Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-15 GTBL042-Callister-v2 August 29, 2007 8:52

642 • Chapter 15 / Composites

Table 15.6 Elastic Modulus, Density, and Cost Data for Glass and

Various Carbon Fibers, and Epoxy Resin

Elastic Modulus Density Cost

Material (GPa)(g/cm^3 )($US/kg)

Glass fibers 72.5 2.58 2.10

Carbon fibers 230 1.80 60.00

(standard modulus)

Carbon fibers 285 1.80 95.00

(intermediate modulus)

Carbon fibers 400 1.80 250.00

(high modulus)

Epoxy resin 2.4 1.14 6.00

Elastic modulus, density, and cost data for the fiber and matrix materials are

contained in Table 15.6.

Solution

(a)It first becomes necessary to determine the required longitudinal modulus of

elasticity for this composite material, consistent with the stipulated criteria.

This computation necessitates the use of the three-point deflection expression

y=

FL^3

48 EI

(15.21)

in whichyis the midpoint deflection,Fis the applied force,Lis the support

point separation distance,Eis the modulus of elasticity, andIis the cross-

sectional moment of inertia. For a tube having inside and outside diameters

ofdianddo, respectively,

I=

π

64

(

d^4 o−d^4 i

)

(15.22)

and

E=

4 FL^3

3 πy

(

do^4 −di^4

) (15.23)

For this shaft design,

F=1000 N

L= 1 .0m

y= 0 .35 mm

do=70 mm

di=50 mm

Thus, the required longitudinal modulus of elasticity for this shaft is

E=

4(1000 N)(1.0m)^3

3 π(0. 35 × 10 −^3 m)[(70× 10 −^3 m)

4

−(50× 10 −^3 m)

4

]

= 69 .3 GPa (9. 9 × 106 psi)

The next step is to determine the fiber and matrix volume fractions for each

of the four candidate fiber materials. This is possible using the rule-of-mixtures