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Chapter 12: Phase Transformations

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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 dG 1 4 3 1 2 r Gv 4r 0 dr dr 3 dr 2 r* Gv 3 * 16 G 2 3Gv H H T T H T v v m v Gv H v TSv H v T Tm Tm Tm 2 2T r* m Gv H vT 3 3 2 * 16 16 Tm G 2 2 2 3Gv 3H 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 3 3 2 16 16 T * 2 2Tm G * m r 2 2 2 3 H T Gv H vT 3Gv v AMSE 205 Spring ‘2016 Chapter 12 - 7 Nucleation Kinetics d AMSE 205 Spring ‘2016 Chapter 12 - 8 Heterogeneous Nucleation IL SI SL cos 2 r* SL GV 16 3 G* SL hetero 2 3Gv * * 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 135C 119C 113C 102C 88C 43C 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.
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  • Quantification of the Microstructures of Hypoeutectic White Cast Iron Using

    Quantification of the Microstructures of Hypoeutectic White Cast Iron Using

    Quantification of the Microstructures of Hypoeutectic White Cast Iron using Mathematical Morphology and an Artificial Neuronal Network Victor Albuquerque, João Manuel R. S. Tavares, Paulo Cortez Abstract This paper describes an automatic system for segmentation and quantification of the microstructures of white cast iron. Mathematical morphology algorithms are used to segment the microstructures in the input images, which are later identified and quantified by an artificial neuronal network. A new computational system was developed because ordinary software could not segment the microstructures of this cast iron correctly, which is composed of cementite, pearlite and ledeburite. For validation purpose, 30 samples were analyzed. The microstructures of the material in analysis were adequately segmented and quantified, which did not happen when we used ordinary commercial software. Therefore, the proposed system offers researchers, engineers, specialists and others, a valuable and competent tool for automatic and efficient microstructural analysis from images. Keywords: hypoeutectic white cast iron, image processing and analysis, mathematical morphology, artificial neuronal network, image quantification. 1 1. Introduction Cast iron is an iron-carbon-silicon alloy used in numerous industrial applications, such as the base structures of manufacturing machines, rollers, valves, pump bodies and mechanical gears, among others. The main families of cast irons are: nodular cast iron, malleable cast iron, grey cast iron and white cast iron (Callister, 2006). Their properties, as of all materials, are influenced by their microstructures and therefore, the correct characterization of their microstructures is highly important. Thus, quantitative metallography is commonly used to determine the quantity, appearance, size and distribution of the phases and constituents of the white cast iron microstructures.