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 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?

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

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 (0.1-10ºC)

Homogeneous Nucleation & Energy Effects Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) g = surface tension DGT = Total Free Energy = DGS + DGV 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.11.2(b), Callister & Rethwisch 3e.

Solidification Note: Hf and  are weakly dependent on T Hf = latent heat of solidification Tm = melting temperature g = surface free energy DT = Tm - T = supercooling r* = critical radius Note: Hf and  are weakly dependent on T  r* decreases as T increases For typical T r* ~ 10 nm

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

Rate of Phase Transformation transformation complete 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. 11.10, Callister & Rethwisch 3e. Avrami equation => y = 1- exp (-kt n) k & n are transformation specific parameters S.A. = surface area fraction transformed time By convention rate = 1 / t0.5

Temperature Dependence of Transformation Rate 1 10 102 104 Adapted from Fig. 11.11, Callister & Rethwisch 3e. (Fig. 11.11 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 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!

Transformations & Undercooling • Eutectoid transf. (Fe-Fe3C system): g Þ a + Fe3C • For transf. to occur, must cool to below 727°C (i.e., must “undercool”) 0.76 wt% C 6.7 wt% C 0.022 wt% C 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) C, wt%C 1148°C T(°C) ferrite 727°C Eutectoid: Equil. Cooling: Ttransf. = 727ºC DT Undercooling by Ttransf. < 727C 0.76 0.022 Adapted from Fig. 10.28,Callister & Rethwisch 3e. (Fig. 10.28 adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)

The Fe-Fe3C Eutectoid Transformation • Transformation of austenite to pearlite: Adapted from Fig. 10.15, Callister & Rethwisch 3e. g a pearlite growth direction Austenite (g) grain boundary cementite (Fe3C) Ferrite (a) Diffusion of C during transformation a g Carbon diffusion • For this transformation, rate increases with [Teutectoid – T ] (i.e., DT). Adapted from Fig. 11.12, Callister & Rethwisch 3e. 675°C (DT smaller) 50 y (% pearlite) 600°C (DT larger) 650°C 100 Coarse pearlite  formed at higher temperatures – relatively soft Fine pearlite  formed at lower temperatures – relatively hard

Generation of Isothermal Transformation Diagrams Consider: • The Fe-Fe3C system, for Co = 0.76 wt% C • A transformation temperature of 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. 11.13,Callister & Rethwisch 3e. (Fig. 11.13 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)

Austenite-to-Pearlite Isothermal Transformation • Eutectoid composition, C0 = 0.76 wt% C • Begin at T > 727°C • Rapidly cool to 625°C • Hold T (625°C) constant (isothermal treatment) 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. 11.14,Callister & Rethwisch 3e. (Fig. 11.14 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) g g

Transformations Involving Noneutectoid Compositions Consider C0 = 1.13 wt% C a TE (727°C) T(°C) time (s) A + C P 1 10 102 103 104 500 700 900 600 800 Adapted from Fig. 10.28, Callister & Rethwisch 3e. 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) C, wt%C T(°C) 727°C DT 0.76 0.022 1.13 Adapted from Fig. 11.16, Callister & Rethwisch 3e. Hypereutectoid composition – proeutectoid cementite

Bainite: Another Fe-Fe3C Transformation Product -- elongated Fe3C particles in a-ferrite matrix -- diffusion controlled • Isothermal Transf. Diagram, C0 = 0.76 wt% C Fe3C (cementite) a (ferrite) 10 3 5 time (s) -1 400 600 800 T(°C) Austenite (stable) 200 P B TE 0% 100% 50% A 100% pearlite 100% bainite 5 mm Adapted from Fig. 11.17, Callister & Rethwisch 3e. (Fig. 11.17 from Metals Handbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.) Adapted from Fig. 11.18, Callister & Rethwisch 3e.

Spheroidite: Another Microstructure for the Fe-Fe3C System Adapted from Fig. 11.19, Callister & Rethwisch 3e. (Fig. 11.19 copyright United States Steel Corporation, 1971.) 60 m a (ferrite) (cementite) Fe3C • Spheroidite: -- Fe3C particles within an a-ferrite matrix -- formation requires diffusion -- heat bainite or pearlite at temperature just below eutectoid for long times -- driving force – reduction of a-ferrite/Fe3C interfacial area

Martensite: A Nonequilibrium Transformation Product -- g(FCC) to Martensite (BCT) Martensite needles Austenite 60 m x potential C atom sites Fe atom sites Adapted from Fig. 11.21, Callister & Rethwisch 3e. Adapted from Fig. 11.23, Callister & Rethwisch 3e. • Isothermal Transf. Diagram • g to martensite (M) transformation.. -- is rapid! (diffusionless) -- % transf. depends only on T to which rapidly cooled 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. 11.22, Callister & Rethwisch 3e. (Fig. 11.22 courtesy United States Steel Corporation.)

Martensite Formation  (FCC)  (BCC) + Fe3C slow cooling quench M (BCT) tempering 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

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. 11.24, Callister & Rethwisch 3e.

Continuous Cooling Transformation Diagrams Cooling curve Conversion of isothermal transformation diagram to continuous cooling transformation diagram Actual processes involves cooling – not isothermal Can’t cool at infinite speed Adapted from Fig. 11.26, Callister & Rethwisch 3e.

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: 42% proeutectoid ferrite and 58% coarse pearlite 50% fine pearlite and 50% bainite 100% martensite 50% martensite and 50% austenite

Solution to Part (a) of Example Problem 42% proeutectoid ferrite and 58% coarse pearlite 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%) Adapted from Fig. 10.29, Callister 5e. Fe-Fe3C phase diagram, for C0 = 0.45 wt% C Isothermally treat at ~ 680°C -- all austenite transforms to proeutectoid a and coarse pearlite. T (°C)

Solution to Part (b) of Example Problem 50% fine pearlite and 50% bainite T (°C) 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%) Adapted from Fig. 10.29, Callister 5e. Fe-Fe3C phase diagram, for C0 = 0.45 wt% C Isothermally treat at ~ 590°C – 50% of austenite transforms to fine pearlite. Then isothermally treat at ~ 470°C – all remaining austenite transforms to bainite.

Solutions to Parts (c) & (d) of Example Problem 100% martensite – rapidly quench to room temperature T (°C) 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%) Adapted from Fig. 10.29, Callister 5e. Fe-Fe3C phase diagram, for C0 = 0.45 wt% C 50% martensite & 50% austenite -- rapidly quench to ~ 290°C, hold at this T c) d)

Mechanical Props: Influence of C Content Adapted from Fig. 10.37, Callister & Rethwisch 3e. C0 > 0.76 wt% C Hypereutectoid Pearlite (med) C ementite (hard) Pearlite (med) ferrite (soft) C0 < 0.76 wt% C Adapted from Fig. 10.34, Callister & Rethwisch 3e. Hypoeutectoid Adapted from Fig. 11.30, Callister & Rethwisch 3e. (Fig. 11.30 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 0.5 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 • Increase C content: TS and YS increase, %EL decreases

Mechanical Props: Fine Pearlite 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 (%RA) fine pearlite coarse spheroidite Hypo Hyper 0.5 1 Adapted from Fig. 11.31, Callister & Rethwisch 3e. (Fig. 11.31 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 Props: Fine Pearlite vs. Martensite 200 wt% C 0.5 1 400 600 Brinell hardness martensite fine pearlite Hypo Hyper Adapted from Fig. 11.33, Callister & Rethwisch 3e. (Fig. 11.33 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.

Tempered Martensite • • Heat treat martensite to form tempered martensite • tempered martensite less brittle than martensite • tempering reduces internal stresses 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. 11.35, Callister & Rethwisch 3e. (Fig. 11.35 adapted from Fig. furnished courtesy of Republic Steel Corporation.) Adapted from Fig. 11.34, Callister & Rethwisch 3e. (Fig. 11.34 copyright by United States Steel Corporation, 1971.) 9 mm • tempering produces extremely small Fe3C particles surrounded by a. • tempering decreases TS, YS but increases %RA

Summary of Possible Transformations Adapted from Fig. 11.37, Callister & Rethwisch 3e. Austenite (g) Pearlite (a + Fe3C layers + a proeutectoid phase) slow cool Bainite (a + elong. Fe3C particles) moderate cool Martensite (BCT phase diffusionless transformation) rapid quench Strength Ductility Martensite T Martensite bainite fine pearlite coarse pearlite spheroidite General Trends Tempered Martensite (a + very fine Fe3C particles) reheat

Precipitation Hardening • Particles impede dislocation motion. • Ex: Al-Cu system • Procedure: 10 20 30 40 50 wt% Cu L +L a a+q q +L 300 400 500 600 700 (Al) T(°C) composition range available for precipitation hardening CuAl2 A -- Pt A: solution heat treat (get a solid solution) B Pt B -- Pt B: quench to room temp. (retain a solid solution) C -- Pt C: reheat to nucleate small q particles within a phase. Other alloys that precipitation harden: • Cu-Be • Cu-Sn • Mg-Al Adapted from Fig. 11.43, Callister & Rethwisch 3e. (Fig. 11.43 adapted from J.L. Murray, International Metals Review 30, p.5, 1985.) Temp. Time Pt A (sol’n heat treat) Pt C (precipitate ) Adapted from Fig. 11.41, Callister & Rethwisch 3e.

Influence of Precipitation Heat Treatment on TS, %EL • 2014 Al Alloy: • Maxima on TS curves. • Increasing T accelerates process. • Minima on %EL curves. %EL (2 in sample) 10 20 30 1min 1h 1day 1mo 1yr 204°C 149 °C precipitation heat treat time precipitation heat treat time tensile strength (MPa) 200 300 400 100 1min 1h 1day 1mo 1yr 204°C non-equil. solid solution many small precipitates “aged” fewer large “overaged” 149°C Adapted 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.)

Melting & Glass Transition Temps. What factors affect Tm and Tg? Both Tm and Tg increase with increasing chain stiffness Chain stiffness increased by presence of Bulky sidegroups Polar groups or sidegroups Chain double bonds and aromatic chain groups Regularity of repeat unit arrangements – affects Tm only Adapted from Fig. 11.47, Callister & Rethwisch 3e. 31 31

Thermoplastics vs. Thermosets Callister, Fig. 16.9 T Molecular weight Tg Tm mobile liquid viscous rubber tough plastic partially crystalline solid • Thermoplastics: -- little crosslinking -- ductile -- soften w/heating -- polyethylene polypropylene polycarbonate polystyrene • Thermosets: -- significant crosslinking (10 to 50% of repeat units) -- hard and brittle -- do NOT soften w/heating -- vulcanized rubber, epoxies, polyester resin, phenolic resin 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.) 32 32

Summary • Heat treatments of Fe-C alloys produce microstructures including: -- pearlite, bainite, spheroidite, martensite, tempered martensite • Precipitation hardening --hardening, strengthening due to formation of precipitate particles. --Al, Mg alloys precipitation hardenable. • Polymer melting and glass transition temperatures

ANNOUNCEMENTS Reading: Core Problems: Self-help Problems: