Askeland D.R., Fulay P.P. Essentials of Materials Science & Engineering
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9
Properly controlled residual stresses and anisotropic behavior may be beneficial.
However, if residual stresses are not property controlled, the materials properties are
greatly impaired.
9
As will be seen in Section 8-6, since the e¤ect of cold working is decreased or
eliminated at higher temperatures, we cannot use cold working as a strengthening
mechanism for components that will be subjected to high temperatures during applica-
tion or service.
9
Some deformation processing techniques can be accomplished only if cold work-
ing occurs. For example, wire drawing requires that a rod be pulled through a die to
produce a smaller cross-sectional area (Figure 8-12). For a given draw force F
d
, a dif-
ferent stress is produced in the original and final wire. The stress on the initial wire must
exceed the yield strength of the metal to cause deformation. The stress on the final wire
must be less than its yield strength to prevent failure. This is accomplished only if the
wire strain hardens during drawing.
Figure 8-12 The wire-drawing process. The force F
d
acts on both the original and final
diameters. Thus, the stress produced in the final wire is greater than that in the original. If the
wire did not strain harden during drawing, the final wire would break before the original wire
was drawn through the die.
EXAMPLE 8-5
Design of a Wire Drawing Process
Design a process to produce 0.5 cm diameter copper wire. The mechanical
properties of copper are to be assumed as those shown in Figure 8-5.
SOLUTION
Wire drawing manufacturing technique will be suitable for this application. To
produce the copper wire as e‰ciently as possible, we make the largest reduc-
tion in the diameter possible. Our design must assure that the wire strain
hardens su‰ciently during drawing to prevent the drawn wire from breaking.
As an example calculation, let’s assume that the starting diameter of the
copper wire is 1 cm and that the wire is in the softest possible condition. The
cold work is:
%CW¼
A
0
A
f
A
0
100 ¼
ðp=4Þd
2
0
ðp=4Þd
2
f
ðp=4Þd
2
0
"#
100
¼
ð1cmÞ
2
ð0:5cmÞ
2
ð1cmÞ
2
"#
100 ¼ 75%
From Figure 8-5, the initial yield strength with 0% cold work is 152 MPa.
The final yield strength with 75% cold work is about 534 MPa (with very little
ductility). The draw force required to deform the initial wire is:
C HA P T E R 8 Strain Hardening and Annealing240
F ¼ s
y
A
0
¼ð152 MPaÞðp=4Þð1cmÞ
2
¼ 11; 943 N
The stress acting on the wire after passing through the die is:
s ¼
F
d
A
f
¼
11; 943 N
ðp=4Þð0:5cmÞ
2
¼ 608 MPa
The applied stress of 608 MPa is greater than the 534 MPa yield strength of the
drawn wire. Therefore, the wire breaks since the percent elongation is almost zero.
We can perform the same set of calculations for other initial diameters,
with the results shown in Table 8-2 and Figure 8-13.
The graph shows that the draw stress exceeds the yield strength of the
drawn wire when the original diameter is about 0.925 cm. To produce the wire
as e‰ciently as possible, the original diameter should be just under 0.925 cm.
TABLE 8-2 9 Mechanical properties of copper wire (see Example 8-5)
d
0
(cm) % CW
Yield Strength of
Drawn Wire (MPa) Force (N)
Draw Stress on
Drawn Wire (MPa)
0.625 36 400 4665 238
0.75 56 469 6718 342
0.875 67 510 9144 466
1 75 534 11,943 608
Figure 8-13
Yield strength and
draw stress of wire
(for Example 8-5).
8-6 The Three Stages of Annealing
Cold working is a useful strengthening mechanism. It is also a very e¤ective tool for
shaping materials using wire drawing, rolling, extrusion, etc. However, cold working
leads to some e¤ects that are sometimes undesirable. For example, the loss of ductility
or development of residual stresses may not be desirable for certain applications. Since
cold working or strain hardening results from increased dislocation density we can
8-6 The Three Stages of Annealing 241
assume that any treatment to rearrange or annihilate dislocations would begin to undo
the e¤ects of cold working.
Annealing is a heat treatment used to eliminate some or all of the e¤ects of cold
working. Annealing at a low temperature may be used to eliminate the residual stresses
produced during cold working without a¤ecting the mechanical properties of the fin-
ished part. Or, annealing may be used to completely eliminate the strain hardening
achieved during cold working. In this case, the final part is soft and ductile but still has
a good surface finish and dimensional accuracy. After annealing, additional cold work
could be done, since the ductility is restored; by combining repeated cycles of cold
working and annealing, large total deformations may be achieved. There are three
possible stages in the annealing process; their e¤ects on the properties of brass are
shown in Figure 8-14.
Note that the term ‘‘annealing’’ is also used to describe other thermal treatments.
For example, glasses may be annealed, or heat treated, to eliminate residual stresses.
Cast irons and steels may be annealed to produce the maximum ductility, even though
no prior cold work was done to the mateiral. These annealing heat treatments will be
discussed in later chapters.
Recovery The original cold-worked microstructure is composed of deformed grains
containing a large number of tang led dislocations. When we first heat the metal, the
additional thermal energy permits the dislocations to move and form the boundaries
of a polygonized subgrain structure (Figure 8-15). The dislocation density, however, is
virtually unchanged. This low-temperature treatment removes the residual stresses due
to cold working without causing a change in dislocation density and is called recovery.
Figure 8-14 The effect of cold work on the properties of a Cu-35% Zn alloy and the effect of
annealing temperature on the properties of a Cu-35% Zn alloy that is cold-worked 75%.
C HA P T E R 8 Strain Hardening and Annealing242
The mechanical properties of the metallic material are relatively unchanged
because the number of dislocations is not reduced during recovery. However, since
residual stresses are reduced or even eliminated when the dislocations are rearranged,
recovery is often called a stress-relief anneal. In additi on, recovery restores high elec-
trical conductivity to the metal, permitting us to manufacture copper or aluminum wire
for transmission of electrical power that is strong yet still has high conductivity. Finally,
recovery often improves the corrosion resistance of the material.
Recrystallization When a cold worked metallic material is heated above a certain
temperature, rapid recovery eliminates residual stresses and produces the polygonized
dislocation structure. New small grains then nucleate at the cell boundaries of the poly-
gonized structure, eliminating most of the dislocations (Figure 8-15). Because the num-
ber of dislocations is greatly reduced, the recrystallized metal has low strength but high
ductility. The temperature at which a microstructure of new grains that have very low
dislocation density appears is known as the recrystallization temperature. The process of
formation of new grains by heat treating a cold-worked material is known as recrystal-
lization. As will be seen in Section 8-7, recrystallization temperature depends on many
variables and is not a fixed temperature similar to melting temperature of elements and
compounds.
Grain Growth At still higher annealing temperatures, both recovery and recrystalliza-
tion occur rapidly, producing a fine, recrystallized grain structure. If the temperature is
high enough, the grains begin to grow, with favored grains consuming the smaller
grains (Figure 8-16). This phenomenon, called grain growth, is driven by the reduction
in grain boundary area and was described in Chapter 5. Illustrated for a copper-zinc
alloy in Figure 8-14, grain growth is almost always undesirable. Remember that grain
growth will occur in most materials if they are subjected to a high enough temperature
and, as such, is not related to cold working. Thus, recrystallization or recovery are not
needed for grain growth to occur.
You may be aware that incandescent light bulbs contain filaments that are made
from tungsten (W). High temperature causing grain growth and the subsequent reduc-
tion in strength is one of the factors that causes the filament to fail.
Ceramic materials, which normally do not show any significant strain hardening,
show a considerable amount of grain growth. Also, abnormal grain growth can occur
in some materials as a result of a formation of liquid phase during their sintering
(Chapter 15). An example of where grain growth is useful is the application of alumina
ceramics for making optical materials used in lighting. In this application, we want very
Figure 8-15 The effect of annealing temperature on the microstructure of cold-worked metals.
(a) cold-worked, (b) after recovery, (c) after recrystallization, and (d) after grain growth.
8-6 The Three Stages of Annealing 243
large grains since the scattering of light from grain boundaries has to be minimized.
Some researchers have also developed methods for growing single crystals of ceramic
materials using grain growth.
8-7 Control of Annealing
In many metallic materials applications, we need a combination of strength and
toughness. Therefore, we need to design processes that involve shaping via cold work-
ing. We then need to control the annealing process to obtain a level of ductility. To
design an appropriate annealing heat treatment, we need to know the recrystallization
temperature and the size of the recrystallized grains.
Recrystallization Temperature This is the temperature at which grains in the cold-
worked microstructure begin to transform into new, equiaxed, and dislocation-free
grains. The driving force for recry stallization is the di¤erence between the internal
energy between a cold worked material and that of a recrystallized material. It is im-
portant for us to emphasize that the recrystallization temperature is not a fixed tem-
perature and is influenced by a variety of processing variables:
9
Recrystallization temperature decreases when the amount of cold work increases.
Greater amounts of cold work make the metallic material less stable and encourage
nucleation of recrystallized grains. There is a minimum amount of cold work, about 30
to 40%, below which recrystallization will not occur.
9
A smaller original cold-worked grain size reduces the recrystallization temper-
ature by providing more sites—the former grain boundaries—at which new grains can
nucleate.
9
Pure metals recrystallize at lower temperatures than alloys.
Figure 8-16 Photomicrographs showing the effect of annealing temperature on grain size
in brass. Twin boundaries can also be observed in the structures. (a) Annealed at 400
C,
(b) annealed at 650
C, and (c) annealed at 800
C(75). (Adapted from Brick, R. and
Phillips, A., The Structure and Properties of Alloys, 1949: McGraw-Hill.)
C HA P T E R 8 Strain Hardening and Annealing244
9
Increasing the annealing time reduces the recrystallization temperature (Figure
8-17), since more time is available for nucleation and growth of the new recrystallized
grains.
9
Higher melting-point alloys have a higher recrystallization temperature. Since
recrystallization is a di¤usion-controlled process, the recrystallization temperature is
roughly proportional to 0.4T
m
Kelvin. Typical recrystallization temperatures for
selected metals are shown in Table 8-3.
The concept of recrystallization temperature is very important since it also defines
the boundary between cold working and hot working of a metallic material. If we con-
duct deformation (shaping) of a material above the recrystallization temperatur e, we
refer to it as hot working. If we conduct the shaping or deformation at a temperature
below the recrystallization temperature, we refer to this as cold working. Therefore, the
Figure 8-17
Longer annealing times reduce the
recrystallization temperature. Note
that the recrystallization temperature
is not a fixed temperature.
TABLE 8-3 9 Typical recrystallization temperatures for
selected metals
Metal
Melting Temperature
(
˚
C)
Recrystallization
Temperature (
˚
C)
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
(From R. Brick, A. Pense and R. Gordon, Structure and Properties
of Engineering Materials, McGraw-Hill, 1977.)
8-7 Control of Annealing 245
terms ‘‘hot’’ and ‘‘cold’’ working refer to whether we are conducting the shaping proc-
ess or deformation at temperatures above or below the recrystallization temperature. As
can be seen from Table 8-3, for lead (Pb) or tin (Sn) deformed at 25
C, we are con-
ducting hot working! This is why iron (Fe) can be cold worked at room temperature but
not lead (Pb). For tungsten (W) being deformed at 1000
C, we are conducting cold
working! In some cases, processes conducted above 0.6 times the melting temperature
(T
m
) of metal (in K) are considered as hot working. Processes conducted below 0.3
times the melting temperature are considered cold working and processes conducted
between 0.3 and 0.6 times T
m
are considered warm working. These descriptions of
ranges that define hot, cold and warm working, however, are approximate and should
be used with caution.
Recrystallized Grain Size A number of factors influence the size of the recrystallized
grains. Reducing the annealing temperature, the time required to heat to the annealing
temperature, or the annealing time reduces grain size by mi nimizing the opportunity for
grain growth. Increasing the initial cold work also reduces final grain size by providing
a greater number of nucleation sites for new grains. Finally, the presence of a second
phase in the microstructure helps prevent grain growth and keeps the recrystallized
grain size small.
8-8 Annealing and Materials Processing
The e¤ects of recovery, recrystallization, and grain growth are important in the pro-
cessing and eventual use of a metal or an alloy.
Deformation Processing By taking advantage of the annealing heat treatment, we can
increase the total amount of deformation we can accomplish. If we are required to
reduce a 12.5 cm thick plate to a 0.125 cm thick sheet, we can do the maximum per-
missible cold work, anneal to restore the metal to its soft, ductile condition, then cold
work again. We can repeat the cold work-anneal cycle until we approach the proper
thickness. The final cold-working step can be designed to produce the final dimensions
and properties required (Example 8-6).
EXAMPLE 8-6
Design of a Process to Produce Copper Strip
We wish to produce a 0.1-cm-thick, 6-cm-wide coppe r strip having at least
414 MPa yield strength and at least 5% elongation. We are able to purchase
6-cm-wide strip only in thick nesses of 5 cm. Design a process to prod uce the
product we need.
SOLUTION
In Example 8-2, we found that the required properties can be obtained with a
cold work of 40 to 45%. Therefore, the starting thickness must be between
0.167 cm and 0.182 cm, and this starting material must be as soft as possible—
that is, in the annealed condition. Since we are able t o purchase only 5-cm-
thick stock, we must reduce the thickness of the 5-cm strip to between 0.167
C HA P T E R 8 Strain Hardening and Annealing246
and 0.182 cm, then anneal the strip prior to final cold working. But can we
successfully cold work from 5 cm to 0.182 cm?
%CW¼
t
o
t
f
t
o
100 ¼
5cm 0 :182 cm
5cm
100 ¼ 96:4%
Based on Figure 8-5, a maximum of about 90% cold work is permitted.
Therefore, we must do a series of cold work and anneal cycles. Although there
are many possible combinations, one is as follows:
1. Cold work the 5-cm strip 80% to 1 cm:
80 ¼
t
o
t
f
t
o
100 ¼
5cm t
i
cm
5cm
100 or t
f
¼ 1cm
2. Anneal the 1-cm strip to restore the ductility. If we don’t know the
recrystallization temperature, we can use the 0.4T
m
relationship to provide
an estimate. The melting point of copper is 1085
C:
T
r
G ð0: 4Þð1085 þ 273Þ¼543 K ¼ 270
C
3. Cold work the 1-cm-thick strip to 0.182 cm:
%CW¼
1cm 0:182 cm
1cm
100 ¼ 81:8%
4. Again anneal the copper at 270
C to restore ductility.
5. Finally cold work 45%, from 0.182 cm to the final dimension of 0.1 cm.
This process gives the correct final dimensions and properties.
High-Temperature Service As mentioned previously, neither strain hardening nor
grain size strengthening (Hall-Petch equation, Chapter 4) are appropriate for an alloy
that is to be used at elevated temperatures, as in creep-resistant applications. When the
cold-worked metal is placed into service at a high temperature, recrystallization imme-
diately causes a catastrophic decrease in strength. In addition, if the temperature is high
enough, the strength continues to decrease bec ause of growth of the newly recrystallized
grains.
Joining Processes Metallic materials can be joined using processes such as welding.
When we join a cold-worked metal using a welding process, the metal adjacent to the
weld heats above the recrystallization and grain growth temperatures and subsequently
cools slowly. This region is called the heat-a¤ected zone (HAZ). The structure and
properties in the heat-a¤ected zone of a weld are shown in Figure 8-18. The mechanical
properties are reduced catastrophically by the heat of the welding process.
Welding processes, such as electron-beam welding or laser welding, which provide
high rates of heat input for brief times, and, thus, subsequent fast cooling, minimize the
exposure of the metallic materials to temperatures above recrystallization and mini-
mize this type of damage. Similarly a process known as friction stir welding pro-
vides almost no HAZ and is being commercially used for welding of aluminum alloys
(Chapter 9).
8-8 Annealing and Materials Processing 247
8-9 Hot Working
We can deform a metal into a useful shape by hot working rather than cold working.
As described previousl y, hot working is defined as plastically deforming the metallic
material at a temperature above the recrystallization temperature. During hot working,
the metallic material is continually recrystallized (Figure 8-19).
Lack of Strengthening No strengthening occurs during deformation by hot working;
consequently, the amount of plastic deformation is almost unlimited. A very thick plate
can be reduced to a thin sheet in a continuous series of operations. The first steps in the
process are carried out well above the recrystallization temperature to take advantage
of the lower strength of the metallic material. The last step is performed just above the
Figure 8-18 The structure and properties surrounding a fusion weld in a cold-worked metal.
Note : only the right-hand side of the heat-affected zone is marked on the diagram. Note the
loss in strength caused by recrystallization and grain growth in the heat-affected zone.
Figure 8-19
During hot working, the elongated,
anisotropic grains immediately
recrystallize. If the hot-working
temperature is properly controlled,
the final hot-worked grain size can be
very fine.
C HA P T E R 8 Strain Hardening and Annealing248
recrystallization temperature, using a large percent deformation in order to produce the
finest possible grain size.
Hot working is well-suited for forming large parts, since the metallic material has a
low yield strength and high ductility at elevated temperatures. In addition, HCP metals
such as magnesium have more active slip systems at hot-working temperatures; the
higher ductility permits larger deformations than are possible by cold working. The
following example illustrates design of a hot-working process.
EXAMPLE 8-7
Design of a Process to Produce a Copper Strip
We want to produce a 0.1-cm-thick, 6-cm-wide copper strip having at least
414 MPa yield strength and at least 5% elongation. We are able to purchase
6-cm-wide strip only in thick nesses of 5 cm. Design a process to produce the
product we need, but in fewer steps than were required in Example 8-6.
SOLUTION
In Example 8-6, we relied on a series of cold work-anneal cycles to obtain the
required thickness. We could reduce the steps by hot rolling to the required
intermediate thickness:
%HW¼
t
o
t
f
t
o
100 ¼
5cm 0 :182 cm
5cm
100 ¼ 96:4%
%HW¼
t
o
t
f
t
o
100 ¼
5cm 0 :167 cm
5cm
100 ¼ 96:7%
Note that the formulas for hot and cold work are the same.
Because recrystallization occurs simultaneously with hot working, we can
obtain these large deformations and a separate annealing treatment is not
required. Thus our design might be:
1. Hot work the 5-cm strip 96.4% to the intermediate thickness of 0.182 cm.
2. Cold work 45% from 0.182 cm to the final dimension of 0.1 cm. This des ign
gives the correct dimensions and properties.
Elimination of Imperfections Some imperfections in the original metallic material
may be eliminated or their e¤ects minimized. Gas pores can be closed and welded shut
during hot working—the internal lap formed when the pore is closed is eliminated by
di¤usion during the forming and cooling process. Composition di¤erences in the metal
can be reduced as hot working brings the surface and center of the plate closer together,
thereby reducing di¤usion distances.
Anisotropic Behavior The final properties in hot-worked parts are not isotropic. The
forming rolls or dies, which are normally at a lower temperature than the metal, cool
the surface more rapidly than the center of the part. The surface then has a finer grain
size than the center. In addition, a fibrous structure is produced because inclusions and
second-phase particles are elongated in the working direction.
Surface Finish and Dimensional Accuracy The surface finish is usually poorer than
that obtained by cold working. Oxygen often reacts with the metallic material at the
surface to form oxides, which are forced into the surface during forming. Hot worked
8-9 Hot Working 249