Ferry M. Direct Stripcasting of Metals and Alloys: Processing, Microstructure and Properties

Overview

of

solidification

processing

53

2.3.3

Fluid flow during casting

When liquid metal is transferred from the melting container to a mould,

convection occurs from momentum effects

and

from density differences

in

the

fluid as a result of thermal gradients generated

by

hot

liquid

in

contact

with

the

mould walls. Therefore, conventional casting of ingots

or

continuous casting of

slabs, billets

or

strip will result

in

a substantial amount of fluid flow and a basic

understanding of this parameter is required for a better appreciation of

solidification. For example, localised fluid flow can melt dendrite arms to

promote the formation of equiaxed grains

(§2.3.1)

as well as modifying the

growth kinetics

and

preferred growth directions of dendrites (§2.3.3.2).

2.3.3.1

Fluidity

of

the

melt

In

processes such as DSC, molten metal enters a moving mould

with

the form

of a belt

or

of either a single roll

or

counter-rotating rolls (see §3.2.3). The

fluidity of metal will influence the solidification behaviour

in

this region which

is influenced

by

a

number

of processing variables and physical characteristics of

the material. These include:

(i)

temperature of the melt; (ii) liquid viscosity; (iii)

latent heat of fusion,

and

(iv) heat flow from the liquid through the mould wall.

The interfacial

heat

flux is controlled

by

the interface resistance, conductivity,

density

and

specific heat of the mould

(§4.5).

The fluidity of a

pure

metal, assuming that frictional effects are negligible, is

given here for a circular channel. In this situation, the flow of a

pure

superheated metal is given

by

(Flemings

1974):

(2.39)

where

L,

the fluidity, is defined as the total length of flow before the channel

entrance solidifies,

l!.T.

is the melt superheat, h the heat transfer coefficient for

heat loss to the surroundings, C

p the heat capacity of the liquid metal,

Ps

the

density of the solid,

v

F

the liquid flow velocity, D the diameter of the circular

cross section of the channel and

Tm

and

To

are the melting and ambient

temperatures, respectively.

It

will

be

clear that fluidity is a function of a

significant number of material

and

processing variables. Alloying additions are

expected to decrease the fluidity of the melt since dendrites that form create a

resistance to fluid flow

in

the early stages of solidification.

2.3.3.2

Growth

behaviour

of

dendrites

An

important consequence of fluid flow during continuous casting is the

growth direction of dendrites originating from a cold mould wall. Dendrites

growing

in

a flowing melt will incline towards the upstream direction (Figure



54

Direct

strip

casting

of

metals

and

alloys

2.19),

with

the degree of inclination affected by factors such as melt chemistry

and flow rate (§5.2.1).

In

a

pure

metal, dendrites grow in

an

undercooled melt

with

their growth

direction determined principally

by

the thermal field around the dendrite tip

(§2.2.2.2).

In

a flowing melt, the temperature around the tip

in

the downstream

direction is higher than

in

the upstream direction, thereby resulting

in

preferred

growth along this direction. For a given undercooling, dendrites growing

against the flow have a sharper tip and thus a higher growth rate than those

growing

in

the direction of the flow (Takatani

et

al.

2000).

In

an

impure material, a flowing melt affects dendritic growth

by

generating

an

asymmetrical solute field

at

the dendrite tip with the highest solute gradient

or

sharpest solute

boundary

layer occurring

on

the upstream side of the dendrite

tip (Takatani

et

al.

2000).

This solute distribution is mainly responsible for the

deviation of the preferred dendrite growth direction from the thermal gradient

as well as a distortion of the dendrite tip (Esaka

et

al.

1996). The effect of fluid

flow

on

the growth direction of dendrites into a constitutionally supercooled

liquid has been modelled by a number of investigators (Esaka

et

al.

1988;

Takatani

et

al.

2000).

....

.......

---

Fluid

Flow

t

R</>

Figure

2.19.

Schematic diagram showing the influence of fluid flow

on

dendritic

growth.

2.4

Typical casting defects

2.4.1 Segregation

of

alloying elements

There are two principal types of segregation:

macrosegregation

and

microsegregation.

The former involves compositional changes over distances

comparable to the dimensions of the casting whereas the latter occurs

on

a local

scale, for example, between growing dendrite arms.



Overview

of

solidification

processing

55

2.4.1.1 Macrosegregation

The cause of macrosegregation

during

casting is thought to be the result of

movement of liquid

or

solid within the semi-solid zone (Flemings 1974). Since

highly segregated phases are present within this zone

during

casting, the

physical displacement of these phases leads to macrosegregation. This may

occur

by

the floating or settling of precipitated phases

or

inclusions early in

solidification

or

by

the movement of liquid within the solid-liquid zone as a

result of thermal contractions, solidification shrinkage, density differences

in

the interdendritic liquid,

in

the liquid ahead of the advancing solid

and

convection currents driven

by

temperature-induced density differences in the

fluid (Flemings 1974). These factors can induce macro segregation

by

causing

mass flow over large distances

during

solidification (Porter and Easterling

1992).

2.4.1.2 Microsegregation

The dendritic solidification of

an

alloy occurs over a range of temperatures and

results

in

an

inhomogeneous distribution of solute atoms between dendrite

arms.

If

cooling occurs rapidly through the two-phase region

(L

+

S),

there is

insufficient time for atomic diffusion processes to redistribute solute

both

within the liquid in the vicinity of the solid-liquid interface

and

within the solid.

This gives rise to gradients

in

solute concentration through the thickness

direction of a given dendrite arm with the likelihood of non-equilibrium phases

forming in the last remaining liquid. The tendency for microsegregation

increases as the temperature range of solidification increases

and

as the

diffusivity of the solute atoms decreases in both the liquid

and

solid phases.

The variation in solute concentration during dendritic solidification

may

be

illustrated using the simplified situation of unidirectional planar-front

solidification of the single-phase binary alloy given

in

Figure 2.10.

It

is assumed

that complete liquid mixing occurs

but

the rapid cooling rate does

not

allow

solid-state diffusion. Figure 2.20a shows the concentration profile in the

vicinity of the solid-liquid interface in the solidifying region between two

dendrites. The variation of solute

concentration

in

the solidified region is given

by

the following mass balance:

(2.40)

Integration

with

boundary

conditions

C,

=

kC

o

at

!. = 0 gives the classic

ScheU

segregation

law:

(2.41)

Figure 2.20b is a schematic diagram of the solute distribution after solidification

which shows that substantial segregation is possible in the final regions of the



56

Direct

strip

casting

of

metals

and

alloys

solidified volume.

It

also indicates that non-equilibrium (eutectic) phases will

form in this extreme case of zero solid-state diffusion.

c

o

:;::::

. iii

VOLUME ELEMENT

Liquid

~

Cot············ .... ·

..

· ............ · ...... ·

......

· .... ·

..

+

..

·

......

·

....

·

........

·

....

·

..............

·

....

·

..

·

....

i

E

o

()

kC

o

1------

(a)

x=O

C

E

...................................................................................................

..

(b)

Distance

(x)

Figure 2.20. (a) Composition profile

during

steady-state unidirectional solidification of

the

alloy

in

Figure 2.10 for

no

solid-state diffusion

and

perfect liquid mixing. (b)

Composition profile after complete solidification

showing

the

marked

variation

in

solute distribution

in

the interdendritic region.

A quantitative description of microsegregation

during

dendritic solidification is

more complex than the simple Scheil analysis (see

e.g.

Won

and

Thomas

2001).

Brody

and

Flemings

(1966)

carried

out

a more rigorous treatment of

microsegregation

by

taking into account the diffusion of solute

in

the solid

during

solidification

and

derived the following

corrected

Scheil equation for

constant

interface growth kinetics:

C =

kC

1-

fs

[

l

k-l

S 0 1 + 4D,t

fk

/

A,z

(2.42a)

where

(2.42b)



Overview

of

solidification

processing

57

and

Ds

is the diffusivity of the solute atoms in the solid,

Do

a frequency factor

and

Qs the activation energy of

bulk

diffusion of the solute atoms.

The parameter a =

4DstJ

/

A?

in

Eq.

2.42a is essentially constant over a

wide

range of cooling rate, which should lead to relative constancy of the segregation

profile for a range of dendrite

arm

spacings. For a «

I,

Eq. 2.42a is considered

to be a good approximation of microsegregation

during

dendritic

growth

but

modifications need to

be

made

for high solid diffusivity,

that

is, larger values of

a (Clyne

and

Kurz 1981).

2.4.1.3

Removal

of

microse~regation

-

homogenisation

The degree of microsegregation

in

a single-phase alloy is governed

by

the

dendrite

arm

spacing

and

the mobility of the solute elements

in

both

the solid

and

liquid state

during

solidification. Microsegregation

needs

to

be

minimised

as

it

results

in

non-equilibrium distribution of solute

that

may

lead to non-

uniform properties of the as-cast material. Furthermore, this type of

segregation

has

a strong influence

on

thermal

and

mechanical properties such

as the rate of recrystallization

during

or

after deformation (chapter

6).

(a)

(b)

c:

o

:;:::;

. iii

o

a.

E

o

()

.................

'C~

,'C';;

.........................................

.

m M

x

Figure 2.21. Schematic

diagram

showing: (a) solidifying plate-like

dendrite

arms,

and

(b) the sinusoidal solute distribution across the

dendrite

arms,

adapted

from Flemings (1974).



58

Direct

strip

casting

of

metals

and

alloys

Homogenisation is a thermal treatment carried

out

to even

out

concentration

gradients between dendrites in the as-cast microstructure. However, a number

of other diffusion-related processes

may

occur

during

homogenisation

(Merchant

et

al.

1988):

(i)

grain coarsening or recrystallization; (ii) precipitation

of supersaturated elements;

(iii) dissolution of unstable phases

or

precipitates;

(iv) coarsening of stable intermetallic particles;

(v)

hydrogen

degassing; (vi)

pore generation

and

agglomeration and (vii) localized melting.

It

is pertinent to

note that, while macro segregation also generates a non-uniform solute and

second-phase distribution in a cast component, the scale of the segregation

makes it almost impossible to alleviate this type of segregation

by

a subsequent

heat treatment.

A large

number

of metallurgical industries rely

on

homogenisation to alleviate

concentration gradients

in

as-cast components. These usually involve extended

annealing times (several hours to days)

at

high temperatures (close to the

melting point of the alloy). As a consequence of the industrial importance of

homogenisation, various models have been proposed (Flemings 1974; Kurz

and

Fisher 1989). That

by

Kattamis

and

Flemings

(1965)

is a useful example as it

illustrates some important parameters that affect the rate of homogenisation.

It

is assumed that, for

an

alloy of mean composition

Co,

the dendrites that form

are simple plates of spacing

1/2

and that a sinusoidal concentration

distribution of a given element exists between these dendrites

with

the

maximum

and

minimum

concentration found

at

the interdendritic region (

C~

)

and

dendrite arm

(C~),

respectively (Figure 2.21). The initial solute

concentration

at

any position,

x,

is:

C(x,D) =

Co

+

(C~

-

Co

)sin(

2~)

(2.43)

The distribution of the solute element as a function of time (t)

and

temperature,

(1) is found

by

solving Fick's second law of diffusion:

(2.44)

Using appropriate boundary conditions, the solution to Eq. 2.44

is:

I ) .

(27ZX)

(4Jl'2D

t)

C(x, t) =

Co

+

\C~

-

Co

sm T exp -

12

s

(2,45)

A close examination of Eq.

2,45

shows that the same dimensionless

group

of

variables as those

in

Eq. 2,42a (Dst / 12) controls the rate of homogenisation. For

a given alloying element,

D, is fixed

(Eq.

2,42b), so the rate of homogenisation

at

a prescribed temperature is a strong function of the dendrite arm spacing.



Overview

of

solidification

processing

59

2.4.2 Other casting defects

2.4.2.1

Porosity

The two principal causes of porosity

in

cast metals are:

(i)

the shrinkage in

volume which accompanies solidification of most metals

and

(ii) gas evolution

during freezing. The former generates macroscopic-scale defects, particularly in

statically cast ingots, whereas the latter generates porosity of the order of the

grain size. Gas porosity is a result of the formation of monotomic (Ar, He etc.),

diatomic

(0

2

, Nl,

H

2

)

or

complex (CO, COl, H

2

0,

S02 etc.) gases during

solidification. Gases have a marked influence

on

the solidification

microstructure since their large solubility in the molten state is reduced

by

up

to

an

order of magnitude during transformation to the solid state (Minkoff 1986).

The solubility of hydrogen in liquid aluminium is:

and

for solid aluminium:

2761

logC

g

=---+2.768

T

2580

logC

g

=---+1.399

T

(2.46a)

(2.46b)

where C

g

is the dissolved gas concentration (cm

3

/lOOg).

In

the vicinity of the

melting point of aluminium

(660°C), the solubility of hydrogen is reduced

by

over 17 x during solidification.

The resultant gas bubbles that form

in

metals

and

alloys after solidification are

usually trapped

in

areas such as interdendritic regions of the casting. Since the

solubility of gases

in

the solid state is low, gas porosity will

be

present to some

degree unless careful degassing operations are carried

out

prior to casting.

2.4.2.2

Inclusions

Inclusions have a major influence

on

the mechanical properties of

an

as-cast

material. There are two principal types:

(i)

primary inclusions which are solid

in the melt above the liquidus temperature of the alloy,

and

(ii) secondary

inclusions

that

form during

or

after· solidification of the major phase of the

casting. Primary inclusions include slag, dross, entrapped mould material,

refractory material, fluxes, salts, oxides etc. whereas secondary inclusions such

as

MnS

in

steel result from the rejection of alloy

or

impurity elements to

interdendritic regions during solidification. The latter are usually small

compared with the dendrite

arm

spacing, i.e.

in

the range

0.1

to 5

11m

and

usually found

in

interdendritic regions after solidification.

An

increase

in

cooling rate tends to refine the size distribution of secondary inclusions (see

§5.3.1.1).

It

is possible to significantly reduce the

number

and

type of inclusions

in

an

as-cast material

by

good melting practice based

on

physical (filtering)

and/or chemical methods (Flemings

1974).

J



60

Direct

strip

casting

of

metals

and

alloys

2.5

Macroscopic heat flow in solidification

The heat flow

and

temperature distribution

during

solidification are often

complex

and

governed

by

a number of factors including the properties of the

liquid metal

and

the container

in

which the metal is solidifying. For example,

when

hot

liquid is

poured

into a cold mould there are thermal resistances

through the liquid, mould-metal interface

and

the mould, as shown

in

Figure

2.22

. Hence, the thermal profile associated

with

processes such as continuous

casting is expected to be mathematically and physically complex since the

geometry of the casting process needs to be considered as well as the thermal

properties of liquid, solid

and

mould, which usually vary

with

temperature.

Most engineering alloys solidify over a range of temperatures and the

temperature profile of such an alloy solidifying unidirectionally in a static

mould is even more complex than that for a

pure

material, Figure

2.23.

Analytical solutions of the heat flow equation to generate the correct thermal

profile are only available for the simplest of casting geometries

and

assumptions such as semi-infinite metal

and

mould, no interface resistance,

constant thermal properties and an even distribution of the heat of fusion over

the solidification range are usually made.

Q)

.....

::I

iii

.....

Q)

a.

E

~

"

.~

..

~,

~~

..-~"

:l '}

Air

:

Mould

"

,

:

,

b:

,~"

, ,

Solid

..........................

,

..............

.

.........

~

..........................

.

,

Distance (x)

Liquid

Figure 2.22. Unidirectional solidification of a

pure

metal against a flat mould wall

showing the temperature distribution

and

interface resistances (see §4.5.1).



Overview

of

solidification

processing

61

In calculations of heat transfer during solidification,

both

the material and

processing conditions need to be taken into consideration, which often results

in a difficult calculation. The thermal profile for stationary ingot casting can be

determined

by

solving the following general (multi-dimensional) transient heat

conduction equation

and

making the necessary assumptions concerning the

properties of the solidifying metal and mould:

(2.47)

where

k,

p

and

C

p

denote thermal conductivity, density

and

heat capacity.

The parameter

a = k /

pCp

is the thermal diffusivity which

may

vary as a

function of position

and

time.

The generalised 3-D heat conduction equation containing heat sources

or

sinks

and where the temperature changes with time is given as (Holman

2002):

where

if

is the energy generated

per

unit volume.

LIQUID

,

:

, Liquidus

TL

···························1······························i··············""···-·

-+-,

----

Ts

..........................

.J

...........................

························f····~~!~?·~·~·······

7;,1----

Distance (x)

,

:

,

:

i

,

:

,

:

,

(2.48)

Figure 2.23. Unidirectional solidification of

an

alloy against a flat

mould

wall

(interface resistances are

not

shown).



62

Direct

strip

casting

of

metals

and

alloys

The most important variables associated

with

heat transfer in continuous

casting are:

(i)

volume

and

temperature distribution of the melt; (ii) velocity of

withdrawal of the ingot/plate/strip;

(iii) thermal properties of

both

the metal

and

mould,

and

(iv) thickness of the material being cast. The basic

steady

state

heat flow equation

at

a fixed location for a continuous casting process in the z

(vertical) direction

and

at

a casting velocity,

v"

is:

(2.49)

where

aT

/

az

accounts for the heat transferred

by

the movement of the ingot in

the vertical direction.

On

close inspection, Eqs 2.32c

and

2.49

are of the same

form.

In DSC, a number of simplifying assumptions are required to arrive at a

reasonable solution to the aforementioned heat flow equations. Chapter 4

provides a more detailed treatment of some important aspects of heat transfer

in DSC

and

appendix A outlines some useful models for calculating heat

transfer behaviour.



Ferry M. Direct Stripcasting of Metals and Alloys: Processing, Microstructure and Properties

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