Chapter 10: Phase Transformations

ISSUES TO ADDRESS...

• Transforming one phase into another takes time.

• How does the rate of transformation depend on

time and temperature?

• Is it possible to slow down transformations so that

non-equilibrium structures are formed?

• Are the mechanical properties of non-equilibrium

structures more desirable than equilibrium ones?

Fe (Austenite) Eutectoid transformation C _FCC Fe₃C (cementite) (ferrite) + (BCC)

Chapter 10:

Phase Transformations

Phase Transformations

Nucleation

– 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 loss

– once nucleated, growth proceeds until equilibrium is attained Driving force to nucleate increases as we increase T

– supercooling (eutectic, eutectoid)

– superheating (peritectic)

Small supercooling  slow nucleation rate - few nuclei - large crystals

Solidification: Nucleation Types

• Homogeneous nucleation

– nuclei form in the bulk of liquid metal

– requires considerable supercooling

(typically 80-300ºC)

• Heterogeneous nucleation

– much easier since stable “nucleating surface” is

already present — e.g., mold wall, impurities in

liquid phase

r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy)

Homogeneous Nucleation & Energy Effects

G

_T = Total Free Energy

=

G

_S

+ G

_V

Surface Free Energy - destabilizes the nuclei (it takes energy to make an interface)

2

4 r

G

_S

= surface tension

Volume (Bulk) Free Energy –

stabilizes the nuclei (releases energy)

G

r

G

_V 3

3

4

volume unit energy free volume G

Solidification

T

H

T

r

f m

2

*

Note:

H

_f

and are weakly dependent on

T

r* decreases as

T

increases

For typical

T

r* ~ 10 nm

H_f = latent heat of solidification

T_m = melting temperature

= surface free energy

T = T_m - T = supercooling

Rate of Phase Transformations

Kinetics - study of reaction rates of phase

transformations

• To determine reaction rate – measure degree

of transformation as function of time (while

holding temp constant)

measure propagation of sound waves –

on single specimen

electrical conductivity measurements –

on single specimen

X-ray diffraction – many specimens required

Rate of Phase Transformation

Avrami equation =>

y

= 1- exp (-k

t

n

₎

– k & n are transformation specific parameters

transformation complete

log t

Frac ti on transformed , y

Fixed T

fraction transformed time 0.5

By convention rate = 1 /

t

_0.5 Adapted from Fig. 10.10, Callister & Rethwisch 8e.

maximum rate reached – now amount unconverted decreases so rate slows

t_0.5

rate increases as surface area increases & nuclei grow

Temperature Dependence of

Transformation Rate

• For the recrystallization of Cu, since

rate = 1/

t

_0.5

rate increases with increasing temperature

• Rate often so slow that attainment of

equilibrium

state not possible!

Adapted from Fig. 10.11, Callister &

Rethwisch 8e.

(Fig. 10.11 adapted from B.F. Decker and D. Harker,

"Recrystallization in Rolled Copper", Trans

AIME, 188, 1950, p.

888.) 135 C 119 C 113 C 102 C 88 C 43 C

Transformations & Undercooling

•

For transf. to occur, must cool to below 727ºC

(i.e., must “undercool”)

•

Eutectoid transf. (Fe-Fe₃C system): + Fe₃C 0.76 wt% C 0.022 wt% C 6.7 wt% C Fe 3 C (c ementit e) 1600 1400 1200 1000 800 600 400 0 1 2 3 4 5 6 6.7 L (austenite) +L +Fe₃C +Fe₃C L+Fe₃C (Fe) _{C, wt%C} 1148ºC T(ºC) ferrite 727ºC Eutectoid:

Equil. Cooling: T_transf. = 727ºC

T Undercooling by T_transf. < 727 C 0 .7 6 0 .0 2 2

Adapted from Fig.

9.24,Callister & Rethwisch

8e. (Fig. 9.24 adapted from Binary Alloy Phase

Diagrams, 2nd ed., Vol. 1,

T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)

The Fe-Fe

₃

C Eutectoid Transformation

Coarse pearlite  formed at higher temperatures – relatively soft Fine pearlite  formed at lower temperatures – relatively hard

• Transformation of austenite to pearlite:

Adapted from Fig. 9.15, Callister & Rethwisch 8e. pearlite growth direction Austenite ( ) grain boundary cementite (Fe₃C) Ferrite ( )

•

For this transformation, rate increases with

[T_eutectoid – T ] (i.e., T). _{Adapted from}

Fig. 10.12, Callister & Rethwisch 8e. 675ºC ( T smaller) 0 50 y (% pea rlit e) _600ºC ( T larger) 650ºC 100 Diffusion of C during transformation Carbon diffusion

Chapter 10 - 11 Adapted from Fig. 10.13,Callister &

Rethwisch 8e. (Fig. 10.13 adapted from H.

Boyer (Ed.) Atlas of Isothermal

Transformation and Cooling

Transformation Diagrams, American

Society for Metals, 1977, p. 369.)

Generation of Isothermal Transformation

Diagrams

• The Fe-Fe₃C system, for C0 = 0.76 wt% C

• A transformation temperature of 675ºC. 100 50 0 1 10 2 10 4

T

= 675ºC

y , % transf orm ed

time (s)

400 500 600 700 1 10 10 2 10 3 10 4 10 5 Austenite (stable)

T

_E

(727

ºC)

Austenite (unstable) Pearlite

T

(ºC)

time (s)

isothermal transformation at 675ºC

Consider:

• Eutectoid composition, C₀ = 0.76 wt% C • Begin at T > 727ºC

• Rapidly cool to 625ºC

• Hold T (625ºC) constant (isothermal treatment)

Adapted from Fig. 10.14,Callister &

Rethwisch 8e. (Fig. 10.14

adapted from H. Boyer (Ed.) Atlas of Isothermal

Transformation and Cooling Transformation Diagrams, American

Society for Metals, 1997, p. 28.)

Austenite-to-Pearlite Isothermal Transformation

400 500 600 700 Austenite (stable)

T

_E

(727ºC)

Austenite (unstable) Pearlite

T

(ºC)

1 10 10 2 10 3 10 4 10 5

time (s)

Transformations Involving

Noneutectoid Compositions

Hyper

eutectoid composition – proeutectoid cementite

Consider C

₀

= 1.13 wt% C

T_E (727ºC) T(ºC) time (s) A A A + C P 1 10 102 ₁₀3 ₁₀4 500 700 900 600 800 A + P

Adapted from Fig. 10.16,

Callister & Rethwisch 8e.

Adapted from Fig. 9.24,

Callister & Rethwisch 8e.

Fe 3 C (c ementit e) 1600 1400 1200 1000 800 600 400 0 1 2 3 4 5 6 6.7 L (austenite) +L +Fe₃C +Fe₃C L+Fe₃C (Fe) _{C, wt%C} T(ºC) 727ºC T 0 .7 6 0 .0 2 2 1.13

10 ₁₀ 3 10 5 time (s) 10 -1 400 600 800 T(ºC) Austenite (stable) 200 P B T_E A A

Bainite: Another Fe-Fe

₃

C

Transformation Product

• Bainite:

-- elongated Fe₃C particles in -ferrite matrix

-- diffusion controlled

• Isothermal Transf. Diagram,

C₀ = 0.76 wt% C

Adapted from Fig. 10.18,

Adapted from Fig. 10.17, Callister &

Rethwisch 8e. (Fig. 10.17 from Metals Handbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American

Society for Metals, Materials Park, OH, 1973.) Fe₃C (cementite) 5 m (ferrite) 100% bainite 100% pearlite

•

Spheroidite

:

-- Fe3C particles within an -ferrite matrix

-- formation requires diffusion

-- heat bainite or pearlite at temperature just below eutectoid for long times -- driving force – reduction

of -ferrite/Fe₃C interfacial area

Spheroidite: Another Microstructure

for the Fe-Fe

₃

C System

Adapted from Fig. 10.19, Callister &

Rethwisch 8e. (Fig. 10.19 copyright

United States Steel Corporation, 1971.)

60 m

(ferrite)

(cementite)

•

Martensite

:

-- (FCC) to Martensite (BCT)

Adapted from Fig. 10.21, Callister &

Rethwisch 8e. (Fig. 10.21 courtesy

United States Steel Corporation.) Adapted from Fig. 10.20,

Callister & Rethwisch 8e.

Martensite: A Nonequilibrium

Transformation Product

Martensite needles Austenite 60 m x x x x x x potential C atom sites Fe atom sites Adapted from Fig. 10.22, Callister & Rethwisch 8e.

• Isothermal Transf. Diagram

•

to martensite (M) transformation.. -- is rapid! (diffusionless)

-- % transf. depends only on T to which rapidly cooled

400 600 800 T(ºC) Austenite (stable) 200 P B T_E A A M + A M + A M + A 0% 50% 90%

(FCC)

(BCC)

+

Fe

₃

C

Martensite Formation

slow cooling

tempering

quench

M (BCT)

Martensite (M)

– single phase

– has body centered tetragonal (BCT)

crystal structure

Diffusionless transformation BCT if C

₀

> 0.15 wt% C

BCT



few slip planes



hard, brittle

Phase Transformations of Alloys

Effect of adding other elements Change transition temp.

Cr, Ni, Mo, Si, Mn

retard

 +

Fe₃C reaction (and formation of pearlite, bainite)

Adapted from Fig. 10.25,

Callister & Rethwisch 8e.

Continuous Cooling

Transformation Diagrams

Conversion of isothermal transformation diagram to continuous cooling transformation diagram Cooling curve

Isothermal Heat Treatment Example

Problems

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

pearlite

b) 50% fine pearlite and 50% bainite

c) 100% martensite

Solution to Part (a) of Example

Problem

a) 42% proeutectoid ferrite and 58% coarse pearlite

Isothermally treat at ~ 680ºC -- all austenite transforms to proeutectoid and coarse pearlite. A + B A + P A + A B P A 50% 0 200 400 600 800 0.1 10 103 ₁₀5 time (s) M (start) M (50%) M (90%) Adapted from Fig. 10.29, Callister 5e.

Fe-Fe₃C phase diagram, for C₀ = 0.45 wt% C W_pearlite C0 0.022 0.76 0.022 = 0.45 0.022 0.76 0.022 = 0.58 W = 1 0.58 = 0.42 T (ºC)

b) 50% fine pearlite and 50% bainite

Solution to Part (b) of Example

Problem

T (ºC) A + B A + P A + A B P A 50% 0 200 400 600 800 0.1 10 103 ₁₀5 time (s) M (start) M (50%) M (90%) Adapted from Fig. 10.29,

Fe-Fe₃C phase diagram, for C₀ = 0.45 wt% C

Then isothermally treat at ~ 470ºC

– all remaining austenite transforms to bainite.

Isothermally treat at ~ 590ºC – 50% of austenite transforms to fine pearlite.

Solutions to Parts (c) & (d) of Example

Problem

c) 100% martensite – rapidly quench to room

temperature

d) 50% martensite

& 50% austenite

-- rapidly quench to ~ 290ºC, hold at this temperature T (ºC) A + B A + P A + A B P A 50% 0 200 400 600 800 0.1 10 103 ₁₀5 time (s) M (start) M (50%) M (90%) Adapted from Fig. 10.29, Callister 5e.

Fe-Fe₃C phase diagram, for C₀ = 0.45 wt% C

d)

Mechanical Props: Influence of C Content

Adapted from Fig. 9.30,

Callister & Rethwisch 8e.

• Increase C content: TS and YS increase, %EL decreases

C₀ < 0.76 wt% C Hypoeutectoid

Pearlite (med)

ferrite (soft)

Adapted from Fig. 9.33,

Callister & Rethwisch 8e. C₀ > 0.76 wt% C

Hypereutectoid

Pearlite (med)

Cementite (hard)

Adapted from Fig. 10.29, Callister &

Rethwisch 8e. (Fig.

10.29 based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.) 300 500 700 900 1100 YS(MPa) TS(MPa) wt% C 0 0.5 1 hardness 0 .7 6 Hypo Hyper wt% C 0 0.5 1 0 50 100 %EL Impa c t e n e rg y ( Iz o d , ft -lb ) 0 40 80 0 .7 6 Hypo Hyper

Mechanical Props: Fine Pearlite vs.

Coarse Pearlite vs. Spheroidite

Adapted from Fig. 10.30, Callister &

Rethwisch 8e. (Fig. 10.30 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.)

• Hardness: • %RA:

fine > coarse > spheroidite fine < coarse < spheroidite

80 160 240 320 wt%C 0 0.5 1 B ri n e ll h a rd n e s s fine pearlite coarse pearlite spheroidite Hypo Hyper 0 30 60 90 wt%C Duc ti lity (%RA ) fine pearlite coarse pearlite spheroidite Hypo Hyper 0 0.5 1

Mechanical Props: Fine Pearlite vs.

Martensite

• Hardness: fine pearlite << martensite.

Adapted from Fig. 10.32,

Callister & Rethwisch 8e. (Fig.

10.32 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.) 0 200 wt% C 0 0.5 1 400 600 B ri n e ll h a rd n e s s martensite fine pearlite Hypo Hyper

Tempered Martensite

• tempered martensite less brittle than martensite

• tempering reduces internal stresses caused by quenching

Adapted from Fig. 10.33, Callister &

Rethwisch 8e. (Fig.

10.33 copyright by United States Steel Corporation, 1971.)

•

tempering decreases TS, YS but increases %RA

•

tempering produces extremely small Fe₃C particles surrounded by

Adapted from Fig. 10.34, Callister & Rethwisch 8e. (Fig. 10.34 adapted from Fig. furnished courtesy of Republic Steel Corporation.) 9 m YS(MPa) TS(MPa) 800 1000 1200 1400 1600 1800 30 40 50 60 200 400 600 Tempering T(ºC) %RA TS YS %RA

Summary of Possible Transformations

Adapted from Fig. 10.36, Callister & Rethwisch 8e.

Austenite ( )

Pearlite

( + Fe₃C layers + a proeutectoid phase)

slow

cool

Bainite

( + elong. Fe₃C particles)

moderate

cool

Martensite

(BCT phase diffusionless transformation)

rapid

quench

Tempered

Martensite

( + very fine Fe₃C particles)

reheat

Stren

gth

Ducti

lity

Martensite

T Martensite

bainite

fine pearlite

coarse pearlite

spheroidite

General Trends

Core Problems:

Self-help Problems:

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