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

GTBL042-08 GTBL042-Callister-v3 October 4, 2007 11:51

2nd Revised Pages

270 • Chapter 8 / Deformation and Strengthening Mechanisms

Time (min)

(Logarithmic scale)

Grain diameter (mm)(Logarithmic scale)

110

850 C

800 C

700 C

600 C

500 C

102 103 104

0.01

0.1

1.0

Figure 8.25 The logarithm of grain diameter versus the logarithm of time for grain growth

in brass at several temperatures. (From J. E. Burke, “Some Factors Affecting the Rate of

Grain Growth in Metals.” Reprinted with permission fromMetallurgical Transactions,Vol.

180, 1949, a publication of The Metallurgical Society of AIME, Warrendale, Pennsylvania.)

For many polycrystalline materials, the grain diameterdvaries with timetac-

cording to the relationship

dn−d 0 n=Kt (8.9)

For grain growth,

dependence of grain

size on time

whered 0 is the initial grain diameter att=0, andKandnare time-independent

constants; the value ofnis generally equal to or greater than 2.

The dependence of grain size on time and temperature is demonstrated in Figure

8.25, a plot of the logarithm of grain size as a function of the logarithm of time for

a brass alloy at several temperatures. At lower temperatures the curves are linear.

Furthermore, grain growth proceeds more rapidly as temperature increases; that

is, the curves are displaced upward to larger grain sizes. This is explained by the

enhancement of diffusion rate with rising temperature.

The mechanical properties at room temperature of a fine-grained metal are usu-

ally superior (i.e., higher strength and toughness) to those of coarse-grained ones.

If the grain structure of a single-phase alloy is coarser than that desired, refinement

may be accomplished by plastically deforming the material, then subjecting it to a

recrystallization heat treatment, as described above.

Deformation Mechanisms

for Ceramic Materials

Although at room temperature most ceramic materials suffer fracture before the

onset of plastic deformation, a brief exploration into the possible mechanisms is

worthwhile. Plastic deformation is different for crystalline and noncrystalline ceram-

ics; however, each is discussed.