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=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-minp
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-minp
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 θQ+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−1D
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 ×10−12p
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
xEfFf
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,
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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