Processing of Metals and Alloys

611 Pages·1996·42.06 MB·English

by  R.W. Cahn (editor)

1 Solidification Processing
Merton C. Flemings
Department of Materials Science and Engineering,
Massachusetts Institute of Technology, Cambridge, MA, U.S.A.
List of Symbols and Abbreviations 2
1.1 Solidification Mode 4
1.2 Plane Front Solidification and Crystal Growing 4
1.3 Heat Flow in Solidification of Castings and Ingots 8
1.4 Alloy Solidification - Traditional and Rapid Solidification Processes 12
1.5 Equiaxed Structures 16
1.6 Heat Flow and Mechanical Properties 20
1.7 Microsegregation in Novel Near-Rapid Solidification Processes 24
1.8 Alloy Solidification - Columnar Growth 26
1.9 Alloy Solidification - Heat Flow into the Bulk Liquid 29
1.10 Mixed Cases of Rapid Solidification 31
1.11 Macrosegregation 33
1.12 Deformation of Semi-Solid Dendritic Structures 38
1.13 Grain Refinement 42
1.14 Semi-Solid Slurries 44
1.15 Flow Characteristics of Semi-Solid Slurries 46
1.16 Semi-Solid Composite Slurries 50
1.17 Processing Non-Dendritic Semi-Solid Slurries 52
1.18 References 54
Materials Science and Technology
Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
2 1 Solidification Processing
List of Symbols and Abbreviations
A surface area
a length scale related to interatomic spacing
0
C constant
C* composition of solid at the interface
C , C composition of a liquid, composition of the initial liquid
L o
c c specific heat of the mold, specific heat of the solidified metal
m9 s
d dendrite arm spacing
D, D, D solute diffusion coefficient, solute diffusion coefficient of a solid, solute dif-
s L
fusion coefficient of a liquid
/ , f fraction liquid, fraction solid
L s
g volume fraction liquid
L
g gravitational acceleration
r
G, G temperature gradient in a solid, temperature gradient in a liquid
s L
H heat of fusion
h casting surface heat transfer coefficient
K permeability
K consistency
k, k\ k partition ratio, effective partition ratio, equilibrium partition ratio
0
fc, /c, k thermal conductivity, thermal conductivity of a solid, thermal conductivity
s L
of a liquid
K K thermal conductivity of a mold, thermal conductivity of a solid
m9 s
L length
l one-half of the dendrite arm spacing
0
m slope of equilibrium liquidus line
L
n power law index
n rate of nucleus formation in growth direction
P pressure
R, R growth rate, isotherm velocity
T
S thickness solidified
T temperature
t, t time, total solidification time of casting
f
T mold temperature
o
T , T equilibrium liquidus temperature, initial temperature
L {
T melting point of the metal being cast
M
V casting volume
v, v velocity, velocity perpendicular to isotherms
x
z distance in growth direction
a, a thermal diffusivity, thermal diffusivity of solid metal
s
P solidification contraction
y constant
y shear rate
5 boundary thickness
List of Symbols and Abbreviations
S distance between nucleation events
g cooling rate
ji viscosity
£> QL> Qm density of a solid, density of a liquid, density of a mold
s
T shear stress
KGT Kurz-Giovanola-Trivedi model
LKT Lipton-Kurz-Trivedi model
M.I.T Massachusetts Institute of Technology
SIMA strain-induced melt activation
U.T.S. ultimate tensile strength
1 Solidification Processing
1.1 Solidification Mode usual structure is columnar dendritic. For
steeper thermal gradient and slower growth
One way to categorize solidification rate, the structure may become cellular.
processes is by their "solidification mode." Lower thermal gradient, agitation, or grain
For the primary phase of usual, non- refinement alters the structure from colum-
faceting binary alloys which solidify over a nar dendritic to equiaxed dendritic. Vigor-
temperature range, there are six of these ous agitation or more effective grain refine-
(Fig. 1-1): columnar dendritic, cellular, equi- ment results in equiaxed non-dendritic
axed dendritic, equiaxed non-dendritic, sin- solidification. Sufficiently steep thermal gra-
gle-phase plane front, and two-phase plane dient at slow growth rate results in plane
front. front solidified alloys that are either single-
For alloys which freeze over a tempera- phase or two-phase, depending on the num-
ture range, and in which thermal gradient is ber of phases present at the equilibrium sol-
sufficiently steep and convection low, the idus of the alloy.
The three structures on the left of Fig. 1-1
Equiaxed Equiaxed are the most common in usual casting and
dendritic non-dendritic crystal growing processes. The structures on
the right belong to processes of emerging or
potential commercial importance.
1.2 Plane Front Solidification
and Crystal Growing
Solidification with a plane front is ob-
Cellular
tained in one of three ways: (1) with an
ideally pure metal, (2) with an alloy at suf-
ficiently high temperature gradient, G, and
low growth rate, R; or (3) at sufficiently
high R. The first way is of little interest
(except as a physical approximation for
treating heat flow in solidification or cast-
ing of ingots which solidify in a narrow
freezing range). (This topic is treated in
Plane Front Plane Front Vol. 5, Chap. 10, Sees. 10.2.2 and 10.2.3.)
(Single-Phase) (Two-Phase)
The third is of emerging interest in "rapid
solidification processing." The second is
the basic technology of crystal growing.
The basic heat flow objectives of all crys-
tal growing techniques are to (1) maintain
a positive thermal gradient across a liquid-
solid interface, and (2) independently con-
trol this gradient so that the liquid-solid
Figure 1-1. Types of solidification structure that can
interface moves at a controlled rate. A heat
be obtained in directionally solidified binary alloys (of
the non-faceting type). balance at a planar liquid-solid interface in
1.2 Plane Front Solidification and Crystal Growing
ooooooooo
Solid I Liquid To inert gas
source or vacuum
oooooQ ooo coo
Heating coils
Crystal
(a)
To inert gas
source or vacuum
Crystal withdrawal
and rotation
Crystal
To inert gas "Floating" liquid zone
source or vacuum
Heating coils
o Figure 1-2. Examples of
crystal-growing methods,
Heating coils (a) Boat method; (b) crystal
pulling; (c) floating zone
(Flemings, 1974, courtesy
of McGraw-Hill Book
(b) (c) Company).
crystal growth from the melt is written The basic feature of all crystal growing
(Flemings, 1974) furnaces is, therefore, the ability to obtain
a controlled flux of heat across the liquid-
solid interface. Fig. 1-2 shows schemati-
where k is thermal conductivity of the cally several types of furnaces to accom-
s
solid metal, k is thermal conductivity of plish this (Flemings, 1974). Principles of
L
the liquid metal, G is temperature gradient crystal growing will be illustrated in the
s
in the solid at the liquid-solid interface, G following sections with reference to the
L
is temperature gradient in the liquid at the type of furnace illustrated in Fig. 1-2 a, in
liquid-solid interface, Q is density of the which metal in a crucible of some length,
S
solid metal, and H is heat of fusion. L, is fully melted and then solidified by
Note from Eq. (1-1) that growth velocity "normal solidification" from one end to the
R is dependent, not on absolute thermal other.
gradient, but on the difference between In the limiting ideal case of "complete
kG and /c G . Hence, thermal gradients diffusion in the liquid" (or very vigorous
s s L L
can be controlled independently of growth convection), no solid diffusion, and equilib-
velocity. This is an important attribute of rium interface kinetics, solute redistribu-
single-crystal-growing furnaces since grow- tion in crystal growth occurs as shown
ing good crystals of alloys requires that the schematically in Fig. 1-3. The liquid com-
temperature gradients be high and growth position during solidification is given by
rate be low. the well-known non-equilibrium lever rule
1 Solidification Processing
LIQUID
LIQUID
2
O 2
c
0 Co
cs
kC0
0 L
DISTANCE—*- DISTANCE •
(a) (b)
Figure 1-3. Solute redistri-
bution in solidification with
no solid diffusion and com-
plete diffusion in the liquid.
(a) At start of solidification;
(b) at temperature T*;
(c) after solidification; (d)
phase diagram (Flemings,
1974, courtesy of McGraw-
Hill Book Company).
kC(
DISTANCE - COMPOSITION •
(c) (d)
which, for constant partition ratio, fc, is In real crystal growing processes, diffu-
written sion in the liquid is not complete, and there
is some buildup of solute in a boundary
—c f^ (1-2)
layer in front of the liquid-solid interface.
where C and f are liquid composition When some convection is present, the
L L
and fraction liquid, respectively, and C is thickness of this boundary layer is taken to
o
initial liquid composition. This equation, be some value 8, usually small compared
also termed the Scheil equation, may be with the size of the liquid pool. Now, even
written in terms of the solid composition at though equilibrium is still maintained at
the interface, C*, and fraction solid, /: the interface, the higher solute content in
s s
the liquid at the interface leads to a higher
C * = fcC (l-/,)<*"" (1-3)
g 0 solute content in the solid.
This equation also describes the final solid For convenience, we now define an "ef-
composition along the length of the crystal, fective partition ratio," k\ which is equal
since it is assumed that no diffusion occurs to the solid composition forming, C*, di-
s
in the solid during or after solidification. vided by the bulk liquid composition (the
1.2 Plane Front Solidification and Crystal Growing
liquid outside the boundary layer). The
relation between k! and k is (Burton et al.,
1953):
k
k (1 4)
o
where D is the solute diffusion coefficient
L
in the liquid. This expression is of consider- oC
sM
able engineering usefulness because it re-
o k'= 1.0
lates the composition of the solid forming
co
in crystal growth to alloy composition and
growth conditions. It can be used to de-
scribe solute redistribution in crucibles of
finite extent, provided only that the thick-
ness 8 of the boundary layer is small com-
pared with the length of the crucible. When DISTANCE, x
Figure 1-4. Final solute distributions for solidification
this is true, a dynamic equilibrium is at-
with limited liquid diffusion and different amounts of
tained between the bulk melt and growing
convection (hence different "effective partition ratios,"
solid and equations identical to Eqs. (1-2)
k!) (Flemings, 1974, courtesy of McGraw-Hill Book
and (1-3) are readily derived, except that Company).
the equilibrium partition ratio k is replaced
by the effective partition ratio k':
smooth interface which moves at constant
* = fc'C (l-/)<*'-1) (1-5 a)
s 0 s velocity. Because of the buildup of solute in
front of the crystal, the "melting point" (liq-
Here C is the bulk liquid composition and uidus temperature of the alloy) increases
L
k' = C*/C . Eqs. (1-5a) and (l-5b) consti- with distance from the interface as shown
L
tute a modified "normal segregation equa- schematically in Fig. 1-5. The actual tem-
tion." perature gradient must be maintained as
Fig. 1-4 shows some calculated distribu- steep or steeper than this to avoid super-
tions of solute for the alloy of the preceding cooling ("constitutional supercooling") in
examples, taking k! equal to fc, unity, and front of the interface. The basic condition
an arbitrary value between the minimum for this, the "constitutional supercooling
(k) and the maximum (unity). As seen from criterion," may be written (Tiller et al.,
Eq. (1-4), the minimum value occurs when 1953):
Rc5/D <^1, that is, at slow growth rate,
L G _m C*(l-fc)
high liquid diffusivity, and maximum stir- L> L s (1-6)
R kD
ring, and so 5 is a minimum. At this limit, L
solute distribution is described by the spe- where m is the slope of the equilibrium
L
cial case given earlier where infinite diffu- liquidus line in the phase diagram.
sivity in the liquid was assumed. The max- As written, this equation is valid regard-
imum value of k! (equal to unity) is less of degree of stirring. For no stirring C*
s
obtained for RS/D > 1. equals C , and for very vigorous stirring it
L o
The major single problem in crystal is the partition ratio times the bulk liquid
growing of alloys is maintaining a flat, composition. Eq. (1-6) illustrates directly
1 Solidification Processing
SOLUTE ENRICHED
LAYER IN FRONT OF
LIQUID-SOLID
INTERFACE
LIQUID CO
o
o
DISTANCE,
(a) (b)
Figure 1-5. Constitutional
supercooling in alloy solidi-
t fication, (a) Phase diagram;
Lad: (b) solute-enriched layer in
UoJr D front of liquid-solid inter-
Z\-D face; (c) stable interface;
< or CONSTITUTIONALLY
c u SUPERCOOLED (d) unstable interface
CL
QL REGION (Flemings, 1974, courtesy
M
E of McGraw-Hill Book
T
Company).
DISTANCE, x1 DISTANCE, x'-
(c) (d)
the reason for the requirement in crystal single crystals in that heat is rarely added
growing of controlling G and R indepen- to the liquid during solidification, and so-
L
dently - it is the ratio of these two that lidification rates are usually much higher.
determines whether a plane front is main- Fig. 1-6 shows the general heat flow
tained. problem for solidification of a pure metal
The constitutional supercooling crite- in a mold, with temperature drops shown
rion, Eq. (1-6), remains today an engineer- across the various resistances to heat flow.
ing tool of great value, although we under- Fig. 1-7 is a similar plot, except for an alloy
stand that the conditions for breakdown of solidifying in columnar dendritic manner.
the plane front are more exactly specified (In this latter plot, mold-metal interface re-
by the stability analysis originally devel- sistance is assumed to be negligible, and
oped by Mullins and Sekerka, and that the mold is assumed to be very thick.) The
significant deviations may occur from this following description of casting processes
equation for faceting alloys or at very high is given for the case of a pure metal being
rates of solidification (Mullins and Sek- cast; differences for the treatment of alloys
erka, 1963; 1964; Sekerka, 1965). (See also are discussed later.
Vol. 15, Chap. 10, Sec. 10.2.4.) A number of important casting pro-
cesses employ mold materials that are rela-
1.3 Heat Flow in Solidification tively insulating compared with the metal
of Castings and Ingots being cast. In "sand casting" the mold is
made of sand, usually bonded with clay or
Solidification processing of castings and with a resin. The pattern to form the mold
ingots is basically different from that of cavity is usually reusable, made of wood,
1.3 Heat Flow in Solidification of Castings and Ingots
AIR SOLID LIQUID
SOLID LIQUID
*S XL
^_
LIQUIDUS
SOLIDUS
5
AT, iyAETAL-MOLD
INTERFACE
LJ
AT, MOLD-AIR To
INTERFACE
DISTANCE, x
DISTANCE
Figure 1-6. Temperature profile in solidification of a Figure 1-7. Unidirectional solidification of an alloy
pure metal (Flemings, 1974, courtesy of McGraw-Hill against a flat mold wall (Flemings, 1974, courtesy of
Book Company). McGraw-Hill Book Company).
COMPLETED
CASTING-
BROKEN OPEN
TO REVEAL
INTERIOR
Figure 1-8. Sketch of sand-
casting processes as used in
manufacture of a house-
hold radiator (Taylor et al.,
1959, courtesy of J. Wiley
and Sons, Inc.).
MOLD SECTION B
metal, or plastic (Fig. 1-8). In "investment thin mold is made by dipping the wax pat-
casting" the pattern is not reusable; it is tern alternatively into the ceramic slurry
made of wax or plastic. The pattern (or and then into a fluidized bed of dry ce-
group of patterns) is surrounded or "in- ramic. After the mold is made, it is fired to
vested" with a slurry of ceramic which is bond the ceramic and to melt and burn out
allowed to "set." In one method a relatively the pattern (Taylor et al., 1959).
10 1 Solidification Processing
The heat flow problem for casting in in- given mold surface area has a fixed ability
sulating molds is simplified by the fact that to absorb heat, it follows that in castings of
heat flow is usually limited primarily by the simple shape the volume of metal solidified
heat diffusion in the mold, as illustrated divided by the casting surface area may be
schematically in Fig. 1-9. When this is the substituted for S in Eq. (1-7). The result
case, and when mold and metal variables may be written as "Chvorinov's rule":
are constant, a simple expression relates
thickness solidified, S, to time t after cast- (1-8)
ing:
T -T where V and A are casting volume and
S = M 0 t (1-7) surface area, respectively, C is a constant,
and t is total solidification time of the cast-
{
where T is melting point of the metal be- ing.
M
ing cast, T is mold temperature, and K , In a large number of casting processes,
o m
g , and c are thermal conductivity, den- heat flow is controlled to a significant ex-
m m
sity, and specific heat, respectively, of the tent by heat transfer resistance at the cast-
mold. This equation predicts a square-root ing surface. These processes include per-
relation of thickness solidified with time manent mold casting, die casting, liquid
that is proportional to certain metal vari- metal atomization, and thin strip casting.
ables and to the square root of the "heat The die casting process is illustrated in Fig.
diffusivity,"K £ c . 1-10, and several rapid solidification pro-
m m m
Heat flow into a concave mold surface is cesses in which heat flow is largely "/z-con-
divergent and therefore somewhat faster troiled" are illustrated in Fig. 1-11.
than into a plane surface, and heat flow When the surface heat transfer coeffi-
with a convex mold surface is slower. How- cient is overriding, the temperature distri-
ever, taking as a first approximation that a bution in the metal and mold is as in Fig.
1-12, and thickness solidified in a given
time t is:
T -T
S = h M 0 (1-9)
;| SAND $ SOLID LIQUID
where h is casting surface (usually metal-
mold) heat transfer coefficient. For castings
of simple shape, Eq. (1-9) can be general-
ized to yield the total solidification time, t,
f
of the casting:
i
H
LaU. Qs (1-10)
h(T -T ) A
M 0
In the limiting case of ingot casting,
when sufficient solid metal has formed, the
DISTANCE , x
mold-metal resistance to heat transfer be-
Figure 1-9. Approximate temperature profile in solid-
comes negligible, and the temperature pro-
ification of a pure metal poured at its melting point
file becomes as in Fig. 1-13 a for a water-
against a flat, smooth mold wall (Flemings, 1974,
courtesy of McGraw-Hill Book Company). cooled mold, and as in Fig. 1-13 b for