Askeland D.R., Fulay P.P. Essentials of Materials Science & Engineering

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SOLUTION

Let us look at the maximum tensile strength and modulus of elasticity for each

polymer.

Polymer

Tensile

Strength

(MPa)

Modulus of

Elasticity

(MPa) Structure

LD polyethylene 21 276 Highly branched, amorphous structure with

symmetrical monomers

HD polyethylene 38 1241 Amorphous structure with symmetrical monomers

but little branching

Polypropylene 41 1517 Amorphous structure with small methyl side groups

Polystyrene 55 3103 Amorphous structure with benzene side groups

Polyvinyl chloride 62 4137 Amorphous structure with large chlorine atoms as

side groups

We can conclude that:

1. Branching, which reduces the density and close packing of chains,

reduces the mechanical properties of polyethylene.

2. Adding atoms or atom groups other than hydrogen to the chain

increases strength and sti¤ness. The methyl group in polypropylene provides

some improvement, the benzene ring of styrene provides higher properties, and

the chlorine atom in polyvinyl chloride provides a large increase in properties.

Creep and Stress Relaxation Thermoplastics also exhibit creep, a time-dependent

permanent deformation with constant stress or load (Figures 16-17 and 16-18).

They also show stress relax ation (i.e., under a constant strain the stress level de-

creases with time) (Chapter 6). Stress relaxation, like creep, is a consequence of the vis-

coelastic behavior of the polymer. Perhaps the most familiar example of this behavior is

a rubber band (an elastomer) stretched around a pile of books. Initially, the tension in

the rubber band is high, when the rubber band is taut. After several weeks, the strain in

the rubber band is unchanged (it still completely encircles the books), but the stress will

have decreased—that is, the band is no longer taut. Similarly, the nylon strings in tennis

rackets are pulled at a higher tension initially since this tension (i.e., stress) decreases

with time.

Applied stress (MPa)

1.4

2.8

4.2

6.9

13.8

27.6

Figure 16-17

The effect of temperature on the

stress-rupture behavior of high-

density polyethylene.

CHAPTER 16 Polymers520

In a simple model, the rate at which stress relaxation occurs is related to the relax-

ation time l, which is considered a property of the polymer (more complex models

consider a distribution of relaxation times). The stress after time t is given by

s ¼ s

expðt=lÞð16-5Þ

where s

is the original stress. The relaxation time, in turn, depends on the viscosity

and, thus, the temperature:

l ¼ l

expðQ=RTÞð16-6Þ

where s

is a constant and Q is the activation energy related to the ease with which

polymer chains slide past each other. Stress relaxation occurs more rapidly at higher

temperatures and for polymers with a low viscosity.

The following example shows how stress relaxation can be accounted for while

designing with polymers.

Figure 16-18

Creep curves for acrylic (PMMA) (colored

lines) and polypropylene (black lines) at



C and several applied stresses.

EXAMPLE 16-9

Design of Initial Stress in a Polymer

A band of polyisoprene is to hold together a bundle of steel rods for up to one

year. If the stress on the band is less than 10 MPa, the band will not hold the

rods tightly. Design the initi al stress that must be applied to a polyisoprene

band when it is slipped over the steel. A series of tests showed that an initial

stress of 7 MPa decreased to 6.8 MPa after six weeks.

SOLUTION

Although the strain of the elastomer band may be constant, the stress will

decrease over time due to stress relaxation. We can use Equation 16-5 and our

initial tests to determine the relaxation time for the polymer:

s ¼ s

exp 



6:8 ¼ 7 exp 



16-7 Mechanical Properties of Thermoplastics 521



¼ ln

6:8



¼ lnð0:97Þ¼0:0305

l ¼

0:0305

¼ 197 weeks

Now that we know the relaxation time, we can determine the stress that must

be initially placed onto the band in order that it still be stressed to 10 MPa

after 1 year (52 weeks).

10 ¼ s

expð52=197Þ¼s

expð0:264Þ¼0:768s

0:768

¼ 13 MPa

The polyisoprene band must be made signiﬁcantly undersized so it can slip

over the materials it is holding together with a tension of 13 MPa. After one

year, the stress will still be 10 MPa.

One more practical measure for high temperature and creep properties of a poly-

mer is the heat deﬂection temperature or heat distortion temperature under load, which is

the temperature at which a given deformation of a beam occurs for a standard load. A

high-heat deﬂection temperature indicates good resistance to creep and permits us to

compare various polymers. The deﬂection temperatures for several polymers are shown

in Table 16-7, which gives the temperature required to cause a 0.025 cm deﬂection for a

1.8 MPa load at the center of a bar resting on supports 10 cm apart. A polymer is

‘‘dishwasher safe’’ if it has a heat distortion temperature greater than @50



TABLE 16-7 9 Deflection temperatures for selected polymers for a

1.8 MPa load

Polymer Deflection Temperature (

Polyester 40

Polyethylene (ultra-high density) 40

Polypropylene 60

Phenolic 80

Polyamide (6,6-nylon) 90

Polystyrene 100

Polyoxymethylene (acetal) 130

Polyamide-imide 280

Epoxy 290

Impact Behavior Viscoelastic behavior also helps us understand the impact properties

of polymers. At very high rates of strain, as in an impact test, there is insu‰cient time

for the chains to slide and cause plastic deformation. For these conditions, the thermo-

plastics behave in a brittle manner and have poor impact values. Polymers may have a

transition temperature. At low temperatures, brittle behavior is observed in an impact

test, whereas more ductile behavior is observed at high temperatures, where the chains

move more easily. These e¤ects of temperature and strain rate are similar to those seen

CHAPTER 16 Polymers522

in metals that exhibit a ductile-to-brittle transition temperature; however, the mecha-

nisms by which ductile to brittle transition occurs are di¤erent.

Deformation of Crystalline Polymers A number of polymers are used in the crys-

talline state. As we discussed earlier, however, the polymers are never completely crys-

talline. Instead, small regions—between crystalline lamellae and between crystalline

spherulites—are amorphous transition regions. Polymer chains in the crystalline region

extend into these amorphous regions as tie chains. When a tensile load is applied to the

polymer, the crystalline lamellae within the spherulites slide past one another and begin

to separate as the tie chains are stretched. The folds in the lamellae tilt and become

aligned with the direction of the tensile load. The crystalline lamellae break into smaller

units and slide past one another, until eventually the polymer is composed of small

aligned crystals joined by tie chains and oriented parallel to the tensile load. The

spherulites also change shape and become elongated in the direction of the applied

stress. With continued stress, the tie chains disentangle or break, causing the polymer to

fail.

Crazing Crazing occurs in thermoplastics when localized regions of plastic deforma-

tion occur in a direction perpendicular to that of the applied stress. In transparent

thermoplastics, such as some of the glassy polymers, the craze produces a translucent or

opaque region that looks like a crack. The craze can grow until it extends across the

entire cross-section of the polymer part. However, the craze is not a crack, and, in fact,

it can continue to support an applied stress. The process is similar to that for the plastic

deformation of the polymer, but the process can proceed even at a low stress over an

extended length of time. Crazing can lead to brittle fracture of the polymer and is often

assisted by the presence of a solvent (known as solvent crazing).

Blushing Blushing or whitening refers to failure of a plastic because of localized crys-

tallization (due to repeated bending, for example) that ultimately causes voids to form.

16-8 Elastomers (Rubbers)

A number of natural and synthetic polymers called elastomers display a large amount

(>200%) of elastic deformation when a force is applied. Rubber bands, automobile

tires, O-rings, hoses, and insulation for electrical wires are common uses for these ma-

terials. Crude natural rubber could erase pencil marks; hence, elastomers got the name

rubber.

Geometric Isomers Some monomers that have di¤erent structures, even though they

have the same composition, are called geometric isomers. Isoprene, or natural rubber,

is an important example (Figure 16-19). The monomer includes two double bonds

between carbon atoms; this type of monomer is called a diene. Polymerization occurs

by breaking both double bonds, creating a new double bond at the center of the mole-

cule and active sites at both ends.

In the trans form of isoprene, the hydrogen atom and the methyl group at the cen-

ter of the repeat unit are located on opposite sides of the newly formed double bond.

This arrangement leads to relatively straight chains; the polymer crystallizes and forms

a hard rigid polymer called gutta percha. This is used to make golf balls and shoe soles.

16-8 Elastomers (Rubbers) 523

In the cis form, however, the hydrogen atom and the methyl group are located on the

same side of the double bond. This di¤erent geometry causes the polymer chains to de-

velop a highly coiled structure, preventing close packing and leading to an amorphous,

rubbery polymer. If a stress is applied to the cis-isoprene, the polymer behaves in a vis-

coelastic manner. The chains uncoil and bonds stretch, producing elastic deforma tion,

but the chains also slide past one another, producing nonrecoverable plastic deforma-

tion. The polymer behaves as a thermoplastic rather than an elastomer (Figure 16-20).

Figure 16-19 The cis and trans structures of isoprene. The cis form is useful for producing the

isoprene elastomer.

Figure 16-20 (a) When the elastomer contains no cross-links, the application of a force causes

both elastic and plastic deformation; after the load is removed, the elastomer is permanently

deformed. (b) When cross-linking occurs, the elastomer still may undergo large elastic

deformation; however, when the load is removed, the elastomer returns to its original shape.

CHAPTER 16 Polymers524

Cross-Linking We prevent viscous plastic deformation while retaining large elastic

deformation by cross-linking the chains. Vulcanization, which uses sulfur atoms, is a

common method for cross-linking. Vulcanization describes how strands of sulfur atoms

can link the polymer chains as the polymer is processed and shaped at temperatures of

about 120 to 180



C (Figure 16-21). The cross-linking steps may include rearranging

a hydrogen atom and replacing one or more of the double bonds with single bonds.

The cross-linking process is not reversible; consequently, the elastomer cannot be re-

cycled easily.

The stress-strain curve for an elastomer is shown in Figure 16-22. Virtually all of

the curve represents elastic deformation; thus, elastomers display a nonlinear elastic

behavior. Initially, the modulus of elasticity decreases because of the uncoiling of the

chains. However, after the chains have been extended, further elastic deformation

occurs by the stretching of the bonds, leading to a higher modulus of elasticity.

The number of cross-links determines the elasticity of the rubber or the amount of

sulfur added to the material. Low sulfur additions leave the rubber soft and ﬂexible, as

in elastic bands or rubber gloves. Increasing the sulfur content restricts the uncoiling of

Figure 16-21

Cross-linking of

polyisoprene chains may

occur by introducing

strands of sulfur atoms.

Sites for attachment of

the sulfur strands occur

by rearrangement or loss

of a hydrogen atom and

the breaking of an

unsaturated bond.

Figure 16-22

The stress-strain curve for an

elastomer. Virtually all of the

deformation is elastic; therefore, the

modulus of elasticity varies as the

strain changes.

16-8 Elastomers (Rubbers) 525

the chains and the rubber becomes harder, more rigid, and brittle (as in rubber used for

motor mounts). Typically, 0.5 to 5% sulfur is added to provide cross-linking in elas-

tomers. Many more e‰cient vulcanizing (EV) systems, which are sulfur free, also have

been developed and used in recent years.

Typical Elastomers Elastomers, which are amorphous polymers, do not easily crys-

tallize during processing. They have a low glass temperature, and chains can easily be

deformed elastically when a force is applied. The typical elastomers (Tables 16-8 and

16-9) meet these requirements. Polyisoprene is a natural rubber. Polychloroprene, or

TABLE 16-8 9 Repeat units and applications for selected elastomers

Polymer Repeat Unit Applications

Polyisoprene Tires, golf balls, shoe

soles

Polybutadiene

(or butadiene

rubber or Buna-S)

Industrial tires, toughening

other elastomers, inner

tubes of tires,

weatherstripping, steam

hoses

Polyisobutylene

(or butyl rubber)

Polychloroprene

(Neoprene)

Hoses, cable sheathing

Butadiene-styrene

(BS or SBR rubber)

Tires

Butadiene-acrylonitrile

(Buna-N)

Gaskets, fuel hoses

Silicones

Gaskets, seals

CHAPTER 16 Polymers526

Neoprene, is a common material for hoses and electrical insulation. Many of the

important synthetic elastomers are copolymers. Polybutadiene (butadiene rubber or

Buna-S) is similar to polyisoprene, but the repeat unit has four carbon atoms consisting

of one double bond. This is a relatively low-cost rubber, though the resistance to sol-

vents is poor. As a result, it is used as a toughening material to make other elastomers.

Butadiene-styrene rubber (BSR or BS), which is also one of the components of ABS

(Figure 16-9), is used for automobile tires. Butyl rubber is di¤erent from polybutadiene

(butadiene rubber). Butyl rubber, or polyisobutadiene, is used to make inner tubes for

tires, vibration mounts, and as weather-stripping material. Silicones are another im-

portant elastomer based on chains composed of silicon and oxygen atoms. Silly Putty

was invented by James Wright of General Electric. It is made using hydroxyl termi-

nated polydimethyl siloxane, boric oxide, and some other additives. At slow strain rates

you can stretch it signiﬁcantly, while if you pull it fast it snaps. The silicone rubbers

(also known as polysiloxanes) provide high-temperature resistance, permitting use of

the elastomer at temperatures as high as 315



C. Low molecular weight silicones form

liquids and are known as silicon oils. Silicones can also be purchased as a two-part

system that can be molded and cured. Chewing gum contains a base that is made from

natural rubber, styrene butadiene, or polyvinyl acetate (PVA).

Thermoplastic Elastomers (TPEs) This is a special group of polymers that do not rely

on cross-linking to produce a large amount of elastic deformation. Figure 16-23 shows

the structure of a styrene-butadiene block copolymer engineered so that the styrene

repeat units are located only at the ends of the chains. Approximately 25% of the chain

is composed of styrene. The styrene ends of several chains form spherical-shaped

domains. The styrene has a high glass temperature; consequently, the domains are

strong and rigid and tightly hold the chains together. Rubbery areas containing buta-

diene repeat units are located between the styrene domains; these portions of the poly-

mer have a glass temperature below room temperature and therefore behave in a soft,

rubbery manner. Elastic deformation occurs by recoverable movement of the chains;

however, sliding of the chains at normal temperatures is prevented by the styrene

domains.

The styrene-butadiene block copolymers di¤er from the BS rubber discussed earlier

in that cross-linking of the butadiene monomers is not necessary and, in fact, is un-

desirable. When the thermoplastic elastomer is heated, the styrene heats above the

glass temperature, the domains are destroyed, and the polymer deforms in a viscous

manner—that is, it behaves as any other thermoplastic, making fabrication very easy.

When the polymer cools, the domains reform and the polymer reverts to its elastomer

TABLE 16-9 9 Properties of selected elastomers

Tensile

Strength

(MPa)

Elongation

Density

(g/cm

)

Polyisoprene 21 800 0.93

Polybutadiene 24 0.94

Polyisobutylene 28 350 0.92

Polychloroprene (Neoprene) 24 800 1.24

Butadiene-styrene (BS or SBR rubber) 21 2000 1.0

Butadiene-acrylonitrile 5 400 1.0

Silicones 7 700 1.5

Thermoplastic elastomers 35 1300 1.06

16-8 Elastomers (Rubbers) 527

characteristics. The thermoplastic elastomers consequently behave as ordinary thermo-

plastics at elevated temperatures and as elastomers at low temperatures. This behavior

also permits the thermoplastic elastomers to be more easily recycled than conventional

elastomers. A useful ﬂuoroelastome r for high temperature and corrosive environments

is Viton

. It is used for seals, O-rings, etc.

16-9 Thermosetting Polymers

Thermosets are highly cross-linked polymer chains that form a three-dimensional

network stru cture. Because the chains cannot rotate or slide, these polymers possess

good strength, sti¤ness, and hardness. However, thermose ts also have poor ductility

and impact properties and a high gl ass temperature. In a tensile test, thermosetting

polymers display the same behavior as a brittle metal or a ceramic.

Thermosetting polymers often begin as linear chains. Depending on the type of

repeat units and the degree of polymerization, the initial polymer may be either a solid

or a liquid resin; in some cases, a two- or three-part liquid resin is used (as in the case of

Figure 16-23 The structure of the styrene-butadiene (SB) copolymer in a thermoplastic

elastomer. The glassy nature of the styrene domains provides elastic behavior without cross-

linking of the butadiene.

CHAPTER 16 Polymers528

the two tubes of epoxy glue that we often use). Heat, pressure, mixing of the various

resins, or other methods initiate the cross-linking process. Cross-linking is not rever-

sible; once formed, the thermosets cannot be reused or recycled conveniently.

The functional groups for a number of common thermosetting polymers are sum-

marized in Table 16-10, and representative properties are given in Table 16-11.

TABLE 16-10 9 Functional units and applications for selected thermosets

Polymer Functional Units Typical Applications

Phenolics Adhesives, coatings, laminates

Amines

Adhesives, cookware, electrical moldings

Polyesters

Electrical moldings, decorative laminates,

polymer matrix in fiberglass

Epoxies

Adhesives, electrical moldings, matrix for

composites

Urethanes

Fibers, coatings, foams, insulation

Silicone

Adhesives, gaskets, sealants

TABLE 16-11 9 Properties of typical thermosetting polymers

Tensile

Strength

(MPa)

Elongation

Elastic

Modulus

(MPa)

Density

(g/cm

)

Phenolics 62 2 9 1.27

Amines 69 1 11 1.50

Polyesters 90 3 5 1.28

Epoxies 103 6 4 1.25

Urethanes 69 6 1.30

Silicone 28 0 8 1.55

16-9 Thermosetting Polymers 529

Askeland D.R., Fulay P.P. Essentials of Materials Science &amp; Engineering

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Askeland D.R., Fulay P.P. Essentials of Materials Science & Engineering