TECHNICAL FIELDThe disclosure relates to polymeric composites. More particularly, the disclosure relates to reinforced polymeric compositions.
BACKGROUNDIn many applications requiring structural members such as studs, beams, decking, framing members, trim pieces, and railings, polymeric materials have replaced wood. Window frames and shutters are made of hollow vinyl profiles. Interior molding and, more recently, screen doors, are made of foamed polyvinyl chloride.
Plastics have advantages over wood, including lower cost and lower maintenance, but often do not have the inherent strength of wood without incorporating other materials, such as wood or metal inserts, as secondary reinforcements to increase stiffness. Adding these types of secondary reinforcements increases the cost of material and labor and introduces complexity because of the additional type of material required.
Structural composites are known. For example, U.S. Pat. No. 4,910,067, discloses a structural composite material comprising a foam core with a thermoplastic layer on one side and a layer of fibrous material on the other. The foam is formed from a liquid resin which cures in contact with the fibrous material, impregnating and bonding it into a fiber-reinforced structure. A process for manufacturing the composite is also taught in this reference.
U.S. Pat. No. 5,700,555 teaches a composite article comprising a first zone made entirely of plastic and a second zone made of plastic plus 10% to 55% natural fiber, both of which are formed by co-extrusion. The fiber-containing zone includes embossing to resemble wood grain and is sufficiently porous to accept paint or stain to simulate the appearance of natural wood.
U.S. Pat. No. 5,738,935 and U.S. Pat. No. 5,858,522, are related to each other and to U.S. Pat. No. 5,700,555, described above, and disclose a process for the preparation of a natural fiber and thermoplastic composite and the resulting products therefrom. The process includes the steps of mixing the synthetic fiber and the thermoplastic in a blender with a porosity aid and an interfacial agent to form a mixture; adding the mixture to a heated extruder; extruding the mixture as a composite; and shaping the composite in a vacuum calibration device to a desired profile. The process further includes the step of co-extruding a second thermoplastic onto the natural fiber/thermoplastic composite for some applications (e.g., windows, doors and siding).
EP 0599404 discloses a process for preparing thermoplastic composites reinforced with continuous fibers. The process includes the steps of: (a) unwinding a continuous filament, constituted by a bundle of fibers, from a bobbin; (b) opening the continuous filament, essentially by disassembling it into its individual continuous fibers; (c) dipping and driving the open filament through a stationary bed constituted by a thermoplastic polymer powder contained in a tank submitted to continuous vibration; and (d) reassembling the filament and arranging around it a sheltering flexible sheath made of a thermoplastic polymer.
EP 0653290, discloses a continuous process for producing a molded thermoplastic fiber-reinforced article having a high resin concentration in at least one surface by coating the surface of that heated fiber mat core with a melted first thermoplastic resin, and then passing the fiber mat core into an extrusion zone wherein a melted second thermoplastic resin is extruded onto it. Then the fiber mat core and thermoplastic resin are molded into a finished article. The continuous process disclosed provides molded finished articles such as roof tile, automobile exterior panels, house siding, etc.
U.S. Pat. No. 5,565,056 discloses a glass fiber-reinforced building panel made by extruding molten first and second webs of polymer compounds through spaced die openings, positioning a mat of randomly oriented short glass fibers between the first and second webs, pressing the webs and mat together, and cooling the resulting building panel.
EP 0747213 discloses a panel comprising a first layer of polypropylene filled with sawdust, wood flour, or wood shavings and at least one additional layer consisting at least partially of fibrous thermoplastic material that are bonded to one face of the first layer by compression and simultaneous, partial fusion. This additional layer retains the fibrous pattern and structure.
U.S. Pat. No. 6,607,798 discloses a fiber-reinforced, hollow-center, composite hollow structure in which hollow center cores made of thermoplastic resin are joined into one body by intermediate layers containing reinforcing long fibers bonded to each other with a thermosetting resin. The structure is then covered with an outer layer of thermoplastic resin.
U.S. Pat. No. 9,079,380 discloses co-extrusion of poly vinyl chloride (PVC) with a composite material, forming a continuous strip which may then be cut into convenient lengths. The PVC forms mounting flanges and ventilation standoffs on the back surface only, with all parts on the front being formed of a composite of cellulose fiber and a thermoplastic resin.
A polymeric composition that has structural levels of stiffness and low manufacturing cost would be advantageous particularly if it conserved natural resources by recycling previously-used materials.
SUMMARYDisclosed herein is a structural composite made primarily of polymeric material but which incorporates at least one reinforcing, stiffening layer in a continuous manufacturing process which results in a well-bonded, non-homogeneous composite. Thus, the appearance of the resulting composite and its durability preserve the advantages of polymeric materials and provide the strength of a reinforced composite for structural applications, and at low cost of manufacture.
The present method may be used to form a polymeric profile that has been engineered by designing the location and composition of one or more stiffening layers inside or on the profile so the composite has the requisite stiffness for its particular application. In addition, the method and materials are such that the cost of the manufacture of the composite may be low because the stiffening layer may be made of readily available recycled materials, including short fibers, and not compromise on strength or adversely affect the exterior appearance of the structural composite.
The adhesive stiffening layer may be further modified by shaping it into a profile that has three dimensions or by modifying its surface with holes or punches to promote composite action with a polymer layer. The polymer layer is then extruded over the stiffening layer to create the finished product. The polymer is chemically compatible with the carrier; that is, chemical bonds form between the polymer and the carrier that resist delamination.
The binding agent is also selected to bind chemically with the carrier, mechanically and also preferably chemically with the mat, and chemically with the extruded polymer profile. The binding of the layers adds strength and avoids delamination. An adhesive may be applied to the carrier to make the filler adhere better to the carrier.
A feature of the disclosure is that the pressing and heating steps are done using at least one pair of heated jacket rollers, and when a second pair of heated jacket rollers is used, the subsequent pair of rollers may be spaced closer together than the first pair to increase the flow of liquefied binder throughout the filler of the mat. The second pair of rollers may also be rotated faster than the first to stretch the mat before it cools. Stretching the mat helps to align the fibers and may result in a stronger stiffening layer.
Another feature of the disclosure is the use of recycled chopped carbon fibers or carbon fiber ribbon; chopped fiberglass fibers; anhydrite fibers derived from waste gypsum; fibers from textile waste or recycled cloth products including cotton, silk and synthetics; cellulose fibers from scrap wood, paper, cardboard or bamboo; metallic wire or other metal fibers; or any combination of the foregoing, as well as normally waste mineral components such as fly ash, zeolites and pozzolans. The fibers do not have to be long but can be short, such as shorter than the width of the mat.
Still another feature of the disclosure is that the carrier, the binder if used and the polymer extruded over them may also be made of recycled materials such as polyethylene terephthalate or high-density polyethylene for the carrier and binder and polyvinyl chloride for the extruded polymer. These materials are chemically compatible in that they tend to form chemical bonds between them.
Another feature of the disclosure is that the stiffening layer may comprise a plurality of types of fibers, at least one carrier and more than one filler layer.
Still another feature of the disclosure is that the fibers may be dispersed by shaking them onto the carrier as the carrier is rolling onto a conveyor, the resulting random orientation providing roughly equal strength across the carrier and parallel to its length.
Still another feature of the disclosure is that the polymer may be extruded over one or more stiffening layers as they are pulled through a cross head die in accordance with an engineered configuration for the product being made.
Yet another feature of the disclosure is that the stiffening layers may either comprise one or more flat layers suitably spaced apart, formed into one or more three-dimensional profiles within the extruded polymeric matrix, or a combination of these, as may be convenient to manufacture while providing structural levels of shear and flexural strength.
These and other features and their advantages will be apparent to those skilled in the art of polymeric extrusions from a careful reading of the detailed description accompanied by the drawing.
BRIEF DESCRIPTION OF THE DRAWINGSIn the figures,
FIG. 1 is a schematic drawing of an apparatus for making the present structural composite;
FIG. 2 is a flow diagram of the method for making the present structural composite;
FIG. 3A-3H illustrate examples of reinforcement configurations and positions for enhanced stiffness and flexural strength;
FIG. 4 is an example of a structural composite product, namely, a door jamb, made according to the present method and apparatus; and,
FIG. 5 shows a simple method for analyzing the distribution of reinforcement within a structural composite product, using the door jamb ofFIG. 4 as an example, yielding a conservative prediction of its stiffness and flexural strength.
DETAILED DESCRIPTIONThe structural composite described herein is a non-homogeneous composition of matter having both compressive strength and stiffness which enables it to be used as a substitute for wood in a wide variety of applications, including those where building code requirements apply. In addition, the present structural composite can substitute for other materials with higher strength modulus than wood, such as aluminum. The term non-homogeneous means that at least some of the constituents are concentrated within the structural composite rather than being homogeneously dispersed. The present composition may be engineered, meaning that its exterior shape and the choice of its components and their locations and shapes may be selected to meet the strength and stiffness required for specific tasks to which that composition is to be put. As a simple example, the present structural composite may be designed with reinforcement spaced away from the neutral axis, analogous to the flanges of an I-beam, providing increased strength and stiffness in one or both axes perpendicular to the cross-section. Because such a structural composite may be designed for load-bearing, the composition is referred to herein as a structural composite.
Referring now toFIGS. 1 and 2, the present composition has at least one stiffening layer that increases the stiffness of the finished structural composite. A stiffening layer is incorporated into a polymeric extrusion either by extruding the polymer onto the stiffening layer so that the stiffening layer is on one side and the polymer on the other and therefore the stiffening layer is visible from the exterior, or by extruding it so that the polymer partly or wholly surrounds the stiffening layer, in which case the stiffening layer may not be visible from the exterior.
The stiffening layer includes a first carrier10. As used herein the term carrier means a fabric or film that is a continuous sheet of a pliable material, which may, for example, be wound onto a spool or core14 so that it can be rolled out for use as part of a continuous manufacturing process. Carrier10 may be made of high density polyethylene (HDPE) or polyethylene terephthalate (PET), or other materials that chemically or mechanically bind with the selected polymer, such as polyethylene terephthalate glycol-modified (PETG), which has properties useful in the present method, such as a low melting temperature. The density of HDPE in the present composition can range from 0.93 to 0.97 g/cm3or 970 kg/m3.
If a fabric is used as carrier10, the fabric may be woven or non-woven and is capable of serving as a surface on which to deposit other constituents of the stiffening layer, as will be presently described, and to bind mechanically and may also bind chemically with the polymer and a binder.
Filler18 is dispersed onto carrier10.Filler18 may include manmade and natural fibers, organic matter, and minerals. If fibers are used asfiller18, they may be recycled, chopped carbon fibers or carbon fiber ribbon; waste fiberglass fibers; anhydrite fibers derived from waste gypsum; fibers from textile waste or recycled cloth products including cotton, silk and synthetics; cellulose fibers from scrap wood, paper, cardboard or bamboo; metallic wire or other metallic fibers; or any combination of the foregoing. Minerals such as zeolites, pozzolans, and fly ash, which is a waste from coal burning, may also be used as filler, and other substances that alter the characteristics of the stiffening layer, facilitate the manufacturing process, or simply add bulk. The polymer may be polyvinyl chloride.
When fibers are used asfiller18, the fibers may be of any length. Chopped carbon fiber and fiberglass fibers work well and may be more cost-effective for most applications than long fibers, particularly if they are a waste product from other manufacturing operations. Similarly, anhydrite whiskers can be made economically from gypsum, which is a waste product of many industrial processes, are extremely strong, and will bond chemically to polyvinyl chloride (PVC) especially if pretreated with polyvinyl alcohol and glutaraldehyde. A mixture of long and short fibers may also be used asfiller18. In one aspect,filler18 will form a layer that nearly fills first carrier10 from side to side and is as long as carrier10.
The dispersion of the material of thefiller18 may be achieved by any method that produces a distribution of material over much of first carrier10, such as by shaking or spreadingfiller18 onto first carrier10 as first carrier10 is being rolled out. For example, a quantity offiller18 may be placed into ahopper22. Asfiller18 descends to the bottom ofhopper22, aroller26 moves the lowermost filler past ablade30 that controls the amount offiller18 passed forward. The filler then falls onto abrush roller34.Brush roller34 brushesfiller18 onto first carrier10 as first carrier10 moves.
To assist in the establishment of amat38 offiller18 on first carrier10, an adhesive40 may be applied to first carrier10 prior to the dispersion offiller18. Adhesive40 in ahopper42 may be sprayed through a nozzle46 onto carrier10 beforefiller18 is dispersed. Ifmat38 is built up in layers, perhaps using a sequence ofhoppers22, additional adhesive spraying may be done to form the filler layer to a designed depth and uniformity.
The quantity offiller18 that may be used to formmat38 depends on the purpose for the composite product, including its mechanical properties, and the choice of filler or fillers that are available and their characteristics and price. Accordingly, the quantity offiller18 dispersed onto first carrier10 may have a thickness of at least a centimeter.
Abinder50 may be applied tomat38 on first carrier10.Binder50 may be in the form of a liquid or of a powder that, when heated, forms a liquid.Binder50 is dispersed ontomat38 so that it falls into gaps and spaces on the surface ofmat38 that is formed by the depositedfiller18.Binder50 may be applied in any manner that is suitable for its distribution, such as spraying, shaking, dripping, or blowing from ahopper54.Binder50 may be a material selected to be compatible with first carrier10, such as HDPE or PET (PETG or PETE) and may be in the form of a mist, a liquid, a powder, or granules such as ground, recycled PETG.
Asecond carrier58 may be applied on top ofmat38 from asecond core48.Second carrier58 may be made of the same material as first carrier10, such as HDPE or PET (PETG or PETE). First carrier10 andfiller18, and optionally withbinder50 and adhesive40 combine to form astiffening layer62.
Stiffeninglayer62 is passed throughheated jacket rollers60,64, which apply heat and pressure to soften and liquefy first carrier10, binder,50, andsecond carrier58 so that they flow throughoutfiller18 ofmat38.Jacket rollers60,64, may be used to both heat and press, or heating may be done by a separate means first, such as infrared heaters, followed by pressing. More than one set ofjacket rollers60,64, may be used.Jacket rollers60,64, may be spaced apart so thatmat38 with carriers10 is compressed in stages when passing between them.Jacket rollers64 may be spaced closer together thanjacket rollers60 to apply incrementally more pressure in order to infusebinder50 throughoutmat38 sobinder50 penetrates intomat38 and binds with first andsecond carriers10,58.
Optionally, successive sets ofjacket rollers60,64, may rotate at successively faster speeds, thereby stretchingstiffening layer62 while it is still cooling thereby partially aligning the fibers offiller18, especially if they are chopped fibers, in the direction of stretching in a manner analogous to the fibers in wood, thus imparting greater strength to layer62 comparable to that achievable with long fibers.
Binder50 binds tofiller18 and may bind mechanically or chemically to first andsecond carriers10,58, depending on the choice of materials of first andsecond carriers10,58. If first andsecond carriers10,58, is a film of PET (PETG or PETE) or HDPE,binder50 made of this same material will bind with it chemically. If carrier10 is a fabric, the binding may be mechanical as binder penetrates between the threads and fibers of the fabric.
Chemical binding herein means that chemical bonds are formed between the atoms or molecules of two different materials. Mechanical binding, or composite action, is used to mean that a fluid material flows around a solid material and when cooled, captures the solid material into the matrix of the cooled material.
Stiffeninglayer62, as described above, may be made in a batch process or in a continuous extrusion process.
Once first andsecond carriers10,58, andbinder50 has cooled, stiffeninglayer62 moves forward to across-head die66 where one or more polymer layers72,76 are extruded over it to form astructural composite68. Polymer layers72,76 may be polyvinyl chloride extruded with or without a foaming agent.
More than onestiffening layer62 may be included in structural composite68 either by forming a plurality of stiffeninglayers62 or by forming onestiffening layer62 and cutting it into narrower strips. Stiffeninglayer62 may be used as a thin flat layer (as made), or may be deformed if desired to have a third dimension to provide multi-dimensional stiffness. Stiffeninglayer62 may be cut into two or more strips or portions that are preferably spaced apart in pairs or groups to impart greater flexural strength than would be achievable had thesame stiffening layer62 be used in one piece or even if strips cut from stiffeninglayer62 had been placed in closer proximity.
Stiffeninglayer62 may be modified prior to being pulled through cross-head die66 to provide mechanical binding betweenstiffening layer62 and the polymer layers72,76. By forming holes in stiffeninglayer62 or punches, both of which drive portions of stiffeninglayer62 outside of the plane otherwise defined by stiffeninglayer62, polymer may flow into and across the plane defined by stiffeninglayer62 and thereby increase the interlock betweenstiffening layer62 and polymer layers72,76. These modifications may be made by additional rollers, dies, punch presses or cutters through whichstiffening layer62 is passed.
Afterstructural composite68 has been extruded, it is cut into desired lengths by traveling saws, lasers, water jets, or other cutting devices.
A method for making a structural composite is illustrated schematically inFIG. 2. The method includes the step of rolling out first carrier10, which may be made of plastic film or fabric.Filler18 is dispersed onto first carrier10 to form amat38. An adhesive40 may be applied to first carrier10 in order to hold thematerial comprising filler18 in place on first carrier10. Abinder50 may also be dispersed ontomat38.
Oncemat38 is formed, it is subjected to heat to melt first carrier10 andbinder50 if used so that they flow intofiller18. To urge the liquefied first carrier10 andbinder50 to flow intofiller18,mat38 is pressed. These two steps can be done at the same time using pairs ofheated jacket rollers60,64, which both heat andpress mat38. Moreover,heated jacket rollers60,64, can stretchmat38 ifjacket rollers64 are made to rotate slightly faster than precedingjacket rollers60. Stretchingmat38 whilebinder50 is solidifying tends to alignfiller18 to improve stiffness. The incremental speed ofjacket heater rollers64 may be determined by a modest amount of experimentation.
The completedstiffener layer62 may then be formed to have a profile that provides stiffness in more than one direction. The term profile means that the—stiffener layer is bent or formed from a two-dimensional layer to extend in a third dimension as well, such as a U-shape, a W-shape, or L-shape. The completedstiffener layer62 may also be cut into strips or segments that are positioned to improved overall stiffness in different directions. The strips may be spaced apart and away from the neutral axis of the composite structural element before adding the polymer. A cross-head die may be used for extruding the polymer around the strips of thestiffener layer62.
Referring now toFIGS. 3A-3H, there are shown some representative ways by which a stiffening layer or layers may be distributed within a composite product. For simplicity, each structural composite is shown as a simple rectangular cross-section in which a stiffening layer or layers are shown in the polymer. By convention in engineering analysis, external loading is shown by an arrow pointed in a downward direction.
In the example shown inFIG. 3A, astiffening layer80 runs generally parallel to and midway between the top and bottom surfaces of a relatively thin finishedcomposite article84. To increase the stiffness of stiffeninglayer80, it is perforated withholes88 through whichpolymer92 can flow to secure itself to stiffeninglayer80 by composite action, which is the binding effect that occurs when stiffeninglayer80 is incorporated into the matrix ofpolymer92.
In the example shown inFIG. 3B, asingle stiffening layer96 runs generally parallel to and midway between the top and bottom surfaces of a relatively thing finishedcomposite article100. To increase the stiffness of stiffeninglayer96, it may be punched from one side or two sides, as shown, to havedepressions104 that also result in composite action betweenstiffening layer96 and the matrix ofpolymer108.
FIG. 3C shows a simple and highly effective reinforcing distribution of stiffeninglayers112,116, in a polymeric matrix120, according to an aspect of the disclosure. Stiffening layers112,116 are set horizontally, parallel to each other and perpendicular to the direction of loading, and spaced apart in that direction within the cross-section of acomposite article124. The result behaves much like a steel I-beam, in which thick horizontal flanges at top and bottom are separated by a typically thinner vertical steel web. When loaded from above, the I-beam's upper flange, stiffening layer112, is placed in compression perpendicular to the beam's cross-section, while the lower flange, stiffeninglayer116, is placed in tension. Since each point along the width of stiffeninglayers112,116, experiences similar tension or compression, the full width may be loaded to nearly the failing stress of the composition ofcomposite article124 before failure occurs.
FIG. 3D shows another simple distribution, here with a plurality of stiffeningmembers128,132,136, set vertically, parallel to the direction of loading. While this configuration takes less advantage of geometry, since only the edges of each stiffeningmember128,132,136, in apolymer138, can be loaded close to the failing stress while portions nearer the center experience less loading, it may still be useful in many cases.
ExampleFIG. 3E shows a combination of vertical and horizontal stiffening layers140,144,148,152, forming a box-likecomposite article156 able to withstand loading from a variety of directions before failure.
FIG. 3F shows a single stiffening layer158 in acomposite article162. Stiffening layer158 has been folded into a three-dimensional shape comprising top andbottom reinforcing planes166,170, joined by avertical web174. In some cases, it may be convenient for a manufacturer to deform a single stiffening layer158 in this manner rather than to cut it apart.
FIGS. 3G and 3H show alternative ways of folding asingle stiffening layer178,178′ into a three-dimensional profile having greater horizontal symmetry than the configuration shown inFIG. 3F. In addition, since fiber-containing reinforcement is typically stronger in tension than in compression, where, if not adequately supported, it tends to crumple, these profiles place a greater amount of the stiffening material at the top to take the compression while a smaller amount is placed at bottom to accept the tension. Mechanical engineers may recognize especially the distribution shown inFIG. 3G since, when fabricated in steel, with minor modifications, it forms the channel structure for UNI-STRUT (a trademark of Atkore International) and similar steel framing systems.
Referring now toFIG. 4, there is shown acomposite product180 for a door jamb, formed using the present method and incorporating a plurality of stiffeninglayers182,184,186,188,190,192, and194 each comprising a narrow strip potentially separated from an originally wider stiffening layer. Stiffening layers182,184,186,188 and190 and the spacing apart of stiffeninglayers192 and194 provide stiffness chiefly in the horizontal direction, while stiffeninglayers192,194 and the spacing apart of stiffeninglayers182,190 and184,186,188 provide stiffness in the vertical direction. Stiffening layers182,184,186,188,180,192, and194 do not have to be flat, as shown, and may be curved or formed in any other shape as may be convenient for manufacture while providing the required shear and flexural strength for a given application.
A simple method for estimating the stiffness and flexural strength of an article made using aspects of the disclosure exists so any distribution of stiffening layer or layers may be evaluated and an optimal configuration selected. The method is based on one often found in engineering textbooks for calculating the bending of beams, and specifically in E. P. Popov,Mechanics of Materials, Second Edition, © 1976 by Prentice-Hall, Inc, though here simplified for convenience. Simplifications are conservative, tending slightly to underestimate stiffness and strength for a greater safety factor.
For purposes of illustration, a cross-section of the structural member shown inFIG. 4 is shown again inFIG. 5. Loading is assumed to come from above, and stiffness and flexural strength in this direction will be estimated. For stiffness and flexural strength in resisting a force from any other direction, the cross-section may simply be rotated placing the force direction once again at top.
The cross-section is first drawn, either at actual size or at some convenient integral fraction (½, ⅕, etc.) or multiple (2, 5, etc.) thereof, either on graph paper or, more preferably, on a computer screen running a design application such as CAD. This may be done, for example, by tracing over a photograph or drawing as shown inFIG. 5A, followed by scale adjustment.
The enclosing polymer is then “removed” from the drawing (in other words, and conservatively, no credit is taken for any strength or stiffness it may contribute). A zeroaxis200 is drawn, anywhere on the drawing although most conveniently at the bottom, as shown inFIG. 5B.
The width, W, of each stiffening layer (here,182 through194) and its distance Y from zero axis are measured, expressed in actual (non-scaled) inches, and recorded in tabular format, for example in a spreadsheet, along with an “h” or “v” showing whether the stiffening layer is oriented horizontally or vertically since at a later stage of analysis the two will be treated differently. In using a spreadsheet, “h” is conveniently replaced with “0”, and “v”, with “1.”
For each layer, W and Y are multiplied together. The widths are also summed, the products of W and Y are summed, then the sum of products is divided by the sum of widths to find the location of theneutral axis216 above zero axis200:
Y′=Σ(W*Y)/Σw,
as shown in the table at the right ofFIG. 5C.
For the example,neutral axis216 is located 0.482 inch above the zero axis. A line representing theneutral axis216 is then added to the drawing. The distance Y-Y′ of each stiffening layer from the neutral axis is found, squared, then multiplied by the width:
(Y-Y)2*W.
This expression represents the relative contribution of each layer to the overall stiffness and flexural strength.
As is obvious from the table ofFIG. 5C, those layers furthest from the neutral axis contribute disproportionately while the contributions of those near it may be so small as to be negligible. This feature of the disclosure demonstrates an advantage over the known prior art, in that the placement of the stiffening material can be varied so as to achieve the greater stiffness and flexural strength even when using short fibers, mixtures of long and short fibers, and mixtures of different kinds of fibers. Also, because the stiffening member can be cut, a single width of stiffening member can provide several stiffening layers in a single extrusion through a cross-head die.
For vertical stiffening layers only, since their strength is distributed over a range of distances from the neutral axis, one further step is needed. The width of such a layer is cubed, then divided by 12. Structural engineers will recognize this as the formula for the moment of inertia of a rectangular beam I=bh3/12, shorn of its base term since, conservatively and for simplicity, all stiffening layers are treated here as simple planes. Using “1” in the spreadsheet to represent a vertical stiffening layer invokes this extra step, while for a horizontal stiffening layer the “0” causes it to be omitted.
All of the (Y-Y′)2*W terms, and for vertical layers only the W3/12 terms, are summed to obtain the total moment of inertia:
Itotal=Σ(Y-Y′)2*W+ΣvertW3/12.
The result is given in units of length cubed. For the example analyzed, the result is 0.589 inches cubed. Moments of inertia are normally expressed in dimensions of length to the fourth power. The difference here is due to the use of pounds per inch of width, rather than pounds per square inch, for the strength and elasticity of the stiffening layer.
A conservative estimate of the structural member's stiffness can be found by multiplying Itotalby the elastic modulus E of the stiffening layer material, again expressed in pounds per inch of width. For samples produced according to the method disclosed, E is about 550,000 pounds per square inch. A typical thickness of 0.08 inch then yields 44,000 pounds per inch of width. Accordingly, the stiffness of the structural member just analyzed is conservatively estimated at 44,000 lbf/in*0.589 in3=25,916 in2lbf, which replaces the usual EI (I=moment of inertia in in4) in most structural calculations.
For example, the maximum deflection of a center-loaded beam supported at the ends (neglecting the weight of the beam itself) is normally calculated as
vmax=PL3/48EI,
where P is the loading in pounds, L the beam's length in inches, and E and I are as defined above. Taking P as 1 pound and L as 96 inches, and replacing EI with 25,916 in2lbf yields a deflection, vmax, equal to 1*643/25,916=0.711 inch, a reasonable value.
Similarly, the flexural strength of a beam—the maximum bending moment it can support without damage—is normally found as
Mmax=σmax*Itotal/c,
where σmaxis the maximum allowable stress in pounds per square inch and c is the distance fromneutral axis216 to the most distant load-bearing element.
In this simplified approach, max is the tensile or compressive strength of the stiffening layer in pounds per inch of width. This is desirably reduced by 20% to provide a known safety factor. I[subtotal] are found inFIG. 5C replaces I. An expected σmaxfor carbon-fiber-reinforced PET according to the method disclosed is 100,000 lb/in2, which with a thickness of 0.08 inch translates to 6400 pounds per inch of width. The greatest distance Y-Y′ for the example inFIG. 5 is 0.438 inch. Again using Itotal=0.451 in3yields a value Mmaxequal to 6400 lbf/in*0.589 in3/0.438 in =8606 inch-pounds of bending moment allowable. This is a surprisingly high value for a small reinforced composite article like a door jamb—certainly higher than would be expected for natural wood—but realistic based on the performance of samples tested.
An advantage of the disclosed composition and method over all known prior art is thus made clear: the flexibility of stiffening layer placement made possible is tractable using simple mathematics, readily implemented via a spreadsheet, to evaluate and optimize placement within a composite article or structural member in order to achieve virtually any desired stiffness or flexural strength with great economy of materials. This advantage is all the more evident in light of the fact that the method disclosed can be carried out with recycled materials.
When introducing elements of the present disclosure or exemplary aspects or embodiment(s) thereof, the articles “a,” “an,” “the” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including” and “having” are intended to be inclusive and mean that there may be additional elements besides the listed elements. Although this disclosure has been described with respect to specific embodiments, the details of these embodiments are not to be construed as limitations.