Chapter 10: Kinetics Heat Treatment,

Transcription

1 Chapter 10: Kinetics Heat Treatment, 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? 1

2 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

3 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 3

4 Homogeneous Nucleation & Energy Effects Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) 2 G S 4 r g g = surface tension G T = Total Free Energy = G S + G V Volume (Bulk) Free Energy stabilizes the nuclei (releases energy) 4 3 G V r G G r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy) 3 volume free energy unit volume 4

5 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 = strong function of T g = weak function of T r* decreases as T increases For typical T r* ca. 100Å 5

6 Temperature dependence of nucleation

7 Solidification temperature Note the exponential rise in the diffusion rate Note that liquid phase instability increases as temperature decreases The rate of nucleation is a product of two curves that represent two opposing factors (instability and diffusivity).

8 Heterogeneous nucleation g g g cos IL SI SL r 2g G SL V g SL 2 3cos cos 16 g SL G S( ) GV 4 3 GV

9 Growth G C exp Q kt Transformation rate increases as we come down to some intermediate temperature The growth rate increases as temperature increases Transformation rate decreases as temperatures lessen The overall transformation rate is the product of the nucleation rate and the growth rate.

10 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 10

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

12 Rate of Phase Transformations 135 C 119 C 113 C 102 C 88 C 43 C 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 12

13 y (% pearlite) Eutectoid Transformation Rate Growth of pearlite from austenite: Austenite (g) grain boundary g a a a a a a g cementite (Fe 3 C) Ferrite (a) pearlite growth direction Recrystallization C rate increases ( T larger) 650 C with T C 0 Diffusive flow of C needed g ( T smaller) a a a g Course pearlite formed at higher T - softer Fine pearlite formed at low T - harder 13

14 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 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

15 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. < 727 C L+Fe 3 C 727 C C o, wt%c 6.7 wt% C

16 Isothermal Transformation Diagrams Time-Temp.-Transformation Diagrams Temperature melting point Half-way point of reaction Initial onset of reaction Completed reaction A time-temperature-transformation (TTT) diagram for a solidification reactin.

17 y, % transformed Fe-C system, C o = 0.76 wt% C Transformation at T = 675 C T = 675 C time (s) T( C) Austenite (unstable) Austenite (stable) Pearlite isothermal transformation at 675 C T E (727 C) time (s)

18 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) 700 Austenite (unstable) Austenite (stable) T E (727 C) 600 g g Pearlite g 500 g g g time (s)

19 As temperature and diffusion coefficients decrease the microstructure becomes finer Phase Diagram As the diffusion coefficient is smaller there s less time for the atoms to arrange themselves, so they tend to form finer and finer sized, alternating layers. TTT diagram for eutectoid steel in relation to the Fe 3 C phase diagram.

20 TTT diagrams are both time and path dependent A slow cooling path that leads to coarse p earlite formation is superimposed on the TTT diagram for eutectoid steel. The interpretation of TTT diagrams requires consideration of the thermal history path.

21 Note the alternating lamellar layered structure The microstructure of pearlite in a 0.8 wt % C steel involves alternating layers of ferrite and cementite, 650.

22 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 22

23 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 T E 100% pearlite pearlite/bainite boundary 100% bainite Fe 3 C (cementite) a (ferrite) 5 mm The microstructure of bainite Extremely fine needles of ferrite and carbide (in contrast to pearlite) time (s) 23

24 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) 60 mm 24

25 60 mm Martensite: Martensite: Fe-C System --g(fcc) to Martensite (BCT) (involves single atom jumps) Fe atom sites Isothermal Transf. Diagram 800 T( C) 600 x x x x x Austenite (stable) A x potential C atom sites P T E Martensite needles Austenite Adapted from Fig , Callister 7e A M + A M + A M + A B 0% 50% 90% time (s) g to M transformation.. -- is rapid! -- % transf. depends on T only.

26 Microstructure of martensite Acicular (needlelike).

27 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 27

28 Martensitic transformation: Diffusionless transformation most commonly associated with the formation of martensite by the quenching of austenite. Note sudden reorientation of Fe and C atoms. The steel moves from a ductile (soft) state to a brittle state ultimately we want to limit this brittle state.

29 Phase Transformations of Alloys Effect of adding other elements Change transition temp. Cr, Ni, Mo, Si, Mn retard g a + Fe 3 C transformation

30 Continuous Cooling Transformation (CCT) For continuous cooling, the time required for a reaction to begin and is delayed Thus, the isothermal curve are shifted to longer times and lower temperatures.

31 Cooling Curve plot temp vs. time 31

32

33

34 Ex. 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 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% time (s) 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% time (s) 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) 0 c) time (s) 37

38 Impact energy (Izod, ft-lb) 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) C ementite (hard) wt% C wt% C More wt% C: TS and YS increase, %EL decreases. 50 Hypo Hyper

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 39

40 Brinell hardness Mechanical Prop: Fe-C System (3) Fine Pearlite vs Martensite: Hypo Hyper 600 martensite fine pearlite wt% C Hardness: fine pearlite << martensite. 40

41 Tempered Martensite Tempering: A thermal history for steel, in which martensite is reheated. Tempering is a thermal history in which martensite, formed by quenching austenite, is reheated.

42 9 mm Tempering Martensite reduces brittleness of martensite, reduces internal stress caused by quenching. TS(MPa) YS(MPa) YS TS %RA %RA Tempering T ( C) produces extremely small Fe 3 C particles surrounded by a. decreases TS, YS but increases %RA 42

43 Martempering: Heat treatment of a steel involving a slow cool through the martensitic transformation range to reduce stresses associated with that crystallographic change.

44 Austempering: Heat treatment of a steel that involves holding just above the martensitic transformation range long enough to completely form bainite. We are basically forming bainite and avoiding the martensite phase all together.

45 Strength Ductility Summary: Processing Options Austenite (g) slow cool moderate cool rapid quench 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) 45

46

47 Hardness, HRC Hardenability--Steels Ability to form martensite Jominy end quench test to measure hardenability. specimen (heated to g phase field) 24 C water flat ground Rockwell C hardness tests Hardness versus distance from the quenched end. Distance from quenched end

48 Hardness, HRC Why Hardness Changes W/Position The cooling rate varies with position T( C) distance from quenched end (in) 0% 100% M(start) M(finish) A M Time (s)

49 Hardness, HRC Hardenability vs Alloy Composition Jominy end quench results, C = 0.4 wt% C "Alloy Steels" (4140, 4340, 5140, 8640) --contain Ni, Cr, Mo (0.2 to 2wt%) --these elements shift the "nose". --martensite is easier to form Distance from quenched end (mm) 800 T( C) A B T E Cooling rate ( C/s) %M shift from A to B due to alloying M(start) M(90%) Time (s)

50 Hardness, HRC Hardenability vs Alloy Composition Jominy end quench results, C = 0.4 wt% C "Alloy Steels" (4140, 4340, 5140, 8640) --contain Ni, Cr, Mo (0.2 to 2wt%) --these elements shift the "nose". --martensite is easier to form Distance from quenched end (mm) 800 T( C) A B T E Cooling rate ( C/s) %M shift from A to B due to alloying M(start) M(90%) Time (s)

51 Precipitation Hardening Particles impede dislocations. Ex: Al-Cu system 700 Procedure: T( C) --Pt A: solution heat treat 600 a (get a solid solution) A Pt B: quench to room temp. C --Pt C: reheat to nucleate 400 small crystals within a crystals. Other precipitation systems: Cu-Be Cu-Sn Mg-Al Temp. Pt A (sol n heat treat) a+l 300 B (Al) wt% Cu Pt C (precipitate ) L a +L composition range needed for precipitation hardening CuAl 2 Pt B Time

52 Precipitation Strengthening Hard precipitates are difficult to shear. Ex: Ceramics in metals (SiC in Iron or Aluminum). Side View precipitate Large shear stress needed to move dislocation toward precipitate and shear it. Top View Unslipped part of slip plane S Slipped part of slip plane Dislocation advances but precipitates act as pinning sites with spacing S. Result: y ~ 1 S

53 Phase Diagram K solid solution Lack of hardening when coarse precipitates form at grain boundaries in an Al-Cu alloy when slowly cooled.

54 Phase Diagram Precipitation hardening: Development of obstacles to dislocation motion (and thus increased hardness) by the controlled precipitation of a second phase. By quenching and then reheating an Al-Cu alloy, a fine dispersion of precipitates forms within the kappa grains.

55 Hardening (a) In overaging, precipitates coalesce and become less effective in hardening the alloy. (b) The variation in hardness with the length of the reheat step (aging time).

56 Schematic of the crystalline geometry of a Guinier-Preston (G.P.) zone (approx. 15 nm 150 nm) Effective for precipitation hardening. Transmission electron micrograph of G.P. zones (720,000 ).

57 Application: Precipitation Strengthening Internal wing structure on Boeing 767 Courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company. Aluminum is strengthened with precipitates formed by alloying. Courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.) 1.5mm

58 Thermal Processing of Metals Annealing: Heat to Tanneal, then cool slowly. Stress Relief: Reduce stress caused by: -plastic deformation -nonuniform cooling -phase transform. Spheroidize (steels): Make very soft steels for good machining. Heat just below T E & hold for h. Process Anneal: Negate effect of cold working by (recovery/ recrystallization) Types of Annealing Full Anneal (steels): Make soft steels for good forming by heating to get g, then cool in furnace to get coarse P. Normalize (steels): Deform steel with large grains, then normalize to make grains small.

59 Cold Work (%CW) Room temperature deformation. Common forming operations change the cross sectional area: -Forging A o die blank -Drawing A o die die force force A d % CW A d tensile force A o A A o d force A o x 100 -Rolling A o -Extrusion ram container billet container roll roll die holder extrusion die A d A d

60 Cold rolling a bar or sheet of metal Cold work: Mechanical deformation of a metal at relatively low temperatures. Cold-drawing a metal bar

61 Dislocations During Cold Work Ti alloy after cold working: Dislocations entangle with one another during cold work. Dislocation motion becomes more difficult. 0.9 mm

62 Dislocation density = Result of Cold Work Carefully grown single crystal total dislocation length unit volume ca mm -2 Deforming sample increases density mm -2 Heat treatment reduces density mm -2 Yield stress increases as r d increases: y1 y0 large hardening small hardening e

63 Impact of Cold Work As cold work is increased Yield strength ( y ) increases. Tensile strength (TS) increases. Ductility (%EL or %AR) decreases.

64 Stress (MPa) - e Behavior vs. Temperature Results for polycrystalline iron: C -100 C C Strain y and TS decrease with increasing test temperature. %EL increases with increasing test temperature. Why? Vacancies help dislocations move past obstacles. 2. vacancies replace atoms on the disl. half plane disl. glides past obstacle 1. disl. trapped by obstacle obstacle

65 tensile strength (MPa) ductility (%EL) Effect of Heating After %CW 1 hour treatment at T anneal... decreases TS and increases %EL. Effects of cold work are reversed! annealing temperature (ºC) tensile strength Annealing stages to discuss ductility 20

66 Recovery Annihilation reduces dislocation density. Scenario 1 Results from diffusion Scenario 2 extra half-plane of atoms 3. Climbed disl. can now move on new slip plane 2. grey atoms leave by vacancy diffusion allowing disl. to climb 1. dislocation blocked; can t move to the right atoms diffuse to regions of tension extra half-plane of atoms Dislocations annihilate and form a perfect atomic plane. 4. opposite dislocations meet and annihilate Obstacle dislocation t R

67 Recrystallization New grains are formed that: -- have a small dislocation density -- are small -- consume cold-worked grains. 0.6 mm 0.6 mm Adapted from Fig (a),(b), Callister 7e. (Fig (a),(b) are courtesy of J.E. Burke, General Electric Company.) 33% cold worked brass New crystals nucleate after 3 sec. at 580 C.

68 The sharp drop in hardness identifies the recrystallization temperature as ~290 o C for the alloy C26000 cartridge brass.

69 Recrystallization temperature and melting temperature fall in a predictable range approximately one third to one half of the melting temperature.

70 For this cold-worked brass alloy, the recrystallization temperature drops slightly with increasing degrees of cold work.

71 º T R = recrystallization temperature T R Note the tradeoff between tensile strength and ductility taking place over the range of structural change º

72 Further Recrystallization All cold-worked grains are consumed. 0.6 mm 0.6 mm Adapted from Fig (c),(d), Callister 7e. (Fig (c),(d) are courtesy of J.E. Burke, General Electric Company.) After 4 seconds After 8 seconds

73 Grain Growth At longer times, larger grains consume smaller ones. Why? Grain boundary area (and therefore energy) is reduced. 0.6 mm 0.6 mm After 8 s, 580ºC Empirical Relation: exponent typ. ~ 2 grain diam. at time t. d After 15 min, 580ºC n d n o Kt coefficient dependent on material and T. elapsed time Ostwald Ripening

74 Fig. 탄소강의열처리온도구간 normalizing be used to refine the grains and produce a more uniform and desirable size distrubution: fine-grained pearlite steels are tougher than coarsegrained ones. Heating at least 55 o C above A 3 (hypo-) and A cm (hyper-). full annealing Be often utilized in low- and medium-carbon steels that will be machined or will experience extensive plastic deformation during a forming operation Coarse peralite Heating at about 50 o C above A 3 and A 1.

75 Shape-memory alloy, SMA Nitinol (Ni-Ti alloy) Copper alloy: Cu-Zn-Al, Cu-Al-Ni Heating at least 55 o C above A 3 (hypo-) and A cm (hyper-).

76 The kinetics of phase transformations for nonmetals FIGURE Typical thermal history for producing a glass-ceramic by the controlled nucleation and growth of crystalline grains.

77 Each grain is a powder particle Sintering: Bonding of powder particles by solid state diffusion. Pore at grain boundary Certain metallurgical samples and many ceramic materials have very high melting temperatures This makes casting these materials impractical An illustration of the sintering mechanism for shrinkage of a powder compact is the diffusion of atoms away from the grain boundary to the pore, thereby filling in the pore.

78 Grain growth hinders densification of a powder compact. Diffusion path from grain boundary to isolated pore is prohibitively long.