Callister - An introduction - 8th edition

viscosities at ambient temperatures, which is accounted for by strong interatomic
bonding. As the temperature is raised, the magnitude of the bonding is diminished,
the sliding motion or flow of the atoms or ions is facilitated, and subsequently there
is an attendant decrease in viscosity. A discussion of the temperature dependence
of viscosity for glasses is deferred to Section 13.9.
12.11 MISCELLANEOUS MECHANICAL
CONSIDERATIONS
Influence of Porosity
Dependence of
modulus of elasticity
on volume fraction
porosity
12.11 Miscellaneous Mechanical Considerations • 489
As discussed in Sections 13.10 and 13.11, for some ceramic fabrication techniques,
the precursor material is in the form of a powder. Subsequent to compaction or
forming of these powder particles into the desired shape, pores or void spaces will
exist between the powder particles. During the ensuing heat treatment, much of this
porosity will be eliminated; however, often this pore elimination process is incomplete
and some residual porosity will remain (Figure 13.17). Any residual porosity
will have a deleterious influence on both the elastic properties and strength. For
example, for some ceramic materials the magnitude of the modulus of elasticity E
decreases with volume fraction porosity P according to
E E 0 11 1.9P 0.9P 2 2
(12.9)
where E 0 is the modulus of elasticity of the nonporous material. The influence of
volume fraction porosity on the modulus of elasticity for aluminum oxide is shown
in Figure 12.35; the curve represented in the figure is according to Equation 12.9.
Porosity is deleterious to the flexural strength for two reasons: (1) pores reduce
the cross-sectional area across which a load is applied, and (2) they also act as stress
concentrators—for an isolated spherical pore, an applied tensile stress is amplified
by a factor of 2. The influence of porosity on strength is rather dramatic; for example,
400
60
Modulus of elasticity (GPa)
300
200
100
50
40
30
20
10
Modulus of elasticity (10 6 psi)
0
0
0.0 0.2 0.4 0.6 0.8 1.0
Volume fraction porosity
Figure 12.35 The influence of porosity on the modulus of elasticity for aluminum oxide
at room temperature. The curve drawn is according to Equation 12.9. (From R. L. Coble
and W. D. Kingery, “Effect of Porosity on Physical Properties of Sintered Alumina,” J. Am.
Ceram. Soc., 39, 11, Nov. 1956, p. 381. Reprinted by permission of the American Ceramic
Society.)