MM - 305 Dr. Kausar Ali Syed

Polymeric Composite Materials

Composite Materials

A composite material is a materials system composed of a mixture or combination of two or more micro or

macro constituents that differ in form and chemical composition and which are essentially insoluble in each

other. The new material so formed is better suited for a particular application than either of the original

material alone. In other words, composites are structures in which two (or more) materials are combined to

produce a new material whose properties would not be attainable by conventional means. Examples include

plywood, concrete, and steel belted tires.

The most prevalent applications for fiber reinforced composites are structural materials where rigidity,

strength, and low density are important. Many tennis rackets, racing bicycles, and skis are now fabricated

from a carbon fiber-epoxy composite that is strong, light, and only moderately expensive. In this composite,

carbon fibers are embedded in a matrix of epoxy. The carbon fibers are strong and rigid but have limited

ductility. Because of this brittleness, it would not be practical to construct a tennis racket or ski from carbon

alone. The epoxy, which in itself is not very strong, plays two important roles. It acts as a medium to transfer

load to the fibers, and the fiber-matrix interface deflects and stops small cracks, thus making the composite

better able to resist cracks than either of its constituent components.

The strength and rigidity of a composite can be controlled by varying the amount of carbon fiber

incorporated into the epoxy. This ability to tailor properties, combined with the inherent low density of the

composite and its (relative) ease of fabrication, makes this material an extremely attractive alternative for

many applications.

Many composite materials comprise just two phases – the matrix, which is continuous and surrounds the

second phase, often called the dispersed phase or the reinforcement.

The properties of composites are a function of the properties of the constituent phases, their

relative amounts, and the geometry of the dispersed phase.

Composites are often classified according to forms of the reinforcement, particulate, fiber, flake,

and laminar composites. Fiber composites can be further divided into those containing

discontinuous or continuous. One simple scheme for the classification of composite materials is

shown in Figure 1, which consists of three main divisions—

Fig. 1

particle-reinforced, fiber-reinforced, and structural composites; also, at least two subdivisions

exist for each. The dispersed phase for particle-reinforced composites is equiaxed (i.e., particle

dimensions are approximately the same in all directions); for fiber-reinforced composites, the

dispersed phase has the geometry of a fiber (i.e., a large length-to-diameter ratio). Structural

composites are combinations of composites and homogenous materials.

Particle-Reinforced Composites

Large particle and Dispersion strengthened composites are two subclassifications of particle-reinforced

composites. The distinction between these is based upon reinforcement or strengthening mechanism.

Dispersion-strengthened Composites

Particles are normally much smaller having diameters between 0.01 and 0.1 µm (10 and 100 nm). Particle–

matrix interactions that lead to strengthening occur on the atomic or molecular level. Metals and metal alloys

may be strengthened and hardened by the uniform dispersion of several volume percent of fine particles of a

very hard inert material. The dispersed phase may be metallic or nonmetallic; oxide materials are often used.

The mechanism of strengthening is like this that the matrix bears the major portion of an applied load, the

small dispersed particles hinder or impedes the motion of dislocations. Thus, plastic deformation is restricted

such that yield and tensile strengths, as well as hardness, improve but ductility is reduced.

The high-temperature strength of nickel alloys may be enhanced significantly by the addition of about 3 vol

% of thoria (ThO2 ) as finely dispersed particles; this material is known as thoria-dispersed (or TD) nickel.

The same effect is produced in the aluminum -aluminum oxide system. A very thin and adherent alumina

coating is caused to form on the surface of extremely small (0.1 to 0.2 m thick) flakes of aluminum, which

are dispersed within an aluminum metal matrix; this material is termed sintered aluminum powder (SAP).

LARGE-PARTICLE COMPOSITES

In metallic matrices, these larger sized particles act to restrain movement of the matrix phase in the vicinity

of the particle rather than interfere and halt dislocation mobility. The matrix then transmits some of the

applied stress to the reinforcing particles and the degree of reinforcement depends on the strength of the

bonding at the interface between the particle and the matrix.

Particulate composites have been used with all three material types (metals, polymers, and ceramics).

Perhaps the most industrially important particulate composites are cemented carbides that are basically

ceramic-particle metal-matrix combinations. For example titanium carbide (TiC) and/or tungsten carbide

(WC) are embedded in a matrix of nickel cobalt alloy and are extensively used for cutting tools and drill bits.

The very hard carbide particles provide the cutting surface but, because they are brittle cannot withstand the

impact loads and stresses without early fracture and failure. Resistance to fracture is enhanced by their

inclusion in a ductile metal-matrix, which isolates the particles from one another, prevents particle to particle

crack propagation, and thereby increases the toughness, or ability to absorb energy without failure.

Some polymeric materials to which fillers have been added are really large-particle composites. Again, the

fillers modify or improve the properties of the material and/ or replace some of the polymer volume with a

less expensive material —the filler.

An outstanding example of polymeric materials reinforced with particulates to improve overall properties is

that of carbon black in rubber. Our use of many of the modern rubbers would be severely restricted without

carbon black as reinforcing particulate materials. Carbon black consists of very small and essentially

spherical particles of carbon, produced by the combustion of natural gas or oil in an atmosphere that has only

a limited air supply. When added to vulcanized rubber, this extremely inexpensive material enhances tensile

strength, toughness, and tear and abrasion resistance. Automobile tires contain on the order of 15 to 30 vol%

of carbon black. For the carbon black to provide significant reinforcement, the particle size must be

extremely small, with diameters between 20 and 50 nm; also, the particles must be evenly distributed

throughout the rubber and must form a strong adhesive bond with the rubber matrix. Particle reinforcement

using other materials (e.g., silica) is much less effective because this special interaction between the rubber

molecules and particle surfaces does not exist. Figure below is an electron micrograph of a carbon black-

reinforced rubber.

Another familiar large-particle composite is concrete, being composed of cement (the matrix), and sand and

gravel (the particulates). Particles can have quite a variety of geometries, but they should be of approximately

the same dimension in all directions (equiaxed). For effective reinforcement the particles should be small and

evenly distributed throughout the matrix.

Properties are influenced by particle size and distribution as well as by the volume concentration employed,

with stiffness or elastic modulus increasing with increased particulate content (provided of course that the

particulate has a higher elastic modulus than the matrix phase. Two mathematical expressions have been

formulated for the dependence of the elastic modulus on the volume fraction of the constituent phases for a

two-phase composite. These ‘rule of mixtures’ equations predict that the elastic modulus should fall between

an upper bound represented by

Ec = Em Vm + Ep Vp

And a lower value given by

Ec = Em Ep / (Em Vp + Ep Vm)

Where E is the elastic modulus, V is the volume fraction, and the subscripts c, m, and p represent composite,

matrix, and particulate phases, respectively.

Fiber-Reinforced Composites

Technologically, the most important composites are those in which the dispersed phase is in the form of a

fiber. Design goals of fiber-reinforced composites often include high strength and /or stiffness on a weight

basis. These characteristics are expressed in terms of specific strength and specific modulus parameters,

which correspond, respectively, to the ratios of tensile strength to specific gravity and modulus of elasticity

to specific gravity. Fiber-reinforced composites with exceptionally high specific strengths and moduli have

been produced that utilize low-density fiber and matrix materials.

Fiber-reinforced composites were developed in response to the needs of aerospace industry. They were first

developed in 1940s. Fiberglass reinforced plastics were used successfully in many applications, including

filament wound rocket motors. Now inexpensive fiberglass composites are used today in numerous

consumer as well as aerospace products. Current availability of new and stronger fibers with properties

superior to fiberglass has extended the performance range of fiber-reinforced composites, ensuring many

future product developments.

Fiber materials

Almost all high-strength, high elastic modulus materials fail by catastrophic propagation of flaws. A fiber of

such a material, however, displays higher strength because of what is called the size effect. Tensile strength

is basically dependent on a statistical distribution of flaws, with larger forms of the same material having

larger and more frequent flaws. They exhibit lower strength values than smaller cross-sectional forms. In

addition, if equal volumes of fibrous and bulk material are compared, we would find that a crack due to a

broken fiber would not easily propagate to cause the entire assemblage of fibers to fail, but failure would

occur in bulk material from a similar flaw.

On the basis of diameter and character, fibers may be grouped into three different classifications: whiskers,

fibers, and wires. Whiskers are very small diameter single crystals that have large length-to-diameter ratios,

for example, 20-50 µm in length and 0.1-1 µm in diameter. As a consequence of their small size and

synthesis, they have a high degree of perfection for their exceptionally high strengths and, in this form, they

are the strongest known materials. In spite of these high strengths, whiskers are not used extensively as a

reinforcement medium because they are expensive, difficult to orient and classify into uniform diameters and

lengths, difficult to deagglomerate and distribute uniformly in a matrix phase, and difficult to bond to in

many instances. Nonetheless, several applications where they are currently employed involve metal and

ceramic matrices to be described. Whisker materials include carbon (as the graphite structure), aluminum

oxide (also known as sapphire whiskers), silicon carbide, and silicon nitride. Some of their characteristics

are given in Table below.

Materials that are classified as fibers are either polycrystalline or amorphous and have diameters larger

than those of whiskers, that is, about 10 µm, and are produced as continuous filaments and are wound on

spools. These include such compositions as glass, carbon, silicon carbide, aluminum oxide, boron, and

polymer aramids. Two types of SiC are available, one of which results from the processing and controlled

decomposition of polycarbosilane to yield continuous filaments of small diameter, essentially amorphous

SiC. The other process involves the chemically vapor deposition of SiC onto a carbon filament substrate to

yield a fine-grained polycrystalline product approximately 125 µm in diameter and also of continuous length.

The same manufacturer of this larger diameter SiC filament produces boron fiber in a similar cross-sectional

diameter. The boron is chemically vapor deposited onto a moving tungsten filament to provide a continuous

boron fiber. Data for these materials are also provided in Table above.

Glass fibers are produced by drawing monofilaments of glass from a furnace containing molten glass,

coating the monofilaments with a polymer to "dull" any surface cracking, and gathering a large number of

these filaments to form a strand of glass fibers, as depicted in Figure 2. The strands then are used to make

glass fiber yams, or rovings, that consist of a collection of bundles of continuous filaments. Considering the

data of above Table, it can be seen that glass fibers have the lowest elastic modulus, if not the lowest tensile

strength, compared to the other fibers. However, because of their much lower cost and ready availability,

glass fibers are by far the most commonly used reinforcing fibers for plastics.

Fig. 2 Fiberglass forming process

Carbon fibers have a combination of very high strength, low density, and high elastic modulus. These

properties make the use of carbon fiber-plastic composite materials especially attractive for aerospace

applications. Carbon fibers are produced mainly from two sources, polyacrylonitrile (PAN) and pitch, which

are called precursors. In general, carbon fibers are produced from PAN precursor fibers by three processing

stages: (1) stabilization, (2) carbonization, and (3) graphitization. In the stabilization stage, the PAN fibers

are first stretched to align the fibrillar networks within each fiber parallel to the fiber axis. Then they are

oxidized in air at about 200-220°C while held in tension in order to provide cross-linking between the fibrils

to avoid melting at the next stage. In the second stage, carbonization, the cross-linked fibrils are pyrolated

(heated) until they become transformed into carbon fibers by the elimination of O, H, and N from the

precursor fiber. This carbonization treatment is carried out in an inert atmosphere in the range of 1000 -

1500°C. During the carbonization process, graphite like fibrils, or ribbons, are formed within each fiber and

provide the great increase in tensile strength observed. The third stage involves complete conversion of the

fiber to oriented graphite crystal form by heating the fiber while under tension to temperatures above

2000°C. Nitrogen is removed and chains are joined into graphite planes. This graphitization procedure can

raise the elastic modulus to levels exceeding 50 x 106 psi (250 GPa). Carbon fibers produced from PAN

precursor material have tensile strengths that range from about 450 to 650 ksi (3.10 to 4.45 GPa) and elastic

moduli that range from 28 to 50 x 106 psi (193 to 250 GPa). The density of the carbonized and graphitized

PAN fibers is usually about 1.8 g/cm3 with fiber diameters of 7 µm to 10 µm.

Aramid fibers were introduced commercially by the DuPont Corporation in 1972 under the trade name

Kevlar and currently these are available in two commercial types, Kevlar 29 and Kevlar 49. Kevlar 29 is a

low-density, high-strength fiber designed for such applications as ropes, cables, and even ballistic armor. The

properties of Kevlar 49 make its fibers useful as reinforcement for plastics in composites for the aerospace,

marine, and automotive industries as well as many other applications.

Fig. 3 Kevlar polymer chain repeating unit, or mer

The chemical repeating unit of the Kevlar polymer chain is that of an aromatic polyamide as shown in

Figure 3. The aromatic ring structure gives high rigidity to the polymer chains, causing them to have a rod-

like structure. Strong covalent bonding in the polymer chains provides the strength and high elastic modulus

character. Kevlar aramid is used for high-performance composite applications where light weight, high

strength, stiffness, and impact and fatigue resistance are important.

Polymer-Matrix Fiber Reinforced Composites

The purpose of matrix polymers is to bind fibers together by virtue of their adhesive characteristics so that

mechanical loads may be transferred from the weak matrices to the higher strength fibers. In these

composites, binding strength between fibers and matrices must be high to minimize fiber pullout, which

causes premature failure. The matrices can also serve to protect the fibers from handling damage and

environmental degradation, and matrix selection generally determines overall service temperature limitations

of a composite as well as processing conditions during fabrication.

Polyester resins are the most commonly used matrices for fiberglass-base composites. These thermosetting

resins offer a combination of low cost, versatility in many processes, and good property performance.

Even though reinforcement efficiency is lower for discontinuous than for continuous fibers, discontinuous

(short length) fiber composites are becoming important in the commercial market because of lower

processing costs. Chopped glass fibers are used extensively in polyester matrices. These short fiber

composites can be produced to have tensile strengths that approach 50% of their continuous fiber

counterparts.

Continuous and Aligned Fiber Composites

Tensile Stress–Strain Behavior—Longitudinal Loading

Mechanical responses of this type of composite depend on several factors to include the stress–strain

behaviors of fiber and matrix phases, the phase volume fractions, and, in addition, the direction in which the

stress or load is applied. Furthermore, the properties of a composite having its fibers aligned are highly

anisotropic, that is, dependent on the direction in which they are measured. Let us first consider the stress–

strain behavior for the situation wherein the stress is applied along the direction of alignment, the

longitudinal direction, which is indicated in Figure 4a.

Figure 4 Schematic representations of fiber reinforced composites.

(a) continuous and aligned, (b) discontinuous and aligned, and (c) discontinuous and randomly oriented

To begin, assume the stress versus strain behaviors for fiber and matrix phases that are represented

schematically in Figure 5a; in this treatment we consider the fiber to be totally brittle and the matrix phase to

be reasonably ductile. Also indicated in this figure are fracture strengths in tension for fiber and matrix, σ f*

and σm* respectively, and their corresponding fracture strains, εf* and εm*; furthermore, it is assumed that

εm* > εf*, which is normally the case.

Figure 5 (a) Schematic stress–strain curves for brittle fiber and ductile matrix materials. Fracture stresses and strains for both

materials are noted. (b) Schematic stress–strain curve for an aligned fiber-reinforced composite that is exposed to a uniaxial stress

applied in the direction of alignment; curves for the fiber and matrix materials shown in part (a) are also superimposed.

A fiber-reinforced composite consisting of these fiber and matrix materials will exhibit the uniaxial stress

strain response illustrated in Figure 5b; the fiber and matrix behaviors from Figure 5a are included to provide

perspective. In the initial Stage I region, both fibers and matrix deform elastically; normally this portion of

the curve is linear. Typically, for a composite of this type, the matrix yields and deforms plastically (at

Figure 5b) while the fibers continue to stretch elastically, in as much as the tensile strength of the fibers is

significantly higher than the yield strength of the matrix. This process constitutes Stage II as noted in the

figure; this stage is ordinarily very nearly linear, but of diminished slope relative to Stage I. Furthermore, in

passing from Stage I to Stage II, the proportion of the applied load that is borne by the fibers increases.

The onset of composite failure begins as the fibers start to fracture, which corresponds to a strain of

approximately as noted in Figure 5b. Composite failure is not catastrophic for a couple of reasons. First, not

all fibers fracture at the same time, since there will always be considerable variations in the fracture strength

of brittle fiber materials . In addition, even after fiber failure, the matrix is still intact inasmuch as (Figure

5a). Thus, these fractured fibers, which are shorter than the original ones, are still embedded within the intact

matrix, and consequently are capable of sustaining a diminished load as the matrix continues to plastically

deform.

Elastic Behavior—Longitudinal Loading (isostrain)

Let us now consider the elastic behavior of a continuous and oriented fibrous composite that is loaded in the

direction of fiber alignment. First, it is assumed that the fiber–matrix interfacial bond is very good, such that

deformation of both matrix and fibers is the same (an isostrain situation). Under these conditions, the total

load sustained by the composite is equal to the sum of the loads carried by the matrix phase Fm and the fiber

phase Ff , or

Fc = Fm + Ff

From the definition of stress, σ = F / A, and thus expressions for Fc , Fm , and Ff in terms of their

respective stresses (σc, σm, and σf ) and cross-sectional areas ( Ac, Am, and Af ) are possible. Substitution of

these into above Equation yields

σc Ac = σm Am + σf Af

and then, dividing through by the total cross-sectional area of the composite, Ac, we have

σc = σm Am / Ac + σf Af / Ac

where Am / Ac and Af / Ac are the area fractions of the matrix and fiber phases, respectively. If the composite,

matrix, and fiber phase lengths are all equal, Am / Ac is equivalent to the volume fraction of the

matrix, Vm and likewise for the fibers, Vf = Af /Ac.

The above equation now becomes

σc = σm Vm + σf Vf

The previous assumption of an isostrain state means that

εc = εm = εf

and when each term in Equation (σc = σm Vm + σf Vf ) is divided by its respective strain,

σc / εc = σm / εm x Vm + σf / εf x Vf

Furthermore, if composite, matrix, and fiber deformations are all elastic, then σc / εc = Ec, σm / εm =

Em, and σf / εf = Ef. and the E’s being the moduli of elasticity for the respective phases. Substitution into

above Equation yields an expression for the modulus of elasticity of a continuous and aligned fibrous

composite in the direction of alignment (or longitudinal direction), as

Ecl = Em Vm + EfVf

or Ecl = Em ( 1 ─ Vf ) + Ef Vf

since the composite consists of only matrix and fiber phases; that is, Vm + Vf = 1.

Thus, Ecl is equal to the volume-fraction weighted average of the moduli of elasticity of the fiber and matrix

phases. Other properties, including density, also have this dependence on volume fractions.

It can also be shown, for longitudinal loading, that the ratio of the load carried

by the fibers to that carried by the matrix is

Ff / Fm = Ef Vf / Em Vm

Longitudinal Tensile Strength

We now consider the strength characteristics of continuous and aligned fiber-reinforced composites that are

loaded in the longitudinal direction. Under these circumstances, strength is normally taken as the maximum

stress on the stress–strain curve, Figure 5b; often this point corresponds to fiber fracture, and marks the onset

of composite failure.Table below lists typical longitudinal tensile strength values for three common fibrous

composites. Failure of this type of composite material is a relatively complex process, and several different

failure modes are possible. The mode that operates for a specific composite will depend on fiber and matrix

properties, and the nature and strength of the fiber–matrix interfacial bond.

If we assume that εf* < εm* (Figure 7a), which is the usual case, then fibers will fail before the matrix. Once

the fibers have fractured, the majority of the load that was borne by the fibers is now transferred to the

matrix. This being the case, it is possible to adapt the expression for the stress on this type of composite,

Equation σc = σm Vm + σf Vf into the following expression for the longitudinal strength of the

composite. Here σ’m is the stress in the matrix at fiber failure (as illustrated in Figure 5a) and, as previously,

σf* is the fiber tensile strength.

σcl* = σ’m (1 – Vf) + σf*Vf

Case 2: When εm* < εf*, then matrix will fail before the

fibers.

σcl* = σ*m (1 – Vf) + σf’Vf

Here σ’f is the stress in the fiber at matrix failure and σm*

is the matrix tensile strength.

Elastic Behavior—Transverse Loading (Isostress)

A continuous and oriented fiber composite may be loaded in the transverse direction; that is, the load is

applied at a 90º angle to the direction of fiber alignment. For this situation the stress σ to which the

composite as well as both phases are exposed is the same, or

σc = σm = σf = σ

This is termed an isostress state. Also, the strain or deformation of the entire composite εc is

εc = εm Vm + εf Vf

but, since ε = σ / E,

σ / Ect = ( σ / Em) (Vm) + (σ / Ef ) (Vf)

where Ect is the modulus of elasticity in the transverse direction. Now, dividing through by σ yields

1 / Ect = Vm / Em + Vf / Ef

which reduces to

Ec = Em Ep / (Em Vp + Ep Vm)

Above Equation is analogous to the lower-bound expression for particulate composites.

Example Problem

A continuous unidirectionally aligned glass fiber-reinforced composite consists of 45 volume percent of

glass fibers having a modulus of elasticity of 10 x 106 psi (69 x 103 MPa) and 55 volume percent of a

polyester resin that has a modulus of 5 x 105 psi (3.5 x 103 MPa).

a. Compute the modulus of elasticity of this composite in the fiber aligned direction.

b. If the cross-sectional area is 0.5 in.2 (323 mm2) and a stress of 10,000 psi (69 MPa) is

applied in this direction, calculate the load carried by each of the fiber and matrix phases.

c. Determine the strain that is sustained by each phase when the stress in part b is applied.

d. Assuming tensile strengths of 500,000 psi (3.5 x 103 MPa) for glass fibers and 10,000 psi (69

MPa) for polyester resin, determine the tensile strength of this fiber composite in the fiber

aligned direction.

Solution

Basic relations for longitudinally reinforced fiber composites with well-bonded axially aligned fibers are

Ec = EfVf + EmVm

σc = σf Vf + σm Vm

εc = εf =εm

Where E is the elastic modulus, σ is the tensile strength, and ε is the strain. The subscripts c, f, and m

represent composite, fiber, and matrix (polymer), respectively.

a. Ec = 69 X 103 MPa (0.45) + 3.5 x 103 MPa (0.55)

= 33 x 103 MPa or 33 GPa

b. To solve this section of the problem, we must find the ratio of fiber load to matrix load. Since

the strains are equal when stress is applied longitudinally,

εc = εm = εf

Since stress / strain = modulus (σ / ε = E) and load / area = stress (F / A = σ), we have

εc = Fc / (Ac Ec) = Ff / (Af Ef) = Fm / (Am Em)

or Ff / Fm = Ef x Af / Em x Am = Ef x Af / Ac] / Em x Am/ Ac

(If the composite, matrix, and fiber phase lengths are all equal, Am / Ac is equivalent to the volume

fraction of the matrix, Vm and likewise for the fibers, Vf = Af /Ac).

Therefore, Ff / Fm = Ef Vf / Em Vm = 69 GPa x 0.45 / 3.5 GPa x 0.55 = 16.09

Ff = 16.09 Fm

Total force sustained by the composite is Fc = Ac σc

Or Fc = 323 mm2 x 69 MPa = 22,287 N

However this total load is just the sum of the loads carried by fiber and matrix phases; that is

Fc = Fm + Ff

Fc = 16.09 Fm + Fm

17.09 Fm = 22,287 or Fm = 1304 N

Whereas Ff = 22287 ─ 1304 = 20,983 N

Thus the fiber phase supports most of the applied load.

c. The stress for both fiber and matrix phases must first be calculated. Then by using the elastic

modulus for each (from part a), the strain values may be determined. For stress calculations, phase

cross-sectional areas are necessary and for continuous equal length fibers, the volume fraction is

equal to the area, not a real fraction, so that

Am = Vm Ac = 0.55 x 323 = 177.65 mm2

Af = Vf Ac = 0.45 x 323 = 145.35 mm2

Thus σm = Fm / Am = 1304 / 177.65 = 7.34 N/mm2 or 7.34 MPa

σf = Ff / Af = 20983 / 144.35 = 144.36 MPa

Finally strains are calculated

εm = σm / Em = 7.34 / 3.5 x 103 = 0.0021

εf = σf / Ef = 144.36 / 69 x 103 = 0.0021

Therefore, strains for both matrix and fiber phases are identical, which they should be.

d For tensile strength, we have

σc = σm Vm + σf Vf

= 3.5 x 103 x 0.45 + 69 x 0.55 = 1613 MPa

The importance of adding glass fiber to increase strength is clearly shown.

NOTE: In fact for tensile strength of composite, first determine which of the two constituents,

fiber or matrix will fail first. At that strain point then determine the corresponding stress on matrix

or fiber. That value of stress is then used in the rule of mixtures to calculate the tensile strength of

the composite.

Discontinuous parallel fibers

The mechanical characteristics of a fiber-reinforced composite depend not only on the properties of the fiber,

but also on the degree to which an applied load is transmitted to the fibers by the matrix phase. Important to

the extent of this load transmittance is the magnitude of the interfacial bond between the fiber and matrix

phases. Under an applied stress, this fiber–matrix bond ceases at the fiber ends, yielding a matrix

deformation pattern as shown schematically in Figure 4; in other words, there is no load transmittance from

the matrix at each fiber extremity.

Some critical fiber length is necessary for effective strengthening and stiffening of the composite material.

This critical length lc is dependent on the fiber diameter d and its ultimate (or tensile) strength σf* and on the

fiber–matrix bond strength (or the shear yield strength of the matrix, whichever is smaller) according to

lc = σf* d / 2τc (1)

Fig. 8

The deformation pattern in the

matrix surrounding a fiber that is

subjected to an applied tensile load.

For a number of glass and carbon fiber–matrix combinations, this critical length is on the order of 1 mm,

which ranges between 20 and 150 times the fiber diameter.

When a stress equal to is applied to a fiber having just this critical length, the stress–position profile shown

in Figure 5a results; that is, the maximum fiber load is achieved only at the axial center of the fiber. As fiber

length l increases, the fiber reinforcement becomes more effective; this is demonstrated in Figure 5b, a

stress–axial position profile for l > lc when the applied stress is equal to the fiber strength. Figure 5c shows

the stress–position profile for l > lc.

Fibers for which l >> lc (normally l >15lc ) are termed continuous; discontinuous or short fibers have lengths

shorter than this. For discontinuous fibers of lengths significantly less than lc the matrix deforms around the

fiber such that there is virtually no stress transference and little reinforcement by the fiber.

These are essentially the particulate composites as described above. To affect a significant improvement in

strength of the composite, the fibers must be continuous.

Figure 5

Stress–position profiles when fiber

length l

(a) is equal to the critical length

(b) is greater than the critical

length, and

(c) is less than the critical length

for a fiber-reinforced composite

that is subjected to a tensile

stress equal to the fiber tensile

strength sf *.

INFLUENCE OF FIBER ORIENTATION AND CONCENTRATION

The arrangement or orientation of the fibers relative to one another, the fiber concentration, and the

distribution all have a significant influence on the strength and other properties of fiber-reinforced

composites. With respect to orientation, two extremes are possible: (1) a parallel alignment of the

longitudinal axis of the fibers in a single direction, and (2) a totally random alignment. Continuous fibers are

normally aligned (Figure 4a), whereas discontinuous fibers may be aligned (Figure 4b), randomly oriented

(Figure 4c), or partially oriented. Better overall composite properties are realized when the fiber distribution

is uniform.

THE MATRIX PHASE

The matrix phase of fibrous composites may be a metal, polymer, or ceramic. In general, metals and

polymers are used as matrix materials because some ductility is desirable; for ceramic-matrix composites, the

reinforcing component is added to improve fracture toughness. The discussion of this section will focus on

polymer and metal matrices.

For fiber-reinforced composites, the matrix phase serves several functions.

First, it binds the fibers together and acts as the medium by which an externally applied stress is transmitted

and distributed to the fibers; only a very small proportion of an applied load is sustained by the matrix phase.

Furthermore, the matrix material should be ductile. In addition, the elastic modulus of the fiber should be

much higher than that of the matrix.

The second function of the matrix is to protect the individual fibers from surface damage as a result of

mechanical abrasion or chemical reactions with the environment. Such interactions may introduce surface

flaws capable of forming cracks, which may lead to failure at low tensile stress levels.

Finally, the matrix separates the fibers and, by virtue of its relative softness and plasticity, prevents the

propagation of brittle cracks from fiber to fiber, which could result in catastrophic failure; in other words, the

matrix phase serves as a barrier to crack propagation. Even though some of the individual fibers fail, total

composite fracture will not occur until large numbers of adjacent fibers, once having failed, form a cluster of

critical size.

It is essential that adhesive bonding forces between fiber and matrix be high to minimize fiber pull-out. In

fact, bonding strength is an important consideration in the choice of the matrix-fiber combination. The

ultimate strength of the composite depends to a large degree on the magnitude of this bond; adequate

bonding is essential to maximize the stress transmittance from the weak matrix to the strong fibers.

Problems with adhesion to carbon and aramid fibers have discouraged the development of polyester

composites that use these fibers. When property requirements justify the additional costs, epoxies and other

resins are used in high-performance commercial applications such as sporting goods (tennis rackets, fishing

rods), printed circuit boards, and chemical piping. Epoxy resins are used far more than all other matrices in

advanced structural applications. Although epoxies are sensitive to moisture in both their cured and uncured

states, they are generally superior to polyesters in resisting moisture and other environmental influences and

offer better mechanical properties at acceptable cost.

Currently, carbon fiber-reinforced epoxy matrices are the most widely used composites for aerospace

structural and other high-performance applications. The main advantage of carbon fibers is that they have

very high strength coupled with high elastic moduli and low density. Carbon fiber-epoxy matrix composites

have replaced much of the aluminum used in modern aircraft structures where weight reduction is so

important.

In engineering-designed structures, fiber-polymer matrix material is laminated using precast fabric plies of

fibers in desired orientations so that tailor-made strength requirements are met. Figure 9 compares

schematics of unidirectional and multidirectional plies for a composite laminate.

Fibers are oriented along 0°, 90°, and ± 45° directions. The thin sheets called the laminae, can be stacked

together in a regular arrangement to make up the laminate composite. If the fibers are stacked 0° and 90°

directions only, the strength of the composite is high along these directions, but such composites have poor

shear resistance. To obtain good shear resistance, the fibers must also be stacked along the ± 45°

orientations. Such laminates are strong in all directions within the plane containing the fibers but are weak

in the direction perpendicular to the fiber planes.

Figure 9. Unidirectional and multidirectional fabric ply laminate composites. Fibers are oriented

along 0°, 90°, and ± 45° directions.

Although the preceding discussion has centered on single-fiber single-matrix combinations, we should be

aware that fiber-reinforced matrix structures can take many hybrid forms. This is particularly true in the

bonded abrasives industry. Case Study below bears out the importance of selecting the correct composite

structure for the job at hand.

Effort is ongoing to extend the service temperature limit of 120°C for epoxy resin systems by investigating

other formulations. Some high temperature resins possess many of the same desirable features as epoxies,

such as fair handle ability, relative ease of processing, and excellent composite bonding behavior. They are

also superior in extending the safe in-service temperature to about 220°C; however, they have a lower

elongation to failure than epoxies and are quite brittle. Work is still continuing to improve this system.

Polyimide resins are available with a maximum in-service temperature of about 260°C. These thermosetting

resins, unlike the others, normally cure by a condensation reaction that releases volatiles. This creates a

problem because the released volatiles produce undesired voids in the composite. Recent effort has been

directed at reducing this problem by using an addition reaction during curing that does not release volatiles.

Although these resins will produce low void content composite parts, they are also brittle, with poor impact

resistance.

The attempts to improve thermosetting resins continue with major efforts focused on raising temperature

stability and decreasing brittleness, which would improve impact resistance. The dual goal of improving

temperature resistance and impact resistance of composite matrices has led to the development and limited

use of new high-temperature thermoplastic resin matrices. These materials are very different from the well-

known thermoplastics, such as polyethylene, polyvinyl chloride, and polystyrene, that are commonly used

as plastic bags, piping, and tableware and have little resistance to elevated temperature.

These high-temperature thermoplastics are tougher and offer the potential of improved temperature

resistance over epoxies. They also exhibit higher strains to failure that should improve impact resistance.

These materials include such resins as polyetherketone (PEEK), polyphenylene sulfide (PPS), and

polyetherimide (PEl), all of which maintain thermoplastic character after processing. The fabrication pro-

cedures necessary for low-cost manufacture of thermoplastic matrix composites are being thoroughly

investigated and major efforts are concerned with determining and understanding the mechanical properties

and behavior of fabricated composites.

PROCESSING OF FIBER-REINFORCEDCOMPOSITES

To fabricate continuous fiber-reinforced plastics that meet design specifications, the

fibers should be uniformly distributed within the plastic matrix and, in most instances,

all oriented in virtually the same direction. Below several techniques (pultrusion,

filament winding, and prepreg production processes) by which useful products of these

materials are manufactured will be discussed.

PULTRUSION

Pultrusion is used for the manufacture of components having continuous lengths and a constant cross-

sectional shape (i.e., rods, tubes, beams, etc.). With this technique, illustrated schematically in Figure 10,

continuous fiber rovings, or tows are first impregnated with a thermosetting resin; these are then pulled

through a steel die that preforms to the desired shape and also establishes the resin /fiber ratio. The stock

then passes through a curing die that is precision machined so as to impart the final shape; this die is also

heated in order to initiate curing of the resin matrix. A pulling device draws the stock through the dies and

also determines the production speed. Tubes and hollow sections are made possible by using center mandrels

or inserted hollow cores. Principal reinforcements are glass, carbon, and aramid fibers, normally added in

concentrations between 40 and 70 vol%. Commonly used matrix materials include polyesters, vinyl esters,

and epoxy resins.

Figure 10. Schematic diagram showing the pultrusion process

Pultrusion is a continuous process that is easily automated; production rates are relatively high, making it

very cost effective. Furthermore, a wide variety of shapes are possible, and there is really no practical limit to

the length of stock that may be manufactured

PREPREG PRODUCTION PROCESSES

Prepreg is the composite industry’s term for continuous fiber reinforcement preimpregnated with a polymer

resin that is only partially cured. This material is delivered in tape form to the manufacturer, who then

directly molds and fully cures the product without having to add any resin. It is probably the composite

material form most widely used for structural applications.

The prepregging process, represented schematically for thermoset polymers in Figure 11, begins by

collimating a series of spool-wound continuous fiber tows.

Figure 11. Schematic diagram illustrating the production of prepreg tape using thermoset polymers

These tows are then sandwiched and pressed between sheets of release and carrier paper using heated rollers,

a process termed ‘‘calendering.’’ The release paper sheet has been coated with a thin film of heated resin

solution of relatively low viscosity so as to provide for its thorough impregnation of the fibers. A ‘‘doctor

blade’’ spreads the resin into a film of uniform thickness and width. The final prepreg product —the thin

tape consisting of continuous and aligned fibers embedded in a partially cured resin —is prepared for

packaging by winding onto a cardboard core. As shown in Figure 7, the release paper sheet is removed as the

impregnated tape is spooled. Typical tape thicknesses range between 0.08 and 0.25 mm (3x10−3 and 10−2

in.), tape widths range between 25 and 1525 mm (1 and 60 in.), whereas resin content usually lies between

about 35 and 45 vol%.

At room temperature the thermoset matrix undergoes curing reactions; therefore, the prepreg is stored at 0 C

(32 F) or lower. Also, the time in use at room temperature (or ‘‘out-time’’) must be minimized. If properly

handled, thermoset prepregs have a lifetime of at least six months and usually longer.

Both thermoplastic and thermosetting resins are utilized; carbon, glass, and aramid fibers are the common

reinforcements.

Actual fabrication begins with the ‘‘lay-up’’ —laying of the prepreg tape onto a tooled surface. Normally a

number of plies are laid up (after removal from the carrier backing paper) to provide the desired thickness.

The lay-up arrangement may be unidirectional, but more often the fiber orientation is alternated to produce a

cross-ply or angle-ply laminate. Final curing is accomplished by the simultaneous application of heat and

pressure.

The lay-up procedure may be carried out entirely by hand (hand lay-up), wherein the operator both cuts the

lengths of tape and then positions them in the desired orientation on the tooled surface. Alternately, tape

patterns may be machine cut, then hand laid. Fabrication costs can be further reduced by automation of

prepreg lay-up and other manufacturing procedures (e.g., filament winding, as discussed below), which

virtually eliminates the need for hand labor. These automated methods are essential for many applications of

composite materials to be cost effective.

FILAMENT WINDING

Filament winding is a process by which continuous reinforcing fibers are accurately positioned in a

predetermined pattern to form a hollow (usually cylindrical) shape. The fibers, either as individual strands or

as tows, are first fed through a resin bath and then continuously wound onto a mandrel, usually using

automated winding equipment (Figure 12). After the appropriate number of layers have been applied, curing

is carried out either in an oven or at room temperature, after which the mandrel is removed. As an

alternative, narrow and thin prepregs (i.e., tow pregs) 10 mm or less in width may be filament wound.

Various winding patterns are possible (i.e., circumferential, helical, and polar) to give the desired mechanical

characteristics. Filament-wound parts have very high strength-to-weight ratios. Also, a high degree of control

over winding uniformity and orientation is afforded with this technique. Furthermore, when automated, the

process is most economically attractive. Common filament-wound structures include rocket motor casings,

storage tanks and pipes, and pressure vessels.

Manufacturing techniques are now being used to produce a wide variety of structural shapes that are not

necessarily limited to surfaces of revolution (e.g., beams). This technology is advancing very rapidly because

it is very cost effective.

Figure 12.

Schematic representations of helical,

circumferential, and polar filament

winding techniques.