Phase Diagram (Phase Transformations)
Phase TransformationsPhase Diagram(Phase Transformations)ENT 145 Materials Engineering- Development set of desirable mechanical characteristic formaterial often result from a phase transformation- Phase transformation – an alteration in the number and/orcharacter phases- Transformation does not occur instantaneously, they begin withformation of small particles of new phases, which increase in sizeuntil transformation completed.- dependence of reaction progress on time/transformation rate.- One limitation of phase diagrams is their ability to indicate the timeperiod required for attainment of equilibrium- Phase transformation divided into 2 stages nucleation and growth- once nucleated, growth proceeds until equilibrium is attainedChapter 10 -Chapter 10 -Phase TransformationsPhase Transformations Phase transformations (change of the microstructure) can be dividedinto three categories: Diffusion-dependent with no change in phase composition ornumber of phases present (e.g. melting, solidification of pure metal,allotropic transformations, recrystallization, etc.) Diffusion-dependent with changes in phase compositions and/ornumber of phases (e.g. eutectic or eutectoid transformations) Diffusionless phase transformation - by cooperative smalldisplacements of all atoms in structure, e.g. martensitictransformation. Phase transformations do not occur instantaneously. Diffusion-dependent phase transformations can be rather slow and thefinal structure often depend on the rate of cooling/heating. Phase transformations involve change in structure and (for multi-phasesystems) composition rearrangement and redistribution of atoms viadiffusion is required. The process of phase transformation involves: Nucleation of the new phase(s) - formation of stable small particles(nuclei) of the new phase(s). Nuclei are often formed at grainboundaries and other defects. Growth of the new phase(s) at the expense of the original phase(s).once nucleated, growth proceeds until equilibrium is attainedDriving force to nucleate increases as we increase T– supercooling (eutectic, eutectoid)– superheating (peritectic)Small supercooling slow nucleation rate - few nuclei - large crystalsWe need to consider the time dependence or kinetics of the phase transformations.Large supercooling rapid nucleation rate - many nuclei - small crystalsChapter 10 - 3Chapter 10 - 4Rate of Phase Transformationrate 1 / t0.5Plotting the transformation time vs temperature results in a characteristicC-shaped curves:Rate of Phase TransformationThe time dependence of solid-state phase transformations at a fixed temperature is oftendescribed in terms of the time dependence of the fraction of transformation (y):Fraction transformed, yTo quantitatively describe the rate of a phase transformation, it can bedefined as reciprocal of time for transformation to proceed halfway tocompletion:transformation completeFixed Tmaximum rate reached – now amountunconverted decreases so rate slows0.5t0.5rate increases as surface area increases& nuclei growlog tAvrami equation y 1- expThe analysis performed above for solidification can also be extended toother phase transformations, e.g. solid-state phase transformations.Chapter 10 - 5fractiontransformed(-kt n)Adapted fromFig. 10.10,Callister &Rethwisch 8e.time– k & n are transformation specific parametersChapter 10 - 61
Temperature Dependence ofTransformation RateThe Fe-Fe3C Eutectoid Transformation Transformation of austenite to pearlite:Austenite (g)grainboundaryPercent recrystallization of pure copper at different T:Adapted fromFig. 9.15,Callister &Rethwisch 8e.aag aaaagagpearlitegrowthdirection For this transformation,rate increases with[Teutectoid – T ] (i.e., T). For the recrystallization of Cu, sincerate 1/t0.5rate increases with increasing temperatureDiffusion of Cduring transformationcementite (Fe3C)Ferrite (a)600ºC( T larger)a50650ºCGeneration of Isothermal TransformationDiagrams (TTT Diagram)Consider:y,% transformed The Fe-Fe3C system, for C0 0.76 wt% C A transformation temperature of 675ºC.Isothermal Transformation(or TTT) Diagrams(Temperature, Time, and % Transformation)T 675ºC010 21T(ºC)Austenite (stable)10 4time (s)0 formed at lower temperatures – relatively hardFine pearliteAustenite(unstable)600Pearliteisothermal transformation at 675ºC50040011010 2 10 3 10 4 10 5time (s)Chapter 10 - 8Austenite-to-Pearlite Isothermal Transformation Eutectoid composition, C0 0.76 wt% CBegin at T 727ºCRapidly cool to 625ºCHold T (625ºC) constant (isothermal treatment)T(ºC)TE (727ºC)Austenite(unstable)gg500Adapted from Fig. 10.13,Callister &Rethwisch 8e. (Fig. 10.13 adapted from H.Boyer (Ed.) Atlas of IsothermalTransformation and CoolingTransformation Diagrams, AmericanSociety for Metals, 1977, p. 369.)Austenite (stable)700600TE (727ºC)700Adapted fromFig. 10.12,Callister &Rethwisch 8e.675ºC( T smaller)Chapter 10 - 750CarbondiffusionCoarse pearlite formed at higher temperatures – relatively soft Rate often so slow that attainment of equilibrium state not possible!100ga100y (% pearlite)Temperature has a strong effect on the kinetics of the phase transformation and,therefore, on the rate of the phase transformation.ggAdapted from Fig.10.14,Callister &Rethwisch 8e. (Fig. 10.14adapted from H. Boyer(Ed.) Atlas of IsothermalTransformation andCooling TransformationDiagrams, AmericanSociety for Metals, 1997,p. 28.)Pearlitegg40011010 210 310 410 5time (s)Chapter 10 - 9 The thickness of the ferrite and cementite layers in pearlite is 8:1. The absolute layer thickness depends on the temperature of the transformation. The higher the temperature, the thicker the layers.Chapter 10 - 10Coarse PearliteFine Pearlite2
Bainite: Another Fe-Fe3CTransformation Product Bainite:-- elongated Fe3C particles ina-ferrite matrix-- diffusion controlled Isothermal Transf. Diagram,C0 0.76 wt% C800Austenite (stable)T(ºC)TEAP600100% pearlite100% bainite400BA200Fe3C(cementite)10a (ferrite)-11010310Isothermal transformationdiagram iron-carbon alloyeutectoid composition5time (s)Austenite-to-Pearlite(A-P)Austenite-to-Bainite (A-B)5 mmAdapted from Fig. 10.18,Callister & Rethwisch 8e.Chapter 10 - 13Spheroidite: Another Microstructurefor the Fe-Fe3C SystemMartensite: A NonequilibriumTransformation Product iron-carbon aloy are rapidly cooled to a relatively low temperature diffusionless transformation- martensitic transformation occur whenthe quenching rate is rapid enough to prevent carbon diffusion. any diffusion will result in the formation of ferrite and cementite martensitic tranformation occur instantaneously- grains nucleateand grow at a very rapid rate- velocity of sound platelike or needlelike appearancea-- Fe3C particles within an a-ferrite matrix (ferrite) Spheroidite:-- formation requires diffusion-- heat bainite or pearlite at temperatureFe3Cjust below eutectoid for long times (cementite)-- Ex. 700C for 18-24h-- driving force – reductionof a-ferrite/Fe3C interfacial areaChapter 10 - 1560 mm60 mmAdapted from Fig. 10.19, Callister &Rethwisch 8e. (Fig. 10.19 copyrightUnited States Steel Corporation,1971.)Martensite needlesAusteniteChapter 10 - 16Martensite: A NonequilibriumTransformation Product Martensite:-- g(FCC) to Martensite (BCT)sites800Austenite (stable)T(ºC)xFe atom Isothermal Transf. DiagramTEApotentialxxxxC atom sitesxP600Adapted fromFig. 10.22,Callister &Rethwisch 8e.400BA2000%M AM AM A10-11050%90%103105time (s)Chapter 10 - 17Chapter 10 -3
Continuous CoolingTransformation DiagramsPhase Transformations of AlloysEffect of adding other elementsChange transition temp.-- TTT Diagram though give very useful information, they are ofless practical importance since an alloy has to be cooledrapidly and then kept at a temperature to allow for respectivetransformation to take place.-- Usually material are cooled continuously, thus CCT diagramsare appropriate.-- For continuous cooling, the time required for a reaction tobegin and end delayed, thus the isothermal curves areshifted to longer times and lower temperatures.-- Main difference between TTT and CCT diagrams: for ironcarbon of euctectoid composition, no space for bainite inCCT diagram as continuous cooling always result information of pearlite.Cr, Ni, Mo, Si, Mnretard g a Fe3Creaction (and formation ofpearlite, bainite)Adapted from Fig. 10.23,Callister & Rethwisch 8e.Chapter 10 - 19Continuous CoolingTransformation DiagramsChapter 10 - 20Example Problem:Isothermal Heat TreatmentConversion of isothermaltransformation diagram tocontinuous coolingtransformation diagramOn the isothermal transformation diagram fora 0.45 wt% C, Fe-C alloy, sketch and labelthe time-temperature paths to produce thefollowing microstructures:a) 50% fine pearlite and 50% bainiteb) 100% martensiteAdapted from Fig. 10.25,Callister & Rethwisch 8e.c) 50% martensite and 50% austeniteCooling curveChapter 10 - 21Solution to Part (b)a) 50% fine pearliteand 50% bainite800AA aPB600Then isothermally treatat 470ºC– all remaining austenitetransforms to bainite.Solutions to Parts (b) & (c)Fe-Fe3C phase diagram,for C0 0.45 wt% CIsothermally treat at 590ºC T (ºC)– 50% of austenite transformsto fine pearlite.c) 50% martensite& 50% austeniteA B50%-- rapidly quench to 290ºC, hold at thistemperatureM (start)M (50%)M (90%)200Fe-Fe3C phase diagram,for C0 0.45 wt% Cb) 100% martensite –rapidly quench to800room temperature T (ºC)A PA400Chapter 10 - 22AA aPB600A PA BA40050%M (start)M (50%)M (90%)c)200b)Adapted fromFig. 10.29,Callister 5e.00.110103time (s)105Chapter 10 - 23Adapted fromFig. 10.29,Callister 5e.00.110103time (s)105Chapter 10 - 244
Mechanical Props: Fine Pearlite vs.Coarse Pearlite vs. SpheroiditePearlite (med)Cementite(hard)C0 0.76 wt% CAdapted from Fig. 9.30,Callister & Rethwisch 050000.5001wt% C0.500.760.76300Impact energy (Izod, ft-lb)TS(MPa)1100YS(MPa)C0 0.76 wt% C Adapted from Fig. 9.33,Hypereutectoid Callister & Rethwisch 8e.HypoHyperAdapted from Fig.10.29, Callister &Rethwisch 8e. (Fig.10.29 based on datafrom MetalsHandbook: HeatTreating, Vol. 4, 9thed., V. Masseria(Managing Ed.),American Society forMetals, 1981, p. 9.)1HypoBrinell hardnessPearlite (med)ferrite oidite160Ductility (%RA)Mechanical Props: Influence of C Content Hardness: %C0.50fine coarse spheroiditefine coarse spheroiditewt% CHyper60800Hypo Increase C content: TS and YS increase, %EL decreases1wt%CAdapted from Fig. 10.30, Callister &Rethwisch 8e. (Fig. 10.30 based ondata from Metals Handbook: HeatTreating, Vol. 4, 9th ed., V. Masseria(Managing Ed.), American Society forMetals, 1981, pp. 9 and 17.)Chapter 10 - 25Chapter 10 - 26Mechanical Props: Fine Pearlite vs.MartensiteBrinell hardnessHypo600martensiteAdapted from Fig. 10.32,Callister & Rethwisch 8e. (Fig.10.32 adapted from Edgar C.Bain, Functions of the AlloyingElements in Steel, AmericanSociety for Metals, 1939, p. 36;and R.A. Grange, C.R. Hribal,and L.F. Porter, Metall. Trans. A,Vol. 8A, p. 1776.)200fine pearlite0-- apply a heat treatment process known as tempering onmartensite to enhance ductility and toughness of martensiteHyper4000.50Tempered Martensite-- tempering – heating a martensitic steel to a temperature beloweutectoid for a specified time-- tempering reduces internal stresses caused by quenching-- normally, tempering is carried out at temperatures between250-650 degree C.1wt% C-- optimum for internal stresses relieved at 200C for 1hour Hardness: fine pearlite martensite.-- nearly hard and strong as martensite, but with substantiallyenhanced ductility and toughnessChapter 10 - 27Tempered MartensiteChapter 10 - 28Summary of Possible TransformationsTS(MPa)Austenite (g)YS10006050%RA40800200400600Tempering T (ºC) tempering produces extremely small Fe3C particles surrounded by a. tempering decreases TS, YS but increases %RAChapter 10 - 29rapidquenchPearliteBainiteMartensite(a elong. Fe3C particles)(BCT phasediffusionlesstransformation)%RA30Adapted fromFig. 10.36,Callister &Rethwisch 8e.(a Fe3C layers aproeutectoid phase)Strength12009 mm1400moderatecoolslowcoolTS1600MartensiteT Martensitebainitefine pearlitecoarse pearlitespheroiditeGeneral (a very fineFe3C particles)Chapter 10 - 305
HomeworkHOMEWORKUsing the isothermal transformation diagram for an iron–carbon alloy of eutectoidcomposition (Refer figure below), specify the nature of the final microstructure (in terms ofmicroconstituents present and approximate percentages of each) of a small specimen thathas been subjected to the following time–temperature treatments. In each case assumethat the specimen begins at 760 C (1033 K) and that it has been held at this temperaturelong enough to have achieved a complete and homogeneous austenitic structure.a)Cool rapidly to 700 C (973 K), hold for 104 s, then quench to room temperature.b)Reheat the specimen in part (a) to 700 C (973 K) for 20 h.c)Rapidly cool to 600 C (873 K), hold for 4 s, rapidly cool to 448 C (721 K), hold for 10 s,then quench to room temperature.d)Cool rapidly to 398 C (671 K), hold for 2 s, then quench to room temperature.e)Cool rapidly to 398 C (671 K), hold for 20 s, then quench to room temperature.f)Cool rapidly to 398 C (671 K), hold for 200 s, then quench to room temperature.g)Rapidly cool to 575 C (848 K), hold for 20 s, rapidly cool to 350 C (623 K), hold for 100 s,then quench to room temperature.h)Rapidly cool to 250 C (523 K), hold for 100 s, then quench to room temperature in water.Reheat to 315 C (588 K) for 1 h and slowly cool to room temperature.1) Describe characteristics of (a) an alloy (b) pearlite,(c) austenite (d) martensite , (e) cementite, (f)spherodite and (g) tempered martensite.2) Choose one engineering application that its materialconsist at least ONE of above microstructures.Explain details of the application with respect to itsfabrication method, mechanical properties and heattreatment procedure. You may review any availableliterature in the library or internet.Chapter 10 - 31Chapter 10 - 32Chapter 10 - 33Chapter 10 - 34ASSIGNMENT In-class assignment.Individual assessment.Submit by today, at the end of tutorial session.Late submission will not be entertained!!!6
Phase transformations involve change in structure and (for multi-phase systems) composition rearrangement and redistribution of atoms via diffusion is required. The process of phase transformation involves: Nucleation of the new phase(s) - formation of stable small particles are often formed at grain Growth of the new phase(s) at the expense of the original phase(s). once nucleated, growth .
WIRING DIAGRAM DIRECTORY WARNING: Wiring direct to battery not recommended. Install actuator after ignition switch, or master power switch. Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Diagram 6 Diagram 7 Diagram 8 Diagram 9 Diagram 10 Diagram 11 Diagram 12 Diagram 13 Diagram 14 Diagram 15 On/Off, 12VDC, 3-wire/3-pin, SPST On/Off, 12VDC, 3 .
Phase Transformation in Metals Development of microstructure in both single- and two-phase alloys involves phase transformations-which involves the alteration in the number and character of the phases. Phase transformations take time and this allows the definition of transformation rate or kinetics. Phase transformations alter the microstructure and there can be three different classes of .
Phase Transformations in Metals and Alloys ( This is the major reference for this course ) D.A.Porter, K.E. Easterling, and M.Y. Sharif CRC Press , Taylor & Francis Group Diffusion in solids Prof. Alok Paul , IISC Banglore NPTEL Web course Phase Transformations Prof. Anandh Subramaniam IIT Kanpur Phase Transformations & Heat Treatment Prof. M.P.Gururajan NPTEL web course Phase Transformations .
Structured analysis Object-oriented analysis System boundary Context diagram Use case diagram Functionality Data flow diagram Activity diagram Interaction diagrams Data Entity-relationship diagram Class diagram Object diagram Control State diagram State diagram Structured methods System as a set of nested processes accessing system data.
Note: The diagram shown above is for reference only. Use the instructions beginning on the next page to draw your Package diagram. Creating a Package Diagram from the Use Case Diagram The package diagram is a type of class diagram and can be created from a use case diagram. 1. Make sure the Use Case diagram c
Figure 2: A sequence diagram that has incoming and outgoing messages Notice that in Figure 2 the diagram's label begins with the letters "sd," for Sequence Diagram. When using a frame element to enclose a diagram, the diagram's label needs to follow the format of: Diagram Type Diagram Name UML basics: The sequence diagram Page 3 of 24 http .
Geometric transformations Geometric transformations will map points in one space to points in another: (x',y',z') f(x,y,z). These transformations can be very simple, such as scaling each coordinate, or complex, such as non-linear twists and bends. We'll focus on transformations that ca
“Am I my Brother’s Keeper?” You Bet You Are! James 5:19-20 If every Christian isn’t familiar with 2 Timothy 3:16-17, every Christian should be. There the Apostle Paul made what most believe is the most important statement in the Bible about the Bible. He said: “All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in .
