CHAPTER 11:
PHASE TRANSFORMATIONS
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
Fe

(Austenite)
C
FCC
Fe C
3
Eutectoid
transformation (cementite)
+

(ferrite)
(BCC)
• 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 the mechanical properties of non-equilibrium
structures better?
1
Phase Transformations
• Introduction and Motivation
– Microstructure  Processing  Properties
– Our previous discussions focused on the equilibrium
phase diagrams
• These tell you what can happen
– Now we will talk about the rates of phase changes to
find out what does happen
– Why is this important? Many materials are not
processed under equilibrium conditions
• Heating/cooling rates
Phase Transformations
•
Phase Transformation
–
–
–
A phase transformation is an alteration in the number and/or
compositions of the phases present in a material
These are usually not instantaneous processes (hence our
interest in rates)
Organize these into 3 categories
1.
2.
3.
Diffusion dependent processes with no change in the composition
or number of phases – solidification, allotropic transformations,
grain boundary growth, recrystallization
Diffusion dependent process with a change in the number and/or
composition of phases – eutectic, eutectoid, peritectic reactions
Diffusionless processes – form metastable states (haven’t seen
these yet)
FRACTION OF TRANSFORMATION
• Fraction transformed depends on time.
Adapted from
Fig. 10.1,
Callister 6e.
• Transformation rate depends on T.
Adapted from Fig.
10.2, Callister 6e.
(Fig. 10.2 adapted
from B.F. Decker and
D. Harker,
"Recrystallization in
Rolled Copper",
Trans AIME, 188,
1950, p. 888.)
• r often small: equil not possible!
2
Phase Transformations
• Kinetics of phase transformations
– Phase transformations are not usually instantaneous
– Hence from a processing viewpoint their rates are of
interest
• These transformations have two key events
– Nucleation – formation of small clusters (~10’s –100’s of atoms)
of the new phase
– Growth – little clusters get bigger
Phase Transformations
• Kinetics of phase transformations
– Nucleation – two types
• Homogeneous nucleation – nuclei of the new phase are
formed uniformly throughout the parent or original phase
• Heterogeneous nucleation – nuclei of the new phase form
preferentially at heterogeneities (surfaces, impurities, etc.)
– The energetics (and hence kinetics) of these
processes are typically different
• The discussion of energetics will use free energies
– Remember the Gibbs free energy DG?
– DG < 0 for transformation occur spontaneously
DG  DH  TDS
TRANSFORMATIONS & SUPERCOOLING
super
Adapted from Fig.
9.21,Callister 6e. (Fig.
9.21 adapted from Binary
Alloy Phase Diagrams,
2nd ed., Vol. 1, T.B.
Massalski (Ed.-in-Chief),
ASM International,
Materials Park, OH, 1990.)
super
For cooling, transformations are shifted to lower temperatures than indicated by the phase
diagram
3
NUCLEATION AND GROWTH
• Reaction rate is a result of nucleation and growth
of crystals.
Adapted from
Fig. 10.1, Callister 6e.
• Examples:
5
Phase Transformations
•
Nucleation
–
–
Homogeneous nucleation – start with simple picture: what is
the free energy of a small spherical particle of a solid in a
continuous media of the liquid (i.e. solidification)
Two major contributions to the free energy
1.
2.
Free energy difference between the solid and liquid phases (book
calls it the volume free energy) DGv
Free energy of the solid-liquid phase boundary
4
1.  r 3 DGv
3
2.  4r 2
Few points: 1) DGv is negative if T < T solidification
2) The surface free energy  is always positive
So,
4
DG  r 3 DGv  4r 2
3
Phase Transformations
•
Nucleation
–
–
Homogeneous nucleation
So what does the plot of DG versus r look like?
4
DG  r 3 DGv  4r 2
3
There is a clear maximum in DG
as a function of r
This size r* has physical meaning
Particles smaller than this will
not lead to nuclei
Particles this size or larger will
grow (they are called nuclei)
DG* can be thought of as an
energy barrier to nucleation
embryo (r < r*)
nucleus (r > r*)
What is the value of DG* ?
Phase Transformations
d DG  d  4 3
2 
  r DGv  4r    0
dr
dr  3

4r 2 DGv  8r  0
 2
r 
DGv

•
Sub into
Original eqn.
Nucleation
–
–
4 3
DG  r DGv  4r 2
3
Homogeneous nucleation
– DG*, r*
Take derivative of DG with
respect to r and set it
equal to zero!
16 3
DG 
2
3DGv 

Some observations – DGv is the driving force for nucleation (solidification)
It is a function of temperature!
At the equilibrium melting temperature Tm its value is zero!
Can I relate this to enthalpies? Of course!
Phase Transformations
•
Nucleation
–
–
DGv 
Homogeneous nucleation – DG*, r*
Relations using enthalpy
DH f Tm  T 
Tm
What do the equations tell you?
Both r* and DG* decrease as T decreases
for T < Tm
T2 < T 1
  2Tm  1 


r 
 DH  T  T 
f  m


*
3 2 

16

Tm 
1
DG *  
 3DH 2  T  T 2
f

 m
Phase Transformations
•
Nucleation
–
Homogeneous nucleation – How many nuclei?
*



D
G
*

n  K1 exp 
 k BT 
  Qd
vd  K 2 exp 
 k BT



Increase T, fewer nuclei (not immediately clear from this!)
Frequency of attachment (how often do clusters collide
and combine) – why is this related to diffusion?
Put all this together … the rate of nucleation is …
*



  Qd

D
G
*
 exp 
N  K 3 n vd  K1 K 2 K 3 exp 
 k BT
  k BT 

K3 is the number of atoms on a nucleus surface



Phase Transformations
•
Nucleation
–
Homogeneous nucleation – rate!

   DG * 
  Qd
*
 exp 
N  K 3 n vd  K1 K 2 K 3 exp 
 k BT
  k BT 



Plots clearly show there is an optimal temperature for maximizing the nucleation rate.
EUTECTOID TRANSFORMATION RATE ~ DT
• Growth of pearlite from austenite:
Adapted from
Fig. 9.13,
Callister 6e.
• Reaction rate
increases with
DT.
Adapted from
Fig. 10.3,
Callister 6e.
4
Phase Transformations
•
Nucleation
–
Homogeneous nucleation – supercooling
•
It can turn out that to have appreciable nucleation take
place the sample temperature must be well below the
equilibrium melting (solidification) temperature
–
This is called supercooling – the degree of supercooling can
be significant!
TRANSFORMATIONS & SUPERCOOLING
Adapted from Fig.
9.21,Callister 6e. (Fig.
9.21 adapted from Binary
Alloy Phase Diagrams,
2nd ed., Vol. 1, T.B.
Massalski (Ed.-in-Chief),
ASM International,
Materials Park, OH, 1990.)
super
For cooling, transformations are shifted to lower temperatures than indicated by the phase
diagram
3
NUCLEATION AND GROWTH
• Reaction rate is a result of nucleation and growth
of crystals.
Adapted from
Fig. 10.1, Callister 6e.
• Examples:
5
Phase Transformations
•
Example Problem 11.1
–
For the solidification of pure gold, calculate r* and DG* if
nucleation is homogeneous. DHf = -1.16 x 109 J/m3,  = 0.132
J/m2. Use supercooling value from table 11.1 (230 C)
  2Tm  1 


r 
 DH  T  T 
f  m


  20.132 J / m 2 1064  273K  1 
*
r 


9
3

1
.
16

10
J
/
m
230
K



*
r *  1.32 10 9 m  1.32nm
 16 3Tm2 
1

DG  
 3DH 2  T  T 2
f

 m
2
2 3



16

0
.
132
J
/
m
1064  273K  
1
*


DG 
 230 K 2 
9
3 2


3  1.16 10 J / m



*


DG *  9.64 10 19 J


*Where did the 1064 C
come from? That is the
melting temperature of
gold!
Phase Transformations
•
Example Problem 11.1
–
(b) Now determine the number of Au atoms in a nucleus of
critical size. Assume a lattice parameter of 0.413 nm.
# unit cells critical nucleus volume

particle
unit cell volume
 
4

r*
# unit cells 3

particle
a3
3
4
 1.32nm 3
3
 137
3
0.413nm
How many atoms: 4 x 137 = 548 atoms/critical nucleus
Phase Transformations
•
Nucleation
–
Heterogeneous nucleation
•
•
Following up on the last point, in fact large degrees of
supercooling are usually not observed
Why? Turns out you can have heterogeneous nucleation
as well
–
•
Exactly what it sounds like – the solid nucleates from an
interface
» Preexisting surface, impurity atom, etc.
Can use similar approach as before to describe energetics
of heterogeneous nucleation
Phase Transformations
•
Nucleation
– Heterogeneous
nucleation
•
Consider a flat surface
or interface and a solid
particle that nucleates
off it
• Now there are three interfacial energy terms
• Interface-liquid (IL), solid-liquid (SL), solid-interface (SI) (*SL
was the one from before)
• If you write a force balance for the surface tension in the plane
of the surface you get
 IL   SI   SL cos 
*Note: there is still a free energy
difference between the solid and
liquid (next slide)
Phase Transformations
• Nucleation
– Heterogeneous nucleation
• Using same approach before to find the maximum Gibbs free energy
(and corresponding r) gives
 2 SL
r 
DGv
*
3


16


SL
 S  
DG  
3 
 3DGv 
Few points about the equations:
1. S() is only a function of the wetting angle
and varies between 0 and 1.
2. r* is the same as before
3. The expression for DG* is similar to before
(except for the S() function)
4. Note that the expression for the free energy
for heterogeneous nucleation is always lower
than that for homogeneous nucleation


DGhet
 DGhom
S  
Phase Transformations
• Nucleation
– Heterogeneous nucleation
• What does this mean physically? Heterogeneous nucleation is
faster than homogeneous nucleation!
• The N vs T curve is shifted to higher temperatures for
heterogeneous nucleation
Phase Transformations
• Growth
– Growth begins once an embryo (or cluster) has exceeded the
critical size r* and becomes a stable nucleus
– Nucleation still occurs during the growth phase
– Growth ceases in a region where particles of the new phase meet
– Physical mechanism of growth – long-range diffusion processes
• Diffusion in the liquid phase to the growing phase
– Since the growth rate is governed by diffusion it can be written in
the form
 Q 

G  C exp 
 k BT 

Phase Transformations
• Growth
– Few comments based on figure below
• Want large grains – solidify the material close to Tm
• Want small grains – solidify far below Tm
• Cool quickly enough – can form non-equilibrium phases
Phase Transformations
• Kinetics of solid-state transformations
– So now you have some idea about the mechanism of
solidification
• How do you describe the kinetics of this?
• Issue 1 – need way to monitor phase transformation
• S-shaped or sigmoidal curves are often observed in plots of
the fraction of transformation ( y) v log(time)
• The mathematical expression is often referred to as the
Avrami equation
y  1  exp( kt n )
k, n are material specific
Another convention is that the rate of transformation is taken as the time needed for the
transformation to proceed halfway (t0.5)
rate 
1
t 0 .5
Phase Transformations
• Kinetics of solid-state transformations
– One other point – the kinetics of the transformation depend
strongly on T
– Now some pictures …
FRACTION OF TRANSFORMATION
• Fraction transformed depends on time.
Adapted from
Fig. 10.1,
Callister 6e.
• Transformation rate depends on T.
Adapted from Fig.
10.2, Callister 6e.
(Fig. 10.2 adapted
from B.F. Decker and
D. Harker,
"Recrystallization in
Rolled Copper",
Trans AIME, 188,
1950, p. 888.)
• r often small: equil not possible!
2
Phase Transformations
• Metastable versus equilibrium structures
– Many ways to induce phase transformations, but temperature is
the easiest
– You have seen that on the phase diagrams
– Additionally, the phase diagrams are based on equilibrium
states, but contain no information about the rate equilibrium is
achieved
– So what? It turns out that in practice the cooling/heating rates to
achieve equilibrium states are prohibitively slow
– Transformations are shifted to lower temperatures than the
phase diagrams indicate
• Ex. Iron-carbon eutectoid is shifted by 10 – 20 C below the
equilibrium T for normal cooling rates used
Phase Transformations
• Metastable versus equilibrium structures
– But there is more
– Often the heating and cooling rates are such that one achieves
metastable states (i.e. non equilibrium states) that exist between
the initial and equilibrium states
• This may actually be very desirable
– This is why kinetics matter!
• Isothermal Transformation Diagrams
– Use these to understand rates of phase transformations
– Consider the iron-iron carbide eutectoid reaction
cooling, heating
 0.767 wt %C  
   0.022wt %C   Fe3C 6.70wt %C 
• This is a very important reaction in
terms of microstructure
development in steel – this reaction
leads to pearlite formation
• The isothermal transformation
diagram will tell you how fast the
pearlite phase forms at a given T
This is the isothermal
transformation diagram
• Isothermal Transformation Diagrams
– How do you read these?
There are two solid lines
One indicates the time at which the
transformation begins
The indicates when the transformation ends
Dashed line – 50% completed
These are also called time-temperaturetransformation (T-T-T) plots
Also note that the initial composition is fixed
in this plot!
ISOTHERMAL
TRANSFORMATION DIAGRAMS
• Fe-C system, Co = 0.77wt%C
• Transformation at T = 675C.
Adapted from Fig. 10.4,Callister 6e.
(Fig. 10.4 adapted from H. Boyer (Ed.)
Atlas of Isothermal Transformation
and Cooling Transformation Diagrams,
American Society for Metals, 1977, p.
369.)
6
• Isothermal Transformation Diagrams
– Figure below shows the same plot now with the isothermal heat
treatment curve included (at the eutectoid composition)
PEARLITE MORPHOLOGY
Two cases:
• Ttransf just below TE
--Larger T: diffusion is faster
--Pearlite is coarser.
• Ttransf well below TE
--Smaller T: diffusion is slower
--Pearlite is finer.
Adapted from Fig. 10.6 (a) and (b),Callister 6e. (Fig. 10.6 from R.M. Ralls et al., An Introduction to
Materials Science and Engineering, p. 361, John Wiley and Sons, Inc., New York, 1976.)
- Smaller DT:
colonies are
larger
- Larger DT:
colonies are
smaller
8
EX: COOLING HISTORY Fe-C SYSTEM
• Eutectoid composition, Co = 0.77wt%C
• Begin at T > 727C
• Rapidly cool to 625C and hold isothermally.
Adapted from Fig.
10.5,Callister 6e.
(Fig. 10.5 adapted from
H. Boyer (Ed.) Atlas of
Isothermal
Transformation and
Cooling Transformation
Diagrams, American
Society for Metals,
1997, p. 28.)
7
Phase Transformations
• Isothermal Transformation Diagrams
– Comments about pearlite structure
– The thickness ratio of ferrite and cementite layers in pearlite is
approximately 8:1
– However, the absolute thickness of the layers depends on the cooling
profile (what T the isothermal transformation is allowed to occur)
– Higher T (closer to eutectoid) – thick layers – coarse pearlite
– Lower T (farther from eutectoid) – thin layers – fine pearlite
Phase Transformations
• Isothermal Transformation Diagrams
– Bainite
• Another microstructure that can form from austenitic
transformations (in addition to Pearlite)
– Note! Not a different phase, a different microstructure
– Bainite is a mixture of ferrite and cementite phases
• It forms as needles or plates – domain sizes are much smaller as
compared to pearlite
– No proeutectoid forms with bainite
Structure obtained with electron
microscopy
Bainite:
Needles of ferrite in a matrix of cementite
• Isothermal Transformation Diagrams
– Looking at the isothermal transformation plot a few points
• Bainite forms at lower temperatures
• Pearlite forms at higher temperatures
– These phases form competitively!
• Either form one microstructure or the other ( Note: there is no
mixture of B+P) on the figure!
Rate of transformation is a
maximum at N
• Isothermal Transformation Diagrams
– Spheroidite
• Another wrinkle – if I take the materials above containing either
pearlite or bainite domains and heat it near the eutectoid
temperature (e.g. 973 K) for a sufficiently long period of time,
(18-24 h) another microstructure forms … spheroidite
• Instead of lamellae (pearlite) or stripes of cementite and ferrite
(bainite), here the cementite domains are spherical encapsulated in
a ferrite matrix
Phase Transformations
• Isothermal Transformation Diagrams
– Spheroidite
• How does this happen? It is due to carbon diffusion with no change
in the composition/relative amounts of ferrite and cementite
• The driving force for this is the reduction of the ferrite-cementite
phase boundary area
• Final point:
– Pearlite, bainite, spheroidite
• These are all ferrite/cementite 2-phase solids
• The difference? The microstructure – size/shape of the
ferrite/cementite domains!
Phase Transformations
• Isothermal Transformation Diagrams
– Martensite
• Get this when you rapidly cool austenized iron-carbon alloys to low
temperatures (e.g. ambient T)
• This is a nonequilibrium single-phase solid
– Diffusionless transformation of austenite ( on phase diagram)
• Transformation product that competes with bainite, pearlite formation
• Observe martensite when quenching is fast enough to prevent
carbon diffusion
Rapid quench
Austenite
(FCC)
Body centered tetragonal (BCT)
Martensite (BCT)
Phase Transformations
• Isothermal Transformation Diagrams
– Martensite
• The BCT structure you get is the the original structure
elongated
• Carbon is still in the interstitial positions – another view is that
martensite is supersaturated in carbon
• Since this transformation does not involve diffusion it occurs
almost instantly
• Martensite and other microconstituents can coexist
Martensite forms as platelets/needles
Phase Transformations
• Isothermal Transformation
Diagrams
– Martensite
• Why don’t you see
martensite on the phase
diagrams?
• You do see it on the
isothermal transformation
diagrams
• See martensite lines
– Note they are horizontal –
why do you think that is?
– Transformations like this
are called athermal –
why? They are only a
function of the quenching
temperature (the
transformation is time
independent)
• Isothermal Transformation Diagrams
– Summary
• Ok, time to wake up! – Here is the picture summarizing all this!
Phase Transformations
•
Example problem 11.2 – using
the figure below, specify the final
microstructures obtained from a
sample, that is initially at 760 C
possessing a homogeneous
austenite structure, which is then
a)
b)
c)
Rapidly cooled to 350 C, held at
350 C for 104 s, and then
quenched to RT
Rapidly cooled to 250 C, held at
250 C for 102 s, and then
quenched to room temperature
Rapidly cooled to 650 C, held at
650 C for 20 s, rapidly cooled to
400 C, held at 400 C for 103 s,
and then quenched to RT
Phase Transformations
•
Example problem 11.2 – using
the figure below, specify the final
microstructures obtained from a
sample, that is initially at 760 C
possessing a homogeneous
austenite structure, which is then
a)
Rapidly cooled to 350 C, held at
350 C for 104 s, and then
quenched to RT
What is the microstructure?
PURE BAINITE
Phase Transformations
•
Example problem 11.2 – using
the figure below, specify the final
microstructures obtained from a
sample, that is initially at 760 C
possessing a homogeneous
austenite structure, which is then
b)
Rapidly cooled to 250 C, held at
250 C for 102 s, and then
quenched to room temperature
What is the microstructure?
PURE MARTENSITE
Phase Transformations
•
Example problem 11.2 – using
the figure below, specify the final
microstructures obtained from a
sample, that is initially at 760 C
possessing a homogeneous
austenite structure, which is then
c)
Rapidly cooled to 650 C, hold at
650 C for 20 s, cool rapidly to
400 C, hold for 103 s, and then
quenched to room temperature
What is the microstructure?
50/50 Pearlite/Bainite
NON-EQUIL TRANSFORMATION
PRODUCTS: Fe-C
• Bainite:
-- lathes (strips) with long
rods of Fe3C
--diffusion controlled.
• Isothermal Transf. Diagram
Fe3C
(cementite)
(ferrite)
5 m
(Adapted from Fig. 10.8, Callister, 6e. (Fig.
10.8 from Metals Handbook, 8th ed.,
Vol. 8, Metallography, Structures, and
Phase Diagrams, American Society for
Metals, Materials Park, OH, 1973.)
Adapted from Fig. 10.9,Callister 6e.
(Fig. 10.9 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and
Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)
9
OTHER PRODUCTS: Fe-C SYSTEM
• Spheroidite:
(1)

-- crystals with spherical Fe3C
(ferrite)
--diffusion dependent.
--heat bainite or pearlite for long times
--reduces interfacial area (driving force) Fe3C
• Isothermal Transf. Diagram
(cementite)
60 m
(Adapted from Fig. 10.10, Callister,
6e. (Fig. 10.10 copyright United
States Steel Corporation, 1971.)
Adapted from Fig. 10.9,Callister 6e.
(Fig. 10.9 adapted from H. Boyer (Ed.) Atlas of
Isothermal Transformation and Cooling
Transformation Diagrams, American Society for
Metals, 1997, p. 28.)
10
OTHER PRODUCTS: Fe-C SYSTEM
(2)
• Martensite:
--(FCC) to Martensite (BCT)
Fe atom
sites
x
x
x
potential
C atom sites
x
x
x
(Adapted from Fig.
10.11, Callister, 6e.
60 m
(involves single atom jumps)
• Isothermal Transf. Diagram
Martentite needles
Austenite
(Adapted from Fig. 10.12, Callister,
6e. (Fig. 10.12 courtesy United
States Steel Corporation.)
Adapted
from Fig.
10.13,
Callister 6e.
•  to M transformation..
-- is rapid!
-- % transf. depends on T only.
11
COOLING EX: Fe-C SYSTEM (1)
Adapted
from Fig.
10.15,
Callister 6e.
12
COOLING EX: Fe-C SYSTEM (2)
Adapted
from Fig.
10.15,
Callister 6e.
13
COOLING EX: Fe-C SYSTEM (3)
Adapted
from Fig.
10.15,
Callister 6e.
14
Phase Transformations
• Continuous Cooling Transformation Diagrams
– Turns out that isothermal heat treatments are not the most practical
(why?)
– Continuous cooling is more practical – this means we need to look
at things differently
• Isothermal transformation diagrams assume T is fixed
• Continuous cooling transformation (CCT) diagrams
– T is changing, the cooling rate is fixed
– Turns out the time required for reaction is longer (why?)
• Continuous Cooling Transformation Diagrams
– Comparison between T-T-T and CCT diagrams
• Big difference – plots for CCT diagrams you are constantly
cooling the sample down instead of holding it at a fixed T!
Does this make sense?
For the slow cooling curves what do I
have at the end?
Where is the bainite? Should there be
any?
Should there be any martensite?
Note: transformation ceases at the point
of intersection
Phase Transformations
• Continuous Cooling Transformation Diagrams
– Comparison between T-T-T and CCT diagrams
Time for the class to talk
1. Tell me with the T-T-T
curves mean
2. What does the CCT
curves mean?
Phase Transformations
• Continuous Cooling Transformation Diagrams
– Martensitic transformations
• To see martensite need to cool
quickly
• Trajectory is tangent or to
the right of the “nose”
• If trajectory does not cross line
indicating 100% pearlite
formation, get pearlite +
martensite, not pearlite +
bainite – why?
Critical cooling rate: minimum
quenching rate that produces
only martensitic structure
Phase Transformations
• Continuous Cooling Transformation Diagrams
– Full story .. “real steel” vs binary mixtures …
MECHANICAL PROP: Fe-C SYSTEM (1)
Adapted from Fig. 9.27,Callister
6e. (Fig. 9.27 courtesy Republic
Steel Corporation.)
Adapted from Fig. 9.30,Callister
6e. (Fig. 9.30 copyright 1971 by
United States Steel Corporation.)
Adapted from Fig.
10.20, Callister 6e.
(Fig. 10.20 based on
data from Metals
Handbook: Heat
Treating, Vol. 4, 9th
ed., V. Masseria
(Managing Ed.),
American Society for
Metals, 1981, p. 9.)
15
MECHANICAL PROP: Fe-C SYSTEM (2)
Adapted from Fig. 10.21, Callister
6e. (Fig. 10.21 based on data from
Metals Handbook: Heat Treating,
Vol. 4, 9th ed., V. Masseria
(Managing Ed.), American Society
for Metals, 1981, pp. 9 and 17.)
16
MECHANICAL PROP: Fe-C SYSTEM (3)
• Fine Pearlite vs Martensite:
Adapted from Fig. 10.23,
Callister 6e. (Fig. 10.23
adapted from Edgar C. Bain,
Functions of the Alloying
Elements in Steel, American
Society for Metals, 1939, p. 36;
and R.A. Grange, C.R. Hribal,
and L.F. Porter, Metall. Trans.
A, Vol. 8A, p. 1776.)
• Hardness: fine pearlite << martensite.
17
TEMPERING MARTENSITE
• reduces brittleness of martensite,
• reduces internal stress caused by quenching.
Adapted from
Fig. 10.25,
Callister 6e.
(Fig. 10.25
adapted from
Fig. furnished
courtesy of
Republic Steel
Corporation.)
Adapted from
Fig. 10.24,
Callister 6e.
(Fig. 10.24
copyright by
United States
Steel
Corporation,
1971.)
18
SUMMARY: PROCESSING OPTIONS
Adapted from
Fig. 10.27,
Callister 6e.
19
Phase Transformations
• Precipitation hardening
– Turns out you can modify the strength/hardness of some metal
alloys by forming a 2nd phase which is small and uniformly
dispersed in the original phase
– This is done by temperature treatments – called precipitation
hardening because the small particles are termed “precipitates”
– Can try to understand this using phase diagrams! (We will stick
to binary mixtures for simplicity…)
Phase Transformations
• Precipitation hardening – consider a theoretical AB
binary mixture
•
Two requisite features
have to be observed in the
phase diagram to “have”
precipitate hardening
1. An appreciable maximum
solubility of one
component in the other
(here point M)
2. A solubility limit that
rapidly decreases as T
decreases
Have both here…
Phase Transformations
• Precipitation hardening – consider a theoretical AB
binary mixture
•
•
Have those two points here … this is necessary but not sufficient!
Two-step process to achieve
precipitation hardening
1. Solution heat treatment –
heat up alloy to form single
solid phase (Co, heat to To).
Follow by rapid cooling (to
T1) to form a solid solution 
phase “supersaturated” in B
Phase Transformations
• Precipitation hardening – consider a theoretical AB
binary mixture
•
Two-step process to achieve
precipitation hardening
1. Solution heat treatment
2. Precipitation hardening treatment – heat
back up to intermediate temperature (T2)
in the two phase region so that diffusion
becomes appreciable. Form b
precipitate phase – final microstructure
of b phase (i.e. domain size) depends on
T chosen as well as the hold time.
Phase Transformations
• Precipitation hardening – consider a theoretical AB
binary mixture
•
How do mechanical properties depend on precipitation
hardening/aging?
Phase Transformations
• Precipitation hardening – microscopic view
– Okay, so what preceded was a “macroscopic” view of the
process that we rationalized via the phase diagrams
– What happens at the microscopic level? – Use Al-Cu as an
example (96-4 Al-Cu by weight)
Idea: this is 2-phase < ~500 C
1. Heat up to get into  phase
2. Quench
3. Then heat to induce
formation of the  phase as
a precipitate
Phase Transformations
• Precipitation hardening – microscopic view
– Use Al-Cu as an example (96-4 Al-Cu by weight)
Idea: this is 2-phase < ~500 C
1. Heat up to get into  phase
2. Quench
3. Then heat to induce
formation of the  phase as
a precipitate
After quench you have 
supersaturated in Cu (a)
Heat up, start to form something
looks like  phase (’,”).
These have considerable
lattice strain (b)
Eventually form  phase (c)
Phase Transformations
• Precipitation hardening
– Few final comments:
• Not all alloys are amenable to precipitation hardening
– Constraints given previously
• Plus: must establish considerable strain at the precipitate-matrix
interface to get the desired enhancement in hardness/strength
– Good practical example of “precipitate hardening”
• Rivets – aluminum alloys
– Driven while soft, and age harden at ambient conditions
PRECIPITATION HARDENING
• Particles impede dislocations.
• Ex: Al-Cu system
• Procedure:
--Pt A: solution heat treat
(get  solid solution)
--Pt B: quench to room temp.
--Pt C: reheat to nucleate
small  crystals within
 crystals.
• Other precipitation
systems:
• Cu-Be
• Cu-Sn
• Mg-Al
Adapted from Fig. 11.22, Callister 6e. (Fig. 11.22 adapted
from J.L. Murray, International Metals Review 30, p.5, 1985.)
Adapted from Fig.
11.20, Callister 6e.
20
PRECIPITATE EFFECT ON TS, %EL
• 2014 Al Alloy:
• TS peaks with
precipitation time.
• Increasing T accelerates
process.
• %EL reaches minimum
with precipitation time.
Adapted from Fig. 11.25 (a) and (b), Callister 6e. (Fig. 11.25 adapted from Metals Handbook:
Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker
(Managing Ed.), American Society for Metals, 1979. p. 41.)
21
SIMULATION: DISLOCATION
MOTION PEAK AGED MATERIAL
• Peak-aged
--avg. particle size = 64b
--closer spaced particles
efficiently stop dislocations.
Simulation courtesy
of Volker Mohles,
Institut für Materialphysik der
Universitåt, Münster, Germany
(http://www.
uni-munster.de/physik
/MP/mohles/). Used with
permission.
Click on image to
begin simulation
22
SIMULATION: DISLOCATION
MOTION
OVERAGED MATERIAL
• Over-aged
--avg. particle size = 361b
--more widely spaced
particles not as effective.
Simulation courtesy
of Volker Mohles,
Institut für Materialphysik der
Universitåt, Münster, Germany
(http://www.
uni-munster.de/physik
/MP/mohles/). Used with
permission.
Click on image to
begin simulation
23
STRENGTHENING STRATEGY 3:
PRECIPITATION STRENGTHENING
• Hard precipitates are difficult to shear.
Ex: Ceramics in metals (SiC in Iron or Aluminum).
1
• Result:  y ~
S
24
SIMULATION:
PRECIPITATION STRENGTHENING
• View onto slip plane of Nimonic PE16
• Precipitate volume fraction: 10%
• Average precipitate size: 64 b (b = 1 atomic slip distance)
Simulation courtesy of Volker
Mohles, Institut für
Materialphysik der Universitåt,
Münster, Germany
(http://www.unimunster.de/physik
/MP/mohles/). Used with
permission.
25
APPLICATION:
PRECIPITATION STRENGTHENING
• Internal wing structure on Boeing 767
Adapted from Fig.
11.0, Callister 5e.
(Fig. 11.0 is
courtesy of G.H.
Narayanan and A.G.
Miller, Boeing
Commercial
Airplane Company.)
• Aluminum is strengthened with precipitates formed
by alloying.
Adapted from Fig.
11.24, Callister 6e.
(Fig. 11.24 is
courtesy of G.H.
Narayanan and A.G.
Miller, Boeing
Commercial
Airplane Company.)
1.5m
26
Phase Transformations
• Time to finish this little voyage with a discussion of a few
things you already know about, and to talk about
polymers
– Crystallization, melting, and glass transitions in polymers
– Ok, you know about two of the three
• Crystallization – process by which, upon cooling, an ordered
crystalline phase forms from a liquid melt of polymer with a highly
random structure
• Melting – you know
• Glass transition – cool polymer from liquid melt that becomes a noncrystalline solid … becomes rigid but has structural ordering
reminiscent of the liquid state
Phase Transformations
• Polymer Crystallization – can describe this using approach
described earlier in the chapter (Avrami eqn, etc.)
– Molecular picture – chains go from a highly disordered state in
the melt to a highly ordered state in the solid upon cooling
• But remember, polymers are usually semicrystalline
– Have regions of crystalline and amorphous polymer
Polypropylene crystallization kinetics
This plot is normalized
Cannot completely crystallize PP
Phase Transformations
• Polymer Melting – go from a solid  liquid melt as the
polymer is heated above some temperature Tm
• Few differences between polymers and metals/ceramics
– Have a range of melting temperatures – the polymer does not
completely melt at one temperature like a molecular compound
• Why?
– Melting behavior depends on the polymer “history”  how it has
been processed
• Why would that be the case?
Phase Transformations
• The glass transition – cool from a melt, but get a
disordered solid instead of a crystalline solid
– Occurs due to reduction of motion of the segments of the
polymer chains with decreasing temperature
– Upon cooling: liquid  rubbery material  rigid solid
– Glass transition temperature (Tg) is when the transformation from
a rubbery material to a rigid solid is observed
• Why do we care about the glass transition? Observe
abrupt changes in material properties at Tg
Phase Transformations
• Tm and Tg are important for polymers –
they define the temperature ranges a
polymer can be used for applications!
• Determine Tm and Tg for polymers by
observing the specific volume as a
function of temperature
• Note differences in the plot for a
crystalline solid, glass, and
semicrystalline solid!
Phase Transformations
•
Factors (some) that influence polymer melting temperatures
1.
2.
3.
Chain stiffness – ease of rotation of bonds along backbone
Molecular weight – generally increase MW Tm increases; but there is a
range of Tm values
Degree of chain branching – what would you expect the correlation to
be here?
Phase Transformations
•
Factors (some) that influence polymer glass transition
temperatures
1.
Chain stiffness
1.
2.
3.
2.
3.
Bulky side groups
Polar side groups
Double-chain bonds and aromatic rings
Molecular weight
Crosslinking
In general terms the same things that increase the melting temperature
also increase the glass transition temperature
Typically Tg ~ 0.5 – 0.8 Tm (K)
ANNOUNCEMENTS
Reading: Chapter 11
HW # 7:Due Monday, March 19th : 11.2; 11.4;
11.9; 11.12
HW # 8: Due Monday, March 26th : 11.15;
11.20; 11.24; 11.28; 11.32; 11.41; 11.44;
11.D2; 11.D5; 11.D8
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