Page 269 - Materials Science and Engineering An Introduction

7.13 Grain Growth • 241

Atomic diffusion
across boundary

850 C
800 C
1.0
700 C
Grain diameter (mm) (Logarithmic scale) 0.1 600 C

500 C

0.01
1 10 10 2 10 3 10 4
Direction of grain Time (min)
boundary motion (Logarithmic scale)
Figure 7.24 Schematic representation Figure 7.25 The logarithm of grain diameter versus the
of grain growth via atomic diffusion. logarithm of time for grain growth in brass at several
(Adapted from L. H. Van Vlack, Elements of temperatures.
Materials Science and Engineering, 6th edition. © (From J. E. Burke, “Some Factors Affecting the Rate of Grain Growth
1989 by Addison-Wesley Publishing Company, Inc.) in Metals.” Reprinted with permission from Metallurgical Transactions,
Vol. 180, 1949, a publication of The Metallurgical Society of AIME,
Warrendale, Pennsylvania.)

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 recrystalliza-
tion heat treatment, as described previously.

EXAMPLE PROBLEM 7.3

Computation of Grain Size after Heat Treatment
3
When a hypothetical metal having a grain diameter of 8.2 10 mm is heated to 500 C for
12.5 min, the grain diameter increases to 2.7 10 mm. Compute the grain diameter when a
2
specimen of the original material is heated at 500 C for 100 min. Assume the grain diameter
exponent n has a value of 2.
Solution
For this problem, Equation 7.9 becomes
2
d - d 0 = Kt (7.10)
2
It is first necessary to solve for the value of K. This is possible by incorporating the first set of
data from the problem statement—that is,
d 0 8.2 10 mm
3
2
d 2.7 10 mm
t 12.5 min
into the following rearranged form of Equation 7.10:
2 2
d - d 0
K =
t