10-1

C H A P T E R 1 0

K I N E T I C S O F P H A S E T R A N S F O R M A T I O N S

10.1 PHASE TRANSFORMATIONS 10.1.1 The Dr iv ing Force for

Transformat ion 10.1.2 Nucleat ion 10.1.3 Growth 10.1.4 K inet ics of Phase

Transformat ion

10.2 ISOTHERMAL TRANSFORMATION DIAGRAMS 10.2.1 Transformat ions in Eutecto id

Stee l 10.2.2 Hypoeutecto id and

Hypereutecto id Stee ls

10.3 CONTINUOUS COOLING TRANSFORMATION DIAGRAMS 10.3.1 Cont inuous Cool ing in Stee ls

10-2

10.1 PHASE TRANSFORMATIONS

• Phase transformations are not instantaneous. The

transformation from one phase to another involves a

change in composition, crystal structure and/or the

number of phases present. This is achieved through the

rearrangement of atoms (often via diffusion), which

requires a finite amount of time.

• The microstructures characterized by the equilibrium phase

diagrams are obtained only when the temperature is

changed extremely slowly, such that a state of equilibrium

is maintained at all times. The phase diagrams do not

indicate the time required for equilibrium microstructures

to develop.

• Under non-equilibrium conditions, the resultant micro-

structure depends on the rate of heating/cooling and the

actual temperature at which phase transformations occur.

These factors also determine the rate of phase

transformation (and hence, the time required).

• The desired microstructure may be therefore be tailored by

controlling the rate (kinetics) of phase transformations.

10-3

10.1.1 The Driving Force for Transformation

• The thermodynamic state of a system is defined by the

Gibbs free energy, G, which is a measure of the internal

energy, as well as the randomness in the system.

• Equilibrium is a state of no spontaneous change, at which

G is a minimum.

• Phase transformations are only possible if such changes

lower G, i.e. !G < 0.

• Consider the solidification of water into ice (Fig. 10.1-1).

Fig. 10.1-1 Gibbs free energy as a function of temperature for ice and water.

10-4

• At the equilibrium transformation temperature, TE = 0°C,

the free energy of ice and water are equal (Gice = Gwater "

!G = 0). A change from water to ice or vice versa would

not lower G, so no spontaneous change occurs.

• When T < TE, Gice < Gwater, so ice is the stable form. The

system can lower its free energy by changing water into

ice (Gice - Gwater < 0 " !G < 0). The decrease in free energy,

!G, becomes larger and larger as T falls further and further

below TE. TE – T = !T is known as the undercooling.

• !G may be thought of as the ‘driving force’ for the

transformation. The greater the degree of undercooling,

!T, the larger the magnitude of !G, and the higher the

driving force.

• Generally, a phase transformation begins with the

nucleation of the new phase within the parent phase,

followed by the growth of the new phase.

10-5

10.1.2 Nucleation

• Consider the nucleation of a solid in a liquid during

solidification. The atoms in a liquid are in a state of

continual random movement. From time to time, a small

group of atoms will, purely by chance, come together to

form a tiny crystal nucleus (Fig. 10.1-2).

Fig. 10.1-2 The random clustering of neighbouring atoms to form a crystal nucleus.

• The nucleus must be of critical size, r*, or larger, in order

to remain stable and grow; nuclei smaller than r* would

simply redissolve back into the liquid.

• An increase in the degree of undercooling, !T, decreases

the critical nucleus size, r*, required. Since there is a higher

probability of atoms randomly clustering in small groups

rather than large ones, nucleation becomes easier and the

nucleation rate is faster with larger !T.

10-6

• However, the random clustering of atoms requires the

local diffusion of atoms, the rate of which decreases with

temperature.

• The net nucleation rate is therefore a balance between the

ease of nucleation and atomic mobility (Fig. 10.1-3). The

maximum nucleation rate occurs in the temperature range

where the driving force for nucleation and diffusion are

both significant.

Fig. 10.1-3 Variation of the net nucleation rate with temperature.

• Nucleation occurs preferentially at sites such as walls of

containers or suspended impurities in a liquid. In solid-to-

solid phase transformations, preferential nucleation sites

include grain boundaries, dislocations, phase boundaries,

and the surfaces of impurities and precipitates.

10-7

10.1.3 Growth

• Once a nucleus of critical size or larger forms, spontaneous

and sustained growth of the nucleus occurs (Fig. 10.1-4).

Growth involves the transport of atoms to the nucleus and

the rearrangement of these atoms into the crystal structure

of the nucleus. These processes are diffusion-controlled,

and the growth rate increases with temperature.

Fig. 10.1-4 Growth of a stable nucleus.

10.1.4 Kinetics of Phase Transformation

• The overall rate (or kinetics) of phase transformation

depends on both nucleation and growth rates (Fig. 10.1-5).

Fig. 10.1-5 (a) Variation of rate of phase transformation with temperature. (b) Corresponding time-temperature-transformation curve or C-curve (Note: time, t #

1

Rate).

10-8

• The progress of a phase transformation with time at any

given temperature is described by a sigmoidal (S-shaped)

curve (Fig. 10.1-6).

Fig. 10.1-6 The fraction of transformed material as a function of time at any

given temperature.

• Characteristics of phase transformation:

1. An incubation period is required for nucleation. There is

no measurable phase transformation during this period.

2. Transformation is slow initially as nuclei form.

3. Once nucleated, the new phase begins to grow at the

expense of the parent phase, and there is a rapid

increase in the amount of new phase present.

4. The growth rate of the new phase decreases eventually

because of the depletion of solute atoms or physical

impingement of the growing phase.

10-9

10.2 ISOTHERMAL TRANSFORMATION DIAGRAMS • Equilibrium phase diagrams define only the microstructures

that develop under equilibrium conditions. In practical situations, the rate of heating/cooling and the actual temperature of transformation (undercooling) determine the resultant microstructure, which may be different from that characterized by the equilibrium phase diagrams.

• Isothermal transformation (IT) diagrams, or time-

temperature-transformation (TTT) diagrams, show the progress of transformation with time, and the final microstructure (including non-equilibrium phases).

• TTT diagrams are derived from a series of experimental

sigmoidal curves at different temperatures (Fig. 10.2-1); each diagram is valid for one alloy composition only.

Fig. 10.2-1

Construction of a TTT diagram from a series

ofexperimental sigmoidal curves at

different temperatures.

10-10

10.2.1 Transformations in Eutectoid Steel

• Recall the eutectoid reaction in steel:

! 727°C! " ! ! ! ! " + Fe3C

• The upper (high-temperature) portion of the TTT diagram

for eutectoid steels (0.76 wt% C) (Figs. 10.2-2 & 10.2-3) shows

the decomposition of austenite to pearlite with time, when

the steel is quenched (cooled rapidly) from the austenite

phase field and held isothermally at various temperatures

below the eutectoid transformation temperature.

Fig. 10.2-2 Isothermal transformation of austenite to pearlite

as a function of time and temperature.

10-11

• Above the eutectoid temperature, only austenite will exist;

transformation from austenite to pearlite will occur only if

the steel is cooled below the eutectoid temperature.

• The solid curves define the onset and completion of the

transformation of austenite to pearlite, while the dashed

curve represents 50% completion (Fig. 10.2-3).

• To the left of the start curve, only austenite (unstable) will

be present; to the right of the finish curve, only pearlite

will exist. In between, the austenite is in the process of

transforming to pearlite, thus both will be present.

Fig. 10.2-3 The isothermal transformation of austenite to pearlite, showing the development of microstructures.

10-12

• Since the transformation to pearlite during the eutectoid

reaction involves redistribution of carbon atoms via

diffusion, the morphology (size and shape) of pearlite

depends on the actual temperature of transformation.

• Near the eutectoid temperature, slow nucleation (few

grains) but fast diffusion (carbon atoms diffuse over long

distances quickly) produces coarse pearlite, consisting of

thick layers of ferrite and cementite with large

interlamellar spacing (Fig 10.2-4a).

• As undercooling increases, incubation becomes faster and

transformation to pearlite occurs earlier. Fast nucleation

(many grains) but slow diffusion (diffuse short distances

only) yields fine pearlite, with thin layers of ferrite and

cementite, and small interlamellar spacing (Fig 10.2-4b).

Fig. 10.2-4 (a) Coarse pearlite;

(b) fine pearlite.

10-13

• Further undercooling produces bainite (Fig. 10.2-5), which is

an even finer distribution of ferrite and cementite than in

fine pearlite. Unlike pearlite, which is lamellar, bainite

consists of extremely fine, elongated cementite particles

between ferrite plates or needles (Fig. 10.2-6).

Fig. 10.2-5 The TTT diagram for eutectoid

steel showing the transformation of

austenite to pearlite and austenite to bainite.

Fig. 10.2-6 Bainite formed at (a) 450°C, and (b) 260°C.

10-14

• The distribution and morphology (size and shape) of the

ferrite and cementite phases in pearlite and bainite differ

due to differences in the temperature at which their

transformations occur, which affect the nucleation and

growth kinetics of ferrite and cementite. However, both

pearlite and bainite are still physical mixtures of ferrite and

cementite, as indicated in the equilibrium phase diagram.

• Once a portion of austenite has transformed to pearlite or

bainite, the pearlite or bainite remains stable upon further

cooling (Fig. 10.2-7). It is not possible for the pearlite to

transform directly into bainite, or vice versa, without first

reheating to form austenite. Only austenite, which is

unstable below the eutectoid temperature, is able to

transform to other, more stable, phases upon cooling.

Fig. 10.2-7 Coarse pearlite remains stable upon cooling.

10-15

• Immediately prior to the eutectoid transformation,

austenite contains 0.76 wt% C, with carbon atoms

dissolved in the octahedral interstitial sites of the FCC

austenite lattice. The transformation of austenite to pearlite

or bainite requires the diffusion of carbon atoms to form

low-carbon ferrite (0.022 wt% C) and high-carbon

cementite (6.67 wt% C) simultaneously.

• When undercooling becomes so great (isothermal trans-

formation temperature below Ms) that carbon diffusion

cannot occur, the diffusive transformation to ferrite and

cementite is suppressed, and a diffusionless transformation

to non-eqiuilibrium martensite takes place (Fig. 10.2-8).

Fig. 10.2-8 The complete TTT diagram for eutectoid steel.

10-16

• Martensite has a BCT (body-centred tetragonal) structure

because carbon atoms remain trapped in the octahedral

interstitial positions of the original FCC austenite and distort

the BCC structure of ferrite into BCT (Figs. 10.2-9 and 10.2-10).

Fig. 10.2-9 The relationship between FCC

austenite and BCT martensite (c>a). Fig. 10.2-10 The BCT unit cell of

martensite produced by the distortion of the BCC unit cell by

interstitial carbon atoms.

• Since carbon atoms are trapped in the BCT structure,

martensite has the same composition as its parent

austenite (0.76 wt% C in the case of eutectoid steel).

• Unlike the transformation to pearlite and bainite, the

amount of austenite that transforms to martensite depends

solely on temperature, not time. Martensite begins to form

only when austenite is quenched to temperature Ms, while

the M50 isotherm indicates the temperature at which 50%

of austenite will transform to martensite (Fig. 10.2-11).

10-17

• The Ms, M50, M90 (or MF) temperatures are not fixed, but

decrease with increases in the carbon content of the steel.

In some steels, complete (100%) transformation to

martensite may require a subzero quench to below MF (Fig.

10.2-11); quenching to temperatures between Ms and MF in

these steels result in untransformed austenite remaining

amidst the martensite as retained austenite.

Fig. 10.2-11 The amount of martensite formed when steel is quenched to room temperature depends on Ms and MF.

• Martensite is metastable; i.e. it is stable with time at room

temperature, but upon reheating (in a process known as

tempering), martensite will decompose to the even more

stable phases of ferrite and cementite, known as tempered

martensite. 10-18

• Martensite is the hardest phase in steel (Fig. 10.2-12) as a result

of the lattice distortion caused by the trapped carbon

atoms. However, it tends to be brittle.

Fig. 10.2-12 Hardness of

martensite and pearlite as a function of carbon content.

• Bainite is generally harder and stronger than pearlite (Fig.

10.2-13) due to its much finer distribution (Sec. 6.3-5) of

cementite particles within ferrite.

Fig. 10.2-13 Hardness and strength of bainite and pearlite as a function of

isothermal transformation temperature.

10-19

Worked Example

Determine the final microstructure (in terms of microconstituents

present and approximate percentages) of a small specimen of

eutectoid steel that has been heated to its austenite phase, and then

subjected to the following treatments.

(a) Rapidly cool to 350°C, hold for 104 s, and quench to room

temperature.

(b) Rapidly cool to 250°C, hold for 100 s, and quench to room

temperature.

(c) Rapidly cool to 650°C, hold for 20 s, rapidly cool to 400°C, hold

for 103 s, and quench to room temperature.

10-20

(a) At 350°C, austenite transforms to bainite, beginning after about

10 s, and is completed at about 500 s. Therefore, by 104 s, the

specimen is 100% bainite, which does not transform further, even

though the final quenching passes through the martensite region

of the TTT diagram.

(b) At 250°C, after 100 s, bainite transformation has not yet begun, so

the specimen is still 100% austenite. Quenching through the

martensite region of the TTT diagram, more and more austenite

transforms to martensite as temperature drops. At room

temperature, most of this transformation is completed (past the

M90 line), so that the final microstructure is roughly 100%

martensite.

(c) At 650°C, austenite transforms to pearlite, beginning after about 7

s. After 20 s, only about 50% of the specimen has transformed to

pearlite, which does not transform further upon cooling.

For the remaining 50% austenite, rapid cooling to 400°C is fast

enough such that virtually no transformation occurs during

cooling, even though cooling occurs through pearlite and bainite

regions of the TTT diagram.

At 400°C, timing for the remaining 50% austenite is reset to zero,

because at each temperature, the kinetics (nucleation/growth

behavioiur with time) of austenite transformation is unique.

Austenite transforms to bainite, beginning after about 4 s, and is

completed at about 100 s. Therefore by 103s, the remaining 50%

of the specimen is 100% bainite, which does not transform further

upon cooling. Final microstructure: 50% pearlite + 50% bainite.

10-21

10.2.2 Hypoeutectoid and Hypereutectoid Steels

• When hyporeutectoid and hypereutectoid steels are

cooled, austenite first transforms to proeutectoid ferrite

and cementite, respectively, before the eutectoid

transformation to pearlite. The formation of proeutectoid

ferrite or cementite adds an extra curve to the TTT

diagram above the pearlite “nose” (Figs 10.2-14 and 10.2-15).

Fig. 10.2-14 TTT diagram for a hypoeutectoid steel (0.5 wt% C) and its corresponding portion of the Fe-Fe3C phase diagram, showing an extra curve due to proeutectoid ferrite formation.

10-22

• Since the transformation of austenite to the proeutectoid

phases requires the diffusion of carbon atoms, the amount

of proeutectoid phase that forms depends on the

undercooling. More proeutectoid phase is formed when

the isothermal transformation temperature is high.

• When the undercooling is so large that bainite or

martensite is obtained, no proeutectoid phase is formed.

Fig. 10.2-15 TTT diagram for a hypereutectoid steel (1.13 wt% C).

10-23

10.3 CONTINUOUS COOLING TRANSFORMATION DIAGRAMS

• Strictly speaking, TTT diagrams are valid only for

isothermal transformations, in which the material is

assumed to be instantaneously quenched from a single-

phase field to a specific temperature and held isothermally

for various times to produce different amounts of the

transformed products.

• In practice, transformations occur during continuous

cooling to room temperature, in which the temperature is

constantly changing as the transformation progresses.

• Therefore, it is more accurate to use continuous-cooling-

transformation (CCT) diagrams.

• CCT diagrams are derived from a series of experimental

sigmoidal curves at different cooling rates. Like the TTT

diagrams, each CCT diagram is valid for one alloy

composition only.

10-24

10.3.1 Continuous Cooling in Steels

• Because the temperature is constantly decreasing when

the steel is cooled continuously, CCT curves are shifted to

longer times and lower temperatures when compared to

TTT diagrams (Fig. 10.3-1).

Fig. 10.3-1 Comparison of TTT and CCT diagrams for eutectoid steel.

• There is no longer any bainite formation when cooling

continuously at any given constant cooling rate because all

the austenite will have transformed to pearlite by the time

bainite transformation becomes possible.

10-25

• The transformation from austenite to pearlite occurs over a

range of temperatures rather than at a single temperature.

• Slow cooling produces coarse pearlite while moderately

fast cooling produces fine pearlite (Fig. 10.3-2).

Fig. 10.3-2 Different cooling rates produces different microstructures.

• There is a critical cooling rate (140°C in Fig. 10.3-3) that will just

miss the “nose” at which the pearlite transformation

begins. It represents the minimum cooling rate that will

avoid pearlite formation and produce a fully martensitic

structure (if cooled below MF). 10-26

• There is a range of cooling rates (between 35 to 140°C/s in Fig. 10.3-3)

over which both pearlite and martensite are produced.

When cooling within this range, there is insufficient time to

complete the austenite-to-pearlite transformation (since

the cooling curves does not reach the pearlite finish curve

on the right). The remaining austenite that does not

transform to pearlite at the higher temperatures will begin

to transform to martensite when the Ms temperature is

reached.

Fig. 10.3-3 Critical cooling rate for a fully martensitic structure.

10-27

Worked Example

Determine the final microstructure of a small specimen of eutectoid

steel that has been cooled from its austenite phase to room

temperature at the following rates: (a) 1°C/s, (b) 20°C/s, (c) 50°C/s,

and (d) 175°C/s.

(a) From Fig. 10.3-3 1°C/s lies to the far right of the CCT diagram,

where nucleation is slow, but growth is fast; the final

microstructure is likely to be coarse pearlite.

(b) 20°C/s lies closer to the cooling curve of 35°C/s, which is the

fastest cooling rate possible in order to still obtain 100% pearlite.

For a faster cooling rate, nucleation is faster, but growth is slower;

the final microstructure is likely to be fine pearlite.

(c) 50°/s lies in the region of split transformation on the CCT diagram

– at high temperatures, pearlite nucleation and growth occurs, but

the rapid drop in temperature means that the transformation from

austenite to pearlite cannot be completed, because diffusion

becomes too slow at lower temperatures. The remaining austenite

transforms to martensite when cooled through the martensite

region of the CCT diagram. Final microstructure is a mixture of

fine pearlite and martensite.

(d) 175°C/s is faster than the critical cooling rate of 135°C/s, at which

there is no time for diffusion to occur, so the final microstructure is

approximately 100% martensite, assuming MF (or at least M90) is

reached.