P + F = C + 2 Gibbs Phase Rule P: # of phases F: Degrees of freedom C: # of components Normally, pressure = 1 atm P + F = C + 1 or F = C - P + 1 Apply to eutectic phase diagram 1 phase field: F = 2 1 + 1 = 2 Change T and C independently in phase field 2 phase field: F = 2 2 + 1 = 1 C depends on T not independent 3 phase point: F = 2 3 +1 = 0 C and T defined only at one point (Eutectic point) (no degrees of freedom)
Phase Diagrams with Intermediate Phases/Compounds Example: Mg-Pb binary phase diagram Terminal phases/solid solutions: α and β Intermediate compound: Mg 2 Pb (line compound)
Phase Diagrams with Intermediate Phases/Compounds Example: Sn-Au binary phase diagram Terminal phases/solid solutions: α and η Intermediate compounds: β, γ, δ, ζ
Phase Diagram: Precipitation Strengthening System Al-Cu Alloys 1 st Precipitation-Hardenable Alloys Homogenize Cool Quickly Supersaturated α-phase Heat Precipitation of Θ or related phases
Precipitation Strengthening In Al-Cu Precipitation in Al-4%Cu (aged at 180 C, 6 h) GP-Zones Precipitation in Al-4%Cu (aged at 200 C, 2 h) θ Phase Precipitation in Al-4%Cu (aged at 450 C, 45 min.) θ Phase
Ceramic Phase Diagrams Example Continuous Solid Solution Components: Al 2 O 3 and Cr 2 O 3 (both have same crystal structure) Ceramic alloy: random occupancy of Al 3+ and Cr 3+ on cation sites
Ceramic Phase Diagrams Identify Components Identify invariant points Identify compound formation
Ceramic Phase Diagrams Identify Components Identify invariant points Identify compound formation
Ceramic Phase Diagrams
Chapter 10: Phase Transformations ISSUES TO ADDRESS... Transforming one phase into another takes time. Fe C FCC γ Fe3C Eutectoid transformation (cementite) (Austenite) + α (ferrite) (BCC) How does the rate of transformation depend on time and T? How can we slow the transformation so that we can engineer non-equilibrium structures? Are the properties of non-equilibrium structures improved?
Fraction of Transformation Fraction transformed depends on time. fraction transformed Avrami Eqn. y = 1 e kt n time 1 y 0.5 0 t 0.5 Transformation rate depends on T. Fixed T log (t) Adapted from Fig. 10.1, Callister 6e. activation energy r = 1 t 0.5 = Ae Q/RT y (%) 100 50 135 C r often small: equil not possible! 119 C 113 C 102 C 88 C Ex: recrystallization of Cu 43 C 0 1 10 10 2 10 4 log (t) min Adapted from Fig. 10.2, Callister 6e. (Fig. 10.2 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)
Transformations and Undercooling Eutectoid transf. (Fe-C System): Can make it occur at:...727ºc (cool it slowly)...below 727ºC ( undercool it!) T( C) α ferrite 1600 1400 1200 1000 800 600 γ+l γ austenite 400 0 1 2 3 4 5 6 (Fe) α+γ 0.022 Eutectoid: 0.77 L γ+fe3c L+Fe3C Equil. cooling: Ttransf. = 727ºC 727 C T α+fe3c Undercooling by T: Ttransf. < 727ºC γ α +Fe 3 C 0.77wt%C0.022wt%C 6.7wt%C Co, wt% C 6.7 Adapted from Fig. 9.21,Callister 6e. (Fig. 9.21 adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.) Fe3C cementite
Eutectoid Transformation Rate ~ T Growth of pearlite from austenite: Austenite (γ) grain boundary α α αα α α Reaction rate increases with T. γ y (% pearlite) γ cementite (Fe3C) ferrite (α) 100 pearlite growth direction 600 C ( T larger) 50 0 650 C Diffusive flow of C needed 0 γ 50 675 C ( T smaller) 1 10 10 2 10 3 time (s) 100 α α α % austenite γ Adapted from Fig. 10.3, Callister 6e. Adapted from Fig. 9.13, Callister 6e.
Nucleation and Growth Reaction rate is a result of nucleation and growth of crystals. 100 % Pearlite 50 0 Examples: Nucleation regime t 50 Growth regime Nucleation rate increases w/ T Growth rate increases w/ T log (time) Adapted from Fig. 10.1, Callister 6e. pearlite γ colony γ γ T just below TE T moderately below TE T way below TE Nucleation rate low Growth rate high Nucleation rate med. Nucleation rate high Growth rate med. Growth rate low
Isothermal Transformation Diagrams Fe-C system, C o = 0.77wt%C Transformation at T = 675C. y, % transformed 100 50 T( C) 700 600 500 400 T=675 C 0 1 10 2 10 4 Austenite (unstable) 100% 50% 0%pearlite Austenite (stable) Pearlite 1 10 10 2 10 3 10 4 10 5 time (s) TE (727 C) isothermal transformation at 675 C time (s) Adapted from Fig. 10.4,Callister 6e. (Fig. 10.4 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)
Ex: Cooling History Fe-C System Eutectoid composition, C o = 0.77 wt%c Begin at T > 727 C Rapidly cool to 625 C and hold isothermally. T( C) 700 Austenite (stable) TE (727 C) 600 γ γ 500 γ γ 100% 50% 0%pearlite γ γ γ Pearlite Adapted from Fig. 10.5,Callister 6e. (Fig. 10.5 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) 1 10 10 2 10 3 10 4 10 5 time (s)
Pearlite Morphology Two cases: Ttransf just below TE --Larger T: diffusion is faster --Pearlite is coarser. Ttransf well below TE --Smaller T: diffusion is slower --Pearlite is finer. 10µm Adapted from Fig. 10.6 (a) and (b),callister 6e. (Fig. 10.6 from R.M. Ralls et al., An Introduction to Materials Science and Engineering, p. 361, John Wiley and Sons, Inc., New York, 1976.) - Smaller T: colonies are larger - Larger T: colonies are smaller
Non-Equil. Transformation Products: Fe-C Bainite: --α lathes (stripes) with long rods of Fe3C --diffusion controlled. Isothermal Transf. Diagram 800 T( C) 600 400 A Austenite (stable) A P 100% pearlite 100% bainite B TE pearlite/bainite boundary Fe3C (cementite) α (ferrite) 5 µm (Adapted from Fig. 10.8, Callister, 6e. (Fig. 10.8 from Metals Handbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.) 200 10-1 0% 50% 100% 10 10 3 10 5 time (s) Adapted from Fig. 10.9,Callister 6e. (Fig. 10.9 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) Bainite reaction rate: r bainite = e Q/RT
Other Products: Fe-C System (1) Spheroidite: --α crystals with spherical Fe3C --diffusion dependent. --heat bainite or pearlite for long times --reduces interfacial area (driving force) Isothermal Transf. Diagram 800 T( C) 600 400 200 A Austenite (stable) A 0% P B 50% TE Spheroidite 100% spheroidite 100% spheroidite 100% α (ferrite) Fe3C (cementite) 60 µm (Adapted from Fig. 10.10, Callister, 6e. (Fig. 10.10 copyright United States Steel Corporation, 1971.) Adapted from Fig. 10.9,Callister 6e. (Fig. 10.9 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) 10-1 10 10 3 10 5 time (s)
Martensite: Other Products: Fe-C System (2) --γ(fcc) to Martensite (BCT) Isothermal Transf. Diagram Adapted from Fig. 10.13, Callister 6e. (involves single atom jumps) Fe atom sites 800 T( C) 600 400 200 x 10-1 A x x x x x potential C atom sites Austenite (stable) A 0% (Adapted from Fig. 10.11, Callister, 6e. P B 50% 100% S TE 0% M + A 50% M + A 90% M + A 10 10 3 10 5 time (s) 60 µm Martentite needles Austenite (Adapted from Fig. 10.12, Callister, 6e. (Fig. 10.12 courtesy United States Steel Corporation.) γ to M transformation.. -- is rapid! -- % transf. depends on T only.
Time-Temperature-Transformation (TTT) Diagrams Isothermal TTT Diagram Continuous Cooling TTT Diagram TTT Diagrams for a Eutectoid Steel
Cooling Ex: Fe-C System (1) Co = Ceutectoid Three histories... Rapid cool to: Hold for: Rapid cool to: Hold for: Rapid cool to: 350 C 10 4 s 10 4 s 800 T( C) 600 400 100%A 200 A Austenite (stable) A Case I 0% P B 50% 100% S 100%B M + A M + A M + A 10-1 10 10 3 10 5 250 C 650 C 0% 50% 90% Adapted from Fig. 10.15, Callister 6e. 100% Bainite time (s) 10 2 s 20s 400 C 10 2 s 10 3 s
Cooling Ex: Fe-C System (2) Co = Ceutectoid Three histories... Rapid cool to: Hold for: Rapid cool to: Hold for: Rapid cool to: 350 C 10 4 s 10 4 s 800 T( C) 600 400 200 A Austenite (stable) A 100%A Case II 0% P B 50% 100% S M + A M + A M + A 10-1 10 10 3 10 5 250 C 650 C 0% 50% 90% M + trace of A time (s) 10 2 s 20s Adapted from Fig. 10.15, Callister 6e. 400 C 10 2 s 10 3 s
Cooling Ex: Fe-C System (3) Co = Ceutectoid Three histories... Rapid cool to: Hold for: Rapid cool to: Hold for: Rapid cool to: 350 C 10 4 s 10 4 s 800 T( C) 100%A 600 A Austenite (stable) A Case III 50%P, 50%A P S B 250 C 650 C 10 2 s 20s 400 C 10 2 s 10 3 s 400 50%P, 50%A 0% 50% 50%P, 50%B 100% 0% 200 M + A M + A 50% 90% M + A 10-1 10 10 3 10 5 50%P, 50%B Adapted from Fig. 10.15, Callister 6e. time (s)
Mechanical Prop: Fe-C System (1) Effect of wt%c Pearlite (med) ferrite (soft) Adapted from Fig. 9.27,Callister 6e. (Fig. 9.27 courtesy Republic Steel Corporation.) TS(MPa) 1100 YS(MPa) 900 700 500 300 Hypo Co<0.77wt%C Hypoeutectoid 0 0.5 1 0.77 Hyper hardness %EL 100 Hypereutectoid 0 0 0.5 1 wt%c wt%c More wt%c: TS and YS increase, %EL decreases. 50 Pearlite (med) Cementite (hard) Co>0.77wt%C Hypo 0.77 Adapted from Fig. 9.30,Callister 6e. (Fig. 9.30 copyright 1971 by United States Steel Corporation.) Hyper 80 40 0 Impact energy (Izod, ft-lb) Adapted from Fig. 10.20, Callister 6e. (Fig. 10.20 based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.)
Mechanical Prop: Fe-C System (2) Fine vs coarse pearlite vs spheroidite Brinell hardness 320 240 160 80 Hypo Hyper Hypo Hyper fine pearlite 0 0.5 1 wt%c coarse pearlite spheroidite Ductility (%AR) Hardness: fine > coarse > spheroidite %AR: fine < coarse < spheroidite 90 60 spheroidite 30 coarse pearlite fine pearlite 0 0 0.5 1 wt%c Adapted from Fig. 10.21, Callister 6e. (Fig. 10.21 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.)
Mechanical Prop: Fe-C System (3) Fine Pearlite vs Martensite: Hypo Hyper Brinell hardness 600 400 200 martensite fine pearlite 0 0 0.5 1 wt%c Adapted from Fig. 10.23, Callister 6e. (Fig. 10.23 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. TS(MPa) YS(MPa) 1800 Adapted from Fig. 10.25, Callister 6e. (Fig. 10.25 adapted from Fig. furnished courtesy of Republic Steel Corporation.) 1600 1400 1200 1000 800 YS %AR TS 60 50 %AR 40 30 200 400 600 Tempering T ( C) 9 µm Adapted from Fig. 10.24, Callister 6e. (Fig. 10.24 copyright by United States Steel Corporation, 1971.) produces extremely small Fe3C particles surrounded by α. decreases TS, YS but increases %AR
Summary: Processing Options slow cool Austenite (γ) moderate cool rapid quench Adapted from Fig. 10.27, Callister 6e. Pearlite (α + Fe3C layers + a proeutectoid phase) Strength Bainite (α + Fe3C plates/needles) Martensite T Martensite bainite fine pearlite coarse pearlite spheroidite General Trends Ductility Martensite (BCT phase diffusionless transformation) reheat Tempered Martensite (α + very fine Fe3C particles)