Page 375 - Materials Science and Engineering An Introduction

Summary • 347

Equation Page
Number Equation Solving For Number

P Mass fraction of eutectic microconstituent for 324
9.10 W e =
P + Q binary eutectic system (per Figure 9.18)

Q Mass fraction of primary a microconstituent for 324
9.11 W a =
P + Q binary eutectic system (per Figure 9.18)
Q + R Mass fraction of total a phase for a binary eutectic 325
9.12 W a =
P + Q + R system (per Figure 9.18)

P Mass fraction of b phase for a binary eutectic 325
9.13 W b =
P + Q + R system (per Figure 9.18)

9.16 P F C N Gibbs phase rule (general form) 330
C 0 - 0.022 For a hypoeutectoid Fe–C alloy, the mass fraction 340
9.20 W r =
0.74 of pearlite (per Figure 9.31)
0.76 - C 0 For a hypoeutectoid Fe–C alloy, the mass fraction 340
9.21 W a =
0.74 of proeutectoid a ferrite phase (per Figure 9.31)
6.70 - C 1 For a hypereutectoid Fe–C alloy, the mass fraction 342
9.22 W p =
5.94 of pearlite (per Figure 9.31)
C 1 - 0.76 For a hypereutectoid Fe–C alloy, the mass fraction 342
9.23 W Fe 3 C’ =
5.94 of proeutectoid Fe 3 C (per Figure 9.31)

List of Symbols
Symbol Meaning

C (Gibbs phase rule) Number of components in a system
C 0 Composition of an alloy (in terms of one of the components)
C 0 Composition of a hypoeutectoid alloy (in weight percent carbon)
C 1 Composition of a hypereutectoid alloy (in weight percent carbon)
F Number of externally controlled variables that must be specified
to completely define the state of a system
N Number of noncompositional variables for a system
P, Q, R Lengths of tie-line segments
P (Gibbs phase rule) Number of phases present in a given system
v a , v b Volumes of a and b phases
r a , r b Densities of a and b phases

Processing/Structure/Properties/Performance Summary
For iron–carbon alloys (i.e., steels), an understanding of microstructures that develop
during relatively slow rates of cooling (i.e., pearlite and a proeutectoid phase) is facili-
tated by the iron–iron carbide phase diagram. Other concepts in this chapter were pre-
sented as a prelude to the introduction of this diagram—the concepts of a phase, phase
equilibrium, metastability, and the eutectoid reaction. In Chapter 10, we explore other
microstructures that form when iron–carbon alloys are cooled from elevated tempera-
tures at more rapid rates. These concepts are summarized in the following concept map: