Askeland D.R., Fulay P.P. Essentials of Materials Science & Engineering

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isothermally at the melting temperature (point D to E ) as the latent heat given o¤ from

continued solidiﬁcation is balanced by the heat lost by cooling. This region between

points D and E, where the temperature is constant, is known as the thermal arrest.A

thermal arrest, or plateau, is produced because of the evolution of the latent heat of

fusion balances the heat being lost because of cooling. At point E, solidiﬁcation is

complete and the solid casting cools from point E to room temperature.

If the liquid is well-inoculated, the extent of undercooling is usually very small. The

undercooling and recalescence are very small and can be observed in cooling curves

only by very careful measurements. If e¤ective heterogeneous nuclei are present in the

liquid, solidiﬁcation begins at the freezing temperature [Figure 9-11(b)]. The latent heat

keeps the remaining liquid at the freezing temperature until all of the liquid has sol-

idiﬁed and no more heat can be evolved. Growth under these conditions is planar. The

total solidiﬁcation time of the casting is the time required to remove both the speciﬁc

heat of the liquid and the latent heat of fusion. Measured from the time of pouring until

solidiﬁcation is complete, this time is given by Chvorinov’s rule. The local solidiﬁcation

time is the time required to remove only the latent heat of fusion at a particular location

in the casting; it is measured from when solidiﬁcation begins until solidiﬁcation is

completed. The local solidiﬁcation times (and the total solidiﬁcation times) for liquids

solidiﬁed via undercooled and inoculated liquids will be slightly di¤erent.

Figure 9-11

(a) Cooling curve for a pure metal

that has not been well inoculated.

Liquid cools as specific heat is

removed (between points A and B).

Undercooling is thus necessary

(between points B and C). As the

nucleation begins (point C), latent

heat of fusion is released causing

an increase in the temperature of

the liquid. This process is known

as recalescence (point C to point

D). Metal continues to solidify at a

constant temperature (T

melting

). At

point E, solidification is complete.

Solid casting continues to cool

from the point. (b) Cooling curve

for a well inoculated, but otherwise

pure, metal. No undercooling is

needed. Recalescence is not

observed. Solidification begins at

the melting temperature.

C H A P TE R 9 Principles and Applications of Solidification270

9-5 Cast Structure

In manufacturing components by casting, molten metals are often poured into molds

and permitted to solidify. The mold produces a ﬁnished shape, known as a casting.In

other cases, the mold produces a simple shape, called an ingot. An ingot usually re-

quires extensive plastic deformation before a ﬁnished product is created. A macro-

structure, somet imes referred to as the ingot structure, consists of as many as three parts

(Figure 9-12). (Recall that in Chapter 2 we had used the term ‘‘macrostructure’’ to de-

scribe the structure of a material at a macroscopic scale. Hence, the term ‘‘ingot struc-

ture’’ may be more appropriate.)

Chill Zone The chill zone is a narrow band of randomly oriented grains at the surface

of the casting. The metal at the mold wall is the ﬁrst to cool to the freezing temperature.

The mold wall also provides many surface sites at which heterogeneous nucleation

takes place.

Columnar Zone The columnar zone contains elongated grains oriented in a particular

crystallographic direction. As heat is removed from the casting by the mold material,

the grains in the chill zone grow in the direction opposite the heat ﬂow, or from the

coldest toward the hottest areas of the casting. This tendency usually means that the

grains grow perpendicular to the mold wall.

Equiaxed Zone Although the solid may continue to grow in a columnar manner until

all of the liquid has solidiﬁed, an equiaxed zone frequently forms in the center of the

casting or ingot. The equiaxed zone contains new, randomly oriented grains, often

caused by a low pouring temperature, alloying elements, or grain reﬁning or inoculating

Figure 9-12

Development of the ingot structure

of a casting during solidification:

(a) Nucleation begins, (b) the chill

zone forms, (c) preferred growth

produces the columnar zone, and

(d) additional nucleation creates the

equiaxed zone.

9-5 Cast Structure 271

agents. Small grains or dendrites in the chill zone may also be torn o¤ by strong con-

vection currents that are set up as the casting begins to freeze. These also provide the

heterogeneous nucleation sites for what ultimately become equiaxed grains. These grains

grow as relatively round, or equiaxed, grains with a random orientation, and they stop

the growth of the columnar grains. The formation of the equiaxed zone is a nucleation-

controlled process and causes that portion of the casting to display isotropic behav ior.

9-6 Solidification Defects

Although there are many defects that potentially can be introduced during solid-

iﬁcation, shrinkage and the porosity deserve special mention. If a casting contains pores

(small holes), the cast component can fail catastrophically when used for load-bearing

applications (e.g., turbine blades).

Shrinkage Almost all materials are more dense in the solid state than in the liquid

state. During solidiﬁcation, the material contracts, or shrinks, as much as 7% (Table 9-2).

Often, the bulk of the shrinkage occurs as cavities, if solidiﬁcation begins at all surfaces

of the casting, or pipes, if one surface solidiﬁes more slowly than the others (Figure 9-13).

The presence of such pipes can pose problems. For example, if in the production of zinc

ingots a shrinkage pipe remains, water vapor can condense in it. This water can lead to

an explosion if the ingot gets introduced in a furnace in which zinc is being remelted for

such applications as hot-dip galvanizing.

A common technique for controlling cavity and pipe shrinkage is to place a riser,or

an extra reservoir of metal, adjacent and connected to the casting. As the casting so-

lidiﬁes and shrinks, liquid metal ﬂows from the riser into the casting to ﬁll the shrinkage

void. We need only assure that the riser solidiﬁes after the casting and that there is an

internal liquid channel that connects the liquid in the riser to the last liquid to solidify in

the casting. Chvorinov’s rule can be used to help design the size of the riser. The fol-

lowing example illustrates how risers can be designed to compensate for shrinkage.

TABLE 9-2 9 Shrinkage during

solidification for selected materials

Material Shrinkage (%)

Al 7.0

Cu 5.1

Mg 4.0

Zn 3.7

Fe 3.4

Pb 2.7

Ga þ3.2 (expansion)

O þ8.3 (expansion)

Low-carbon steel 2.5–3.0

High-carbon steel 4.0

White Cast Iron 4.0–5.5

Gray Cast Iron þ1.9 (expansion)

Note: Some data from DeGarmo, E.P., Black,

J.T., and Koshe, R.A., Materials and Processes

in Manufacturing (1997), Prentice Hall.

C H A P TE R 9 Principles and Applications of Solidification272

Figure 9-13

Several types of macroshrinkage

can occur, including cavities and

pipes. Risers can be used to help

compensate for shrinkage.

EXAMPLE 9-4

Design of a Riser for a Casting

Design a cylindrical riser, with a height equal to twice its diameter, that will

compensate for shrinkage in a 2 cm  8cm 16 cm casting (Figure 9-14).

SOLUTION

We know that the riser must freeze after the casting. To be conservative, how-

ever, we typically require that the riser take 25% longer to solidify than the

casting. Therefore:

riser

¼ 1:25t

casting

or B



¼ 1:25B



Subscripts r and c stand for riser and casting, respectively.

The mold constant B is the same for both casting and riser, so:

ðV=AÞ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1:25ðV=AÞ

¼ð2Þð8Þð16Þ¼256 cm

¼ð2Þð2Þð8Þþð2Þð2Þð16Þþð2Þð8Þð16Þ¼352 cm

We can write equations for the volume and area of a cylindrical riser, noting

that H ¼ 2D:

¼ðp=4ÞD

H ¼ðp=4ÞD

ð2DÞ¼ðp=2ÞD

¼ 2ðp=4ÞD

þ pDH ¼ 2ðp=4ÞD

þ pDð2DÞ¼ð5p=2ÞD

ðp=2ÞðDÞ

ð5p=2ÞðDÞ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ð1:25Þð256Þ

352

D ¼ 4:77 cm H ¼ 2D ¼ 9:54 cm V

¼ 170:5cm

Although the volume of the riser is less than that of the casting, the riser sol-

idiﬁes more slowly because of its compact shape.

Figure 9-14

The geometry of the casting and riser

(for Example 9-4).

9-6 Solidification Defects 273

Interdendritic Shrinkage This consists of small shrinkage pores between dendrites.

This defect, also called microshrinkage or shrinkage porosity, is di‰cult to prevent by

the use of risers. Fast cooling rates may reduce problems with interdendritic shrinkage;

the dendrites may be shorter, permitting liquid to ﬂow through the dendritic network to

the solidifying solid interface. In addition, any shrinkage that remains may be ﬁner and

more uniformly distributed.

Gas Porosity Many metals dissolve a large quantity of gas when they are molten.

Aluminum, for example, dissolves hydrogen. When the aluminum solidiﬁes, however,

only a small fraction of the hydrogen is retained, since the solubility is remarkably

lower. The excess hydrogen that cannot be incorporated in the solid metal or alloy

crystal structure forms bubbles that may be trapped in the solid metal, producing gas

porosity. The amount of gas that can be dissolved in molten metal is given by Sievert’s

law:

Percent of gas ¼ K

ﬃﬃﬃﬃﬃﬃﬃﬃ

gas

ð9-7Þ

where p

gas

is the partial pressure of the gas in contact with the metal and K is a constant

which, for a particular metal-gas system, increases with increasing temperature. We can

minimize gas porosity in castings by keeping the liquid temperature low, by adding

materials to the liquid to combine with the gas and form a solid, or by assuring that

the partial pressure of the gas remains low. The latter may be achieved by placing the

molten metal in a vacuum chamber or bubbling an inert gas through the metal. Because

gas

is low in the vacuum, the gas leaves the metal, enters the vacuum, and is carried

away. Gas ﬂushing is a process in which bubbles of a gas, inert or reactive, are injected

into a molten metal to remove undesirable elements from molten metals and alloys. For

example, hydrogen in aluminum can be removed using nitrogen or chlorine. Degassing

a molten metal is important in the production of steels and many other alloys.

9-7 Casting Processes for Manufacturing Components

Figure 9-15 summarizes four of the dozens of commercial casting processes. In some

processes the same mold can be used; in others the mold is expendable. Sand casting

processes include green sand molding, for which silica (SiO

) sand grains bonded with

wet clay are packed around a removable pattern. Ceramic casting process es use a ﬁne-

grained ceramic material as the mold; a slurry containing the ceramic may be poured

around a reusable pattern, which is removed after the ceramic hardens. In investment

casting, the ceramic slurry of a material such as colloidal silica (consisting of nano-sized

ceramic particles) coats a wax pattern. After the ceramic hardens (i.e., the colloidal

silica dispersion gels), the wax is melted and drained from the ceramic shell, leaving

behind a cavity that is ﬁlled with molten metal. The investment casting process, also

known as the lost wax process, is best suited for generating most complex shapes. Den-

tists and jewelers originally used the precision investment casting process. Currently,

this process is used to produce such components as turbine blades, titanium heads of

golf clubs, and parts for knee and hip prosthesis. In another process known as the lost

foam process, polystyrene beads, similar to those used to make co¤ee cups or packaging

materials, are used to produce a foam pattern. Loose sand is compacted around the

C H A P TE R 9 Principles and Applications of Solidification274

Figure 9-15 Four typical casting processes: (a) and (b) Green sand molding, in which clay-

bonded sand is packed around a pattern. Sand cores can produce internal cavities in the

casting. (c) The permanent mold process, in which metal is poured into an iron or steel mold.

(d) Die casting, in which metal is injected at high pressure into a steel die. (e) Investment

casting, in which a wax pattern is surrounded by a ceramic; after the wax is melted and

drained, metal is poured into the mold.

9-7 Casting Processes for Manufacturing Components 275

pattern to produce a mold. When molten metal is poured into the mold, the polymer

foam pattern melts and decomposes, with the metal taking the place of the pattern.

In the permanent mold and pressure die casting processes, a cavity is machined

from metallic material. After the liquid poured into the cavity solidiﬁes, the mold is

opened, the casting is removed, and the mold is reused. The processes using metallic

molds tend to give the highest strength castings because of the rapid solidiﬁcation. Ce-

ramic molds, including those used in investment casting, are good insulators and give

the slowest-cooling and lowest-strength castings. Millions of truck and car pistons are

made in foundries using permanent mold casting. Good surface ﬁnish and dimensional

accuracy are the advantages of permanent mold casting technique. High mold costs and

limited complexity in shape are the limitations of this technique.

In pressure die casting, molten metallic material is forced into the mold under high

pressures and is held under pressure during solidiﬁcation. Many zinc, aluminum, and

magnesium-based alloys are processed using pressure die casting. Extremely smooth

surface ﬁnishes, very good dimensional accuracy, the ability to cast intricate shapes,

and high production rates are the advantages of the pressure die casting process. Since

the mold is metallic and must withstand high pressures, the dies used are expensive and

the technique is limited to smaller sized components.

9-8 Continuous Casting, Ingot Casting, and Single Crystal Growth

As discussed in the prior section, casting is a tool used for the manufacturing of com-

ponents. It is also a process for producing ingots or slabs that can be further processed

into di¤erent shapes (e.g., rods, bars, wires, etc.). In the steel industry, millions of

pounds of steels are produced using a blast furnace, an electric arc furnace and other

processes. Although the details change, most metals and alloys (e.g., copper and zinc)

are extracted from their ores using similar processes. Certain metals, such as aluminum,

are produced using an electrolytic process since aluminum oxide is too stable and can

not be readily reduced to aluminum metal using coke or other reducing agents.

In many cases, we begin with scrap metals and recyclable alloys. In this case, the

scrap metal is melted and processed, removing the impurities and adjusting the com-

position. Considerable amounts of steels, aluminum, zinc, stainless steels, titanium, and

many other materials are recycled every year.

In ingot casting, molten steels or alloys obtained from a furnace are cast into large

molds. The resultant castings, called ingots, are then processed for conversion into useful

shapes via thermomechanical processing, often at another location. In the continuous

casting process, the idea is to go from molten metallic material to some more useful

‘‘semi-ﬁnished’’ shape such as a plate, slab, etc. The liquid metal is fed from a holding

vessel (a tundish) into a water-cooled oscillating copper mold, which rapidly cools

the surface of the steel. The partially solidiﬁed steel is withdrawn from the mold at

the same rate that additional liquid steel is introduced . The center of the steel casting

ﬁnally solidiﬁes well after the casting exits the mold. The continuously cast material is

then cut into appropriate lengths by special cutting machines.

The secondary processing steps in the processing of steels and other alloys are

shown in Figure 9-16.

There are some applications for which a small equiaxed grain structure in the cast-

ing is not desired. Castings used for blades and vanes in turbine engines are an example

C H A P TE R 9 Principles and Applications of Solidification276

(Figure 9-17). These castings are often made of titanium, cobalt or nickel-based super-

alloys using precision investment casting.

In conventionally cast parts, an equiaxed grain structure is often produced. How-

ever, blades and vanes for turbine and jet engines fail along transverse grain boundaries.

Better creep and fracture resistance are obtained using the directional solidiﬁcation (DS)

growth technique. In the DS process, the mold is heated from one end and cooled from

Figure 9-16 Secondary processing steps in processing of steel and alloys. (Source:

www.steel.org. Used with permission of the American Iron and Steel Institute.)

Figure 9-17

Controlling grain

structure in turbine

blades: (a) conventional

equiaxed grains,

(b) directionally solidified

columnar grains, and

9-8 Continuous Casting, Ingot Casting, and Single Crystal Growth 277

the other, producing a columnar microstructure with all of the grain boundaries running

in the longitudinal direction of the part. No grain boundaries are present in the trans-

verse direction [Figure 9-17(b)].

Still better properties are obtained by using a single crystal (SC) technique. Solid-

iﬁcation of columnar grains again begins at a cold surface; how ever, due to the helical

connection, only one columnar grain is able to grow to t he main body of the casting

[Figure 9-17(c)]. The single crystal casting has no grain boundaries, so its crystallo-

graphic planes and directions can be directed in an optimum orientation.

Single Crystal Growth One of the most important applications of solidiﬁcation is the

growth of single crystals. Polycrystalline materials cannot be used e¤ectively in many

electronic and optical applications. Grain boundaries and other defects interfere with

the mechanisms that provide useful electrical or optical functions. For example, in order

to utilize the semiconducting behavior of doped silicon, high-purity single crystals must

be used. The current technology for silicon makes use of large (up to 12-in. diameter)

single crystals.

9-9 Solidification of Polymers and Inorganic Glasses

Similar to the processing of metals and alloys, the processing of thermoplastics depends

critically on our ability to melt and process them via extrusion and other processes. We

will discuss these processes in later chapters.

Many polymers do not crystallize, but solidify, when cooled. In these materials, the

thermodynamic driving force may exist; however, the rate of nucleation of the solid may

be too slow, or the complexity of the polymer chains may be so great that a crystalline

solid does not form. Crystallization in polymers is almost never complete and is sig-

niﬁcantly di¤erent from that of metalli c materials, requiring long polymer chains to be-

come closely aligned over relatively large distances. By doing so, the polymer grows as

lamellar, or plate-like, crystals (Figure 9-18). Amorphous regions are present between

Figure 9-18

A spherulite in polystyrene (8000).

(From R. Young and P. Lovell,

Introduction to Polymers, 2nd Ed.,

Chapman & Hall, 1991).

C H A P TE R 9 Principles and Applications of Solidification278

the individual lamella, bundles of lamellae, and individual spherulites. In addition,

bundles of la mellae grow from a common nucleus, but the crystallographic orientation

of the lamellae within any one bundle is di¤erent from that in another. As the bundles

grow, they may produce a spheroidal shape called a spherulite. The spherulite is com -

posed of many individual bundles of di¤erently oriented lamellae.

Many polymers of commercial interest develop crystallinity during their processing.

Crystallinity can originate from cooling as discussed previously, or from the application

of stress. For example, PET plastic bottles are prepared using the blow-stretch process,

and they can develop considerable crystallinity during formation. This crystallization is

a result of the application of stress, and thus, is di¤erent from that encountered in the

solidiﬁcation of metals and alloys. In general, such polymers as nylon and polyethylene

crystallize more easily when compared to many other ther moplastics. Increased crys-

tallinity due to ﬁne crystals adds to the strength of thermoplastics.

Inorganic glasses, such as silicate glasses, also do not crystallize easily for kinetic

reasons. While the thermodynamic driving force exists, similar to the solidiﬁcation of

metals and alloys; however, the melts are often too viscous and the di¤usion is too slow

for crystallization to proceed during solidiﬁcation. The ﬂoat-glass process is used to

melt and cast large ﬂat pieces of glasses. In this process, molten glass is made to ﬂoat on

molten tin. As discussed in Chapters 6 and 7, since the strength of inorganic glasses

depends critic ally on surface ﬂaws produced by the manufacturing process or the re-

action with atmospheric moisture, most glasses are strengthened using tempering.

When safety is not a primary concern, annealing is used to reduce stresses. Long lengths

of glass ﬁbers, such as those used with ﬁber optics, are produced by melting a high-

purity glass rod known as a preform. As mentioned earlier, careful control of nucleation

in glasses can lead to glass-ceramics, colored glasses, and photochromic glasses (glasses

that can change their color or tint upon exposure to sunlight).

9-10 Joining of Metallic Materials

In brazing, an alloy, known as a ﬁller, is used to join one metal to itself or to another

metal. The brazing ﬁller metal has a melting temperature above about 450



C. Soldering

is a brazing process in which the ﬁller has a melting temperature below 450



C. Lead-tin

and antimony-tin alloys are the most common mater ials used for soldering. New lead-

free soldering materials have been developed, since lead is toxic. Alloys being developed

include those that are based on Sn-Cu-Ag. In brazing and soldering, the metallic mate-

rials being joined do not melt; only the ﬁller material melts. In both brazing and sol-

dering, the composition of the ﬁller material is di¤erent from that of the base material

being joined. Various aluminum-silicon, copper, magnesium and precious metals are

used for brazing.

Solidiﬁcation is also important in the joining of metals through fusion welding.In

the fusion-welding processes, a portion of the metals to be joined is melted and, in

many instances, additional molten ﬁller metal is added. The pool of liquid metal

is called the fusion zone (Figures 9-19 and 9-20). When the fusion zone subsequently

solidiﬁes, the original pieces of metal are joined together. During solidiﬁcation of the

fusion zone, nucleation is not required. The solid simply begins to grow from existing

grains, frequently in a columnar manner. Growth of the solid grains in the fusion zone

from the pre-existing grains is via epitaxial growth.

9-10 Joining of Metallic Materials 279

Askeland D.R., Fulay P.P. Essentials of Materials Science &amp; Engineering

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Askeland D.R., Fulay P.P. Essentials of Materials Science & Engineering