transformation of phases in physical metallurgy, engineering precipitaion and age hardening

1. Chapter 11
Phase
TransformationsFe3C (cementite)- orthorhombic
Martensite - BCT
Austenite - FCC
Ferrite - BCC

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 80-300°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. Nucleation of a spherical solid particle in a liquid
Liquid

The change in free energy ∆G (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, ∆GV); and
2) the solid-liquid phase boundary (surface free
energy, ∆GS).

Transforming one phase into another takes time.
∆G = ∆GS + ∆GV
Fe
γ
(Austenite)
Eutectoid
transformation
C FCC
Fe3C
(cementite)
α
(ferrite)
+
(BCC)

7. r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy)
Homogeneous Nucleation & Energy Effects
∆GT = Total Free Energy
= ∆GS + ∆GV
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
γπ=∆ 2
4 rGS
γ = surface tension
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
υ∆π=∆ GrGV
3
3
4
volumeunit
energyfreevolume
=∆ υG

8. Solidification
TH
T
r
f
m
∆∆
γ−
=
2
*
Note: ∆Hf and γ are weakly dependent on ∆T
∴ r* decreases as ∆T increases
For typical ∆T r* ~ 10 nm
∆Hf = latent heat of solidification (fusion)
Tm = melting temperature
γ = surface free energy
∆T = Tm - T = supercooling
r* = critical radius

9. Transformations & Undercooling
• For transformation to occur,
must cool to below 727°C
• Eutectoid transformation (Fe-Fe3C system): γ ⇒ α + Fe3C
0.76 wt% C
0.022 wt% C
6.7 wt% C
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ +Fe3C
α +Fe3C
L+Fe3C
δ
(Fe) C, wt% C
1148°C
T(°C)
α
ferrite
727°C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
∆T
Undercooling by Ttransf. < 727°C
0.76
0.022

10. 2
• Fraction transformed depends on time.
fraction
transformed time
y = 1− e
−ktn
Avrami Eqn.
• Transformation rate depends on T.
1 10 102 1040
50
100
135°C
119°C113°C102°C
88°C
43°C
y (%)
log (t) min
Ex: recrystallization of Cu
r =
1
t
0.5
= Ae
−Q /RT
activation energy
• r often small: equil not possible
y
log (t)
Fixed
T
0
0.5
1
t0.5
FRACTION OF TRANSFORMATION

11. Generation of Isothermal Transformation Diagrams
• The Fe-Fe3C system, for Co = 0.76 wt% C
• A transformation temperature of 675°C.
100
50
0
1 102 104
T = 675°C
%transformed
time (s)
400
500
600
700
1 10 102 103 104 105
0%pearlite
100%
50%
Austenite (stable)
TE (727°C)Austenite
(unstable)
Pearlite
T(°C)
time (s)
isothermal transformation at 675°C
Consider:

12. Coarse pearlite  formed at higher temperatures – relatively soft
Fine pearlite  formed at lower temperatures – relatively hard
• Transformation of austenite to pearlite:
γα
α
α
α
α
α
pearlite
growth
direction
Austenite (γ)
grain
boundary
cementite (Fe3C)
Ferrite (α)
γ
• For this transformation,
rate increases with ( ∆T)
[Teutectoid – T ].
675°C
(∆T smaller)
0
50
%pearlite
600°C
(∆T larger)
650°C
100
Diffusion of C
during transformation
α
α
γ
γ
α
Carbon
diffusion
Eutectoid Transformation Rate ~ ∆T

13. 5
• Reaction rate is a result of nucleation and growth of crystals.
• Examples:
% Pearlite
0
50
100
Nucleation
regime
Growth
regime
log (time)t50
Nucleation rate increases w/ ∆T
Growth rate increases w/ T
Nucleation rate high
T just below TE T moderately below TE T way below TE
Nucleation rate low
Growth rate high
γ γ γ
pearlite
colony
Nucleation rate med .
Growth rate med. Growth rate low
Nucleation and Growth

14. Isothermal Transformation Diagrams
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.

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

16. Transformations Involving
Noneutectoid Compositions
Hypereutectoid composition – proeutectoid cementite
Consider C0 = 1.13 wt% C
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ +Fe3C
α+Fe3C
L+Fe3C
δ
(Fe)
C, wt%C
T(°C)
727°C
∆T
0.76
0.022
1.13

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

18. Coarse pearlite (high diffusion rate) and (b) fine pearlite
- Smaller ∆T:
colonies are
larger
- Larger ∆T:
colonies are
smaller

19. 10 103
105
time (s)
10-1
400
600
800
T(°C)
Austenite (stable)
200
P
B
TE
0%
100%
50%
A
A
Bainite: Non-Equil Transformation Products
 elongated Fe3C particles in α-ferrite matrix
 diffusion controlled
 α lathes (strips) with long rods of Fe3C
100% bainite
100% pearlite
Martensite
Cementite
Ferrite

20. 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).

21. 10
 Fe3C particles within an α-ferrite matrix
 diffusion dependent
 heat bainite or pearlite at temperature just below eutectoid for long times
 driving force – reduction of α-ferrite/Fe3C interfacial area
Spheroidite: Nonequilibrium Transformation
10 103 105time (s)10-1
400
600
800
T(°C)
Austenite (stable)
200
P
B
TE
0%
100%
50%
A
A
Spheroidite
100% spheroidite
100% spheroidite

22. Pearlitic Steel partially transformed to Spheroidite

23.  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
Martensite Formation
• Isothermal Transformation Diagram
10 10
3
10
5
time (s)10
-1
400
600
800
T(°C)
Austenite (stable)
200
P
B
TE
0%
100%50%
A
A
M + A
M + A
M + A
0%
50%
90%
Martensite needles
Austenite

24. 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.

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

26. 
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;
Effect of Adding
Other Elements
4340 Steel
plain
carbon
steel
nose

Plain carbon steel: primary
alloying element is carbon.

27. 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%

28. Martensite,
100%
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%

29. Bainite, 50%
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
Final:
50% Bainite,
50% Pearlite

30. Continuous Cooling
Transformation Diagrams
 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 (dotted 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.

31.  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.

The austenite-pearlite region
(A---B) terminates just below
the nose. Continued cooling
(below Mstart) of austenite will
form martensite.

32. 
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

33. 
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.

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

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

36. Mechanical Properties: Fe-C System

37.  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 α-ferrite. US Steel Corp.
Tempered Martensite
4340 steel

38. Hardness as a function of carbon
concentration for steels

39. Hardness versus tempering time for a water-quenched eutectoid plain carbon steel (1080);
room temperature.
Rockwell C and Brinell Hardness

41. 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.
• Other 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

42. 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 (α phase solid
solution supersaturated with B
atoms; alloy is soft, weak-no ppts).
Phase Diagram for Precipitation Hardened Alloy

43. 
The supersaturated α solid
solution is usually heated to an
intermediate temperature T2
within the α+β region (diffusion
rates increase).

The β 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.
Precipitation Heat Treatment – the 2nd
stage

44. 0 10 20 30 40 50
wt% Cu
L
α+Lα
α+θ
θ
θ+L
300
400
500
600
700
(Al)
T(°C)
composition range
available for precipitation hardening
CuAl2
A
Precipitation Hardening
• Particles impede dislocation motion.
• Ex: Al-Cu system
• Procedure:
-- Pt B: quench to room temp.
(retain α solid solution)
-- Pt C: reheat to nucleate
small θ particles within
α phase.
Temp.
Time
-- Pt A: solution heat treat
(get α solid solution)
Pt A (solution heat treat)
B
Pt B
C
Pt C (precipitate θ)
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).

45. Precipitation Heat Treatment – the 2nd
stage

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.

46. 24
• Hard precipitates are difficult to shear.
Ex: Ceramics in metals (SiC in Iron or Aluminum).
Large shear stress needed
to move dislocation toward
precipitate and shear it.
Side View
Top View
Slipped part of slip plane
Unslipped part of slip plane
S
Dislocation
“advances” but
precipitates act as
“pinning” sites with
spacing S.
precipitate
• Result: σy ~
1
S
PRECIPITATION STRENGTHENING

47. Several stages in the formation of the equilibrium
PPT (θ) phase.
(a)supersaturated α solid solution;
(b)transition (θ”) PPT phase;
(c)equilibrium θ phase within the α matrix phase.

48. • 2014 Al Alloy:
• TS peak with precipitation time.
• Increasing T accelerates
process.
Influence of Precipitation Heat Treatment on
Tensile Strength (TS), %EL
precipitation heat treat time
tensilestrength(MPa)
200
300
400
100
1min 1h 1day 1mo 1yr
204°C
non-equil.
solidsolution
manysmall
precipitates“aged”
fewerlarge
precipitates
“overaged”
149°C
• %EL reaches minimum
with precipitation time.
%EL(2insample)
10
20
30
0
1min 1h 1day 1mo 1yr
204°C 149°C
precipitation heat treat time

49. 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.

50. Aluminum rivets

Alloys that experience significant
precipitation hardening at room
temp and 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.