Chapter 10: Phase Transformations

Transcription

1 Chapter 10: Phase Transformations ISSUES TO ADDRESS... Transforming one phase into another takes time. Fe C FCC g (Austenite) Eutectoid transformation Fe 3 C (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? Chapter 10-1

2 Phase transformation Takes time (transformation rates: kinetics). Involves movement/rearrangement of atoms. Usually involves changes in microstructure 1. Simple diffusion-dependent transformation: no change in number of compositions of phases present (e.g. solidification of pure elemental metals, allotropic transformation, recrystallization, grain growth). 2. Diffusion-dependent transformation: transformation with alteration in phase composition and, often, with changes in number of phases present (e.g. eutectoid reaction). 3. Diffusionless transformation: e.g. rapid T quenching to trap metastable phases. Chapter 10-2

3 º T R = recrystallization temperature T R Adapted from Fig. 7.22, Callister 7e. The influence of annealing T on the tensile strength and ductility of a brass alloy. º Chapter 10-3

4 Fe 3 C (cementite) Eutectoid cooling: 1600 d T( C) a Iron-Carbon Phase Diagram g g +L (austenite) R B g (0.76 wt% C) g g g g 1148 C R S L cool heat A g+fe 3 C 727 C = Teutectoid a+fe 3 C a (0.022 wt% C) + Fe 3 C (6.7 wt% C) L+Fe 3 C S (Fe) 0.76 C eutectoid 4.30 Fe 3 C (cementite-hard) a (ferrite-soft) Adapted from Fig. 9.24,Callister 7e. C o, wt% C Chapter 10-4

5 Nucleation Phase Transformations 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) Small supercooling few nuclei - large crystals Large supercooling rapid nucleation - many nuclei, small crystals Chapter 10-5

6 Solidification: Nucleation Processes Homogeneous nucleation nuclei form in the bulk of liquid metal requires supercooling (typically 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 ºC supercooling Chapter 10-6 Phase 1 (e.g. liquid) Nucleation of 2 nd phase Growth

7 Homogeneous Nucleation Thermodynamic parameters: Free energy G (or Gibbs free energy) Enthalpy H: internal energy of the system and the product of its volume multiplied by the pressure Entropy S: randomness or disorder of the atoms or molecules ΔG is important---a phase transformation will occur spontaneously only when ΔG has a negative value. ΔG = ΔH - TΔS Chapter 10-7

8 Homogeneous Nucleation Chapter 10-8

9 Homogeneous Nucleation & Energy Effects Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) 2 G S 4r g Activation Free Energy g = surface energy G T = Total Free Energy = G S + G V r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy) Adapted from Fig.10.2(b), Callister 7e. Volume (Bulk) Free Energy stabilizes the nuclei (releases energy) 4 3 G V r G G 3 volume free energy unit volume Chapter 10-9

10 Kinetics of solid state reactions Critical nucleus size (r c ) and the activation energy (G*) G = 4 r 3 3 G v 4r Take the derivative and set equal to zero to find max. d( G) 4 2 ( Gv )(3r dr 3 Substitution in to overall G equation r c 2 g 2g G v ) 4g (2r) 0 G * 3 16g 3( ) G v 2 Chapter The volume free energy change is the driving force for the solidification transformation

11 Kinetics of solid state reactions In terms of latent heat of fusion H f (i.e. energy release upon solidification): G v H f ( T T) T With this definition, we then have: m m Tells us how G v changes with temperature Equilibrium solidification temperature T 1 > T 2 r c 2g H f Tm Tm T G * 16g 3H 3 2 f Tm Tm T 2 As T decreases both r c and G* become smaller Number of stable nuclei: n * G exp kt Chapter LIQUID INSTABILITY at LOWER TEMPERTURES *

12 Solidification r* 2gTm H T S r* = critical radius g = surface free energy T m = melting temperature H S = latent heat of solidification T = T m - T = supercooling Note: H S g = strong function of T = weak function of T r* decreases as T increases For typical T r* ca. 100Å Chapter 10-12

13 Kinetics of solid state reactions We also need to consider diffusion: Faster diffusion leads to more collisions between atoms. More collisions means higher probability of atoms sticking to each other. Recall diffusion D Do exp Qd kt Then, the frequency of atoms sticking together is directly related to diffusion: Frequency of attachment: v d exp Qd kt Chapter 10-13

14 Nucleation rate Kinetics of solid state reactions Combining liquid instability and diffusion effects together: Rate of Nucleation (units: nuclei per unit volume per second) dn dt Kn* v d K' exp G * exp kt Qd kt Contribution from liquid instability Contribution from diffusion n * exp G kt * v d exp Qd kt Net rate Liquid instability Diffusion T m T Chapter 10-14

15 Example problem: critical radius and activation energy for nucleation A) If pure liquid gold is cooled to 230 o C below its melting point, calculate the critical radius and the activation energy. Values for the latent heat of fusion and surface free energy are -1.16x10 9 J/m 3 and 0.132J/m 2, respectively. 2g T m r c H f Tm T 1.32nm G B) Calculate the number of atoms per nucleus of this critical size. Au is FCC with a = 0.413nm. 4 3 r * critical nucleus volume # unit cells/particle unit cell volume a * 3 16g Tm 2 3 H Tm T f 9.64x10-19 J 2 4 atoms/unit cell 548 atoms/critical nucleus Chapter 10-15

16 Rate of Phase Transformations Kinetics time dependence of nucleation, growth and transformation rates. Hold temperature constant & measure transformation vs. time How is transformation measured? microscopic examination X-ray diffraction have to do many samples electrical conductivity follow one sample sound waves one sample Chapter 10-16

17 Fraction transformed, y Rate of Phase Transformation Fixed T All out of material - done 0.5 log t Avrami rate equation => y = 1- exp (-kt n ) maximum rate reached now amount unconverted decreases so rate slows t 0.5 rate increases as surface area increases & nuclei grow Adapted from Fig , Callister 7e. fraction transformed k & n fit for specific sample time By convention r = 1 / t 0.5 Chapter 10-17

18 Cu Rate of Phase Transformations 135C 119C 113C 102C 88C 43C Adapted from Fig , Callister 7e. (Fig 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/t 0.5 = A e -Q/RT R = gas constant T = temperature (K) A = preexponential factor Q = activation energy r often small: equilibrium not possible! Arrhenius expression Chapter 10-18

19 Eutectoid cooling: g (0.76 wt% C) cool heat a (0.022 wt% C) + Fe 3 C (6.7 wt% C) Chapter 10-19

20 y (% pearlite) Eutectoid Transformation Rate Growth of pearlite from austenite: Austenite (g) grain boundary Adapted from Fig. 9.15, Callister 7e. a a aa a a Recrystallization rate increases with T. g g cementite (Fe 3 C) Ferrite (a) 100 pearlite growth direction 600 C (T larger) C Diffusive flow of C needed g 675 C (T smaller) a a a g Adapted from Fig , Callister 7e. Course pearlite formed at higher T - softer Fine pearlite formed at low T - harder Chapter 10-20

21 Reaction rate is a result of nucleation and growth of crystals. 100 % Pearlite 50 Examples: Nucleation and Growth 0 Nucleation regime g pearlite colony t 0.5 Growth regime Nucleation rate increases with T Growth rate increases with T log (time) g Adapted from Fig , Callister 7e. g T just below T E Nucleation rate low Growth rate high T moderately below T E Nucleation rate med. Growth rate med. T way below T E Nucleation rate high Growth rate low Chapter 10-21

22 Fe 3 C (cementite) Transformations & Undercooling Eutectoid transf. (Fe-C System): Can make it occur at:...727ºc (cool it slowly)...below 727ºC ( undercool it!) T( C) a ferrite 1600 d g g+l (austenite) g a + Fe 3 C 0.76 wt% C wt% C (Fe) Eutectoid: 1148 C L g +Fe 3 C Equil. Cooling: T transf. = 727ºC T a +Fe 3 C Undercooling by T transf. < 727C L+Fe 3 C 727 C C o, wt%c 6.7 wt% C Adapted from Fig. 9.24,Callister 7e. (Fig adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.- in-chief), ASM International, Materials Park, OH, 1990.) Chapter 10-22

23 y, % transformed Isothermal Transformation Diagrams Fe-C system, C o = 0.76 wt% C Transformation at T = 675 C. T: hold constant T-T-T plots T = 675 C T( C) Austenite (unstable) Austenite (stable) Pearlite isothermal transformation at 675 C time (s) T E (727C) time (s) Only for Fe-C alloy of eutectoid composition Adapted from Fig ,Callister 7e. (Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.) Chapter 10-23

24 Effect of Cooling History in Fe-C System Eutectoid composition, C o = 0.76 wt% C Begin at T > 727 C Rapidly cool to 625 C and hold isothermally. T( C) g g A Austenite (unstable) Austenite (stable) B C D g g g g Pearlite T E (727C) Adapted from Fig ,Callister 7e. (Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) time (s) Chapter 10-24

25 Pearlite Coarse (quenched to higher T) Fine (quenched to lower T) Chapter 10-25

26 Fe 3 C (cementite) Transformations with Proeutectoid Materials C O = 1.13 wt% C T( C) A + A C A A + P P T E (727 C) a 1600 d T( C) g g+l (austenite) T L g +Fe 3 C a+fe 3 C L+Fe 3 C 727 C Adapted from Fig , Callister 7e. time (s) (Fe) Adapted from Fig. 9.24, Callister 7e. C o, wt%c Hypereutectoid composition proeutectoid cementite Chapter 10-26

27 0.76 Fe 3 C (cementite) Fe 3 C g g g g g g g g g g g g w Fe3 C =r/(r +s) wg =(1-w Fe3 C) wa =S/(R+S) w Fe3 C =(1-w a) 1600 d T( C) a Hypereutectoid Steel g g+l (austenite) R pearlite (Fe) w pearlite = wg r C o s pearlite S 1148 C L g +Fe 3 C a +Fe 3 C L+Fe 3 C C o, wt%c (Fe-C System) 60 mm Hypereutectoid steel proeutectoid Fe 3 C Adapted from Figs and 9.32,Callister 7e. (Fig adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in- Chief), ASM International, Materials Park, OH, 1990.) Adapted from Fig. 9.33,Callister 7e. Chapter 10-27

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

29 Spheroidite: Fe-C System Spheroidite: --a grains with spherical Fe 3 C --diffusion dependent. --heat bainite or pearlite for long times --reduces interfacial area (driving force) a (ferrite) Fe 3 C (cementite) For example: 700 o C, 18-24h 60 mm (Adapted from Fig , Callister, 7e. (Fig copyright United States Steel Corporation, 1971.) Chapter 10-29

30 60 mm Martensite: --g(fcc) to Martensite (BCT) Isothermal Transf. Diagram Adapted from Fig , Callister 7e. Martensite: Fe-C System (involves single atom jumps) Fe atom sites 800 T( C) x 10-1 A x x x x (Adapted from Fig , Callister, 7e. Austenite (stable) A x M + A M + A M + A potential C atom sites P B T E time (s) Martensite needles Austenite (Adapted from Fig , Callister, 7e. (Fig courtesy United States Steel Corporation.) g to M transformation.. -- is rapid! Diffusionless transformation -- % transf. depends on T only. 0% 50% 90% Chapter 10-30

31 Martensite Formation g (FCC) slow cooling a (BCC) + Fe 3 C 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 Chapter 10-31

32 Phase Transformations of Alloys Effect of adding other elements Change transition temp. Cr, Ni, Mo, Si, Mn retard g a + Fe 3 C transformation Plain carbon steels Alloy steels Adapted from Fig , Callister 7e. Chapter 10-32

33 Cooling Curve plot temp vs. time Isothermal heat treatment is not the most practical to conduct Continuous cooling Adapted from Fig , Callister 7e. Chapter 10-33

34 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: a) 42% proeutectoid ferrite and 58% coarse pearlite b) 50% fine pearlite and 50% bainite c) 100% martensite d) 50% martensite and 50% austenite Chapter 10-34

35 Example Problem for C o = 0.45 wt% a) 42% proeutectoid ferrite and 58% coarse pearlite first make ferrite then pearlite course pearlite higher T T ( C) A A M (start) M (50%) M (90%) A + a P B A + P A + B 50% Adapted from Fig , Callister 5e time (s) Chapter 10-35

36 Example Problem for C o = 0.45 wt% b) 50% fine pearlite and 50% bainite first make pearlite then bainite fine pearlite lower T T ( C) A A M (start) M (50%) M (90%) A + a P B A + P A + B 50% Adapted from Fig , Callister 5e time (s) Chapter 10-36

37 Example Problem for C o = 0.45 wt% c) 100 % martensite quench = rapid cool d) 50 % martensite and 50 % austenite T ( C) A A M (start) M (50%) M (90%) A + a P B A + P A + B 50% d) Adapted from Fig , Callister 5e. 0 c) time (s) Chapter 10-37

38 Impact energy (Izod, ft-lb) Adapted from Fig. 9.30,Callister 7e. (Fig courtesy Republic Steel Corporation.) Mechanical Prop: Fe-C System (1) Effect of wt% C Pearlite (med) ferrite (soft) TS(MPa) 1100 YS(MPa) Hypo C o < 0.76 wt% C Hypoeutectoid Hyper hardness %EL 100 C o > 0.76 wt% C Hypereutectoid Pearlite (med) Cementite (hard) wt% C wt% C More wt% C: TS and YS increase, %EL decreases. 50 Hypo Adapted from Fig. 9.33,Callister 7e. (Fig copyright 1971 by United States Steel Corporation.) Hyper Adapted from Fig , Callister 7e. (Fig based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.) Chapter 10-38

39 Brinell hardness Ductility (%AR) Mechanical Prop: Fe-C System (2) Fine vs coarse pearlite vs spheroidite Hardness: %RA: Hypo fine pearlite Hyper coarse pearlite spheroidite wt%c fine > coarse > spheroidite fine < coarse < spheroidite Hypo Hyper spheroidite 30 coarse pearlite fine pearlite wt%c Adapted from Fig , Callister 7e. (Fig 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.) Chapter 10-39

40 Brinell hardness Mechanical Prop: Fe-C System (3) Fine Pearlite vs Martensite: Hypo Hyper martensite fine pearlite wt% C Hardness: fine pearlite << martensite. Adapted from Fig , Callister 7e. (Fig 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 ) Martensite: not related to microstructure, rather to the effectiveness of the interstitial carbon atoms in hindering dislocation motion, and the relatively few slip systems for BCT structure. Chapter 10-40

41 9 mm Tempering Martensite reduces brittleness of martensite, reduces internal stress caused by quenching. TS(MPa) YS(MPa) 1800 Adapted from Fig , Callister 7e. (Fig adapted from Fig. furnished courtesy of Republic Steel Corporation.) YS %RA TS %RA Tempering T( C) Adapted from Fig , Callister 7e. (Fig copyright by United States Steel Corporation, 1971.) produces extremely small Fe 3 C particles surrounded by a. decreases TS, YS but increases %RA Chapter 10-41

42 Strength Ductility Summary: Processing Options slow cool Austenite (g) moderate cool rapid quench Adapted from Fig , Callister 7e. Pearlite (a + Fe 3 C layers + a proeutectoid phase) Bainite (a + Fe 3 C plates/needles) Martensite T Martensite bainite fine pearlite coarse pearlite spheroidite General Trends Martensite (BCT phase diffusionless transformation) reheat Tempered Martensite (a + very fine Fe 3 C particles) Chapter 10-42