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CHAPTER 10Kinetics—Heat
Treatment
The microstructure of a rapidly cooled “eutec-tic” soft solder (≈ 38 wt % Pb − 62 wt %Sn) consists of globules of lead-rich solid so-lution (dark) in a matrix of tin-rich solid solu-tion (white), 375X. The contrast to the slowly-cooled microstructure at the opening of Chap-ter 9 illustrates the effect of time on microstruc-tural development. (From ASM Handbook,Vol. 3: Alloy Phase Diagrams, ASM Interna-tional, Materials Park, Ohio, 1992.)
T
t
tx
(a) (b)
T
Tmp
Completion of reaction
Figure 10-1 Schematic illustration of the approach to equilibrium. (a) The time for solidi-fication to go to completion is a strong function of temperature, with the minimum timeoccurring 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 plot-ted on a logarithmic scale.
Liquid
(a) (b)
(c) (d)
Solid
Crystalnucleus
Crystalgrowth
Figure 10-2 (a) On a microscopic scale, a solid precipitate in a liquid matrix. The pre-cipitation process is seen on the atomic scale as (b) a clustering of adjacent atoms toform (c) a crystalline nucleus followed by (d) the growth of the crystalline phase.
Net
ene
rgy
chan
ge
Net energy change
Surface energy addition
Volume energy reduction
rcr0
+
–
Figure 10-3 Classical nucleation theory involves an energy balancebetween the nucleus and its surrounding liquid. A nucleus (clus-ter of atoms) as shown in Figure 10–2(c) will be stable only iffurther growth reduces the net energy of the system. An ideallyspherical nucleus will be stable if its radius, r , is greater than acritical value, rc .
Contribution of diffusion (clustering of atoms)
Contribution of liquid phase instability
Net nucleation rate (= product of two dashed lines)
Nucleation rate, N (s–1)
Tm
Tem
pera
ture
, T
Figure 10-4 The rate of nucleation is a product of two curves that represent twoopposing factors (instability and diffusivity).
Overall transformation rate
Rate, (s–1)
Tm
Tem
pera
ture
, T
N
G
Figure 10-5 The overall transformation rate is the product of the nucleationrate N (from Figure 10–4) and the growth rate G (given by Equation 10.1).
Time, t (logarithmic scale)
Temperature, T
1 50 100 % completion of reaction
Curve shown in Figure 10-1
Tmp
Figure 10-6 A time–temperature–transformation diagram for the solidification reac-tion of Figure 10–1 with various percent completion curves illustrated.
Time, seconds0.10
100
200
300
400
500
600
700
727˚
800
˚C
1 10 102 103 104 105 0 0.77wt % C
Coarse pearlite
Fine pearlite
Bainite
1 sec 1 hour1 min 1 day
Figure 10-7 TTT diagram for eutectoid steel shown in relation to the Fe–Fe3C phasediagram (see Figure 9–39). This shows that, for certain transformation tempera-tures, bainite rather than pearlite is formed. In general, the transformed microstruc-ture is increasingly fine-grained as the transformation temperature is decreased. Nu-cleation rate increases and diffusivity decreases as temperature decreases. The solidcurve on the left represents the onset of transformation (∼ 1% completion). Thedashed curve represents 50% completion. The solid curve on the right representsthe effective (∼ 99%) completion of transformation. This convention is used insubsequent TTT diagrams. (TTT diagram after Atlas of Isothermal Transforma-tion and Cooling Transformation Diagrams, American Society for Metals, MetalsPark, Ohio, 1977.)
Temperature
Time (logarithmic scale)
Coarse pearlite
Figure 10-8 A slow cooling path that leads to coarse pearlite formation is superimposedon 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 fineneedles of α-Fe and Fe3C, in contrast to the lamellar structureof pearlite (see Figure 9–2), 535×. (From Metals Handbook,8th Ed., Vol. 7: Atlas of Microstructures, American Societyfor Metals, Metals Park, Ohio, 1972.)
Temperature
Time (logarithmic scale)
Coarse pearlite
Coarse pearlite remains upon cooling
Figure 10-10 The interpretation of TTT diagrams requires considerationof the thermal history “path.” For example, coarse pearlite, once formed,remains stable upon cooling. The finer-grain structures are less stablebecause of the energy associated with the grain boundary area. (Bycontrast, phase diagrams represent equilibrium and identify stable phasesindependent of the path used to reach a given state point.)
Time, seconds0.1
0
100
200
300
400
500
600
700
727˚
800
˚C
1 10 102 103 104 105 0 0.77wt % C
Coarse pearlite
Fine pearlite
Bainite
1 sec
M90
M50
Ms
1 hour1 min 1 day
Figure 10-11 A more complete TTT diagram for eutectoid steel than was givenin Figure 10–7. The various stages of the time-independent (or diffusion-less) martensitic transformation are shown as horizontal lines. Ms repre-sents the start, M50 50% transformation, and M90 90% transformation. Onehundred percent transformation to martensite is not complete until a finaltemperature (Mf ) of −46◦C.
a0
a
c
a0|! 2
(a) (b)
Figure 10-12 For steels, the martensitic transformation involves the sudden reorientation of C and Fe atoms fromthe 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 〈100〉α 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 inter-stitially dissolved carbon atom. This illustration of the martensitic transformation was first presented by Bain in1924, and while subsequent study has refined the details of the transformation mechanism, this remains a usefuland popular schematic. (After J. W. Christian, in Principles of Heat Treatment of Steel, G. Krauss, Ed., Ameri-can Society for Metals, Metals Park, Ohio, 1980.)
Figure 10-13 Acicular, or needlelike, microstructure of martensite 1000×. (FromMetals Handbook, 8th Ed., Vol. 7: Atlas of Microstructures, American So-ciety for Metals, Metals Park, Ohio, 1972.)
Time, seconds
Continuous coolingtransformation
Isothermaltransformation
Rapid cooling rate
Moderate cooling rate
Slow cooling rate
1
2
1
2
3
3
0.10
100
200
300
400
500
600
700
727˚
800
˚C
1 10 102 103 104 105
1 sec 1 hour 1 day1 min
M90
M50
Ms
Figure 10-14 A continuous cooling transformation (CCT) diagram is shown superimposedon the isothermal transformation diagram of Figure 10–11. The general effect of contin-uous cooling is to shift the transformation curves downward and toward the right. (AfterAtlas of Isothermal Transformation and Cooling Transformation Diagrams, AmericanSociety for Metals, Metals Park, Ohio, 1977.)
Time, seconds0.1
0
100
200
300
400
500
600
700
727˚
880˚
Ms
M50
M90
800
900
˚C
1 10 102 103 104 105 0 1.13wt % C
1 sec 1 min 1 hour 1 day
Figure 10-15 TTT diagram for a hypereutectoid composition (1.13 wt % C) comparedto the Fe–Fe3C phase diagram. Microstructural development for the slow coolingof this alloy was shown in Figure 9–40. (TTT diagram after Atlas of IsothermalTransformation and Cooling Transformation Diagrams, American Society for Met-als, Metals Park, Ohio, 1977.)
Time, seconds0.1
100
200
300
400
500
600
700
727˚
770˚800
900
˚C
1 10 102 103 104 105 0 0.5wt % C
1 sec 1 min
Ms
M50
M90
1 hour 1 day
Figure 10-16 TTT diagram for a hypoeutectoid composition (0.5 wt % C)compared to the Fe–Fe3C phase diagram. Microstructural developmentfor the slow cooling of this alloy was shown in Figure 9–41. By compar-ing Figures 10–11, 10–15, and 10–16, one will note that the martensitictransformation occurs at decreasing temperatures with increasing car-bon content in the region of the eutectoid composition. (TTT diagramsafter Atlas of Isothermal Transformation and Cooling TransformationDiagrams, American Society for Metals, Metals Park, Ohio, 1977.)
Temperature
Time (logarithmic scale)
Tempering temperature
Thermal history for center of part being heat-treated
Thermal history for surface of part being heat-treated
Tempered martensiteMartensite
Transformation
Ms
Mf
Figure 10-17 Tempering is a thermal history [T = f n(t)] in which marten-site, formed by quenching austenite, is reheated. The resulting temperedmartensite consists of the equilibrium phase of α-Fe and Fe3C but in a mi-crostructure 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, forsimplicity, that of eutectoid steel. As a practical matter, tempering is gener-ally done in steels with slower diffusional reactions permitting less severequenches.)
Figure 10-18 The microstructure of tempered martensite, althoughan equilibrium mixture of α-Fe and Fe3C, differs from thosefor pearlite (Figure 9–2) and bainite (Figure 10–9), 825×. Thisparticular microstructure is for a 0.50 wt % C steel comparablewith that described for Figure 10–16. (From Metals Handbook,8th Ed., Vol. 7: Atlas of Microstructures, American Society forMetals, Metals Park, Ohio, 1972.)
Temperature
Time (logarithmic scale)
Tempering temperature
Surface
Center
Tempered martensiteMartensite
Transformation
Figure 10-19 In martempering, the quench is stopped just above Ms. Slow cool-ing through the martensitic transformation range reduces stresses associ-ated with the crystallographic change. The final reheat step is equivalent tothat in conventional tempering. (After Metals Handbook, 8th Ed., Vol. 2,American Society for Metals, Metals Park, Ohio, 1964.)
Temperature
Time (logarithmic scale)
Surface
Center
Bainite
Transformation
Figure 10-20 As with martempering, austempering avoids the distortion andcracking associated with quenching through the martensitic transforma-tion range. In this case, the alloy is held long enough just above Ms to al-low full transformation to bainite. (After Metals Handbook, 8th Ed., Vol.2, American Society for Metals, Metals Park, Ohio, 1964.)
(a)
(b)(c)
t
DT
tTDQuench rate =
Water spray
Specimen
Figure 10-21 Schematic illustration of the Jominy end-quenchtest for hardenability. (After W. T. Lankford et al., Eds.,The Making, Shaping, and Treating of Steel, 10th Ed., UnitedStates Steel, Pittsburgh, Pa., 1985. Copyright 1985 by UnitedStates Steel Corporation.)
0 10 20 30
1
2111000
2
5
10
20
50
100
200
500
2
40
Distance from quenched end, Dqe(Jominy distance)
Distance from quenched end, inches
Coo
ling
rate
at 7
00˚C
, C
/sec
50 mm
1
2
1
4
1
8
Figure 10-22 The cooling rate for the Jominy bar (see Figure 10–21) varies alongits length. This curve applies to virtually all carbon and low-alloy steels. (Af-ter L. H. Van Vlack, Elements of Materials Science and Engineering, 4th Ed.,Addison-Wesley Publishing Co., Inc., Reading, Mass., 1980.)
Distance from quenched end – sixteenths of an inch
Roc
kwel
l har
dnes
s C
sca
le
0
60
55
50
45
40
35
30
25
20
15
10
5
4 8 1220 6 10 14 18 22 26 3016 20 24 28 32
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, 10thEd., United States Steel, Pittsburgh, Pa., 1985. Copyright 1985 by UnitedStates Steel Corporation.)
Roc
kwel
l har
dnes
s C
sca
le
4340
9840
4140
8640
5140
010
15
20
25
30
35
40
45
50
55
60
65
4 82 6 10 14 18 22 26 3012 16 20 24 28 32
Distance from quenched end—sixteenths of an inch
Figure 10-24 Hardenability curves for various steels with the same carbon con-tent (0.40 wt %) and various alloy contents. The codes designating the alloycompositions 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.)
Slow cool
Timewt % Al
10090 95
700˚C
600
500
400
300
200
100
0
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 phasediagram to the two-phase (θ + κ ) region. These isolated precipitates do littleto affect alloy hardness.
taging
Fine dispersion ofprecipitates within grains(retained upon cooling)
Timewt % Al
10090 95
700˚C
600
500
400
300
200
100
0
Solution treatment
Quench
Figure 10-26 By quenching and then reheating an Al–Cu (4.5 wt %) alloy, a fine dispersion of precipi-tates 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, orage hardening.
Coarse precipitateswithin grains
Temperature
Time
(a)
Hardness(arbitrary units)
taging (hours)
(b)
0.01 0.1 1 10 100 1000
taging
Figure 10-27 (a) By extending the reheat step, precipitates coalesce and becomeless 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 ge-ometry of a Guinier–Preston (G.P.) zone. This struc-ture is most effective for precipitation hardening, andis the structure developed at the hardness maximumin Figure 10–27b. Note the coherent interfaces length-wise along the precipitate. The precipitate is approxi-mately 15 nm × 150 nm. (From H. W. Hayden, W. G.Moffatt, and J. Wulff, The Structure and Propertiesof Materials, Vol. 3: Mechanical Behavior, John Wi-ley & Sons, Inc., New York, 1965.)
(b)
(a)
Figure 10-29 Examples of cold-working operations: (a) cold-rolling of a baror sheet and (b) cold-drawing a wire. Note in these schematic illustrationsthat the reduction in area caused by the cold-working operation is associ-ated with a preferred orientation of the grain structure.
(a) (b) (c)
(d) (e)
Figure 10-30 Annealing can involve the complete recrystallization and subsequentgrain growth of a cold-worked microstructure. (a) A cold-worked brass (de-formed through rollers such that the cross-sectional area of the part was reducedby 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 recrystal-lization has occurred. (e) After 1 h at 580◦C, substantial grain growth has oc-curred. The driving force for this is the reduction of high-energy grain bound-aries. The predominant reduction in hardness for this overall process had oc-curred by step (d). All micrographs at magnification of 75×. (Courtesy of J. E.Burke, General Electric Company, Schenectady, N.Y.)
200120
110
100
90
800 200 400100 300 500 700600 800
400 600 800
Temperature, ˚F
Har
dnes
s, H
RH
Temperature, ˚C
1000 1200
C26000
1400
Figure 10-31 The sharp drop in hardness identifies the recrystallization tem-perature as ∼ 290◦C for the alloy C26000, “cartridge brass.” (From Met-als Handbook, 9th Ed., Vol. 4, American Society for Metals, Metals Park,Ohio, 1981.)
Pb
Melting temperature, K
Rec
ryst
alliz
atio
n te
mpe
ratu
re, K
Rec
ryst
alliz
atio
n te
mpe
ratu
re, ˚
C
0
1000
2000
20000 4000
15000
WTa
BeNi
FeAs
Pt
ZuAu
AsAl
MgCd
Sn
TiPt
CuZu
Pb
Au
Mo1000
500
0
Melting temp.1
2
Melting temp.1
3
Figure 10-32 Recrystallization temperature versus melting points for variousmetals. This plot is a graphic demonstration of the rule of thumb that atomicmobility is sufficient to affect mechanical properties above approximately 1
3to 1
2Tm on an absolute temperature scale. (From L. H. Van Vlack, Elementsof Materials Science and Engineering, 3rd Ed., Addison-Wesley PublishingCo., Inc., Reading, Mass, 1975.)
Temperature, ˚C
00
100
Har
dnes
s, B
HN
200
100
65 Cu–35 Zn
60% cold work
40% cold work
20% cold work
200 300 400
Figure 10-33 For this cold-worked brass alloy, the recrystallization temperature dropsslightly with increasing degrees of cold work. (From L. H. Van Vlack, Elementsof Materials Science and Engineering, 4th Ed., Addison-Wesley Publishing Co.,Inc., Reading, Mass. 1980.)
Tensile strength
Ductility
Annealing temperature (˚C)
Newgrains
Cold workedand recovered
grains
Recovery Recrystallization Grain growth
600 60
50
40
30
20
500
Tens
ile s
tren
gth
(MP
a)G
ain
size
(m
m)
Duc
tilit
y (%
EL
)
400
0.040
0.030
0.020
0.010
300
100 200 300 400 500 600 700
Figure 10-34 Schematic illustration of the effect of annealing temperature on thestrength and ductility of a brass alloy shows that most of the softening of thealloy occurs during the recrystallization stage. (After G. Sachs and K. R. VanHorn, Practical Metallurgy: Applied Physical Metallurgy and the IndustrialProcessing of Ferrous and Nonferrous Metals and Alloys, American Societyfor Metals, Cleveland, Ohio, 1940.)
0.5
0.4
0.3
0.2
0.1
0
2.00
2.50
3.33
5.00
10.020.0
–60 –40 –20 0 20
Rat
e, h
r–1
Tim
e, h
r
Temperature, ˚C
∞
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.)
Figure 10-36 TTT diagram for (a) thefractional crystallization (10−4 vol%) of a simple glass of compositionNa2O · 2SiO2 and (b) the fractionalcrystallization (10−1 vol%) of a glassof composition CaO·Al2O3·2SiO2.[Part (a) from G. S. Meiling and D.R. Uhlmann, Phys. Chem. Glasses8, 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.]
100
200
300
4001 10 102 103 104 105 106 107 108
Und
erco
olin
g (K
)
Time (sec)
Tmelt1550
950
1050
1150
1250
1350
1450
850105104103102
Tem
pera
ture
(˚C
)
Time (sec)
(a)
(b)
Glass formation
CrystallizationMelting
Forming
Nucleation
Growth
T
t
Figure 10-37 Typical thermal history for producing a glass ceramic by the controlled nu-cleation and growth of crystalline grains.
Figure 10-38 Transmission electron micrograph of monoclinic zirconiashowing a microstructure characteristic of a martensitic transforma-tion. Included in the evidence are twins labeled T. See Figure 4–15for an atomic-scale schematic of a twin boundary and Figure 10–13for the microstructure of martensitic steel. (Courtesy of Arthur H.Heuer)
Figure 10-39 An illustration of the sintering mech-anism for shrinkage of a powder compact isthe diffusion of atoms away from the grainboundary to the pore, thereby “filling in” thepore. Each grain in the microstructure wasoriginally a separate powder particle in theinitial compact.
Figure 10-40 Grain growth hinders the densifi-cation of a powder compact. The diffusionpath from grain boundary to pore (now iso-lated within a large grain) is prohibitively long.