Learning ObjectivesAfter careful study of this chapter you should be able to do the following:1. Make a schematic fraction transformationversus-logarithm of time plot for a typicalsolid–solid transformation; cite the equationthat describes this behavior.2. Briefly describe the microstructure for each ofthe following microconstituents that are foundin steel alloys: fine pearlite, coarse pearlite,spheroidite, bainite, martensite, and temperedmartensite.3. Cite the general mechanical characteristics foreach of the following microconstituents: finepearlite, coarse pearlite, spheroidite, bainite,martensite, and tempered martensite. Now, interms of microstructure (or crystal structure),briefly explain these behaviors.4. Given the isothermal transformation (or continuouscooling transformation) diagram for someiron–carbon alloy, design a heat treatment thatwill produce a specified microstructure.

The development of microstructure in both single- and two-phase alloys ordinarilyinvolves some type of phase transformation—an alteration in the number and/or character of the phases-The transformation rate is the dependance of reaction progress on time-Many phase transformations are important in the processing of materials-Phase transformations usually involve some alteration of microstructure-Simple phase transformations covered here are as follows:1.Simple diffusion dependent transformations with no change in number or composition of phases present(e.g. Pure species, allotropic, recrystallization, and grain growth)2.Eutectoid type transformations that involve altering phase concentrations or number of phases3.A diffusionless process that involves a metastable phase is produced (e.g. martensitic xfrm)

Kinetics of Phase TransformationsUsually at least one new phase createdUsually not instantaneousMost often, new phase starts as small particles in the old phase, which then increases in size until completion.The progress of phase transformations may be broken into two distinct stages:Nucleation (appearance of very small particles, or nuclei, of the new phase)Growth (increase in size of nuclei, resulting in some or all of parent phase disappearing.

NucleationThere are two types of nucleation: Heterogeneous and HomogeneousHomogeneous nucleation occurs uniformly throughout parent phase, with even distribution of nucleiHeterogeneous nucleation occurs when nuclei occur preferentially at structural features (cracks, scratches, impurities, insoluble stuff, dislocations, etc)

A process is spontaneous only if DeltaG is negativeThe DeltaG in phase transformations is dependant on two factors

1. The free energy difference of the liquid and solid phases or volume free energyDeltaGvIs negative if temperature is below eq solidification temperature, and is represented by DeltaGv*4/3(pi)r^3

2. The formation of the solid-liquid phase boundary also causes a difference in gibbs free energy

This term is represented by the boundary surface free energy, gamma, and the surface area of the nucleus, or:(gamma)*4(pi)r^2

Therefore, the total change of free energy is the sum of the two:DeltaG=4/3*pi*r^3*DeltaGv+(gamma)*4*pi*r^2A graph of free energy change of each of the terms alone and the final function shows the DeltaG values to reach a maximum (DeltaG*) at some radius (r*), then decrease precipitouslyThis DeltaG* is the activation energy for the formation of a stable nucleus. It must be overcome for a nucleus to truly form. Since this DeltaG* is at a maximum on the curve, its derivative should equal zeroThus: d(DeltaG)/dr=4*pi*DeltaGv*r^2+8*pi*gamma=0Solving this differential gives: r*=(-2gamma)/DeltaGvSubstituting this r* into DeltaG(r) gives:DeltaG*=16*pi/3*(gamma^3)/(DeltaGv)^2If the DeltaHf (heat of fusion) is known, it can be shown that DeltaGv depends on temperature in:DeltaGv=[DeltaHf*(Tmelt-T)]/TmeltSubstitution shows:

If a DeltaG* value is known, n* is a function of temperature representing the number of stable nuclei as follows:n*=K1*e^(-DeltaG*/(k*T)Where K1 is a function of the total number of nuclei in solid phaseWhere k is boltzmann's constant: 1.38*10^-23Another quantity, vd, is the frequency when liquid atoms attach themselves to the solid nucleusIt can be represented as a function of temperature and coefficient of diffusion:vd=K2exp(-Qd/(k*T))Where K2 is a T-independent constantWhere k is again boltzmann's constantThe rate of nucleation or nucleation rate Ndot can be expressed as follows:

Where K3 is the number of atoms on a nucleus surface.

Heterogeneous nucleationAt an interface(container wall, other solid phase, any preexisting surface or interface), the solid nucleus spreads like a drop of water, with liquid surrounding it on the other side. The system then has three infterfacial energies that exist at two phase boundaries:(all vectors::) gamma(Solid-Liquid), gamma(Solid-Interface) and gamma(Interface-Liquid).Gamma(SL) exists tangent to the solid surface at the point of contact with the preexisting surfaceGamma(SI) exists projecting from the outermost solid/surface contact inward towards the center of the nucleusGamma(IL) exists starting at the same point as Gamma(SI) then extending (SI) in the opposite direction

There also exists a “wetting angle,” theta, that is the angle between gamma(SL) and gamma(SI)It can be shown the following is true:gamma(IL)=gamma(SI)+gamma(SL)*cos(theta)It can be derived:

Where S(theta) is a function of theta describing the shape of the nucleus (0<S<Unity)IT CAN BE SHOWN:DeltaG*het= DeltaG*hom*S(theta)

Nucleation Rate, when plotted versus change in T from Tm(DeltaT, degree of supercooling), shows heterogeneous nucleation rate curve hitting a max some many degrees sooner than the homogeneous

GrowthThe growth rate, Gdot, can be shown to be a function of temperature:Gdot=Cexp(-Q/(kT))Where k is, naturally, boltzmann's constantWhere Q is the activation energyWhere C is a preexponential remainder of solving the diff eq(both constant)High T, Low rate → Few large, coarse phase particles (Slow nucleation, Fast Growth)Low T, Fast rate → Many small, possibly “cored” nuclei (Fast nucleation, Slow Growth)

Kinetic considerations of solid-state transformationsThe time dependance of rate is referred to as kinetics of a transformation.This is often a key consideration in material heat treatmentsIn kinetic experiments, the % reacted is measured by either microscopic methods or by measuring a physical property, like conductivity over a period of timeThis can then be plotted, and also yields a function for the fraction of transformation, y:y=1-exp(-kt^n)This equation is often referred to as the Avrami EquationBy convention, the rate of a transformation is taken when half the time required for the transformation has elapsed, t(0.5):rate=1/(t(0.5))Heat treatment is the easiest way to to induce phase transformationsDuring phase transformation, alloy → equilibrium defined by phase diagramRate of approach to equilibrium for solid systems is slow, true equilibrium rarely reachedPhase transformations occur at lower temperatures than equilibrium transformation when coolingPhase transformations occur at higher temperatures than equilibrium transformation when heatingThis phenomenon is referred to as supercooling and superheatingThe degree of each depends upon the rate of temperature change, greater heat/cool → greater superheating/supercoolingKinetic information about a system is often more valuable than a knowledge of the final equilibrium state

Microstructural and Property Changes in Iron-Carbon AlloysIsothermal Transformation DiagramsPearlite-Recall iron-iron carbide eutectoid reaction:

gamma(0.76wt%C) → cooling → alpha(0.022wt% C)+ Fe3C(6.70wt% C)-Austentite has an intermediate carbon content, and cools to ferrite, with low carbon content, and cementite, with a much higher carbon content-Greater degrees of supercooling cause significantly shorter transformation times-Plots of the time (s) it takes to start, 50%, and complete the transformation vs temperature yield a very relevant diagram, as in figure 11.13-These are called isothermal transformation diagrams.-In Fe-C system, the widths of ferrite and cementite layers in pearlite vary according to Temperatures -At temperatures near the eutectoid, ferrite and cementite both form fairly thick layers-As temperature decreases, layers progressively become thinner-Pearlite with thick layers is called coarse pearlite, and forms on the right of the isothermal xfrm diagram-Pearlite with thin layers is called fine pearlite, and forms on the left of isothermal xfrm diagram-Proeutectoid phases require more complex isothermal transformation diagramsBainite-Bainite is another possible microconstituent of austenitic transformation-Microstructure has ferrite and cementite phases (diffusion involved) and forms as needles or plates, depending on formation temperature-The microstrucural details of bainite are so fine electron microscope needed-Bainite is represented in isothermal transformation diagrams that are an extension of the same one as pearlite with different and always lower temperatures-Bainite and Pearlite are competative in formation, and if one forms as part of an alloy, the other cannot form without re-heating to austentiteSpheroidite-Heating a bainitic or pearlitic alloy to just under eutectoid temperature for a long enough time will cause spheroidite to form. -Fe3C congregates in speroids amidst sea of ferrite (hence name)-Cementite and Ferrite phase compositions unchanged by formation-Added heat with const. T gives enough energy to aid diffusion, so Fe3C naturally tries to reduce boundary surface area with ferrite-Pearlitic/Bainitic steel can partially transform to spheroidite, and over a long enough period of time, would likely occur in all such steelsMartensite-Formed by austentized alloy being cooled rapidly (i.e. quenched) to low temperatures within degrees of ambient-Nonequilibrium single-phase structure. -The short time period makes diffusion processes negligible; any diffusion causes other species to form-This is a polymorphic transformation of FCC austentite going to body-centered tetragonal martensite-Carbon found as interstitial impurities on edges of tetragonal-Many steels can retain martensitic structures at room temperature indefinately-Can also be found in other alloy systems and is characterized largely by diffusionless transforms-Appears as horizontal line on isothermal transformation diagrams, and called an athermal transformation-Steels where carbon is the main alloying component are called plain carbon steels-Steels with appreciable quantities of alloying compenents other than carbon called alloy steels

Continuous Cooling Transformation DiagramsConstant cooling processes shift the start and completion curves of regular transformation diagram right, and often down. Such diagrams called Continuous Cooling Transformation (CCT) Diagrams

Mechanical Behavior of Iron-Carbon Alloys-Cementite is harder but more brittle than ferrite.Pearlite-It would follow that pearlite, being a mixture of the two, will yield a harder and stronger material, -

but decrease the ductility (compared to ferrite)-Fine pearlite is stronger and less ductile than Coarse pearlite-Cementite layers bind and restrict ferrite layers, as though reinforcing the ferrite-In fine pearlite, more phase layers mean more phase boundaries where this can occur, increasing the strength accordingly.-Also, fine pearlite has many more grain boundaries than coarse, boundaries dislocations must pass through for plastic deformation