NUWC-NPT Reprint Report 11,774
`
`5 November 2006
`
`Air-Inflated Fabric Structures
`
`Paul V. Cavallaro
`NUWC Division Newport
`
`Ali M. Sadegh
`The City College of New York
`
`NEWPORT
`
`Naval Undersea Warfare Center Division
`Newport, Rhode Island
`
`Approved for public release; distribution is unlimited.
`
`Reprint of a chapter in Marks' Standard Handbook for
`Mechanical Engineers, Eleventh Edition, McGraw-Hill,
`New York, 2006.
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`Bestway Exhibit 1018-0001
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`TABLE OF CONTENTS
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`Page
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`L IST O F IL L U ST RA T IO N S .......................................................................................................
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`11i
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`IN T R O D U C T IO N ...........................................................................................................................
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`D E S C R IP T IO N ................................................................................................................................
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`FIBER MATERIALS AND YARN CONSTRUCTIONS ........................................................
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`EFFECTS OF FABRIC CONSTRUCTION ON STRUCTURAL BEHAVIOR ........................
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`O P E RA T IO N ...................................................................................................................................
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`INFLATION AND PRESSURE RELIEF VALVES .................................................................
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`CONTINUOUS MANUFACTURING AND SEAMLESS FABRICS ......................................
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`IMPROVED DAMAGE TOLERANCE METHODS ...............................................................
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`R IG ID IF IC A T IO N ..........................................................................................................................
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`A IR B E A M S ....................................................................................................................................
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`D R O P-ST IT C H ED FA B RIC S ..................................................................................................
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`EFFECTS OF AIR COMPRESSIBILITY ON STRUCTURAL STIFFNESS .........................
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`EXPERIMENTS ON PLAIN-WOVEN FABRICS ..................................................................
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`A STRAIN ENERGY-BASED DEFLECTION SOLUTION FOR BENDING OF
`AIR BEAMS WITH SHEAR DEFORMATIONS ...........................................................
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`ANALYTICAL & NUMERICAL MODELS ..........................................................................
`U nit C ell N um erical M odels .................................................................................................
`Exam ple of a U nit C ell M odel ..........................................................................................
`Structural A ir B eam M odels ............................................................................................
`C onclud in g R em ark s ..................................................................................................................
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`R E F E R E N C E S ..............................................................................................................................
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`LIST OF ILLUSTRATIONS
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`Figure
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`I Various fabric architectures used in air-inflated fabric structures .............................. 2
`2 Yarn tensile testing using Instron® textile grips ........................................................
`4
`Examples of Pierce's geometric model for plain-woven fabrics
`3
`w ith bi-directional and uni-directional crim p ........................................................
`R ip-stop fabric architectu re ........................................................................................
`4
`5 Yarn tensions in a plain-woven pressurized fabric cylinder and definition of
`yam density ratio ................................................................................................
`Idealized distribution of warp yarn forces due to bending of a plain-woven
`fab ric air b eam ...................................................................................................
`Combined pressure and bending induced forces in warp yarns at various distances
`along a plain-woven air beam based on a simple stress balance analysis ........... 12
`Superposition of pressure and bending induced yarn forces in plain-woven air beam
`a triaxial braided air beam and a dual axial strap-reinforced braided air beam ...... 12
`4-Point flexure test on a 6 inch diameter plain-woven air beam constructed of
`3,000-denier, 2:1 Y D R V ectran fabric .................................................................
`Experimental load vs. deflection plot for an uncoated 6-inch diameter air beam
`constructed of 3,000-denier non-twisted Vectran yarns in a plain-woven 2:1
`Yarn Density Ratio fabric using a 37-inch span between load points and an
`85-inch span betw een support points ...................................................................
`Plot of total load vs mid-span deflection for a 2-inch diameter plain-woven air
`beam constructed of 1,500-denier, 2:1 YDR Vectran fabric ...............................
`Comparison of 2-inch diameter Vectran and PEN plain-woven air beams
`subjected to 4-point bending tests at various load point displacement rates ......
`15
`Section view of an example drop-stitch construction for air-inflated fabrics ........... 16
`Stages of axial stiffness for woven fabric subjected to tension .................................
`17
`Picture frame test fixture for pure shear loading of fabrics ........................................
`18
`Stages of shear stiffness for pure shear loading of a 2:1 Yarn Density Ratio
`w oven fabric ................................................................................................
`Combined biaxial tension and in-plane shear test fixture. (U.S.
`Patent N o. 6,860,156) ........................................................................................
`. . 19
`4-Point bending arrangement for shear deformable beam deflection equation ......
`20
`Treatment of yam kinematics in unit cell models ......................................................
`23
`Example unit cell model and loading procedure ......................................................
`23
`Example of an air beam global finite element model subjected to 4-point bending ...... 25
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`AIR-INFLATED FABRIC STRUCTURES: A CHAPTER FOR MARKS' STANDARD
`HANDBOOK FOR MECHANICAL ENGINEERS
`
`INTRODUCTION
`
`Air-inflated fabric structures fall within the category of tensioned structures and provide
`unique advantages in their use over traditional structures. These advantages include light weight
`designs, rapid and self-erecting deployment, enhanced mobility, large deployed-to-packaged
`volume ratios, fail-safe collapse, and possible rigidification.
`
`Most of the research and development pursued in air-inflated structures can be traced to
`space, military, commercial, marine engineering and recreational applications. Examples include
`air ships, weather balloons, inflatable antennas and radomes, temporary shelters, pneumatic
`muscles and actuators, inflatable boats, temporary bridging, and energy absorbers such as
`automotive air bags. However, the advent of today's high performance fibers combined with
`continuous textile manufacturing processes has produced an emerging interest in air-inflated
`structures. Air-inflated structures can be designed as viable alternatives
`to conventional
`structures.
`
`Because these structures combine both the textile and structural engineering disciplines,
`the structural designer should become familiar with the terminology used in textile materials and
`their manufacturing processes. A glossary is provided in reference [1].
`
`DESCRIPTION
`
`Air-inflated fabric structures are constructed of lightweight fabric skins that enclose a
`volume of pressurized air. The fabric is typically formed in a variety of textile architectures
`including those shown in figure (1). Each architecture has its own design, manufacturing, tooling
`and cost implications. Structurally, these architectures will behave differently when subjected to
`loads.
`
`The plain-weave architecture provides orthogonal yarn placement resulting in extensional
`stiffness along the two yarn axes; however, it lacks shear stiffness for off-axis loads. While the
`braided architecture provides the fabric with shear stiffness due to the non-orthogonality of the
`yarns, it lacks extensional stiffness. The angle between the braid axis and the yarns, 0, is referred
`to as the braid angle or bias angle. Both the triaxial braid and axial strap-reinforced braid
`architectures behave similarly
`in
`that they afford
`the fabric with extensional and shear
`stiffnesses.
`
`The air pressure develops a biaxial pre-tensioning stress throughout the fabric. This pre-
`tensioning stress enables the structure to generate its intended shape, provides stiffness to resist
`deflections and affords stability against collapse from external loads. Fabric materials can often
`be idealized as tension-only materials for design purposes, that is, their in-plane compressive
`moduli and bending moduli are considered negligible.
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`Fy
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`FxF
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`Weave
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`Braid
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`Triaxial Braid
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`Strap-Reinforced Braid
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`Figure 1. Various fabric architectures used in air-inflated fabric structures.
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`Stiffness of the structure is primarily a function of the inflation pressure. As the inflation
`pressure increases, the pre-tensioning stresses throughout the fabric increase and, in turn, stiffen
`the structure. Once external loads are applied, stresses from these loads superimpose with the
`pre-tensioning stresses in the fabric. As a result, a complete redistribution of stress occurs. This
`stress redistribution balances the loads and maintains the structure in a state of static equilibrium.
`Depending upon the type of air-inflated fabric structure (i.e.; beam, arch, etc.) and applied loads
`(i.e.; tension, compression, shear, bending, torsion, etc.), the redistribution of stresses can either
`increase or decrease the net tension stresses in the fabric skin. However, stability of the structure
`is only ensured when no regions of the fabric experience a net loss in tensile stress. Otherwise, if
`the stresses from applied loads begin to relax the pre-tensioning stress (i.e.; the tension
`approaches zero), the onset of wrinkling is said to have occurred within the structure. Wrinkling
`decreases the structure's load carrying capability and upon further loading, eventual buckling or
`collapse will result.
`
`There are two significant and unique characteristics that air-inflated fabric structures
`provide over conventional structures. First, upon an overload condition, a collapse of an air-
`inflated structure does not necessarily damage the fabric membrane. When the overload
`condition is removed, the air-inflated fabric structure simply restores itself to its design load
`configuration. Second, since wrinkling can be visually detected,
`it can serve as a warning
`indicator prior to collapse.
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`FIBER MATERIALS AND YARN CONSTRUCTIONS
`
`Proper selection of fiber materials and yam constructions are important factors that must
`be considered in the design of air-inflated fabric structures. Both should be optimized together to
`achieve the desired performance characteristics at the fabric and structural levels.
`
`Many of today's air-inflated fabric structures use yams constructed of high performance
`continuous fibers such as Vectran® (thermoplastic liquid crystal polymer) PEN
`(polyethylene
`naphthalate), DSP® (dimensionally stable polyester), and others. These fibers provide improved
`structural performance (high strength, low elongation, fatigue, flex-fold, cyclic loadings, creep,
`etc.) and enhanced environmental resistance (ultraviolet rays, heat, humidity, moisture, abrasion,
`chemicals, etc). Other fibers used in air-inflated fabric structures include Kevlar®, Dacron®,
`nylon, Spectra® and polyester. Hearle[21 provides additional information on fiber materials and
`their mechanical properties.
`
`Yams are constructed from fibers that may be aligned unidirectionally or arranged in a
`number of twisted bundles. Twist is used to improve the handling susceptibility of the yarns by
`grouping the fibers together especially during textile processing. Twist, which is measured in
`turns per unit yam length, affects the yam tensile properties. For discontinuous or staple fiber
`yams, twist can increase the yarn breaking strength because the internal forces at the ends of a
`fiber can transfer to neighboring fibers via inter-fiber shear forces. However, twist in continuous
`fiber yarns can reduce the yarn breaking strength as observed by Hearle 31. Therefore, a minimal
`twist is recommended for providing adequate handling protection to continuous fiber yams.
`
`Hearle[31 experimentally investigated the effects of twist on the tensile behavior of several
`continuous fiber yams. His results showed that yam tenacity (defined as tensile strength
`measured in grams-force per denier or grams-force per tex) decreased with increasing twist for 3
`prescribed yam tensions used during twist formation.
`In general, the yam modulus decreased
`with increasing twist, yarn elongation at break increased with increasing twist, and yam
`elongation decreased with increasing yam tension. A difference in the load-extension behavior
`of twisted and non-twisted yams is that a twisted yarn when subjected to tension will undergo
`compaction of its cross section through migration of its fibers and develop greater inter-fiber
`frictional forces than a non-twisted yam. Like fabrics, the structural performance of yams can be
`tailored by changes in their architecture and processing.
`
`Once the yarns are processed into the fabric (i.e.; by weaving, braiding, etc.), it is
`recommended that tensile tests be performed on sample yarns removed from the fabric. This will
`allow the "as-processed" yam properties to be compared to the design requirements.
`For
`example, the "as-woven" tensile properties of continuous-fiber, non-twisted yarns removed from
`a plain-woven fabric air beam were measured 4] using an Instron machine configured with textile
`grips as shown in figure (2). The cross sectional areas of the yams were computed based on
`fiber diameter and quantity. The tests revealed that the average breaking stress of the weft yarns
`was nearly 20% less than that of the warp yams. The reduction in breaking stress of the weft
`yams was due to fiber damage caused by the use of higher tensions in these yarns during
`weaving.
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`Figure 2. Yarn tensile testing using Instron® textile grips.
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`EFFECTS OF FABRIC CONSTRUCTION ON STRUCTURAL BEHAVIOR
`
`Fabric materials are constructed from yams that cross over and under each other in a
`repetitive, undulating pattern. The undulations shown in figure (3) are referred to as crimp,
`which is based on Pierce's geometric fabric modelI5 .
`
`02-
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`h12
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`VVeft Yarns
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`D
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`-
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`d
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`at
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`h
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`Bi-Directional Crimp
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`PWarp Yarns
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`Uni-Directional Crimp
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`Figure 3. Examples of Pierce's geometric model for plain-woven fabrics
`with bi-directional and uni-directional crimp.
`
`Pierce's geometric model relates these parameters as they are coupled among yarn
`families. The crimp height, h, is related to the crimp angle, a, and yam length, L, as measured
`between yarns, and the sum of yarn diameters at the cross over points by the following equations
`described by Grosberg [3]:
`
`p = (L-Da)cosa+Dsina
`h =(L - Da)sin a + D(L - cos a)
`D = hi + h,.
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`4
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`(1)
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`These equations were based on idealized geometry and assumptions such as restricting the yams
`to circular cross sections and no consideration of force or stiffness effects.
`
`Plain-woven and braided fabrics behave differently under load because their yam
`families are aligned at different angles. Plain-woven fabrics utilize a nearly orthogonal yarn
`placement of warp and weft (or fill) yams. By general textile definitions, warp yarns are
`identified as those yams running parallel to the selvage and are virtually unlimited in their
`length. Weft yarns are at right angles to the selvage and are limited in length by the width of the
`weaving equipment. On the other hand, braided fabrics have a +0/-0 yam placement, where 0 is
`commonly referred to as the bias angle, with respect to the braid axis.
`
`The biaxial stress-strain behavior of plain-woven fabrics is initially dominated by crimp
`interchange rather than yam elasticity. Because the factors of safety used in air-inflated fabric
`structures are typically within the range of 4-6, the operating stresses are designed to be low with
`respect to fabric strength. Therefore, the structural performance of fabrics must address the
`influences of crimp interchange. The relative yarn motions (slip and rotation) affect the stiffness
`properties. The crimp ratio, which is denoted as C, is defined as the waviness of the yarns and is
`obtained by measuring the length of a yarn in its fabric state, Liobric , and the length of that same
`yam after it has been extracted from the fabric, L .
`and straightened out according to equation
`(2).
`
`C
`
`L-
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`-Llabric
`L ab,.ic
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`The following equation described by Grosberg relates the crimp height to C.
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`h
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`4ý
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`24
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`I
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`C2.
`
`(2)
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`(3)
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`Consider a plain-woven fabric subject to a tensile load along the direction of one yam
`family. The loaded yarns will attempt to straighten, decrease their crimp heights and elongate
`their effective lengths. However, the yams of the crossing family are forced to increase their
`crimp heights resulting in contractions of their effective lengths. The effect associated with
`changes in crimp is referred to as crimp interchange and is similar to the Poisson's effect
`exhibited in metals. Crimp interchange is a coupling effect exhibited between yam families.
`When a fabric is loaded in tension, the crimp contents become mutually altered as the yams
`attempt to straighten. In tests of plain-woven fabrics along the direction of a given yam family,
`crimp interchange can be easily observed by reducing the width of the specimen. Crimp
`interchange is a source of nonlinear load-extension behavior for fabrics.
`
`Backerr3I describes a limiting phenomenon to crimp interchange. As the biaxial tensile
`loads continually increase for a given loading ratio, a configuration results in which yarn
`kinematics (i.e.; slip at the cross over points) cease and the spacing between yarns converge to
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`minimum values. This configuration is referred to as the extensional jamming point, which can
`prevent a family of yams from straightening and thereby not achieve its full strength. Crimp
`interchange depends upon the ratio of initial crimp between yam axes and the ratio of stress
`between yam axes rather than the levels of stress. Crimp interchange introduces significant
`nonlinear effects in the mechanical response of the fabric.
`
`Now consider the plain-woven fabric subjected to shearing by applying a uniaxial load at
`±45 degrees to either yarn family. The yam families will rotate at the crossover points with
`respect to each other and become increasingly skewed as the angle between the yams changes.
`The change in angle is referred to as the shear angle. At larger shear angles, the available space
`between yam families decreases and rotational jamming (locking) of the yam families occur.
`This phenomenon is known as shear-jamming and the angle at which the yam families become
`jammed is referred to as the shear-jamming angle. The shear-jamming angle decreases with
`increasing yarn density ratio and can be estimated from Pierce's geometric fabric model or
`obtained experimentally with various trellising or biaxial test fixtures. Continued loading
`beyond the onset of shear-jamming will produce shear wrinkles leading to localized out-of-plane
`deformations.
`
`It is important to determine the extension- and shear-jamming points for both fabric
`manufacturing and structural stiffness concerns. In general, jamming is related to the maximum
`number of weft yams that can be woven into a fabric for a given warp yarn size and spacing.
`
`OPERATION
`
`Today's air-inflated fabric structures can be operated at various pressure levels depending
`upon fabric architecture, service loads and ambient temperatures. Woven structures are
`generally designed to operate at pressures up to 20 psi while triaxial braided and axial strap-
`reinforced braided structures are generally capable of higher inflation pressures. Blowers, which
`may be used for inflation pressures up
`to 3 psi, provide a high volumetric air flow rate.
`However, air compressor systems will be required for higher inflation pressures.
`Air
`compressors are available
`in single and dual stage configurations. The single stage air
`compressor delivers a high-pressure capability but at a low volumetric air flow rate. The
`volumetric flow rate is measured
`in standard cubic feet per minute (scfm). Dual stage air
`compressors are designed to provide an initial high volumetric air flow rate at low pressures in
`the first stage and can be followed by a low volumetric air flow rate at high pressure. When a
`dual stage air compressor is used, the first stage is most beneficial to erecting the fabric structure.
`At this time, no appreciable resistance to the design loads is available. However, the second
`stage mode of the compressor is used to fully inflate the fabric structure to its proper operating
`pressure so that the design loads can be supported. Because the dual stage compressor can
`achieve the desired inflation pressure much more rapidly than the single stage compressor, it is
`more appropriate for those applications in which the need for rapid deployment justifies the
`additional cost.
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`INFLATION AND PRESSURE RELIEF VALVES
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`Valves designed for use in air-inflated fabric structures must consider several criteria
`including locations, orifice size, pressure relief controls and potential strength degradation in the
`surrounding fabric regions.
`Ideally, valves should be positioned in structural elements that
`interface with the fabric and bladder such as metal clamps, discs or end plates at the end
`termination zones of the structure. This avoids the need for cutting additional penetration holes
`through the fabric or repositioning the yams to accommodate holes for valve placement, thus
`preventing stress concentrations. When fibers must be removed to accommodate insertion of
`valves, fabric reinforcement layers should be bonded and stitched to the main fabric in the
`surrounding region. The valves should be readily accessible for user access but should not
`jeopardize the integrity of the fabric when the structure is subjected to handling events (such as
`drops, impacts, etc.). Valve locations should be further optimized to mitigate the effects of
`interference with other objects when the structure is deployed or stowed.
`
`A variety of pneumatic valve designs
`threaded valves, quick connect-
`including
`disconnect valves, check valves (one-way, two-way), pressure relief valves, etc. are readily
`available. The use of pressure relief valves is recommended to avoid accidental overpressures
`and pressure increases due to changes in ambient temperatures. Valves can also be configured to
`manifold inflation lines in air inflated structures containing multiple pressure chambers. This
`also provides capabilities for self-erecting and controlled deployments by sequencing
`the
`inflation timing of multiple chambers. Sizing of the valve orifices should be matched to provide
`the optimal inflation and deflation times for the air volumes and operating pressures required by
`the structure.
`
`CONTINUOUS MANUFACTURING AND SEAMLESS FABRICS
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`Prior to continuous circular weaving and braiding processes in use today, air-inflated
`fabric structures were constructed using adhesively bonded, piece-cut manufacturing methods.
`These methods were limited to relatively low pressures because of fabric failures and air leakage
`through the seams. Continuous weaving and braiding processes can eliminate or minimize the
`number of seams resulting in improved reliability, increased pressure capacities and greater
`structural
`load carrying capability. However, when seams can not be avoided,
`the seam
`construction should be designed in such a way that failure of the surrounding fabric occurs rather
`than the seam. For the safe and reliable use of air-inflated fabric structures, sufficient factors of
`safety against burst and seam failures must be provided. To guard against burst, for example, a
`minimum factor of safety of 4-6 is used on yam strength for each yam family.
`
`Like traditional composite materials, fabrics can be tailored to meet specific structural
`performance requirements. Fiber placement can be optimized for air-inflated fabric structures by
`varying the denier of the yams (defined as the mass in grams of a 9,000 meter length yam) and
`yarn counts along the each direction. For instance, consider a pressurized fabric cylinder. The
`ratio of hoop stress per unit length to axial stress per unit circumference is 2:1. One can ensure
`equal factors of safety against yam burst in the weft (hoop) and warp (longitudinal) yams by
`weaving twice as many weft yams per unit length of air beam than the number of warp yams per
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`unit circumference. Alternatively, the same can be accomplished by doubling the denier of the
`weft yams in comparison to the denier of the warp yams.
`
`IMPROVED DAMAGE TOLERANCE METHODS
`
`Assorted methods are used to enhance the reliability of air-inflated fabric structures
`against various damage mechanisms. Resistance to punctures, impacts, tears and abrasion can be
`improved by using high-density weaves, rip-stop fabrics and coatings. High-density weaves are
`less susceptible to penetrations and provide greater coverage protection for bladders. Rip-stop
`fabrics have periodic inclusions of high tenacity yams woven in a cellular arrangement used to
`prevent fractures of the basic yams from propagating across cells as shown in figure (4). (The
`breaking strength of a yam is referred to as tenacity which is defined in units of grams-force per
`denier. Denier is a mass per unit length measure expressed as the mass in grams of a 9,000
`meter long yam.) The high tenacity yams contain fractures of the basic yarns and prevent
`fractures from propagating across cells.
`
`High
`Tenacity
`Yarns
`
`Basic
`Yarns Z
`
`,=,
`
`Fractured
`Yarns
`
`Figure 4. Rip-stop fabric architecture.
`
`Additionally, coatings protect the fabric against environmental exposure to ultraviolet
`rays, moisture, fire, chemicals, etc. Coating such as urethane, PVC (polyvinyl chloride),
`neoprene, EPDM (ethylene propylene diene monomer) are commonly used. Additives such as
`Hypalon further enhance a coating's resistance to ultraviolet light and abrasion. Coatings can be
`applied in two stages. First, coating the yams prior to forming the fabric by a liquid bath
`immersion provides the best treatment to the fibers. Second, coatings can be applied by
`spraying, painting or laminating directly to the fabric after forming. This stage coats the yams
`and bridges the gaps formed between adjacent yams. The maximum protection is achieved when
`both stages are utilized. While protective coatings have been shown to increase the stiffness of
`the fabric by restricting relative yam motions, they remain flexible enough to not adversely
`impact the stowing and packaging operations of the structure. Additional information on coating
`materials and processes is provided by Fung~6 .
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`8
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`RIGIDIFICATION
`
`Air-inflated fabric structures can be rigidified by coating the fabric with resins such as
`thermoplastics, thermosets, shape memory polymers, etc. Prior to inflation, these particular
`coatings are applied to the fabric and remain initially uncured, thus acting as flexible coatings.
`After the structure is inflated and properly erected, a phase change is triggered in the coating by a
`controlled chemical reaction (curing process) activated by exposure to elevated temperature,
`ultraviolet light, pressure, diffusion, etc. Once the phase change is fully developed, the coatings
`bind the yarns together, stiffen the fabric in tension, compression and shear, and behave similar
`to a matrix material found in traditional fiber-reinforced composites. The air-inflated fabric
`structure is now rigidified and no longer requires the inflation pressure to maintain its shape and
`stiffness. Depending upon the coating used, the transition process may be permanent or
`reversible (except where thermoset plastics are used). Reversible rigidification is especially
`suited for those applications requiring multiple long-term deployments.
`
`The performance of the rigidified fabric structure can be assessed using laminated shell
`theory (LST) as described by Jones 71. Unlike the inflated version of the structure, the elastic and
`shear moduli of the rigidified structure are based on the constituent properties of the fibers and
`cured coating. As such, the elastic and shear moduli can be readily estimated by using LST.
`However,
`the rigidified structure may have different failure modes
`than
`its pressurized
`counterpart. The designer must guard against new failure modes including localized shell
`buckling and compression rather than wrinkling.
`
`Rigidification is of particular interest for space structures because of restrictions on
`payload weights and stowage volumes. Cadogan et al08' 91 have pursued the use of shape memory
`composites for rigidizing deployable space frames.
`
`AIR BEAMS
`
`Fabric air beams are examples of air-inflated structural elements that are capable of
`supporting a variety of loads similar to conventional beams. To date, seamless air beams have
`been constructed using continuous manufacturing methods that have produced diameters ranging
`up to 42 inches. They are constructed of an outer fabric skin that contains an internally sealed
`film or bladder made of an impermeable elastomer-like material. The bladder contains the air,
`prevents leakage and transfers the pressure to the fabric. The air beam has a cylindrical cross
`section and its length can be configured to a straight or curved shape such as an arch. The ends
`are closed using a variety of end termination methods consisting of bonding, stitching,
`mechanical clamps, etc. depending upon the inflation pressure and loading requirements.
`Clamping methods are available to permit disassembly, repair and replacement of the bladder
`and fabric layers.
`
`Once an air beam is sufficiently pressurized, the fabric becomes pre-tensioned and
`provides the air beam with a plurality of stiffnesses including axial, bending, shear, and torsion.
`Upon inflation, the ratio of hoop (cylindrical) stress per unit length of beam to the longitudinal
`stress per unit circumference is 2:1 as shown in figure (5).
`
`9
`
`Bestway Exhibit 1018-0012
`PGR2017-00003
`
`

`

`weft
`
`Weft yarn tension per unit length of cylinder = pr
`Warp yarn tension per unit circumference = pr/2
`
`Yarn density ratio (YDR) =
`
`# weft yarns per unit length of cylinder
`
`# warp yarns per unit circumference
`
`Figure 5. Yarn tensions in a plain-woven pressurized fabric cylinder and
`definition of yarn density ratio.
`
`In the context of plain-woven air beams, the warp yams are aligned parallel to the
`longitudinal axis of the air beam and resist axial and bending loads. The weft yams spiral
`through the weave and are located at nearly 900 to the warp axis, thus lying along the hoop
`direction of the air beam. Weft yarns provide stability against collapse by maintaining the
`circular cross section of the air beam.
`
`For braided air beams, the braid axis is aligned with the longitudinal axis of the air beam.
`If the ends of a braided air beam are unconstrained from moving in the longitudinal direction, the
`fibers will exhibit a scissoring effect causing the length of the beam to expand or shorten with
`pressure depending upon the selection of 0. Eventually, the braided yams will achieve a
`maximum rotation and the fabric will become fully jarmned. This phenomenon can be easily
`demonstrated with
`the well-known Chinese finger trap
`toy. Unlike plain-woven fabric
`structures, the bias angle of braided fabric structures can be controlled to allow expansion or
`contraction of the structure when inflated. For an uncon