Higgins R.A. Engineering Metallurgy: Applied Physical Metallurgy

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interstitial gaps will be larger in these regions. This hypothesis affords an

explanation of the yield-point effect in mild steel (2.31), and was a signifi-

cant triumph in support of the dislocation theory in its earlier days.

In Fig. 8.11 the yield point, A, corresponds to the stress necessary to

move dislocations away from their atmosphere of interstitial carbon atoms

by which they have become anchored, whilst the point B indicates the stress

necessary to keep the dislocations moving once movement has begun.

This yield-point effect in mild steel causes non-uniform localised defor-

mation, which leads to the formation of 'stretcher strains' (or 'Luder's

lines') on the surface of such products as deep-drawn motorcar bodies.

Such markings disfigure the surface, and their formation is avoided by

applying slight initial deformation to the stock material, for example, by

means of a light rolling pass. As this deformation is taking place in com-

pression instead of in tension, stretcher strains will not form.

Assume that, during this treatment, the stock material was stressed to

the point X (Fig. 8.11). Since the material has now yielded, no further

yield point will be encountered during the subsequent deep-drawing pro-

cess.

Thus, the stress-strain curve will follow XZ. If, however, the pre-

stressed steel is allowed to remain at room temperature for a few months,

or if it is heated to 300

C for a few hours, carbon atoms are able to move

back to their initial positions relative to the dislocations and form their

original 'atmosphere', so that the yield-point effect returns. Since there

are now more dislocations than were present in the original unstressed

material, the new yield point will be at Y. This effect, which is known as

'strain-ageing', can be caused by the presence of as little as 0.003% carbon

or nitrogen. It is sometimes used to strengthen springs after coiling, but

its effect in material destined for deep drawing must be avoided. Conse-

quently, such material is usually deep-drawn within twenty-four hours of

the pre-stressing operation mentioned above.

STRESS

Fig.

8.11.

8.62 Dispersion Hardening The presence of small separate particles

in the microstructure can impede the movement of dislocations provided

that these particles are stronger than the matrix in which they are embed-

ded. The degree of strengthening produced also depends on the size of

STRAIN

particles, their distance apart

and the

tenacity

of the

bond between

par-

ticles

and

matrix.

The

passage

of a

dislocation through

alloy containing

isolated particles

represented

in Fig. 8.12.

Assuming that

the

particles

are stronger than

the

matrix,

the

dislocation cannot pass through them,

but

if the

stress

high enough,

the

dislocation

can

by-pass them leaving

'dislocation loop' around each particle. This will make

the

passage

of a

second dislocation much more difficult, particularly since dislocations have

greater difficulty

passing between particles which

are

near

each other.

Particles

of a

separate phase

are

often precipitated from

solid solution

during cooling.

The

cementite platelets

pearlite

are an

example,

and

their presence effectively strengthens steel. Such particles which have

sep-

arated

form their

own

individual crystal structures

are

referred

to as

non-coherent precipitates. Prior

to the

actual precipitation

separate

particles, however,

intermediate state often exists where atoms associ-

ated with

the

solute material begin

form groups within

the

crystal lattice

the

solvent metal. These

are

small regions

less than

one

hundred

atoms

on an

edge,

and are

called 'coherent precipitates'. Although still

part

of the

continuous crystal structure

of the

matrix, they

are

attempting

to form their

own

separate crystals, which will have

different crystal

pattern.

The

presence

these coherent precipitates produces severe elas-

tic distortions which impede

the

movement

dislocations. They

are

gener-

ally more effective than non-coherent precipitates.

The

nature

coherent

precipitates, which give rise

to the

'precipitation hardening'

some

alu-

minium alloys, beryllium bronzes

and a

number

other alloys, will

dealt with more fully later (9.92).

DISLOCATION

Fig.

8.12 The

movement

of a

dislocation resisted

by the

presence

strong particles.

Exercises

Show

how the

positions

of two

metals relative

each other

in the

Periodic

Table

are

likely

affect

the

manner

which they associate

in a

metallic alloy.

(8.14)

RESIDUAL

DISLOCATION

LOOPS

Discuss the factors which may limit or even prevent the formation of a substi-

tutional solid solution in a binary alloy. (8.23)

Describe, with the aid of sketches, the various types of solid solution which may

be formed in metallic alloys. Show, in each case, how the structure of the solid

solution affects its behaviour during heat-treatment, giving typical examples

among important engineering alloys. (8.22)

Describe, with the aid of sketches, how a cored structure develops in a substi-

tutional solid solution. Outline a theory which seeks to explain how the coring

can be dispersed when such a solid solution is annealed at a sufficiently high

temperature. (8.23-8.24)

State Fick's First Law of Diffusion and show how it applies to the diffusion

which takes place in a metallic solid solution. What factors influence the rate of

such diffusion? (8.25)

6. (a) Into which Hume-Rothery ratios dp the following electron compounds fit:

(i) AuZn

(ii) AgCd; (iii) Cu

; (iv) Cu

Si? (b) What are interstitial com-

pounds and why are many of them important in engineering alloys? (8.31)

Explain the following terms: (i) substitutional solid solution; (ii) interstitial solid

solution; (iii) electron compound; (iv) valence compound. What factors affect

the formation of these phases?

(8.23;

8.24 and 8.31)

8. What are the main characteristics which define a eutectic?

Distinguish between eutectic and eutectoid. (8.40 and 8.43)

9. (a) Explain, with the aid of sketches, why binary solid solutions are usually

stronger than the pure metals they contain, (b) Show how the Dislocation

Theory helps to explain the 'yield-point effect' peculiar to normalised low-

carbon steels. (8.61)

Bibliography

Cahn, R. W., Physical Metallurgy, North Holland, 1980.

Goldschmidt, H. J.,

Interstitial

Alloys, Butterworths, 1967.

Hume-Rothery, W., Smallman, R. E. and Howarth, C. W., The

Structure

Metals

and Alloys, Institute of Metals, 1988.

Hume-Rothery, W., The Structure of Alloys of Iron, Pergamon Press, 1966.

Martin, J. W. and Doherty, R. D., Stability of

Microstructures

in Metallic Systems,

Cambridge University Press, 1976.

Porter, D. A. and Easterling, K. E., Phase Transformations in Metals and Alloys,

Van Nostrand Reinhold Co., 1981.

Thermal Equilibrium

Diagrams

9.10 The subject of phase equilibrium was briefly discussed in Chapter

7 to introduce the reader to this very important field of study in as

painless a manner as possible. The reader will have acquired a general

impression of the significance of equilibrium diagrams, since no useful

examination of the microstructures of alloys is possible without reference

to the appropriate diagram, which, for this reason, becomes one of the

metallurgists most useful 'tools'. With its aid he can predict with precision

the structure of a given alloy at any given temperature provided that the

alloy's thermal-treatment history is known. In the thermodynamical sense,

'equilibrium' refers to the state of balance which exists, or which tends to

be attained, between the phases in the structure of an alloy after a chemical

or physical change has taken place. In some cases equilibrium may not be

reached for long periods after the change has begun. In fact, rapid cooling

(or 'quenching') to room temperature may suppress the chemical or physi-

cal change involved to such an extent that equilibrium will never be reached

so long as the alloy remains at room temperature. Reheating (or 'temper-

ing') followed by slow cooling to room temperature will allow the physical

or chemical change to proceed in some degree towards completion; the

extent to which equilibrium is thus attained being dependent upon the

temperature reached, the time the alloy remains at that temperature and

the rate of cooling to room temperature or at whatever other temperature

equilibrium is being studied.

9.11 We have already seen that physical and chemical changes which

take place after solidification in carbon steel do so with relative ease

because the small carbon atoms can move quickly through the crystal

lattice of face-centred cubic iron. Thus, during the process of normalising,

a steel will attain structural equilibrium. In some alloy systems, however,

physical changes which take place after solidification are so sluggish that

it is doubtful if equilibrium is ever attained. Often we have no means of

telling whether or not equilibrium has been reached, even after extremely

slow rates of cooling involving periods of days or even weeks. There is

therefore a tendency these days to refer to these charts as 'constitutional

diagrams' instead of 'thermal-equilibrium diagrams'. The latter term, how-

ever, is still in general use, and we shall employ it throughout this book.

9.12 The thermal-equilibrium diagram is in reality a chart which shows

the relationship between the composition, temperature and structure of

any alloy in a series. Let us consider briefly how these diagrams are con-

structed.

A pure metal will complete its solidification without change of tempera-

ture (3.12), whilst an alloy will solidify over a range of temperature which

will depend upon the composition of the alloy (7.41). Consider, for

example, a number of alloys of different composition containing the two

metals A and B which form a series of solid solutions (Fig. 9.1). For

successive compositions containing diminishing amounts of the metal A,

freezing commences at a\, <z

, «3, etc., and ends at bi, fc, b

, etc. Thus, if

we join all points ai, ai,

a?>,

etc., we shall obtain a line called the liquidus,

indicating the temperature at which any given alloy in the series will com-

mence to solidify. Similarly, if we join the points £>i, bi, ^3, etc., we have

a line, called the solidus, showing the temperature at which any alloy in

the series will become completely solid. Hence the liquidus can be defined

as the line above which all indicated alloy compositions represent com-

pletely homogeneous liquids, whilst the solidus can be defined as the line

below which all represented alloy compositions of A and B are completely

solid. For temperatures and compositions corresponding to the co-

ordinates of points between the two lines both liquid solutions and solid

solutions can co-exist in equilibrium.

9.13 Such a system as this occurs when the two metals are soluble in

TEMPERATURE

Fig.

9.1 The construction of a simple equilibrium diagram of the solid solution type using

cooling curves of a series of alloys.

O°/oB

IOO°/oA

COMPOSITION

IOO^bB

O^oA

time-temperature cooling curves

solid only

liquid only

liquid

solid

liquidus

solidus

m.pt.

OfB

m.pi.

of A

each other in all proportions in both the liquid and solid states, as in the

case of copper and nickel or gold and silver. When, on the other hand,

the metals are completely insoluble in the solid state a eutectic type of

equilibrium diagram represents the system (Fig. 9.2). Since the eutectic

part of the structure of any alloy in the series solidifies at the same tempera-

ture,

and is the portion of the alloy with the lowest melting point, the line

ACEDB will be the solidus whilst AEB is the liquidus.

9.14 Diagrams of this type can be constructed by using the appropriate

points (obtained from time-temperature cooling curves) which indicate

where freezing began and where it was complete. Thus the liquidus and

solidus temperatures for a number of alloys in the series between 100% A

and 100% B can be obtained and then plotted on a temperature-compo-

sition diagram as indicated in Figs. 9.1 and 9.2. Such cooling curves will

determine the positions of the liquidus and solidus; and if the alloy system

is one in which further structural changes occur after the alloy has solidi-

fied, then the metallurgist must resort to other methods of investigation

to determine the phase boundary lines. These methods include the use

of X-rays, electrical-conductivity measurements, dilatometric methods

(which measure changes in volume) and exhaustive microscopical examin-

ation following the quenching of representative specimens from different

temperatures.

9.15 The construction of equilibrium diagrams, then, is the result of

much tedious experimental work, and, since the conditions under which

the work is carried out can be so variable, it is not surprising that the

values assigned to compositions and temperatures at which phase changes

occur are under constant review by research metallurgists. The reader

will, therefore, find that the equilibrium diagrams printed in books on

metallurgy often differ in small detail. In general, however, the variations

are so small as not to affect the treatment of most of the industrially

TEMPERATURE

time-temperature

cooling curves

liquid

only

liquid

+ solid

solid

only

0<#>B

IOO°/oA

COMPOSITION

10O

YoB

O*yoA

Fig.

9.2 The construction of a simple equilibrium diagram of the eutectic type using cooling

curves of a series of alloys.

important alloys. As an example, the accepted value for the carbon content

of a completely eutectoid carbon steel (7.55) has varied between 0.80 and

0.89% during recent years, whilst the eutectoid temperature (the lower

critical temperature of plain carbon steels) has varied between 698 and

732°C.

The Phase Rule

9.20 In the previous chapter a 'phase' was described as either a pure

metal, a solid solution or some form of intermediate compound so long

as it was a single homogeneous substance. Similarly a single element or

compound can exist in different physical forms, each one a separate phase.

Thus the chemical substance 'H

O' can exist as ice, water or water vapour,

each of these conditions constituting a 'phase'. The 'phase structure' of

O is governed by the prevailing conditions of temperature and pressure

as indicated in the phase diagram in Fig. 9.3. This diagram shows the effects

which variations of temperature and pressure will have on the stability of

a given phase. The 'fusion curve' is an almost vertical line and this indicates

that variation in pressure has very little effect on the melting point of ice.

The same is true of the effects of pressure on the melting points of alloys

for which reason we can neglect pressure when studying the phase equilib-

rium of liquid or solid alloys.

The 'vaporisation curve' however indicates that the boiling point of water

is very dependent on pressure. Water boils at 100

C when the pressure is

equivalent to 760 mm of mercury. If the pressure is reduced to, say, 300 mm

of mercury then water will boil at about 50

C which is the reason why tea

cannot be brewed successfully near the summit of Everest.

PRESSURE

(mm

Hg)

fusion

TEMPERATURE (

Fig.

9.3 The ice-water-water-vapour phase diagram.

WATER VAPOUR

WATER

VAPOUR

WATER

ICE

sublimation

The 'sublimation curve' shows that at low pressures solid ice can vaporise

—or 'sublime'—without passing through the liquid phase. Some sub-

stances, notably carbon dioxide ('dry ice') and iodine, do this at normal

atmospheric pressures when heated to the 'sublimation temperature'.

9.21 In 1876 Gibbs (8.13) introduced his Phase Rule which predicts

the relationship between the number of phases, the number of components

(or pure chemical substances) and the conditions of temperature and pres-

sure which prevail. The general form of the rule can be written:

P + F = C + E

where P = the number of different phases present;

C = the number of components (stable chemical substances);

F = the degrees of 'freedom', or 'variance';

E = the environmental factors (temperature and pressure).

9.22 The implications of this rule can be explained more easily by

reference to examples. Consider point A in Fig. 9.3. Here there is only

one phase in the system (water vapour) and one component (the chemical

compound, H2O) whilst there are two environmental factors (temperature

and pressure) to be considered. Hence, since—

F= C + E

1 + F= 1 + 2

ie F= 2

This means that two degrees of freedom are involved so that both tempera-

ture and pressure can be altered independently without altering the number

of phases in the system, which is consequently said to be bivariant.

Now consider the point B. This indicates that water is boiling at 100

and 760 mm pressure so we have two phases (water and water vapour)

present at the same time, but still one component (H

O). Applying the

Phase Rule:

2 + F= 1 + 2

or F= 1

This means that only one degree of freedom is available and if tempera-

ture is increased pressure must also be increased in sympathy if the water

is to continue to boil steadily. Conversely if, say, pressure were reduced

then the boiling point of water would decrease in sympathy so that con-

ditions were still represented by a point on the 'vaporisation curve'. Failure

to observe these conditions would mean that one phase would disappear

—either the water would cease to boil or it would turn very quickly to

steam. The system represented by B is said to be univariant.

At the triple point T all three phases, ice, water and water vapour can

exist together. Hence:

+ F = 1 + 2

F=O

In this case there

is no

degree

freedom

and if

either temperature

pressure

are

altered then

least

one of the

phases will disappear. This

system

invariant.

9.23

will

now

consider

the

Phase Rule

as it

applies

to a

study

metallic alloys. Here

the

components

in the

system

are

pure metals

elements from which

the

alloy

made, whilst

the

phases produced will

be either liquids, solid solutions, intermediate compounds

or,

rarely, pure

metals.

are

usually dealing with alloy systems

in the

liquid

and

solid states

at atmospheric pressure. Since small variations

atmospheric pressure

will have virtually

effect

on the

stability

phases

we can

neglect

the

effect

pressure

and

standardise

at 'one

atmosphere'.

As we are now

dealing with only

one

variable environmental factor, temperature,

we can

adapt Gibbs' Phase Rule

so:

F=CH-I

Moreover since

one

environmental factor

has

disappeared

we can

still

express

two-component system

in a

two-dimensional diagram, variation

in composition replacing variation

pressure.

will

now

examine such

a system

(Fig. 9.4).

Point

represents

completely homogeneous molten alloy containing

a single liquid phase composed

of the two

components bismuth

and cad-

mium. Hence:

+ F =2+ 1

F=I

TEMPERATURE

Fig.

9.4 The

bismuth-cadmium phase

(or

thermal equilibrium) diagram.

(OOqbCd

OfcBi

COMPOSITION

iooyo

4- Cd

liquid

There are two degrees of freedom so that both temperature and compo-

sition may be varied independently without altering the single-phase

structure.

On cooling the alloy to B the liquid becomes saturated with cadmium

so that solid cadmium begins to form. There are now two phases present

and:

2 + F =2+ 1

and F = 1

Thus there is one degree of freedom and if the temperature is altered the

composition of the remaining liquid must alter so that B remains on CE.

At E solid cadmium and solid bismuth co-exist with remaining liquid so

that there are three phases and:

3 + F= 2 + 1

and F = 0

Therefore the system at E is invariant and any alteration of temperature

or composition will lead to the disappearance of at least one of the phases.

Conversely if the alloy of composition indicated by E is cooling, then the

temperature must remain constant until the liquid has crystallised com-

pletely. That is, a eutectic crystallises at a constant temperature.

9.24 In the interpretation of thermal equilibrium diagrams it is often

more convenient to make use of a set of definitions and rules which are

derived from Gibbs' Phase Rule and also from some observations made

by the French metallurgist A. Portevin:

(a) The areas of the diagram are called 'phase fields', and on crossing

any sloping boundary line from one field to the next, the number of

phases will always change by one, ie two single-phase fields will always

be separated by a double-phase field containing both of the phases. In

a binary system three phases can only exist together at a point, such as

the eutectic point E in Fig. 9.4.

(b) In Fig. 9.5 the point P represents some particular alloy mixture in

both composition and temperature. The diagram indicates that at P both

liquid and solid will exist together. If a 'temperature horizontal' (usually

known as a tie-line) is drawn through P the composition of the solid is

given by X, and the composition of the liquid solution in equilibrium

with it by Y. P itself represents the overall composition of the mixture.

relative lengths PX and PY-

Weight of solid solution Weight of liquid solution

(composition X) x PX = (composition Y) x PY