material science slide of addis ababa university

1. Chapter 1
Phase
Transformations in
MetalsFe3C (cementite)- orthorhombic
Martensite - BCT
Austenite - FCC
Ferrite - BCC

2. Why do we study phase transformations?
 The tensile strength of an Fe-C alloy of eutectoid
composition can be varied between 700-2000 MPa
depending on HT process adopted.
 Desirable mechanical properties of a material can be
obtained as a result of phase transformations using the
right HTprocess.
 In order to design a HT for some alloy with desired RT
properties, time & temperature dependencies of some
phase transformations can be represented on modified
phase diagrams.
Based on this, we will learn:
A. Phase transformations in metals
B. Microstructure and property dependence in Fe-C alloy system
C. Precipitation Hardening

3. Topics to be covered:
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

4. 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, re-
crystallization, grain growth

More complicated diffusion-dependent

Change in # of phases

Change in composition

Example: eutectoid reaction

Diffusion-less

Example: meta-stable phase : martensite

5. Phase Transformations -Stages

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.
1. Homogeneous nucleation - nuclei form uniformly throughout the
parent phase; requires considerable supercooling (typically 80-
300°C).
2. Heterogeneous nucleation - form at structural in-homogeneities
(container surfaces, impurities, grain boundaries, dislocations) in
liquid phase much easier since stable “nucleating surface” is
already present; requires slight super-cooling (0.1-10ºC).

6. 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 super-cooling
or under-cooling.

The driving force to nucleate increases as ∆T increases

Small super-cooling  slow nucleation rate - few nuclei -
large crystals

Large super-cooling  rapid nucleation rate - many nuclei
- small crystals

7. Kinetics of Solid State Reactions
Transformations involving diffusion depend on time.
Time is also necessary for the energy increase associated with
the phase boundaries between parent and product phases.
Moreover, nucleation, growth of the nuclei, formation of grains
and grain boundaries and establishment of equilibrium take
time.
As a result we can say the transformation rate is a function of
time.
The fraction of reaction completed is measured as a function of
time at constant T.
Tranformation progress can be measured by microscopic
examination or measuring a physical property (e.g.,
conductivity).
The obtained data is plotted as fraction of the transformation
versus logarithm of time.

8. 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
t
0.5
FRACTION OF TRANSFORMATION

9. Percent recrystallization as a function of time
and at constant temperature for pure copper.

10. 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

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

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. Eutectoid Transformation Rate
At T just below 727°C, very long times (on the order of 105
s) are
required for 50% transformation and therefore transformation rate is
slow.
The transformation rate increases as T decreases, for example, at
540°C 3 s is required for 50% completion.
This observation is in clear contradiction with the equation of
This is because in T range of 540°C-727°C, the transformation
rate is mainly controlled by the rate of pearlite nucleation and
nucleation rate decreases with increasing T. Q in this equation
is the activation energy for nucleation and it increases with T
increase.
It has been found that at lower T, the austenite decomposition
is diffusion controlled and the rate behavior can be calculated
using Q for diffusion which is independent of T.
r =
1
t
0.5
= Ae
−Q /RT
activation energy

14. 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

15. Isothermal Transformation Diagrams
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.

16. • 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

17. 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

18. Strength
DuctilityMartensite
T Martensite
bainite
fine pearlite
coarse pearlite
spheroidite
General Trends
Possible Transformations

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

20. 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-Equilibrium 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

21. Bainite Microstructure
Bainite: formed as a result of transformation of
austenite.
Bainite consists of ferrite and cementite and diffusion
processes take place as a result.
This structure looks like needles or plates. There is no
proeutectoid phase in bainite.
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.

22. 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

23. Pearlitic Steel partially transformed to Spheroidite

24. Design a heat treatment to produce the pearlite structure
shown in Figure
micrograph of the pearlite
lamellae (x 2000)
The effect of the austenite
transformation temperature on
the interlamellar spacing in
pearlite.
7.14

25. A
B C
D
E

26. A
B C

27. The Martensitic Reaction and Tempering
Martensiteis : is result of a diffusionless solid-state transfomation .
•The growth rate is so high → nucleation is controlling step.
• is an athermal transformation (i.e. the reaction depends only
on the temperature, not on the time)
FCC austenite
upon quenching,
In steels (< 0.2% C) nonequilibrium supersaturated
BCC martensite structure
In steels (>0.2% C)
FCC austenite
upon quenching, BCT (body-centered tetragonal)
martensite
BCT caused by the Carbon
atoms in the (1/2, 0, 0) site
being trapped during the
transformation to the BCC
%C(martensite) = %C (the starting austenite)

29.  single phase
 body centered tetragonal (BCT) crystal structure
 BCT if C0 > 0.15 wt% C
 Diffusion-less transformation
 BCT  few slip planes  hard, brittle
 % transformation depends only on T of rapid cooling
Martensite Formation
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

30. 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.

31. Iron-carbon alloy
with eutectoid
composition.

A: Austenite

P: Pearlite

B: Bainite

M: Martensite

32. 
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.

33. Example 1:
 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%

34. Martensite,
100%
Example 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%

35. Bainite, 50%
Example 3:
 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

36. 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.

37. 
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.

38. 
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

39. 
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.

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

41. 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)

42. Mechanical Properties: Fe-C System

43. Example: P10.37
For a eutectoid steel, describe isothermal
heat treatments that would be required to
yield specimens having the following Brinell
Hardnesses:
1. 180 HB
2. 220 HB
3. 500 HB

44. Martensite is hard but also very brittle so that it can not be used in
most of the applications.
Any internal stress that has been introduced during quenching has a
weakening effect.
The ductility and toughness of the material can be enhanced by heat
treatment called tempering. This also helps to release any internal
stress.
Tempering is performed by heating martensite to a T below eutectoid
temperature (250°C-650°C) and keeping at that T for specified period
of time.
The formation of tempered martensite is by diffusion.
Tempered Martensite

45.  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

46. Tempered martensite may be nearly as hard and strong as martensite,
but with substantially enhanced ductility and toughness.
The hardness and strength may be due to large area of phase
boundary per unit volume of the material.
The phase boundary acts like a barrier for dislocations. The
continuous ferrite phase in tempered martensite adds ductility and
toughness to the material.
The size of the cementite particles is important factor determining
the mechanical behavior.
As the cementite particle size increases, material becomes softer
and weaker. The temperature of tempering determines the
cementite particle size. Since martensite-tempered martensite
transformation involves diffusion, Increasing T will accelerate the
diffusion and rate of cementite particle growth and rate of
softening as a result.
Tempered Martensite

47. Hardness as a function of carbon
concentration for steels

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

50. Example: P10.25
Briefly describe the simplest continuous cooling
heat treatment procedure that would be used in
converting a 4340 steel from microstructure to
another.
1. (Martensite + Ferrite + Bainite) to (Martensite +
Ferrite + pearlite + Bainite)
2. (Martensite + Ferrite + Bainite) to (spheroidite)
3. (Martensite + Ferrite + Bainite) to (tempered
Martensite)

51. 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

52. 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

53. 
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

54. 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).

55. 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.

56. 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

57. 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.

58. • 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

59. 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.

60. 
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.