Chapter 11: Phase Transformations ISSUES TO ADDRESS... • Transforming one phase into another takes time. Fe g (Austenite) Eutectoid transformation C FCC Fe3C (cementite) a (ferrite) + (BCC) • How does the rate of transformation depend on time and T ? • How can we slow down the transformation so that we can engineering non-equilibrium structures? • Are the mechanical properties of non-equilibrium structures better?

Kinetics : the science of time-dependent phase transformations TTT diagram : temperature, time and transformation ◈ Time-the third dimension The time required for a liquid phase to transform to the solid phase is a strong function of temperature.

To understand the “ knee-shaped” transformation curve, some fundamental concepts of kinetics theory are needed 핵의 생성(nucleation) homogeneous nucleation : the precipitation occurs within a completely homogeneous medium heterogeneous nucleation : the precipitation occurs at some structural imperfection

Classical nucleation theory Total change in energy

critical radius for homogeneous nucleation The rate of nucleation ① The driving force for solidification increases with decreasing temperature, and the rate of nucleation increases sharply. ② The clustering of atoms to form a nucleus decrease in rate with decreasing temperature (diffusion) ③ The overall nucleation rate reflects these two factors (① & ②)

The growth rate (핵의 성장)

-The overall transformation rate : product of

◈ The TTT Diagram - Temperature, time, and transformation

Phase Transformations 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) superheating (peritectic) In Chapter 9 we looked at the equilibrium phase diagram . This indicated phase structure if we wait long enough. But due to slow diffusion may not reach equilibrium We need to consider time- kinetics - energy of phase boundaries may be high. – also nucleation Transformation rate How fast do the phase transformations occur? First need nuclei (seeds) to form for the rest of the material to crystallize Small supercooling  few nuclei - large crystals Large supercooling  rapid nucleation - many nuclei, small crystals

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

Solidification Note: HS = strong function of T HS = latent heat of solidification Tm = melting temperature g = surface free energy DT = Tm - T = supercooling r* = critical radius Note: HS = strong function of T  = weak function of T  r* decreases as T increases

Rate of Phase Transformations Kinetics - measure approach to equilibrium vs. time Hold temperature constant & measure conversion vs. time How is conversion measured? X-ray diffraction – have to do many samples electrical conductivity – follow one sample sound waves – one sample

Rate of Phase Transformation All out of material - done Fixed T Fraction transformed, y 0.5 maximum rate reached – now amount unconverted decreases so rate slows rate increases as surface area increases & nuclei grow t0.5 log t Adapted from Fig. 10.10, Callister 7e. Avrami rate equation => y = 1- exp (-ktn) k & n fit for specific sample S.A. = surface area fraction transformed time By convention r = 1 / t0.5

Rate of Phase Transformations 135C 119C 113C 102C 88C 43C 1 10 102 104 Adapted from Fig. 10.11, Callister 7e. (Fig. 10.11 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.) In general, rate increases as T  r = 1/t0.5 = A e -Q/RT R = gas constant T = temperature (K) A = preexponential factor Q = activation energy Arrhenius expression r often small: equilibrium not possible!

Eutectoid Transformation Rate • Growth of pearlite from austenite: Adapted from Fig. 9.15, Callister 7e. g a pearlite growth direction Austenite (g) grain boundary cementite (Fe3C) Ferrite (a) Diffusive flow of C needed a g • Recrystallization rate increases with DT. Adapted from Fig. 10.12, Callister 7e. 675°C (DT smaller) 50 y (% pearlite) 600°C (DT larger) 650°C 100 Course pearlite  formed at higher T - softer Fine pearlite  formed at low T - harder

Nucleation and Growth • Reaction rate is a result of nucleation and growth of crystals. % Pearlite 50 100 Nucleation regime Growth log (time) t 0.5 Nucleation rate increases with T Growth rate increases with T Adapted from Fig. 10.10, Callister 7e. • Examples: T just below TE Nucleation rate low Growth rate high g pearlite colony T moderately below TE g Nucleation rate med . Growth rate med. Nucleation rate high T way below TE g Growth rate low

Transformations & Undercooling • Eutectoid transf. (Fe-C System): g Þ a + Fe3C • Can make it occur at: 0.76 wt% C 6.7 wt% C ...727ºC (cool it slowly) 0.022 wt% C ...below 727ºC (“undercool” it!) Fe3C (cementite) 1600 1400 1200 1000 800 600 400 1 2 3 4 5 6 6.7 L g (austenite) +L +Fe3C a L+Fe3C d (Fe) Co , wt%C 1148°C T(°C) ferrite 727°C Eutectoid: Equil. Cooling: Ttransf. = 727ºC DT Undercooling by DTtransf. < 727C 0.76 0.022 Adapted from Fig. 9.24,Callister 7e. (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.)

Isothermal Transformation Diagrams • Fe-C system, Co = 0.76 wt% C • Transformation at T = 675°C. 100 T = 675°C y, % transformed 50 2 4 1 10 10 time (s) 400 500 600 700 1 10 2 3 4 5 0%pearlite 100% 50% Austenite (stable) TE (727C) Austenite (unstable) Pearlite T(°C) time (s) isothermal transformation at 675°C Adapted from Fig. 10.13,Callister 7e. (Fig. 10.13 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)

Effect of Cooling History in Fe-C System • Eutectoid composition, Co = 0.76 wt% C • Begin at T > 727°C • Rapidly cool to 625°C and hold isothermally. 400 500 600 700 0%pearlite 100% 50% Austenite (stable) TE (727C) Austenite (unstable) Pearlite T(°C) 1 10 2 3 4 5 time (s) Adapted from Fig. 10.14,Callister 7e. (Fig. 10.14 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) g g

Transformations with Proeutectoid Materials CO = 1.13 wt% C TE (727°C) T(°C) time (s) A + C P 1 10 102 103 104 500 700 900 600 800 Adapted from Fig. 10.16, Callister 7e. Adapted from Fig. 9.24, Callister 7e. Fe3C (cementite) 1600 1400 1200 1000 800 600 400 1 2 3 4 5 6 6.7 L g (austenite) +L +Fe3C a L+Fe3C d (Fe) Co , wt%C T(°C) 727°C DT 0.76 0.022 1.13 Hypereutectoid composition – proeutectoid cementite

Non-Equilibrium Transformation Products: Fe-C • Bainite: --a lathes (strips) with long rods of Fe3C --diffusion controlled. • Isothermal Transf. Diagram Fe3C (cementite) a (ferrite) 10 3 5 time (s) -1 400 600 800 T(°C) Austenite (stable) 200 P B TE 0% 100% 50% pearlite/bainite boundary A 100% pearlite 100% bainite 5 mm (Adapted from Fig. 10.17, Callister, 7e. (Fig. 10.17 from Metals Handbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.) Adapted from Fig. 10.18, Callister 7e. (Fig. 10.18 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)

Spheroidite: Fe-C System (Adapted from Fig. 10.19, Callister, 7e. (Fig. 10.19 copyright United States Steel Corporation, 1971.) 60 m a (ferrite) (cementite) Fe3C • Spheroidite: --a grains with spherical Fe3C --diffusion dependent. --heat bainite or pearlite for long times --reduces interfacial area (driving force)

Martensite: Fe-C System --g(FCC) to Martensite (BCT) Martensite needles Austenite 60 m x potential C atom sites Fe atom sites (involves single atom jumps) (Adapted from Fig. 10.20, Callister, 7e. • Isothermal Transf. Diagram 10 3 5 time (s) -1 400 600 800 T(°C) Austenite (stable) 200 P B TE 0% 100% 50% A M + A 90% (Adapted from Fig. 10.21, Callister, 7e. (Fig. 10.21 courtesy United States Steel Corporation.) Adapted from Fig. 10.22, Callister 7e. • g to M transformation.. -- is rapid! -- % transf. depends on T only.

Martensite Formation  (FCC)  (BCC) + Fe3C slow cooling quench M (BCT) tempering M = martensite is body centered tetragonal (BCT) Diffusionless transformation BCT if C > 0.15 wt% 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 transformation Adapted from Fig. 10.23, Callister 7e.

Cooling Curve plot temp vs. time Actual processes involves cooling – not isothermal Can’t cool at infinite speed Adapted from Fig. 10.25, Callister 7e.

Dynamic Phase Transformations On the isothermal transformation diagram for 0.45 wt% C Fe-C alloy, sketch and label the time-temperature paths to produce the following microstructures: 42% proeutectoid ferrite and 58% coarse pearlite 50% fine pearlite and 50% bainite 100% martensite 50% martensite and 50% austenite

Example Problem for Co = 0.45 wt% 42% proeutectoid ferrite and 58% coarse pearlite first make ferrite then pearlite course pearlite  higher T A + B A + P A + a A B P 50% 200 400 600 800 0.1 10 103 105 time (s) M (start) M (50%) M (90%) T (°C) Adapted from Fig. 10.29, Callister 5e.

Example Problem for Co = 0.45 wt% 50% fine pearlite and 50% bainite first make pearlite then bainite fine pearlite  lower T A + B A + P A + a A B P 50% 200 400 600 800 0.1 10 103 105 time (s) M (start) M (50%) M (90%) T (°C) Adapted from Fig. 10.29, Callister 5e.

Example Problem for Co = 0.45 wt% 100 % martensite – quench = rapid cool 50 % martensite and 50 % austenite A + B A + P A + a A B P 50% 200 400 600 800 0.1 10 103 105 time (s) M (start) M (50%) M (90%) c) T (°C) d) Adapted from Fig. 10.29, Callister 5e.

Mechanical Prop: Fe-C System (1) • Effect of wt% C Pearlite (med) Pearlite (med) C ementite ferrite (soft) (hard) Co < 0.76 wt% C Co > 0.76 wt% C Adapted from Fig. 9.30,Callister 7e. (Fig. 9.30 courtesy Republic Steel Corporation.) Adapted from Fig. 9.33,Callister 7e. (Fig. 9.33 copyright 1971 by United States Steel Corporation.) Hypoeutectoid Hypereutectoid 300 500 700 900 1100 YS(MPa) TS(MPa) wt% C 0.5 1 hardness 0.76 Hypo Hyper wt% C 0.5 1 50 100 %EL Impact energy (Izod, ft-lb) 40 80 0.76 Hypo Hyper Adapted from Fig. 10.29, Callister 7e. (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.) • More wt% C: TS and YS increase , %EL decreases.

Mechanical Prop: Fe-C System (2) • Fine vs coarse pearlite vs spheroidite 80 160 240 320 wt%C 0.5 1 Brinell hardness fine pearlite coarse spheroidite Hypo Hyper 30 60 90 wt%C Ductility (%AR) fine pearlite coarse spheroidite Hypo Hyper 0.5 1 Adapted from Fig. 10.30, Callister 7e. (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: fine > coarse > spheroidite • %RA: fine < coarse < spheroidite

Mechanical Prop: Fe-C System (3) • Fine Pearlite vs Martensite: 200 wt% C 0.5 1 400 600 Brinell hardness martensite fine pearlite Hypo Hyper Adapted from Fig. 10.32, Callister 7e. (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.) • Hardness: fine pearlite << martensite.

Tempering Martensite • • • reduces brittleness of martensite, • reduces internal stress caused by quenching. YS(MPa) TS(MPa) 800 1000 1200 1400 1600 1800 30 40 50 60 200 400 600 Tempering T (°C) %RA TS YS Adapted from Fig. 10.34, Callister 7e. (Fig. 10.34 adapted from Fig. furnished courtesy of Republic Steel Corporation.) Adapted from Fig. 10.33, Callister 7e. (Fig. 10.33 copyright by United States Steel Corporation, 1971.) 9 mm produces extremely small Fe3C particles surrounded by a. • • decreases TS, YS but increases %RA

Summary: Processing Options Austenite (g) Bainite (a + Fe3C plates/needles) Pearlite (a + Fe3C layers + a proeutectoid phase) Martensite (BCT phase diffusionless transformation) Tempered (a + very fine Fe3C particles) slow cool moderate rapid quench reheat Strength Ductility T Martensite bainite fine pearlite coarse pearlite spheroidite General Trends Adapted from Fig. 10.36, Callister 7e.

PRECIPITATION HARDENING • Particles impede dislocations. • Ex: Al-Cu system • Procedure: --Pt A: solution heat treat (get a solid solution) --Pt B: quench to room temp. --Pt C: reheat to nucleate small q crystals within a 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

STRENGTHENING STRATEGY : PRECIPITATION STRENGTHENING • Hard precipitates are difficult to shear. Ex: Ceramics in metals (SiC in Iron or Aluminum). • Result: 24

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. 1.5mm Adapted from Fig. 11.24, Callister 6e. (Fig. 11.24 is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.) 26