MSE 3231

Lecture 03

Solidification and Crystallisation

1. Heat transfer
Ref:
[1] A. Ohno, The Solidification of Metals, Chijin Shokan Co. Ltd., 1976
[2] J. Campbell, Castings, Butterworth-Heinemann, 1991
Courtesy: AKMB Rashid, Dept. of MME, BUET

Topics to discuss today ….

1. Introduction
2. The ingot structure
3. Transfer of heat from liquid
 1. Introduction

 Most metal products (except P/M and electroplated products)

undergo solidification at some stages of their manufacturing.

 The structure formed immediately after solidification determines

the properties of the final products.

 Defects formed at this stage cannot be eliminated

during subsequent operations (forging, heat treatment etc.).

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 There are two types of solidification

1. Glass formation
Physical properties (e.g., viscosity) change smoothly across the solidifying region

2. Phase transition
Some physical properties (such as viscosity, heat capacity) change abruptly

Liquid  Glass Liquid  Crystal

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 crystal

Density
Temperature
latent heat
liquid
glass
Tm crystal
liquid
glass

Time Tm Temperature

Viscosity

glass

crystal
Tm Temperature
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Polycrystalline
Single crystal (one seed only)

Nanostructured material
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 2. The ingot structure
 Various types of structures formed during freezing of molten metal
depending on the
1. Amount and properties of solute in liquid
2. Properties, size and shape of the mould
3. Pouring temperature and technique

Possible ingot structures in pure metals and in alloys

(a) (b) (c) (d)

columnar grains columnar grains & fine equiaxed chill grains, equiaxed grains
only equiaxed grains at columnar grains & equiaxed only
the centre grains at the centre 7/27

Structures shown in (b) and (c)

 Most common
 Seldom homogeneous;
contains segregation defects

Structures shown in (d)

 Most desirable
 Random orientation
 Homogeneous and isotropic properties
 Most suitable for subsequent fabrication work (rolling, etc.)

Knowledge on how the structure is formed and

on the techniques of controlling structure is important
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 3. Transfer of heat from liquid

 The liquid metal must loose

heat first before it solidifies. Tm
random fluctuation
as a result of
 The hot molten liquid takes time convection
to loose its heat and solidify. DT

 Resistances to heat flow :

1. The liquid T0 air gap
2. The solidified metal
mould solid liquid
3. The metal-mould interface metal metal
4. The mould surroundings
5. The surroundings of mould
temperature profile across a casting
freezing in a mould
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 In nearly all cases, resistance (1) offered by liquid is negligible

due to bulk flow of liquid metal by forced convection during filling and
thermal convection during cooling
the turbulent flow and mixing quickly transport heat and so smooth out the
temperature gradient
this happens quickly as the bulk flow of liquid is fast compared to diffusion
process in solids which controls the other resistances

 In many cases, resistance (5) offered by the surroundings is also

negligible in practice
for normal sand mould, the atmosphere does not affect solidification as the
outer surface of the mould hardly warm by the time casting solidified inside
exceptions: thin-walled moulds (e.g., investment/shell moulding),
metal dies (cool faster when the back of the dies are cooled by water)

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  Major fundamental resistance to heat flow from castings
are items (2), (3) and (4).
all of these resistances can be simulated with varying degree of success
by different software
but the problem is both physically and mathematically complex, especially
for castings of complex geometry

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Resistance (2): the casting

 Applicable in cases when less conductive metals are

cast in more conductive moulds
 Pb-Sb alloy into steel dies (battery grids & terminals)
 steel into a copper mould
 wax patterns for investment casting into metal dies
 plastics in metal die for plastics industry

For unidirectional transient heat flow

T 2T
= as 2 as = thermal diffusivity of solid
t x
Using boundary conditions (x=0, T=T0 ; x=S, T=Tm) ,
the solution is
S = a t - b (constants a 25 mm s–1/2, b 3 mm)

The delay (b) at the beginning of solidification occurs due to

(1) loss of superheat due to turbulence, and
(2) interface resistance. Unidirectional solidification of pure iron against
a cast iron mould coated with a protective wash
 Resistance (3): the metal-mould interface

 Applicable to cases when both casting and mould are conductive

 use of insulating mould coat in die casting of light alloys
 formation an air gap as the casting cools and shrinks away from the mould

Air Gap Formation

• As the casting cools and the mould heats up, the two remain in good thermal contact
while the interface is still in liquid condition.
• When casting starts to solidify, it rapidly gains strength and contracts away from the
mould. In turn, the mould expands as its temperature rises.
• If all these expansions are homogeneous, the air-gap size d as a function of casting
diameter D can be estimated to be
Tf = freezing temperature
d / D = ac (Tf – T) + am (Tmi – T0) Tmi = mould interface temperature
T0 = original mould temperature
E.g., for Al casting at room temperature It is worth mentioning that the name 'air gap' is
D=1m D = 2 mm perhaps a misnomer. The gap usually contains about
d = 10 mm d = 10 mm 50% mould gases (high in hydrogen) and 50% air.

• Our simple air gap formula assumes that the mould

expands homogeneously.

• A rigid mould and/or a convex interface will tend to cause

inward expansion, reducing the gap
• a flat interface will often be unstable, buckling either way

• The situation in shaped castings is complicated

and is only just being tackled with some degree
of success by computer models. 14/27
 For unidirectional heat flow, rate of heat released during solidification of a casting
of density rs and latent heat L

q = -rs L A S The heat transfer coefficient, h,

t across the metal/mould
interface is simply defined as
The heat transfer coefficient h for a sufficiently large mould the rate of transfer of energy, q,
across unit area of the interface,
q per unit temperature difference
h = -
A (Tm – T0) across the interface
The total transfer of heat across
Equating and integrating from S = 0 at t = 0 gives the interface may be written as
the sum of three components:
h (Tm – T0) ht = hs + hg + hr
S = t
rs L
where hs is the conduction
through the solid contacts, hg is
For simple-shaped castings, S may be generalised to the conduction through the gas
modulus (or, V/A ratio) to calculate the solidification time phase, and hr is that transferred
by radiation.
rs L V
tf =
h (Tm – T0) A
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Resistance (4): the mould

 Applicable to cases when the mould is relatively insulating compared to the casting

T 2T
For unidirectional transient heat flow = am 2
t x
2 Tm – T0
The final solution to this differential equation is S = Kmrmcm t
p rs L

metal mould
(Kmrmcm )½ = heat diffusivity, a measure
of the rate of heat absorbed by the mould

Replacing S with V/A for simple-shaped castings,

we have the well-known Chvorinov’s Rule for determining the solidification time

B = constant for a given metal-mould system and mould

tf = B (V/A)2
temperature (its value varies from 1.5 to 2.0)

 most accurate for the highly conducting non-ferrous metals

 less good for iron and steel
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 Freezing times for plate-shaped castings in different alloys and moulds
17/27

 Chvorinov’s rule is one of the most useful guides to the casting designer.
• It provides a powerful general method of tackling the feeding of castings to ensure
their soundness.
• Since a feeder and a casting are both within the same mould and fill with the same
metal under the same conditions, Chvorinov’s rule can be used to ensure that the
casting will solidify before the feeder by designing a feeder with a higher modulus
than the casting.

 Chvorinov’s rule has some limitations:

• It is an application of one-dimensional analytical model into a three-dimensional actual
casting.
• Shape has a definite effect on the solidification time and the actual solidification time.

 Considering a shape factor, n, Chvorinov’s can be corrected as follows:

T 2T nT
= am +
t r2 rr
n = 0 for plate
V Tm – T0 2 Tm – T0 n Km t 1 for cylinder
= Kmrmcm t + 2 for sphere
A rs L p rs L 2r
 Mould and metal constants

Thermal properties of mould and chill materials at 20 C

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3.1 Increased Heat Transfer

 Fine grained castings produced by faster cooling have excellent

mechanical properties

 In practice, the casting engineer can manipulate the rate of heat

extraction from a casting using a number of tricks.

 Common ways to increase the rate of heat transfer:

1. Use of metal moulds
2. In sand moulds
(a) use of chill (external / internal) blocks in the mould, adjacent to the casting
(b) use of fins (solid / cast-on) attached to the casting

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 Use of Chill

 Various refractory mould materials - sand, investment and plaster - are all
poor absorbers of heat.
 The various chill materials are all in a league of their own, having chilling
powers orders of magnitude higher than the refractory mould materials.

 Metal pieces, placed adjacent to the pattern and subsequently packing

the sand around it to make the rest of the mould in the normal way, are
strictly known as external chills.

 Internal chills are metal pieces that are deliberately put inside the mould
cavity to cause localised cooling and become integral part with the casting.
• To have an effective bonding with the liquid metal and to eliminate causing
porosity problem, the metal piece must be cleaned thoroughly (devoid of any
oxide film and moisture).
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thickness, t

casting chill

Freezing time of a plate 225 x 150 x 50 mm

in Al-5Si-3Cu alloy at various distances
from the chilled end

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  The ability of a metal to be a chill depends on its capacity of absorbing heat,
known as heat diffusivity, (KrC)1/2
K = thermal conductivity Thermal diffusivity = K/rC
r= density
C = heat capacity
 A full chilling power of a material can
only be developed if the material is
Heat diffusivity
Material infinitely thick
(J m-2 K-1 s-1/2)
otherwise, the piece of metal becomes
Copper 37000
saturated with the heat and, after a
Graphite 22136 time, it can absorb no more heat
Pure iron 16186
Sand 1015  The amount of heat a chill can actually
Investment 671 absorb can be defined by the term
Plaster 566 volumetric heat capacity, rCV, i.e.
heat absorb per unit volume.
Copper has the highest chilling power r = density of chill material
C = sp. heat of chill material
V = volume of chill
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 Use of Fins

• When the wall forming the upright of the T-junction is thin, it acts as a cooling fin,
chilling the junction and the adjacent wall (the top cross of the T) of the casting.
• When the upright of the T-section has increased to a thickness of half the casting
section thickness then the junction is close to thermal balance, the cooling effect of
the fin balancing the hot-spot effect of the concentration of metal in the junction.

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 Fins are thin projections of solids

T-junction showing
used for localised cooling. successive position
of the freezing front

• Solid fins are more effective

on cast fins
• Length (L) and thickness (t)
of the fin must be optimum
2L
Effectiveness of fin =
t
The position fins added to T- and L-
junctions to eliminate cavity is shown
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Next Class
MSE 3231, Lecture 04

Solidification and Crystallisation

2. Nucleation and growth of solid