Chapter 12: Phase Transformations

ISSUES TO ADDRESS... • Transforming one phase into another takes time.

Fe Fe C Eutectoid 3 γ transformation (cementite) (Austenite) + α C FCC (ferrite) (BCC)

• 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?

AMSE 205 Spring ‘2016 Chapter 12 - 1 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 ΔT – supercooling (eutectic, eutectoid) – superheating (peritectic)

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

Large supercooling  rapid nucleation rate - many nuclei - small crystals

AMSE 205 Spring ‘2016 Chapter 12 - 2 Solidification: Nucleation Types

• Homogeneous nucleation – nuclei form in the bulk of liquid metal – requires considerable supercooling (typically 80-300 °C)

• Heterogeneous nucleation – much easier since stable “nucleating surface” is already present — e.g., mold wall, impurities in liquid phase – only very slight supercooling (0.1-10 °C)

AMSE 205 Spring ‘2016 Chapter 12 - 3 Homogeneous Nucleation & Energy Effects Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface)

γ = surface tension

ΔGT = Total Free Energy = ΔGS + ΔGV

Volume (Bulk) Free Energy – stabilizes the nuclei (releases energy)

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

Adapted from Fig.12.2(b), Callister & Rethwisch 9e. AMSE 205 Spring ‘2016 Chapter 12 - 4  d G 1 4 1   3  2   r Gv   4 r  0 dr dr  3  dr  2  r*   Gv  3 * 16 G  2  3Gv     H  H T T  H T G  H T S  HT v   v m  v v v v v  T  T T    m  m m

* 2  2 T r     m     Gv H v T  3  3 2 * 16 16 Tm G  2   2 2 3 Gv 3 H v T

AMSE 205 Spring ‘2016 Chapter 12 - 5 Solidification

r* = critical radius γ = surface free energy

Tm = melting temperature

ΔHf = latent heat of solidification

ΔT = Tm -T= supercooling

Note: ΔHf and γ are weakly dependent on ΔT

 r* decreases as ΔT increases

For typical ΔT r* ~ 10 nm

AMSE 205 Spring ‘2016 Chapter 12 - 6 G  G 3 T3 2 2 2T * 16 16 * m   v  H m r      2 2 2 G H T 3 3 v T v v

AMSE 205 Spring ‘2016 Chapter 12 - 7 Nucleation Kinetics

d

AMSE 205 Spring ‘2016 Chapter 12 - 8 Heterogeneous Nucleation

       cos IL SI SL * 2 SL  r   G V   16 3  G*    SL  hetero  3 G 2   v  * * Ghetero  Ghomo S( )

AMSE 205 Spring ‘2016 Chapter 12 - 9 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) How is degree of transformation measured? X-ray diffraction – many specimens required electrical conductivity measurements – on single specimen measure propagation of sound waves – on single specimen

AMSE 205 Spring ‘2016 Chapter 12 - 10 Rate of Phase Transformation x

transformation complete Fixed T

0.5 maximum rate reached – now amount unconverted decreases so rate slows rate increases as interfacial surface area increases & nuclei grow t0.5 Fig. 12.10, Fraction transformed, log t Callister & Rethwisch 9e.

Jonson-Mehl-Avrami (JMA) equation => x = 1- exp (-kt n) K: reaction rate constant fraction time transformed n : Avrami exponent

By convention rate = 1 / t0.5

AMSE 205 Spring ‘2016 Chapter 12 - 11 Rate of Phase Transformation The kinetics of recrystallization for some alloys obey the JMA equation and the Avrami exponent, n, is 3.1. If the fraction of recrystallized is 0.3 after 20 min, determine the rate of recrystallization.

AMSE 205 Spring ‘2016 Chapter 12 - 12 Temperature Dependence of Transformation Rate Fig. 12.11, Callister & Rethwisch 9e. (Reprinted with permission 135C 119C 113C 102C 88C 43C from Metallurgical Transactions, Vol. 188, 1950, a publication of The Metallurgical Society of AIME, Warrendale, PA. Adapted from B. F. Decker and D. Harker, “Recrystallization in Rolled Copper,” Trans. AIME, 110102 104 188, 1950, p. 888.)

• For the recrystallization of Cu, since

rate = 1/t0.5 rate increases with increasing temperature

• Rate often so slow that attainment of equilibrium state not possible!

AMSE 205 Spring ‘2016 Chapter 12 - 13 Transformations & Undercooling

• Eutectoid transf. (Fe-Fe3C system): γ  α + Fe3C • For transf. to occur, must 0.76 wt% C 6.7 wt% C cool to below 727 oC 0.022 wt% C (i.e., must “undercool”) T(°C) 1600 Fig. 11.23, Callister & Rethwisch 9e. δ [Adapted from Binary Alloy Phase L Diagrams, 2nd edition, Vol. 1, T. B. 1400 Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM γ γ+L International, Materials Park, OH.] 1200 1148°C L+Fe C (austenite) 3 1000 γ+Fe C α Eutectoid: 3 ferrite 800 Equil. Cooling: Ttransf. = 727°C 727°C

ΔT α+Fe C C (cementite) 600 3 3 Undercooling by Ttransf. < 727°C Fe 400 0.76 0 0.022 1234566.7 (Fe) C, wt%C AMSE 205 Spring ‘2016 Chapter 12 - 14 The Fe-Fe3C Eutectoid Transformation • Transformation of austenite to pearlite: Diffusion of C Austenite (γ) cementite (Fe3C) during transformation grain α Ferrite (α) α boundary γ α γ α γ Adapted from α pearlite α γ Fig. 11.14, growth α Callister & α Rethwisch 9e. direction α Carbon • For this transformation, 100 diffusion rate increases with 600°C (ΔT larger) 650°C [Teutectoid – T ] (i.e., ΔT). 50 Adapted from 675°C Fig. 12.12, (ΔT smaller) Callister & (% pearlite) Rethwisch 9e.

y 0

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

AMSE 205 Spring ‘2016 Chapter 12 - 15 Generation of Isothermal Transformation Diagrams Consider:

• The Fe-Fe3C system, for C0 = 0.76 wt% C • A transformation temperature of 675 ºC.

100 T = 675°C , y 50

0 % transformed 2 4 Fig. 12.13, Callister & Rethwisch 9e. 110 10 time (s) [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, 1977. T(°C) Reproduced by permission of ASM Austenite (stable) T (727 oC) International, Materials Park, OH.] 700 Austenite E (unstable) 600 Pearlite isothermal transformation at 675°C 500

400 2 3 4 5 time (s) 1101010 AMSE10 20510 Spring ‘2016 Chapter 12 - 16 Austenite-to-Pearlite Isothermal Transformation

• Eutectoid composition, C0 = 0.76 wt% C • Begin at T > 727°C • Rapidly cool to 625 oC • Hold T (625 oC) constant (isothermal treatment)

T(ºC) Austenite (stable) o TE (727 C) 700 Austenite (unstable)

Fig. 12.14, Callister & Rethwisch 9e. 600 Pearlite [Adapted from H. Boyer (Editor), Atlas of γ γ Isothermal Transformation and Cooling Transformation Diagrams, 1977. γ Reproduced by permission of ASM γ γ γ International, Materials Park, OH.] 500

400

110102 103 104 105 time (s) AMSE 205 Spring ‘2016 Chapter 12 - 17 Transformations Involving Noneutectoid Compositions

Consider C0 = 1.13 wt% C T(oC) T(oC) 900 1600 δ A L 800 1400 A TE (727°C) γ+L + 1200 γ L+Fe3C 700 A C (austenite) P 1000 + P a γ+Fe3C 600 A 800 727°C C (cementite) 500 600 α+Fe3C 3 Fe 2 3 4

1101010 10 400 0.76 0 0.022 1234566.7 time (s) (Fe)

1.13 C, wt%C Fig. 12.16, Callister & Rethwisch 9e. Fig. 11.23, Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. and Cooling Transformation Diagrams, 1977. Reproduced by 1, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.] permission of ASM International, Materials Park, OH.] Hypereutectoid composition – proeutectoid cementite

AMSE 205 Spring ‘2016 Chapter 12 - 18 Bainite: Another Fe-Fe3C Transformation Product • Bainite:

-- elongated Fe3C particles in α-ferrite matrix -- diffusion controlled Fe3C • Isothermal Transf. Diagram, (cementite) α (ferrite) C0 = 0.76 wt% C 800 Austenite (stable) T(°C) A TE P 600 100% pearlite 5 μm Fig. 12.17, Callister & Rethwisch 9e. (From Metals Handbook, Vol. 8, 8th edition, 100% bainite Metallography, Structures and Phase Diagrams, B 1973. Reproduced by permission of ASM 400 A International, Materials Park, OH.)

200

10-1 10 103 105 time (s) Fig. 12.18, Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, 1977. Reproduced by permissionAMSE 205 of ASM Spring Internati ‘2016onal, Materials Park, OH.] Chapter 12 - 19 Spheroidite: Another Microstructure

for the Fe-Fe3C System

• Spheroidite: α -- Fe3C particles within an α-ferrite matrix (ferrite) -- formation requires diffusion

-- heat bainite or pearlite at temperature Fe3C just below eutectoid for long times (cementite) -- driving force – reduction

of α-ferrite/Fe3C interfacial area

60 μm Fig. 12.19, Callister & Rethwisch 9e. (Copyright United States Steel Corporation, 1971.)

AMSE 205 Spring ‘2016 Chapter 12 - 20 Martensite: A Nonequilibrium Transformation Product • Martensite: -- γ(FCC) to Martensite (BCT)

Fe atom x potential

현재 이 이미지를 표시할 수 x 없습니다. x sites x C atom sites 현재 이 이미지를 표시할 수 x 없습니다. x Adapted from Fig. 12.20, 60 μm Callister & Rethwisch 9e. • Isothermal Transf. Diagram 800 Austenite (stable) Martensite needles Austenite T(°C) A TE P Fig. 12.21, Callister & Rethwisch 9e. 600 (Courtesy United States Steel Corporation.)

Adapted from Fig. 12.22, B Callister & 400 A • γ to martensite (M) transformation. Rethwisch 9e. -- is rapid! (diffusionless) 0% -- % transformation depends only 200 M + A 50% M + A 90% on T to which rapidly cooled M + A 10-1 10 103 105 time (s) AMSE 205 Spring ‘2016 Chapter 12 - 21 Martensite Formation

slow cooling γ (FCC) α (BCC) + Fe3C quench tempering M (BCT)

Martensite (M) – single phase – has body centered tetragonal (BCT) crystal structure

Diffusionless transformation BCT if C0 > 0.15 wt% C BCT  few slip planes  hard, brittle

AMSE 205 Spring ‘2016 Chapter 12 - 22 Phase Transformations of Alloys

Effect of adding other elements Change transition temp.

Cr, Ni, Mo, Si, Mn

retard γ  α + Fe3C reaction (and formation of pearlite, bainite)

Fig. 12.23, Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, 1977. Reproduced by permission of ASM International, Materials Park, OH.]

AMSE 205 Spring ‘2016 Chapter 12 - 23 Continuous Cooling Transformation Diagrams

Conversion of isothermal transformation diagram to continuous cooling transformation diagram

Fig. 12.25, Callister & Rethwisch 9e. [Adapted from H. Boyer (Editor), Atlas of Isothermal Transformation and Cooling Transformation Diagrams, 1977. Reproduced by permission of ASM International, Materials Park, OH.] Cooling curve

AMSE 205 Spring ‘2016 Chapter 12 - 24 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 d) 50% martensite and 50% austenite

AMSE 205 Spring ‘2016 Chapter 12 - 25 Solution to Part (a) of Example Problem a) 42% proeutectoid ferrite and 58% coarse pearlite

Fe-Fe3C phase diagram, Isothermally treat at ~ for C0 = 0.45 wt% C 680°C 800 A + α T (°C) A -- all austenite transforms A + P to proeutectoid α and 600 P coarse pearlite. B A + B A 400 50% M (start) M (50%) M (90%) 200

0 Figure 12.39, Callister & Rethwisch 9e. 0.1 10 103 105 (Adapted from Atlas of Time-Temperature Diagrams for Irons and Steels, G. F. Vander Voort, Editor, 1991. Reprinted by permission time (s) of ASM International, Materials Park, OH.) AMSE 205 Spring ‘2016 Chapter 12 - 27 Solutions to Parts (c) & (d) of Example Problem c) 100% martensite – rapidly quench to room Fe-Fe C phase diagram, temperature 3 for C0 = 0.45 wt% C d) 50% martensite 800 A + α T (°C) A & 50% austenite A + P -- rapidly quench to 600 P ~ 290°C, hold at this B A + B temperature A 400 50% M (start) M (50%) d) M (90%) 200 c) 0 Figure 12.39, Callister & Rethwisch 9e. 0.1 10 103 105 (Adapted from Atlas of Time-Temperature Diagrams for Irons and Steels, G. F. Vander Voort, Editor, 1991. Reprinted by permission time (s) of ASM International, Materials Park, OH.) AMSE 205 Spring ‘2016 Chapter 12 - 28 Mechanical Props: Influence of C Content

Pearlite (med) Pearlite (med) Cementite ferrite (soft) (hard) Fig. 11.29, Callister & Rethwisch 9e. C0 < 0.76 wt% C C0 > 0.76 wt% C Fig. 11.32, Callister & Rethwisch 9e. (Courtesy of Republic Steel Corporation.) (Copyright 1971 by United States Steel Hypoeutectoid Hypereutectoid Corporation.) Hypo Hyper Hypo Hyper TS(MPa) 1100 %EL 80 YS(MPa) 100 Fig. 12.29, Callister & Rethwisch 9e. 900 [Data taken from Metals hardness Handbook: Heat Treating, 40 Vol. 4, 9th edition, V. 700 Masseria (Managing 50 Editor), 1981. Reproduced by permission of ASM 500 International, Materials 0 Park, OH.] 300

0 Impact energy ft-lb) (Izod, 0 0.5 1 0 0.5 1

0.76 wt% C 0.76 wt% C • Increase C content: TS and YS increase, %EL decreases

AMSE 205 Spring ‘2016 Chapter 12 - 29 Mechanical Props: Fine Pearlite vs. Coarse Pearlite vs. Spheroidite

Hypo Hyper 90 Hypo Hyper 320 fine pearlite spheroidite 60 240 coarse pearlite spheroidite 160 30 coarse Ductility (%RA) pearlite

Brinell hardness fine 80 pearlite 0 0 0.5 1 0.5 1 wt%C 0 wt%C Fig. 12.30, Callister & Rethwisch 9e. • Hardness: fine > coarse > spheroidite [Data taken from Metals Handbook: Heat Treating, Vol. 4, 9th edition, V. Masseria • %RA: fine < coarse < spheroidite (Managing Editor), 1981. Reproduced by permission of ASM International, Materials Park, OH.]

AMSE 205 Spring ‘2016 Chapter 12 - 30 Mechanical Props: Fine Pearlite vs. Martensite

• Hardness: fine pearlite << martensite.

AMSE 205 Spring ‘2016 Chapter 12 - 31 Tempered Martensite Heat treat martensite to form tempered martensite • tempered martensite less brittle than martensite • tempering reduces internal stresses caused by quenching TS(MPa) YS(MPa) 1800

1600 TS Fig. 12.34, Figure 12.33, Callister & 1400 YS Callister & Rethwisch 9e. Rethwisch 9e. (Adapted from Edgar (Copyright 1971 by C. Bain, Functions of 1200 9 μm United States Steel the Alloying 60 Corporation.) Elements in Steel, 1939. Reproduced 1000 50 by permission of %RA %RA ASM International, 40 Materials Park, OH.) 800 30 200 400 600 Tempering T(°C)

• tempering produces extremely small Fe3C particles surrounded by α. • tempering decreases TS, YS but increases %RA

AMSE 205 Spring ‘2016 Chapter 12 - 32 Shape Memory Alloy Nitinol: (Ni-Ti Naval Ordnance Laboratory)

AMSE 205 Spring ‘2016 Chapter 12 - 33 Shape Memory Effect

AMSE 205 Spring ‘2016 Chapter 12 - Pseudo Elasticity (Super Elasticity)

AMSE 205 Spring ‘2016 Chapter 12 - Summary of Possible Transformations

Adapted from Austenite (γ) Fig. 12.36, Callister & Rethwisch 9e. slow moderate rapid cool cool quench

Pearlite Bainite Martensite

(α + Fe3C layers + a (α + elong. Fe3C particles) (BCT phase proeutectoid phase) diffusionless transformation) Martensite reheat T Martensite bainite Tempered fine pearlite Martensite (α + very fine Ductility Strength coarse pearlite spheroidite Fe3C particles) General Trends AMSE 205 Spring ‘2016 Chapter 12 - 36