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

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steels and other metals are often subjected to a ‘‘pickling’’ treatment in which acids are

used to dissolve the oxide scale. In some metals, such as tungsten (W) and beryllium

(Be), hot-working must be done in a protective atmosphere to prevent oxidation.

The dimensional accuracy is also more di‰cult to control during hot working. A

greater elastic strain must be considered, since the modulus of elasticity is low at hot-

working temperatures. In addition, the metal contracts as it cools from the hot-working

temperature. The combination of elastic strain and thermal contraction requires that

the part be made oversi ze during deformation; forming dies must be carefully designed,

and precise temperature control is necessary if accurate dimensions are to be obtained.

SUMMARY

V When a metallic material is deformed by cold working, strain hardening occurs

as additional dislocations are introduced into the structure. Very large increases

in strength may be obtained in this manner. The ductility of the strain hardened

metallic material is reduced.

V Wire drawing, stamping, rolling, and extrusion are some examples of manufactur-

ing methods for shaping metallic materials. Some of the underlying principles for

these processes can also be used for the manufacturing of polymeric materials.

V Annealing of metallic materials is a heat treatment intended to eliminate all, or a

portion of, the e¤ects of strain hardening. The annealing process may involve as

many as three steps.

V Recovery occurs at low temperatures, eliminating residual stresses and restoring

electrical conductivity without reducing the strength. A ‘‘stress relief anneal’’ refers

to recovery.

V Recrystallization occurs at higher temperatures and eliminates almost all of the

e¤ects of strain hardening. The disloc ation density decreases dramatically during

recrystallization as new grains nucleate and grow.

V Grain growth, which normally should be avoided, occurs at still higher temper-

atures. In cold-worked metallic materials, grain growth follows recovery and re-

crystallization.

V Hot working combines plastic deformation and annealing in a single step, permit-

ting large amounts of plastic deformation without embrittling the material.

V Residual stresses in materials need to be controlled. In cold-worked metallic mate-

rials, residual stresses can be eliminated using a stress-relief anneal.

GLOSSARY

Annealing In the context of metallic material, annealing is a heat treatment used to eliminate

part or all of the e¤ects of cold working. For glasses, annealing is a heat treatment that removes

thermally induced stresses.

Bauschinger effect A material previously plastically deformed under tension shows decreased

ﬂow stress when tested again under compression or vice versa.

Cold working Deformation of a metal below the recrystallization temperature. During cold

working, the number of dislocations increases, causing the metal to be strengthened as its shape is

changed.

C HA P T E R 8 Strain Hardening and Annealing250

Deformation processing Techniques for the manufacturing of metallic and other materials using

such processes as rolling, extrusion, drawing, etc.

Drawing A deformation processing technique in which a material is pulled through an opening

in a die (e.g., wire drawing).

Extrusion A deformation processing technique in which a material is pushed through an open-

ing in a die. Used for metallic and polymeric materials.

Fiber texture A preferred orientation of grains obtained during the wire drawing process. Cer-

tain crystallographic directions in each elongated grain line up with the drawing direction, caus-

ing anisotropic behavior.

Formability The ability of a material to stretch and bend without breaking. Forming diagrams

describe the ability to stretch and bend materials.

Frank-Read source A pinned dislocation that, under an applied stress, produces additional dis-

locations. This mechanism is at least partly responsible for strain hardening.

Heat-affected zone (HAZ) The volume of material adjacent to a weld that is heated during the

welding process above some critical temperature at which a change in the structure, such as grain

growth or recrystallization, occurs.

Hot working Deformation of a metal above the recrystallization temperature. During hot

working, only the shape of the metal changes; the strength remains relatively unchanged because

no strain hardening occurs.

Polygonized subgrain structure A subgrain structure produced in the early stages of annealing.

The subgrain boundaries are a network of dislocations rearranged during heating.

Recovery A low-temperature annealing heat treatment designed to eliminate residual stresses

introduced during deformation without reducing the strength of the cold-worked material. This is

the same as a stress-relief anneal.

Recrystallization A medium-temperature annealing heat treatment designed to eliminate all of

the e¤ects of the strain hardening produced during cold working.

Recrystallization temperature A temperature above which essentially dislocation-free and new

grains emerge from a material that was previously cold worked. This depends upon the extent of

cold work, time of heat treatment, etc., and is not a ﬁxed temperature.

Residual stresses Stresses introduced in a material during processing. These can originate as a

result of cold working or di¤erential thermal expansion and contraction. A stress-relief anneal in

metallic materials and the annealing of glasses minimize residual stresses. Compressive residual

stresses deliberately introduced on the surface by the tempering of glasses or shot peening of

metallic materials improve their mechanical properties.

Sheet texture A preferred orientation of grains obtained during the rolling process. Certain

crystallographic directions line up with the rolling direction, and certain preferred crystallo-

graphic planes become parallel to the sheet surface.

Shot peening Introducing compressive residual stresses at the surface of a part by bombarding

that surface with steel shot. The residual stresses may improve the overall performance of the

material.

Strain hardening Strengthening of a material by increasing the number of dislocations by de-

formation, or cold working. Also known as ‘‘work hardening.’’

Glossary 251

Strain-hardening exponent (n) A parameter that describes susceptibility of a material to cold

working. It describes the e¤ect that strain has on the resulting strength of the material. A material

with a high strain-hardening coe‰cient obtains high strength with only small amounts of de-

formation or strain.

Strain rate The rate at which a material is deformed.

Strain-rate sensitivity (m) The rate at which stress develops changes as a function of strain rate.

A material may behave much di¤erently if it is slowly pressed into a shape rather than trans-

formed rapidly into a shape by an impact loading.

Stress-relief anneal The recovery stage of the annealing heat treatment during which residual

stresses are relieved without reducing the mechanical properties of the material.

Texture strengthening Increase in the yield strength of a material as a result of preferred crys-

tallographic texture.

Thermomechanical processing Processes involved in the manufacturing of metallic components

using mechanical deformation and various heat treatments.

Thermoplastics A class of polymers that consist of large, long spaghetti-like molecules that are

intertwined (e.g., polyethylene, nylon, PET, etc.).

Warm working A term used to indicate the processing of metallic materials in a temperature

range that is between those that deﬁne cold and hot working (usually a temperature between 0.3

to 0.6 of melting temperature in K).

Work hardening A term sometimes used instead of strain hardening or cold working to describe

the e¤ect of deformation on the strengthening of metallic materials.

PROBLEMS

Section 8-1 Relationship of Cold Working to the

Stress-Strain Curve

8-1 A 1.263-cm-diameter metal bar with a 5-cm gage

length l

is subjected to a tensile test. The following

measurements are made in the plastic region:

Force (N)

Change in Gage

length (cm) (Dl )

Diameter

(cm)

122,320 0.5258 1.2

120,100 1.107 1.1415

114,310 1.7493 1.0858

Determine the strain-hardening exponent for the

metal. Is the metal most likely to be FCC, BCC, or

HCP? Explain.

8-2 Deﬁne the following terms: strain-hardening ex-

ponent (n), strain-rate sensitivity (m), and plastic

strain ratio (r). Use appropriate equations.

8-3 A 1.5-cm-diameter metal bar with a 3-cm gage

length (l

) is subjected to a tensile test. The fol-

lowing measurements are made:

Force (N)

Change in Gage

Length (cm) (Dl )

Diameter

(cm)

16,240 0.6642 1.2028

19,066 1.4754 1.0884

19,273 2.4663 0.9848

Determine the strain-hardening coe‰cient for the

metal. Is the metal most likely to be FCC, BCC,

or HCP? Explain.

8-4 A true stress-true strain curve is shown in Figure

8-20. Determine the strain-hardening exponent for

the metal.

8-5 A Cu-30% Zn alloy tensile bar has a strain-

hardening coe‰cient of 0.50. The bar, which has

an initial diameter of 1 cm and an initial gage

C HA P T E R 8 Strain Hardening and Annealing252

length of 3 cm, fails at an engineering stress of

120 MPa. After fracture, the gage length is 3.5 cm

and the diameter is 0.926 cm. No necking oc-

curred. Calculate the true stress when the true

strain is 0.05 cm/cm.

Section 8-2 Strain-Hardening Mechanisms

Section 8-3 Properties versus Percent Cold Work

8-6 A 0.625-cm-thick copper plate is to be cold

worked 63%. Find the ﬁnal thickness.

8-7 A 0.625-cm-diameter copper bar is to be cold

worked 63%. Find the ﬁnal diameter.

8-8 A 5-cm-diameter copper rod is reduced to a 3.75-cm

diameter, then reduced again to a ﬁnal diameter of

2.5 cm. In a second case, the 5-cm-diameter rod is

reduced in one step from a 5 cm to a 2.5-cm

diameter. Calculate the % CW for both cases.

8-9 A 3105 aluminum plate is reduced from 4.38 cm

to 2.88 cm. Determine the ﬁnal properties of the

plate. Note 3105 designates a special composition

of aluminum alloy. (See Figure 8-21.)

8-10 A Cu-30% Zn brass bar is reduced from a 2.5-cm

diameter to a 1.13-cm diameter. Determine the

ﬁnal properties of the bar. (See Figure 8-22.)

8-11 A 3105 aluminum bar is reduced from a 2.5-cm

diameter, to a 2-cm diameter, to a 1.5-cm diame-

ter, to a ﬁnal 1-cm diameter. Determine the %

CW and the properties after each step of the

process. Calculate the total percent cold work.

Note 3105 designates a special composition of

aluminum alloy. (See Figure 8-21.)

8-12 We want a Cu-30% Zn brass plate originally

3-cm thick to have a yield strength greater than

345 MPa and a % elongation of at least 10%.

What range of ﬁnal thicknesses must be ob-

tained? (See Figure 8-22.)

Figure 8-20 True stress-true strain curve (for Problem

8-4).

Figure 8-21 The effect of percent cold work on the

properties of a 3105 aluminum alloy (for Problems

8-9 and 8-11).

Figure 8-22 The effect of percent cold work on the

properties of a Cu-30% Zn brass (for Problems 8-10

and 8-12).

Problems 253

8-13 A 3105 aluminum plate previously cold worked

20% is 5-cm thick. It is then cold worked further

to 3.25 cm. Calculate the total percent cold work

and determine the ﬁnal properties of the plate.

Note 3105 designates a special composition of

aluminum alloy. (See Figure 8-21.)

Section 8-4 Microstructure, Texture

Strengthening, and Residual Stresses

Section 8-5 Characteristics of Cold Working

8-14 Aluminum cans made by deep drawing derive

considerable strength during their fabrication.

Explain why.

8-15 Such metals as magnesium can not be e¤ectively

strengthened using cold working. Explain why.

8-16 We want to draw a 0.75-cm-diameter copper wire

having yield strength of 138 MPa into a 0.625-

cm-diameter wire.

(a) Find the draw force, assuming no friction;

(b) Will the drawn wire break during the draw-

ing process? Show why. (See Figure 8-5.)

8-17 A 3105 aluminum wire is to be drawn to give a

1-mm-diameter wire having yield strength of

138 MPa. Note 3105 designates a special compo-

sition of aluminum alloy.

(a) Find the original diameter of the wire;

(b) Calculate the draw force required; and

break during the process. (See Figure 8-21.)

Section 8-6 The Three Stages of Annealing

8-18 The following data were obtained when a cold-

worked metal was annealed.

(a) Estimate the recovery, recrystallization, and

grain growth temperatures;

(b) Recommend a suitable temperature for a

stress-relief heat treatment;

working process; and

(d) Estimate the melting temperature of the

alloy.

Annealing

Temperature

(

Electrical

Conductivity

(ohm

·cm

)

Yield

Strength

(MPa)

Grain

Size

(mm)

400 3:04  10

86 0.10

500 3:05  10

85 0.10

600 3:36  10

84 0.10

700 3:45  10

83 0.098

800 3:46  10

52 0.030

900 3:46  10

47 0.031

1000 3:47  10

44 0.070

1100 3:47  10

42 0.120

8-19 The following data were obtained when a cold-

worked metallic material was annealed.

(a) Estimate the recovery, recrystallization, and

grain growth temperatures;

(b) Recommend a suitable temperature for

obtaining a high-strength, high-electrical-

conductivity wire;

Figure 8-21 (Repeated for Problems 8-13, 8-17 and

8-22.) The effect of percent cold work on the

properties of a 3105 aluminum alloy.

Figure 8-5 (Repeated for Problems 8-16 and 8-23.)

The effect of cold work on the mechanical properties

of copper.

C HA P T E R 8 Strain Hardening and Annealing254

working process; and

(d) Estimate the melting temperature of the alloy.

Annealing

Temperature

(

Residual

Stresses

(MPa)

Tensile

Strength

(MPa)

Grain

Size

(cm)

250 145 359 0.0075

275 145 359 0.0075

300 35 359 0.0075

325 0 359 0.0075

350 0 234 0.0025

375 0 207 0.0025

400 0 186 0.0088

425 0 172 0.0018

Section 8-7 Control of Annealing

8-20 Two sheets of steel have cold works of 20% and

80%, respectively. Which one would likely have a

lower recrystallization temperature? Why?

Section 8-8 Annealing and Materials Processing

8-21 Using the data in Table 8-3, plot the recrystalli-

zation temperature versus the melting temper-

ature of each metal, using absolute temperatures

(Kelvin). Measure the slope and compare with

the expected relationship between these two tem-

peratures. Is our approximation a good one?

8-22 We wish to produce a 0.75-cm-thick plate of 3105

aluminum having a tensile strength of at least

172 MPa and a % elongation of at least 5%. The

original thickness of the plate is 7.5 cm. The max-

imum cold work in each step is 80%. Describe

the cold working and annealing steps required to

make this product. Compare this process with

what you would recommend if you could do the

initial deformation by hot working. (See Figure

8-21.)

8-23 We wish to produce a 0.5-cm-diameter wire of

copper having a minimum yield strength of

414 MPa and a minimum % elongation of 5%.

The original diameter of the rod is 5 cm and the

maximum cold work in each step is 80%. Describe

the cold working and annealing steps required to

make this product. Compare this process with

what you would recommend if you could do the

initial deformation by hot working. (See Figure

8-5.)

8-24 What is a heat-a¤ected zone? Why do some

welding processes result in a joint where the ma-

terial in the heat-a¤ected zone is weaker than the

base metal?

8-25 What welding techniques can be used to avoid

loss of strength in the material in the heat-

a¤ected zone? Explain why these techniques are

e¤ective.

Section 8-9 Hot Working

8-26 The amount of plastic deformation that can

be performed during hot working is almost un-

limited. Justify this statement.

8-27 Compare and contrast hot working and cold

working.

Design Problems

8-28 Design, using one of the processes discussed in

this chapter, a method to produce each of the

following products. Should the process include

hot working, cold working, annealing, or some

combination of these? Explain your decisions.

(a) paper clips;

(b) I-beams that will be welded to produce a

portion of a bridge;

cet to the main copper plumbing;

(d) the steel tape in a tape measure; and

(e) a head for a carpenter’s hammer formed

from a round rod.

8-29 We plan to join two sheets of cold-worked copper

by soldering. Soldering involves heating the metal

TABLE 8-3 9 Typical recrystallization temperatures for

selected metals (Repeated for Problem 8-21)

Metal

Melting Temperature

(

Recrystallization

Temperature (

Sn 232 4

Pb 327 4

Zn 420 10

Al 660 150

Mg 650 200

Ag 962 200

Cu 1085 200

Fe 1538 450

Ni 1453 600

Mo 2610 900

W 3410 1200

(Source: Adapted from Structure and Properties of Engineering

Materials, by R. Brick, A. Pense, and R. Gordon, 1977.

permission.)

Problems 255

to a high enough temperature that a ﬁller mate-

rial melts and is drawn into the joint (Chapter 9).

Design a soldering process that will not soften the

copper. Explain. Could we use higher soldering

temperatures if the sheet material were a Cu-30%

Zn alloy? Explain.

8-30 We wish to produce a 1-mm-diameter copper

wire having a minimum yield strength of

414 MPa and a minimum % elongation of 5%.

We start with a 20-mm-diameter rod. Design the

process by which the wire can be drawn. Include

all-important details and explain.

C HA P T E R 8 Strain Hardening and Annealing256

Principles and Applications of

Solidiﬁcation

Have You Ever Wondered?

9 Whether water really does ‘‘freeze’’ at 0



C and ‘‘boil’’ at 100



9 What is the process used to produce several million kilograms of steels and other alloys?

9 What factors determine the strength of a cast product?

9 What is a Liquidmetal

Of all the processing techniques used in the

manufacturing of materials, solidification is

probably the most important. All metallic mate-

rials, as well as many ceramics, inorganic

glasses, and thermoplastic polymers, are liquid

or molten at some point during processing. Like

water freezes to ice, molten materials solidify as

they cool below their freezing temperature. In

Chapter 2, we learned how materials are classi-

fied based on their atomic, ionic, or molecular

order. During the solidification of materials that

crystallize, the atomic arrangement changes from

a short-range order (SRO) in a liquid to a long-

range order (LRO) in the crystalline solid. The

257

solidification of materials that crystallize requires

two steps: In the first step, ultra-fine crystallites,

known as the nuclei of a solid phase, form from

the liquid. In the second step, which can overlap

with the first, the ultra-fine solid crystallites be-

gin to grow as atoms from the liquid are attached

to the nuclei until no liquid remains. Some ma-

terials, such as inorganic silicate glasses, will

turn into a solid without developing a long-range

order (i.e., they remain amorphous). Many poly-

meric materials may develop partial crystallinity

during solidification or processing.

The solidification of metallic, polymeric, and

ceramic materials is an important process to study

because of its effect on the properties of the ma-

terials involved. In Chapter 8, we examined how

strain hardening can be used to strengthen and

shape metallic materials. We learned in Chapter 4

that grain size plays an important role in de-

termining the strength of metallic materials. In

this chapter, we will study the principles of solid-

ification as they apply to pure metals. We will dis-

cuss solidification of alloys and more complex

materials in subsequent chapters. We will first

discuss the technological significance of solid-

ification, and then examine the mechanisms by

which solidification occurs. This will be followed

by an examination of the microstructure of cast

metallic materials and its effect on the material’s

mechanical properties. We will also examine the

role of casting as a materials shaping process. We

will examine how techniques such as welding,

brazing, and soldering are used for joining metallic

materials. Applications of the solidification process

in single crystal growth and the solidification of

glasses and polymers also will be discussed.

9-1 Technological Significance

The ability to use ﬁre to produce, melt, and cast metals such as copper, bronze, and

steel indeed is regarded as an important hallmark in the development of mankind. The

use of ﬁre for reducing naturally occurring ores into metals and alloys led to the pro-

duction of useful tools and other products. Today, thousands of years later, solidiﬁ-

cation is still considered one of the most important manufacturing processes. Several

million pounds of steel, aluminum alloys, copper, and zinc are produced through the

casting process. The solidiﬁcation process is also used to manufacture speciﬁc compo-

nents (e.g., aluminum alloy for automotive wheels) (Figure 9-1). Industry also uses the

solidiﬁcation process as a primary processing step to produce metallic slabs or ingots (a

simple, and often large casting that is processed later into useful shapes). The ingots or

slabs are then hot and cold worked through secondary processing steps into more useful

shapes (i.e., sheets, wires, rods, plates, etc.). Solidiﬁcation also is applied when joining

metallic materials using techniques such as welding, brazing, and soldering.

We also use solidiﬁcation for processing inorganic glasses; silicate glass, for exam-

ple, is processed using the ﬂoat-glass process. High-quality optical ﬁbers and other

materials, such as ﬁberglass ﬁbers, also are produced from the solidiﬁcation of molten

glasses. During the solidiﬁcation of inorganic glasses, amorphous rather than crystal-

line, materials are produced. In the manufacture of glass-ceramics, we ﬁrst shape the

materials by casting amorphous glasses, and then crystallize them using a heat treat-

ment to enhance their strength. Many thermoplastic materials such as polyethylene,

polyvinyl chloride (PVC), polypropylene, and the like are processed into useful shapes

(i.e., ﬁbers, tubes, bottles, toys, utensils, etc.) using a process that involves melting and

C H A P TE R 9 Principles and Applications of Solidification258

solidiﬁcation. Therefore, solidiﬁcation is an extremely important technology used to

control the properties of many melt-derived products as well as a tool for the manu-

facturing of modern engineered materials. In the sections that follow, we ﬁrst discuss

the nucleation and growth processes.

9-2 Nucleation

In the context of solidiﬁcation, the term nucleation refers to the formation of the ﬁrst

nano-sized crystallites from molten material. For example, as water begins to freeze,

nano-sized ice crystals, known as nuclei, form ﬁrst. In a broader sense, the term nucle-

ation refers to the initial stage of formation of one phase from another phase. When a

vapor condenses into liquid, the nanoscale sized drops of liquid that appear when the

condensation begins are referred to as nuclei. Later, we will also see that there are many

systems in which the nuclei of a solid (b) will form a second solid material (a) (i.e., a-to

b-phase transformation). What is interesting about these transformations is that, in

most engineered materials, many of them occur while the material is in the solid state

(i.e., there is no melting involved). Therefore, although we discuss nucleation from a

solidiﬁcation perspective, it is important to note that the phenomenon of nucleation is

general and is associated with phase transformations.

We expect a material to solidify when the liquid cools to just below its freezing (or

melting) temperature, because the energy associated with the crystalline structure of the

solid is then less than the energy of the liquid. This energy di¤erence between the liquid

and the solid is the free energy per unit volume ðDG

Þ and is the driving force for

solidiﬁcation.

When the solid forms a solid-liquid interface is created (Figure 9-2). A surface free

energy s

is associated with this interface; the larger the solid, the greater the increase

in surface energy. Thus, the total change in energy DG, shown in Figure 9-3, is:

Figure 9-1

Aluminum alloy wheels for

automobiles. (Courtesy of Simon

Askham/Stockphoto.)

9-2 Nucleation 259

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

Подождите немного. Документ загружается.

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