1. Chapter 10: Phase Transformations – Considering Kinetic and Heat Treatment
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
• How does the rate of transformation depend on
time and T ?
• How can we slow down the transformation so that
we can engineer non-equilibrium structures?
• Are there other means to improve mechanical behavior? Fe g
(Austenite)
Eutectoid
transformation C
FCC
Fe3C
(cementite) a
(ferrite) +
(BCC)

2. Phase Transformations
Nucleation
nuclei (like biological seeds) act as template to grow crystals
for nuclei to form, the rate of addition of atoms to any nucleus must be faster than rate of loss
once nucleated, the “seed” must grow until they reach the predicted equilibrium

3. Phase Transformations
Driving force to nucleate increases as we increase T
supercooling (eutectic, eutectoid)
superheating (peritectic)
With a Small amount of supercooling  few nuclei - large crystals
With a Large amount of supercooling  rapid nucleation - many nuclei, small crystals
In Chapter 9 we looked at the equilibrium phase diagram . This indicated phase structure if we wait long enough. But due to slow diffusion may not reach equilibrium We need to consider time- kinetics - energy of phase boundaries may be high. – also nucleation
Transformation rate
How fast do the phase transformations occur?
First need nuclei (seeds) to form for the rest of the material to crystallize

4. Solidification: Nucleation Processes
Homogeneous nucleation
nuclei form in the bulk of liquid metal (as “native chemistry”)
requires sufficient supercooling (typically °C max)
Heterogeneous nucleation
much easier since stable “nucleus” is already present (they are non-native chemically)
Could be wall of mold or impurities in the liquid phase
allows solidification with only minimal supercooling (0.1-10ºC)

5. Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
g = surface tension
DGT = Total Free Energy
= DGS + DGV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)

6. Solidification Note: HS is a strong function of T
 is a weak function of T
HS = latent heat of solidification
Tm = melting temperature
g = surface free energy
DT = Tm - T = supercooling
r* = critical radius
 r* decreases as T increases
For typical T r* is around 100Å (10 nm)

7. Rate of Phase Transformations
Kinetics - measures approach to equilibrium vs. time
Hold temperature constant & measure conversion vs. time
How is the amount of conversion measured?
X-ray diffraction – have to do many samples
electrical conductivity – follows a single sample
sound waves (insitu ultrasonic) – follows a single sample

8. Thus, the rate of nucleation is a product of two curves that represent two opposing factors (instability and diffusivity).

9. Rate of Phase Transformation
All out of material – “done!”
Fixed Temp.
maximum rate reached – now amount
unconverted decreases so rate slows
rate increases as surface area increases & nuclei grow
Log Time
t0.5
S.A. = surface area
Modeled by the Avrami Rate Equation:

10. Avrami Equation Avrami rate equation → y = 1- exp (-ktn)
k & n are fit for any specific sample
By convention we define: r = 1 / t0.5 as “the rate of transformation” – it is simply the inverse of the time to complete half of the transformation
The initial slow rate can be attributed to the time required for a significant number of nuclei of the new phase to form and begin growing.
During the intermediate period the transformation is rapid as the nuclei grow into particles and consume the old phase while nuclei continue to form in the remaining parent phase.
Once the transformation begins to near completion there is little untransformed material for nuclei to form in and the production of new particles begins to slow. Further, the particles already existing begin to touch one another, forming a boundary where growth stops.

11. Rate of Phase Transformations
135C
119C
113C
102C
88C
43C 1 10
102
104
adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.
In general, rate increases as T 
r = 1/t0.5 = A e -Q/RT
R = gas constant
T = temperature (K) (higher causes higher rate too)
A = ‘preexponential’ rate factor
Q = activation energy
r is often small so equilibrium is not possible!
Arrhenius expression

12. Transformations & UndercoolingÞ a +
Fe3C
0.76 wt% C
0.022 wt% C
6.7 wt% C •
Eutectoid transf. (Fe-C System): •
M. Eng. Can make it occur at:
...727ºC (cool it slowly)
...below 727ºC (“supercool” or “Undercool” it!)
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L g
(austenite) +L
+Fe3C a
L+Fe3C d
(Fe)
Co , wt%C
1148°C
T(°C)
ferrite
727°C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC DT
Undercooling by DTtransf. < 727C
0.76
0.022
adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990

13. Eutectoid Transformation Rate
• Growth of pearlite from austenite:
Adapted from Fig. 9.15, Callister 7e. g a
pearlite
growth
direction
Austenite (g)
grain
boundary
cementite (Fe3C)
Ferrite (a)
Diffusive flow
of C needed a g
• Recrystallization
rate increases
with DT.
52°C
(675˚C) 50
y (% pearlite)
127°C
(600 ˚C)
77°C
100
Coarse pearlite  formed at higher T - softer
Fine pearlite  formed at low T - harder

14. Nucleation and Growth
• Reaction rate is a result of nucleation and growth
of crystals.
• Examples from previous slide:
T: just below TE
Nucleation rate low
Growth rate high g
pearlite
colony
T: moderately below TE g
Nucleation rate med
Growth rate med.
Nucleation rate high
T: way below TE g
Growth rate low

15. The ideas of “reality” and the “ideal” meet in the Material Engineering’s Transformation Curves

16. Isothermal Transformation (TTT) Diagrams
• Fe-C system, Co = 0.76 wt% C
• Transformation at T = 675°C.
100
T = 675°C y,
% transformed 50 2 4 1 10 10
time (s)
400
500
600
700 1 10 2 3 4 5
0%pearlite
100%
50%
Austenite (stable)
TE (727C)
Austenite
(unstable)
Pearlite
T(°C)
time (s)
isothermal transformation at 675°C
adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.

17. Effect of Cooling History in Fe-C System
• Eutectoid composition, Co = 0.76 wt% C
• Begin at T > 727°C
• Rapidly cool to 625°C and hold isothermally.
400
500
600
700
0%pearlite
100%
50%
Austenite (stable)
TE (727C)
Austenite
(unstable)
Pearlite
T(°C) 1 10 2 3 4 5
time (s) g g
adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.

18. Transformations with Proeutectoid Materials
CO = 1.13 wt% C
TE (727°C)
T(°C)
time (s) A + C P 1 10
102
103
104
500
700
900
600
800
Adapted from Fig , Callister 7e.
Adapted from Fig. 9.24, Callister 7e.
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L g
(austenite) +L
+Fe3C a
L+Fe3C d
(Fe)
Co , wt%C
T(°C)
727°C DT
0.76
0.022
1.13
Hypereutectoid composition – proeutectoid cementite

19. Non-Equilibrium Transformation Products in Fe-C
• Bainite:
--a lathes (strips) with long
rods of Fe3C
--diffusion controlled.
• Isothermal Transf. Diagram
Fe3C
(cementite) a
(ferrite) 10 3 5
time (s) -1
400
600
800
T(°C)
Austenite (stable)
200 P B TE 0%
100%
50%
pearlite/bainite boundary A
100% pearlite
100% bainite
5 mm
from Metals Handbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.)
adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.

20. TTT Curves showing the Bainite Transformation (a) Plain Carbon Steels; (b) Alloy Steel w/ distinct Bainite “Nose”
From: George Krauss, Steels: Processing, Structure, and Performance, ASM International, 2006.

21. Martensite: Fe-C System
--g(FCC) to Martensite (BCT)
Martensite needles
Austenite
60 m x
potential
C atom sites
Fe atom
sites
(involves single atom jumps)
• Isothermal Transf. Diagram 10 3 5
time (s) -1
400
600
800
T(°C)
Austenite (stable)
200 P B TE 0%
100%
50% A
M + A
90%
courtesy United States Steel Corporation.
• g to M transformation..
-- is rapid!
-- % transf. depends on T only.

22. Transformation to Martensite
Martensite formation requires that the steel be subject to a minimum – Critical – Cooling Rate (this value is ‘TTT’ or ‘CCT’ chart dependent for alloy of interest)
For most alloys it indicates a quench into a RT oil or water bath

23. Martensite Formation  (FCC)  (BCC) + Fe3C slow cooling quench
M (BCT)
tempering
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation BCT if C > 0.15 wt%
BCT  few slip planes  hard, brittle

24. Martensite Transformation Crystallography: FCC Austenite to BCT Martensite
From: George Krauss, Steels: Processing, Structure, and Performance, ASM International, 2006.

25. Austenite to Martensite: Size Issues and Material Response
From: George Krauss, Steels: Processing, Structure, and Performance, ASM International, 2006.

26. Spheroidite: Fe-C System
(Fig copyright United States Steel Corporation, 1971.)
60 m a
(ferrite)
(cementite)
Fe3C
• Spheroidite:
--a grains with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times (below the AC1 critical temperature)
--driven by a reduction in interfacial area of Carbide

27. Phase Transformations of Alloys
Effect of adding other elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard    + Fe3C
transformation delaying the time to entering the diffusion controlled transformation reactions – thus promoting “Hardenability’ or Martensite development

28. Continuous Cooling Transformations (CCT)
Isothermal Transformations are “Costly” requiring careful “gymnastics” with heated (and cooling) products
CC Transformations change the observed behavior concerning transformation
With Plain Carbon Steels when cooled “continuously” we find that the Bainite Transformation is suppress(see Figure 10.26)

29. Cooling Curve Plot: temp vs. time
Actual processes involves cooling – not isothermal
Can’t cool at infinite speed

30. CCT for Eutectoid Steel
Figure: 10-26

31. CCT for Eutectoid Steel
f10_27_pg338.jpg

32. Alloy Steel CCT Curve – again note distinct Bainite Nose
Adapted from Fig , Callister 7e.

33. Dynamic Phase Transformations
On the isothermal transformation diagram for 0.45 wt% C Fe-C alloy, sketch and label the time-temperature paths to produce the following microstructures:
42% proeutectoid ferrite and 58% coarse pearlite
50% fine pearlite and 50% bainite
100% martensite
50% martensite and 50% austenite

34. Example Problem for Co = 0.45 wt%
42% proeutectoid ferrite and 58% coarse pearlite
first make ferrite
then pearlite
coarse pearlite
 higher T
A + B
A + P
A + a A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%)
T (°C)
Adapted from Fig ,
Callister 5e.

35. Example Problem for Co = 0.45 wt%
50% fine pearlite and 50% bainite
first make pearlite
then bainite
fine pearlite
 lower T
A + B
A + P
A + a A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%)
T (°C)
NOTE: This “2nd step” is sometimes referred to as an “Austempering” step, quenching into a heated salt bath held at the temperature of need
Adapted from Fig , Callister 5e.

36. Example Problem for Co = 0.45 wt%
100 % martensite: 380C/s {( )/.7s} d)
A + B
A + P
A + a A B P
50%
200
400
600
800
0.1 10
103
105
time (s)
M (start)
M (50%)
M (90%) c)
T (°C)
50%martensite/50%(retained) austenite
Adapted from Fig , Callister 5e.

37. CT for CrMo Med-carbon steel
Hardness of cooled samples at various cooling rates in bubbles -- Dashed lines are IT solid lines are CT regions

38. Tempering Martensite • • • reduces brittleness of martensite,
• reduces internal stress caused by quenching.
YS(MPa)
TS(MPa)
800
1000
1200
1400
1600
1800 30 40 50 60
200
400
600
Tempering T (°C)
%RA TS YS
from Fig. furnished courtesy of Republic Steel Corporation.)
copyright by United States Steel Corporation, 1971.
9 mm
produces extremely small Fe3C particles surrounded by a. • •
decreases TS, YS but increases %RA

39. The microstructure of tempered martensite, although an equilibrium mixture of α-Fe and Fe3C, differs from those for pearlite and bainite. This micrograph produced in a scanning electron microscope (SEM) shows carbide clusters in relief above an etched ferrite. (From ASM Handbook, Vol. 9: Metallography and Microstructures, ASM International, Materials Park, OH, 2004.)

40. Temper Martensite Embrittlement – an issue in Certain Steels
From: George Krauss, Steels: Processing, Structure, and Performance, ASM International, 2006.
Suspected to be due to the deposition of very fine carbides during 2nd and 3rd phase tempering along original austenite G. B. from the transformation of retained austenite,

41. Increasing Strength and Hardness of Alloy involves some Heat Treatment
The effect of quenching in steels is determined by the Jominey End Quench Test
Precipitation Hardness is a method used for may alloy systems (mostly Non-Ferrous ones)
Grain Size control is also an important consideration – which can be controlled by annealing processes
Recovery after cold work (cold work can also increase strength of alloys)
Recrystalization
Grain Growth

42. Schematic illustration of the Jominy end-quench test for hardenability
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, Copyright 1985 by United States Steel Corporation.)

43. Hardenability--Steels
• Ability to form martensite
• Jominy end quench test to measure hardenability.
24°C water
specimen
(heated to g
phase field)
flat ground
Rockwell C hardness tests
(adapted from A.G. Guy, Essentials of Materials Science, McGraw-Hill Book Company, New York, 1978.)
• Hardness versus distance from the quenched end.
Hardness, HRC
Distance from quenched end

44. Figure 10. 22 The cooling rate for the Jominy bar (see Figure 10
Figure 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, MA, 1980.)

45. Figure 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, Copyright 1985 by United States Steel Corporation.)

46. Why Hardness Changes W/Position
• The cooling rate varies with position. 60
Martensite
Martensite + Pearlite
Fine Pearlite
Pearlite
Hardness, HRC 40 20
distance from quenched end (in) 1 2 3
600
400
200 A M P
0.1 1 10
100
1000
T(°C)
M(start)
Time (s) 0%
100%
M(finish)
(adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 376.)

47. Hardenability vs Alloy Composition
Cooling rate (°C/s)
Hardness, HRC 20 40 60 10 30 50
Distance from quenched end (mm) 2
100 3
4140
8640
5140
1040 80 %M
4340
• Jominy end quench
results, C = 0.4 wt% C
(adapted from figure furnished courtesy Republic Steel Corporation.)
• "Alloy Steels"
(4140, 4340, 5140, 8640)
--contain Ni, Cr, Mo
(0.2 to 2wt%)
--these elements shift
the "nose".
--martensite is easier
to form.
T(°C) 10 -1 3 5
200
400
600
800
Time (s)
M(start)
M(90%)
shift from
A to B due
to alloying B A TE

48. Figure 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 (From W. T. Lankford et al., Eds., The Making, Shaping, and Treating of Steel, 10th ed., United States Steel, Pittsburgh, PA, Copyright 1985 by United States Steel Corporation.)

49. Quenching Medium & Geometry
• Effect of quenching medium:
Medium
air
oil
water
Severity of Quench
low
moderate
high
Hardness
low
moderate
high
• Effect of geometry:
When surface-to-volume ratio increases:
--cooling rate increases
--hardness increases
Position
center
surface
Cooling rate
low
high
Hardness

50. Precipitation Hardening
• Particles impede dislocations.
• Ex: Al-Cu system
• Procedure: 10 20 30 40 50
wt% Cu L
+L a
a+q q
+L
300
400
500
600
700
(Al)
T(°C)
composition range
needed for precipitation hardening
CuAl2 A
--Pt A: solution heat treat (get a solid solution) B
Pt B
--Pt B: quench to room temp. C
--Pt C: reheat to nucleate small q crystals within a crystals.
Other precipitation systems: • Cu-Be • Cu-Sn • Mg-Al
Adapted from Fig , Callister 7e. (Fig adapted from J.L. Murray, International Metals Review 30, p.5, 1985.)
Temp.
Time
Pt A (sol’n heat treat)
Consider: 17-4 PH St. Steel and Ni-Superalloys too!
Pt C (precipitate )

51. Figure 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.

52. Figure 10. 26 By quenching and then reheating an Al–Cu (4
Figure 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 process is known as precipitation hardening, or age hardening.

53. Figure (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).

54. Figure (a) 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 shown 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., NY, 1965.) (b) Transmission electron micrograph of G.P. zones at 720,000×. (From ASM Handbook, Vol. 9: Metallography and Microstructures, ASM International, Materials Park, OH, 2004.)

55. Figure 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.
All micrographs have a magnification of 75×. (Courtesy of J. E. Burke, General Electric Company, Schenectady, NY.)
(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 growth is the reduction of high-energy grain boundaries. The predominant reduction in hardness for this overall process had occurred by step (d)

56. Figure 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, OH, 1981.)

57. Recrystallization Temperature, TR
TR = recrystallization temperature = point of highest rate of property change
TR  Tm (K)
Due to diffusion  annealing time TR = f(t) shorter annealing time => higher TR
Higher %CW => lower TR – strain hardening
Pure metals lower TR due to easier dislocation movements

58. Figure 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 1/3 to 1/2 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, MA, 1975.)

59. Figure 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, MA, 1980.)

60. Grain Growth • At longer times, larger grains consume smaller ones.
• Why? Grain boundary area (and therefore energy)
is reduced.
After 8 s,
580ºC
After 15 min,
0.6 mm
Adapted from Fig (d),(e), Callister 7e. (Fig (d),(e) are courtesy of J.E. Burke, General Electric Company.)
coefficient dependent on material & Temp.
• Empirical Relation:
elapsed time
Exponent is typ.  2
grain dia. At time t.
This is: Ostwald Ripening

61. Figure 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, OH, 1940.)

62. Figure Examples of cold-working operations: (a) cold-rolling 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.

63. We can then find that the “cold working of an alloy” is an effect tool for improving performance –
if done properly!
so as not to cause the material to exceed its % EL which was a fracture deformation limit as we saw earlier
If we impose appropriate intermediate recrystalization (and maybe even grain growth steps)
Finish with a cold working step to achieve the desired hardness and finished size

64. Coldwork Hardening Example
A cylindrical rod of brass originally 0.40 in (10.2 mm) in diameter is to be cold worked by drawing. The circular cross section will be maintained during deformation. A cold-worked tensile strength in excess of 55,000 psi (380 MPa) and a ductility of at least 15 %EL are desired. Further more, the final diameter must be 0.30 in (7.6 mm). Explain how this may be accomplished.

65. Coldwork Calculations Solution
If we directly draw to the final diameter what happens?
Brass
Cold
Work D f
= 0.30 in D o
= 0.40 in

66. Coldwork Calc Solution: Cont.
420
540 6
For %CW = 43.8%
y = 420 MPa
TS = 540 MPa > 380 MPa
%EL = 6 < 15
This doesn’t satisfy criteria…… what can we do?

67. Coldwork Calc Solution: Cont.
380 12 15 27
Adapted from Fig. 7.19, Callister 7e.
For TS > 380 MPa
> 12 %CW
For %EL > 15
< 27 %CW
 our working range is limited to %CW = 12 – 27%

68. This process Needs an Intermediate Recrystallization
i.e.: Cold draw-anneal-cold draw again
For objective we need a cold work of %CW  12-27
We’ll use %CW = 20
Diameter after first cold draw (before 2nd cold draw)
must be calculated as follows:
So after the cold draw & anneal D02=0.335m 
Intermediate diameter =

69. Coldwork Calculations Solution
Summary:
Initial Cold work D01= 0.40 in  Df1 = in
Anneal above TR Ds2 = Df1
Secondary Cold work Ds2= in  Df 2 =0.30 in
Therefore, we have met all requirements 