Engineering Materials Vol II (microstructures processing design) 2nd ed. - M. Ashby_ D. Jones (1999) Episode 13 pptx

Examine the Pb–Sn phase diagram and list the composition range for which aeutectic reaction is possible.3.4 We defined a eutectic reaction e.g.. At 577°C the eutectic reaction takes plac

not Examine the Pb–Sn phase diagram and list the composition range for which aeutectic reaction is possible.

3.4 We defined a eutectic reaction (e.g that of the lead–tin system) as a three-phasereaction by which, on cooling, a liquid transforms into two solids In general:

L → α + β 5

Liquid (Pb–Sn) → (Pb) + (Sn) 7What happens on heating?

Eutectic structure

The aluminium casting alloys are mostly based on the Al–Si system (phase diagram

Fig A1.31) It is a classic eutectic system, with a eutectic point at about 11% Si and

Fig A1.31.

577°C Consider the cooling of an Al–6% Si casting alloy The liquidus is reached atabout 635°C, when solid (Al) starts to separate out (top of Fig A1.32) As the temper-ature falls further the liquid composition moves along the liquidus line, and the amount

of solid (Al) increases When the eutectic temperature (577°C) is reached, about halfthe liquid has solidified (middle of Fig A1.32) The solid that appears in this way is

called primary solid, primary (Al) in this case.

At 577°C the eutectic reaction takes place: the liquid decomposes into solid (Al)mixed with solid Si, but on a finer scale than before (bottom of Fig A1.32) This

intimate mixture of secondary (Al) with secondary Si is the eutectic structure.

On further cooling to room temperature the composition of the (Al) changes – itdissolves less silicon at the lower temperature So silicon must diffuse out of the (Al),and the amount of Si must increase a little But the final structure still looks like thebottom of Fig A1.32

Dendrites

When a metal is cast, heat is conducted out of it through the walls of the mould Themould walls are the coldest part of the system, so solidification starts there In the Al–Sicasting alloy, for example, primary (Al) crystals form on the mould wall and grow inwards.Their composition differs from that of the liquid: it is purer, and contains less silicon

This means that silicon is rejected at the surface of the growing crystals, and the liquid

grows richer in silicon: that is why the liquid composition moves along the liquidus line

Fig A1.32.

Fig A1.33.

Fig A1.34. Dendrites of silver in a copper–silver eutectic matrix, ×330 (After G A Chadwick, Metallography

of Phase Transformations, Butterworth, 1972.)

The rejected silicon accumulates in a layer just ahead of the growing crystals, and

lowers the melting point of the liquid there That slows down the solidification, because

more heat has to be removed to get the liquid in this layer to freeze But suppose aprotrusion or bump on the solid (Al) pokes through the layer (Fig A1.33) It finds itself

in liquid which is not enriched with silicon, and can solidify So the bump, if it forms,

is unstable and grows rapidly Then the (Al) will grow, not as a sphere, but in a

branched shape called a dendrite Many alloys show primary dendrites (Fig A1.34); and

the eutectic, if it forms, fills in the gaps between the branches

If an 80 at% Pb alloy is cooled, the first solid appears at 305°C, and is primary (Pb)with a composition of about 90% Pb (see Fig A1.35) From 305 to 255°C the amount ofprimary (Pb) increases, and its composition, which (at equilibrium) follows the solidus

line, changes: it becomes richer in tin This means that lead must diffuse out of the solid (Pb), and tin must diffuse in.

This diffusion takes time If cooling is slow, time is available and equilibrium ismaintained But if cooling is rapid, there is insufficient time for diffusion, and, al-though the new primary (Pb), on the outside of the solid, has the proper composition,the inside (which solidified first) does not The inside is purer than the outside; there is

a composition gradient in each (Pb) grain, from the middle to the outside This gradient

is called segregation, and is found in almost all alloys (see Fig A1.36).

The phase diagram describes the equilibrium constitution of the alloy – the onegiven by very slow cooling In the last example all the liquid should have solidified at

the point marked 2 on Fig A1.35, when all the solid has moved to the composition XPb

= 80% and the temperature is 255°C Rapid cooling prevents this; the solid has not had

time to move to a composition XPb= 80% Instead, it has an average composition about

half-way between that of the first solid to appear (XPb= 90%) and the last (XPb= 80%),

that is, an average composition of about XPb= 85% This “rapid cooling” solidus lies to

Fig A1.35.

Fig A1.36.

Figure A1.37 shows the iron–carbon phase diagram up to 6.7 wt% carbon (to the firstintermetallic compound, Fe3C) Of all the phase diagrams you, as an engineer, willencounter, this is the most important So much so that you simply have to learn thenames of the phases, and the approximate regimes of composition and temperaturethey occupy The phases are:

Ferrite: α (b.c.c.) iron with up to 0.035 wt% C dissolved in solid solution

Austenite: γ (f.c.c.) iron with up to 1.7 wt% C dissolved in solid solution

δ-iron: δ (b.c.c.) with up to 0.08 wt% C dissolved in solid solution

Cementite: Fe3C, a compound, at the right of the diagram

Ferrite (or α) is the low-temperature form of iron On heating, it changes to austenite(or γ) at 914°C when it is pure, and this form remains stable until it reaches 1391°Cwhen it changes to δ-iron (if you have forgotten this, check back to p 319) The phase

Fig A1.37.

diagram shows that carbon changes the temperatures of these transitions, stabilising γover a wider temperature interval.

The iron–carbon system has a eutectic: find it and mark it on the diagram (Fig A1.37)

At the eutectic point the phase reaction, on cooling, is

Liquid → austenite + cementite

But the diagram shows another feature which looks like a eutectic: it is the V at thebottom of the austenite field The transformation which occurs there is very like the

eutectic transformation, but this time it is a solid, austenite, which transforms on ing to two other solids The point at the base of the V is called a eutectoid point.

cool-DEF A eutectoid reaction is a three-phase reaction by which,

on cooling, a solid transforms into two other solid phases at thesame time If the bottom of a single-phase solid field closes

(and provided the adjacent two-phase fields are solid also), it

does so with a eutectoid point

The compositions of the two new phases are given by the ends of the tie line throughthe eutectoid point

Questions

3.5 The copper–zinc system (which includes brasses) has one eutectoid reaction Markthe eutectoid point on the phase diagram (Fig A1.38)

3.6 The copper–tin system (which includes bronzes) has four eutectoids (Fig A1.39).

One is obvious; the other three take a little hunting for Remember that, if the

Fig A1.38.

Fig A1.39.

bottom of the single-phase field for a solid closes, then it does so with a eutectoid.Try to locate (and ring carefully) the four eutectoid points on the copper–tin phasediagram

Eutectoid structures

Eutectoid structures are like eutectic structures, but much finer in scale The ginal solid decomposes into two others, both with compositions which differ from the

ori-original, and in the form (usually) of fine, parallel plates To allow this, atoms of B

must diffuse away from the A-rich plates and A atoms must diffuse in the oppositedirection, as shown in Fig A1.40 Taking the eutectoid decomposition of iron as

an example, carbon must diffuse to the carbon-rich Fe3C plates, and away from the(carbon-poor) α-plates, just ahead of the interface The colony of plates then grows tothe right, consuming the austenite (γ) The eutectoid structure in iron has a special

name: it is called pearlite (because it has a pearly look) The micrograph (Fig A1.41)

shows pearlite

Fig A1.41. Pearlite in a eutectoid-composition plain-carbon steel, ×500 (After K J Pascoe, An Introduction

to the Properties of Engineering Materials, Van Nostrand Reinhold, London, 1978.)

Fig A1.40.

Peritectics

Eutectics and eutectoids are common features of engineering alloys At their simplest,they look like a V resting on a horizontal line (see Fig A1.42) The phase reactions, oncooling, are

Liquid L → α + β (eutectic)

Solid β → α + γ (eutectoid)

Fig A1.43.

Fig A1.42.

Many phase diagrams show another feature It looks like an upside-down V (i.e a

⵩) touching a horizontal line It is a peritectic reaction, and the tip of the ⵩ is a peritectic point (see Fig A1.43).

DEF A peritectic reaction is a three-phase reaction by which,

on cooling, two phases (one of them liquid) react to give

a single new solid phase

On Fig A1.43, the peritectic reaction is

Liquid + solid α → solid β

The composition of the β which forms (in this example) is 50 at% B

Questions

3.7 The iron–carbon diagram (Fig A1.37) has a peritectic point Ring it on the diagram

3.8 The copper–zinc system shown in Fig A1.38 has no fewer than five peritecticreactions Locate them and ring the peritectic points (Remember that when asingle-phase field closes above at a point, the point is a peritectic point.)

DEF A peritectoid is a three-phase reaction by which, on cooling,

two solid phases react to give a single new solid phase.

On Fig A1.44 the peritectoid reaction is

A + B → δ

Fig A1.44.

Answers to questions: part 3

3.1 (See Fig A1.45.) 550°C, 67%; 580°C, 11%; 1350°C, 49%

3.2 The reduced (constant pressure) phase rule is

F = C − P + 1.

There are two components; the three phases (two solids and one liquid) coexist So

F = 0, that is, the three phases can coexist only at a point (the eutectic point)

3.3 From XPb= 1.45% to XPb= 71%

3.4 Remember that this is an equilibrium diagram Any point on the diagram

corres-ponds to a unique constitution So, on heating, the reaction simply goes in reverse.The two solids “react” to give a single liquid In general:

(Pb) + (Sn) → Liquid (Pb–Sn) 73.5 (Also 3.8) (See Fig A1.46.)

3.6 Eutectoids ringed with solid circles (see Fig A1.47)

3.7 (See Fig A1.48.)

Fig A1.45.

Fig A1.46. 䊊 = peritectic; ⵧ = eutectoid.

Fig A1.47.

Fig A1.48.

high pressure phases can be “trapped”, and are observed at atmospheric ature and pressure (diamond, for instance, is a high-pressure form of carbon It isonly metastable at atmospheric pressure: the stable form is graphite.)

temper-A roughly spherical meteorite of pure iron passes through the Earth’s phere, causing surface heating, and impacts in the Mill pool (a local pond) creating

atmos-a (uniform) pressure watmos-ave, atmos-and atmos-a certatmos-ain atmos-amount of consternatmos-ation The meteorite isrecovered and sectioned It shows signs of having melted externally, and of havinghad an outer shell of γ-iron, an inner shell of ε-iron and a core of α-iron Use the

p–T phase diagram for iron to deduce the approximate magnitude of the

press-ure wave Express the result in atmospheres (see Fig A1.49)

Fig A1.49.

4.2 Your ancient granny dies and leaves you her most prized possession: an Urn ofPure Gold One afternoon, while mixing paint-remover in the urn, you are dis-turbed to note that it has turned an evil green in colour Whipping out yourmagnifying glass, you observe that the paint remover, in attacking the urn, hasalso etched it, clearly revealing the presence of two phases This (of course) raises

in your mind certain nagging doubts as to the Purity of the Gold Your friend with

an electron microprobe analyser performs a quick chemical analysis for you, withthe distressing result:

4.3 Describe, using the copper–nickel (“monel”) system as an example, the process of

zone-refining (Figure A1.51 shows a system with complete solid solubility.) How

many phases are present in an alloy of 60 wt% Ni and 40 wt% Cu at:

(a) 1400°C;

(b) 1300°C;

(c) 1000°C

4.4 Figure A1.52 shows the Ti–Al phase diagram (important for the standard

commer-cial alloy Ti–6% Al–4% V It shows two peritectic reactions, at each of which liquid

reacts with a solid phase to give an intermetallic compound (a) Ring the peritecticsand give the (approximate) chemical formula for the two compounds (b) Shade all

Fig A1.51.

Fig A1.52.

two-phase fields (c) At what temperature does a Ti–6 wt% Al alloy start to melt?(d) Over what temperature range does it change from the α (c.p.h.) to the β (b.c.c.)structure?

4.5 Figure A1.53 shows the aluminium–silicon system, basis of most aluminium ing alloys

cast-(a) What is the eutectic composition and temperature?

(b) How many phases are present in an alloy of eutectic composition at 1000°C,and at 400°C?

(c) Describe the solidification of an alloy of eutectic composition, and the resultingstructure.

(d) Compare and contrast this with the formation of a eutectoid structure

4.6 A hypothetical equilibrium diagram between two elements A and B shows thefollowing features:

A has three solid allotropic forms with change temperatures of 800°C and 1150°Cand melts at 1980°C These form solid solutions α, β and γ containing B, α beingthe low-temperature one

An intermediate compound A2B3 melts at 1230°C It has a limited solid solubilityfor A, forming solid solution ε and no solid solubility for B

B melts at 800°C and has negligible solid solubility for A

immediately below each temperature at which a reaction occurs.

Answers to questions: part 4

4.1 Between about 11.5 and 13.0 GPa or 1.14 × 105− 1.28 × 105 atm

4.2 (a) See (Fig A1.54)

Fig A1.54.

Fig A1.55.

(a) 1

(b) 2

(c) 1

4.4 (a) AlTi, Al3Ti

(b) See Fig A1.55

×

× + × = B by weight Hence equilibrium diagram is as

given in Fig A1.56 On cooling 30% B mixture from 1600°C: at 1397°C, tion commences by separation of γ crystals Just above 1300°C 22 (= 81.5%) liquid(35% B) + 5

solidifica-27 (= 18.5%) γ (8% B) At 1300°C, all γ + some liquid form β in peritecticreaction Just below 1300°C 15 (= 75%) liquid (35% B) + 5

20 (= 25%) β (15% B).1300°C → 1000°C, more β separates Just above 1000°C 5

30 (= 17%) liquid (55% B) +

25 (= 83%) β (25% B) At 1000°C all liquid forms β and ε in eutectic reaction Justbelow 1000°C 5

35 (= 14.3%) ε (60% B) + 30 (= 85.7%) β (25% B) 1000°C → 600°C, β

Fig A1.56.

precipitates ε and ε precipitates β Just above 600°C 18 (= 34%) ε (65% B) + 35 (=66%) β (12% B) At 600°C all β forms α and ε in eutectoid reaction Just below600°C 25 (= 42%) ε (65% B) + 35 (= 58%) α (5% B) 600°C → 300°C, α precipitates εand ε precipitates α Just above 300°C 27 (= 41%) ε (69% B) + 39 (= 59%) α (3% B)

At 300°C all ε and some α form δ in peritectoid reaction Just below 300°C 27 (=73%) δ (40% B) + 10 (= 27%) α (3% B) 300°C → 0°C, amount of α decreases and δincreases At 0°C 30 (= 86%) δ (35% B) + 5

35 (= 14%) α (0% B)

Appendix 2

Symbols and formulae

List of principal symbols

Symbol Meaning(units)

Note: Multiples or sub-multiples of basic units indicate the unit suffixes normally

used in materials data

CCR critical cooling rate (°C s−1)

DP degree of polymerisation (dimensionless)

E Young’s modulus of elasticity (GPa)

g acceleration due to gravity on the Earth’s surface (m s−2)

G Gibbs function (J)

G c toughness (kJ m−2)

∆H latent heat of transformation (J)

I second moment of area of structural section (mm4)

k ratio of Csolid/Cliquid on phase diagram (dimensionless)

k Boltzmann’s constant (J K−1)

k shear yield strength (MPa)

KIC fracture toughness (MPa m1/2)