Composite Materials

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Encyclopedia of Physical Science and Technology

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Composite Materials M. Knight D. Curliss Air Force Research Laboratory

I. II. III. IV. V. VI.

Characteristics Constituent Materials Properties of Composites Analysis of Composites Fabrication of Composites Uses of Composites

GLOSSARY Advanced composites Composite materials applicable to aerospace construction and consisting of a highstrength, high-modulus fiber system embedded in an essentially homogeneous matrix. Anisotropic Not isotropic; having mechanical and/or physical properties that vary with direction relative to a natural reference axis inherent in the materials. Balanced laminate Composite laminate in which all laminae at angles other than 0◦ and 90◦ occur only in ±pairs. Constituent In general, an element of a larger grouping. In advanced composites, the principal constituents are the fibers and the matrix. Cure To change the properties of a thermosetting resin irreversibly by chemical reaction. Fiber Single homogeneous strand of material, essentially one-dimensional in the macrobehavior sense. Interface Boundary between the individual, physically distinguishable constituents of a composite.

Isotropic Having uniform properties in all directions. The measured properties are independent of the axis of testing. Lamina Single ply or layer in a laminate made of a series of layers. Laminate Unit made by bonding together two or more layers or laminae of materials. Matrix Essentially homogeneous material in which the reinforcement system of a composite is embedded. Orthotropic Having three mutually perpendicular planes of elastic symmetry. Transversely isotropic Material having identical properties along any direction in a transverse plane. Woven fabric composite Form of composite in which the reinforcement consists of woven fabric. 1, or x, axis Axis in the plane of the laminate that is used as the 0◦ reference for designating the angle of a lamina. 2, or y, axis Axis in the plane of the laminate that is perpendicular to the x axis. 3, or z, axis Reference axis normal to the plane of the laminate x, y axes.

455

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FIGURE 1 Cross section of a graphite fiber–reinforced epoxy polymer.

A COMPOSITE MATERIAL is described in this chapter as a material composed of two or more distinct phases and the interfaces between them. At a macroscopic scale, the phases are indistinguishable, but at some microscopic scales, the phases are clearly separate, and each phase exhibits the characteristics of the pure material. In this chapter, we are only describing the characteristics, analysis, and processing of high-performance structural composite materials. This special class of composites always consists of a reinforcing phase and a matrix phase. The reinforcing phase is typically a graphite, glass, ceramic, or polymer fiber, and the matrix is typically a polymer, but may also be ceramic or metal. The fibers provide strength and stiffness to the composite component, while the matrix serves to bind the reinforcements together, distribute mechanical loads through the part, provide a means to process the material into a net shape part, and provide the primary environmental resistance of the composite component. In Fig. 1, we can see the distinct cross section of graphite fibers in an epoxy matrix.

Composite Materials

Composites occur very commonly in nature. Some of the best examples are wood, bone, various minerals, mollusk shells, and insect exoskeletons. In wood, the cellulose fibers of the cell wall are “glued” together by the lignin matrix. Bone is composed of calcium hydroxyapatite crystals in a protein matrix. Mollusk shells are composites of calcium carbonate layers in various geometries bound together by a multilayer matrix. Insect exoskeletons bear a striking resemblance to man-made fiber-reinforced composites. Some insects even exhibit apparent “layers” of fibrous chitin embedded in a protein matrix, where the orientation of the fibers varies from layer to layer, much as we might design a man-made fiber-reinforced composite. This example of a natural composite can be clearly seen in Fig. 2. Modern materials engineers have used the composite concept—reinforcement in a matrix—to create a class of modern materials that offers opportunities significantly greater than those of more common engineering materials. Composites can be made of a such a wide variety of materials that it is impractical to discuss each one individually. One of the principal characteristics of all composites is that they have a reinforcement phase distinct from the matrix phase. The individual characteristics of the two phases combine to give the composite its unique properties. Classes of materials commonly used for reinforcements are glasses, metals, polymers, ceramics, and graphite. The reinforcement can be in many forms, such as continuous fibers or filaments, chopped fibers, woven fibers or yarns, particles, or ribbons. The criteria for selecting the type and form of reinforcement vary in accordance with the design requirement for the composite. However, certain general qualities are desirable, including high strength, high modulus, light weight, environmental resistance, good elongation, low cost, good handleability, and ease of manufacture. By far, the most widely used reinforcement is E-glass.

I. CHARACTERISTICS Many materials can be classified as composites. They are composed of several distinctly different and microscopically identifiable substances. Composites are widely used in many industries and applications today, driven by the need for strong, lightweight materials. The composites reduce weight and allow for designs that tailor the mechanical properties of the material to meet the loading requirements of the structure. In addition, composites are replacing traditional engineering materials in many industrial, recreational, architectural, transportation, and infrastructure applications.

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

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Composite Materials

E-glass offers excellent strength, compatibility with common matrix polymers, and is very low in cost. Various types of graphite fibers are commonly used in aerospace and the recreational products industry, where light weight and maximum material performance are very important to the designer. The matrix binds the reinforcement together and enhances the distribution of the applied load within the composite. Polymeric materials are widely used as matrix materials. Two general classes of polymers are used: thermosets and thermoplastics. Thermosets are initially low molecular weight molecules that are often viscous liquids at room temperature—what we commonly think of as “resins.” Their low viscosity and fluid behavior make them very suitable to low-cost processing. The thermoset resins undergo chemical reactions when heated (or initiated by some other energy source such as UV light, electron beam, or microwave) and form a high molecular weight cross-linked polymer. In contrast, thermoplastics are high molecular weight linear polymers that are fully formed prior to processing as a composite matrix. When heated to temperatures well above their glass transition temperature, Tg , they soften and exhibit a viscosity low enough to flow and consolidate the composite. In general, they must be heated to much higher temperatures than thermosets, exhibit much higher melt viscosity, and require higher pressures to form well-consolidated composite laminates. Thermoplastics offer some advantages such as reprocessability, recyclability, and, in general, higher toughness. However, thermoplastics also have several limitations that have restricted their wider acceptance as matrix materials for fiber-reinforced composites. Thermoplastics have lower solvent resistance than thermosets and require more expensive processing equipment, there are fewer commercially available thermoplastic matrix preforms available than for thermosets, and modern toughened thermosets offer similar performance to thermoplastic matrix composites. For such economic and performance reasons, thermoplastics are not widely used as thermosets for advanced composite matrix polymers. Other matrix materials are metals, ceramics, glasses, and carbon. They perform the same function in composites as the polymer matrix. These materials (with the exception of carbon) are still experimental, and their combined fraction of the composite matrix materials market is insignificant. Carbon has been used since the 1970s for exotic high-temperature ablative applications such as rocket motor nozzles. The Properties of Composites and Analysis of Composites sections of this article are general and apply to these developmental composite materials. The Processing and Applications sections, however, are concerned only with polymer matrix composites.

The matrix influences the service temperature, service environment, and fabrication process for composites. Compatibility with the reinforcement is a consideration in selecting the matrix. The matrix must adhere to the reinforcement and be capable of distributing the loads applied to the composite. The properties of a composite can be tailored by the engineer to provide a wide range of responses, which increases their usefulness. Composites can be made to exhibit some interesting responses when loaded: They can be designed to twist and bend when loaded in plane and to extend or contract when loaded in bending. Analysis approaches are available for predicting these responses. There are many processes for the fabrication of composites. These often result in reduction in number of parts, reduction in production time, and savings in overall manufacturing cost. The number of industries using composites and the various uses of composites continues to grow. It is difficult to foresee what the future of this class of materials will be.

II. CONSTITUENT MATERIALS A composite can contain several chemical substances. There are additives, for example, to improve processability and serviceability. However, the two principal constituents that are always present in advanced composites are the matrix and the reinforcement. Generally, they are combined without chemical reaction and form separate and distinct phases. Ideally, the reinforcement is uniformly distributed throughout the matrix phase. The combination of the properties of the reinforcement, the form of the reinforcement, the amount of reinforcement, and matrix properties gives the composite its characteristic properties. The matrix phase contributes to several characteristics of the composite. The matrix provides some protection for the reinforcement from deleterious environmental conditions such as harmful chemicals. The matrix plays an important role in determining the physical and thermophysical properties of the composite. In continuous filament, unidirectionally reinforced composites, the properties transverse to the filaments are strongly influenced by the properties of the matrix. The distribution of the applied load throughout the composite is influenced by the properties of the matrix. Table I shows typical values of selected properties of common matrix materials. The properties are tensile strength, F tu , Young’s modulus, E t , total strain (or strainto-failure), εt , coefficient of thermal expansion, α, and specific gravity. It can be seen that there is a wide variation in these values between types of matrix materials.

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Composite Materials TABLE I Matrix Materials Property

Epoxy

E tu (MPa) E t (GPa)

Polyimide

Polyester

Polysulfone

Polyether ether ketone

Al 2024

Ti 6-4

6.2–103

90

21–69

69

69

414

924

2.8–3.4 4.5

2.8 7–9

3.4–5.6 0.5–5.0

2.8 50–100

3.6 2.0

72 10

110 8

0.56 1.20

0.51 1.43

0.4–0.7 1.1–1.4

0.56 1.24

0.5 1.2

24 2.77

9.6 4.43

εt (%) α (10−6 m m−1 K−1 ) Specific gravity

There is great variety in polymers typically used for composite matrix materials. As discussed earlier, thermosets and thermoplastics make up the two general families of engineering polymers; but there are many different polymers within each family that exhibit very diverse properties, depending on their chemical composition. Thermosets are generally named for the characteristic reactive group of the resin (e.g., epoxy, maleimide), whereas thermoplastics are generally named for either their building block (“mer” unit; e.g., polystyrene, polyethylene, polypropylene, polyvinyl chloride) or for a characteristic repeating chemical group within the thermoplastic polymer (e.g., polysulfone, polyimide). It is more appropriate to refer to the matrix polymer as a resin system, the system being a mixture of the base polymer (or thermoset resin and curing agents). Diluents, fillers, tougheners, and other modifiers are sometimes added to the resin system to alter viscosity, increase toughness, modify reactivity of the thermosets, or change other properties of the base polymer system. Because there are so many starting combinations, it is easy to see how there can be a wide variation in the properties of materials in the same general class (e.g., based on the same basic polymer, but with different additives). The other principal constituent of a composite is the reinforcement. There are several types of materials, and their various forms are used as reinforcements. The continuous fiber has been used most extensively for the development of advanced composites. This form of reinforcement provides the highest strength and modulus. It can be used to make other forms such as woven

fabric, chopped fibers, and random fiber mats. These reinforcement forms typically reduce the mechanical performance compared to unidirectional fibers, but offer benefits in fabrication. Glass, graphite, and polymeric fibers are generally produced as bundles of many filaments of very small diameter. Metal, boron, and ceramic reinforcements are usually single fibers. After fabrication, fibers are processed with surface treatments for protection during handling and weaving and also for chemical compatibility with the matrix systems. After forming and treating, the filaments are typically wound on spools for use by manufacturers in fabricating composites, producing unidirectional preforms, or weaving into various geometries of textile preforms. Table II lists the properties of some of the fibers, measured in the longitudinal direction (along the axis of the fiber), used in composite materials: tensile strength F tu , Young’s modulus E t , coefficient of expansion α, strain-tofailure εt , diameter, and density ρ. Mechanical properties transverse to the longitudinal axis are not shown. Because of the small diameter of the fibers, transverse properties are not measured directly. Variations in the fiber properties can be caused by several factors. There can be variations in the composition of the starting material such as in E-, S-, and C-glass fibers. There can be variations in processing such as in the way the processing temperature is changed to vary the strength and modulus of graphite fibers. Also, the difficulty of performing mechanical testing on fibers contributes to uncertainty and scatter in the measured properties of fibers.

TABLE II Fiber Materials Property E tu (MPa) E t (GPa) α (10−6 m m−1 K−1 ) ρ (g cm−3 ) Diameter (10−3 m) ε t (%)

Boron

Carbon

Graphite

Aramid

Alumina

Silicon carbide

E-glass

S-glass 4.6

2.8–3.4

0.4–2.1

0.81–3.6

2.8

1.4

3.3

3.4

379–414

241–517

34–552

124

345–379

427

69

83

4.9 2.5–3.3

−0.09 1.55

−0.09 1.55

−4.0 1.60

3.4 3.90

.40 3.07

5.1 2.55

3.4 2.5

0.05–0.2

0.008

0.008

0.013

0.38–0.64

0.14

0.005–0.013

0.009–0.010

0.67

1.0–2.0

0.4–2.0

2.5

0.4

0.6

4.8

5.4

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Composite Materials

The reinforcement is the main load-bearing phase of the composite. It provides strength and stiffness. There is a direct relationship between an increase in volume fraction of reinforcement and an increase in strength and stiffness of the composite material. This relationship depends on the assumption of compatibility with the matrix and on the existence of good bonding to the fibers. The reinforcement and matrix are combined either before or at the time of fabrication of the composite. This depends on the fabrication process. A common practice in making continuous-fiber-reinforced laminates is to combine the constituents before fabrication into a continuous “tapelike” preform that is used much like broadgoods in that shapes are cut out of the preform and fabricated into parts. To produce this preform product, fibers are combined with resin, typically by drawing the fiber bundle through a resin or resin solution bath. Several bundles of resin-impregnated fibers are then aligned and spread into very thin layers (0.127 mm thick) on a release ply backing. The resin is usually partially cured during production of the preform to reduce its “tackiness” and improve the handleability of the preform. This tapelike preform is known as prepreg, or unidirectional tape. It is an expensive method for producing a preform, but the preform is a continuous, well-characterized, well-controlled method to combine the matrix resin and the reinforcing fiber. After prepregging, the material is usually stored in a freezer to retard the chemical reaction until the material is used. If the matrix system is a thermoplastic polymer, then no reaction can occur, and the material may be stored indefinitely at room temperature. These layers of unidirectional fibers and resin are used to make laminates by stacking many layers in directions specified by the engineer. The number of “plies” in a laminate and the direction of fibers in each layer is dependent on the mechanical properties required for the part. The next two sections, Properties of Composites and Analysis of Composites, describe how an engineer would design a composite laminate to have the properties needed for an application. It is exactly this tailorability that makes composites attractive for engineering applications.

III. PROPERTIES OF COMPOSITES In many of the applications in which composite materials are used, they can be considered to be constructed of several layers stacked on top of one another. These layers, or laminae, typically exhibit properties similar to those of orthotropic materials. Orthotropic materials have three mutually perpendicular planes of material property symmetry. Figure 3 shows a lamina with its coordinate system and two of the planes of symmetry. We will first discuss the

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459 properties of the lamina and some factors that influence them. Next, the properties of laminates will be discussed. The lamina is made of one thickness of reinforcement embedded in the matrix. The elastic and strength properties of the reinforcement and the elastic and strength properties of the matrix combine to give the lamina its properties. In addition to the properties of the constituents, the amount of reinforcement, the form of the reinforcement, and the orientation and distribution of the reinforcement all influence the properties of the lamina. The reinforcement provides the strength and stiffness of the composite. Increasing the amount of reinforcement increases the strength and stiffness of the composite in the direction parallel to the reinforcement. The effect of the form of the reinforcement is not as simple. However, some general observations can be made. Laminae reinforced by long, continuous, parallel fibers have greater strength and stiffness than laminae reinforced by short, randomly oriented fibers. Woven fiber–reinforced laminae usually have greater strength perpendicular to the principal fiber direction than do unwoven fiber–reinforced laminae. The strength and stiffness of laminae reinforced by unwoven continuous fibers decrease as the angle of loading changes from parallel to the fibers to perpendicular to the fibers. Table III shows typical values for some properties of composite materials made of unwoven continuous fiber reinforcements. The table shows the strength and elastic properties of a laminate made of several laminae stacked on top of one another with all the fibers aligned in the same direction. The properties in the direction parallel to the fibers are much greater than the properties in the direction perpendicular to the fibers. This variation of properties with the orientation of the lamina axis is called anisotropy. The single lamina serves as a building block. The engineer can select the orientation and number of each of the laminae in a laminate and design the laminate such that it has the required response. This designing of a laminate has some interesting implications that the engineer should understand. Two important factors are balance and symmetry. Balance and symmetry simplify the analysis of the laminate and give it more conventional response characteristics. Balance in a laminate means that for each lamina with a positive angle of orientation there must be a lamina with an equal negative angle of orientation. Both laminae must have the same mechanical and physical characteristics. This is important in controlling the laminate’s overall response to loading both in service and in fabrication. Symmetry means that for every lamina above the midplane of the laminate there is a lamina an equal distance below the midplane that is of the same type with the same orientation. Symmetry also influences the laminate response to loads.

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Composite Materials TABLE III Typical Properties of Composite Materials: Laminates Reinforced With Unidirectional Continuous Fibers Property Parallel to the fibers Tensile strength σxT Tensile modulus E xT Poisson’s ratio νxy Total strain ε T

Unit

E-glass epoxy

Aramid epoxy

Graphite epoxy

Boron epoxy

MPa GPa

1100 39.3

1380 75.8

1240 131

1296 207

—

0.25

0.34

0.25

0.21

%

2.2

1.8

1.21

0.66

Compressive strength σxc

MPa

586

276

1100

2426

Compressive modulus E xc

GPa MPa

39.3 62.0

75.8 44.1

131 62.0

221 132

GPa

3.45

2.07

4.83

6.2

MPa

34.5

27.6

41.4

62.7

GPa

8.96

5.5

6.2

18.6

MPa GPa —

138 8.96 2.08

138 5.5 1.38

138 6.2 1.52

310 24.1 2.01

%

∼50

∼60

∼62

∼50

Shear strength τx y Shear modulus G x y Transverse to the fibers Tensile strength σyT Tensile modulus E yT Compressive strength σ yc Compressive modulus E yc Specific gravity Fiber volume V f

FIGURE 3 Lamina coordinate axis and planes of symmetry.

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Composite Materials

FIGURE 4 Orientation and location of laminae in a laminate.

If a laminate is not balanced and symmetrical, it will twist or bend when in-plane loads are applied. Laminates may also extend or contract when bending loads are applied. Whether the results are good or bad depends on whether they were planned or unplanned during the design of the laminate. Figure 4 shows how the laminae are oriented and stacked in a laminate.

IV. ANALYSIS OF COMPOSITES Composite materials are complex. The properties of the constituents are different, and the fiber properties are anisotropic. The composite may also be constructed by layers, with the fiber directions varying layer to layer. Analysis of the mechanical properties of such laminates is a sophisticated process; research into better methods to predict composite performance is being pursued. However, acceptable engineering analysis methods have been developed that allow structural parts to be designed with composite materials. Further research is required to develop sound engineering methods to predict failure in composite materials, especially when subjected to severe environments that may degrade the matrix, the reinforcement, or the interfaces of the composite material. In this section, a brief summary of the currently accepted

approach to performing stress analysis of composites is presented. The emphasis has been focused on unidirectional fiberreinforced composites. The lamina or ply form of advanced composites has been developed into the basic unit for analysis. Most of the structural applications of advanced composites involve material in a laminated form. The laminates are constructed of plies or laminae laid up to a designed configuration (see Fig. 4). The approach to the analysis of composites starts with the lamina and its elastic properties. Then these are related to the geometry of the lay-up for the laminate. The elastic properties and orientation of the laminae are used to calculate the modulus and stiffness of the laminate. The constitutive relationship and a selected failure criterion are used to estimate failure. In developing the analysis of the lamina, several assumptions were made. It was assumed that (1) the fibers and matrix were bonded together, (2) the lamina was void free, (3) the lamina’s thickness was small in comparison with its width and length, (4) the lamina was a homogeneous orthotropic material, and (5) the fibers were uniformly distributed within the matrix. The lamina is analyzed as a macroscopic, homogeneous, orthotropic material in a plane stress condition. If the coordinate axes for the laminate are oriented parallel

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and transverse to the fiber axis (see Fig. 3), the constitutive equation relating stress α and strain ε is      σ1 Q 11 Q 12 ε1 0      Q σ Q 0 = (1)  2   12   ε2  22 0 0 Q 66 τ12 γ12 where Q is called the reduced stiffness and is defined as Q 11 =

E1 ; 1 − ν12 ν21

Q 22 =

E2 1 − ν12 ν21

lamina in the laminate coordinate systems. This is done through a transformation. By a combination of mathematical transformation and substitution, the following relationship between stress and strain for an arbitrary lamina k is developed:        Q¯ 11 Q¯ 12 Q¯ 16   εx   σx              (6)  σ y  =  Q¯ 12 Q¯ 22 Q¯ 26   ε y         Q¯ 16 Q¯ 26 Q¯ 66  γx y  τ x y  k

(2)

k

k

ν12 E 2 ; Q 66 = G 12 1 − ν12 ν21 where E 1 is Young’s modulus in the direction parallel to the fibers; E 2 is Young’s modulus in the direction perpendicular to the fibers; ν12 and ν21 are the major Poisson’s ratio and minor Poisson’s ratio, respectively; and G 12 is the in-plane shear modulus. Equation (1) can be inverted to give the form      ε1 S11 S11 0 σ1      (3)  ε2  =  S12 S22 0   σ2  γ12 τ12 0 0 S66

The Q¯ terms are the components of the stiffness matrix for the lamina referred to an arbitrary axis. They are defined as

where the S terms are the compliance coefficients and are defined as

Q¯ 66 = (Q 11 + Q 22 − 2Q 12 − 2Q 66 ) sin2 θ cos2 θ

Q 12 =

S11 = 1/E t ; S12 = −ν12 /E 1 ;

S22 = 1/E 2 S66 = 1/G 12

(4)

Equation (4) relates the compliance coefficients to the engineering constants. These can be determined by mechanical testing. Also, estimates of the engineering constants can be made by using equations developed by micromechanics. In this approach, the properties of the constituents are used in equations for the engineering constants. These are E 1 = E f V f + E m Vm ν12 = ν f V f + νm Vm P/Pm = (1 + ξ ηV f )/(1 − ηV f ) η=

(5)

(P f /Pm ) − 1 (P f /Pm ) + ξ

where V f , Vm are the volume fraction of the fiber and matrix, respectively; ν f , νm are Poisson’s ratio of the fiber and matrix, respectively; P is the composite modulus E 2 , G 12 , or G 23 ; P f is the corresponding fiber modulus E f , G f , or ν f , respectively; Pm is the corresponding matrix modulus E m , G m , or νm , respectively; and ξ is a factor related to the arrangement and geometry of the reinforcement; for square packing ξ = 2, and for hexagonal packing ξ = 1. Because not all laminae in a laminate are oriented with the fibers parallel or transverse to the laminate coordinate axis x–y, there must be a way to find the properties of the

Q¯ 11 = Q 11 cos4 θ + 2(Q 12 + 2Q 66 ) sin2 θ cos2 θ + Q 22 sin4 θ Q¯ 22 = Q 11 sin4 θ + 2(Q 12 + 2Q 66 ) sin2 θ cos2 θ + Q 22 cos4 θ Q¯ 12 = (Q 11 + Q 22 − 4Q 66 ) sin2 θ cos2 θ + Q 22 (sin4 θ + cos4 θ )

(7)

+ Q 66 (sin4 θ + cos4 θ ) Q¯ 16 = (Q 11 − Q 12 − 2Q 66 ) sin2 θ cos3 θ + (Q 12 − Q 22 + 2Q 66 ) sin3 θ cos θ Q¯ 26 = (Q 11 − Q 12 − 2Q 66 ) sin2 θ cos θ + (Q 12 − Q 22 + 2Q 66 ) sin θ cos3 θ where θ is the ply angle according to the Tsai convention (see Fig. 4). Counterclockwise rotations are positive and clockwise rotations are negative. The constitutive relationships for the lamina and linear small deformation theory were used to develop the analysis for composite structures. Some assumptions that were made are as follows: (1) The laminae are bonded together, and they do not slip relative to one another when load is applied; (2) the normals to the undeformed midplane of the laminate are straight, and they remain so with no change in length after deformation; (3) the thickness of the plate is small compared with the length and width; and (4) the strain in the thickness direction is negligible. The in-plane strain is assumed constant for all the laminae. The stress varies from lamina to lamina. As a simplification, the force and moment resultants were defined. The force resultants N x , N y , and N x y were defined as the sum of the laminae stresses per unit width. The moment resultants Mx , M y , and Mx y were defined as the sum of the respective stresses, times the area over which they act, multiplied by the appropriate moment arm. The in-plane strains at the

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midplane, εx0 , ε 0y , and γx0y , and the curvatures, κx , κ y , and κx y , are related to the resultants as shown in Eq. (8).      ε0 Nx  x A A A B B B 11 12 16 11 12 16 N   ε0   y  A   B12 B22 B26   0y     12 A22 A26   Nx y    γ     A16 A26 A66 B16 B26 B66   x y   - - -  - - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - - - -     D11 D12 D16     M   B11 B12 B16  x    κx     B12 B22 B26 D12 D22 D26     My   κy  B16 B26 B66 D16 D26 D66 Mx y κx y      

strains, curvatures, forces, or moments are known in a given situation. The definitions for the elements of the [ A], [B], and [D] matrices are n

Ai j = ( Q¯ i j )k (h k − h k−1 ) (9)



k=1



Bi j =

n  1

( Q¯ i j )k h 2k − h 2k−1 2 k=1

(10)

Di j =

n  1

( Q¯ i j )k h 3k − h 3k−1 3 k=1

(11)

      

(8) where N x , N y , and N x y are force resultants; Mx , M y , and Mx y are moment resultants; [A] is the in-plane stiffness matrix for a laminate; [B] is the coupling stiffness matrix for a laminate; [D] is the bending stiffness matrix for a laminate; εx0 , ε 0y , and γx0y are the strains at the laminate geometric mid-plane; and κx , κ y , and κx y are the curvatures of the laminate. Examination of Eq. (8) shows that the [A] matrix is the coefficients for the in-plane strains. The [B] matrix relates the curvatures to the force resultants and the in-plane strains to the moment resultants. The [D] matrix relates the curvatures to the moment resultants. Equation (8) can be partially or fully inverted, depending on whether the

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

h/2 σx     (12)  Ny  =  σ y  dz −h/2 Nx y τx y and



   Mx

h/2 σx      My  =  σ y  z dz −h/2 Mx y τx y

FIGURE 5 Relationship of laminae to the laminate coordinates.

(13)

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FIGURE 6 Force resultants on an element.

where σx , σ y , and τx y are the stresses in the laminate coordinate system and z is the distance from the midplane in the direction normal to the midplane. Figures 6 and 7 show how the force and monment resultants act on an element in the laminate. Equation (8) is the constitutive equation for a general laminated plate. Significant simplifications of Eq. (8) are possible. If the [B] is made zero, the set of equations for the stress and moment resultants is uncoupled. “Uncou-

pled” means that in-plane loads generate only in-plane responses, and bending loads generate only bending responses. The [B] can be made zero if for each lamina above the midplane there is a lamina with the same properties, orientation, and thickness located at the same distance below the midplane. This is significant not only in simplifying the calculations but also in the physical response to load and in fabrication. If the [B] is zero, the laminate will not warp when cured, and no bending will be induced

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

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when the laminate is under becomes    Nx A11     N y  =  A12 Nx y A16 and



  Mx D11    M =  y   D12 Mx y D16

in-plane loads. Equation (8) A12 A22 A26

  εx0 A16  0  A26   ε y  γx0y A66

(14)

D12 D22 D26

  k x0 D16  0  D26   k y  k x0y D66

(15)

In the preceding discussion, only the elastic properties of the laminate were considered. The elastic behavior of a laminate can be used to analyze the strength behavior of a laminate. To determine the strength of a laminate, we need a failure criterion for the lamina. It is assumed that the response of the lamina will be the same when it is in the laminate under the same stresses or strains. The strength of the laminate will be related to the strength of the individual lamina. The general approach is to determine the force and moment resultants or the mid-plane strains and curvatures for the laminate by using the laminate plate equation or an inverted form. The stress or strain is calculated for each lamina in the laminate axis system, and then it is transformed into the lamina axis system for each lamina and the failure criteria applied to determine if failure occurred in the lamina. If the first-ply failure concept for the laminates is applied, the laminate is considered to have failed when the first lamina fails. No single approach has been universally accepted for strength analysis of laminates after first-ply failure.

V. FABRICATION OF COMPOSITES Fabrication of components from composite materials is somewhat different from that using traditional engineering materials in that the properties of a composite are highly dependent on the geometry of the reinforcement. The structural designer must consider the issues associated with processing the composite part to ensure that reinforcement volume fraction, reinforcement geometry, and other material properties can be produced economically. The diversity of composite applications has stimulated the development of a wide range of techniques for fabricating structural composites. In fact, one of the principal reasons for the success of composites is the ease of fabrication and the many different processes with widely varying levels of sophistication and cost that are available for their production. Structural and decorative composites can be fabricated with techniques ranging from very crude hand lay-up processes without molds to very

sophisticated techniques with complex molds, woven 3D reinforcement preforms, and artificial intelligence–guided computer-controlled resin infusion and curing. The configuration of the part, along with the basic manufacturing considerations such as volume, production speed, and market conditions, determine whether a part will be built in open or closed molds, by compression molding, or by an automated system. Composite fabrication technologies can be classified as either open or closed molding, the choice of appropriate technique being governed by factors mentioned earlier. We can group most of the processes into two classes: open molding and closed molding. The main distinction is that open molds are one piece and use low pressure or no pressure, and closed molds are two pieces and can be used 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 common open-mold methods to produce composite products. Many products are suited to these manufacturing methods, including aerospace structures, tanks, piping, boat hulls and structures, recreational vehicle components, commercial truck cabs and components, structural members, and plumbing applications (e.g., tubs, showers, pools, and spas). In spray-up and wet hand lay-up open molding, the mold surface typically has a high-quality finish and is the visual surface of the finished part. Common to all open molding techniques is mold preparation. To prepare the mold surface prior to spray-up, hand lay-up, or vacuum infusion, the mold is treated with a release agent to aid in composite part removal and then may be coated with a “gel coat” (a color-tinted layer of resin that becomes the visual surface of the finished part). In spray-up fabrication, the thermoset resin is sprayed into the prepared mold simultaneously with chopped reinforcing fiber. The random sprayed-up mat of fiber and resin may then be compacted with hand rollers prior to cure to produce a more dense part. A hand lay-up component, the resin, and reinforcement (usually a fabric or random fiber mat) are laid into the mold, compacted with rollers, and allowed to cure. Often hand lay-up is combined with spray-up techniques depending on the structural requirements of the part. Fiber volumes of 15 to 25% are typically achieved with these techniques. There are several variations of the basic process. A vacuum bag made of a nonporous, nonadhering material can be placed over the lay-up. Then a vacuum is drawn inside the bag. The atmospheric pressure outside the bag eliminates the voids

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and forces out entrapped air and excess resin. Another approach is to use a pressure bag. The bag is placed against the lay-up and the mold covered with a pressure plate. Air or steam pressure is applied between the bag and the plate. Vacuum infusion is an open molding process that is very suitable for large components for many important reasons. Vacuum infusion uses an airtight membrane over the entire part to provide vacuum pressure on the reinforcement and to prevent any volatile resin products from escaping into the atmosphere. The resin is introduced after the entire reinforcement is laid into the mold and the vacuum membrane is in place; this reduces some issues associated with the working time of the resin prior to cure. Finally, higher volume fractions of reinforcement are achievable since the reinforcement is compacted by vacuum pressure and only the minimum amount of resin necessary is added. Reinforcement volume fractions up to 70% have been reported. An open-mold technique that is widely used in the aerospace industry and is slightly different from the preceding processes is autoclaving. One difference in this process is that the entire assembly (the lay-up and supporting unit) is placed inside an autoclave. An autoclave is a large pressure vessel that is used to provide heat and pressure to the lay-up during cure. Autoclaves are usually cylindrical, with an end that opens for full access to the interior. They have provision to pull vacuum on the layup assembly, and they often have multiple temperature sensors that are used to monitor the temperature of the part during cure. The curing takes place under pressure, 1–10 bar (15–150 psi), and at elevated temperature. The lay-up assembly is slightly different (Fig. 8). The top surface of the lay-up is covered with a perforated or porous release film, and if necessary bleeder plies of dry cloth are added to absorb excess resin. Then the assembly is sealed within a nonporous sheet material and placed into the autoclave. The application of pressure and control of temperature is critical. This process offers better quality control than other low- or no-pressure molding processes.

Another process that is used extensively is filament winding. The concept of wrapping filaments around articles to improve their performance is very old. The modern practice of filament winding was developed in response to the requirements for lightweight pressure vessels. Filament winding uses continuous reinforcement to maximize the use of fiber strength. Preimpregnated tape, or a single strand that has passed through a resin bath, is wound onto a mandrel in a prescribed pattern. Design and winding technique allow the maximum fiber strength to be developed in the direction desired. When the winding is completed, the assembly is cured either at room temperature or in an oven. After cure, the mandrel is removed. This process provides 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 then pulled through a die that controls the resin content and final shape. The die can be heated to cure the resin, or the material 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 cavity in the shape of the article to be molded. The molds are usually made of metal with smooth cavity surfaces. Higher pressures and temperatures than those in open molding are usually used. The processes produce very accurate moldings. Most of the processes are attractive for mass production. Matched die molding is a closed-mold process. There are variations to this process. The main variations concern the form of the starting material and the manner in which it is introduced into the mold. In some cases, the reinforcement is first made into a preform and placed into the mold and then a metered amount of resin is added— this is known as resin transfer molding, or RTM. RTM is a widely used technique for production of components that require accurate dimensional tolerances, since the outer

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

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surface of the part is determined by the tool surface. In other cases, a resin–reinforcement mixture is made and a premeasured amount placed into the mold. The molding compound can be introduced automatically or manually. The molding temperatures range from 100◦ C (212◦ F) to 140◦ C (284◦ F). Pressures range from 7 to 20 bar. Cure cycles can be as short as minutes. The selection of a fabrication process depends on several factors, including the materials to be processed, the size and design of the article, the number of articles, and the rate of production. Processes differ in their capacity to use different forms of reinforcement and to achieve the proper distribution and amount of reinforcement. The chemistry and rheology of the resin are important factors in process selection. Closed molds require higher temperatures and pressures. The size and shape of the article to be produced affect the selection. Very large articles such as boat hulls and vehicle bodies and components are more easily and economically produced in open-mold processes. Small gears and precision electrical parts are more suitably produced in closed molds. Shapes that are surfaces of revolution are ideal for filament winding. Very large cylindrical containers have been fabricated by this process. In most openmold processes, the molds are made of low-cost materials and are easily fabricated but have shorter lives. Autoclave processing of composites, while considered an open-mold technique, requires accurate, robust tools because of the relatively high temperatures and pressures used in the autoclave. Autoclave techniques are well suited to large structural components for aerospace applications; hence, dimensional accuracy of the tools is critical. Open-mold, hand lay-up processes have higher labor cost. If one is making a large number of parts and requires high production rates, mold life and labor cost are important factors. Open-mold processes are usually more costly in these two areas than closed-mold processes. Also, some closedmold processes can be automated. Automating the fabrication of advanced composites and improving processing science for composites are two current goals. The advantages of advanced composites are lighter weight, higher strength- and modulus-to-weight ratios, flexibility in design and fabrication, and usually fewer parts per component. Automating the fabrication process could result in a reduction in labor cost and an improvement in quality. The computer-aided manufacturing technology could be utilized to reduce the total labor hours. The application of higher precision control technology could improve quality and lower rejection rates. Work in processing science should result in increased understanding of the cure process, which will aid the development of resin systems and automating production cycles.

Fabrication processes for other matrix materials are important for the use and continued development of these composites. However, not as much work has been done in these areas. The use of these materials represents a small part of the overall uses of composite materials.

VI. USES OF COMPOSITES Composite materials have been introduced into almost every industry in some form or fashion. We shall look at some of the advantages of using composites and discuss some of the industries that have made used of these materials. The wide range of property values attained with composites and the ability to tailor the properties is an advantage. Composite materials also generally have higher strength- and modulus-to-weight ratios than traditional engineering materials. These features can reduce the weight of a system by as much as 20 to 30%. The weight savings translates into energy savings or increased performance. Advanced composites exhibit desirable dynamic properties and have high creep resistance and good dampening characteristics. In fact, the superior fatigue performance of composite materials enables them to be used to repair metallic airframes with fatigue damage. Since composite materials can be manufactured into almost any shape, they allow great design flexibility and offer reduced parts count for articles. The opportunity to select the constituents, tailor them to obtain the required properties, and then through design make the optimum use of the properties is a situation that makes composites very attractive to many industries. The matrix polymer can impart great chemical and corrosion resistance to composites. The transportation industry has made extensive use of composite materials. The light weight and high strength and the ability to easily manufacture aerodynamic shapes have resulted in lower fuel costs. The lack of corrosion of the materials and the low maintenance cost have reduced the cost of ownership and extended the service life of many parts and products. Examples of products in this industry include auto and truck bodies and parts, trailers, tanks, special-purpose vehicles, and manufacturing equipment. Composites have added new dimensions to the design and construction of buildings. Their ease of manufacture, light weight, high strength, low maintenance, decorativeness, and functionality have had a significant impact on the industry. New-construction time has been reduced and more flexibility has been added to the design of structures. Composite materials affected the marine industry very early in their development, and their influence continues to grow. Lack of corrosion, low maintenance, and design flexibility have contributed to the acceptance of

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468 composites. The ease of fabricating very large and strong articles in one piece has been another. In addition to pleasure boats, large military and commercial boats and ship hulls have been fabricated. Large tanks for fuel, water, and cargo have been used aboard ships. Composites have made the greatest impact in the sporting goods industry, replacing traditional materials at a revolutionary pace. Applications such as golf club shafts, fishing poles, tennis rackets, skiing equipment, boating applications, and many other sports equipment products are now produced almost exclusively using advanced composites. In most cases, the change in material has translated into an improvement in performance or safety for participants. The aerospace and military markets are the two areas that have accounted for the largest effort in the development and advancement in composite technology. The need for stronger, stiffer, and lighter structures was an opportunity for composite materials to demonstrate their superiority over more commonly used materials. Durability and low maintenance are additional assets. These increase the service life and reduce the cost of maintaining systems. The development of new and the improvement of existing fabrication processes have brought about a reduction in manufacturing cost. There have been reductions in the number of parts required to construct some components by using molding and composite materials. The unique features of composites have enabled designers to formulate advanced systems that could be made only of composite materials. New military aircraft almost exclusively utilize advanced composites for structure. Rocket motor cases, nozzles, and nose cones are missile applications. Radar domes, rotor blades, propellers, and many secondary structure components such as fairings, doors, and access panels are also fabricated from advanced composites. Numerous pressure vessels, armaments, and items of space hardware are made of selected composite materials.

Composite Materials

The use of composite materials will continue to grow. As more engineers come to understand composites, more opportunities will be recognized for their use. As the use of composites increases, more developments will take place in the areas of constituent materials, analysis, design, and fabrication. Composite materials offer tremendous for tailorability, design flexibility, and low-cost processing with low environment impact. These attributes create a very bright future composite materials.

SEE ALSO THE FOLLOWING ARTICLES ADHESION AND ADHESIVES • BIOPOLYMERS • CARBON FIBERS • FRACTURE AND FATIGUE • METAL MATRIX COMPOSITES • POLYMERS, MECHANICAL BEHAVIOR • POLYMERS, THERMALLY STABLE • SANDWICH COMPOSITES

BIBLIOGRAPHY Ashton, J. E., Halpin, J. C., and Petit, P. H. (1969). “Primer on Composite Materials: Analysis,” Technomic Publishing Company, Stamford, CT. Hull, D. (1981). “An Introduction to Compositive Materials,” Cambridge University Press, London. Jones, R. M. (1975). “Mechanics of Composite Materials,” Scripta Book Company, Washington, D.C. Sih, G. C., and Hsu, S. E. (1987). “Advanced Composite Materials and Structures,” 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 Materials,” Technomic Publishing Company, Westport, CT. Whitney, J. M., Daniel, I. M., and Pipes, R. B. (1982). “Experimental Mechanics of Fiber Reinforced Composite Materials,” Society for Experimental Stress Analysis, Brookfield Center, CT. Industry Overview: FRP Materials, Manufacturing Methods and Markets, (1999). Composites Technol. 5, 6–20.