Chapter 11:Phase TransformationsPhase Transformations
ISSUES TO ADDRESS...• Transforming one phase into another takes time.
Fe Eutectoid
transformation
Fe3C(cementite)
(Austenite)C FCC
(ferrite)
+(BCC)
• How does the rate of transformation depend ontime and temperature ?
• Is it possible to slow down transformations so that• Is it possible to slow down transformations so that non-equilibrium structures are formed?
• Are the mechanical properties of non-equilibrium
Chapter 11 - 1
structures more desirable than equilibrium ones?
Phase TransformationsNucleation
– nuclei (seeds) act as templates on which crystals grow– for nucleus to form rate of addition of atoms to nucleus must be
faster than rate of lossfaster than rate of loss– once nucleated, growth proceeds until equilibrium is attained
Driving force to nucleate increases as we increase TDriving force to nucleate increases as we increase T– supercooling (eutectic, eutectoid)– superheating (peritectic)
Small supercooling slow nucleation rate - few nuclei - large crystals
Large supercooling rapid nucleation rate - many nuclei - small crystals
Chapter 11 - 2
Solidification: Nucleation Typesyp
• Homogeneous nucleationHomogeneous nucleation– nuclei form in the bulk of liquid metal– requires considerable supercooling q p g
(typically 80-300°C)
• Heterogeneous nucleation• Heterogeneous nucleation– much easier since stable “nucleating surface” is
already present — e.g., mold wall, impurities in y p g , , pliquid phase
– only very slight supercooling (0.1-10ºC)
Chapter 11 - 3
Homogeneous Nucleation & Energy EffectsSurface Free Energy- destabilizes the nuclei (it takes energy to make an interface)an interface)
24 rGS
= surface tension
GT = Total Free Energy
= surface tension
T gy= GS + GV
Volume (Bulk) Free Energy –Volume (Bulk) Free Energystabilizes the nuclei (releases energy)
GrGV3
343
volume unitenergy free volume
G
Chapter 11 - 4
r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy) Adapted from Fig.11.2(b), Callister & Rethwisch 3e.
Solidification
T2r* = critical radius
THTr
f
m
2*
H l t t h t f lidifi tiTm = melting temperature= surface free energy
Hf = latent heat of solidificationT = Tm - T = supercooling
Note: Hf and are weakly dependent on T
r* decreases as T increases
For typical T r* ~ 10 nm
Chapter 11 - 5
Overall transformation rate:
T N G T N G
Chapter 11 - 6
Rate of Phase Transformations
Kinetics - study of reaction rates of phaseKinetics study of reaction rates of phase transformations
• To determine reaction rate measure degree• To determine reaction rate – measure degree of transformation as function of time (while holding temp constant)holding temp constant)
How is degree of transformation measured?
electrical conductivity measurements –i l i
X-ray diffraction – many specimens required
measure propagation of sound waves –on single specimen
on single specimen
Chapter 11 - 7
on single specimen
Rate of Phase Transformationtransformation complete
med
, yFixed T
trans
form Fixed T
0.5 maximum rate reached – now amount unconverted decreases so rate slows
ract
ion
t unconverted decreases so rate slows
t0.5
rate increases as surface area increases & nuclei grow
A i ti > 1 ( kt n)
log tFr
Adapted from Fig. 11.10, Callister & R th i h 3Avrami equation => y = 1- exp (-kt n)
fraction transformed
time
Rethwisch 3e.
– k & n are transformation specific parameterstransformed
B ti t 1 / tChapter 11 - 8
By convention rate = 1 / t0.5
Temperature Dependence of Transformation RateTransformation Rate
Adapted from Fig. 11.11, Callister & Rethwisch 3eRethwisch 3e.(Fig. 11.11 adapted from B.F. Decker and D. Harker, "Recrystallization in R ll d C " T
135C 119C 113C 102C 88C 43C
Rolled Copper", Trans AIME, 188, 1950, p. 888.)1 10 102 104
• For the recrystallization of Cu, since
rate = 1/t0.5
rate increases with increasing temperature
• Rate often so slow that attainment of equilibrium t t t ibl !
Chapter 11 - 9
state not possible!
Transformations & Undercoolingg
• For transf. to occur, must • Eutectoid transf. (Fe-Fe3C system): + Fe3C
0.76 wt% C0 022 t% C
6.7 wt% Ccool to below 727°C (i.e., must “undercool”)
0.022 wt% C
T(°C)1600
1400 L
T( C)Adapted from Fig. 10.28,Callister & Rethwisch 3e. (Fig. 10.28 adapted from Binary Alloy Phase
ntite
)
00
1200 (austenite)
+LL+Fe3C1148°C
Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)
(cem
en1000
800
+Fe3Cferrite
727°C
Eutectoid:Equil. Cooling: Ttransf. = 727ºC
Fe3C
600
400
+Fe3C727 C
TUndercooling by Ttransf. < 727C
.76
022
Chapter 11 - 10
4000 1 2 3 4 5 6 6.7(Fe) C, wt%C
0.0.0
The Fe-Fe3C Eutectoid Transformation3• Transformation of austenite to pearlite:
Austenite () cementite (Fe3C)Diffusion of C during transformation
Austenite ()grain boundary
cementite (Fe3C)Ferrite ()
during transformation
Adapted from Fig. 10.15, Callister & Rethwisch 3e.
pearlite growth direction
• For this transformation,
rate increases with [T – T ] (i e T) 50ar
lite) 600°C
(T larger)650°C
100
Carbon diffusion
[Teutectoid – T ] (i.e., T). Adapted from Fig. 11.12, Callister & Rethwisch 3e.
675°C (T smaller)
0
50y
(% p
ea 650 C
Coarse pearlite formed at higher temperatures – relatively soft
Chapter 11 - 11
Fine pearlite formed at lower temperatures – relatively hard
Generation of Isothermal Transformation DiagramsDiagrams
• The Fe-Fe3C system, for Co = 0.76 wt% CConsider:
• A transformation temperature of 675°C.
100T = 675°Crm
ed
50
0
T = 675 C
y,
% tr
ansf
or
01 102 104% time (s)
Austenite (stable) T (727 C)T(°C)
Adapted from Fig. 11.13,Callister & ( f
600
700Austenite (stable) TE (727C)
Austenite (unstable)
PearliteRethwisch 3e. (Fig. 11.13 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)
500
600isothermal transformation at 675°C
Chapter 11 - 12
y , , p )400
1 10 102 103 104 105 time (s)
Austenite-to-Pearlite Isothermal Transformation• Eutectoid composition, C0 = 0.76 wt% C• Begin at T > 727°C• Rapidly cool to 625°C• Rapidly cool to 625 C• Hold T (625°C) constant (isothermal treatment)
Austenite (stable)T(°C)700
Austenite (stable) TE (727C)Austenite (unstable)
T( C)
Adapted from Fig. 11.14,Callister & Rethwisch 3e. (Fig. 11.14 adapted from H. Boyer (Ed ) Atlas of Isothermal
600 Pearlite
(Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997,
500
p. 28.)400
1 10 102 103 104 105
Chapter 11 - 13
1 10 102 103 104 105
time (s)
Transformations Involving Noneutectoid CompositionsNoneutectoid Compositions
Consider C0 = 1 13 wt% CConsider C0 1.13 wt% CT(°C)900 1600
T(°C)
TE (727°C)A
A
A+C700
800
entit
e)
1400
1200
L
(austenite)
+LL+Fe3C
P
700
600 A+
P
3C (c
eme
1000
800 +Fe3C
727°CT
time (s)1 10 102 103 104
500 Fe3
600
4000 1 2 3 4 5 6 6.7
+Fe3C
(Fe) C %C
T
0.76
0.02
2
13( )Adapted from Fig. 11.16, Callister & Rethwisch 3e.
Adapted from Fig. 10.28, Callister & Rethwisch 3e.
(Fe) C, wt%C1.
Chapter 11 - 14
Hypereutectoid composition – proeutectoid cementite
Bainite: Another Fe-Fe3C Transformation ProductTransformation Product
• Bainite:-- elongated Fe3C particles in
-ferrite matrix-- diffusion controlled
• Isothermal Transf. Diagram,Fe3C(cementite)
800
T(°C)Austenite (stable)
TEA
Isothermal Transf. Diagram, C0 = 0.76 wt% C
( )(ferrite)
600
T( C)P
TEA
Adapted from Fig. 11.17, Callister & Rethwisch 3e. (Fig. 11.17 from Metals
5 m
100% bainite
100% pearlite
400 BA
( gHandbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.)
100% bainite
10 103 10510-1
200
Chapter 11 - 15
10 10time (s)
10Adapted from Fig. 11.18, Callister & Rethwisch 3e.
Spheroidite: Another Microstructure for the Fe Fe C System
• Spheroidite:
for the Fe-Fe3C System
• Spheroidite:-- Fe3C particles within an -ferrite matrix-- formation requires diffusion
(ferrite)
-- heat bainite or pearlite at temperature just below eutectoid for long times
-- driving force – reduction (cementite)
Fe3C
of -ferrite/Fe3C interfacial area
60 mAdapted from Fig. 11.19, Callister & Rethwisch 3e. (Fig. 11.19 copyright United States Steel Corporation, 1971.)
Chapter 11 - 16
Martensite: A Nonequilibrium Transformation Product
• Martensite:-- (FCC) to Martensite (BCT)
Transformation Product( ) ( )
0 m
xx x
x
x potential C atom sites
Fe atom sites
Adapted from Fig. 11.21, Callister & Rethwisch 3e.
60x xx
• Isothermal Transf. Diagram
Adapted from Fig. 11.22, Callister & R th i h 3 (Fi 11 22 t
Martensite needlesAustenite
600
800
T(°C)Austenite (stable)
PTEA
Rethwisch 3e. (Fig. 11.22 courtesy United States Steel Corporation.)
Adapted from Fig. 11.23, Callister & • to martensite (M) transformation..400
600
BARethwisch 3e.
to martensite (M) transformation..-- is rapid! (diffusionless)-- % transf. depends only on T to
which rapidly cooled200
A
M + AM + A
0%50%90%
Chapter 11 - 17
which rapidly cooled
10 103 105 time (s)10-1
M AM + A
90%
Martensite Formation
slow cooling (FCC) (BCC) + Fe3Cslow cooling
quench
tempering
q
M (BCT)
Martensite (M) – single phase – has body centered tetragonal (BCT)
crystal structure
Diffusionless transformation BCT if C0 > 0.15 wt% CBCT few slip planes hard, brittle
Chapter 11 - 18
BCT few slip planes hard, brittle
Phase Transformations of AlloysyEffect of adding other elements
Ch t iti tChange transition temp.
Cr, Ni, Mo, Si, MnCr, Ni, Mo, Si, Mn
retard + Fe3C reaction (and formation of (pearlite, bainite)
Chapter 11 - 19
Adapted from Fig. 11.24, Callister & Rethwisch 3e.
Continuous Cooling T f ti DiTransformation Diagrams
C i f i th lConversion of isothermal transformation diagram to continuous cooling transformation diagramtransformation diagram
Adapted from Fig. 11.26,Callister & Rethwisch 3eCallister & Rethwisch 3e.
Cooling curve
Chapter 11 - 20
Isothermal Heat Treatment Example ProblemsProblems
On the isothermal transformation diagram for a 0.45 wt% C, Fe-C alloy, sketch and label the time-temperature paths to produce the following microstructures:a) 42% proeutectoid ferrite and 58% coarse ) p
pearliteb) 50% fine pearlite and 50% bainiteb) 50% fine pearlite and 50% bainitec) 100% martensited) 50% t it d 50% t itd) 50% martensite and 50% austenite
Chapter 11 - 21
Solution to Part (a) of Example ProblemProblem
a) 42% proeutectoid ferrite and 58% coarse pearliteFe-Fe3C phase diagram
Isothermally treat at ~ 680°C
all austenite transformsA + A
800
Fe Fe3C phase diagram, for C0 = 0.45 wt% C
T (°C)-- all austenite transforms to proeutectoid and coarse pearlite. A + P
BP600
T ( C)
A + BB
A50%400 M (start)
Wpearlite C0 0.0220.76 0.022
200
M (start)M (50%)M (90%)
= 0.45 0.022
0.76 0.022 = 0.58
0
200
Ad t d f
W = 1 0.58 = 0.42
Chapter 11 - 22
00.1 10 103 105
time (s)Adapted from Fig. 10.29,Callister 5e.
Solution to Part (b) of Example Problem
b) 50% fine pearlite and 50% bainiteProblem
Fe-Fe3C phase diagram
T (°C)A + A
800
Fe Fe3C phase diagram, for C0 = 0.45 wt% C
Isothermally treat at ~ 590°C T ( C)
A + PBP600
y– 50% of austenite transforms
to fine pearlite.
A + BB
A50%400 M (start)
Then isothermally treat at ~ 470°C
all remaining austenite
200
M (start)M (50%)M (90%)
– all remaining austenite transforms to bainite.
0
200
Ad t d f
Chapter 11 - 23
00.1 10 103 105
time (s)Adapted from Fig. 10.29,Callister 5e.
Solutions to Parts (c) & (d) of Example ProblemProblem
c) 100% martensite – rapidly quench to room temperature Fe-Fe3C phase diagramtemperature
d) 50% martensite T (°C)
A + A800
Fe Fe3C phase diagram, for C0 = 0.45 wt% C
& 50% austenite-- rapidly quench to
290°C h ld t thi T
T ( C)
A + PBP600
~ 290°C, hold at this TA + B
B
A50%400 M (start)
200
M (start)M (50%)M (90%) d)
0
200
Ad t d f
c)
Chapter 11 - 24
00.1 10 103 105
time (s)Adapted from Fig. 10.29,Callister 5e.
Mechanical Props: Influence of C Contentp
Pearlite (med)Pearlite (med)Cementite
Adapted from Fig. 10.34, Callister & Rethwisch 3e.
C0 < 0.76 wt% CHypoeutectoid
Pearlite (med)ferrite (soft)
Adapted from Fig. 10.37, Callister & Rethwisch 3e.
C0 > 0.76 wt% CHypereutectoid
Cementite(hard)
yp yp
Adapted from Fig. 1100YS(MPa)
TS(MPa) Hypo Hyper
100%EL
t-lb)
80Hypo Hyper
11.30, Callister & Rethwisch 3e. (Fig. 11.30 based on data from Metals Handbook: Heat
700
900hardness
50 gy (I
zod,
ft
40
Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals 1981 p 9 )300
50050
mpa
ct e
ner
0
• Increase C content: TS and YS increase %EL decreases
Metals, 1981, p. 9.)
wt% C0 0.5 1
0.76 wt% C0 0.5 1
0 Im
0.76
Chapter 11 - 25
• Increase C content: TS and YS increase, %EL decreases
Mechanical Props: Fine Pearlite vs. Coarse Pearlite vs SpheroiditePearlite vs. Spheroidite
320 fine pearlite
Hypo Hyper 90
A)
spheroidite
Hypo Hyper
240
hard
ness coarse
pearlitespheroidite
60
ctili
ty (%
RA spheroidite
80
160
Brin
ell
0
30Duc
fine pearlite
coarsepearlite
Adapted from Fig. 11.31, Callister & Rethwisch 3e. (Fig. 11.31 based on • Hardness: fine > coarse > spheroidite
wt%C0 0.5 1 0wt%C0 0.5 1
( gdata from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, pp. 9 and 17.)
• %RA:fine coarse spheroiditefine < coarse < spheroidite
Chapter 11 - 26
Mechanical Props: Fine Pearlite vs. MartensiteMartensite
Hypo Hyper
Adapted from Fig. 11.33, Callister & Rethwisch 3e. (Fig. 11.33 adapted from Edgar C Bain400
600ha
rdne
ss martensite
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,
d L F P t M t ll T A200
400
Brin
ell
fine pearlite and L.F. Porter, Metall. Trans. A, Vol. 8A, p. 1776.)
0wt% C0 0.5 1
fine pearlite
• Hardness: fine pearlite << martensite.
Chapter 11 - 27
Tempered Martensitep• tempered martensite less brittle than martensiteHeat treat martensite to form tempered martensite
• tempering reduces internal stresses caused by quenching
YS(MPa)TS(MPa)
1800
Adapted from Fig. 11 34 C lli t &
Adapted from Fi 11 35 m
1600
1800
TS
YS 11.34, Callister & Rethwisch 3e. (Fig. 11.34 copyright by United States Steel Corporation, 1971.)
Fig. 11.35, Callister & Rethwisch 3e. (Fig. 11.35 adapted from
9 m
1200
1400
5060
YS
Fig. furnished courtesy of Republic Steel Corporation.) 800
1000
304050
%RA%RA
• tempering produces extremely small Fe3C particles surrounded by
200 400 600Tempering T (°C)
Chapter 11 - 28• tempering decreases TS, YS but increases %RA
p g p y 3 p y
Summary of Possible TransformationsyAdapted from Fig. 11.37, Callister & R th i h 3
Austenite ()Rethwisch 3e.
slow cool
moderatecool
rapid quench
Pearlite( + Fe3C layers + a
Bainite( + elong. Fe3C particles)
Martensite(BCT phase
proeutectoid phase)( pdiffusionless
transformation)
reheatMartensite
Tempered
reheat
ngth
tility
Martensite T Martensite
bainite Martensite ( + very fine
Fe3C particles)
Stre
n
Duc
tfine pearlite coarse pearlite
spheroidite
Chapter 11 - 29
spheroiditeGeneral Trends
Precipitation Hardening
L700
T(°C) C Al
p g• Particles impede dislocation motion.• Ex: Al-Cu system
L+L
+L
500
600T( C) CuAl2
A
• Procedure:-- Pt A: solution heat treat
(get solid solution)
300
400-- Pt B: quench to room temp.(retain solid solution)
-- Pt C: reheat to nucleate
(get solid solution)C
0 10 20 30 40 50wt% Cu
300(Al)
composition range available for precipitation hardening
-- Pt C: reheat to nucleatesmall particles within phase.
• Other alloys that precipitation
B
p p gAdapted from Fig. 11.43, Callister & Rethwisch 3e. (Fig. 11.43 adapted from J.L. Murray, International Metals Review 30, p.5, 1985.)
• Other alloys that precipitationharden:• Cu-Be
Temp.Pt A (sol’n heat treat)
Adapted from Fig
• Cu-Sn• Mg-Al Pt C (precipitate
Chapter 11 - 30
Adapted from Fig. 11.41, Callister & Rethwisch 3e.
TimePt B
Influence of Precipitation Heat Treatment on TS %EL
• 2014 Al Alloy:
M i TS
Treatment on TS, %EL
Mi i %EL• Maxima on TS curves.• Increasing T accelerates
process
• Minima on %EL curves.
process.
h (M
Pa)
400
mpl
e)
20
30
e st
reng
th
200
300
204°C149°C
L(2
in s
a
10
20
204°C 149°C
precipitation heat treat time
tens
ile
100 1min 1h 1day 1mo 1yr
204°C%
EL
0 1min 1h 1day 1mo 1yr
204 C
precipitation heat treat time
Chapter 11 - 31Adapted from Fig. 11.45 (a) and (b), Callister & Rethwisch 3e. (Fig. 11.45 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.)
precipitation heat treat time precipitation heat treat time
Diff t h
Chapter 11 -
Coherent lattice Different phase appears.Uniform alloying elements
Melting & Glass Transition Temps.g pWhat factors affect Tm and Tg?
• Both Tm and Tg increase with increasing chain stiffness
• Chain stiffness increased by ypresence of1. Bulky sidegroups2 Polar groups or sidegroups2. Polar groups or sidegroups3. Chain double bonds and
aromatic chain groups
• Regularity of repeat unit arrangements – affects Tm only
Chapter 11 - 3333
Adapted from Fig. 11.47, Callister & Rethwisch 3e.
Thermoplastics vs. Thermosets
• Thermoplastics:
p
Callister, T
i rubber-- little crosslinking-- ductile-- soften w/heating
,Fig. 16.9
T
Tmmobile liquid
viscousliquid
rubber
tough plastic
-- polyethylenepolypropylenepolycarbonate
Tgp
partially crystallinepolycarbonate
polystyrene
Th Molecular weight
crystalline solidcrystalline
solid
• Thermosets:-- significant crosslinking
(10 to 50% of repeat units)
Adapted from Fig. 11.48, Callister & Rethwisch 3e. (Fig. 11.48 is from F.W. Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley and Sons, Inc., 1984.)
Molecular weight
( p )-- hard and brittle-- do NOT soften w/heating-- vulcanized rubber epoxies
Chapter 11 - 3434
vulcanized rubber, epoxies,polyester resin, phenolic resin
Summary
• Heat treatments of Fe-C alloys produce microstructures
y
Heat treatments of Fe C alloys produce microstructures including:-- pearlite, bainite, spheroidite, martensite, tempered
t itmartensite• Precipitation hardening
--hardening, strengthening due to formation of a de g, s e g e g due o o a o oprecipitate particles.
--Al, Mg alloys precipitation hardenable.Pol mer melting and glass transition temperat res• Polymer melting and glass transition temperatures
Chapter 11 - 35