Industrial Engineering Chapter 10 However The Polymer Extrudate Speed Given Therefore The Linewidth Given Mms And

=3.792 ×107N/m

E

Material E(GPa) d(mm)

Aluminum 70a0.542

Steel 200a0.190

ABS, nylon 1.4 27.1

Polyesters 2.0 19.0

10.81 In Sections 10.5 and 10.6, we listed several plas-

tics and their applications. Rearrange this in-

formation, respectively, by making a table of

products and the type of plastics that can be

Housings Acetals, ABS, polypropylene,

polysulfone, aminos

Low wear Nylon, polyethylene

Guards Cellulosics, polycarbonates

Pipes ABS, cellulosics, polypropylene,

PVC

10.82 Determine the dimensions of a tubular steel

drive shaft for a typical automobile. If you now

replace this shaft with shafts made of unrein-

forced and reinforced plastic, respectively, what

should be the shaft’s new dimensions to trans-

mit the same torque for each case? Choose the

32 D4

The shear stress under pure torsion for a tubu-

lar shaft is given by

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Dip = 0), the required outer diameter of the

ABS shaft is

or

their reinforcement, and describe your observa-

tions.

Material propertya(ave) (ave) %

Acetal UTS 62.5 135 73

E2.45 10.0 75.5

E2.0 10.2 82

Polyprop- UTS 27.5 70 43

10.84 In Example 10.4, what would be the percent-

age of the load supported by the fibers if their

strength is 1250 MPa and the matrix strength

is 240 MPa? What if the strength is unaffected,

but the elastic modulus of the fiber is 600 GPa

Ec= (0.2)(600) + (1 −0.2)(50) = 120 + 40

or Ec= 160 GPa. Also,

Fm

(0.8)(50) =120

40 = 3

or

Ff= 0.75Fc

10.85 Estimate the die clamping force required for

priate length and diameter.

eject. Instead, we will use central sprues with

Arunners = 2(0.25 in.)(10 in) = 5 in2

Note that we have allowed some extra space to

have clearance between the disks. The total

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10.86 A two-liter plastic beverage bottle is made

from a parison with the same diameter as the

threaded neck of the bottle and has a length

As stated in the problem, the parison is a tubu-

lar piece 5 in. long, and its diameter is the same

as the threaded neck of a two-liter bottle, i.e.,

about 11

8in., as measured. Let’s assume that,

The solution requires consideration of the data

given in Fig. 10.12b on p. 597. As an exam-

ple, consider rigid PVC at 190◦C. The following

data is interpolated from the curve:

The plot is constructed from this data as fol-

lows:

10.88 An extruder has a barrel diameter of 100 mm.

The screw rotates at 100 rpm, has a channel

depth of 6 mm, and a flight angle of 17.5◦.

What is the highest flow rate of polypropylene

that can be achieved?

10.89 The extruder in Problem 10.88 has a pumping

section that is 2.5 m long and is used to ex-

trude round polyethylene solid rod. The die

has a land of 1 mm and a diameter of 5 mm.

If the polyethylene is at a mean temperature of

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Q=π2(0.100)2(0.006)(100) sin 17.5◦cos 17.5◦

Q= 0.00849 m3/min

−2.13 ×10−12 m5/N-minp

For this die, the die characteristic is given by

Eq. (10.25) on p. 621, where K is evaluated from

Eq. (10.26) as

K=πD4

d

128ηld

=π(0.005)4

128(80)(0.001)

or K= 1.15 ×10−10 m5/N-min. Therefore, the

die characteristic is given by

Q=Kp =1.15 ×10−10 m5/N-minp

We now have two equations and two unknowns;

0.00833 m3/min.

p= 2.7 MPa.

10.90 An extruder has a barrel diameter of 4 in., a

channel depth of 0.25 in., a flight angle of 18◦,

0.00210 = 3.333 ksi

From Eq. (10.23), the extruder characteristic is

N=2

π2D2Hsin θcos θQ+πDH3sin2θ

12ηl p

or

N=2

π2(4)2(0.25) sin 18◦cos 18◦

×7 + π(4)(0.25)3sin218◦

12 (100 ×10−4) (72)(3333)

or N= 2.45 rev/s, or 147 rpm.

10.91 What flight angle should be used on a screw so

that a flight translates a distance equal to the

barrel diameter with every revolution?

Refer to the following figure:

D

Barrel

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θ= tan−1D

spot with diameter of 0.25 mm, determine the

cure depth and the cured line width in stere-

π

4(0.25 mm)2= 2.04 ×1011 J/m2

For Dp= 100 µm=0.1 mm, Eq. (10.29) on

6.36 ×1010 

= 0.116 mm

or Lw= 0.19 mm. Note that this is smaller

cent lines overlap each other by 10% and the

0.19 mm, the allowable linewidth to incorporate

10 MW = 10 kJ

0.25 mmv

10.94 The extruder head in a fused-deposition-

modeling setup has a diameter of 1 mm (0.04

Note that although the calculations are given

below, in practice, the rapid-prototyping soft-

shape is not easily determined from the infor-

mation given in the problem statement. How-

ever, the polymer extrudate speed is given as 50

= 39.27 mm3/s

include any porosity, and it assumes that ex-

10.95 Using the data for Problem 10.94 and assum-

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=π

4(88 mm)2(6 mm)

+π(88 mm)(100 mm)(6 mm)

Since the support material has a porosity

10.96 What would the answer to Example 10.5 be

n= 0.5? What if n= 0.2?

If the same die characteristic can be used, then

there are two equations and two unknowns.

= 1.94 ×10−5−3.75 ×10−12p

If the same die characteristic can be used, there

(i.e., the stress as a function of time) if a unit

Consider first the simple spring and dashpot

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10.99 Estimate the number of molecules in a typical

automobile tire. Estimate the number of atoms.

Although tires come in a wide variety of sizes,

weight of carbon is 12.011 and that of hydro-

a mole of such mers (or 10 moles of atoms)

fibers made of (a) high-modulus carbon and (b)

Kevlar 29.

20.4 GPa. Using Eq. (10.15),

Ff

=AfEf

=xAEf

=xEf

xEfFf

or

Fc=1 + (1 −x)Em

(0.2)(415) Ff= 1.10Ff

or Ff= 0.91Fc. For the Kevlar fiber-reinforced

(0.2)(62) Ff= 1.65Ff

10.101 Calculate the stress in the fibers and in the ma-

Therefore,

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10.102 Consider a composite consisting of reinforcing

fibers with Ef= 300 GPa. If the allowable fiber

stress is 200 MPa and the matrix strength is 50

MPa, what should be the matrix stiffness so

that the fibers and matrix fail simultaneously?

From Eq. (10.15),

or 200

50 =300

Em

which is solved as Em= 75MP a.

10.103 Assume that you are asked to give a quiz to stu-

dents on the contents of this chapter. Prepare

five quantitative problems and five qualitative

10.104 Make a survey of the recent technical litera-

ture and present data indicating the effects of

10.105 Discuss the design considerations involved in re-

placing a metal beverage container with a con-

tainer made of plastic.

under internal pressure (which typically is on

the order of about 120 psi) or buckling under

in unopened plastic bottles after a certain pe-

riod of time. Other important considerations

By the student. Reinforced plastics are supe-

rior to conventional plastics in terms of strength

10.107 Make a list of products, parts, or components

that are not currently made of plastics, and of-

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10.108 In order to use a steel or aluminum container to

hold an acidic material, such as tomato juice or

7.)

dissolve a thermosetting polymer in a chemical

By the student. This is a challenging topic

and suitable for a technical paper. Consider,

erating temperature should be below the melt-

10.110 Would a composite material with a strong and

stiff matrix and soft and flexible reinforcement

have any practical uses? Explain.

10.111 Make a list of products for which the use of com-

posite materials could be advantageous because

amples: cables, packaging tape, pressure ves-

sels and tubing, tires (steel-belted radials), and

specific strength and specific stiffness are im-

10.113 Describe designs and applications in which

strength in the thickness direction of a com-

posite is important.

10.114 Design and describe a test method to determine

lem, and a literature search will be useful as

a guide to developing appropriate techniques.

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with metal plates, and then pulling the plates

apart by some suitable means. A feasible and

10.115 We have seen that reinforced plastics can be ad-

versely affected by environmental factors, such

10.116 As with other materials, the mechanical prop-

erties of composites are obtained by preparing

appropriate specimens and testing them. Ex-

plain what problems you might encounter in

preparing specimens for testing and in the ac-

10.117 Add a column to Table 10.1, describing the ap-

pearance of these plastics, including available

colors and opaqueness.

10.118 It is possible to weave fibers in three dimen-

sions, and to impregnate the weave with a cur-

the accompanying figure, to give a perspective

to the items listed below.

In general, the following comments can be made

regarding three-dimensional weaves as com-

pared to laminate composites:

easily to allow for changes in the structure

of such a material.

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10.119 Conduct a survey of various sports equipment

and identify the components that are made of

lowing:

10.120 Instead of a having a constant cross section, it

may be possible to make fibers or whiskers with

a varying cross section or a fiber with a wavy

surface. What advantages would such fibers

have?

By the student. Perhaps the most compelling

reason for this approach is associated with the

your thoughts, considering die geometry and

7.5.3). The polymers must have sufficient rigid-

ity, strength, and wear resistance. Considering

these desirable characteristics, the use of plastic

dies is likely to be appropriate and economical

for relatively short production runs, and light

forming forces. The main reason that poly-

mer tooling has become of greater interest is

10.122 For ease of sorting for recycling, all plastic prod–

ucts are now identified with a triangular symbol

with a single-digit number at its center and two

5 Polypropylene

6 Polystyrene

7 Other

10.123 Obtain different kinds of toothpaste tubes,

carefully cut them across with a sharp razor

blade, and comment on your observations re-

technologies to produce ice sculptures. De-

tions:

•A machine based on the principles of

ballistic particle manufacturing (such as

three-dimensional printing) to spray small

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