CHAPTER
10
Kinetics—Heat
Treatment
The microstructure of a rapidly cooled “eutectic” soft solder ( ≈ 38 wt % Pb − 62 wt %
Sn) consists of globules of lead-rich solid solution (dark) in a matrix of tin-rich solid solution (white), 375X. The contrast to the slowlycooled microstructure at the opening of Chapter 9 illustrates the effect of time on microstructural development. (From ASM Handbook,
Vol. 3: Alloy Phase Diagrams, ASM International, Materials Park, Ohio, 1992.)
T
Completion of reaction
T
t
Tmp
t
x
(a)
(b)
Figure 10-1 Schematic illustration of the approach to equilibrium. (a) The time for solidification to go to completion is a strong function of temperature, with the minimum time
occurring for a temperature considerably below the melting point. (b) The temperature–
time plane with “transformation curve.” We shall see later that the time axis is often plotted on a logarithmic scale.
Liquid
Solid
(a)
(b)
Crystal
growth
Crystal
nucleus
(c)
(d)
Figure 10-2 (a) On a microscopic scale, a solid precipitate in a liquid matrix. The precipitation process is seen on the atomic scale as (b) a clustering of adjacent atoms to
form (c) a crystalline nucleus followed by (d) the growth of the crystalline phase.
Surface energy addition
Net energy change
+
Net energy change
0
r
rc
–
Volume energy reduction
Figure 10-3 Classical nucleation theory involves an energy balance
between the nucleus and its surrounding liquid. A nucleus (cluster of atoms) as shown in Figure 10–2(c) will be stable only if
further growth reduces the net energy of the system. An ideally
spherical nucleus will be stable if its radius, r , is greater than a
critical value, rc .
Temperature, T
Tm
Contribution of diffusion (clustering of atoms)
Net nucleation rate (= product of two dashed lines)
Contribution of liquid phase instability
Nucleation rate, N (s–1)
Figure 10-4 The rate of nucleation is a product of two curves that represent two
opposing factors (instability and diffusivity).
Temperature, T
Tm
G
N
Overall transformation rate
Rate, (s–1)
Figure 10-5 The overall transformation rate is the product of the nucleation
rate Ṅ (from Figure 10–4) and the growth rate Ġ (given by Equation 10.1).
Temperature, T
Tmp
1
50
100
% completion of reaction
Curve shown in Figure 10-1
Time, t (logarithmic scale)
Figure 10-6 A time–temperature–transformation diagram for the solidification reaction of Figure 10–1 with various percent completion curves illustrated.
˚C
800
727˚
700
Coarse pearlite
600
500
Fine pearlite
400
Bainite
300
200
100
1 sec
0
0.1
1
1 hour
1 min
10
102
Time, seconds
103
1 day
104
105
0
0.77
wt % C
Figure 10-7 TTT diagram for eutectoid steel shown in relation to the Fe–Fe 3 C phase
diagram (see Figure 9–39). This shows that, for certain transformation temperatures, bainite rather than pearlite is formed. In general, the transformed microstructure is increasingly fine-grained as the transformation temperature is decreased. Nucleation rate increases and diffusivity decreases as temperature decreases. The solid
curve on the left represents the onset of transformation ( ∼ 1% completion). The
dashed curve represents 50% completion. The solid curve on the right represents
the effective ( ∼ 99%) completion of transformation. This convention is used in
subsequent TTT diagrams. (TTT diagram after Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, Metals
Park, Ohio, 1977.)
Temperature
Coarse pearlite
Time (logarithmic scale)
Figure 10-8 A slow cooling path that leads to coarse pearlite formation is superimposed
on the TTT diagram for eutectoid steel. This type of thermal history was assumed,
in general, throughout Chapter 9.
Figure 10-9 The microstructure of bainite involves extremely fine
needles of α -Fe and Fe 3 C, in contrast to the lamellar structure
of pearlite (see Figure 9–2), 535 × . (From Metals Handbook,
8th Ed., Vol. 7: Atlas of Microstructures, American Society
for Metals, Metals Park, Ohio, 1972.)
Temperature
Coarse pearlite
Coarse pearlite remains upon cooling
Time (logarithmic scale)
Figure 10-10 The interpretation of TTT diagrams requires consideration
of the thermal history “path.” For example, coarse pearlite, once formed,
remains stable upon cooling. The finer-grain structures are less stable
because of the energy associated with the grain boundary area. (By
contrast, phase diagrams represent equilibrium and identify stable phases
independent of the path used to reach a given state point.)
˚C
800
727˚
700
Coarse pearlite
600
500
Fine pearlite
400
Bainite
300
Ms
200
M50
M90
100
1 sec
0
0.1
1
1 min
10
102
Time, seconds
1 hour
103
1 day
104
105
0
0.77
wt % C
Figure 10-11 A more complete TTT diagram for eutectoid steel than was given
in Figure 10–7. The various stages of the time-independent (or diffusionless) martensitic transformation are shown as horizontal lines. Ms represents the start, M50 50% transformation, and M90 90% transformation. One
hundred percent transformation to martensite is not complete until a final
temperature ( Mf ) of − 46 ◦ C.
a0
c
a
a0|! 2
(a)
(b)
Figure 10-12 For steels, the martensitic transformation involves the sudden reorientation of C and Fe atoms from
the fcc solid solution of γ -Fe (austenite) to a body-centered tetragonal (bct) solid solution (martensite). In (a),
the bct unit cell is shown relative to the fcc lattice by the h 100 iα axes. In (b), the bct unit cell is shown before (left)
and after (right) the transformation. The open circles represent iron atoms. The solid circle represents an interstitially dissolved carbon atom. This illustration of the martensitic transformation was first presented by Bain in
1924, and while subsequent study has refined the details of the transformation mechanism, this remains a useful
and popular schematic. (After J. W. Christian, in Principles of Heat Treatment of Steel, G. Krauss, Ed., American Society for Metals, Metals Park, Ohio, 1980.)
Figure 10-13 Acicular, or needlelike, microstructure of martensite 1000 × . (From
Metals Handbook, 8th Ed., Vol. 7: Atlas of Microstructures, American Society for Metals, Metals Park, Ohio, 1972.)
˚C
800
727˚
700
2
1
Continuous cooling
transformation
3
Isothermal
transformation
600
500
1
Rapid cooling rate
400
2
Moderate cooling rate
3
Slow cooling rate
300
Ms
200
M50
M90
100
1 sec
0
0.1
1
1 min
10
102
Time, seconds
1 hour
103
1 day
104
105
Figure 10-14 A continuous cooling transformation (CCT) diagram is shown superimposed
on the isothermal transformation diagram of Figure 10–11. The general effect of continuous cooling is to shift the transformation curves downward and toward the right. (After
Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American
Society for Metals, Metals Park, Ohio, 1977.)
˚C
900
880˚
800
727˚
700
600
500
400
300
200
Ms
M50
100
1 sec
M90
1 min
1 hour
1 day
0
0.1
1
10
102
Time, seconds
103
104
105
0
1.13
wt % C
Figure 10-15 TTT diagram for a hypereutectoid composition (1.13 wt % C) compared
to the Fe–Fe 3 C phase diagram. Microstructural development for the slow cooling
of this alloy was shown in Figure 9–40. (TTT diagram after Atlas of Isothermal
Transformation and Cooling Transformation Diagrams, American Society for Metals, Metals Park, Ohio, 1977.)
˚C
900
800
770˚
727˚
700
600
500
400
Ms
300
M50
M90
200
100
1 sec
0.1
1
1 min
10
102
Time, seconds
1 hour
103
1 day
104
105
0
0.5
wt % C
Figure 10-16 TTT diagram for a hypoeutectoid composition (0.5 wt % C)
compared to the Fe–Fe 3 C phase diagram. Microstructural development
for the slow cooling of this alloy was shown in Figure 9–41. By comparing Figures 10–11, 10–15, and 10–16, one will note that the martensitic
transformation occurs at decreasing temperatures with increasing carbon content in the region of the eutectoid composition. (TTT diagrams
after Atlas of Isothermal Transformation and Cooling Transformation
Diagrams, American Society for Metals, Metals Park, Ohio, 1977.)
Temperature
Thermal history for center of part being heat-treated
Thermal history for surface of part being heat-treated
Tempering temperature
Ms
Transformation
Mf
Tempered martensite
Martensite
Time (logarithmic scale)
Figure 10-17 Tempering is a thermal history [ T = f n(t) ] in which martensite, formed by quenching austenite, is reheated. The resulting tempered
martensite consists of the equilibrium phase of α -Fe and Fe 3 C but in a microstructure different from both pearlite and bainite (note Figure 10–18).
(After Metals Handbook, 8th Ed., Vol. 2, American Society for Metals,
Metals Park, Ohio, 1964. It should be noted that the TTT diagram is, for
simplicity, that of eutectoid steel. As a practical matter, tempering is generally done in steels with slower diffusional reactions permitting less severe
quenches.)
Figure 10-18 The microstructure of tempered martensite, although
an equilibrium mixture of α -Fe and Fe 3 C, differs from those
for pearlite (Figure 9–2) and bainite (Figure 10–9), 825 × . This
particular microstructure is for a 0.50 wt % C steel comparable
with that described for Figure 10–16. (From Metals Handbook,
8th Ed., Vol. 7: Atlas of Microstructures, American Society for
Metals, Metals Park, Ohio, 1972.)
Temperature
Surface
Center
Tempering temperature
Transformation
Martensite
Tempered martensite
Time (logarithmic scale)
Figure 10-19 In martempering, the quench is stopped just above Ms . Slow cooling through the martensitic transformation range reduces stresses associated with the crystallographic change. The final reheat step is equivalent to
that in conventional tempering. (After Metals Handbook, 8th Ed., Vol. 2,
American Society for Metals, Metals Park, Ohio, 1964.)
Temperature
Surface
Center
Transformation
Bainite
Time (logarithmic scale)
Figure 10-20 As with martempering, austempering avoids the distortion and
cracking associated with quenching through the martensitic transformation range. In this case, the alloy is held long enough just above Ms to allow full transformation to bainite. (After Metals Handbook, 8th Ed., Vol.
2, American Society for Metals, Metals Park, Ohio, 1964.)
(a)
(c)
(b)
DT
Quench rate =
t
DT
t
Specimen
Water spray
Figure 10-21 Schematic illustration of the Jominy end-quench
test for hardenability. (After W. T. Lankford et al., Eds.,
The Making, Shaping, and Treating of Steel, 10th Ed., United
States Steel, Pittsburgh, Pa., 1985. Copyright 1985 by United
States Steel Corporation.)
Distance from quenched end, inches
Cooling rate at 700˚C, C/sec
1000
1
1
1
8
4
2
1
1
1
2
2
500
200
100
50
20
10
5
2
0
10
20
30
40
50 mm
Distance from quenched end, Dqe
(Jominy distance)
Figure 10-22 The cooling rate for the Jominy bar (see Figure 10–21) varies along
its length. This curve applies to virtually all carbon and low-alloy steels. (After L. H. Van Vlack, Elements of Materials Science and Engineering, 4th Ed.,
Addison-Wesley Publishing Co., Inc., Reading, Mass., 1980.)
60
55
Rockwell hardness C scale
50
45
40
35
30
25
20
15
10
5
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
Distance from quenched end – sixteenths of an inch
Figure 10-23 Variation in hardness along a typical Jominy bar. (From W. T.
Lankford et al., Eds., The Making, Shaping, and Treating of Steel, 10th
Ed., United States Steel, Pittsburgh, Pa., 1985. Copyright 1985 by United
States Steel Corporation.)
65
60
Rockwell hardness C scale
55
50
45
40
4340
35
9840
30
4140
25
8640
20
5140
15
10
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
Distance from quenched end—sixteenths of an inch
Figure 10-24 Hardenability curves for various steels with the same carbon content (0.40 wt %) and various alloy contents. The codes designating the alloy
compositions are defined in Table 11.1. (From W. T. Lankford et al., Eds.,
The Making, Shaping, and Treating of Steel, 10th Ed., United States Steel,
Pittsburgh, Pa., 1985. Copyright 1985 by United States Steel Corporation.)
˚C
700
600
500
400
300
Slow cool
200
100
90
95
wt % Al
0
100
Time
Figure 10-25 Coarse precipitates form at grain boundaries in an Al–Cu (4.5 wt
%) alloy when slowly cooled from the single-phase ( κ ) region of the phase
diagram to the two-phase ( θ + κ ) region. These isolated precipitates do little
to affect alloy hardness.
˚C
700
600
Solution treatment
500
400
Quench
300
taging
Fine dispersion of
precipitates within grains
(retained upon cooling)
200
100
90
95
wt % Al
0
100
Time
Figure 10-26 By quenching and then reheating an Al–Cu (4.5 wt %) alloy, a fine dispersion of precipitates forms within the κ grains. These precipitates are effective in hindering dislocation motion and,
consequently, increasing alloy hardness (and strength). This is known as precipitation hardening, or
age hardening.
Temperature
Coarse precipitates
within grains
taging
Time
(a)
Hardness
(arbitrary units)
0.01
0.1
1
10
100
1000
taging (hours)
(b)
Figure 10-27 (a) By extending the reheat step, precipitates coalesce and become
less effective in hardening the alloy. The result is referred to as “overaging.”
(b) The variation in hardness with the length of the reheat step (“aging time”).
Figure 10-28 Schematic illustration of the crystalline geometry of a Guinier–Preston (G.P.) zone. This structure is most effective for precipitation hardening, and
is the structure developed at the hardness maximum
in Figure 10–27b. Note the coherent interfaces lengthwise along the precipitate. The precipitate is approximately 15 nm × 150 nm. (From H. W. Hayden, W. G.
Moffatt, and J. Wulff, The Structure and Properties
of Materials, Vol. 3: Mechanical Behavior, John Wiley & Sons, Inc., New York, 1965.)
(a)
(b)
Figure 10-29 Examples of cold-working operations: (a) cold-rolling of a bar
or sheet and (b) cold-drawing a wire. Note in these schematic illustrations
that the reduction in area caused by the cold-working operation is associated with a preferred orientation of the grain structure.
(a)
(b)
(d)
(e)
(c)
Figure 10-30 Annealing can involve the complete recrystallization and subsequent
grain growth of a cold-worked microstructure. (a) A cold-worked brass (deformed through rollers such that the cross-sectional area of the part was reduced
by one-third). (b) After 3 s at 580 ◦ C, new grains appear. (c) After 4 s at 580 ◦ C,
many more new grains are present. (d) After 8 s at 580 ◦ C, complete recrystallization has occurred. (e) After 1 h at 580 ◦ C, substantial grain growth has occurred. The driving force for this is the reduction of high-energy grain boundaries. The predominant reduction in hardness for this overall process had occurred by step (d). All micrographs at magnification of 75 × . (Courtesy of J. E.
Burke, General Electric Company, Schenectady, N.Y.)
Temperature, ˚F
200
120
400
600
1000
800
1200
1400
Hardness, HRH
C26000
110
100
90
80
0
100
200
300
400
500
600
700
800
Temperature, ˚C
Figure 10-31 The sharp drop in hardness identifies the recrystallization temperature as ∼ 290◦ C for the alloy C26000, “cartridge brass.” (From Metals Handbook, 9th Ed., Vol. 4, American Society for Metals, Metals Park,
Ohio, 1981.)
1
2
Melting temp.
Mo
1000
Be
Ni
Fe
As
Al
Mg
Au Cu
Cd
Zu
Sn
Pb
0
0
15000
Ta
Ti
Pt
1
Melting temp.
3
W
1000
500
Recrystallization temperature, ˚C
Recrystallization temperature, K
2000
0
2000
4000
Melting temperature, K
Figure 10-32 Recrystallization temperature versus melting points for various
metals. This plot is a graphic demonstration of the rule of thumb that atomic
mobility is sufficient to affect mechanical properties above approximately 13
to 12 Tm on an absolute temperature scale. (From L. H. Van Vlack, Elements
of Materials Science and Engineering, 3rd Ed., Addison-Wesley Publishing
Co., Inc., Reading, Mass, 1975.)
60% cold work
Hardness, BHN
200
40% cold work
20% cold work
100
65 Cu–35 Zn
0
0
100
200
300
400
Temperature, ˚C
Figure 10-33 For this cold-worked brass alloy, the recrystallization temperature drops
slightly with increasing degrees of cold work. (From L. H. Van Vlack, Elements
of Materials Science and Engineering, 4th Ed., Addison-Wesley Publishing Co.,
Inc., Reading, Mass. 1980.)
600
60
50
500
40
30
400
Ductility (%EL)
Tensile strength (MPa)
Tensile strength
Ductility
20
300
Recovery
Recrystallization
Grain growth
Gain size (mm)
Cold worked
and recovered
grains
New
grains
0.040
0.030
0.020
0.010
100
200
300
400
500
600
700
Annealing temperature (˚C)
Figure 10-34 Schematic illustration of the effect of annealing temperature on the
strength and ductility of a brass alloy shows that most of the softening of the
alloy occurs during the recrystallization stage. (After G. Sachs and K. R. Van
Horn, Practical Metallurgy: Applied Physical Metallurgy and the Industrial
Processing of Ferrous and Nonferrous Metals and Alloys, American Society
for Metals, Cleveland, Ohio, 1940.)
2.00
0.4
2.50
0.3
3.33
0.2
5.00
0.1
10.0
20.0
0
–60
–40
–20
Temperature, ˚C
0
Time, hr
Rate, hr–1
0.5
∞
20
Figure 10-35 Rate of crystallization of rubber as a function of temperature. (From L.
A. Wood, in H. Mark and G. S. Whitby, Eds., Advances in Colloid Science, Vol. 2,
Wiley Interscience, New York, 1946, pp. 57–95.)
Undercooling (K)
100
200
300
400
1
10
102
103
104 105
Time (sec)
106
107
108
(a)
1550
Tmelt
1450
Temperature (˚C)
Figure 10-36 TTT diagram for (a) the
fractional crystallization (10−4 vol
%) of a simple glass of composition
Na 2 O · 2SiO 2 and (b) the fractional
crystallization (10 −1 vol%) of a glass
of composition CaO · Al 2 O 3 · 2SiO 2 .
[Part (a) from G. S. Meiling and D.
R. Uhlmann, Phys. Chem. Glasses
8, 62 (1967) and part (b) from H.
Yinnon and D. R. Uhlmann, in Glass:
Science and Technology, Vol. 1, D.
R. Uhlmann and N. J. Kreidl, Eds.,
Academic Press, New York, 1983,
pp. 1–47.]
1350
1250
1150
1050
950
850
102
103
104
Time (sec)
(b)
105
T
Glass formation
Crystallization
Melting
Forming
Growth
Nucleation
t
Figure 10-37 Typical thermal history for producing a glass ceramic by the controlled nucleation and growth of crystalline grains.
Figure 10-38 Transmission electron micrograph of monoclinic zirconia
showing a microstructure characteristic of a martensitic transformation. Included in the evidence are twins labeled T. See Figure 4–15
for an atomic-scale schematic of a twin boundary and Figure 10–13
for the microstructure of martensitic steel. (Courtesy of Arthur H.
Heuer)
Figure 10-39 An illustration of the sintering mechanism for shrinkage of a powder compact is
the diffusion of atoms away from the grain
boundary to the pore, thereby “filling in” the
pore. Each grain in the microstructure was
originally a separate powder particle in the
initial compact.
Figure 10-40 Grain growth hinders the densification of a powder compact. The diffusion
path from grain boundary to pore (now isolated within a large grain) is prohibitively long.