Composite Materials

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Encyclopedia of Physical Science and Technology EN003D-128 June 13, 2001 22:40

Composite MaterialsM. KnightD. CurlissAir Force Research Laboratory

I. CharacteristicsII. Constituent MaterialsIII. Properties of CompositesIV. Analysis of CompositesV. Fabrication of Composites

VI. Uses of Composites

GLOSSARY

Advanced composites Composite materials applicableto aerospace construction and consisting of a high-strength, high-modulus fiber system embedded in anessentially homogeneous matrix.

Anisotropic Not isotropic; having mechanical and/orphysical properties that vary with direction relative toa natural reference axis inherent in the materials.

Balanced laminate Composite laminate in which alllaminae at angles other than 0◦ and 90◦ occur onlyin ±pairs.

Constituent In general, an element of a larger grouping.In advanced composites, the principal constituents arethe fibers and the matrix.

Cure To change the properties of a thermosetting resinirreversibly by chemical reaction.

Fiber Single homogeneous strand of material, essentiallyone-dimensional in the macrobehavior sense.

Interface Boundary between the individual, physicallydistinguishable constituents of a composite.

Isotropic Having uniform properties in all directions. Themeasured properties are independent of the axis oftesting.

Lamina Single ply or layer in a laminate made of a seriesof layers.

Laminate Unit made by bonding together two or morelayers or laminae of materials.

Matrix Essentially homogeneous material in which thereinforcement system of a composite is embedded.

Orthotropic Having three mutually perpendicular planesof elastic symmetry.

Transversely isotropic Material having identical proper-ties along any direction in a transverse plane.

Woven fabric composite Form of composite in whichthe reinforcement consists of woven fabric.

1, or x, axis Axis in the plane of the laminate that is usedas the 0◦ reference for designating the angle of a lamina.

2, or y, axis Axis in the plane of the laminate that isperpendicular to the x axis.

3, or z, axis Reference axis normal to the plane of thelaminate x, y axes.

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456 Composite Materials

FIGURE 1 Cross section of a graphite fiber–reinforced epoxypolymer.

A COMPOSITE MATERIAL is described in this chap-ter as a material composed of two or more distinct phasesand the interfaces between them. At a macroscopic scale,the phases are indistinguishable, but at some microscopicscales, the phases are clearly separate, and each phase ex-hibits the characteristics of the pure material. In this chap-ter, we are only describing the characteristics, analysis,and processing of high-performance structural compositematerials. This special class of composites always consistsof a reinforcing phase and a matrix phase. The reinforcingphase is typically a graphite, glass, ceramic, or polymerfiber, and the matrix is typically a polymer, but may alsobe ceramic or metal. The fibers provide strength and stiff-ness to the composite component, while the matrix servesto bind the reinforcements together, distribute mechani-cal loads through the part, provide a means to process thematerial into a net shape part, and provide the primaryenvironmental resistance of the composite component. InFig. 1, we can see the distinct cross section of graphitefibers in an epoxy matrix.

I. CHARACTERISTICS

Many materials can be classified as composites. They arecomposed of several distinctly different and microscopi-cally identifiable substances. Composites are widely usedin many industries and applications today, driven by theneed for strong, lightweight materials. The compositesreduce weight and allow for designs that tailor the me-chanical properties of the material to meet the loadingrequirements of the structure. In addition, composites arereplacing traditional engineering materials in many indus-trial, recreational, architectural, transportation, and infras-tructure applications.

Composites occur very commonly in nature. Some ofthe best examples are wood, bone, various minerals, mol-lusk shells, and insect exoskeletons. In wood, the cellulosefibers of the cell wall are “glued” together by the ligninmatrix. Bone is composed of calcium hydroxyapatite crys-tals in a protein matrix. Mollusk shells are composites ofcalcium carbonate layers in various geometries bound to-gether by a multilayer matrix. Insect exoskeletons bear astriking resemblance to man-made fiber-reinforced com-posites. Some insects even exhibit apparent “layers” offibrous chitin embedded in a protein matrix, where theorientation of the fibers varies from layer to layer, muchas we might design a man-made fiber-reinforced compos-ite. This example of a natural composite can be clearlyseen in Fig. 2. Modern materials engineers have used thecomposite concept—reinforcement in a matrix—to createa class of modern materials that offers opportunities sig-nificantly greater than those of more common engineeringmaterials.

Composites can be made of a such a wide variety ofmaterials that it is impractical to discuss each one indi-vidually. One of the principal characteristics of all com-posites is that they have a reinforcement phase distinctfrom the matrix phase. The individual characteristics ofthe two phases combine to give the composite its uniqueproperties.

Classes of materials commonly used for reinforcementsare glasses, metals, polymers, ceramics, and graphite. Thereinforcement can be in many forms, such as continuousfibers or filaments, chopped fibers, woven fibers or yarns,particles, or ribbons. The criteria for selecting the type andform of reinforcement vary in accordance with the designrequirement for the composite. However, certain generalqualities are desirable, including high strength, high mod-ulus, light weight, environmental resistance, good elonga-tion, low cost, good handleability, and ease of manufac-ture. By far, the most widely used reinforcement is E-glass.

FIGURE 2 Scanning electron microscope (SEM) image of abessbeetle (Odontotaenius disjunctus) elytra fracture surface.



Composite Materials 457

E-glass offers excellent strength, compatibility with com-mon matrix polymers, and is very low in cost. Varioustypes of graphite fibers are commonly used in aerospaceand the recreational products industry, where light weightand maximum material performance are very important tothe designer.

The matrix binds the reinforcement together and en-hances the distribution of the applied load within thecomposite. Polymeric materials are widely used as ma-trix materials. Two general classes of polymers are used:thermosets and thermoplastics. Thermosets are initiallylow molecular weight molecules that are often viscous liq-uids at room temperature—what we commonly think ofas “resins.” Their low viscosity and fluid behavior makethem very suitable to low-cost processing. The thermosetresins undergo chemical reactions when heated (or ini-tiated by some other energy source such as UV light,electron beam, or microwave) and form a high molecu-lar weight cross-linked polymer. In contrast, thermoplas-tics are high molecular weight linear polymers that arefully formed prior to processing as a composite matrix.When heated to temperatures well above their glass tran-sition temperature, Tg, they soften and exhibit a viscos-ity low enough to flow and consolidate the composite.In general, they must be heated to much higher tempera-tures than thermosets, exhibit much higher melt viscosity,and require higher pressures to form well-consolidatedcomposite laminates. Thermoplastics offer some advan-tages such as reprocessability, recyclability, and, in gen-eral, higher toughness. However, thermoplastics also haveseveral limitations that have restricted their wider ac-ceptance as matrix materials for fiber-reinforced com-posites. Thermoplastics have lower solvent resistancethan thermosets and require more expensive process-ing equipment, there are fewer commercially availablethermoplastic matrix preforms available than for ther-mosets, and modern toughened thermosets offer simi-lar performance to thermoplastic matrix composites. Forsuch economic and performance reasons, thermoplasticsare not widely used as thermosets for advanced compos-ite matrix polymers. Other matrix materials are metals,ceramics, glasses, and carbon. They perform the samefunction in composites as the polymer matrix. These ma-terials (with the exception of carbon) are still experimen-tal, and their combined fraction of the composite matrixmaterials market is insignificant. Carbon has been usedsince the 1970s for exotic high-temperature ablative ap-plications such as rocket motor nozzles. The Properties ofComposites and Analysis of Composites sections of thisarticle are general and apply to these developmental com-posite materials. The Processing and Applications sec-tions, however, are concerned only with polymer matrixcomposites.

The matrix influences the service temperature, ser-vice environment, and fabrication process for composites.Compatibility with the reinforcement is a consideration inselecting the matrix. The matrix must adhere to the rein-forcement and be capable of distributing the loads appliedto the composite.

The properties of a composite can be tailored by theengineer to provide a wide range of responses, whichincreases their usefulness. Composites can be made toexhibit some interesting responses when loaded: Theycan be designed to twist and bend when loaded inplane and to extend or contract when loaded in bend-ing. Analysis approaches are available for predicting theseresponses.

There are many processes for the fabrication of com-posites. These often result in reduction in number of parts,reduction in production time, and savings in overall manu-facturing cost. The number of industries using compositesand the various uses of composites continues to grow. It isdifficult to foresee what the future of this class of materialswill be.

II. CONSTITUENT MATERIALS

A composite can contain several chemical substances.There are additives, for example, to improve processabilityand serviceability. However, the two principal constituentsthat are always present in advanced composites are the ma-trix and the reinforcement. Generally, they are combinedwithout chemical reaction and form separate and distinctphases. Ideally, the reinforcement is uniformly distributedthroughout the matrix phase. The combination of the prop-erties of the reinforcement, the form of the reinforcement,the amount of reinforcement, and matrix properties givesthe composite its characteristic properties.

The matrix phase contributes to several characteristicsof the composite. The matrix provides some protectionfor the reinforcement from deleterious environmental con-ditions such as harmful chemicals. The matrix plays animportant role in determining the physical and thermo-physical properties of the composite. In continuous fila-ment, unidirectionally reinforced composites, the proper-ties transverse to the filaments are strongly influenced bythe properties of the matrix. The distribution of the ap-plied load throughout the composite is influenced by theproperties of the matrix.

Table I shows typical values of selected propertiesof common matrix materials. The properties are tensilestrength, Ftu , Young’s modulus, Et , total strain (or strain-to-failure), εt , coefficient of thermal expansion, α, andspecific gravity. It can be seen that there is a wide varia-tion in these values between types of matrix materials.




TABLE I Matrix Materials

PolyetherProperty Epoxy Polyimide Polyester Polysulfone ether ketone Al 2024 Ti 6-4

Etu (MPa) 6.2–103 90 21–69 69 69 414 924

Et (GPa) 2.8–3.4 2.8 3.4–5.6 2.8 3.6 72 110

εt (%) 4.5 7–9 0.5–5.0 50–100 2.0 10 8

α (10−6 m m−1 K−1) 0.56 0.51 0.4–0.7 0.56 0.5 24 9.6

Specific gravity 1.20 1.43 1.1–1.4 1.24 1.2 2.77 4.43

There is great variety in polymers typically used forcomposite matrix materials. As discussed earlier, ther-mosets and thermoplastics make up the two general fam-ilies of engineering polymers; but there are many differ-ent polymers within each family that exhibit very diverseproperties, depending on their chemical composition.Thermosets are generally named for the characteristic re-active group of the resin (e.g., epoxy, maleimide), whereasthermoplastics are generally named for either their build-ing block (“mer” unit; e.g., polystyrene, polyethylene,polypropylene, polyvinyl chloride) or for a characteristicrepeating chemical group within the thermoplastic poly-mer (e.g., polysulfone, polyimide). It is more appropriateto refer to the matrix polymer as a resin system, the systembeing a mixture of the base polymer (or thermoset resinand curing agents). Diluents, fillers, tougheners, and othermodifiers are sometimes added to the resin system to al-ter viscosity, increase toughness, modify reactivity of thethermosets, or change other properties of the base poly-mer system. Because there are so many starting combina-tions, it is easy to see how there can be a wide variationin the properties of materials in the same general class(e.g., based on the same basic polymer, but with differentadditives). The other principal constituent of a compositeis the reinforcement. There are several types of materi-als, and their various forms are used as reinforcements.The continuous fiber has been used most extensively forthe development of advanced composites. This form ofreinforcement provides the highest strength and modu-lus. It can be used to make other forms such as woven

TABLE II Fiber Materials

SiliconProperty Boron Carbon Graphite Aramid Alumina carbide E-glass S-glass

Etu (MPa) 2.8–3.4 0.4–2.1 0.81–3.6 2.8 1.4 3.3 3.4 4.6

Et (GPa) 379–414 241–517 34–552 124 345–379 427 69 83

α (10−6 m m−1 K−1) 4.9 −0.09 −0.09 −4.0 3.4 .40 5.1 3.4

ρ (g cm−3) 2.5–3.3 1.55 1.55 1.60 3.90 3.07 2.55 2.5

Diameter (10−3 m) 0.05–0.2 0.008 0.008 0.013 0.38–0.64 0.14 0.005–0.013 0.009–0.010

εt (%) 0.67 1.0–2.0 0.4–2.0 2.5 0.4 0.6 4.8 5.4

fabric, chopped fibers, and random fiber mats. These rein-forcement forms typically reduce the mechanical perfor-mance compared to unidirectional fibers, but offer ben-efits in fabrication. Glass, graphite, and polymeric fibersare generally produced as bundles of many filaments ofvery small diameter. Metal, boron, and ceramic reinforce-ments are usually single fibers. After fabrication, fibersare processed with surface treatments for protection duringhandling and weaving and also for chemical compatibilitywith the matrix systems. After forming and treating, the fil-aments are typically wound on spools for use by manufac-turers in fabricating composites, producing unidirectionalpreforms, or weaving into various geometries of textilepreforms.

Table II lists the properties of some of the fibers, mea-sured in the longitudinal direction (along the axis of thefiber), used in composite materials: tensile strength Ftu ,Young’s modulus Et , coefficient of expansion α, strain-to-failure εt , diameter, and density ρ. Mechanical propertiestransverse to the longitudinal axis are not shown. Becauseof the small diameter of the fibers, transverse propertiesare not measured directly. Variations in the fiber proper-ties can be caused by several factors. There can be vari-ations in the composition of the starting material such asin E-, S-, and C-glass fibers. There can be variations inprocessing such as in the way the processing temperatureis changed to vary the strength and modulus of graphitefibers. Also, the difficulty of performing mechanical test-ing on fibers contributes to uncertainty and scatter in themeasured properties of fibers.




The reinforcement is the main load-bearing phase of thecomposite. It provides strength and stiffness. There is adirect relationship between an increase in volume fractionof reinforcement and an increase in strength and stiffnessof the composite material. This relationship depends onthe assumption of compatibility with the matrix and onthe existence of good bonding to the fibers.

The reinforcement and matrix are combined either be-fore or at the time of fabrication of the composite. Thisdepends on the fabrication process. A common practice inmaking continuous-fiber-reinforced laminates is to com-bine the constituents before fabrication into a continuous“tapelike” preform that is used much like broadgoods inthat shapes are cut out of the preform and fabricated intoparts. To produce this preform product, fibers are com-bined with resin, typically by drawing the fiber bundlethrough a resin or resin solution bath. Several bundles ofresin-impregnated fibers are then aligned and spread intovery thin layers (0.127 mm thick) on a release ply back-ing. The resin is usually partially cured during produc-tion of the preform to reduce its “tackiness” and improvethe handleability of the preform. This tapelike preform isknown as prepreg, or unidirectional tape. It is an expen-sive method for producing a preform, but the preform isa continuous, well-characterized, well-controlled methodto combine the matrix resin and the reinforcing fiber. Af-ter prepregging, the material is usually stored in a freezerto retard the chemical reaction until the material is used.If the matrix system is a thermoplastic polymer, then noreaction can occur, and the material may be stored indefi-nitely at room temperature. These layers of unidirectionalfibers and resin are used to make laminates by stackingmany layers in directions specified by the engineer. Thenumber of “plies” in a laminate and the direction of fibersin each layer is dependent on the mechanical propertiesrequired for the part.

The next two sections, Properties of Composites andAnalysis of Composites, describe how an engineer woulddesign a composite laminate to have the properties neededfor an application. It is exactly this tailorability that makescomposites attractive for engineering applications.

III. PROPERTIES OF COMPOSITES

In many of the applications in which composite materi-als are used, they can be considered to be constructed ofseveral layers stacked on top of one another. These layers,or laminae, typically exhibit properties similar to thoseof orthotropic materials. Orthotropic materials have threemutually perpendicular planes of material property sym-metry. Figure 3 shows a lamina with its coordinate systemand two of the planes of symmetry. We will first discuss the

properties of the lamina and some factors that influencethem. Next, the properties of laminates will be discussed.

The lamina is made of one thickness of reinforcementembedded in the matrix. The elastic and strength proper-ties of the reinforcement and the elastic and strength prop-erties of the matrix combine to give the lamina its prop-erties. In addition to the properties of the constituents, theamount of reinforcement, the form of the reinforcement,and the orientation and distribution of the reinforcementall influence the properties of the lamina.

The reinforcement provides the strength and stiffnessof the composite. Increasing the amount of reinforcementincreases the strength and stiffness of the composite in thedirection parallel to the reinforcement. The effect of theform of the reinforcement is not as simple. However, somegeneral observations can be made. Laminae reinforcedby long, continuous, parallel fibers have greater strengthand stiffness than laminae reinforced by short, randomlyoriented fibers. Woven fiber–reinforced laminae usuallyhave greater strength perpendicular to the principal fiberdirection than do unwoven fiber–reinforced laminae. Thestrength and stiffness of laminae reinforced by unwovencontinuous fibers decrease as the angle of loading changesfrom parallel to the fibers to perpendicular to the fibers.

Table III shows typical values for some properties ofcomposite materials made of unwoven continuous fiberreinforcements. The table shows the strength and elasticproperties of a laminate made of several laminae stackedon top of one another with all the fibers aligned in the samedirection. The properties in the direction parallel to thefibers are much greater than the properties in the directionperpendicular to the fibers. This variation of propertieswith the orientation of the lamina axis is called anisotropy.

The single lamina serves as a building block. The en-gineer can select the orientation and number of each ofthe laminae in a laminate and design the laminate suchthat it has the required response. This designing of a lam-inate has some interesting implications that the engineershould understand. Two important factors are balance andsymmetry.

Balance and symmetry simplify the analysis of the lam-inate and give it more conventional response characteris-tics. Balance in a laminate means that for each lamina witha positive angle of orientation there must be a lamina withan equal negative angle of orientation. Both laminae musthave the same mechanical and physical characteristics.This is important in controlling the laminate’s overall re-sponse to loading both in service and in fabrication. Sym-metry means that for every lamina above the midplane ofthe laminate there is a lamina an equal distance below themidplane that is of the same type with the same orienta-tion. Symmetry also influences the laminate response toloads.




TABLE III Typical Properties of Composite Materials: Laminates Reinforced With UnidirectionalContinuous Fibers

E-glass Aramid Graphite BoronProperty Unit epoxy epoxy epoxy epoxy

Parallel to the fibers

Tensile strength σ Tx MPa 1100 1380 1240 1296

Tensile modulus ETx GPa 39.3 75.8 131 207

Poisson’s ratio νxy — 0.25 0.34 0.25 0.21

Total strain εT % 2.2 1.8 1.21 0.66

Compressive strength σ cx MPa 586 276 1100 2426

Compressive modulus Ecx GPa 39.3 75.8 131 221

Shear strength τxy MPa 62.0 44.1 62.0 132

Shear modulus Gxy GPa 3.45 2.07 4.83 6.2

Transverse to the fibers

Tensile strength σ Ty MPa 34.5 27.6 41.4 62.7

Tensile modulus ETy GPa 8.96 5.5 6.2 18.6

Compressive strength σ cy MPa 138 138 138 310

Compressive modulus Ecy GPa 8.96 5.5 6.2 24.1

Specific gravity — 2.08 1.38 1.52 2.01

Fiber volume V f % ∼50 ∼60 ∼62 ∼50

FIGURE 3 Lamina coordinate axis and planes of symmetry.




FIGURE 4 Orientation and location of laminae in a laminate.

If a laminate is not balanced and symmetrical, it willtwist or bend when in-plane loads are applied. Laminatesmay also extend or contract when bending loads are ap-plied. Whether the results are good or bad depends onwhether they were planned or unplanned during the de-sign of the laminate. Figure 4 shows how the laminae areoriented and stacked in a laminate.

IV. ANALYSIS OF COMPOSITES

Composite materials are complex. The properties of theconstituents are different, and the fiber properties areanisotropic. The composite may also be constructed bylayers, with the fiber directions varying layer to layer.Analysis of the mechanical properties of such laminatesis a sophisticated process; research into better methodsto predict composite performance is being pursued. How-ever, acceptable engineering analysis methods have beendeveloped that allow structural parts to be designed withcomposite materials. Further research is required to de-velop sound engineering methods to predict failure incomposite materials, especially when subjected to se-vere environments that may degrade the matrix, the re-inforcement, or the interfaces of the composite material.In this section, a brief summary of the currently accepted

approach to performing stress analysis of composites ispresented.

The emphasis has been focused on unidirectional fiber-reinforced composites. The lamina or ply form of ad-vanced composites has been developed into the basic unitfor analysis. Most of the structural applications of ad-vanced composites involve material in a laminated form.The laminates are constructed of plies or laminae laid upto a designed configuration (see Fig. 4).

The approach to the analysis of composites starts withthe lamina and its elastic properties. Then these are relatedto the geometry of the lay-up for the laminate. The elas-tic properties and orientation of the laminae are used tocalculate the modulus and stiffness of the laminate. Theconstitutive relationship and a selected failure criterion areused to estimate failure.

In developing the analysis of the lamina, several as-sumptions were made. It was assumed that (1) the fibersand matrix were bonded together, (2) the lamina was voidfree, (3) the lamina’s thickness was small in comparisonwith its width and length, (4) the lamina was a homoge-neous orthotropic material, and (5) the fibers were uni-formly distributed within the matrix.

The lamina is analyzed as a macroscopic, homoge-neous, orthotropic material in a plane stress condition. Ifthe coordinate axes for the laminate are oriented parallel




and transverse to the fiber axis (see Fig. 3), the constitutiveequation relating stress α and strain ε is

σ1

σ2

τ12

=

Q11 Q12 0

Q12 Q22 0

0 0 Q66

ε1

ε2

γ12

(1)

where Q is called the reduced stiffness and is defined as

Q11 = E1

1 − ν12ν21; Q22 = E2

1 − ν12ν21(2)

Q12 = ν12 E2

1 − ν12ν21; Q66 = G12

where E1 is Young’s modulus in the direction parallel tothe fibers; E2 is Young’s modulus in the direction perpen-dicular to the fibers; ν12 and ν21 are the major Poisson’sratio and minor Poisson’s ratio, respectively; and G12 isthe in-plane shear modulus.

Equation (1) can be inverted to give the form

ε1

ε2

γ12

=

S11 S11 0

S12 S22 0

0 0 S66

σ1

σ2

τ12

(3)

where the S terms are the compliance coefficients and aredefined as

S11 = 1/Et ; S22 = 1/E2

S12 = −ν12/E1; S66 = 1/G12(4)

Equation (4) relates the compliance coefficients to the en-gineering constants. These can be determined by mechan-ical testing. Also, estimates of the engineering constantscan be made by using equations developed by microme-chanics. In this approach, the properties of the constituentsare used in equations for the engineering constants. Theseare

E1 = E f V f + Em Vm

ν12 = ν f V f + νm Vm

P/Pm = (1 + ξηV f )/(1 − ηV f ) (5)

η = (Pf /Pm) − 1

(Pf /Pm) + ξ

where V f , Vm are the volume fraction of the fiber and ma-trix, respectively; ν f , νm are Poisson’s ratio of the fiber andmatrix, respectively; P is the composite modulus E2, G12,or G23; Pf is the corresponding fiber modulus E f , G f , orν f , respectively; Pm is the corresponding matrix modulusEm , Gm , or νm , respectively; and ξ is a factor related tothe arrangement and geometry of the reinforcement; forsquare packing ξ = 2, and for hexagonal packing ξ = 1.

Because not all laminae in a laminate are oriented withthe fibers parallel or transverse to the laminate coordinateaxis x–y, there must be a way to find the properties of the

lamina in the laminate coordinate systems. This is donethrough a transformation. By a combination of mathemat-ical transformation and substitution, the following rela-tionship between stress and strain for an arbitrary laminak is developed:

∣∣∣∣∣∣∣σx

σy

τxy

∣∣∣∣∣∣∣k

=

∣∣∣∣∣∣∣Q̄11 Q̄12 Q̄16

Q̄12 Q̄22 Q̄26

Q̄16 Q̄26 Q̄66

∣∣∣∣∣∣∣k

∣∣∣∣∣∣∣εx

εy

γxy

∣∣∣∣∣∣∣k

(6)

The Q̄ terms are the components of the stiffness matrix forthe lamina referred to an arbitrary axis. They are definedas

Q̄11 = Q11 cos4 θ + 2(Q12 + 2Q66) sin2 θ cos2 θ

+ Q22 sin4 θ

Q̄22 = Q11 sin4 θ + 2(Q12 + 2Q66) sin2 θ cos2 θ

+ Q22 cos4 θ

Q̄12 = (Q11 + Q22 − 4Q66) sin2 θ cos2 θ

+ Q22 (sin4 θ + cos4 θ ) (7)

Q̄66 = (Q11 + Q22 − 2Q12 − 2Q66) sin2 θ cos2 θ

+ Q66 (sin4 θ + cos4 θ )

Q̄16 = (Q11 − Q12 − 2Q66) sin2 θ cos3 θ

+ (Q12 − Q22 + 2Q66) sin3 θ cos θ

Q̄26 = (Q11 − Q12 − 2Q66) sin2 θ cos θ

+ (Q12 − Q22 + 2Q66) sin θ cos3 θ

where θ is the ply angle according to the Tsai convention(see Fig. 4). Counterclockwise rotations are positive andclockwise rotations are negative.

The constitutive relationships for the lamina and linearsmall deformation theory were used to develop the analy-sis for composite structures. Some assumptions that weremade are as follows: (1) The laminae are bonded together,and they do not slip relative to one another when load isapplied; (2) the normals to the undeformed midplane ofthe laminate are straight, and they remain so with nochange in length after deformation; (3) the thickness ofthe plate is small compared with the length and width; and(4) the strain in the thickness direction is negligible. Thein-plane strain is assumed constant for all the laminae. Thestress varies from lamina to lamina. As a simplification,the force and moment resultants were defined. The forceresultants Nx , Ny , and Nxy were defined as the sum of thelaminae stresses per unit width. The moment resultantsMx , My , and Mxy were defined as the sum of the respec-tive stresses, times the area over which they act, multipliedby the appropriate moment arm. The in-plane strains at the




midplane, ε0x , ε

0y , and γ 0

xy , and the curvatures, κx , κy , andκxy , are related to the resultants as shown in Eq. (8).

Nx

Ny

Nxy

- - -

Mx

My

Mxy

A11 A12 A16 B11 B12 B16

A12 A22 A26 B12 B22 B26

A16 A26 A66 B16 B26 B66

- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - -B11 B12 B16 D11 D12 D16

B12 B22 B26 D12 D22 D26

B16 B26 B66 D16 D26 D66

ε0x

ε0y

γ 0xy

- - -

κx

κy

κxy

(8)

where Nx , Ny , and Nxy are force resultants; Mx , My , andMxy are moment resultants; [A] is the in-plane stiffnessmatrix for a laminate; [B] is the coupling stiffness matrixfor a laminate; [D] is the bending stiffness matrix for alaminate; ε0

x , ε0y , and γ 0

xy are the strains at the laminate ge-ometric mid-plane; and κx , κy , and κxy are the curvaturesof the laminate.

Examination of Eq. (8) shows that the [A] matrix is thecoefficients for the in-plane strains. The [B] matrix re-lates the curvatures to the force resultants and the in-planestrains to the moment resultants. The [D] matrix relatesthe curvatures to the moment resultants. Equation (8) canbe partially or fully inverted, depending on whether the

FIGURE 5 Relationship of laminae to the laminate coordinates.

strains, curvatures, forces, or moments are known in agiven situation.

The definitions for the elements of the [A], [B], and [D]matrices are

Ai j =n∑

k=1

(Q̄i j )k(hk − hk−1) (9)

Bi j = 1

2

n∑k=1

(Q̄i j )k(h2

k − h2k−1

)(10)

Di j = 1

3

n∑k=1

(Q̄i j )k(h3

k − h3k−1

)(11)

Figure 5 shows how k and h are defined for the laminae.The force resultants and moment resultants are defined

as

Nx

Ny

Nxy

=

∫ h/2

−h/2

σx

σy

τxy

dz (12)

and

Mx

My

Mxy

=

∫ h/2

−h/2

σx

σy

τxy

z dz (13)




FIGURE 6 Force resultants on an element.

where σx , σy , and τxy are the stresses in the laminate co-ordinate system and z is the distance from the midplane inthe direction normal to the midplane. Figures 6 and 7 showhow the force and monment resultants act on an elementin the laminate.

Equation (8) is the constitutive equation for a generallaminated plate. Significant simplifications of Eq. (8) arepossible. If the [B] is made zero, the set of equations forthe stress and moment resultants is uncoupled. “Uncou-

FIGURE 7 Moment resultants on an element (following the right-hand rule).

pled” means that in-plane loads generate only in-planeresponses, and bending loads generate only bending re-sponses. The [B] can be made zero if for each laminaabove the midplane there is a lamina with the same proper-ties, orientation, and thickness located at the same distancebelow the midplane. This is significant not only in sim-plifying the calculations but also in the physical responseto load and in fabrication. If the [B] is zero, the laminatewill not warp when cured, and no bending will be induced




when the laminate is under in-plane loads. Equation (8)becomes

Nx

Ny

Nxy

=

A11 A12 A16

A12 A22 A26

A16 A26 A66

ε0x

ε0y

γ 0xy

(14)

and

Mx

My

Mxy

=

D11 D12 D16

D12 D22 D26

D16 D26 D66

k0x

k0y

k0xy

(15)

In the preceding discussion, only the elastic propertiesof the laminate were considered. The elastic behavior ofa laminate can be used to analyze the strength behaviorof a laminate. To determine the strength of a laminate, weneed a failure criterion for the lamina. It is assumed thatthe response of the lamina will be the same when it is in thelaminate under the same stresses or strains. The strengthof the laminate will be related to the strength of the indi-vidual lamina. The general approach is to determine theforce and moment resultants or the mid-plane strains andcurvatures for the laminate by using the laminate plateequation or an inverted form. The stress or strain is cal-culated for each lamina in the laminate axis system, andthen it is transformed into the lamina axis system for eachlamina and the failure criteria applied to determine if fail-ure occurred in the lamina. If the first-ply failure conceptfor the laminates is applied, the laminate is considered tohave failed when the first lamina fails. No single approachhas been universally accepted for strength analysis of lam-inates after first-ply failure.

V. FABRICATION OF COMPOSITES

Fabrication of components from composite materials issomewhat different from that using traditional engineer-ing materials in that the properties of a composite arehighly dependent on the geometry of the reinforcement.The structural designer must consider the issues associ-ated with processing the composite part to ensure thatreinforcement volume fraction, reinforcement geometry,and other material properties can be produced economi-cally. The diversity of composite applications has stimu-lated the development of a wide range of techniques forfabricating structural composites. In fact, one of the prin-cipal reasons for the success of composites is the ease offabrication and the many different processes with widelyvarying levels of sophistication and cost that are avail-able for their production. Structural and decorative com-posites can be fabricated with techniques ranging fromvery crude hand lay-up processes without molds to very

sophisticated techniques with complex molds, woven 3Dreinforcement preforms, and artificial intelligence–guidedcomputer-controlled resin infusion and curing. The con-figuration of the part, along with the basic manufactur-ing considerations such as volume, production speed, andmarket conditions, determine whether a part will be builtin open or closed molds, by compression molding, or byan automated system. Composite fabrication technologiescan be classified as either open or closed molding, thechoice of appropriate technique being governed by fac-tors mentioned earlier.

We can group most of the processes into two classes:open molding and closed molding. The main distinctionis that open molds are one piece and use low pressure orno pressure, and closed molds are two pieces and can beused with higher pressure.

A. Open-Mold Processes

Open-mold processes such as spray-up, wet hand lay-up,autoclave, filament winding, vacuum infusion, pultrusion,or combinations of these techniques are the most com-mon open-mold methods to produce composite products.Many products are suited to these manufacturing methods,including aerospace structures, tanks, piping, boat hullsand structures, recreational vehicle components, commer-cial truck cabs and components, structural members, andplumbing applications (e.g., tubs, showers, pools, andspas).

In spray-up and wet hand lay-up open molding, themold surface typically has a high-quality finish and is thevisual surface of the finished part. Common to all openmolding techniques is mold preparation. To prepare themold surface prior to spray-up, hand lay-up, or vacuuminfusion, the mold is treated with a release agent to aidin composite part removal and then may be coated with a“gel coat” (a color-tinted layer of resin that becomes thevisual surface of the finished part).

In spray-up fabrication, the thermoset resin is sprayedinto the prepared mold simultaneously with chopped re-inforcing fiber. The random sprayed-up mat of fiber andresin may then be compacted with hand rollers prior tocure to produce a more dense part. A hand lay-up com-ponent, the resin, and reinforcement (usually a fabric orrandom fiber mat) are laid into the mold, compacted withrollers, and allowed to cure. Often hand lay-up is combinedwith spray-up techniques depending on the structural re-quirements of the part. Fiber volumes of 15 to 25% aretypically achieved with these techniques. There are sev-eral variations of the basic process. A vacuum bag madeof a nonporous, nonadhering material can be placed overthe lay-up. Then a vacuum is drawn inside the bag. Theatmospheric pressure outside the bag eliminates the voids




and forces out entrapped air and excess resin. Another ap-proach is to use a pressure bag. The bag is placed againstthe lay-up and the mold covered with a pressure plate. Airor steam pressure is applied between the bag and the plate.

Vacuum infusion is an open molding process that is verysuitable for large components for many important reasons.Vacuum infusion uses an airtight membrane over the en-tire part to provide vacuum pressure on the reinforcementand to prevent any volatile resin products from escapinginto the atmosphere. The resin is introduced after the en-tire reinforcement is laid into the mold and the vacuummembrane is in place; this reduces some issues associatedwith the working time of the resin prior to cure. Finally,higher volume fractions of reinforcement are achievablesince the reinforcement is compacted by vacuum pres-sure and only the minimum amount of resin necessary isadded. Reinforcement volume fractions up to 70% havebeen reported.

An open-mold technique that is widely used in theaerospace industry and is slightly different from the pre-ceding processes is autoclaving. One difference in thisprocess is that the entire assembly (the lay-up and sup-porting unit) is placed inside an autoclave. An autoclaveis a large pressure vessel that is used to provide heat andpressure to the lay-up during cure. Autoclaves are usuallycylindrical, with an end that opens for full access to theinterior. They have provision to pull vacuum on the lay-up assembly, and they often have multiple temperaturesensors that are used to monitor the temperature of thepart during cure. The curing takes place under pressure,1–10 bar (15–150 psi), and at elevated temperature. Thelay-up assembly is slightly different (Fig. 8). The top sur-face of the lay-up is covered with a perforated or porousrelease film, and if necessary bleeder plies of dry clothare added to absorb excess resin. Then the assembly issealed within a nonporous sheet material and placed intothe autoclave. The application of pressure and control oftemperature is critical. This process offers better qualitycontrol than other low- or no-pressure molding processes.

FIGURE 8 Cross section of the composite laminate lay-up and vacuum bagging processing method.

Another process that is used extensively is filamentwinding. The concept of wrapping filaments around arti-cles to improve their performance is very old. The modernpractice of filament winding was developed in responseto the requirements for lightweight pressure vessels. Fila-ment winding uses continuous reinforcement to maximizethe use of fiber strength. Preimpregnated tape, or a singlestrand that has passed through a resin bath, is wound onto amandrel in a prescribed pattern. Design and winding tech-nique allow the maximum fiber strength to be developedin the direction desired. When the winding is completed,the assembly is cured either at room temperature or in anoven. After cure, the mandrel is removed. This processprovides for a high level of fiber content.

The process of pultrusion is the opposite of extrusion.The reinforcement is passed through a resin bath and thenpulled through a die that controls the resin content andfinal shape. The die can be heated to cure the resin, or thematerial can be passed through an oven for curing.

B. Closed-Mold Processes

The closed-mold processes use a two-part mold or die.When the two parts are put together, they form a cavityin the shape of the article to be molded. The molds areusually made of metal with smooth cavity surfaces. Higherpressures and temperatures than those in open moldingare usually used. The processes produce very accuratemoldings. Most of the processes are attractive for massproduction.

Matched die molding is a closed-mold process. Thereare variations to this process. The main variations con-cern the form of the starting material and the manner inwhich it is introduced into the mold. In some cases, thereinforcement is first made into a preform and placed intothe mold and then a metered amount of resin is added—this is known as resin transfer molding, or RTM. RTM is awidely used technique for production of components thatrequire accurate dimensional tolerances, since the outer




surface of the part is determined by the tool surface. Inother cases, a resin–reinforcement mixture is made and apremeasured amount placed into the mold. The moldingcompound can be introduced automatically or manually.The molding temperatures range from 100◦C (212◦F) to140◦C (284◦F). Pressures range from 7 to 20 bar. Curecycles can be as short as minutes.

The selection of a fabrication process depends on sev-eral factors, including the materials to be processed, thesize and design of the article, the number of articles, andthe rate of production. Processes differ in their capacityto use different forms of reinforcement and to achievethe proper distribution and amount of reinforcement. Thechemistry and rheology of the resin are important factorsin process selection. Closed molds require higher temper-atures and pressures.

The size and shape of the article to be produced affectthe selection. Very large articles such as boat hulls andvehicle bodies and components are more easily and eco-nomically produced in open-mold processes. Small gearsand precision electrical parts are more suitably producedin closed molds. Shapes that are surfaces of revolution areideal for filament winding. Very large cylindrical contain-ers have been fabricated by this process. In most open-mold processes, the molds are made of low-cost materialsand are easily fabricated but have shorter lives. Autoclaveprocessing of composites, while considered an open-moldtechnique, requires accurate, robust tools because of therelatively high temperatures and pressures used in theautoclave. Autoclave techniques are well suited to largestructural components for aerospace applications; hence,dimensional accuracy of the tools is critical. Open-mold,hand lay-up processes have higher labor cost. If one ismaking a large number of parts and requires high pro-duction rates, mold life and labor cost are important fac-tors. Open-mold processes are usually more costly in thesetwo areas than closed-mold processes. Also, some closed-mold processes can be automated.

Automating the fabrication of advanced composites andimproving processing science for composites are two cur-rent goals. The advantages of advanced composites arelighter weight, higher strength- and modulus-to-weightratios, flexibility in design and fabrication, and usuallyfewer parts per component. Automating the fabricationprocess could result in a reduction in labor cost and animprovement in quality. The computer-aided manufactur-ing technology could be utilized to reduce the total laborhours. The application of higher precision control tech-nology could improve quality and lower rejection rates.Work in processing science should result in increased un-derstanding of the cure process, which will aid the de-velopment of resin systems and automating productioncycles.

Fabrication processes for other matrix materials are im-portant for the use and continued development of thesecomposites. However, not as much work has been done inthese areas. The use of these materials represents a smallpart of the overall uses of composite materials.

VI. USES OF COMPOSITES

Composite materials have been introduced into almost ev-ery industry in some form or fashion. We shall look at someof the advantages of using composites and discuss someof the industries that have made used of these materials.

The wide range of property values attained with com-posites and the ability to tailor the properties is an ad-vantage. Composite materials also generally have higherstrength- and modulus-to-weight ratios than traditional en-gineering materials. These features can reduce the weightof a system by as much as 20 to 30%. The weight savingstranslates into energy savings or increased performance.Advanced composites exhibit desirable dynamic proper-ties and have high creep resistance and good dampeningcharacteristics. In fact, the superior fatigue performanceof composite materials enables them to be used to repairmetallic airframes with fatigue damage.

Since composite materials can be manufactured intoalmost any shape, they allow great design flexibility andoffer reduced parts count for articles. The opportunity toselect the constituents, tailor them to obtain the requiredproperties, and then through design make the optimum useof the properties is a situation that makes composites veryattractive to many industries.

The matrix polymer can impart great chemical and cor-rosion resistance to composites. The transportation indus-try has made extensive use of composite materials. Thelight weight and high strength and the ability to easilymanufacture aerodynamic shapes have resulted in lowerfuel costs. The lack of corrosion of the materials and thelow maintenance cost have reduced the cost of ownershipand extended the service life of many parts and products.Examples of products in this industry include auto andtruck bodies and parts, trailers, tanks, special-purpose ve-hicles, and manufacturing equipment.

Composites have added new dimensions to the designand construction of buildings. Their ease of manufacture,light weight, high strength, low maintenance, decorative-ness, and functionality have had a significant impact onthe industry. New-construction time has been reduced andmore flexibility has been added to the design of structures.

Composite materials affected the marine industry veryearly in their development, and their influence contin-ues to grow. Lack of corrosion, low maintenance, anddesign flexibility have contributed to the acceptance of




composites. The ease of fabricating very large and strongarticles in one piece has been another. In addition to plea-sure boats, large military and commercial boats and shiphulls have been fabricated. Large tanks for fuel, water,and cargo have been used aboard ships. Composites havemade the greatest impact in the sporting goods industry,replacing traditional materials at a revolutionary pace. Ap-plications such as golf club shafts, fishing poles, tennisrackets, skiing equipment, boating applications, and manyother sports equipment products are now produced almostexclusively using advanced composites. In most cases, thechange in material has translated into an improvement inperformance or safety for participants.

The aerospace and military markets are the two areasthat have accounted for the largest effort in the develop-ment and advancement in composite technology. The needfor stronger, stiffer, and lighter structures was an opportu-nity for composite materials to demonstrate their superi-ority over more commonly used materials. Durability andlow maintenance are additional assets. These increase theservice life and reduce the cost of maintaining systems.The development of new and the improvement of exist-ing fabrication processes have brought about a reductionin manufacturing cost. There have been reductions in thenumber of parts required to construct some componentsby using molding and composite materials. The uniquefeatures of composites have enabled designers to formu-late advanced systems that could be made only of com-posite materials. New military aircraft almost exclusivelyutilize advanced composites for structure. Rocket motorcases, nozzles, and nose cones are missile applications.Radar domes, rotor blades, propellers, and many sec-ondary structure components such as fairings, doors, andaccess panels are also fabricated from advanced compos-ites. Numerous pressure vessels, armaments, and items ofspace hardware are made of selected composite materials.

The use of composite materials will continue to grow.As more engineers come to understand composites, moreopportunities will be recognized for their use. As the use ofcomposites increases, more developments will take placein the areas of constituent materials, analysis, design, andfabrication. Composite materials offer tremendous for tai-lorability, design flexibility, and low-cost processing withlow environment impact. These attributes create a verybright future composite materials.

SEE ALSO THE FOLLOWING ARTICLES

ADHESION AND ADHESIVES • BIOPOLYMERS • CAR-BON FIBERS • FRACTURE AND FATIGUE • METAL MA-TRIX COMPOSITES • POLYMERS, MECHANICAL BEHAV-IOR • POLYMERS, THERMALLY STABLE • SANDWICH

COMPOSITES

BIBLIOGRAPHY

Ashton, J. E., Halpin, J. C., and Petit, P. H. (1969). “Primer on Compos-ite Materials: Analysis,” Technomic Publishing Company, Stamford,CT.

Hull, D. (1981). “An Introduction to Compositive Materials,” CambridgeUniversity Press, London.

Jones, R. M. (1975). “Mechanics of Composite Materials,” Scripta BookCompany, Washington, D.C.

Sih, G. C., and Hsu, S. E. (1987). “Advanced Composite Materials andStructures,” VNU Science Press, Utrecht, The Netherlands.

Tsai, S. W. (1985). “Composites Design—1985,” Think Composites,Dayton, OH.

Tsai, S. W., and Hahn, H. T. (1980). “Introduction to Composite Mate-rials,” Technomic Publishing Company, Westport, CT.

Whitney, J. M., Daniel, I. M., and Pipes, R. B. (1982). “ExperimentalMechanics of Fiber Reinforced Composite Materials,” Society forExperimental Stress Analysis, Brookfield Center, CT.

Industry Overview: FRP Materials, Manufacturing Methods and Mar-kets, (1999). Composites Technol. 5, 6–20.

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