hypo eutectoid steel
DESCRIPTION
T (°C). 1600. d. L. 1400. g. + L. g. g. g. 1200. L +Fe 3 C. 1148°C. (austenite). g. g. g. 1000. g. g. + Fe 3 C. g. g. Fe 3 C (cementite). r. s. 800. a. g. g. 727°C. a. a. a. g. g. R. S. 600. a. + Fe 3 C. w. =. s. /(. r. +. s. ). a. w. =. (1-. w. - PowerPoint PPT PresentationTRANSCRIPT
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Hypoeutectoid Steel
Fe 3
C (
cem
entit
e)
1600
1400
1200
1000
800
600
4000 1 2 3 4 5 6 6.7
L
(austenite)
+L
+ Fe3C
+ Fe3C
L+Fe3C
(Fe) Co , wt% C
1148°C
T(°C)
727°C
C0
0.76
proeutectoid ferritepearlite
100 m
R S
w =S/(R+S)wFe3C =(1-w)
wpearlite = wpearlite
r s
w =s/(r+s)w =(1- w)
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Proeuctectoid Ferrite – Pearlite
0.38 wt% C: Plain Carbon – Medium Carbon Steel
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Hypereutectoid Steel
Fe 3
C (
cem
entit
e)
1600
1400
1200
1000
800
600
4000 1 2 3 4 5 6 6.7
L
(austenite)
+L
+Fe3C
+Fe3C
L+Fe3C
(Fe) Co , wt%C
1148°C
T(°C)
0.7
6 Co
Adapted from Fig. 9.33,Callister 7e.
proeutectoid Fe3C
60 m
pearlite
R S
w =S/(R+S)wFe3C =(1-w )
wpearlite = wpearlite
sr
wFe3C =r/(r+s)w =(1-w Fe3C )
Fe3C
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Proeutectoid Cementite - Pearlite
1.4 wt% C: Plain Carbon – High Carbon Steel
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Phase Transformations• We just studied Phase Diagrams which are thermodynamic
maps which tell us the equilibrium phases present at any specific combination of temperature, pressure, and composition
• These phase diagrams are based on the concept of Gibbs Free Energy, G, which we have briefly introduced before: G is the thermodynamic driving force for a reaction If G is negative then there is a probability that a reaction will
occur. The more negative G becomes, the more driving force there is for
the reaction Thermodynamics tells us the probability of a reaction but not the
rate – the rate of a reaction is determined by Kinetics
Now we are going to shift perspectives and discuss the details of how we transform from one phase to another
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Phase Transformations
Let’s categorize with 3 types:
1. Simple diffusion-dependent transformations in which there is no change in the number or composition of the phases present
Examples: Solidification of a pure metal Allotropic transformations Recrystallization and Grain Growth
2. Diffusion-dependent transformations in which there is a change in the phase compositions and or number of phases present
Examples: Eutectoid reaction Peritectic reaction
3. Diffusion-less transformations, in which a metastable phase is producedExamples: Martensitic and Bainitic transformations
Phase transformations involve some form of change in the microstructure
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Nucleation
– nuclei (seeds) act as template to grow crystals– for nucleus to form, rate of addition of atoms to nucleus must
be faster than rate of loss– once nucleated, grow until reach equilibrium
Driving force to nucleate increases as we increase T– supercooling (eutectic, eutectoid reactions)
Small supercooling few nuclei - large crystals
Large supercooling rapid nucleation - many nuclei, small crystals
During Phase transformation – new phase formed with different physical/ chemical characteristics than the parent phase
Diffusion based Phase Transformations do not occur instantaneously – nucleated
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Solidification: Nucleation Processes
• Homogeneous nucleation – nuclei form in the bulk of liquid metal– requires supercooling (typically 80-300°C max)
• Heterogeneous nucleation– much easier since stable “nucleus” is already present
• Could be wall of mold or impurities in the liquid phase– allows solidification with only 0.1-10ºC supercooling
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Consider Solidification First
Let’s assume spherical nuclei
Why? Sphere has the smallest surface area/ surface energy for a given volume
Let’s Determine the equations that define behavior
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r* = critical nucleus: nuclei < r* shrink; nuclei>r* 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)
24 rGS
= surface tension
Volume (Bulk) Free Energy – stabilizes the nuclei (releases energy)
GrGV3
3
4
volume unit
energy free volume G
Surface area of sphere
G = free energy difference between the parent and daughter phase
embryo nucleus
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Solidification
TH
Tr
S
m
2*
Note: HS = strong function of T
= weak function of T
r* decreases as T increases
For typical T r* ca. 100Å
HS = latent heat of solidification
Tm = melting temperature
= surface free energy
T = Tm - T = supercooling
r* = critical radius
T1 > T2
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Other Effects of Temperature
Number of stable nuclei follows Arrhenius behavior (like vacancy densities)
Clustering of atoms by short range diffusion – Diffusivity has Arrhenius behavior
Maximum Nucleation Rate occurs at intercept of two curves
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Heterogenous Nucleation
ml sm sl cos
cos (ml sm )
sl
Young’s Law:
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3 2
2
44 ( )
3
(1 cos )( ) (2 cos )
4
het s v sl sl sm sm sm ml
het v sl
G V G A A A
G r G r S
S
r*2slGv
G*16sl3
3Gv2
S( )
Heterogeneous Nucleation
Note:G*het = Ghom S()
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Heterogeneous vs Homogenous
G*het = Ghom S()
Lower activation energy barrier Less undercooling required Faster transformation rate
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Nucleation vs Growth Rates• Growth is determined by long
range diffusion
• Arrhenius activation energy behavior
Overall transformation is equal to the product of Ġ and Ń
Rate = 1/time
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Kinetics of Phase Transformation
• Discussed Thermodynamic driving forces in detail
• Kinetics – measures the approach to equilibrium vs. time– Hold temperature constant & measure conversion vs.
time
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Rate of Phase Transformation
Avrami rate equation => y = 1- exp (-ktn)
– k & n fit for specific sample
All out of material - done
log tFra
ctio
n tr
an
sfo
rme
d, y
Fixed T
fraction transformed
time
0.5
By convention r = 1 / t0.5
maximum rate reached – now amount unconverted decreases so rate slows
t0.5
rate increases as surface area increases & nuclei grow
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Rate of Phase Transformations
• In general, rate increases as T
r = 1/t0.5 = A e -Q/RT
– R = gas constant– T = temperature (K)– A = pre-exponential factor– Q = activation energy
Arrhenius expression
• r often small: equilibrium not possible!
135C 119C 113C 102C 88C 43C
1 10 102 104
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Eutectoid Transformation Rate
Course pearlite formed at higher T - softer
Fine pearlite formed at low T - harder
Diffusive flow of C needed
• Growth of pearlite from austenite:
Adapted from Fig. 9.15, Callister 7e.
pearlite growth direction
Austenite ()grain boundary
cementite (Fe3C)
Ferrite ()
• Transformation rate increases with T.
675°C (T smaller)
0
50
y (%
pea
rlite
)
600°C (T larger)
650°C
100
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Reaction rate is a result of nucleation and growth of crystals.
• Examples:
Nucleation and Growth
% Pearlite
0
50
100
Nucleation regime
Growth regime
log (time)t0.5
Nucleation rate increases with T
Growth rate increases with T
T just below TE
Nucleation rate low
Growth rate high
pearlite colony
T moderately below TE
Nucleation rate med Growth rate med.
Nucleation rate high
T way below TE
Growth rate low
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Consider Eutectoid Transformation …
Eutectoid transformation (Fe-C): + Fe3C0.76 wt% C
0.022 wt% C6.7 wt% C
Fe 3
C (
cem
entit
e)
1600
1400
1200
1000
800
600
4000 1 2 3 4 5 6 6.7
L
(austenite)
+L
+Fe3C
+Fe3C
L+Fe3C
(Fe) Co , wt%C
1148°C
T(°C)
ferrite
727°C
Eutectoid:Equil. Cooling: Ttransf. = 727ºC
T
Undercooling by Ttransf. < 727C
0.7
6
0.0
22
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Isothermal Transformation Diagrams
• Fe-C system, Co = 0.76 wt% C• Transformation at T = 675°C.
100
50
01 102 104
T = 675°C
y,
% tr
ansf
orm
ed
time (s)
400
500
600
700
1 10 102 103 104 105
0%pearlite
100%
50%
Austenite (stable) TE (727C)Austenite (unstable)
Pearlite
T(°C)
time (s)
isothermal transformation at 675°C
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• Eutectoid composition, Co = 0.76 wt% C• Begin at T > 727°C• Rapidly cool to 625°C and hold isothermally.
Effect of Cooling History in Fe-C System
400
500
600
700
0%pearlite
100%
50%
Austenite (stable)TE (727C)
Austenite (unstable)
Pearlite
T(°C)
1 10 102 103 104 105
time (s)