1. Phase Transformations
Ferrite - BCC
Martensite - BCT
Austenite - FCC
Chapter 11
Phase Transformations
Fe3C (cementite)- orthorhombic

2. Phase Transformations
Transformation rate
Kinetics of Phase Transformation
Nucleation: homogeneous, heterogeneous
Free Energy, Growth
Isothermal Transformations (TTT diagrams)
Pearlite, Martensite, Spheroidite, Bainite
Continuous Cooling
Mechanical Behavior
Precipitation Hardening

3. Phase Transformations
Phase transformations – change in the number or character of phases.
Simple diffusion-dependent
No change in # of phases
No change in composition
Example: solidification of a pure metal, allotropic transformation, recrystallization, grain growth
More complicated diffusion-dependent
Change in # of phases
Change in composition
Example: eutectoid reaction
Diffusionless
Example: metastable phase - martensite

4. Phase Transformations
Most phase transformations begin with the formation of numerous small particles of the new phase that increase in size until the transformation is complete.
Nucleation is the process whereby nuclei (seeds) act as templates for crystal growth.
Homogeneous nucleation - nuclei form uniformly throughout the parent phase; requires considerable supercooling (typically °C).
Heterogeneous nucleation - form at structural inhomogeneities (container surfaces, impurities, grain boundaries, dislocations) in liquid phase much easier since stable “nucleating surface” is already present; requires slight supercooling (0.1-10ºC).

5. Supercooling
During the cooling of a liquid, solidification (nucleation) will begin only after the temperature has been lowered below the equilibrium solidification (or melting) temperature Tm. This phenomenon is termed supercooling (or undercooling.
The driving force to nucleate increases as T increases
Small supercooling  slow nucleation rate - few nuclei - large crystals
Large supercooling  rapid nucleation rate - many nuclei - small crystals

6. c11tf01

7. Nucleation and Growth
• Rate is a result of nucleation and growth of crystals.
• Examples:

8. Nucleation of a spherical solid particle in a liquid
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The change in free energy DG (a function of the internal energy and enthalpy of the system) must be negative for a transformation to occur.
Assume that nuclei of the solid phase form in the interior of the liquid as atoms cluster together- similar to the packing in the solid phase.
Also, each nucleus is spherical and has a radius r.
Free energy changes as a result of a transformation: 1) the difference between the solid and liquid phases (volume free energy, DGV); and 2) the solid-liquid phase boundary (surface free energy, DGS).
Transforming one phase into another takes time.
Liquid
DG = DGS + DGV Fe g
(Austenite)
Eutectoid
transformation C
FCC
Fe3C
(cementite) a
(ferrite) +
(BCC)

9. 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: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy)

10. Solidification Note: Hf and  are weakly dependent on T
Hf = latent heat of solidification (fusion)
Tm = melting temperature
g = surface free energy
DT = Tm - T = supercooling
r* = critical radius
Note: Hf and  are weakly dependent on T
 r* decreases as T increases
For typical T r* ~ 10 nm

11. Transformations & UndercoolingÞ a + •
Eutectoid transformation (Fe-Fe3C system):
Fe3C •
For transformation to occur, must cool to below 727°C
0.76 wt% C
6.7 wt% C
0.022 wt% C
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)
C, wt% C
1148°C
T(°C)
ferrite
727°C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC DT
Undercooling by Ttransf. < 727C
0.76
0.022

12. Rate of Phase Transformation
transformation complete
Fixed T
Fraction transformed, y
0.5
maximum rate reached – now amount
unconverted decreases so rate slows
rate increases as surface area increases & nuclei grow
t0.5
Fraction transformed depends on time
log t
Avrami equation => y = 1- exp (-kt n)
S.A. = surface area
fraction transformed
time
By convention rate = 1 / t0.5
Avrami relationship - the rate is defined as the inverse of the time to complete half of the transformation. This describes most solid-state transformations that involve diffusion. 12 12

13. Temperature Dependence of Transformation Rate1 10
102
104
Adapted from Fig , Callister 7e. (Fig 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)
A = ‘preexponential’ rate factor
Q = activation energy
r is often small so equilibrium is not possible.
Arrhenius expression 13

14. Generation of Isothermal Transformation Diagrams
Consider:
• The Fe-Fe3C system, for Co = 0.76 wt% C
• A transformation temperature of 675°C.
100
T = 675°C
% 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

15. Eutectoid Transformation Rate ~ DT
• Transformation of austenite to pearlite: g a
pearlite
growth
direction
Austenite (g)
grain
boundary
cementite (Fe3C)
Ferrite (a)
Diffusion of C
during transformation a g
Carbon diffusion
• For this transformation,
rate increases with ( DT)
[Teutectoid – T ].
675°C
(DT smaller) 50
% pearlite
600°C
(DT larger)
650°C
100
Coarse pearlite  formed at higher temperatures – relatively soft
Fine pearlite  formed at lower temperatures – relatively hard

16. Isothermal Transformation Diagrams
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2 solid curves are plotted:
one represents the time required at each temperature for the start of the transformation;
the other is for transformation completion.
The dashed curve corresponds to 50% completion.
The austenite to pearlite transformation will occur only if the alloy is supercooled to below the eutectoid temperature (727˚C).
Time for process to complete depends on the temperature.

17. Isothermal Transformation Diagram
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• Eutectoid iron-carbon alloy; composition, Co = 0.76 wt% C
• Begin at T > 727˚C
• Rapidly cool to 625˚C and hold isothermally.
Austenite-to-Pearlite

18. Transformations Involving Noneutectoid Compositions
Consider C0 = 1.13 wt% C
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)
C, wt%C
T(°C)
727°C DT
0.76
0.022
1.13
Hypereutectoid composition – proeutectoid cementite 18

19. Transformations Involving Noneutectoid Compositions
Consider C0 = 1.13 wt% C a
TE (727°C)
T(°C)
time (s) A + C P 1 10
102
103
104
500
700
900
600
800
Adapted from Fig , Callister & Rethwisch 3e.
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)
C, wt%C
T(°C)
727°C DT
0.76
0.022
1.13
Adapted from Fig , Callister & Rethwisch 3e.
Hypereutectoid composition – proeutectoid cementite 19 19

21. Possible Transformations
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Strength
Ductility
Martensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends

22. Coarse pearlite (high diffusion rate) and (b) fine pearlite
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23. Bainite: Non-Equil Transformation Products
elongated Fe3C particles in a-ferrite matrix
diffusion controlled
a lathes (strips) with long rods of Fe3C
Martensite 10 3 5
time (s) -1
400
600
800
T(°C)
Austenite (stable)
200 P B TE 0%
100%
50% A
100% pearlite
100% bainite
Cementite
Ferrite

24. Bainite Microstructure
• Bainite consists of acicular (needle-like) ferrite with very small cementite particles dispersed throughout.
• The carbon content is typically greater than 0.1%.
• Bainite transforms to iron and cementite with sufficient time and temperature (considered semi-stable below 150°C).

25. Spheroidite: Nonequilibrium Transformation
Fe3C particles within an a-ferrite matrix
diffusion dependent
heat bainite or pearlite at temperature just below eutectoid for long times
driving force – reduction of a-ferrite/Fe3C interfacial area 10

26. Pearlitic Steel partially transformed to Spheroidite
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27. Martensite Formation • Isothermal Transformation Diagram TE T(°C)10 3 5
time (s) -1
400
600
800
T(°C)
Austenite (stable)
200 P B TE 0%
100%
50% A
M + A
90%
Martensite needles
Austenite
single phase
body centered tetragonal (BCT) crystal structure
BCT if C0 > 0.15 wt% C
Diffusionless transformation
BCT  few slip planes  hard, brittle
% transformation depends only on T of rapid cooling

28. An micrograph of austenite that was polished flat and then allowed to transform into martensite. The different colors indicate the displacements caused when martensite forms.

29. Isothermal Transformation Diagram
Iron-carbon alloy with eutectoid composition.
A: Austenite
P: Pearlite
B: Bainite
M: Martensite

30. Effect of Adding Other Elements
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4340 Steel
Other elements (Cr, Ni, Mo, Si and W) may cause significant changes in the positions and shapes of the TTT curves:
Change transition temperature;
Shift the nose of the austenite-to-pearlite transformation to longer times;
Shift the pearlite and bainite noses to longer times (decrease critical cooling rate);
Form a separate bainite nose;
nose
plain carbon
steel
Plain carbon steel: primary alloying element is carbon.

31. c11f23
Example 11.2:
Iron-carbon alloy with eutectoid composition.
Specify the nature of the final microstructure (% bainite, martensite, pearlite etc) for the alloy that is subjected to the following time–temperature treatments:
Alloy begins at 760˚C and has been held long enough to achieve a complete and homogeneous austenitic structure.
Treatment (a)
Rapidly cool to 350 ˚C
Hold for 104 seconds
Quench to room temperature
Bainite, 100%

32. c11f23 Example 11.2: Iron-carbon alloy with eutectoid composition.
Specify the nature of the final microstructure (% bainite, martensite, pearlite etc) for the alloy that is subjected to the following time–temperature treatments:
Alloy begins at 760˚C and has been held long enough to achieve a complete and homogeneous austenitic structure.
Treatment (b)
Rapidly cool to 250 ˚C
Hold for 100 seconds
Quench to room temperature
Austenite, 100%
Martensite, 100%

33. c11f23 Example 11.2: Iron-carbon alloy with eutectoid composition.
Specify the nature of the final microstructure (% bainite, martensite, pearlite etc) for the alloy that is subjected to the following time–temperature treatments:
Alloy begins at 760˚C and has been held long enough to achieve a complete and homogeneous austenitic structure.
Treatment (c)
Rapidly cool to 650˚C
Hold for 20 seconds
Rapidly cool to 400˚C
Hold for 103 seconds
Quench to room temperature
Austenite, 100%
Almost 50% Pearlite, 50% Austenite
Bainite, 50%
Final:
50% Bainite,
50% Pearlite

34. Continuous Cooling Transformation Diagrams
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Isothermal heat treatments are not the most practical due to rapidly cooling and constant maintenance at an elevated temperature.
Most heat treatments for steels involve the continuous cooling of a specimen to room temperature.
TTT diagram (dashed curve) is modified for a CCT diagram (solid curve).
For continuous cooling, the time required for a reaction to begin and end is delayed.
The isothermal curves are shifted to longer times and lower temperatures.

35. c11f27
Moderately rapid and slow cooling curves are superimposed on a continuous cooling transformation diagram of a eutectoid iron-carbon alloy.
The transformation starts after a time period corresponding to the intersection of the cooling curve with the beginning reaction curve and ends upon crossing the completion transformation curve.
Normally bainite does not form when an alloy is continuously cooled to room temperature; austenite transforms to pearlite before bainite has become possible.

36. c11f28
For continuous cooling of a steel alloy there exists a critical quenching rate that represents the minimum rate of quenching that will produce a totally martensitic structure.
This curve will just miss the nose where pearlite transformation begins

37. c11f29
Continuous cooling diagram for a 4340 steel alloy and several cooling curves superimposed.
This demonstrates the dependence of the final microstructure on the transformations that occur during cooling.
Alloying elements used to modify the critical cooling rate for martensite are chromium, nickel, molybdenum, manganese, silicon and tungsten.

38. Mechanical Properties
Hardness
Brinell, Rockwell
Yield Strength
Tensile Strength
Ductility
% Elongation
Effect of Carbon Content

39. Mechanical Properties: Influence of Carbon Content
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C0 > 0.76 wt% C
Hypereutectoid
Pearlite (med)
Cementite
(hard)
Pearlite (med)
ferrite (soft)
C0 < 0.76 wt% C
Hypoeutectoid

40. Mechanical Properties: Fe-C System
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41. Tempered Martensite c11f34
Tempered martensite is less brittle than martensite; tempered at 594 °C.
Tempering reduces internal stresses caused by quenching.
The small particles are cementite; the matrix is a-ferrite. US Steel Corp.
4340 steel

42. Hardness as a function of carbon concentration for steels
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43. Rockwell C and Brinell Hardness
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Hardness versus tempering time for a water-quenched eutectoid plain carbon steel (1080) that has been rapidly quenched to form martensite.

44. c11tf02

45. Precipitation Hardening
The strength and hardness of some metal alloys may be improved by the formation of extremely small, uniformly dispersed particles (precipitates) of a second phase within the original phase matrix.
Alloys that can be precipitation hardened or age hardened:
Copper-beryllium (Cu-Be)
Copper-tin (Cu-Sn)
Magnesium-aluminum (Mg-Al)
Aluminum-copper (Al-Cu)
High-strength aluminum alloys

46. c11f40 Phase Diagram for Precipitation Hardened Alloy Criteria:
Maximum solubility of 1 component in the other (M);
Solubility limit that rapidly decreases with decrease in temperature (M→N).
Process:
Solution Heat Treatment – first heat treatment where all solute atoms are dissolved to form a single-phase solid solution.
Heat to T0 and dissolve B phase.
Rapidly quench to T1
Nonequilibrium state (a phase solid solution supersaturated with B atoms; alloy is soft, weak-no ppts).

47. Precipitation Heat Treatment
c11f43
The supersaturated a solid solution is usually heated to an intermediate temperature T2 within the a+b region (diffusion rates increase).
The b precipitates (PPT) begin to form as finely dispersed particles. This process is referred to as aging.
After aging at T2, the alloy is cooled to room temperature.
Strength and hardness of the alloy depend on the ppt temperature (T2) and the aging time at this temperature.

48. Solution Heat Treatment
Heat treatable aluminum alloys gain strength from subjecting the material to a sequence of processing steps called solution heat treatment, quenching, and aging.
The primary goal is to create sub-micron sized particles in the aluminum matrix, called precipitates that in turn influence the material properties.
While simple in concept, the process variations required (depending on alloy, product form, desired final property combinations, etc.) make it sufficiently complex that heat treating has become a professional specialty.
The first step in the heat treatment process is solution heat treatment. The objective of this process step is to place the elements into solution that will eventually be called upon for precipitation hardening.
Developing solution heat treatment times and temperatures has typically involved extensive trial and error, partially due to the lack of accurate process models.

49. Aging-microstructure
The supersaturated solid solution is unstable and if, left alone, the excess q will precipitate out of the a phase. This process is called aging.
Types of aging:
Natural aging process occurs at room temperature
Artificial aging If solution heat treated, requires heating to speed up the precipitation

50. Overaging
After solution heat treatment the material is ductile, since no precipitation has occurred. Therefore, it may be worked easily.
After a time the solute material precipitates and hardening develops.
As the composition reaches its saturated normal state, the material reaches its maximum hardness.
The precipitates, however, continue to grow. The fine precipitates disappear. They have grown larger, and as a result the tensile strength of the material decreases. This is called overaging.

51. Precipitation Heat Treatment
c11f43
PPT behavior is represented in the diagram:
With increasing time, the hardness increases, reaching a maximum (peak), then decreasing in strength.
The reduction in strength and hardness after long periods is overaging (continued particle growth).
Small solute-enriched regions in a solid solution where the lattice is identical or somewhat perturbed from that of the solid solution are called Guinier-Preston zones.
Guinier-Preston (GP) zones - Tiny clusters of atoms that precipitate from the matrix in the early stages of the age-hardening process.

52. Hardness vs. Time
The hardness and tensile strength vary during aging and overaging.

53. Influence of Precipitation Heat Treatment on Tensile Strength (TS), %EL
• 2014 Al Alloy:
• TS peak with precipitation time.
• Increasing T accelerates
process.
• %EL reaches minimum
with precipitation time.
%EL (2 in sample) 10 20 30
1min 1h
1day
1mo
1yr
204°C
149 °C
precipitation heat treat time
precipitation heat treat time
tensile strength (MPa)
200
300
400
100
1min 1h
1day
1mo
1yr
204°C
non-equil.
solid solution
many small
precipitates
“aged”
fewer large
“overaged”
149°C

54. Effects of Temperature
c11f45
Effects of Temperature
Characteristics of a 2014 aluminum alloy (0.9 wt% Si, 4.4 wt% Cu, 0.8 wt% Mn, 0.5 wt% Mg) at 4 different aging temperatures.

55. Aluminum rivets
Alloys that experience significant precipitation hardening at room temp, after short periods must be quenched to and stored under refrigerated conditions.
Several aluminum alloys that are used for rivets exhibit this behavior. They are driven while still soft, then allowed to age harden at the normal room temperature.

56. c11f44
Several stages in the formation of the equilibrium PPT (q) phase.
supersaturated a solid solution;
transition (q”) PPT phase;
equilibrium q phase within the a matrix phase.

57. Precipitation Hardening
• Particles impede dislocation motion.
• 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
available for precipitation hardening
CuAl2 A
-- Pt A: solution heat treat (get a solid solution) B
Pt B
-- Pt B: quench to room temp. (retain a solid solution) C
-- Pt C: reheat to nucleate small q particles within a phase.
Temp.
Time
At room temperature the stable state of an aluminum-copper alloy is an aluminum-rich solid solution (α) and an intermetallic phase with a tetragonal crystal structure having nominal composition CuAl2 (θ).
Pt A (solution heat treat)
Pt C (precipitate )

58. PRECIPITATION STRENGTHENING
• Hard precipitates are difficult to shear.
Ex: Ceramics in metals (SiC in Iron or Aluminum).
• Result: 24

59. Aging
Aging either at room or moderately elevated temperature after the quenching process is used to produce the desired final product property combinations.
The underlying metallurgical phenomenon in the aging process is precipitation hardening. Due to the small size of the precipitate particles, early understanding was hampered by the lack of sufficiently powerful microscopes to actually see them.
With the availability of the transmission electron microscope (TEM) with nanometer-scale resolution, researchers were able to actually image many precipitate phases and build on this knowledge to develop improved aluminum alloy products.

60. Aluminum
Aluminum is light weight, but engineers want to improve the strength for high performance applications in automobiles and aerospace.
To improve strength, they use precipitation hardening.
The figure shows the solubility line PS, which indicates a decrease in solubility of the q phase in the a phase as the temperature decreases. If a metal with composition X is heated above the solubility line to a temperature T1, the q phase will dissolve and uniformly disperse into the homogeneous solid a solution. Upon slow cooling, the phase will reform, and below PS solubility line the metal will once again consist of two distinct phases, q and a .
If the metal with composition X is heated to T1, and quenched, the dispersed submicroscopic phase is trapped in the a solution. The solution a is said to be supersaturated, because it contains more q particles at room temperature than it can hold in its lattice structure. This process is called solution heat-treating.
Age-hardening heat treatment phase diagram 60

61. Changes in Microstructure due to quenching
Quenching is the second step in the process.
Its purpose is to retain the dissolved alloying elements in solution for subsequent precipitation hardening.
Generally the more rapid the quench the better, from a properties standpoint, but this must be balanced against the concerns of part distortion and residual stress if the quench is non-uniform.
Changes in Microstructure due to quenching