Ferry M. Direct Stripcasting of Metals and Alloys: Processing, Microstructure and Properties
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DSC
process
variables
and
cast
strip
quality
123
defects
in
soft aluminium alloys and heat lines
in
harder alloys (Merchant
et
al.
1989).
These casting defects can be minimised
by
computerised monitoring of
casting temperatures, roll torque
and
roll separating force.
E
S
.s:::.
15..
Q)
10
"C 5
c.
E
:::::I
en
I
0.5
Ii:
.l~/
V :
.-sl
y//
Il. (l =
50mm
....
I
...
(l=64mm
V
(l
=
102mm
1 5
Casting speed (m/min)
Figure
4.19.
Effect of twin roll caster speed Gumbo
3CTM
caster of Pechiney)
on
liquid
metal
sump
depth
for various tip setbacks (strip thickness is 6
mm
and
roll
diameter is
960
mm), after Bercovici
(1985)
(with
kind
permission of
The Metals, Minerals and Materials Society,
USA).
4.4.4.2 Strip exit temperature
Figure
4.18
demonstrated that the liquid
sump
profile is strongly affected by
casting speed with an increase in this parameter raising the exit temperature of
the strip. For other parameters remaining constant, this temperature increase
is to be expected since there is less time available to cool the strip via heat flow
through the metal/roll interfaces.
It
can be seen
in
Figure
4.20
that, for
horizontal
TRe, both an increase in casting speed and a decrease
in
the contact
length between the metal and rolls
(Le.
decreasing
a)
substantially increases
the strip exit temperature to a point where the metal
may
leave the rolls
in
the
semi-solid state, as discussed in §4.4.4.1.
The effect of casting velocity on the exit temperature of aluminium strip for
steel and copper rolls is shown in Figure
4.21.
For low casting speeds, the strip
exits
at
a low temperature
but
beyond a critical casting velocity there is a
significant increase
in
the temperature of the strip as a result of a sudden
decrease
in
interfacial heat transfer between the strip
and
the rolls. The
decrease in heat transfer is associated with incomplete solidification of the strip
and the semi-solid shells entering the roll bite are unable to exert sufficient
force on the rolls for efficient heat extraction (see §4.5.2). Unfortunately, a
124
Direct
strip
casting
of
metals
and
alloys
simple decrease in casting velocity does
not
reproduce the initial temperature
profile and a hysteresis loop is generated that requires a substantial decrease in
operating speed to alleviate the initial rise in temperature. Figure
4.21
shows
that higher conductivity (copper) rolls increase the critical casting velocity
which is a result of
an
increase in the interfacial heat transfer coefficient; this
factor is also controlled by various other means
(§4.5.3)
.
2.4
r-------,--~-____;,__-___."..--__,
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c.
en
.~
0.8
u;
co
()
O~--~---L--~------~----~
o
20
40
50
80
Strip/roll contact length (mm)
100
Figure
4.20.
Calculated strip exit temperature as a function of casting speed
and
strip/
roll contact length (strip thickness
=
6.5
mm), after Iricibar
and
Jin
(1984)
(with kind
permission of The Metals, Minerals and Materials Society,
USA).
-500
t:
~
.3
~
Q)
E
400
2
-
'x
Q)
C.
'
L:
CiS
200
15
Steel
rO
~
II
~
S
...
".
...
_-
.....
L
:;..
iq
. U.
id
..
__
..
20
25
30
35
40
Casting speed (mm/s)
Figure
4.21.
Effect of twin roll casting speed
and
roll type
on
strip exit temperature
for AI-2%Cu alloy, adapted from Bagshaw
et
al.
(1986).
DSC
process
variables
and
cast
strip quality
125
4.4.5
Some factors affecting as-cast strip thickness
The thickness of the strip as it exits the caster is highly dependent
on
the type
of mould and varies from tens of centimetres (slab casting) to micron-scale
(melt spinning).
Since solidification proceeds
by
heat extraction from the
slab/strip to the mould, a number of factors are likely to influence as-cast
thickness, i.e.: mould surface integrity, casting velocity, thermophysical
properties of the mould and metal and temperature of the melt. The influence
of casting velocity on strip/slab thickness for a wide range of metals and alloys
is given in Figure 4.22 for various continuous casting processes. There is a
very consistent trend over four orders of magnitude of casting velocity for
which the experimental data conforms reasonably to the following simple
power relation:
1000 r----------------------------------,
100
........
10
E
E
.....,
~
.2
u
:.c:
I-
0.1
0.01
0.001
0.001
x Cramb (1995)
. X
·····qoXX
o Thin slab casting
... Single roll casting
il. Twin roll casting
• Melt spinning
0.01
•
••
0 X
0
••
..
.•.
..
J.
••••
X
¢ Planar flow casting
-
••
tt>
IfIiS.
••
il. 'If
...
il.~.t.X
•••
il.
¢..
"f>~,
..
0.1
1
10
Casting velocity (mls)
..
..
..
..
100 1000
(4.2)
Figure
4.22.
Influence of casting velocity
on
thickness of as-cast slab/strip
in
twin-belt,
twin-roll
and
single-roll casting, free-jet melt spinning
and
planar flow casting,
adapted from Cramb
(1995)
and
Wang
and
Matthys (1996).
The generalised diagram of Figure
4.22
does
not
take into account the variation
in
processing parameters between casters
and
the different properties of the
cast metals. Nevertheless, the trend shown is supported
by
specific researches
on
a wide range of ferrous
and
non-ferrous metals with, for example, Figure
4.23
showing the effect of casting speed during twin roll casting of
AISI
304
stainless steel (copper rolls) and aluminium (steel rolls).
126
Direct
strip
casting
of
metals
and
alloys
3.0,---------------,
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r-
oo
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c:
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2.2
t-
o.
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US
1.8
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1.25
(a)
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.i1
4
o
£
0.
·c
2
US
'?
c\
\.~
·~····o···
....
·
...................................
o
(b)
I
O~_~_~_~_~_~_~
1.5
1.75
2.0
2.25
0
0.05
0.1
0.15
0.2
0.25
3.0
Roll speed (m/s) Casting speed (m/s)
Figure
4.23.
Effect
of
casting velocity on cast strip thickness
for:
(a)
TRC
of
AISI
304
stainless steel,
Kim
et
al.
(2001)
(with kind permission
of
Iron and Steel
Society,
USA);
and (b)
TRC
of
aluminium, adapted from Thomas
(2003).
The reduction
in
gauge thickness
with
increasing casting speed
in
DSC is
related to the time available for the solidifying shell
or
shells to thicken which,
in
turn, is governed
by
the thermophysical properties of
the
metal
and
mould.
For TRC of steel, initial solidification occurs
at
the meniscus
with
the two
thickening shells rotating
with
the rolls
and
final solidification occurs before
or
at
the roll nip. Therefore, the time to solidify in TRC and, hence, the achievable
strip thickness is also related to the solidification contact length which
depends
in
turn
on
the roll diameter
and
the metal head (Guthrie
and
Tavares 1998).
For
many
casting operations, the thickness of a solidifying shell, d
t
,
is normally
given
by
the following relation (Flemings 1974):
d
=ke/
2
t s
(4.3)
where
t s is the contact time between the melt
and
the
mould
wall
(solidification time)
and
k is the solidification rate constant. Equation 4.2 is
reasonably accurate for various types of casting processes
where
the cast
thickness is large (Flemings 1974). However, Kasama
et
al.
(1987)
observed that
solidification of thin-gauge strip does
not
conform to Eq. 4.2
and
found the
following relation to
be
more appropriate:
(4.4)
where L
f
is the latent
heat
of fusion taking into account the effect of melt
superheat
and
a a constant.
DSC
process
variables
and
cast
strip quality
127
Figure 4.24 shows experimental data from Kasama
et
al.
(1987)
for shell
thickness (half the total strip thickness) as a function of solidification time
during vertical
TRe
of AISI
304
stainless steel. The solid line
in
this figure is
the predicted shell thickness using
Eq.
4.4
and
shows good agreement
with
the
data. These workers used this relation to control the solidification conditions
required to generate the desired strip thickness. For a given roll diameter,
t,
is
related to casting velocity (Kasama
et
al.
1987), which allows Eq. 4.4 to be used
to predict strip thickness of a given metal based
on
casting velocity as well as
melt superheat
and
thermophysical properties of the metal
and
mould.
It
must
be assumed, however, that the roll separating force is
not
sufficient to
significantly modify the final gauge of the strip.
1.2
r---------------,
E
50.8
If)
If)
Q)
C
..IC
()
;S
Qi
.r:.
C/)
0.4
o
o
0.02
0.04
0.06 0.08
Solidification time (miri/2)
Figure 4.24. Relationship
between
shell thickness
and
solidification time for
TRe
of
AISI 304 stainless steel, after Kasama et
al.
(1987)
(with
kind
permission
of
The
Iron
and
Steel Society, USA).
The main processing variables controlling strip dimensions
in
the process of
planar flow casting (Figure 4.11a) are melt temperature which affects density,
p, substrate velocity,
v"
ejection pressure, P,
and
nozzle cross-sectional area.
The following empirical relation of Fiedler
et
al.
(1984)
is found to be valid for
the formation of thin-gauge strip
by
this process:
d
y
= 2w
(~)1/4(2P)1/2
3v, W p
(4.5)
where g is the height of the gap between the nozzle
and
wheel
and
w is the
width
of the orifice slot, Figure 4.11b.
If
all other variables remain constant, Eq.
4.5
shows that d
y
is inversely proportional to substrate velocity.
128
Direct
strip
casting
of
metals
and
alloys
4.5
Heat transfer in strip casting
During strip casting, the molten metal solidifies
by
losing heat through the
interface
between the solidifying strip and the rolls, belts
or
stationary walls of
the caster. The interface is important as it affects
both
the heat flux during
solidification
and
the nucleation
and
growth behaviour of solidifying grains
at
the melt/substrate interface as well as markedly influencing strip quality
(Cramb
1995;
Wang
and
Matthys
1996;
Strezov
and
Herbertson 1998; Blejde
et
al.
2000a,b). This section outlines the principal modes of interfacial heat
transfer
and
some of the more important factors affecting heat flux in
DSC.
4.5.1 Principal modes
of
heat transfer
When molten metal is brought into contact
with
the wall of a mould, the
magnitude of the interfacial heat flux is determined
by
the temperature
difference between the two surfaces and the interface resistance to heat flow
(Flemings 1974). During solidification, latent heat is also released
at
the
moving solid-liquid interface
(Eq.
2.20)
with the major impediments to its
removal being the solidifying metal itself, the metal/mould interface
and
the
mould. Figure 4.25 is a schematic diagram of the interface region between a
solidifying metal
and
the mould showing two possible modes of heat transfer:
(i)
heat flux through metal/mould
and
(ii) heat flux through metal/gas regions.
Interfacial
Conduction
Metal/Gas
Heat Transfer
Molten metal
Substrate
Figure
4.25.
Schematic diagram of the metal/mould interface during solidification,
adapted from Loulou
et
al
. (1999).
Conduction heat transfer - The rate of heat flow
by
conduction is governed
by
the temperature gradient that exists in a
body
(dT/dx)
and
its thermal
conductivity,
k.
For the simple case of 1-D heat flow in a material
(x
direction)
through
an
area, A, the heat transfer rate is given
by
Fourier's law of heat
conduction:
aT
q=
-
kA-
ax
(4.6)
DSC
process
variables
and
cast
strip quality 129
For the case of direct metal contact
with
the
mould
(or
if
oxide, grease or
lubricant is present
at
the interface), conduction
through
these regions is
expected to be the principal mode of heat transfer (Strezov
et
al.
2000).
Convection heat transfer - The heat flow from the solidifying metal is often
limited
by
metal/mould thermal resistance
in
the form of entrapped gases
(Figure
4.25). The rate of heat transfer across the gas interface
by
convection for
a metal
at
temperature T
m
,
to the surface of a
mould
of temperature, T
M'
is
given
by
Newton's law of cooling:
(4.7)
where h is the
convective
heat transfer coefficient. This
mode
of heat transfer is
different to conduction
and
is a result of the movement of fluid relative to the
mould surface. Nevertheless, interfacial thermal conductance can also be
quantified using a relation of the same form as
Eq.
4.7.
Radiation heat transfer - Heat may also be transferred
by
the process of
electromagnetic (thermal) radiation if a gap exists between the metal
and
the
mould wall
during
casting (Figure 4.25). The rate of heat transfer is given as:
(4.8)
where
0"
is the Stefan-Boltzmann constant (5.669 x
lO-8
W
/m2K4),
Fe
is
an
emissivity function that takes into account the non-ideality of the radiating
surfaces (gray bodies)
and
FG
a geometric 'view factor'
due
to the linear nature
of propagation of radiation such that
not
all radiation leaving one surface may
reach the other surface.
The three modes of heat transfer play a role in direct strip casting, i.e. heat
transfer
at
the metal/mould interface can occur
by
conduction through the
points of intimate contact, together
with
radiation, convection
and
conduction
across any entrapped gas in the interfacial gap
or
through
any surface films
that may be present
on
the mould.
It
was pointed
out
by
Strezov
et
al.
(2000)
that thermal conductance through a gaseous interfacial film corresponds to >
98%
of the heat flux with only minor contributions from radiation
and
convective heat transfer. Hence,
if
a gas film of average thickness,
Og'
is
present
at
the interface,
an
important mechanism of heat transfer is heat
conduction through the film. We can write:
(4.9)
This relation shows that
h_=
kg
/Og
where
kg
is the effective thermal
conductivity of the gas
and
h corresponds to
an
average value of the heat
transfer coefficient
but
transient values can be considerably different, §4.5.2.
130
Direct
strip
casting
of
metals
and
alloys
Melt/mould
interface
heat
transfer
resistance
Taking the simple case of a semi-infinite solid with
no
heat sources,
Eq.
2.47
reduces
to:
(4.10)
If
perfect
thermal contact exists between two adjacent materials (i.e. metal and
the mould)
at
different initial temperatures,
Eq.
4.10
can be solved analytically
using appropriate boundary conditions to give the interfacial heat flux as a
function of contact time,
t:
(4.11)
This relation shows that an infinite rate of interfacial heat flux occurs at the
initial contact
(t
=
0)
which is clearly
not
realistic either
in
strip casting
or
other
casting processes. As indicated previously, there is always some form of
interface
resistance
to heat flow from the melt/mould interface
in
any casting
process; this is simply a result of two surfaces not fitting perfectly.
An
average
interface resistance,
R
i
, may be computed from:
(4.12)
where flTi is the temperature difference across the interface
with
the average
resistance computed
by
taking into account the various types of resistance
in
either series or parallel (Holman
2002).
Equation 4.12 is particularly important
if the mould surface is coated
and
when the interface contains films of gas,
oxides, grease, lubricant, etc.
The following example illustrates the role of the interface
on
heat flow and the
corresponding heat transfer coefficient for steady state conditions. Figure 4.26a
shows the interface between the solidifying metal
and
mould wall where there
are:
(i)
regions of solid-solid contact of area,
Ac,
and
(ii) regions of
no
direct
contact (voids) of area,
Av,
with average thickness,
Og.
It
is pertinent to note
that this example is deceptively complex since
Ac,
Av
and
0 g are difficult to
determine (Holman
2002).
The temperature distribution
at
the interface is given
in Figure 4.26b which shows the thermal resistance,
flTi = T m - T
M'
across the
interface.
Using Eq.
4.12,
the conductive heat flow across the interface
is:
(4.13)
DSC
process
variables
and
cast
strip quality 131
The interfacial (contact) heat transfer coefficient is:
(4
.
14)
This relation is useful for determining the influence of strip casting variables
on
heat transfer (§4.5.3). For example, twin roll casting
may
generate
an
entrapped
gas film
at
the meniscus between the solidifying strip
and
the
moving rolls (Guthrie
et
ai.
2000).
Hence, if the film is continuous, heat flow is
governed predominantly
by
conduction through the film
and
Ii
=
kg
/Og
.
(b)
t
··
f··
···
···
···
·····
··
··
···
···
t!.7;
J
...........
...
...
..
...
..
. .
Distance~
Figure
4.26.
Schematic diagram
of:
(a)
Interfacial region between metal
and
the mould
and
(b) temperature profile at the interface.
4.5.2 Variation
of
heat transfer in strip casting
It
is generally acknowledged that interfacial heat transfer
during
solidification
is a strongly dynamic phenomenon with the interfacial
heat
transfer coefficient
varying throughout the process (Buchner
and
Schmitz 1992; Vangala
et
al.
1992;
Wang
and
Matthys
1996,
2002;
Kopp
et
al.
1998;
Strezov
and
Herbertson
1998;
Todoroki
et
ai
. 1997,
1998;
Loulou
et
ai.
1999;
Guthrie
et
ai.
2000;
Bouchard
et
ai.
2002). During casting, the molten metal cools
and
solidifies
and
any
thermal
expansion
or
contraction of
both
the metal
and
mould
will change the contact
configuration
at
the interface
and
result
in
a variation
in
heat transfer.
Furthermore,
when
molten metal makes contact with the mould, there is
an
initial increase in
mould
temperature with
both
the metal
and
mould
eventually decreasing
in
temperature over time.
It
is clear that a single value of
132
Direct
strip
casting
of
metals
and
alloys
h is
not
realistic although average values are almost exclusively reported.
Careful measurements
and
analysis are therefore necessary to obtain accurate
heat transfer coefficients
during
the entire process. The time evolution of
heat
flux
can"
be
readily determined
by
careful thermocouple measurements
and
numerical solution of the heat flow equations (§A.3.1).
4.5.2.1
Transient
heat
flux
The transient interface heat flux patterns
during
the initial stages of
solidification
in
a range of metals have been determined
by
various
experimental
and
modelling techniques (Kumar
and
Prabhu
1991; Wang
and
Matthys 1994,
2002;
Todoroki
et
al.
1997;
Strezov
and
Herbertson
1998;
Loulou
et
al.
1999). Strezov
and
Herbertson
(1998)
measured the change
in
temperature
during
solidification of AISI 304 stainless steel
and
calculated the variation in
heat flux using a modified version of the inverse heat conduction algorithm
developed
by
Beck
and
co-workers (1985). Figure 4.27 gives a typical result,
showing the calculated heat flux history for the initial
50
ms
of contact between
molten metal
and
a copper substrate.
It
can
be
seen
that
the
heat
flux increases
to a maximum of -
20
MW/m2
in
about the first
10
ms
of contact, before
gradually declining after
50
ms to - 5 MW/m2. The
peak
was
attributed to
nucleation
at
the melt/substrate interface
during
solidification
with
its effect
on
nucleation behaviour given
in
detail
in
§5.2.2.1. The
peak
was
also thought to
be
a quantitative reflection of the effectiveness of initial melt/substrate contact
with
its magnitude influenced
by
various casting parameters:
mould
topography, melt superheat
and
atmosphere, immersion velocity
and
melt
composition (§4.5.3).
30r-------------------------------,
O~----~----~----~------~----~
o
10
20
30
Time
(ms)
40
50
Figure
4.27.
Calculated interfacial
heat
flux as a function of contact time
during
solidification of AISI
304
stainless steel onto a copper substrate,
adapted
from Strezov
and
Herbertson
(1998).