lecture #15: fracture & phase diagrams · lecture #15: phase diagrams engr 151: materials of...

LECTURE #15: PHASE DIAGRAMS

ENGR 151: Materials of Engineering

TENSILE TESTING VIDEO

https://www.youtube.com/watch?v=-qukVZo2JSE

PROPERTIES OF ISOMORPHOUS ALLOYS

Solid solution strengthening

For Ni-Cu alloy

tensile strength increases with increasing Ni wt%

However, ductility decreases

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

Example: Copper-silver system

Three single-phase regions (α,β,L)

Alpha(α): copper as solvent, FCC

Beta(β): silver as solvent, FCC

Pure copper and pure silver are considered to

be α and β phases respectively

BINARY EUTECTIC SYSTEMS

Below BEG line: only a limited amount of metal

will dissolve in other metal for α, β phases

Solubility limit for α phase corresponds to

boundary line CBA

Notice maximum amount of silver possible for

α phase.

Increases to a certain temperature, then decreases

to zero at the melting point of pure copper

BINARY EUTECTIC SYSTEMS

Solubility limit line separating α and α+β

phases is solvus line

Solubility limit line separating α and α+L

phases is solidus line

Solubility limit line separating β and α+β

phases is solvus line

Solubility limit line separating β and β+L

phases is solidus line

BINARY EUTECTIC SYSTEMS

Horizontal line BEG can also be considered a

solidus line (lowest temperature at which liquid

exists for alloy at equilibrium)

BINARY EUTECTIC SYSTEMS

Three two-phase regions: α+L, β+L, α+β

Tie-lines and lever rule stills apply to these

regions

COPPER-SILVER PHASE DIAGRAM

As silver is added to copper, temperature decreases at which alloy becomes liquid (melting point lowered by addition of silver)

Also works the other way around (liquidus lines meet at point E)

Invariant point: associated with composition (CE) and temperature (TE),

71.9 wt% Ag and 779°C

BINARY EUTECTIC SYSTEMS

As temperature passes through invariant point (TE),

reaction occurs:

Liquid is transformed into two solid phases at TE

(opposite reaction upon heating)

Eutectic reaction (easily melted)

CαE, CβE are compositions of α and β phases at TE (tie-

line)

( ) ( ) ( )cooling

E E Eheating

L C C C

(71.9 % ) (8.0 % ) (91.2 % )cooling

heatingL wt Ag wt Ag wt Ag

BINARY EUTECTIC SYSTEMS

General rules:

At most two phases may be in equilibrium within a

phase field (no α+β+L, only at equilibrium line)

Single phase regions are separated by two-phase

regions

Horizontal solidus line BEG at TE is called a

eutectic isotherm

BINARY EUTECTIC SYSTEMS

If a binary eutectic solution is cooled through

the invariant point, direct solidification occurs

No intermediate “L” phase

For binary phase system, no more than two

phases may be in equilibrium within a phase

field

At points along a eutectic isotherm, three phases

may be in equilibrium (e.g. point B)

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

Lead-Tin (Pb-Sn) system:

Notice that 60-40 Sn-Pb melts at 185°C (365°F),

attractive for soldering.

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

These values add

up to 1.0

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

BINARY EUTECTIC SYSTEMS

These values add

up to 1.0

EUTECTIC ALLOY DEVELOPMENT

For Lead-Tin alloy at 1

wt% Sn decreasing in

temperature from L

phase:

Remains liquid until

crossing of liquidus

line at 330°C

Continued cooling

creates more α

Solidification is

completed at solidus

line

EUTECTIC ALLOY DEVELOPMENT

For Lead-Tin alloy at

15 wt% Sn

decreasing in

temperature from L

phase:

Past the solidus

line, small β-phase

particles form

Continued cooling

slightly increases

the presence of β

EUTECTIC MICROSTRUCTURE

For Lead-Tin alloy at 61.9 wt% Sn decreasing in

temperature from L phase (invariant point, CE):

No change until TE is reached

Liquid transforms into two phases α, β

(61.9 % Sn) (18.3 % Sn) (97.8 % Sn)cooling

heatingL wt wt wt

EUTECTIC MICROSTRUCTURE

EUTECTIC MICROSTRUCTURE

For Lead-Tin alloy at 61.9

wt% Sn:

Distribution of α & β phases

are accomplished by atomic

diffusion (alternating layers

of α & β, lamellae)

Eutectic Structure

Lead atoms diffuse towards

α-phase

Tin diffuses towards β-phase

EUTECTIC MICROSTRUCTURE

EUTECTIC MICROSTRUCTURE

For Lead-Tin alloy at 40 wt% Sn decreasing in

temperature from L phase:

α-phase is present both in a eutectic structure and

α+L region

α-phase in eutectic structure is called eutectic α

α-phase primary to eutectic isotherm is called

primary α

HOMEWORK

HW (Due Monday, April 17th)

9.5, 9.6, 9.10, 9.13, 9.14

HOMEWORK

HW (Due Monday, April 24th)

9.21, 9.27, 9.34, 9.37, 9.44

EUTECTIC MICROSTRUCTURE

Microconstituent: an element of the

microstructure having an identifiable and

characteristic structure

In 40 wt% Sn, there exist two microconstituents in

the α+β phase (primary α and eutectic structure)

EUTECTIC MICROSTRUCTURE

Computing the amounts of eutectic and primary α microconstituents:

Use lever rule from solvus line to eutectic composition

We, fraction of eutectic microconstituent is equal to fraction of liquid WL from which it transforms

Wα, fraction of primary α is equal to fraction of α phase in existence prior to transformation

EUTECTIC MICROSTRUCTURE

EUTECTIC MICROSTRUCTURE

Eutectic α Primary α

Total α (w.r.t entire solution)

EUTECTIC MICROSTRUCTURE

Total β (w.r.t entire solution)

Total α (w.r.t entire solution)