along the loading direction allows a
void arrangement
that would otherwise exhibit a significantly positive Poisson's ratio (e.g.,
FIGS. 6A-6C
illustrate slots with an inclination angle a = 0 degrees, resulting in a
Poisson's Ratio = 0.27)
to achieve a negative Poisson's ratio (e.g., FIGS. 7A-7C illustrate slots with
an inclination
angle a = 75 degrees, resulting in a Poisson's Ratio = -0.0001).
Distorted and angled S-
shaped through slots help retain NPR behavior at much lower porosity than
normal NPR S-
shaped slots. When normal NPR S-shaped slots are separated by the required
distance to
achieve a low-porosity-level requirement, the horizontal and vertical S-shaped
through slots
tend to stop interacting during deformation, making the structure lose its NPR
behavior.
With the distorted, angled S-shaped through slot structure, the S-shaped slots
are elongated
within the thickness of material, allowing them to be placed further apart
than the normal S-
shaped slots while still retaining the NPR behavior. With the improved film
cooling
effectiveness of the angle S-shaped through slot structure, the temperature on
the structure is
reduced, leading to a decrease in thermal stress
[0038] Distorted NPR slot shapes, for instance, Z-shaped slots 412A (FIG. 4A)
and S-shaped
slots (FIG. 4B), can be developed by changing cap length 411A and 411B and/or
cap height
413A and 413B to provide a horizontal projection that is dissimilar to an
existing or
"standard" S-shape/Z-shape. The size and shape of the caps can be varied to
achieve a
desired combination of auxetic behavior and film cooling performance. Film
cooling
performance of angled effusion S-shaped slots or, equivalently, Z-shaped slots
can be
improved by producing a longer cooling thermal layer above the hot surface. A
longer
cooling thermal layer can be created by increasing the lateral area of the
slots normal to the
free mainstream fluid by rotating the S-shaped slot cap in the counter-
clockwise direction (or
clockwise direction for Z-shaped slot caps). This cap rotation angle 415A and
415B can be
varied to achieve a desired combination of auxetic behavior and film cooling
performance.
By rotating the caps of the S-shaped slots in the counter-clockwise direction,
the maximum
mechanical stress at the top of the caps will be reduced and the film cooling
performance of
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the effusion slots will be improved due to the increased coverage of the
cooling thermal layer
above the hot surface.
[0039] As an exemplary implementation of the disclosed features, one can
consider a
combustor liner with sheet metal walls, in which conventional round effusion
holes or normal
effusion slots are replaced with a pattern of angled, distorted S-shaped
through slots forming
an auxetic structure. Cooling air fed through the slots removes the heat from
the structure
and produces an even distribution of cooling air over the surface. These
angled slots, which
have an increased internal surface area, enhance film cooling performance and
improve
mechanical response. Moreover, angled and distorted NPR slots are capable of
sustaining
higher flame temperatures, and help impart to the sheet a much longer life
compared to the
conventional sheet with normal effusion voids.
[0040] FIG. 6A-6C are finite element (FE) models illustrating radial
displacement under axial
tension of a cylindrical structure with normal S-shaped through slots. By way
of comparison,
FIGS. 7A-7C are finite element (FE) models illustrating radial displacement
under axial
tension of a cylindrical auxetic structure with distorted NPR S-shaped through
slots. The
longitudinal axes of the cylinders are horizontal in the illustrated examples,
as are the
directions of the tensile forces applied to these cylinders. As indicated
above, the void
configuration of FIGS. 6A-6C consists of S-shaped through slots that are
normal to the
thickness of the structure (i.e., an inclination angle a = 0 degrees)
resulting in a positive
Poisson's Ratio of PR = 0.27. Contrastingly, the void configuration of FIGS.
7A-7C consists
of distorted S-shaped NPR slots that are oblique to the thickness of the
structure (i.e., an
inclination angle a = 75 degrees) resulting in a negative Poisson's Ratio of
PR = -0.0001.
Further angling of the slots will further decrease the Poisson's Ratio value.
Blue regions 601,
701 indicate NPR-type behavior, whereas red regions 703 indicate non-NPR-type
behavior.
In FIG. 6A, there is no projection vector as the voids are cut at a zero-
degree angle. FIG. 6B
is a close-up of one of the horizontal S-shaped slots while FIG. 6C is a close-
up of one of the
vertical S-shaped slots. In FIG. 7A, the projection vector of the slots is
parallel to the
direction of tensile loading.
[0041] Aspects of this disclosure are also directed to methods of
manufacturing and methods
of using auxetic structures. By way of example, a method is presented for
manufacturing an
auxetic structure, such as the auxetic structures described above with respect
to FIGS. 3-5.
The method includes, as an inclusive yet non-exclusive set of acts: providing
an elastically
rigid body, such as the elastically rigid body 310 of FIGS. 3A and 3B, with
opposing top and
bottom surfaces; adding to the elastically rigid body a first plurality of
apertures, such as the
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elongated S-shaped slots 312 of FIGS. 3A and 3B, extending through the
elastically rigid
body from the top surface to the bottom surface; and, adding to the
elastically rigid body a
second plurality of apertures, such as the elongated S-shaped slots 318 of
FIGS. 3A and 3B,
extending through the elastically rigid body from the top surface to the
bottom surface. The
first and second pluralities of apertures are arranged in rows and columns.
The apertures of
the first and/or second plurality have distorted shapes projected through the
elastically rigid
body at oblique angles. The first and second pluralities of apertures are
cooperatively
configured to provide a desired stress performance while exhibiting a negative
Poisson's
Ratio (NPR) behavior under macroscopic planar loading conditions. By way of
example, the
elongated apertures are engineered with a predefined porosity, a predetermined
pattern,
and/or a predetermined aspect ratio to achieve the desired NPR behavior.
[0042] In some embodiments, the method includes at least those steps
enumerated above and
illustrated in the drawings. It is also within the scope and spirit of the
present invention to
omit steps, include additional steps, and/or modify the order presented above.
It should be
further noted that the foregoing method can be representative of a single
sequence for
designing and fabricating an auxetic structure. However, it is expected that
the method will
be practiced in a systematic and repetitive manner.
[0043] The present invention is not limited to the precise construction and
compositions
disclosed herein. Rather, any and all modifications, changes, combinations,
permutations and
variations apparent from the foregoing descriptions are within the scope and
spirit of the
invention as defined in the appended claims. Moreover, the present concepts
expressly
include any and all combinations and subcombinations of the preceding elements
and aspects.
