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

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The structure and properties of the fusion zone depend on many of the same vari-

ables as in a metal casting. Addition of inoculating agents to the fusion zone reduces

the grain size. Fast cooling rates or short solidiﬁcation times promote a ﬁner micro-

structure and improved properties. Factors that increase the cooling rate include in-

creased thickness of the metal, smaller fusion zones, low original metal temperatures,

and certain types of welding processes. Oxyacetylene welding, for example, uses a rela-

tively low-intensity heat source; consequently, welding times are long and the sur-

rounding solid metal, which become s very hot, is not an e¤ective heat sink. Arc-welding

processes provide a more intense heat source, thus reducing heating of the surrounding

metal and providing faster cooling. Laser welding and electron-beam welding are ex-

ceptionally intense heat sources and produce very rapid cooling rates and potentially

strong welds. The friction stir welding process has been developed for Al and Al-Li

alloys for aerospace applications.

9-11 Bulk Metallic Glasses (BMG)

Typically, metals and alloys crystallize easily during solidiﬁcation. However, in certain

complex alloys, it is possible to conduct the solidiﬁcation process in such a way that

bulk metallic glasses (BMG) are formed. In ceramic systems, such as those based on

silica, the formation of amorphous glasses is relatively easy because the kinetics of

crystallization is quite slow (Chapter 15). However, in metallic materials, special for-

mulations need to be developed so as to form bulk metallic glasses. Formation of met-

allic glasses as such was observed in the 1960s with a Au-Si alloy. What is new with

bulk metallic glasses is that relatively large (>10 mm) pieces of materials can be pre-

pared using conventional casting process with cooling rates of as low as 1 to 100



C/s.

This is very di¤erent from the cooling rates used in rapid solidiﬁcation of metallic alloys

(Section 9-3).

Figure 9-19

A schematic diagram of the fusion zone and

solidification of the weld during fusion

welding: (a) initial prepared joint, (b) weld at

the maximum temperature, with joint filled

with filler metal, and (c) weld after

solidification.

C H A P TE R 9 Principles and Applications of Solidification280

Figure 9-20 (a) Schematic diagram showing interaction between the heat source and the base

metal. Three distinct regions in the weldment are the fusion zone, the heat-affected zone, and

the base metal. (Source: From Fig 2 from David & DebRoy, Science, 257: 497–502, (1992).

Reprinted with permission from AAAS.) (b) Room temperature engineering compression stress-

strain curves for titanium- and copper-based bulk metallic glasses. The inset curves show the

true stress-true strain relationships. (Source: Ref. Das, J., Kim, K.B., Xu, W., Wei, B.C., Zhang,

Z.F., Wang, W.H., Wi, S., and Eckert, J. Mater. Trans., Vol. 47, p. 2606 (2006). Adapted from

Yavari, A.R., Lewandowski, J.J., and Eckert, J. in MRS Bulletin, Vol. 32, pages 635–638,

August 2007.)

9-11 Bulk Metallic Glasses (BMG) 281

An example of a bulk metallic-glass alloy is a material known as Vitreoly 1 or V1.

Its composition is Zr

41:2

13:8

12:5

10:0

22:5

. Such compositions of materials that

form BMG show very deep eutectics (Chapter 11), unusually high viscosities, and also

lower thermodynamic driving force for crystallization.

As can be expected, the mechanical properties of metallic glasses are di¤erent from

those of polycrystalline metals and alloys. Since there are no dislocations and slip sys-

tems (Chapter 4), slip is not possible in amorphous materials. As a result, metallic

glasses exhibit much higher elastic strains (@2%), as opposed to @0.2% in polycrystal-

line metals and alloys (Chapter 6). This large elastic deformation can be seen in the

stress-strain compression test curves for Cu- and Ti-based metallic glasses [Fig-

ure 9-20(b)]. Under tensile loadi ng, the ductility of metallic glasses is limited, however,

it is better than that for many ceramics (Chapter 15).

The combination of to develop high elastic strain (like polymers) and high yield

stress provides for high ‘‘spring back’’ for these materials (Table 9-3). Bulk metallic

glasses have been used to make golf club heads. Liquidmetal

technology also makes

use of bulk metallic glasses for sports equipment applications, including tennis rackets.

Some recent research has shown it may be possible to enhance the apparent ductility of

bulk metallic glasses by using shot peening to introduce compressive stresses at the

surface.

SUMMARY

V Transformation of a liquid to a solid is probably the most important phase trans-

formation in applications of materials science and engineering.

V Nucleation produces a criti cal-size solid particle from the liquid melt. Formation of

nuclei is determined by the thermodynamic driving force for solidiﬁcation, and is

opposed by the energy needed to create a solid-liquid interface.

V Homogeneous nucleation requires large undercoolings of the liquid and is not ob-

served in the normal solidiﬁcation processing. By introducing foreign particles or

external surfaces into the liquid, sites are provided for heterogeneous nucleation.

This is done in practice by inoculation or grain reﬁning. This process permits the

grain size of the casting to be controlled.

V Rapid cooling of the liquid can prevent nucleation and growth, giving amorphous

solids, or glasses, with unusual mechanical and physical properties. Polymeric,

metallic, and inorganic materials can be made in the form of amorphous glasses.

TABLE 9-3 9 Properties of V1 bulk metallic glass alloy compared to other materials

Properties

V1 Bulk

Metallic

Glass Al-Alloys Ti-Alloys Steels

Density g/cm

6.1 2.6–2.9 4.3–5.1 7.8

Yield Strength (Tensile) 1.9 0.1–0.63 0.18–1.32 0.5–1.6

Elastic Strain Limit 2% @0.5% @0.5% 0.5%

Fracture Toughness K

(MPam

1=2

Þ 20–140 23–45 55–115 50–154

Specific Strength (GPag

1

3

) 0.32 <0.24 <0.31 <0.21

(Source: Telford, M., Materials Today, March 2004, pp. 36–44.)

C H A P TE R 9 Principles and Applications of Solidification282

V In solidiﬁcation from melts, growth occurs as the nuclei grow into the liquid melt.

Either planar or dendritic modes of growth may be observed.

V Cooling curves can be used to determine pouring temperature, observe any under-

cooling, recalescence, and time for solidiﬁcation.

V Porosity and shrinkage are major defects that can be present in cast products. If

present, it can cause cast products to fail catastrophically.

V Sand casting, investment casting, and pressure die casting are some of the processes

for casting components. Ingot casting and continuous casting are employed in the

production and recycling of metals and alloys.

V Many metal joinin g processes (e.g., welding) involve solidiﬁcation.

GLOSSARY Brazing An alloy, known as a ﬁller, is used to join two materials to one another. The composi-

tion of the ﬁller, which has a melting temperature above about 450



C, is quite di¤erent from the

metal being joined.

Bulk metallic glasses (BMG) Amorphous metallic glasses made from compositions that show

unusually high liquid viscosities and resistance to crystallization. They exhibit high (@2% elastic

strain limit) and strength and have found applications in sporting goods.

Cavities Small holes present in a casting.

Cavity shrinkage A large void within a casting caused by the volume contraction that occurs

during solidiﬁcation.

Chill zone A region of small, randomly oriented grains that forms at the surface of a casting as

a result of heterogeneous nucleation.

Chvorinov’s rule The solidiﬁcation time of a casting is directly proportional to the square of the

volume-to-surface area ratio of the casting.

Columnar zone A region of elongated grains having a preferred orientation that forms as a re-

sult of competitive growth during the solidiﬁcation of a casting.

Continuous casting A process to convert molten metal or an alloy into a semi-ﬁnished product

such as a slab.

Critical radius ( r



) The minimum size that must be formed by atoms clustering together in the

liquid before the solid particle is stable and begins to grow.

Dendrite The treelike structure of the solid that grows when an undercooled liquid solidiﬁes.

Directional solidification (DS) A solidiﬁcation technique in which cooling in a given direction

leads to preferential growth of grains in the opposite direction, leading to an anisotropic-oriented

microstructure.

Embryo A tiny particle of solid that forms from the liquid as atoms cluster together. The embryo

may grow into a stable nucleus or redissolve.

Equiaxed zone A region of randomly oriented grains in the center of a casting produced as a

result of widespread nucleation.

Fusion welding Joining processes in which a portion of the materials must melt in order to

achieve good bonding.

Glossary 283

Fusion zone The portion of a weld heated to produce all liquid during the welding process.

Solidiﬁcation of the fusion zone provides joining.

Gas flushing A process in which a stream of gas is injected into a molten metal in order to

eliminate a dissolved gas that might produce porosity.

Gas porosity Bubbles of gas trapped within a casting during solidiﬁcation, caused by the lower

solubility of the gas in the solid compared with that in the liquid.

Glass-ceramics Polycrystalline, ultraﬁne grained ceramic materials obtained by controlled

crystallization of amorphous glasses.

Grain refinement The addition of heterogeneous nuclei in a controlled manner to increase the

number of grains in a casting.

Growth The physical process by which a new phase increases in size. In the case of solidiﬁcation,

this refers to the formation of a stable solid as the liquid freezes.

Heterogeneous nucleation Formation of a critically-sized solid from the liquid on an impurity

or an external surface.

Homogeneous nucleation Formation of a critically sized solid from the liquid by the clustering

together of a large number of atoms at a high undercooling (without an external interface).

Ingot A simple casting that is usually remelted or reprocessed by another user to produce a

more useful shape.

Ingot casting The process of casting ingots. This is di¤erent from the continuous casting route.

Ingot structure The macrostructure of a casting, including the chill zone, columnar zone, and

equiaxed zone.

Inoculants Materials that provide heterogeneous nucleation sites during the solidiﬁcation of a

material.

Inoculation The addition of heterogeneous nuclei in a controlled manner to increase the number

of grains in a casting.

Interdendritic shrinkage Small pores between the dendrite arms formed by the shrinkage that

accompanies solidiﬁcation. Also known as microshrinkage or shrinkage porosity.

Investment casting A casting process that is used for making complex shapes such as turbine

blades, also known as the lost wax process.

Lamellar A plate-like arrangement of crystals within a material.

Latent heat of fusion (DH

) The heat evolved when a liquid solidiﬁes. The latent heat of fusion

is related to the energy di¤erence between the solid and the liquid.

Local solidification time The time required for a particular location in a casting to solidify once

nucleation has begun.

Lost foam process A process in which a polymer foam is used as a pattern to produce a casting.

Lost wax process A casting process in which a wax pattern is used to cast a metal—same as

investment casting.

Microshrinkage Small, frequently isolated pores between the dendrite arms formed by the

shrinkage that accompanies solidiﬁcation. Also known as microshrinkage or shrinkage porosity.

C H A P TE R 9 Principles and Applications of Solidification284

Mold constant (B) A characteristic constant in Chvorinov’s rule.

Nucleation The physical process by which a new phase is produced in a material. In the case of

solidiﬁcation, this refers to the formation of a tiny, stable solid particles in the liquid.

Nuclei Tiny particles of solid that form from the liquid as atoms cluster together. Because these

particles are large enough to be stable, nucleation has occurred and growth of the solid can begin.

Permanent mold casting A casting process in which a mold can be used many times.

Pipe shrinkage A large conical-shaped void at the surface of a casting caused by the volume

contraction that occurs during solidiﬁcation.

Planar growth The growth of a smooth solid-liquid interface during solidiﬁcation, when no

undercooling of the liquid is present.

Pouring temperature The temperature of a metal or an alloy when it is poured into a mold

during the casting process.

Pressure die casting A casting process in which molten metal/alloys is forced into a die under

pressure.

Primary processing Processes involving casting of molten metals into ingots or semi-ﬁnished

useful shapes such as slabs.

Rapid solidification processing Producing unique material structures by promoting unusually

high cooling rates during solidiﬁcation.

Recalescence The increase in temperature of an undercooled liquid metal as a result of the

liberation of heat during nucleation.

Riser An extra reservoir of liquid metal connected to a casting. If the riser freezes after the

casting, the riser can provide liquid metal to compensate for shrinkage.

Sand casting A casting process using sand molds.

Secondary dendrite arm spacing (SDAS) The distance between the centers of two adjacent sec-

ondary dendrite arms.

Secondary processing Processes such as rolling, extrusion, etc. used to process ingots or slabs

and other semi-ﬁnished shapes.

Shrinkage Contraction of a casting during solidiﬁcation.

Shrinkage porosity Small pores between the dendrite arms formed by the shrinkage that

accompanies solidiﬁcation. Also known as microshrinkage or interdendritic porosity.

Sievert’s law The amount of a gas that dissolves in a metal is proportional to the partial pres-

sure of the gas in the surroundings.

Soldering Soldering is a joining process in which the ﬁller has a melting temperature below

450



C, no melting of the base materials occurs.

Solidification front Interface between a solid and liquid.

Solidification process Processing of materials involving solidiﬁcation (e.g., single crystal

growth, continuous casting, etc.).

Specific heat The heat required to change the temperature of a unit mass of the material one

degree.

Glossary 285

Spherulite Spherical-shaped crystals produced when certain polymers solidify.

Superheat The pouring temperature minus the freezing temperature.

Thermal arrest A plateau on the cooling curve during the solidiﬁcation of a material caused by

the evolution of the latent heat of fusion during solidiﬁcation. This heat generation balances the

heat being lost as a result of cooling.

Total solidification time The time required for the casting to solidify completely after the cast-

ing has been poured.

Undercooling The temperature to which the liquid metal must cool below the equilibrium

freezing temperature before nucleation occurs.

PROBLEMS

Section 9-1 Technological Significance

Section 9-2 Nucleation

9-1 Deﬁne the following terms: nucleation, embryo,

heterogeneous nucleation, and homogeneous

nucleation.

9-2 Suppose that liquid nickel is undercooled until ho-

mogeneous nucleation occurs. Calculate

(a) the critical radius of the nucleus required; and

(b) the number of nickel atoms in the nucleus.

Assume that the lattice parameter of the solid FCC

nickel is 0.356 nm.

9-3 Suppose that liquid iron is undercooled until ho-

mogeneous nucleation occurs. Calculate

(a) the critical radius of the nucleus required; and

(b) the number of iron atoms in the nucleus.

Assume that the lattice parameter of the solid BCC

iron is 2.92 A



9-4 Suppose that solid nickel was able to nucleate ho-

mogeneously with an undercooling of only 22



How many atoms would have to group together

spontaneously for this to occur? Assume that

the lattice parameter of the solid FCC nickel is

0.356 nm.

9-5 Suppose that solid iron was able to nucleate ho-

mogeneously with an undercooling of only 15



How many atoms would have to group together

spontaneously for this to occur? Assume that the

lattice parameter of the solid BCC iron is 2.92 A



9-6 Calculate the fraction of solidiﬁcation that occurs

dendritically when iron nucleates

(a) at 10



C undercooling;

(b) at 100



C undercooling; and

The speciﬁc heat of iron is 5.78 J/cm





Section 9-3 Growth Mechanisms

9-7 Calculate the fraction of solidiﬁcation that occurs

dendritically when silver nucleates

(a) at 10



C undercooling;

(b) at 100



C undercooling; and

The speciﬁc heat of silver is 3.25 J/cm





9-8 Analysis of a nickel casting suggests that 28% of

the solidiﬁcation process occurred in a dendritic

manner. Calculate the temperature at which nu-

cleation occurred. The speciﬁc heat of nickel is

4.1 J/cm





9-9 Write down Chvorinov’s rule and explain the

meaning of each term.

9-10 A 5-cm cube solidiﬁes in 4.6 min. Calculate

(a) the mold constant in Chvorinov’s rule; and

(b) the solidiﬁcation time for a 1.25 cm 1.25 cm 

15 cm bar cast under the same conditions.

Assume that n ¼ 2.

9-11 A 5-cm-diameter sphere solidiﬁes in 1050 s. Cal-

culate the solidiﬁcation time for a 0.3 cm 

10 cm  20 cm plate cast under the same con-

ditions. Assume that n ¼ 2.

9-12 Find the constants B and n in Chvorinov’s rule

by plotting the following data on a log-log plot:

C H A P TE R 9 Principles and Applications of Solidification286

Casting Dimensions

(cm)

Solidification Time

(min)

1.25  20  30 3.48

5  7.5  25 15.78

6.25 cube 10.17

2.5  10  22.5 8.13

9-13 Find the constants B and n in Chvorinov’s rule

by plotting the following data on a log-log plot:

Casting Dimensions

(cm)

Solidification Time

(s)

1  1  6 28.58

2  4  4 98.30

4  4  4 155.89

8  6  5 306.15

9-14 A 7.5-cm-diameter casting was produced. The

times required for the solid-liquid interface to reach

di¤erent distances beneath the casting surface were

measured and are shown in the following table:

Distance from Surface

(cm)

Time

(s)

0.25 32.6

0.75 73.5

1.25 130.6

1.875 225.0

2.5 334.9

Determine

(a) the time at which solidiﬁcation begins at the

surface; and

(b) the time at which the entire casting is ex-

pected to be solid.

idiﬁed in 720 s. Explain why this time might

di¤er from the time calculated in part (b).

9-15 A 10-cm-diameter aluminum bar solidiﬁes to a

depth of 1.25 cm beneath the surface in 5 minutes.

After 20 minutes, the bar has solidiﬁed to a depth

of 3.75 cm. How much time is required for the bar

to solidify completely?

9-16 Design the thickness of an aluminum alloy cast-

ing whose length is 30 cm and width is 20 cm, in

order to produce a tensile strength of 276 MPa.

The mold constant in Chvorinov’s rule for alu-

minum alloys cast in a sand mold is 7.2 min/cm

Assume that data shown in Figures 9-9 and 9-10

can be used.

9-17 Find the constants c and m relating the secondary

dendrite arm spacing to the local solidiﬁcation

time by plotting the following data on a log-log

plot:

Solidification Time

(s)

SDAS

(cm)

156 0.0176

282 0.0216

606 0.0282

1356 0.0374

Figure 9-9 (Repeated for Problem 9-16) The effect of

solidification time on the secondary dendrite arm

spacings of copper, zinc, and aluminum.

Figure 9-10 (Repeated for Problem 9-16) The effect

of the secondary dendrite arm spacing on the

properties of an aluminum casting alloy.

Problems 287

Section 9-4 Cooling Curves

Section 9-5 Cast Structure

9-18 Sketch a cooling curve for a pure metal and label

di¤erent regions carefully.

9-19 A cooling curve is shown in Figure 9-21. Deter-

mine

(a) the pouring temperature;

(b) the solidiﬁcation temperature;

(d) the cooling rate, just before solidiﬁcation

begins;

(e) the total solidiﬁcation time;

(f) the local solidiﬁcation time; and

(g) the probable identity of the metal.

(h) If the cooling curve was obtained at the cen-

ter of the casting sketched in the ﬁgure,

determine the mold constant, assuming that

n ¼ 2.

9-20 A cooling curve is shown in Figure 9-22. Deter-

mine

(a) the pouring temperature;

(b) the solidiﬁcation temperature;

(d) the cooling rate, just before solidiﬁcation

begins;

(e) the total solidiﬁcation time;

(f) the local solidiﬁcation time;

(g) the undercooling; and

(h) the probable identity of the metal.

(i) If the cooling curve was obtained at the center

of the casting sketched in the ﬁgure, determine

the mold constant, assuming that n ¼ 2.

9-21 Figure 9-23 shows the cooling curves obtained

from several locations within a cylindrical alu-

minum casting. Determine the local solid-

iﬁcation times and the SDAS at each location,

then plot the tensile strength versus distance from

the casting surface. Would you recommend that

the casting be designed so that a large or small

amount of material must be machined from the

surface during ﬁnishing? Explain.

9-22 Calculate the volume, diameter, and height of the

cylindrical riser required to prevent shrinkage in

a10cm 25 cm  50 cm casting if the H/D of

the riser is 1.5.

Figure 9-21 Cooling curve (for Problem 9-19).

5 cm

Figure 9-22 Cooling curve (for Problem 9-20).

Figure 9-23 Cooling curves (for Problem 9-21).

C H A P TE R 9 Principles and Applications of Solidification288

Section 9-6 Solidification Defects

9-23 In general, compared to components prepared

using forging, rolling, extrusion, etc., cast prod-

ucts tend to have lower fracture toughness. Ex-

plain why this may be the case.

9-24 What is a riser? Why should it be designed so as

to freeze after the casting?

9-25 Calculate the volume, diameter, and height of the

cylindrical riser required to prevent shrinkage in a

2.5 cm  15 cm  15 cm casting if the H/D of the

riser is 1.0.

9-26 Figure 9-24 shows a cylindrical riser attached to

a casting. Compare the solidiﬁcation times for

each casting section and the riser and determine

whether the riser will be e¤ective.

9-27 Figure 9-25 shows a cylindrical riser attached to

a casting. Compare the solidiﬁcation times for

each casting section and the riser and determine

whether the riser will be e¤ective.

9-28 A 10-cm-diameter sphere of liquid copper is al-

lowed to solidify, producing a spherical shrinkage

cavity in the center of the casting. Compare the

volume and diameter of the shrinkage cavity in

the copper casting to that obtained when a 10-cm

sphere of liquid iron is allowed to solidify.

9-29 A 10-cm cube of a liquid metal is allowed to sol-

idify. A spherical shrinkage cavity with a diame-

ter of 3.725 cm is observed in the solid casting.

Determine the percent volume change that occurs

during solidiﬁcation.

9-30 A2cm 4cm6 cm magnesium casting is

produced. After cooling to room temperature, the

casting is found to weigh 80 g. Determine

(a) the volume of the shrinkage cavity at the

center of the casting; and

(b) the percent shrinkage that must have oc-

curred during solidiﬁcation.

9-31 A5cm 20 cm  25 cm iron casting is produced

and, after cooling to room temperature, is found

to weigh 19 kg. Determine

(a) the percent of shrinkage that must have oc-

curred during solidiﬁcation; and

(b) the number of shrinkage pores in the casting

if all of the shrinkage occurs as pores with a

diameter of 0.125 cm.

9-32 Liquid magnesium is poured into a 2 cm  2cm

24 cm mold and, as a result of directional solid-

iﬁcation, all of the solidiﬁcation shrinkage occurs

along the length of the casting. Determine the

length of the casting immediately after solid-

iﬁcation is completed.

9-33 A liquid cast iron has a density of 7.65 g/cm

Immediately after solidiﬁcation, the density of

the solid cast iron is found to be 7.71 g/cm

. De-

termine the percent volume change that occurs

during solidiﬁcation. Does the cast iron expand

or contract during solidiﬁcation?

Section 9-7 Casting Processes

for Manufacturing Components

9-34 An alloy is cast into a shape using a sand mold

and a metallic mold. Which casting will be ex-

pected to be stronger and why?

Section 9-8 Continuous Casting, Ingot Casting,

and Single Crystal Growth

Section 9-9 Solidification of Polymers

and Inorganic Glasses

9-35 Why do most plastics contain amorphous and

crystalline regions?

9-36 Explain why silicate glasses tend to form amor-

phous glasses, however, metallic melts typically

crystallize easily.

Section 9-10 Joining of Metallic Materials

9-37 Deﬁne the terms brazing and soldering.

Figure 9-24 Step-block casting (for Problem 9-26).

Figure 9-25 Step-block casting (for Problem 9-27).

Problems 289

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