11 / Phase Transformations - Amazon S3s3.amazonaws.com/zanran_storage/mehr.sharif.ir/ContentPages/... · 11 / Phase Transformations T op: ... PHASE TRANSFORMATIONS IN METALS ... The

C h a p t e r 11 / Phase Transformations

Top: A Boeing 767 airplane in flight. (Photograph courtesy of the Boeing Commercial Airplane Company.) Bottom: A

transmission electron micrograph showing the microstructure of the aluminum alloy that is used for the upper wing

skins, parts of the internal wing structures, and selected areas of the fuselage of the Boeing 767 above. This is a 7150–

T651 alloy (6.2Zn, 2.3Cu, 2.3Mg, 0.12Zr, the balance Al) that has been precipitation hardened. The light matrix phase in

the micrograph is an aluminum solid solution. The majority of the small plate-shaped dark precipitate particles are a

transition �� phase, the remainder being the equilibrium � (MgZn2) phase. Note that grain boundaries are ‘‘decorated’’

by some of these particles. 80,475�. (Electron micrograph courtesy of G. H. Narayanan and A. G. Miller, Boeing Commer-

cial Airplane Company.)

design a heat treatment for some alloy that willyield the desired room-temperature mechanicalproperties. For example, the tensile strength of aniron–carbon alloy of eutectoid composition (0.76wt% C) can be varied between approximately 700MPa (100,000 psi) and 2000 MPa (300,000 psi) de-pending on the heat treatment employed.

Why Study Phase Transformations?

The development of a set of desirable mechanicalcharacteristics for a material often results from aphase transformation, which is wrought by a heattreatment. The time and temperature dependenciesof some phase transformations are conveniently rep-resented on modified phase diagrams. It is impor-tant to know how to use these diagrams in order to

323

L e a r n i n g O b j e c t i v e sAfter careful study of this chapter you should be able to do the following:

1. Make a schematic fraction transformation-versus-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 continu-ous cooling transformation) diagram for someiron–carbon alloy, design a heat treatment thatwill produce a specified microstructure.

11.1 INTRODUCTION

Mechanical and other properties of many materials depend on their microstructures,which are often produced as a result of phase transformations. In the first portionof this chapter we discuss the basic principles of phase transformations. Next, weaddress the role these transformations play in the development of microstructurefor iron–carbon, as well as other alloys, and how the mechanical properties areaffected by these microstructural changes. Finally, we treat crystallization, melting,and glass transition transformations in polymers.

P H A S E T R A N S F O R M A T I O N S I N M E T A L SOne reason for the versatility of metallic materials lies in the wide range of mechani-cal properties they possess, which are accessible to management by various means.Three strengthening mechanisms were discussed in Chapter 8, namely, grain sizerefinement, solid-solution strengthening, and strain hardening. Additional tech-niques are available wherein the mechanical properties are reliant on the characteris-tics of the microstructure.

The development of microstructure in both single- and two-phase alloys ordi-narily involves some type of phase transformation—an alteration in the numberand/or character of the phases. The first portion of this chapter is devoted to abrief discussion of some of the basic principles relating to transformations involvingsolid phases. Inasmuch as most phase transformations do not occur instantaneously,consideration is given to the dependence of reaction progress on time, or thetransformation rate. This is followed by a discussion of the development of two-phase microstructures for iron–carbon alloys. Modified phase diagrams are intro-duced which permit determination of the microstructure that results from a specificheat treatment. Finally, other microconstituents in addition to pearlite are pre-sented, and, for each, the mechanical properties are discussed.

324

5. Using a phase diagram, describe and explainthe two heat treatments that are used to precipi-tation-harden a metal alloy.

6. Make a schematic plot of room-temperaturestrength (or hardness) versus the logarithm oftime for a precipitation heat treatment at con-stant temperature. Explain the shape of thiscurve in terms of the mechanism of precipita-tion hardening.

7. Schematically plot specific volume versus tem-perature for crystalline, semicrystalline, andamorphous polymers, noting glass transitionand melting temperatures.

�8. List four characteristics or structural compo-nents of a polymer that affect both its meltingand glass transition temperatures.�

11.3 The Kinetics of Solid-State Reactions ● 325

11.2 BASIC CONCEPTS

A variety of phase transformations are important in the processing of materials,and usually they involve some alteration of the microstructure. For purposes ofthis discussion, these transformations are divided into three classifications. In onegroup are simple diffusion-dependent transformations in which there is no changein either the number or composition of the phases present. These include solidifica-tion of a pure metal, allotropic transformations, and, recrystallization and graingrowth (see Sections 8.13 and 8.14).

In another type of diffusion-dependent transformation, there is some alterationin phase compositions and often in the number of phases present; the final micro-structure ordinarily consists of two phases. The eutectoid reaction, described byEquation 10.19, is of this type; it receives further attention in Section 11.5.

The third kind of transformation is diffusionless, wherein a metastable phaseis produced. As discussed in Section 11.5, a martensitic transformation, which maybe induced in some steel alloys, falls into this category.

11.3 THE KINETICS OF SOLID-STATE REACTIONS

Most solid-state transformations do not occur instantaneously because obstaclesimpede the course of the reaction and make it dependent on time. For example,since most transformations involve the formation of at least one new phase thathas a composition and/or crystal structure different from that of the parent one,some atomic rearrangements via diffusion are required. Diffusion is a time-depen-dent phenomenon, as discussed in Section 6.4. A second impediment to the forma-tion of a new phase is the increase in energy associated with the phase boundariesthat are created between parent and product phases.

From a microstructural standpoint, the first process to accompany a phasetransformation is nucleation—the formation of very small (often submicroscopic)particles, or nuclei, of the new phase, which are capable of growing. Favorablepositions for the formation of these nuclei are imperfection sites, especially grainboundaries. The second stage is growth, in which the nuclei increase in size; duringthis process, of course, some volume of the parent phase disappears. The transforma-tion reaches completion if growth of these new phase particles is allowed to proceeduntil the equilibrium fraction is attained.

As would be expected, the time dependence of the transformation rate (whichis often termed the kinetics of a transformation) is an important consideration inthe heat treatment of materials. With many kinetic investigations, the fraction ofreaction that has occurred is measured as a function of time, while the temperatureis maintained constant. Transformation progress is usually ascertained by eithermicroscopic examination or measurement of some physical property (such as electri-cal conductivity) the magnitude of which is distinctive of the new phase. Data areplotted as the fraction of transformed material versus the logarithm of time; an S-shaped curve similar to that in Figure 11.1 represents the typical kinetic behavior formost solid-state reactions. Nucleation and growth stages are indicated in the figure.

For solid-state transformations displaying the kinetic behavior in Figure 11.1,the fraction of transformation y is a function of time t as follows:

y � 1 � exp(�ktn) (11.1)

where k and n are time-independent constants for the particular reaction. Theabove expression is often referred to as the Avrami equation.

By convention, the rate of a transformation r is taken as the reciprocal of timerequired for the transformation to proceed halfway to completion, t0.5 , or

r �1

t0.5(11.2)

This t0.5 is also noted in Figure 11.1.Temperature is one variable in a heat treatment process that is subject to

control, and it may have a profound influence on the kinetics and thus on the rateof a transformation. This is demonstrated in Figure 11.2, where y-versus-log tS-shaped curves at several temperatures for the recrystallization of copper areshown.

For most reactions and over specific temperature ranges, rate increases withtemperature according to

r � Ae�Q/RT (11.3)

326 ● Chapter 11 / Phase Transformations

Frac

tion

of

tran

sfor

mat

ion,

y

Nucleation Growth

t0.5

Logarithm of heating time, t

0

0.5

1.0 FIGURE 11.1 Plot of fractionreacted versus the logarithm oftime typical of many solid-statetransformations in whichtemperature is held constant.

FIGURE 11.2 Percent recrystallization as a function of time and at constanttemperature for pure copper. (Reprinted with permission from MetallurgicalTransactions, Vol. 188, 1950, a publication of The Metallurgical Society ofAIME, Warrendale, Pennsylvania. Adapted from B. F. Decker and D. Harker,‘‘Recrystallization in Rolled Copper,’’ Trans. AIME, 188, 1950, p. 888.)

Time (min)(Logarithmic scale)

Per

cent

rec

ryst

alliz

ed

1 10 102 1040

20

40

60 135°C 119°C 113°C 102°C 88°C 43°C

80

100

11.4 Multiphase Transformations ● 327

where

R � the gas constant

T � absolute temperature

A � a temperature-independent constant

Q � an activation energy for the particular reaction

It may be recalled that the diffusion coefficient has the same temperature depen-dence (Equation 6.8). Processes the rates of which exhibit this relationship withtemperature are sometimes termed thermally activated.

11.4 MULTIPHASE TRANSFORMATIONS

Phase transformations may be wrought in metal alloy systems by varying tempera-ture, composition, and the external pressure; however, temperature changes bymeans of heat treatments are most conveniently utilized to induce phase transforma-tions. This corresponds to crossing a phase boundary on the composition–temperature phase diagram as an alloy of given composition is heated or cooled.

During a phase transformation, an alloy proceeds toward an equilibrium statethat is characterized by the phase diagram in terms of the product phases, theircompositions, and relative amounts. Most phase transformations require some finitetime to go to completion, and the speed or rate is often important in the relationshipbetween the heat treatment and the development of microstructure. One limitationof phase diagrams is their inability to indicate the time period required for theattainment of equilibrium.

The rate of approach to equilibrium for solid systems is so slow that trueequilibrium structures are rarely achieved. Equilibrium conditions are maintainedonly if heating or cooling is carried out at extremely slow and unpractical rates.For other than equilibrium cooling, transformations are shifted to lower tempera-tures than indicated by the phase diagram; for heating, the shift is to higher tempera-tures. These phenomena are termed supercooling and superheating, respectively.The degree of each depends on the rate of temperature change; the more rapidthe cooling or heating, the greater the supercooling or superheating. For example,for normal cooling rates the iron–carbon eutectoid reaction is typically displaced10 to 20�C (18 to 36�F) below the equilibrium transformation temperature.

For many technologically important alloys, the preferred state or microstructureis a metastable one, intermediate between the initial and equilibrium states; onoccasion, a structure far removed from the equilibrium one is desired. It thusbecomes imperative to investigate the influence of time on phase transformations.This kinetic information is, in many instances, of greater value than a knowledgeof the final equilibrium state.

M I C R O S T R U C T U R A L A N D P R O P E R T YC H A N G E S I N I R O N – C A R B O N A L L O Y S

Some of the basic kinetic principles of solid-state transformations are now extendedand applied specifically to iron–carbon alloys in terms of the relationships betweenheat treatment, the development of microstructure, and mechanical properties.

This system has been chosen because it is familiar and because a wide variety ofmicrostructures and mechanical properties are possible for iron–carbon (or steel)alloys.

11.5 ISOTHERMAL TRANSFORMATION DIAGRAMS

PEARLITEConsider again the iron–iron carbide eutectoid reaction

�(0.76 wt% C) UUUUUUUucooling

heating�(0.022 wt% C) � Fe3C(6.70 wt% C) (10.19)

which is fundamental to the development of microstructure in steel alloys. Uponcooling, austenite, having an intermediate carbon concentration, transforms to aferrite phase, having a much lower carbon content, and also cementite, with amuch higher carbon concentration. Pearlite is one microstructural product of thistransformation (Figure 10.29), and the mechanism of pearlite formation was dis-cussed previously (Section 10.19) and demonstrated in Figure 10.30.

Temperature plays an important role in the rate of the austenite-to-pearlitetransformation. The temperature dependence for an iron–carbon alloy of eutectoidcomposition is indicated in Figure 11.3, which plots S-shaped curves of the percent-age transformation versus the logarithm of time at three different temperatures.For each curve, data were collected after rapidly cooling a specimen composed of100% austenite to the temperature indicated; that temperature was maintainedconstant throughout the course of the reaction.

A more convenient way of representing both the time and temperature depen-dence of this transformation is in the bottom portion of Figure 11.4. Here, thevertical and horizontal axes are, respectively, temperature and the logarithm oftime. Two solid curves are plotted; one represents the time required at each tempera-ture for the initiation or start of the transformation; the other is for the transforma-tion conclusion. The dashed curve corresponds to 50% of transformation completion.These curves were generated from a series of plots of the percentage transformationversus the logarithm of time taken over a range of temperatures. The S-shapedcurve [for 675�C (1247�F)], in the upper portion of Figure 11.4, illustrates how thedata transfer is made.


Time (s)

Per

cent

pea

rlit

e

Per

cent

aus

teni

te

1 10 102 1030 100

50

0

50 600°C 650°C 675°C

100 FIGURE 11.3 For aniron–carbon alloy ofeutectoid composition(0.76 wt% C),isothermal fractionreacted versus thelogarithm of time forthe austenite-to-pearlite transformation.

11.5 Isothermal Transformation Diagrams ● 329

In interpreting this diagram, note first that the eutectoid temperature [727�C(1341�F)] is indicated by a horizontal line; at temperatures above the eutectoid andfor all times, only austenite will exist, as indicated in the figure. The austenite-to-pearlite transformation will occur only if an alloy is supercooled to below theeutectoid; as indicated by the curves, the time necessary for the transformation tobegin and then end depends on temperature. The start and finish curves are nearlyparallel, and they approach the eutectoid line asymptotically. To the left of thetransformation start curve, only austenite (which is unstable) will be present,whereas to the right of the finish curve, only pearlite will exist. In between, theaustenite is in the process of transforming to pearlite, and thus both microconstitu-ents will be present.

According to Equation 11.2, the transformation rate at some particular tempera-ture is inversely proportional to the time required for the reaction to proceed to50% completion (to the dashed curve in Figure 11.4). That is, the shorter this time,the higher the rate. Thus, from Figure 11.4, at temperatures just below the eutectoid(corresponding to just a slight degree of undercooling) very long times (on theorder of 105 s) are required for the 50% transformation, and therefore the reactionrate is very slow. The transformation rate increases with decreasing temperaturesuch that at 540�C (1000�F) only about 3 s is required for the reaction to go to50% completion.

This rate–temperature behavior is in apparent contradiction of Equation 11.3,which stipulates that rate increases with increasing temperature. The reason for thisdisparity is that over this range of temperatures (i.e., 540 to 727�C), the transforma-

Time (s)

Tem

pera

ture

(°C

)P

erce

nt o

f au

sten

ite

tran

sfor

med

to

pear

lite

Tem

pera

ture

(°F)

1 10 102 103 104

800

1000

1200

1400

105

1 10

Transformationtemperature 675°C

Transformationbegins

Austenite(unstable)

Pearlite

50% Completion curve

Completion curve(~100% pearlite)

Begin curve(~0% pearlite)

Eutectoid temperature

Transformationends

103 104 105

400

500

600

700

0

50

100

Austenite (stable)

Time (s)

102

FIGURE 11.4Demonstration of howan isothermal transfor-mation diagram (bot-tom) is generated frompercent transformation-versus-logarithm of timemeasurements (top).(Adapted from H. Boyer,Editor, Atlas of Isother-mal Transformation andCooling TransformationDiagrams, American So-ciety for Metals, 1977,p. 369.)

tion rate is controlled by the rate of pearlite nucleation, and nucleation rate de-creases with rising temperature (i.e., less supercooling). This behavior may beexplained by Equation 11.3, wherein the activation energy Q for nucleation is afunction of, and increases with, increasing temperature. We shall find that at lowertemperatures, the austenite decomposition transformation is diffusion-controlledand that the rate behavior is as predicted by Equation 11.3, with a temperature-independent activation energy for diffusion.

Several constraints are imposed on using diagrams like Figure 11.4. First, thisparticular plot is valid only for an iron–carbon alloy of eutectoid composition; forother compositions, the curves will have different configurations. In addition, theseplots are accurate only for transformations in which the temperature of the alloyis held constant throughout the duration of the reaction. Conditions of constanttemperature are termed isothermal; thus, plots such as Figure 11.4 are referred toas isothermal transformation diagrams, or sometimes as time–temperature–transformation (or T–T–T) plots.

An actual isothermal heat treatment curve (ABCD) is superimposed on theisothermal transformation diagram for a eutectoid iron–carbon alloy in Figure 11.5.Very rapid cooling of austenite to a temperature is indicated by the near-verticalline AB, and the isothermal treatment at this temperature is represented by thehorizontal segment BCD. Of course, time increases from left to right along thisline. The transformation of austenite to pearlite begins at the intersection, point C(after approximately 3.5 s), and has reached completion by about 15 s, corresponding


1 10 102 103 104 105

Time (s)

Denotes that a transformationis occurring

Austenite ® pearlitetransformation

Austenite (stable)Eutectoid

temperature

Coarse pearliteFerrite

Fe3C

Fine pearlite

800

500

600

700

1000

1200

1400

1 day1 h1 min1 s

Tem

pera

ture

(�C

)

727�C

Tem

pera

ture

(�F

)

� �

��

�

� �

�

A

B

C

D

FIGURE 11.5 Isothermal transformation diagram for a eutectoid iron–carbonalloy, with superimposed isothermal heat treatment curve (ABCD). Microstruc-tures before, during, and after the austenite-to-pearlite transformation areshown. (Adapted from H. Boyer, Editor, Atlas of Isothermal Transformation andCooling Transformation Diagrams, American Society for Metals, 1977, p. 28.)


to point D. Figure 11.5 also shows schematic microstructures at various times duringthe progression of the reaction.

The thickness ratio of the ferrite and cementite layers in pearlite is approxi-mately 8 to 1. However, the absolute layer thickness depends on the temperatureat which the isothermal transformation is allowed to occur. At temperatures justbelow the eutectoid, relatively thick layers of both the �-ferrite and Fe3C phasesare produced; this microstructure is called coarse pearlite, and the region at whichit forms is indicated to the right of the completion curve on Figure 11.5. At thesetemperatures, diffusion rates are relatively high, such that during the transformationillustrated in Figure 10.30 carbon atoms can diffuse relatively long distances, whichresults in the formation of thick lamellae. With decreasing temperature, the carbondiffusion rate decreases, and the layers become progressively thinner. The thin-layered structure produced in the vicinity of 540�C is termed fine pearlite; this isalso indicated in Figure 11.5. To be discussed in Section 11.7 is the dependence ofmechanical properties on lamellar thickness. Photomicrographs of coarse and finepearlite for a eutectoid composition are shown in Figure 11.6.

For iron–carbon alloys of other compositions, a proeutectoid phase (eitherferrite or cementite) will coexist with pearlite, as discussed in Section 10.19. Thusadditional curves corresponding to a proeutectoid transformation also must beincluded on the isothermal transformation diagram. A portion of one such diagramfor a 1.13 wt% C alloy is shown in Figure 11.7.

FIGURE 11.6 Photomicrographs of (a) coarse pearlite and (b) fine pearlite.3000�. (From K. M. Ralls, et al., An Introduction to Materials Science andEngineering, p. 361. Copyright 1976 by John Wiley & Sons, New York.Reprinted by permission of John Wiley & Sons, Inc.)

BAINITEIn addition to pearlite, other microconstituents that are products of the austenitictransformation exist; one of these is called bainite. The microstructure of bainiteconsists of ferrite and cementite phases, and thus diffusional processes are involvedin its formation. Bainite forms as needles or plates, depending on the temperatureof the transformation; the microstructural details of bainite are so fine that theirresolution is possible only using electron microscopy. Figure 11.8 is an electronmicrograph that shows a grain of bainite (positioned diagonally from lower left toupper right); it is composed of needles of ferrite that are separated by elongatedparticles of the Fe3C phase; the various phases in this micrograph have been labeled.In addition, the phase that surrounds the needle is martensite, the topic to whicha subsequent section is addressed. Furthermore, no proeutectoid phase formswith bainite.

The time–temperature dependence of the bainite transformation may also berepresented on the isothermal transformation diagram. It occurs at temperaturesbelow those at which pearlite forms; begin-, end-, and half-reaction curves are justextensions of those for the pearlitic transformation, as shown in Figure 11.9, theisothermal transformation diagram for an iron–carbon alloy of eutectoid composi-tion that has been extended to lower temperatures. All three curves are C-shapedand have a ‘‘nose’’ at point N, where the rate of transformation is a maximum. Asmay be noted, whereas pearlite forms above the nose—that is, over the temperaturerange of about 540 to 727�C (1000 to 1341�F)—for isothermal treatments at tempera-tures between about 215 and 540�C (420 and 1000�F), bainite is the transforma-tion product.

It should also be noted that pearlitic and bainitic transformations are reallycompetitive with each other, and once some portion of an alloy has transformedto either pearlite or bainite, transformation to the other microconstituent is notpossible without reheating to form austenite.

In passing, it should be mentioned that the kinetics of the bainite transformation(below the nose in Figure 11.9) obey Equation 11.3; that is, rate (1/t0.5 , Equation11.2) increases exponentially with rising temperature. Furthermore, the kinetics of


Time (s)

Tem

pera

ture

(°C

)

Tem

pera

ture

(°F)

1 10 102 103 104

1000

1200

1400

1600

500

600

700

800

A

A+

CA

P


900

A+

P

FIGURE 11.7Isothermal transforma-tion diagram for a 1.13wt% C iron–carbonalloy: A, austenite; C,proeutectoid cementite;P, pearlite. (Adaptedfrom H. Boyer, Editor,Atlas of IsothermalTransformation andCooling Transforma-tion Diagrams, Ameri-can Society for Metals,1977, p. 33.)


Martensite

Cementite

Ferrite

FIGURE 11.8 Replica transmission electron micrograph showing the structure ofbainite. A grain of bainite passes from lower left to upper right-hand corners,which consists of elongated and needle-shaped particles of Fe3C within a ferritematrix. The phase surrounding the bainite is martensite. (Reproduced with per-mission from Metals Handbook, Vol. 8, 8th edition, Metallography, Structuresand Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.)

Time (s)

Tem

pera

ture

(�C

)

Tem

pera

ture

(�F

)

10�1 1 10 102 103 104 105

400

600

800

1000

1200

1400Eutectoid temperatureA

A

A

50%

N

B

P

100

200

300

400

500

600

700

800

A+

P

A + B

FIGURE 11.9Isothermal transforma-tion diagram for aniron–carbon alloy of eu-tectoid composition, in-cluding austenite-to-pearlite (A–P) andaustenite-to-bainite(A–B) transformations.(Adapted from H.Boyer, Editor, Atlas ofIsothermal Transfor-mation and CoolingTransformation Dia-grams, American Soci-ety for Metals, 1977,p. 28.)

many solid-state transformations are represented by this characteristic C-shapedcurve (Figure 11.9).

SPHEROIDITEIf a steel alloy having either pearlitic or bainitic microstructures is heated to, andleft at, a temperature below the eutectoid for a sufficiently long period of time—forexample, at about 700�C (1300�F) for between 18 and 24 h—yet another microstruc-ture will form. It is called spheroidite (Figure 11.10). Instead of the alternatingferrite and cementite lamellae (pearlite), or the microstructures observed for bainite,the Fe3C phase appears as spherelike particles embedded in a continuous � phasematrix. This transformation has occurred by additional carbon diffusion with nochange in the compositions or relative amounts of ferrite and cementite phases.The photomicrograph in Figure 11.11 shows a pearlitic steel that has partiallytransformed to spheroidite. The driving force for this transformation is the reductionin �–Fe3C phase boundary area. The kinetics of spheroidite formation are notincluded on isothermal transformation diagrams.

MARTENSITEYet another microconstituent or phase called martensite is formed when austenit-ized iron–carbon alloys are rapidly cooled (or quenched) to a relatively low tempera-ture (in the vicinity of the ambient). Martensite is a nonequilibrium single-phasestructure that results from a diffusionless transformation of austenite. It may bethought of as a transformation product that is competitive with pearlite and bainite.The martensitic transformation occurs when the quenching rate is rapid enough toprevent carbon diffusion. Any diffusion whatsoever will result in the formation offerrite and cementite phases.

The martensitic transformation is not well understood. However, large num-bers of atoms experience cooperative movements, in that there is only a slightdisplacement of each atom relative to its neighbors. This occurs in such a waythat the FCC austenite experiences a polymorphic transformation to a body-centered tetragonal (BCT) martensite. A unit cell of this crystal structure (Figure


FIGURE 11.10 Photomicrograph of a steelhaving a spheroidite microstructure. Thesmall particles are cementite; thecontinuous phase is � ferrite. 1000�.(Copyright 1971 by United States SteelCorporation.)


11.12) is simply a body-centered cube that has been elongated along one of itsdimensions; this structure is distinctly different from that for BCC ferrite. Allthe carbon atoms remain as interstitial impurities in martensite; as such, theyconstitute a supersaturated solid solution that is capable of rapidly transformingto other structures if heated to temperatures at which diffusion rates becomeappreciable. Many steels, however, retain their martensitic structure almostindefinitely at room temperature.

The martensitic transformation is not, however, unique to iron–carbon alloys.It is found in other systems and is characterized, in part, by the diffusionlesstransformation.

Since the martensitic transformation does not involve diffusion, it occurs almostinstantaneously; the martensite grains nucleate and grow at a very rapid rate—thevelocity of sound within the austenite matrix. Thus the martensitic transformationrate, for all practical purposes, is time independent.

Martensite grains take on a platelike or needlelike appearance, as indicated inFigure 11.13. The white phase in the micrograph is austenite (retained austenite)

FIGURE 11.11 A photomicrograph ofa pearlitic steel that has partiallytransformed to spheroidite. 1400�.(Courtesy of United States SteelCorporation.)

FIGURE 11.12 The body-centered tetragonal unit cell formartensitic steel showing iron atoms (circles) and sites thatmay be occupied by carbon atoms (crosses). For thistetragonal unit cell, c � a.

c

aa

that did not transform during the rapid quench. As has already been mentioned,martensite as well as other microconstituents (e.g., pearlite) can coexist.

Being a nonequilibrium phase, martensite does not appear on the iron–ironcarbide phase diagram (Figure 10.26). The austenite-to-martensite transformationis, however, represented on the isothermal transformation diagram. Since the mar-


FIGURE 11.13 Photomicrograph showingthe martensitic microstructure. The needle-shaped grains are the martensite phase, andthe white regions are austenite that failed totransform during the rapid quench. 1220�.(Photomicrograph courtesy of United StatesSteel Corporation.)

Time (s)

Tem

pera

ture

(�C

)

Tem

pera

ture

(�F

)

10�1 1 10 102 103 104 105

200

400

800

600

1000

1200

1400Eutectoid temperatureA

A

A

M + A

M(start)

M(50%)

M(90%)

50%

P

B

100

0

200

300

400

500

600

700

800

A

A

+

+

P

B

FIGURE 11.14 Thecomplete isothermaltransformation diagramfor an iron–carbonalloy of eutectoidcomposition: A,austenite; B, bainite;M, martensite; P,pearlite.


tensitic transformation is diffusionless and instantaneous, it is not depicted in thisdiagram like the pearlitic and bainitic reactions. The beginning of this transformationis represented by a horizontal line designated M(start) (Figure 11.14). Two otherhorizontal and dashed lines, labeled M(50%) and M(90%), indicate percentages ofthe austenite-to-martensite transformation. The temperatures at which these linesare located vary with alloy composition but, nevertheless, must be relatively lowbecause carbon diffusion must be virtually nonexistent. The horizontal and linearcharacter of these lines indicates that the martensitic transformation is independentof time; it is a function only of the temperature to which the alloy is quenched orrapidly cooled. A transformation of this type is termed an athermal transformation.

Consider an alloy of eutectoid composition that is very rapidly cooled from atemperature above 727�C (1341�F) to, say, 165�C (330�F). From the isothermaltransformation diagram (Figure 11.14) it may be noted that 50% of the austenitewill immediately transform to martensite; and as long as this temperature is main-tained, there will be no further transformation.

The presence of alloying elements other than carbon (e.g., Cr, Ni, Mo, and W)may cause significant changes in the positions and shapes of the curves in theisothermal transformation diagrams. These include (1) shifting to longer times thenose of the austenite-to-pearlite transformation (and also a proeutectoid phase nose,if such exists), and (2) the formation of a separate bainite nose. These alterationsmay be observed by comparing Figures 11.14 and 11.15, which are isothermaltransformation diagrams for carbon and alloy steels, respectively.

Time (s)

Tem

pera

ture

(°C

)

Tem

pera

ture

(°F)

1 10 102 103 104 105 106

200

400

800

600

1000

1200

1400


A

A

A + F F + P

A + B

M + A

M(start)

M(50%)

M(90%)

50% B

M100

0

200

300

400

500

600

700

800

A + F + P

FIGURE 11.15Isothermal transforma-

tion diagram for analloy steel (type 4340):A, austenite; B, bainite;P, pearlite; M, martens-ite; F, proeutectoid fer-rite. (Adapted from H.Boyer, Editor, Atlas of

Isothermal Transfor-mation and Cooling

Transformation Dia-grams, American Soci-

ety for Metals, 1977,p. 181.)

Steels in which carbon is the prime alloying element are termed plain carbonsteels, whereas alloy steels contain appreciable concentrations of other elements,including those cited in the preceding paragraph. Chapter 13 tells more about theclassification and properties of ferrous alloys.

EXAMPLE PROBLEM 11.1

Using the isothermal transformation diagram for an iron–carbon alloy of eutec-toid composition (Figure 11.14), specify the nature of the final microstructure(in terms of microconstituents present and approximate percentages) of a smallspecimen that has been subjected to the following time–temperature treatments.In each case assume that the specimen begins at 760�C (1400�F) and that it hasbeen held at this temperature long enough to have achieved a complete andhomogeneous austenitic structure.

(a) Rapidly cool to 350�C (660�F), hold for 104 s, and quench to room temper-ature.

(b) Rapidly cool to 250�C (480�F), hold for 100 s, and quench to room temper-ature.

(c) Rapidly cool to 650�C (1200�F), hold for 20 s, rapidly cool to 400�C (750�F),hold for 103 s, and quench to room temperature.

S O L U T I O N

The time–temperature paths for all three treatments are shown in Figure 11.16.In each case the initial cooling is rapid enough to prevent any transformationfrom occurring.

(a) At 350�C austenite isothermally transforms to bainite; this reaction beginsafter about 10 s and reaches completion at about 500 s elapsed time. Therefore,by 104 s, as stipulated in this problem, 100% of the specimen is bainite, and nofurther transformation is possible, even though the final quenching line passesthrough the martensite region of the diagram.

(b) In this case it takes about 150 s at 250�C for the bainite transformation tobegin, so that at 100 s the specimen is still 100% austenite. As the specimen iscooled through the martensite region, beginning at about 215�C, progressivelymore of the austenite instantaneously transforms to martensite. This transfor-mation is complete by the time room temperature is reached, such that thefinal microstructure is 100% martensite.

(c) For the isothermal line at 650�C, pearlite begins to form after about 7 s;by the time 20 s has elapsed, only approximately 50% of the specimen hastransformed to pearlite. The rapid cool to 400�C is indicated by the verticalline; during this cooling, very little, if any, remaining austenite will transformto either pearlite or bainite, even though the cooling line passes through pearliteand bainite regions of the diagram. At 400�C, we begin timing at essentiallyzero time (as indicated in Figure 11.16); thus, by the time 103 s has elapsed, allof the remaining 50% austenite will have completely transformed to bainite.Upon quenching to room temperature, any further transformation is not possi-ble inasmuch as no austenite remains; and so the final microstructure at roomtemperature consists of 50% pearlite and 50% bainite.


11.7 Mechanical Behavior of Iron–Carbon Alloys ● 339

11.6 CONTINUOUS COOLING TRANSFORMATION

DIAGRAMS (CD-ROM)

11.7 MECHANICAL BEHAVIOR OF IRON–CARBON ALLOYS

We shall now discuss the mechanical behavior of iron–carbon alloys having themicrostructures discussed heretofore, namely, fine and coarse pearlite, spheroidite,bainite, and martensite. For all but martensite, two phases are present (i.e., ferriteand cementite); and so an opportunity is provided to explore several mechanicalproperty–microstructure relationships that exist for these alloys.

Time (s)

Tem

pera

ture

(°C

)

Tem

pera

ture

(°F)

10 1 1 10 102 103 104 105

200

400

800

600

1000

1200

1400Eutectoid temperature

A

AP

B

(c)

(c)

(a)

(b)

(b)100%

Martensite

(c)50% Pearlite50% Bainite

(a)100%Bainite

A

M(start)

M(50%)

M(90%)

100

0

200

300

400

500

600

700

800

A + B

P + A

FIGURE 11.16 Isothermal transformation diagram for an iron–carbon alloy ofeutectoid composition and the isothermal heat treatments (a), (b), and (c) in Ex-ample Problem 11.1.


PEARLITECementite is much harder but more brittle than ferrite. Thus, increasing thefraction of Fe3C in a steel alloy while holding other microstructural elementsconstant will result in a harder and stronger material. This is demonstrated inFigure 11.21a, in which the tensile and yield strengths as well as the Brinellhardness number are plotted as a function of the weight percent carbon (orequivalently as the percent of Fe3C) for steels that are composed of fine pearlite.All three parameters increase with increasing carbon concentration. Inasmuchas cementite is more brittle, increasing its content will result in a decrease inboth ductility and toughness (or impact energy). These effects are shown inFigure 11.21b for the same fine pearlitic steels.

The layer thickness of each of the ferrite and cementite phases in the microstruc-ture also influences the mechanical behavior of the material. Fine pearlite is harderand stronger than coarse pearlite, as demonstrated in Figure 11.22a, which plotshardness versus the carbon concentration.

The reasons for this behavior relate to phenomena that occur at the �–Fe3Cphase boundaries. First, there is a large degree of adherence between the twophases across a boundary. Therefore, the strong and rigid cementite phase severelyrestricts deformation of the softer ferrite phase in the regions adjacent to theboundary; thus the cementite may be said to reinforce the ferrite. The degree ofthis reinforcement is substantially higher in fine pearlite because of the greaterphase boundary area per unit volume of material. In addition, phase boundariesserve as barriers to dislocation motion in much the same way as grain boundaries(Section 8.9). For fine pearlite there are more boundaries through which a disloca-tion must pass during plastic deformation. Thus, the greater reinforcement andrestriction of dislocation motion in fine pearlite account for its greater hardnessand strength.

Coarse pearlite is more ductile than fine pearlite, as illustrated in Figure 11.22b,which plots percent reduction in area versus carbon concentration for both micro-structure types. This behavior results from the greater restriction to plastic deforma-tion of the fine pearlite.

SPHEROIDITEOther elements of the microstructure relate to the shape and distribution ofthe phases. In this respect, the cementite phase has distinctly different shapesand arrangements in the pearlite and spheroidite microstructures (Figures 11.6and 11.10). Alloys containing pearlitic microstructures have greater strength andhardness than do those with spheroidite. This is demonstrated in Figure 11.22a,which compares the hardness as a function of the weight percent carbon forspheroidite with both the other pearlite structure types. This behavior is againexplained in terms of reinforcement at, and impedance to, dislocation motionacross the ferrite–cementite boundaries as discussed above. There is less boundaryarea per unit volume in spheroidite, and consequently plastic deformation isnot nearly as constrained, which gives rise to a relatively soft and weak material.In fact, of all steel alloys, those that are softest and weakest have a spheroiditemicrostructure.

As would be expected, spheroidized steels are extremely ductile, much morethan either fine or coarse pearlite (Figure 11.22b). In addition, they are notablytough because any crack can encounter only a very small fraction of the brittlecementite particles as it propagates through the ductile ferrite matrix.

11.7M

echan

icalB

ehavior

ofIron

–Carb

onA

lloys●

341

Composition (wt% C)

Percent Fe3C

10

3 p

si

MP

a

Bri

nell

hard

ness

num

ber

Yiel

d an

d te

nsile

str

engt

h

0 0.2 0.4 0.6 0.8 1.0

100

150

200

250

300

350

40300

400

500

600

700

800

900

1000

1100

1200

60

80

100

120

140

160

3 6 9 12 150

(a)

Pearlite + ferrite

Tensile strength

Brinell hardness

Yield strength

Pearlite+

Fe3C

Composition (wt% C)

Percent Fe3C

Izod

impa

ct e

nerg

y (f

t-lb

f)

Duc

tilit

y (%

)0 0.2 0.4 0.6 0.8 1.0

80

60

40

20

0

20

0

40

60

80

100

120

3 6 9 12 150

(b)

Pearlite + ferrite

Izod impactenergy

Reductionin area

Elongation

Pearlite+ Fe3C

FIGURE 11.21 (a) Yield strength, tensile strength, and Brinell hardness versus carbon concentration for plain carbon steelshaving microstructures consisting of fine pearlite. (b) Ductility (%EL and %RA) and Izod impact energy versus carbonconcentration for plain carbon steels having microstructures consisting of fine pearlite. (Data taken from Metals Handbook:Heat Treating, Vol. 4, 9th edition, V. Masseria, Managing Editor, American Society for Metals, 1981, p. 9.)

BAINITEBecause bainitic steels have a finer structure (i.e., smaller �-ferrite and Fe3C parti-cles), they are generally stronger and harder than pearlitic ones; yet they exhibit adesirable combination of strength and ductility. Figure 11.23 shows the influence oftransformation temperature on the tensile strength and hardness for an iron–carbonalloy of eutectoid composition; temperature ranges over which pearlite and bainiteform (consistent with the isothermal transformation diagram for this alloy, Figure11.9) are noted at the top of Figure 11.23.

MARTENSITEOf the various microstructures that may be produced for a given steel alloy, marten-site is the hardest and strongest and, in addition, the most brittle; it has, in fact,negligible ductility. Its hardness is dependent on the carbon content, up to about0.6 wt% as demonstrated in Figure 11.24, which plots the hardness of martensiteand fine pearlite as a function of weight percent carbon. In contrast to pearlitic steels,strength and hardness of martensite are not thought to be related to microstructure.


Composition (wt% C)

Percent Fe3C

Bri

nell

hard

ness

num

ber

Roc

kwel

l har

dnes

s

0 0.2 0.4 0.6

Spheroidite

Coarse pearlite

Fine pearlite

0.8 1.0

80

120

160

200

240

280

3200 3 6 9 12 15

35HRC

30

25

20

(a)

100HRB

90

60

70

80

Composition (wt% C)

Percent Fe3C

Duc

tilit

y (%

RA

)

0 0.2 0.4 0.6

Fine pearlite

Spheroidite

Coarse pearlite

0.8 1.0

10

0

20

30

40

50

60

90

80

70

0 3 6 9 12 15

(b)

FIGURE 11.22 (a) Brinell and Rockwell hardness as a function of carbonconcentration for plain carbon steels having fine and coarse pearlite as well asspheroidite microstructures. (b) Ductility (%RA) as a function of carbonconcentration for plain carbon steels having fine and coarse pearlite as well asspheroidite microstructures. (Data taken from Metals Handbook: Heat Treating,Vol. 4, 9th edition, V. Masseria, Managing Editor, American Society for Metals,1981, pp. 9 and 17.)

11.7 Mechanical Behavior of Iron–Carbon Alloys ● 343

Rather, these properties are attributed to the effectiveness of the interstitial carbonatoms in hindering dislocation motion (as a solid-solution effect, Section 8.10),and to the relatively few slip systems (along which dislocations move) for theBCT structure.

Austenite is slightly denser than martensite, and therefore, during the phasetransformation upon quenching, there is a net volume increase. Consequently,relatively large pieces that are rapidly quenched may crack as a result of internalstresses; this becomes a problem especially when the carbon content is greater thanabout 0.5 wt%.

Transformation temperature (°C)

Bri

nell

hard

ness

num

ber

Tens

ile s

tren

gth

(MP

a)

200 300 400 500 600 700 800

500

0

1000

1500

2000

0

100

200

300

400

500

600PearliteBainite FIGURE 11.23

Brinell hardness and tensilestrength as a function of iso-thermal transformation tem-perature for an iron–carbonalloy of eutectoid composi-tion, taken over the tempera-ture range at which bainiticand pearlitic microstructuresform. (Adapted from E. S.Davenport, ‘‘IsothermalTransformation in Steels,’’Trans. ASM, 27, 1939, p.847. Reprinted by permis-sion of ASM International.)

FIGURE 11.24 Hard-ness as a function of carbonconcentration for plain carbonmartensitic, temperedmartensitic [tempered at371�C (700�F)], and pearliticsteels. (Adapted from EdgarC. Bain, Functions of theAlloying 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. 1776.)

Composition (wt% C)

Bri

nell

hard

ness

num

ber

Roc

kwel

l har

dnes

s, H

RC

0.0 0.2 0.4 0.6 0.8 1.0

20

30

40

50

60

65

0

100

200

300

400

500

600

700

0 3 6 9

Percent Fe3C

12 15

Martensite

Tempered martensite(tempered at 371°C)

Fine pearlite

11.8 TEMPERED MARTENSITE

In the as-quenched state, martensite, in addition to being very hard, is so brittlethat it cannot be used for most applications; also, any internal stresses that mayhave been introduced during quenching have a weakening effect. The ductility andtoughness of martensite may be enhanced and these internal stresses relieved bya heat treatment known as tempering.

Tempering is accomplished by heating a martensitic steel to a temperaturebelow the eutectoid for a specified time period. Normally, tempering is carried outat temperatures between 250 and 650�C (480 and 1200�F); internal stresses, however,may be relieved at temperatures as low as 200�C (390�F). This tempering heattreatment allows, by diffusional processes, the formation of tempered martensite,according to the reaction

martensite (BCT, single phase) � tempered martensite (� � Fe3C phases)

(11.4)

where the single-phase BCT martensite, which is supersaturated with carbon, trans-forms to the tempered martensite, composed of the stable ferrite and cementitephases, as indicated on the iron–iron carbide phase diagram.

The microstructure of tempered martensite consists of extremely small anduniformly dispersed cementite particles embedded within a continuous ferrite ma-trix. This is similar to the microstructure of spheroidite except that the cementiteparticles are much, much smaller. An electron micrograph showing the microstruc-ture of tempered martensite at a very high magnification is presented in Figure 11.25.

Tempered martensite may be nearly as hard and strong as martensite, but withsubstantially enhanced ductility and toughness. For example, on the hardness-versus-weight percent carbon plot of Figure 11.24 is included a curve for temperedmartensite. The hardness and strength may be explained by the large ferrite–cementite phase boundary area per unit volume that exists for the very fine andnumerous cementite particles. Again, the hard cementite phase reinforces the ferritematrix along the boundaries, and these boundaries also act as barriers to dislocationmotion during plastic deformation. The continuous ferrite phase is also very ductileand relatively tough, which accounts for the improvement of these two propertiesfor tempered martensite.


FIGURE 11.25 Electronmicrograph of temperedmartensite. Temperingwas carried out at 594�C(1100�F). The smallparticles are thecementite phase; thematrix phase is � ferrite.9300�. (Copyright 1971by United States SteelCorporation.)

11.8 Tempered Martensite ● 345

The size of the cementite particles influences the mechanical behavior oftempered martensite; increasing the particle size decreases the ferrite–cementitephase boundary area and, consequently, results in a softer and weaker materialyet one that is tougher and more ductile. Furthermore, the tempering heattreatment determines the size of the cementite particles. Heat treatment variablesare temperature and time, and most treatments are constant-temperature pro-cesses. Since carbon diffusion is involved in the martensite-tempered martensitetransformation, increasing the temperature will accelerate diffusion, the rate ofcementite particle growth, and, subsequently, the rate of softening. The depen-dence of tensile and yield strength and ductility on tempering temperature foran alloy steel is shown in Figure 11.26. Before tempering, the material wasquenched in oil to produce the martensitic structure; the tempering time at eachtemperature was 1 h. This type of tempering data is ordinarily provided by thesteel manufacturer.

The time dependence of hardness at several different temperatures is presentedin Figure 11.27 for a water-quenched steel of eutectoid composition; the time scaleis logarithmic. With increasing time the hardness decreases, which corresponds tothe growth and coalescence of the cementite particles. At temperatures approachingthe eutectoid [700�C (1300�F)] and after several hours, the microstructure will havebecome spheroiditic (Figure 11.10), with large cementite spheroids embedded withinthe continuous ferrite phase. Correspondingly, overtempered martensite is relativelysoft and ductile.

TEMPER EMBRITTLEMENTThe tempering of some steels may result in a reduction of toughness as measuredby impact tests (Section 9.8); this is termed temper embrittlement. The phenomenon

Tempering temperature (°C)

Tempering temperature (°F)

Tens

ile a

nd y

ield

str

engt

h

200

400 600 800 1000 1200

300 400 500

Reductionin area

Yield strength

Red

ucti

on in

are

a (%

)

Tensile strength

600

30

40

50

60

100

120800

1000

1200

1400

1600

1800

140

160

180

200

220

240

260

MP

a

10

3 p

si

280

FIGURE 11.26Tensile and yieldstrengths and ductility(%RA) versustemperingtemperature for anoil-quenched alloysteel (type 4340).(Adapted from figurefurnished courtesyRepublic SteelCorporation.)

occurs when the steel is tempered at a temperature above about 575�C (1070�F)followed by slow cooling to room temperature, or when tempering is carried outat between approximately 375 and 575�C (700 and 1070�F). Steel alloys that aresusceptible to temper embrittlement have been found to contain appreciable concen-trations of the alloying elements manganese, nickel, or chromium and, in addition,one or more of antimony, phosphorus, arsenic, and tin as impurities in relativelylow concentrations. The presence of these alloying elements and impurities shiftsthe ductile-to-brittle transition to significantly higher temperatures; the ambienttemperature thus lies below this transition in the brittle regime. It has been observedthat crack propagation of these embrittled materials is intergranular; that is, thefracture path is along the grain boundaries of the precursor austenite phase. Further-more, alloy and impurity elements have been found to preferentially segregate inthese regions.

Temper embrittlement may be avoided by (1) compositional control; and/or (2) tempering above 575�C or below 375�C, followed by quenching to roomtemperature. Furthermore, the toughness of steels that have been embrittled maybe improved significantly by heating to about 600�C (1100�F) and then rapidlycooling to below 300�C (570�F).

11.9 REVIEW OF PHASE TRANSFORMATIONS FOR

IRON–CARBON ALLOYS

In this chapter several different microstructures that may be produced in iron–carbon alloys depending on heat treatment have been discussed. Figure 11.28 sum-


Time (s)

205°C (400°F)

315°C (600°F)

425°C (800°F)

535°C (1000

°F)

Roc

kwel

l har

dnes

s, H

RC

Bri

nell

hard

ness

num

ber

101 102 103 104 105

300

400

500

600

700

1 day1 h1 min

30

35

40

45

50

55

60

65

70

FIGURE 11.27 Hardness versus tempering time for a water-quenched eutectoidplain carbon (1080) steel. (Adapted from Edgar C. Bain, Functions of the AlloyingElements in Steel, American Society for Metals, 1939, p. 233.)

11.10 Heat Treatments ● 347

marizes the transformation paths that produce these various microstructures. Here,it is assumed that pearlite, bainite, and martensite result from continuous coolingtreatments; furthermore, the formation of bainite is only possible for alloy steels(not plain carbon ones) as outlined above.

P R E C I P I T A T I O N H A R D E N I N GThe strength and hardness of some metal alloys may be enhanced by the formationof extremely small uniformly dispersed particles of a second phase within theoriginal phase matrix; this must be accomplished by phase transformations that areinduced by appropriate heat treatments. The process is called precipitation harden-ing because the small particles of the new phase are termed ‘‘precipitates.’’ ‘‘Agehardening’’ is also used to designate this procedure because the strength developswith time, or as the alloy ages. Examples of alloys that are hardened by precipitationtreatments include aluminum–copper, copper–beryllium, copper–tin, and magne-sium–aluminum; some ferrous alloys are also precipitation hardenable.

Precipitation hardening and the treating of steel to form tempered martensiteare totally different phenomena, even though the heat treatment procedures aresimilar; therefore, the processes should not be confused. The principal differencelies in the mechanisms by which hardening and strengthening are achieved. Theseshould become apparent as precipitation hardening is explained.

11.10 HEAT TREATMENTS

Inasmuch as precipitation hardening results from the development of particles ofa new phase, an explanation of the heat treatment procedure is facilitated by useof a phase diagram. Even though, in practice, many precipitation-hardenable alloyscontain two or more alloying elements, the discussion is simplified by reference toa binary system. The phase diagram must be of the form shown for the hypotheticalA–B system in Figure 11.29.

Austenite

Bainite(� + Fe3C phases)

Martensite(BCT phase)

Pearlite(� + Fe3C) +

a proeutectoid phase

Tempered martensite(� + Fe3C phases)

Slowcooling

Moderatecooling

Rapidquench

Reheat

FIGURE 11.28 Possibletransformations involvingthe decomposition ofaustenite. Solid arrows,transformations involvingdiffusion; dashed arrow,diffusionless transformation.

Two requisite features must be displayed by the phase diagrams of alloy systemsfor precipitation hardening: an appreciable maximum solubility of one componentin the other, on the order of several percent; and a solubility limit that rapidlydecreases in concentration of the major component with temperature reduction.Both these conditions are satisfied by this hypothetical phase diagram (Figure 11.29).The maximum solubility corresponds to the composition at point M. In addition,the solubility limit boundary between the � and � � � phase fields diminishes fromthis maximum concentration to a very low B content in A at point N. Furthermore,the composition of a precipitation-hardenable alloy must be less than the maximumsolubility. These conditions are necessary but not sufficient for precipitation harden-ing to occur in an alloy system. An additional requirement is discussed below.

SOLUTION HEAT TREATINGPrecipitation hardening is accomplished by two different heat treatments. The firstis a solution heat treatment in which all solute atoms are dissolved to form a single-phase solid solution. Consider an alloy of composition C0 in Figure 11.29. Thetreatment consists of heating the alloy to a temperature within the � phase field—say, T0—and waiting until all the � phase that may have been present is completelydissolved. At this point, the alloy consists only of an � phase of composition C0 .This procedure is followed by rapid cooling or quenching to temperature T1 , whichfor many alloys is room temperature, to the extent that any diffusion and theaccompanying formation of any of the � phase is prevented. Thus, a nonequilibriumsituation exists in which only the � phase solid solution supersaturated with B atomsis present at T1 ; in this state the alloy is relatively soft and weak. Furthermore, formost alloys diffusion rates at T1 are extremely slow, such that the single � phaseis retained at this temperature for relatively long periods.

PRECIPITATION HEAT TREATINGFor the second or precipitation heat treatment, the supersaturated � solid solutionis ordinarily heated to an intermediate temperature T2 (Figure 11.29) within the� � � two-phase region, at which temperature diffusion rates become appreciable.The � precipitate phase begins to form as finely dispersed particles of compositionC� , which process is sometimes termed ‘‘aging.’’ After the appropriate aging time


Composition (wt% B)

Tem

pera

ture

AB

b

b + L� + L

L

a + b

T1

Ca C0

N

Ma

T2

T0

Cb

FIGURE 11.29 Hypotheticalphase diagram for aprecipitation hardenable alloyof composition C0 .

11.11 Mechanism of Hardening ● 349

at T2 , the alloy is cooled to room temperature; normally, this cooling rate is notan important consideration. Both solution and precipitation heat treatments arerepresented on the temperature-versus-time plot, Figure 11.30. The character ofthese � particles, and subsequently the strength and hardness of the alloy, dependon both the precipitation temperature T2 and the aging time at this temperature.For some alloys, aging occurs spontaneously at room temperature over extendedtime periods.

The dependence of the growth of the precipitate � particles on time and temper-ature under isothermal heat treatment conditions may be represented by C-shapedcurves similar to those in Figure 11.9 for the eutectoid transformation in steels.However, it is more useful and convenient to present the data as tensile strength,yield strength, or hardness at room temperature as a function of the logarithm ofaging time, at constant temperature T2 . The behavior for a typical precipitation-hardenable alloy is represented schematically in Figure 11.31. With increasing time,the strength or hardness increases, reaches a maximum, and finally diminishes. Thisreduction in strength and hardness that occurs after long time periods is known asoveraging. The influence of temperature is incorporated by the superposition, ona single plot, of curves at a variety of temperatures.

11.11 MECHANISM OF HARDENING

Precipitation hardening is commonly employed with high-strength aluminum alloys.Although a large number of these alloys have different proportions and combina-

Solution heattreatment

Quench

Precipitationheat treatment

Time

Tem

pera

ture

T0

T2

T1

FIGURE 11.30 Schematictemperature-versus-time plotshowing both solution andprecipitation heat treatments forprecipitation hardening.

FIGURE 11.31 Schematicdiagram showing strengthand hardness as a functionof the logarithm of agingtime at constanttemperature during theprecipitation heattreatment.

Str

engt

h or

har

dnes

s

Zones

Overaging

Logarithm of aging time

�

�'�"

tions of alloying elements, the mechanism of hardening has perhaps been studiedmost extensively for the aluminum–copper alloys. Figure 11.32 presents the alumi-num-rich portion of the aluminum–copper phase diagram. The � phase is a substitu-tional solid solution of copper in aluminum, whereas the intermetallic compoundCuAl2 is designated the � phase. For an aluminum–copper alloy of, say, composition96 wt% Al–4 wt% Cu, in the development of this equilibrium � phase during theprecipitation heat treatment, several transition phases are first formed in a specificsequence. The mechanical properties are influenced by the character of the particlesof these transition phases. During the initial hardening stage (at short times, Figure11.31), copper atoms cluster together in very small and thin discs that are only oneor two atoms thick and approximately 25 atoms in diameter; these form at countlesspositions within the � phase. The clusters, sometimes called zones, are so smallthat they are really not regarded as distinct precipitate particles. However, withtime and the subsequent diffusion of copper atoms, zones become particles as theyincrease in size. These precipitate particles then pass through two transition phases(denoted as � and �), before the formation of the equilibrium � phase (Figure11.33c). Transition phase particles for a precipitation-hardened 7150 aluminumalloy are shown in the electron micrograph of the chapter-opening photograph forthis chapter.

The strengthening and hardening effects shown in Figure 11.31 result from theinnumerable particles of these transition and metastable phases. As noted in thefigure, maximum strength coincides with the formation of the � phase, which maybe preserved upon cooling the alloy to room temperature. Overaging results fromcontinued particle growth and the development of � and � phases.

The strengthening process is accelerated as the temperature is increased. Thisis demonstrated in Figure 11.34a, a plot of tensile strength versus the logarithm oftime for a 2014 aluminum alloy at several different precipitation temperatures.Ideally, temperature and time for the precipitation heat treatment should be de-signed to produce a hardness or strength in the vicinity of the maximum. Associatedwith an increase in strength is a reduction in ductility. This is demonstrated inFigure 11.34b for the same 2014 aluminum alloy at the several temperatures.


(CuAl2)

�

�

700

600

500

400

300

1200

1000

800

600

Tem

pera

ture

(�C

)

Tem

pera

ture

(�F

)

0 5 10 20 30

(Al)

0 10 20 30 40 50

L

Composition (at% Cu)

Composition (wt% Cu)

� �+

� + L� + L

FIGURE 11.32 Thealuminum-rich side ofthe aluminum–copper

phase diagram.(Adapted from J. L.

Murray, InternationalMetals Review, 30, 5,

1985. Reprinted bypermission of ASM

International.)

11.12 Miscellaneous Considerations ● 351

Not all alloys that satisfy the aforementioned conditions relative to compositionand phase diagram configuration are amenable to precipitation hardening. In addi-tion, lattice strains must be established at the precipitate–matrix interface. Foraluminum–copper alloys, there is a distortion of the crystal lattice structure aroundand within the vicinity of particles of these transition phases (Figure 11.33b). Duringplastic deformation, dislocation motions are effectively impeded as a result of thesedistortions, and, consequently, the alloy becomes harder and stronger. As the �phase forms, the resultant overaging (softening and weakening) is explained by areduction in the resistance to slip that is offered by these precipitate particles.

Alloys that experience appreciable precipitation hardening at room tempera-ture and after relatively short time periods must be quenched to and stored underrefrigerated conditions. Several aluminum alloys that are used for rivets exhibitthis behavior. They are driven while still soft, then allowed to age harden at thenormal ambient temperature. This is termed natural aging; artificial aging is carriedout at elevated temperatures.

11.12 MISCELLANEOUS CONSIDERATIONS

The combined effects of strain hardening and precipitation hardening may beemployed in high-strength alloys. The order of these hardening procedures isimportant in the production of alloys having the optimum combination ofmechanical properties. Normally, the alloy is solution heat treated and thenquenched. This is followed by cold working and finally by the precipitationhardening heat treatment. In the final treatment, little strength loss is sustainedas a result of recrystallization. If the alloy is precipitation hardened before coldworking, more energy must be expended in its deformation; in addition, crackingmay also result because of the reduction in ductility that accompanies theprecipitation hardening.

Most precipitation-hardened alloys are limited in their maximum service tem-peratures. Exposure to temperatures at which aging occurs may lead to a loss ofstrength due to overaging.

(a) (b) (c)

Solvent (Al) atom Solute (Cu)atom

�" Phase particle � Phase particle

FIGURE 11.33 Schematic depiction of several stages in the formation of theequilibrium precipitate (�) phase. (a) A supersaturated � solid solution. (b) Atransition, �, precipitate phase. (c) The equilibrium � phase, within the � matrixphase. Actual phase particle sizes are much larger than shown here.

C R Y S T A L L I Z A T I O N , M E L T I N G , A N D G L A S ST R A N S I T I O N P H E N O M E N A I N P O L Y M E R S

Phase transformation phenomena are important with respect to the design andprocessing of polymeric materials. In the succeeding sections we discuss three ofthese phenomena—viz., crystallization, melting, and the glass transition.

Crystallization is the process by which, upon cooling, an ordered (i.e., crystal-line) solid phase is produced from a liquid melt having a highly random molecularstructure. The melting transformation is the reverse process that occurs when apolymer is heated. The glass-transition phenomenon occurs with amorphous ornoncrystallizable polymers which, when cooled from a liquid melt, become rigid


Tens

ile s

tren

gth

(ksi

)70

80

60

50

40

30

400

300

200

500

1 min 1 h 1 day 1 month 1 year

1 min 1 h 1 day 1 month 1 year

Tens

ile s

tren

gth

(MP

a)

10

30

20

0

Duc

tilit

y (%

EL

in 2

in.

or 5

0 m

m)

121°C(250°F)

121°C(250°F)

149°C(300°F)

149°C(300°F)

204°C(400°F)

204°C(400°F)

260°C(500°F)

260°C(500°F)

Duration of precipitation heat treatment (h)

0 10–2 10–1 1 10 102 103 104

(a)

Duration of precipitation heat treatment (h)

0 10–2 10–1 1 10 102 103 104

(b)

FIGURE 11.34 Theprecipitation hardening

characteristics of a 2014aluminum alloy (0.9

wt% Si, 4.4 wt% Cu, 0.8wt% Mn, 0.5 wt% Mg)at four different aging

temperatures: (a)tensile strength, and (b)

ductility (%EL).(Adapted from MetalsHandbook: Properties

and Selection:Nonferrous Alloys and

Pure Metals, Vol. 2, 9thedition, H. Baker,Managing Editor,

American Society forMetals, 1979, p. 41.)

11.13 Crystallization ● 353

solids yet retain the disordered molecular structure that is characteristic of theliquid state. Of course, alterations of physical and mechanical properties attendcrystallization, melting, and the glass transition. Furthermore, for semicrystallinepolymers, crystalline regions will experience melting (and crystallization), whilenoncrystalline areas pass through the glass transition.

11.13 CRYSTALLIZATION

An understanding of the mechanism and kinetics of polymer crystallization is impor-tant inasmuch as the degree of crystallinity influences the mechanical and thermalproperties of these materials. The crystallization of a molten polymer occurs bynucleation and growth processes, topics discussed in the context of phase transfor-mations for metals in Section 11.3. For polymers, upon cooling through the meltingtemperature, nuclei form wherein small regions of the tangled and random mole-cules become ordered and aligned in the manner of chain-folded layers, Figure4.13. At temperatures in excess of the melting temperature, these nuclei are unstabledue to the thermal atomic vibrations that tend to disrupt the ordered moleculararrangements. Subsequent to nucleation and during the crystallization growth stage,nuclei grow by the continued ordering and alignment of additional molecular chainsegments; that is, the chain-folded layers increase in lateral dimensions, or, forspherulitic structures (Figure 4.14) there is an increase in spherulite radius.

The time dependence of crystallization is the same as for many solid-statetransformations—Figure 11.1; that is, a sigmoidal-shaped curve results when fractiontransformation (i.e., fraction crystallized) is plotted versus the logarithm of time(at constant temperature). Such a plot is presented in Figure 11.35 for the crystalliza-tion of polypropylene at three temperatures. Mathematically, fraction crystallizedy is a function of time t according to the Avrami equation, Equation 11.1, as

y � 1 � exp(�kt n) (11.1)

where k and n are time-independent constants, which values depend on the crys-tallizing system. Normally, the extent of crystallization is measured by specimenvolume changes since there will be a difference in volume for liquid and crystallizedphases. Rate of crystallization may be specified in the same manner as for the

Nor

mal

ized

fra

ctio

n cr

ysta

llize

d

1.0

0.8

0.6

0.4

0.2

0.0

Time (min)(Logarithmic scale)

140°C 150°C 160°C

10 102 103 104

FIGURE 11.35 Plot ofnormalized fractioncrystallized versus thelogarithm of time forpolypropylene at constanttemperatures of 140�C,150�C, and 160�C.(Adapted from P. Parriniand G. Corrieri,Makromol. Chem., 62, 83,1963. Reprinted bypermission of Huthig &Wepf Publishers, Zug,Switzerland.)

transformations discussed in Section 11.3, and according to Equation 11.2; that is,rate is equal to the reciprocal of time required for crystallization to proceed to 50%completion. This rate is dependent on crystallization temperature (Figure 11.35)and also on the molecular weight of the polymer; rate decreases with increasingmolecular weight.

For polypropylene, the attainment of 100% crystallinity is not possible. There-fore, in Figure 11.35, the vertical axis is scaled as ‘‘normalized fraction crystallized.’’A value of 1.0 for this parameter corresponds to the highest level of crystallizationthat is achieved during the tests, which, in reality, is less than complete crystallization.

11.14 MELTING

The melting of a polymer crystal corresponds to the transformation of a solidmaterial, having an ordered structure of aligned molecular chains, to a viscousliquid in which the structure is highly random; this phenomenon occurs, uponheating, at the melting temperature, Tm . There are several features distinctive tothe melting of polymers that are not normally observed with metals and ceramics;these are consequences of the polymer molecular structures and lamellar crystallinemorphology. First of all, melting of polymers takes place over a range of tempera-tures; this phenomenon is discussed in more detail below. In addition, the meltingbehavior depends on the history of the specimen, in particular the temperatureat which it crystallized. The thickness of chain-folded lamellae will depend oncrystallization temperature; the thicker the lamellae, the higher the melting tempera-ture. And finally, the apparent melting behavior is a function of the rate of heating;increasing this rate results in an elevation of the melting temperature.

�As Section 8.18 notes, polymeric materials are responsive to heat treatmentsthat produce structural and property alterations. An increase in lamellar thicknessmay be induced by annealing just below the melting temperature. Annealing alsoraises the melting temperature of the polymer.�

11.15 THE GLASS TRANSITION

The glass transition occurs in amorphous (or glassy) and semicrystalline polymers,and is due to a reduction in motion of large segments of molecular chains withdecreasing temperature. Upon cooling, the glass transition corresponds to the grad-ual transformation from a liquid to a rubbery material, and finally, to a rigid solid.The temperature at which the polymer experiences the transition from rubbery torigid states is termed the glass transition temperature, Tg . Of course, this sequenceof events occurs in the reverse order when a rigid glass at a temperature below Tg

is heated. In addition, abrupt changes in other physical properties accompanythis glass transition: e.g., stiffness �(Figure 7.28),� heat capacity, and coefficient ofthermal expansion.

11.16 MELTING AND GLASS TRANSITION

TEMPERATURES

Melting and glass transition temperatures are important parameters relative to in-service applications of polymers. They define, respectively, the upper and lowertemperature limits for numerous applications, especially for semicrystalline poly-


11.17 Factors That Influence Melting and Glass Transition Temperatures (CD-ROM) ● 355

mers. The glass transition temperature may also define the upper use temperaturefor glassy amorphous materials. Furthermore, Tm and Tg also influence the fabrica-tion and processing procedures for polymers and polymer-matrix composites. �Theseissues are discussed in other chapters.�

The temperatures at which melting and/or the glass transition occur for apolymer are determined in the same manner as for ceramic materials—from a plotof specific volume (the reciprocal of density) versus temperature. Figure 11.36 issuch a plot, wherein curves A and C, for amorphous and crystalline polymers,respectively.1 For the crystalline material, there is a discontinuous change in specificvolume at the melting temperature Tm . The curve for the totally amorphous materialis continuous but it experiences a slight decrease in slope at the glass transitiontemperature, Tg . The behavior is intermediate between these extremes for a semi-crystalline polymer (curve B), in that both melting and glass transition phenomenaare observed; Tm and Tg are properties of the respective crystalline and amorphousphases in this semicrystalline material. As discussed above, the behaviors repre-sented in Figure 11.36 will depend on the rate of cooling or heating. Representativemelting and glass transition temperatures of a number of polymers are containedin Table 11.1 and Appendix E.

11.17 FACTORS THAT INFLUENCE MELTING AND

GLASS TRANSITION TEMPERATURES (CD-ROM)

Spe

cifi

c vo

lum

e

Temperature

Liquid

A

B

C

Tg Tm

Glass

Semicrystalline solid

Crystalline solid

FIGURE 11.36 Specific volume versustemperature, upon cooling from theliquid melt, for totally amorphous(curve A), semicrystalline (curve B),and crystalline (curve C) polymers.

1 It should be noted that no engineering polymer is 100% crystalline; curve C is includedin Figure 11.36 to illustrate the extreme behavior that would be displayed by a totallycrystalline material.

S U M M A R YThe first set of discussion topics for this chapter has included phase transformationsin metals—modifications in the phase structure or microstructure—and how theyaffect mechanical properties. Some transformations involve diffusional phenomena,which means that their progress is time dependent. For these, some of the basickinetic concepts were explored, including the relation between degree of reactioncompletion and time, the notion of transformation rate, and how rate dependson temperature.

As a practical matter, phase diagrams are severely restricted relative to trans-formations in multiphase alloys, because they provide no information as to phasetransformation rates. The element of time is incorporated into both isothermaltransformation and continuous cooling transformation diagrams; transformationprogress as a function of temperature and elapsed time is expressed for a spe-cific alloy at constant temperature �and for continuous cooling� treatments, respec-tively. Diagrams of both types were presented for iron–carbon steel alloys,and their utility with regard to the prediction of microstructural products was dis-cussed.

Several microconstituents are possible for steels, the formation of which de-pends on composition and heat treatment. These microconstituents include fineand coarse pearlite, and bainite, which are composed of ferrite and cementitephases and result from the decomposition of austenite via diffusional processes. Aspheroidite microstructure (also consisting of ferrite and cementite phases) may beproduced when a steel specimen composed of any of the preceding microstructuresis heat treated at a temperature just below the eutectoid. The mechanical characteris-tics of pearlitic, bainitic, and spheroiditic steels were compared and also explainedin terms of their microconstituents.

Martensite, yet another transformation product in steels, results when austen-ite is cooled very rapidly. It is a metastable and single-phase structure that maybe produced in steels by a diffusionless and almost instantaneous transformationof austenite. Transformation progress is dependent on temperature rather thantime, and may be represented on both isothermal �and continuous cooling�transformation diagrams. Furthermore, alloying element additions retard theformation rate of pearlite and bainite, thus rendering the martensitic transforma-tion more competitive. Mechanically, martensite is extremely hard; applicability,


Table 11.1 Melting and Glass Transition Temperatures forSome of the More Common Polymeric Materials

Glass Transition MeltingTemperature Temperature

Material [ �C ( �F)] [ �C ( �F)]

Polyethylene (low density) �110 (�165) 115 (240)Polytetrafluoroethylene �97 (�140) 327 (620)Polyethylene (high density) �90 (�130) 137 (279)Polypropylene �18 (0) 175 (347)Nylon 6,6 57 (135) 265 (510)Polyester (PET) 69 (155) 265 (510)Polyvinyl chloride 87 (190) 212 (415)Polystyrene 100 (212) 240 (465)Polycarbonate 150 (300) 265 (510)

References ● 357

however, is limited by its brittleness. A tempering heat treatment increases theductility at some sacrifice of strength and hardness. During tempering, martensitetransforms to tempered martensite, which consists of the equilibrium ferrite andcementite phases. Embrittlement of some steel alloys results when specificalloying and impurity elements are present, and upon tempering within a definitetemperature range.

Some alloys are amenable to precipitation hardening, that is, to strengtheningby the formation of very small particles of a second, or precipitate, phase.Control of particle size, and subsequently the strength, is accomplished by twoheat treatments. For the second or precipitation treatment at constant temperature,strength increases with time to a maximum and decreases during overaging. Thisprocess is accelerated with rising temperature. The strengthening phenomenonis explained in terms of an increased resistance to dislocation motion by latticestrains, which are established in the vicinity of these microscopically smallprecipitate particles.

Relative to polymeric materials, the molecular mechanics of crystallization,melting, and the glass transition were discussed. The manner in which meltingand glass transition temperatures are determined was outlined; these parametersare important relative to the temperature range over which a particular polymermay be utilized and processed. �The magnitudes of Tm and Tg increase withincreasing chain stiffness; stiffness is enhanced by the presence of chain doublebonds and side groups that are either bulky or polar. Molecular weight anddegree of branching also affect Tm and Tg .�

I M P O R T A N T T E R M S A N D C O N C E P T S

Alloy steelArtificial agingAthermal transformationBainiteCoarse pearliteContinuous cooling transfor-

mation diagramFine pearliteGlass transition tempera-

ture

Isothermal transformationdiagram

KineticsMartensiteMelting temperatureNatural agingNucleationOveragingPhase transformationPlain carbon steel

Precipitation hardeningPrecipitation heat treatmentSolution heat treatmentSpheroiditeSupercoolingSuperheatingTempered martensiteThermally activated transfor-

mationTransformation rate

R E F E R E N C E S

Atkins, M., Atlas of Continuous Cooling Transfor-mation Diagrams for Engineering Steels, Brit-ish Steel Corporation, Sheffield, England,1980.

Atlas of Isothermal Transformation and CoolingTransformation Diagrams, American Societyfor Metals, Metals Park, OH, 1977.

Billmeyer, F. W., Jr., Textbook of Polymer Sci-ence, 3rd edition, Wiley-Interscience, NewYork, 1984. Chapter 10.

Brooks, C. R., Principles of the Heat Treatmentof Plain Carbon and Low Alloy Steels, ASMInternational, Materials Park, OH, 1996.

Brophy, J. H., R. M. Rose, and J. Wulff, TheStructure and Properties of Materials, Vol. II,Thermodynamics of Structure, John Wiley &Sons, New York, 1964. Reprinted by Bookson Demand, Ann Arbor, MI.

Porter, D. A. and K. E. Easterling, Phase Trans-formations in Metals and Alloys, Van Nos-


trand Reinhold (International) Co. Ltd.,Workingham, Berkshire, England, 1981. Re-printed by Chapman and Hall, New York,1992.

Shewmon, P. G., Transformations in Metals,McGraw-Hill Book Company, New York,1969. Reprinted by Williams Book Company,Tulsa, OK.

Vander Voort, G. (Editor), Atlas of Time–

Temperature Diagrams for Irons and Steels,ASM International, Materials Park, OH, 1991.

Vander Voort, G. (Editor), Atlas of Time–Temperature Diagrams for Nonferrous Alloys,ASM International, Materials Park, OH, 1991.

Young, R. J. and P. Lovell, Introduction to Poly-mers, 2nd edition, Chapman and Hall, Lon-don, 1991.

Q U E S T I O N S A N D P R O B L E M S

Note: To solve those problems having an asterisk (*) by their numbers, consultation of supplementarytopics [appearing only on the CD-ROM (and not in print)] will probably be necessary.

11.1 Name the two stages involved in the for-mation of particles of a new phase. Brieflydescribe each.

11.2 For some transformation having kineticsthat obey the Avrami equation (Equation11.1), the parameter n is known to havea value of 1.7. If, after 100 s, the reactionis 50% complete, how long (total time)will it take the transformation to go to99% completion?

11.3 Compute the rate of some reaction thatobeys Avrami kinetics, assuming that theconstants n and k have values of 3.0 and7 � 10�3, respectively, for time expressedin seconds.

11.4 It is known that the kinetics of recrystalli-zation for some alloy obey the Avramiequation and that the value of n in theexponential is 2.5. If, at some temperature,the fraction recrystallized is 0.40 after 200min, determine the rate of recrystallizationat this temperature.

11.5 The kinetics of the austenite-to-pearlitetransformation obey the Avrami relation-ship. Using the fraction transformed–timedata given below, determine the total timerequired for 95% of the austenite to trans-form to pearlite:

Fraction Transformed Time (s)0.2 12.60.8 28.2

11.6 Below, the fraction recrystallized–timedata for the recrystallization at 600�C ofa previously deformed steel are tabulated.Assuming that the kinetics of this processobey the Avrami relationship, determinethe fraction recrystallized after a total timeof 22.8 min.

Fraction Recrystallized Time (min)0.20 13.10.70 29.1

11.7 (a) From the curves shown in Figure 11.2and using Equation 11.2, determine the rateof recrystallization for pure copper at theseveral temperatures.

(b) Make a plot of ln(rate) versus the recip-rocal of temperature (in K�1), and deter-mine the activation energy for this recrys-tallization process. (See Section 6.5.)

(c) By extrapolation, estimate the lengthof time required for 50% recrystallizationat room temperature, 20�C (293 K).

11.8 In terms of heat treatment and the develop-ment of microstructure, what are two majorlimitations of the iron–iron carbide phasediagram?

11.9 (a) Briefly describe the phenomena of su-perheating and supercooling.

(b) Why do they occur?

11.10 Suppose that a steel of eutectoid composi-tion is cooled to 550�C (1020�F) from 760�C

Questions and Problems ● 359

(1400�F) in less than 0.5 s and held at thistemperature.

(a) How long will it take for the austenite-to-pearlite reaction to go to 50% comple-tion? To 100% completion?

(b) Estimate the hardness of the alloy thathas completely transformed to pearlite.

11.11 Briefly explain why the reaction rate forthe austenite-to-pearlite transformation, asdetermined from Figure 11.5 and utilizingEquation 11.2, decreases with increasingtemperature, in apparent contradictionwith Equation 11.3.

11.12 Briefly cite the differences between pearl-ite, bainite, and spheroidite relative to mi-crostructure and mechanical properties.

11.13 What is the driving force for the formationof spheroidite?

11.14 Using the isothermal transformation dia-gram for an iron–carbon alloy of eutectoidcomposition (Figure 11.14), specify the na-ture of the final microstructure (in terms ofmicroconstituents present and approximatepercentages of each) of a small specimenthat has been subjected to the followingtime–temperature treatments. In each caseassume that the specimen begins at 760�C(1400�F) and that it has been held at thistemperature long enough to have achieveda complete and homogeneous austeniticstructure.

(a) Cool rapidly to 700�C (1290�F), holdfor 104 s, then quench to room temperature.

(b) Reheat the specimen in part a to 700�C(1290�F) for 20 h.

(c) Rapidly cool to 600�C (1110�F), holdfor 4 s, rapidly cool to 450�C (840�F), holdfor 10 s, then quench to room temperature.

(d) Cool rapidly to 400�C (750�F), hold for2 s, then quench to room temperature.

(e) Cool rapidly to 400�C (750�F), hold for20 s, then quench to room temperature.

(f) Cool rapidly to 400�C (750�F), hold for200 s, then quench to room temperature.

(g) Rapidly cool to 575�C (1065�F), holdfor 20 s, rapidly cool to 350�C (660�F), holdfor 100 s, then quench to room temperature.

(h) Rapidly cool to 250�C (480�F), hold for100 s, then quench to room temperature inwater. Reheat to 315�C (600�F) for 1 h andslowly cool to room temperature.

11.15 Make a copy of the isothermal transforma-tion diagram for an iron–carbon alloy ofeutectoid composition (Figure 11.14) andthen sketch and label on this diagram time–temperature paths to produce the followingmicrostructures:

(a) 100% coarse pearlite.

(b) 100% tempered martensite.

(c) 50% coarse pearlite, 25% bainite, and25% martensite.

11.16 Using the isothermal transformation dia-gram for a 0.45 wt% C steel alloy (Figure11.38), determine the final microstructure(in terms of just the microconstituents pres-ent) of a small specimen that has been sub-jected to the following time–temperaturetreatments. In each case assume that thespecimen begins at 845�C (1550�F), and thatit has been held at this temperature longenough to have achieved a complete andhomogeneous austenitic structure.

(a) Rapidly cool to 250�C (480�F), hold for103 s, then quench to room temperature.

(b) Rapidly cool to 700�C (1290�F), holdfor 30 s, then quench to room temperature.

(c) Rapidly cool to 400�C (750�F), hold for500 s, then quench to room temperature.

(d) Rapidly cool to 700�C (1290�F), holdat this temperature for 105 s, then quenchto room temperature.

(e) Rapidly cool to 650�C (1200�F), hold atthis temperature for 3 s, rapidly cool to400�C (750�F), hold for 10 s, then quenchto room temperature.

(f) Rapidly cool to 450�C (840�F), hold for10 s, then quench to room temperature.

(g) Rapidly cool to 625�C (1155�F), holdfor 1 s, then quench to room temperature.

(h) Rapidly cool to 625�C (1155�F), holdat this temperature for 10 s, rapidly cool to400�C (750�F), hold at this temperature for5 s, then quench to room temperature.


FIGURE 11.38 Isother-mal transformation dia-gram for a 0.45 wt% Ciron–carbon alloy: A,

austenite; B, bainite; F,proeutectoid ferrite; M,martensite; P, pearlite.

(Adapted from Atlas ofTime-Temperature Dia-

grams for Irons andSteels, G. F. Vander

Voort, Editor, 1991. Re-printed by permission

of ASM International,Materials Park, OH.)

11.17 For parts a, c, d, f, and h of Problem 11.16,determine the approximate percentages ofthe microconstituents that form.

11.18 Make a copy of the isothermal transforma-tion diagram for a 0.45 wt% C iron–carbonalloy (Figure 11.38), and then sketch andlabel on this diagram the time–temperaturepaths to produce the following microstruc-tures:

(a) 42% proeutectoid ferrite and 58%coarse pearlite.

(b) 50% fine pearlite and 50% bainite.

(c) 100% martensite.

(d) 50% martensite and 50% austenite.

11.19* Name the microstructural products of eu-tectoid iron–carbon alloy (0.76 wt% C)specimens that are first completely trans-formed to austenite, then cooled to roomtemperature at the following rates: (a)200�C/s, (b) 100�C/s, and (c) 20�C/s.

11.20* Figure 11.39 shows the continuous coolingtransformation diagram for a 1.13 wt% Ciron–carbon alloy. Make a copy of this fig-

ure and then sketch and label continuouscooling curves to yield the following micro-structures:

(a) Fine pearlite and proeutectoid ce-mentite.

(b) Martensite.

(c) Martensite and proeutectoid cementite.

(d) Coarse pearlite and proeutectoid ce-mentite.

(e) Martensite, fine pearlite, and proeutec-toid cementite.

11.21 Cite two major differences between mar-tensitic and pearlitic transformations.

11.22* Cite two important differences betweencontinuous cooling transformation dia-grams for plain carbon and alloy steels.

11.23* Briefly explain why there is no bainite trans-formation region on the continuous coolingtransformation diagram for an iron–carbonalloy of eutectoid composition.

11.24* Name the microstructural products of 4340alloy steel specimens that are first com-pletely transformed to austenite, then

Time (s)

A

A

A + P

A + F

PB

A + B

50%

Tem

pera

ture

(°C

)

Tem

pera

ture

(°F)

M (start)

M (50%)

M (90%)

1600

1400

1200

1000

800

600

400

200

900

800

700

600

500

400

300

200

100

00.1 1 10 102 103 104 105


800

600

400

200

00.1

Time (s)

10 103 105

A C

Tem

pera

ture

(°C

)

AP

A M

FIGURE 11.39 Continuouscooling transformation diagramfor a 1.13 wt% C iron–carbonalloy.

cooled to room temperature at the follow-ing rates: (a) 10�C/s, (b) 1�C/s, (c) 0.1�C/s,and (d) 0.01�C/s.

11.25* Briefly describe the simplest continuouscooling heat treatment procedure thatwould be used in converting a 4340 steelfrom one microstructure to another.

(a) (Martensite � bainite) to (ferrite �pearlite).

(b) (Martensite � bainite) to spheroidite.

(c) (Martensite � bainite) to (martensite �bainite � ferrite).

11.26* On the basis of diffusion considerations,explain why fine pearlite forms for the mod-erate cooling of austenite through the eu-tectoid temperature, whereas coarse pearl-ite is the product for relatively slowcooling rates.

11.27 (a) Which is the more stable, the pearliticor the spheroiditic microstructure?

(b) Why?

11.28 Briefly explain why fine pearlite is harderand stronger than coarse pearlite, which inturn is harder and stronger than spher-oidite.

11.29 Cite two reasons why martensite is so hardand brittle.

11.30 Rank the following iron–carbon alloys andassociated microstructures from the highestto the lowest tensile strength: (a) 0.25 wt%Cwith spheroidite, (b) 0.25 wt%C with coarsepearlite, (c) 0.6 wt%C with fine pearlite,and (d) 0.6 wt%C with coarse pearlite. Jus-tify this ranking.

11.31 Briefly explain why the hardness of tem-pered martensite diminishes with temper-ing time (at constant temperature) and withincreasing temperature (at constant tem-pering time).

11.32* Briefly describe the simplest heat treatmentprocedure that would be used in convertinga 0.76 wt% C steel from one microstructureto the other, as follows:

(a) Spheroidite to tempered martensite.

(b) Tempered martensite to pearlite.

(c) Bainite to martensite.

(d) Martensite to pearlite.

(e) Pearlite to tempered martensite.

(f) Tempered martensite to pearlite.

(g) Bainite to tempered martensite.

(h) Tempered martensite to spheroidite.

11.33 (a) Briefly describe the microstructural dif-ference between spheroidite and tem-pered martensite.


(b) Explain why tempered martensite ismuch harder and stronger.

11.34 Estimate the Rockwell hardnesses for spec-imens of an iron–carbon alloy of eutectoidcomposition that have been subjected tothe heat treatments described in parts b, d,f, g, and h of Problem 11.14.

11.35 Estimate the Brinell hardnesses for speci-mens of a 0.45 wt% C iron–carbon alloy thathave been subjected to the heat treatmentsdescribed in parts a, d, and h of Problem11.16.

11.36* Determine the approximate tensilestrengths for specimens of a eutectoid iron–carbon alloy that have experienced the heattreatments described in parts a and c ofProblem 11.19.

11.37 For a eutectoid steel, describe isothermalheat treatments that would be required toyield specimens having the following Rock-well hardnesses: (a) 93 HRB, (b) 40 HRC,and (c) 27 HRC.

11.38 The room-temperature tensile strengths ofpure copper and pure silver are 209 MPaand 125 MPa, respectively.

(a) Make a schematic graph of the room-temperature tensile strength versus compo-sition for all compositions between purecopper and pure silver.

(b) On this same graph schematically plottensile strength versus composition at600�C.

(c) Explain the shapes of these two curves,as well as any differences between them.

11.39 Compare precipitation hardening (Sections11.10 and 11.11) and the hardening of steelby quenching and tempering (Sections 11.5,11.6, and 11.8) with regard to

(a) The total heat treatment procedure.

(b) The microstructures that develop.

(c) How the mechanical properties changeduring the several heat treatment stages.

11.40 What is the principal difference betweennatural and artificial aging processes?

11.41* For each of the following pairs of polymers,plot and label schematic specific volume-

versus-temperature curves on the samegraph (i.e., make separate plots for parts a,b, and c):

(a) Spherulitic polypropylene, of 25% crys-tallinity, and having a weight-averagemolecular weight of 75,000 g/mol; spheru-litic polystyrene, of 25% crystallinity, andhaving a weight-average molecular weightof 100,000 g/mol.

(b) Graft poly(styrene-butadiene) copoly-mer with 10% of available sites crosslinked;random poly(styrene-butadiene) copoly-mer with 15% of available sites crosslinked.

(c) Polyethylene having a density of 0.985g/cm3 and a number-average degree of po-lymerization of 2500; polyethylene havinga density of 0.915 g/cm3 and a degree ofpolymerization of 2000.

11.42* For each of the following pairs of polymers,do the following: (1) state whether or notit is possible to determine whether onepolymer has a higher melting temperaturethan the other; (2) if it is possible, notewhich has the higher melting temperatureand then cite reason(s) for your choice; and(3) if it is not possible to decide, thenstate why.

(a) Isotactic polystyrene that has a densityof 1.12 g/cm3 and a weight-average molecu-lar weight of 150,000 g/mol; syndiotacticpolystyrene that has a density of 1.10 g/cm3

and a weight-average molecular weight of125,000 g/mol.

(b) Linear polyethylene that has a number-average degree of polymerization of 5,000;linear and isotactic polypropylene that hasa number-average degree of polymeriza-tion of 6,500.

(c) Branched and isotactic polystyrene thathas a weight-average degree of polymer-ization of 4,000; linear and isotactic poly-propylene that has a weight-average degreeof polymerization of 7,500.

11.43* Make a schematic plot showing how themodulus of elasticity of an amorphous poly-mer depends on the glass transition temper-ature. Assume that molecular weight isheld constant.

and a minimum ductility of 52%RA. Is suchan alloy possible? If so, what will be its com-position and microstructure (coarse and finepearlites and spheroidite are alternatives)?If this is not possible, explain why.

11.D4 (a) For a 1080 steel that has been waterquenched, estimate the tempering time at425�C (800�F) to achieve a hardness of 50HRC.

(b) What will be the tempering time at315�C (600�F) necessary to attain thesame hardness?

11.D5 An alloy steel (4340) is to be used in anapplication requiring a minimum tensilestrength of 1380 MPa (200,000 psi) and aminimum ductility of 43%RA. Oil quench-ing followed by tempering is to be used.Briefly describe the tempering heattreatment.

11.D6 Is it possible to produce an oil-quenchedand tempered 4340 steel that has a minimumyield strength of 1400 MPa (203,000 psi)and a ductility of at least 42%RA? If this ispossible, describe the tempering heat treat-ment. If it is not possible, explain why.

11.D7 Copper-rich copper–beryllium alloys areprecipitation hardenable. After consulting


Tem

pera

ture

(°C

)

1000

800

600

400

0

(Cu)

1 2 3 4

Composition (wt% Be)

Composition (at% Be)

5 10 15 20

Liquid

866°C

~620°C

1� �+

2� �+

� + L

�

0

FIGURE 11.40 The copper-richside of the copper–berylliumphase diagram. (Adapted fromBinary Alloy Phase Diagrams,2nd edition, Vol. 2, T. B.Massalski, Editor-in-Chief, 1990.Reprinted by permission ofASM International, MaterialsPark, OH.)

11.44 Name the following polymer(s) that wouldbe suitable for the fabrication of cups tocontain hot coffee: polyethylene, polypro-pylene, polyvinyl chloride, PET polyester,and polycarbonate. Why?

11.45 Of those polymers listed in Table 11.1,which polymer(s) would be best suited foruse as ice cube trays? Why?

Design Problems

11.D1 Is it possible to produce an iron–carbonalloy of eutectoid composition that has aminimum hardness of 90 HRB and a mini-mum ductility of 35%RA? If so, describethe continuous cooling heat treatment towhich the alloy would be subjected toachieve these properties. If it is not possible,explain why.

11.D2 Is it possible to produce an iron–carbonalloy that has a minimum tensile strengthof 690 MPa (100,000 psi) and a minimumductility of 40%RA? If so, what will be itscomposition and microstructure (coarse andfine pearlites and spheroidite are alterna-tives)? If this is not possible, explain why.

11.D3 It is desired to produce an iron–carbon alloythat has a minimum hardness of 175 HB


the portion of the phase diagram (Figure11.40), do the following:

(a) Specify the range of compositions overwhich these alloys may be precipitationhardened.

(b) Briefly describe the heat-treatment pro-cedures (in terms of temperatures) thatwould be used to precipitation harden analloy having a composition of your choos-ing, yet lying within the range given forpart a.

11.D8 A solution heat-treated 2014 aluminumalloy is to be precipitation hardened to have

a minimum tensile strength of 450 MPa(65,250 psi) and a ductility of at least15%EL. Specify a practical precipitationheat treatment in terms of temperature andtime that would give these mechanical char-acteristics. Justify your answer.

11.D9 Is it possible to produce a precipitation-hardened 2014 aluminum alloy having aminimum tensile strength of 425 MPa(61,625 psi) and a ductility of at least12%EL? If so, specify the precipitation heattreatment. If it is not possible, explain why.

Documents

11 / Phase Transformations - Amazon S3s3.amazonaws.com/zanran_storage/mehr.sharif.ir/ContentPages/... · 11 / Phase Transformations T op: ... PHASE TRANSFORMATIONS IN METALS ... The