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Materials Science and Engineering. An Introduction

William D. Callister

Chapter 16

Composites - all with Video Answers

Educators

Chapter Questions

01:00

Problem 1

The mechanical properties of cobalt may be improved by incorporating fine particles of tungsten carbide (WC). Given that the moduli of elasticity of these materials are, respectively, $200 \mathrm{GPa}\left(30 \times 10^6 \mathrm{psi}\right)$ and 700 GPa $\left(102 \times 10^6 \mathrm{psi}\right)$, plot modulus of elasticity versus the volume percent of WC in Co from 0 to $100 \mathrm{vol} \%$, using both upper- and lowerbound expressions.

Manik Pulyani
Manik Pulyani
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01:19

Problem 2

Estimate the maximum and minimum thermal conductivity values for a cermet that contains $90 \mathrm{vol} \%$ titanium carbide (TiC) particles in a nickel matrix. Assume thermal conductivities of 27 and $67 \mathrm{~W} / \mathrm{m}-\mathrm{K}$ for TiC and Ni , respectively.

Manik Pulyani
Manik Pulyani
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01:15

Problem 3

A large-particle composite consisting of tungsten particles within a copper matrix is to be prepared. If the volume fractions of tungsten and copper are 0.70 and 0.30 , respectively, estimate the upper limit for the specific stiffness of this composite given the data that follow.
$$
\begin{array}{lcc}
\hline & \begin{array}{c}
\text { Specific } \\
\text { Gravity }
\end{array} & \begin{array}{c}
\text { Modulus of } \\
\text { Elasticity (GPa) }
\end{array} \\
\hline \text { Copper } & 8.9 & 110 \\
\text { Tungsten } & 19.3 & 407 \\
\hline
\end{array}
$$

Manik Pulyani
Manik Pulyani
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01:42

Problem 4

(a) What is the distinction between cement and concrete?
(b) Cite three important limitations that restrict the use of concrete as a structural material.
(c) Briefly explain three techniques that are utilized to strengthen concrete by reinforcement.

Hunza Gilgit
Hunza Gilgit
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01:24

Problem 5

Cite one similarity and two differences between precipitation hardening and dispersion strengthening.

Hunza Gilgit
Hunza Gilgit
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00:56

Problem 6

For some glass fiber-epoxy matrix combination, the critical fiber length-fiber diameter ratio is 40 . Using the data in Table 16.4, determine the fiber-matrix bond strength.

Manik Pulyani
Manik Pulyani
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01:45

Problem 7

(a) For a fiber-reinforced composite, the efficiency of reinforcement $\eta$ is dependent on fiber length $l$ according to

$$
\eta=\frac{l-2 x}{l}
$$

where $x$ represents the length of the fiber at each end that does not contribute to the load transfer. Make a plot of $\eta$ versus $l$ to $l=50$ mm ( 2.0 in .) assuming that $x=1.25 \mathrm{~mm}$ ( 0.05 in.$)$.
(b) What length is required for a 0.90 efficiency of reinforcement?

Manik Pulyani
Manik Pulyani
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00:56

Problem 8

A continuous and aligned fiber-reinforced composite is to be produced consisting of $45 \mathrm{vol} \%$ aramid fibers and $55 \mathrm{vol} \%$ of a polycarbonate matrix; mechanical characteristics of these two materials are as follows:
$$
\begin{array}{lcc}
\hline & \begin{array}{c}
\text { Modulus } \\
\text { of Elasticity } \\
{[\text { GPa }(\boldsymbol{p s i})]}
\end{array} & \begin{array}{c}
\text { Tensile } \\
\text { Strength } \\
{[\boldsymbol{M P a}(\boldsymbol{p s i})]}
\end{array} \\
\hline \text { Aramid fiber } & 131\left(19 \times 10^6\right) & 3600(520,000) \\
\text { Polycarbonate } & 2.4\left(3.5 \times 10^5\right) & 65(9425) \\
\hline
\end{array}
$$
Also, the stress on the polycarbonate matrix when the aramid fibers fail is 35 MPa ( 5075 psi ).
For this composite, compute
(a) the longitudinal tensile strength, and
(b) the longitudinal modulus of elasticity

Manik Pulyani
Manik Pulyani
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01:37

Problem 9

Is it possible to produce a continuous and oriented aramid fiber-epoxy matrix composite having longitudinal and transverse moduli of elasticity of $35 \mathrm{GPa}\left(5 \times 10^6 \mathrm{psi}\right)$ and $5.17 \mathrm{GPa}\left(7.5 \times 10^5 \mathrm{psi}\right)$, respectively? Why or why not? Assume that the elastic modulus of the epoxy is $3.4 \mathrm{GPa}\left(4.93 \times 10^5\right.$ psi ).

Penny Riley
Penny Riley
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01:26

Problem 10

For a continuous and oriented fiberreinforced composite, the moduli of elasticity in the longitudinal and transverse directions are 33.1 and $3.66 \mathrm{GPa}\left(4.8 \times 10^6\right.$ and $5.3 \times 10^5 \mathrm{psi}$, respectively. If the volume fraction of fibers is 0.30 , determine the moduli of elasticity of fiber and matrix phases.

Manik Pulyani
Manik Pulyani
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02:01

Problem 11

(a) Verify that Equation 16.11, the expression for the fiber load-matrix load ratio $\left(F_f / F_m\right)$, is valid.
(b) What is the $F_f / F_c$ ratio in terms of $E_f, E_m$, and $V_f$ ?

Manik Pulyani
Manik Pulyani
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01:41

Problem 12

In an aligned and continuous carbon fiberreinforced nylon 6,6 composite, the fibers are to carry $97 \%$ of a load applied in the longitudinal direction.
(a) Using the data provided, determine the volume fraction of fibers that will be required.
(b) What will be the tensile strength of this composite? Assume that the matrix stress at fiber failure is $50 \mathrm{MPa}(7250 \mathrm{psi})$.
$$
\begin{array}{lcc}
\hline & \begin{array}{c}
\text { Modulus } \\
\text { of } \text { Elasticity } \\
{[\text { GPa }(\text { psi } i)]}
\end{array} & \begin{array}{c}
\text { Tensile } \\
\text { Strength } \\
{[\text { MPa }(\text { psi })]}
\end{array} \\
\hline \text { Carbon fiber } & 260\left(37 \times 10^6\right) & 4000(580,000) \\
\text { Nylon } 6,6 & 2.8\left(4.0 \times 10^5\right) & 76(11,000) \\
\hline
\end{array}
$$

Manik Pulyani
Manik Pulyani
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01:12

Problem 13

Assume that the composite described in Problem 16.8 has a cross-sectional area of $480 \mathrm{~mm}^2\left(0.75 \mathrm{in}^2\right)$ and is subjected to a longitudinal load of $53,400 \mathrm{~N}\left(12,000 \mathrm{lb}_{\mathrm{f}}\right)$.
(a) Calculate the fiber-matrix load ratio.
(b) Calculate the actual loads carried by both fiber and matrix phases.
(c) Compute the magnitude of the stress on each of the fiber and matrix phases.
(d) What strain is experienced by the composite?

Dominador Tan
Dominador Tan
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01:39

Problem 14

A continuous and aligned fibrous reinforced composite having a cross-sectional area of $970 \mathrm{~mm}^2\left(1.5 \mathrm{in}^2\right.$ ) is subjected to an external tensile load. If the stresses sustained by the fiber and matrix phases are 215 MPa ( $31,300 \mathrm{psi}$ ) and 5.38 MPa ( 780 psi ), respectively, the force sustained by the fiber phase is $76,800 \mathrm{~N}\left(17,265 \mathrm{lb}_{\mathrm{f}}\right)$, and the total longitudinal composite strain is $1.56 \times 10^{-3}$, then determine
(a) the force sustained by the matrix phase
(b) the modulus of elasticity of the composite material in the longitudinal direction, and
(c) the moduli of elasticity for fiber and matrix phases.

Manik Pulyani
Manik Pulyani
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01:31

Problem 15

Compute the longitudinal strength of an aligned carbon fiber-epoxy matrix composite having a 0.20 volume fraction of fibers, assuming the following: (1) an average fiber diameter of $6 \times 10^{-3} \mathrm{~mm}\left(2.4 \times 10^{-4} \mathrm{in}\right.$.), (2) an average fiber length of $8.0 \mathrm{~mm}(0.31 \mathrm{in}$.$) ,$ (3) a fiber fracture strength of 4.5 GPa $\left(6.5 \times 10^5 \mathrm{psi}\right.$ ), (4) a fiber-matrix bond strength of $75 \mathrm{MPa}(10,900 \mathrm{psi}),(5)$ a matrix stress at composite failure of $6.0 \mathrm{MPa}(870 \mathrm{psi})$,
and (6) a matrix tensile strength of 60 MPa ( $8,700 \mathrm{psi}$ ).

Manik Pulyani
Manik Pulyani
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01:05

Problem 16

It is desired to produce an aligned carbon fiber-epoxy matrix composite having a longitudinal tensile strength of $500 \mathrm{MPa}(72,500$ psi ). Calculate the volume fraction of fibers necessary if (1) the average fiber diameter and length are $0.01 \mathrm{~mm}\left(3.9 \times 10^{-4} \mathrm{in}\right.$.) and 0.5 mm ( $2 \times 10^{-2} \mathrm{in}$.), respectively; (2) the fiber fracture strength is $4.0 \mathrm{GPa}\left(5.8 \times 10^5\right.$ psi ); (3) the fiber-matrix bond strength is 25 MPa ( 3625 psi ); and (4) the matrix stress at composite failure is $7.0 \mathrm{MPa}(1,000 \mathrm{psi})$.

Manik Pulyani
Manik Pulyani
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01:07

Problem 17

Compute the longitudinal tensile strength of an aligned glass fiber-epoxy matrix composite in which the average fiber diameter and length are $0.015 \mathrm{~mm}\left(5.9 \times 10^{-4} \mathrm{in}\right.$.) and $2.0 \mathrm{~mm}(0.08 \mathrm{in}$.$) , respectively, and$ the volume fraction of fibers is 0.25 . Assume that (1) the fiber-matrix bond strength is $100 \mathrm{MPa}(14,500 \mathrm{psi})$, (2) the fracture strength of the fibers is $3500 \mathrm{MPa}\left(5 \times 10^5 \mathrm{psi}\right)$, and (3) the matrix stress at composite failure is $5.5 \mathrm{MPa}(800 \mathrm{psi})$.

Manik Pulyani
Manik Pulyani
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01:30

Problem 18

(a) From the moduli of elasticity data in Table 16.2 for glass fiber-reinforced polycarbonate composites, determine the value of the fiber efficiency parameter for each of 20 , 30 , and $40 \mathrm{vol} \%$ fibers.
(b) Estimate the modulus of elasticity for $50 \mathrm{vol} \%$ glass fibers.

Manik Pulyani
Manik Pulyani
Numerade Educator
01:41

Problem 19

For a polymer-matrix fiber-reinforced composite,
(a) List three functions of the matrix phase.
(b) Compare the desired mechanical characteristics of matrix and fiber phases.
(c) Cite two reasons why there must be a strong bond between fiber and matrix at their interface.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
00:53

Problem 20

(a) What is the distinction between matrix and dispersed phases in a composite material?
(b) Contrast the mechanical characteristics of matrix and dispersed phases for fiberreinforced composites.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:32

Problem 21

(a) Calculate and compare the specific longitudinal strengths of the glass-fiber, carbonfiber, and aramid-fiber reinforced epoxy composites in Table 16.5 with the following alloys: cold-rolled $17-7 \mathrm{PH}$ stainless steel, normalized 1040 plain-carbon steel, 7075-T6 aluminum alloy, cold-worked (H04 temper) C26000 cartridge brass, extruded AZ31B magnesium alloy, and annealed Ti-5Al-2.5Sn titanium alloy.
(b) Compare the specific moduli of the same three fiber-reinforced epoxy composites with the same metal alloys. Densities (i.e., specific gravities), tensile strengths, and moduli of elasticity for these metal alloys may be found in Tables B.1, B.4, and B.2, respectively, in Appendix B.

Manik Pulyani
Manik Pulyani
Numerade Educator
01:11

Problem 22

(a) List four reasons why glass fibers are most commonly used for reinforcement.
(b) Why is the surface perfection of glass fibers so important?
(c) What measures are taken to protect the surface of glass fibers?

Hunza Gilgit
Hunza Gilgit
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01:02

Problem 23

Cite the distinction between carbon and graphite.

Hunza Gilgit
Hunza Gilgit
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01:11

Problem 24

(a) Cite several reasons why fiberglassreinforced composites are utilized extensively.
(b) Cite several limitations of this type of composite.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:10

Problem 25

(a) What is a hybrid composite?
(b) List two important advantages of hybrid composites over normal fiber composites.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:50

Problem 26

(a) Write an expression for the modulus of elasticity for a hybrid composite in which all fibers of both types are oriented in the same direction.
(b) Using this expression, compute the longitudinal modulus of elasticity of a hybrid composite consisting of aramid and glass fibers in volume fractions of 0.25 and 0.35 , respectively, within a polyester resin matrix $\left[E_m=4.0 \mathrm{GPa}\left(6 \times 10^5 \mathrm{psi}\right)\right]$.

Manik Pulyani
Manik Pulyani
Numerade Educator
01:28

Problem 27

Derive a generalized expression analogous to Equation 16.16 for the transverse modulus of elasticity of an aligned hybrid composite consisting of two types of continuous fibers.

Manik Pulyani
Manik Pulyani
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Problem 28

Briefly describe pultrusion, filament winding, and prepreg production fabrication processes; cite the advantages and disadvantages of each.

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00:54

Problem 29

Briefly describe laminar composites. What is the prime reason for fabricating these materials?

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:31

Problem 30

(a) Briefly describe sandwich panels.
(b) What is the prime reason for fabricating these structural composites?
(c) What are the functions of the faces and the core?

Hunza Gilgit
Hunza Gilgit
Numerade Educator