Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 12.15, Problem 40AAP

A unidirectional carbon fiber–epoxy resin composite contains 68% by volume of carbon fiber and 32% epoxy resin. The density of the carbon fiber is 1.79 g/cm3 and that of the epoxy resin is 1.20 g/cm3. (a) What are the weight percentages of carbon fibers and epoxy resin in the composite? (b) What is the average density of the composite?

(a)

Expert Solution
Check Mark
To determine

The weight percentage of carbon fibers in the composite.

The weight percentage of epoxy resin in the composite.

Answer to Problem 40AAP

The weight percentage of carbon fibers in the composite is 76%.

The weight percentage of epoxy resin in the composite is 24%.

Explanation of Solution

Write the expression to calculate mass of carbon fiber in the composite (mcf).

 mcf=ρcfVcf                                                                                                               (I)

Here, density of carbon fiber is ρcf and volume fraction of carbon fiber is Vcf.

Write the expression to calculate mass of epoxy resin in the composite (mer).

 mer=ρerVer                                                                                                             (II)

Here, density of epoxy resin is ρer and volume fraction of epoxy resin is Ver.

Write the expression to calculate total mass of the composite (m).

 m=mcf+mer                                                                                                          (III)

Here, density of epoxy resin is ρer and volume fraction of epoxy resin is Ver.

Write the expression to calculate weight percentage of carbon fiber in the composite (%Wcf).

 %Wcf=mcfm×100%                                                                                               (IV)

Write the expression to calculate weight percentage of epoxy resin in the composite (%Wer).

 %Wer=merm×100%                                                                                                 (V)

Conclusion:

Substitute 1.79g/cm3 for ρcf and 0.68 for Vcf in Equation (I).

 mcf=(1.79g/cm3)(0.68)=1.217g

Substitute 1.20g/cm3 for ρer and 0.32 for Ver in Equation (II).

 mer=(1.20g/cm3)(0.32)=0.384g

Substitute 1.217g for mcf and 0.384g for mer in Equation (III).

 m=1.217g+0.384g=1.601g

Substitute 1.217g for mcf and 1.601g for m in Equation (IV).

 %Wcf=1.217g1.601g×100%=76%

Substitute 0.384g for mer and 1.601g for m in Equation (V).

 %Wer=0.384g1.601g×100%=24%

Thus, the weight percentage of carbon fibers in the composite is 76% and the weight percentage of epoxy resin in the composite is 24%.

(b)

Expert Solution
Check Mark
To determine

The average density of the composite.

Answer to Problem 40AAP

The average density of the composite is 1.601g/cm3.

Explanation of Solution

Write the expression to calculate average density of the composite (ρc).

 ρc=mV                                                                                                                   (VI)

Here, total volume of composite is V.

Conclusion:

Substitute 1.601g for m and 1cm3 for V in Equation (I).

 ρc=1.601g1cm3=1.601g/cm3

Thus, the average density of the composite is 1.601g/cm3.

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Chapter 12 Solutions

Foundations of Materials Science and Engineering

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