Page 371 - Materials Science and Engineering An Introduction

9.19 Development of Microstructure in Iron–Carbon Alloys • 343

Solution
(a) This part of the problem is solved by applying the lever rule expressions using a tie
line that extends all the way across the a + Fe 3 C phase field. Thus, C 0 is 0.35 wt% C,
and

6.70 - 0.35
W a = = 0.95
6.70 - 0.022
and

0.35 - 0.022
W Fe 3 C = = 0.05
6.70 - 0.022
(b) The fractions of proeutectoid ferrite and pearlite are determined by using the lever rule
and a tie line that extends only to the eutectoid composition (i.e., Equations 9.20 and 9.21).
We have
0.35 - 0.022
W p = = 0.44
0.76 - 0.022
and

0.76 - 0.35
W a = = 0.56
0.76 - 0.022

(c) All ferrite is either as proeutectoid or eutectoid (in the pearlite). Therefore, the sum of
these two ferrite fractions equals the fraction of total ferrite; that is,

W a + W ae = W a
where W ae denotes the fraction of the total alloy that is eutectoid ferrite. Values for W a and
W a¿ were determined in parts (a) and (b) as 0.95 and 0.56, respectively. Therefore,

W ae = W a - W a = 0.95 - 0.56 = 0.39

Nonequilibrium Cooling
In this discussion of the microstructural development of iron–carbon alloys, it has been
3
assumed that, upon cooling, conditions of metastable equilibrium have been continu-
ously maintained; that is, sufficient time has been allowed at each new temperature for
any necessary adjustment in phase compositions and relative amounts as predicted
from the Fe–Fe 3 C phase diagram. In most situations these cooling rates are impracti-
cally slow and unnecessary; in fact, on many occasions nonequilibrium conditions are
desirable. Two nonequilibrium effects of practical importance are (1) the occurrence of
phase changes or transformations at temperatures other than those predicted by phase
boundary lines on the phase diagram, and (2) the existence at room temperature of
nonequilibrium phases that do not appear on the phase diagram. Both are discussed in
Chapter 10.

3 The term metastable equilibrium is used in this discussion because Fe 3 C is only a metastable compound.