Heat Treatment
Content
Laboratory #3
HEAT TREATMENT OF STEELS
INTRODUCTION
Pure iron has three solid phases. At temperatures from 1394 °C to 1538 °C, it exists
as a bcc structure called delta iron. From 912 °C to 1394 °C, it has an FCC structure called
gamma iron or austenite. And from -273 °C to 912 °C, it resumes a BCC structure and is
called alpha iron or ferrite.
Austenite can dissolve a maximum of 2.11% carbon, but ferrite can only dissolve
0.02% carbon. This is shown in Fig. 1, which is the phase diagram of the iron-carbon
system. When austenite is cooled and changes phase to ferrite, this excess carbon combines
with iron to form a compound called Cementite, Fe3C.
At a composition of 0.77% carbon and a temperature of 727 °C, austenite changes
directly to ferrite and cementite. This is called the eutectoid reaction and occurs at particular
temperature and composition, called the eutectoid temperature and eutectoid composition.
The ferrite and cementite form a unique, lamellar structure in which plates of ferrite are
interleaved with plates of cementite, as shown in Fig. 2. This structure is called Pearlite.
For carbon contents less than 0.77% C, ferrite forms at temperatures above 727 °C in
the form of two phase field -- ferrite plus austenite, (shown in Fig. 1). This ferrite is called
free ferrite, or primary ferrite, since it is not bound up in the pearlite structure. Upon cooling
from this two phase field, the austenite which has not transformed to free ferrite will
transform to pearlite at a temperature of 727 °C.
If the cooling rate is very high, these transformations may be suppressed and a
metastable phase called martensite is formed. Martensite consists of excess carbon atoms
trapped in the bcc crystal. These excess atoms greatly strain the crystal and cause it to stretch
into a body-centered-tetragonal crystal structure in which one side is longer than the other
two. The martensite is very hard but brittle. For most engineering purposes, it is too brittle
to be used. The brittleness can be substantially reduced without too much loss in hardness by
heating the martensite for a period of time. This is called tempering and produces tempered
33
martensite. Tempered martensite is of great commercial importance because of its high
strength and reasonable ductility.
The transformation from austenite to pearlite does not occur instantaneously, as does
the transformation to martensite. Instead, time is required for the reaction to begin and for
the carbon atoms to diffuse through the austenite to form cementite. This time dependence is
shown by means of diagrams called Isothermal Transformation (IT) Diagrams. They are
constructed by holding the temperature constant and observing the phase changes as a
function of time.
An IT diagram is shown in Fig. 3 for a steel having 0.8% C, which is essentially the
eutectoid composition. In this figure the line labeled ts gives the time required to start the
phase transformation as a function of temperature. The line labeled tf gives the time required
to finish the transformation. The dotted line labeled Ms gives the temperature at which the
martensite transformation starts, and the dotted line labeled Mf gives the temperature this
transformation is finished. Since the martensite transformation is instantaneous, time is not a
variable. The amount of martensite formed depends only on the temperature. Between Ms
and Mf not all of the austenite transforms to martensite. The austenite that does not
transform remains as austenite and is called retained austenite.
In Fig. 3, Carbide refers to cementite, α stands for ferrite, γ for austenite and M for
martensite. If we were to hold the temperature at 600 °C for 100 seconds, we would still
have these same phases. Martensite could not form because all of the austenite has already
been transformed to ferrite and cementite.
Figure 3 has a pronounced "nose" at about 575 °C and 1 second. At this point the
transformation occurs in the shortest time. Above this nose pearlite is formed. Below this
nose and above the martensite start line, another arrangement of ferrite and cementite is
formed. This arrangement is called Bainite, and is composed of fine particles of cementite in
a ferrite matrix. For steel that has less than 0.77% C, an additional line has to be added to the
IT diagram. This is the line showing the formation of free ferrite. This line is shown in Fig.4
as the top most line. Figure 4 is for a steel having 0.45% C.
The IT diagram is constructed by holding the temperature constant. In many
applications, the steel cools continuously over time. To show the transformations for this
case, another diagram is used. This is called the Continuous Cooling Transformation (CCT)
Diagram and is shown in Fig. 5 for a steel containing 0.4% C. In this diagram the primary
34
alpha is the same as the free ferrite, and no martensite finish line is shown. It is difficult in
practice to find this finish temperature. The lines on the CCT are displaced to lower
temperatures and longer times relative to the IT diagram. Also, the bainite transformation is
not as strongly affected by continuous cooling as is the pearlite reaction. Therefore, the
bainite reaction occurs at shorter times than the pearlite reaction.
As can be seen from Fig. 3, extremely rapid cooling rates are required to achieve
martensitic structures. These structures are desired because they can be tempered to high
strengths with reasonable ductilities (called tempered martensite). One of the main effects of
adding alloying elements to steels is to permit slower cooling rates to achieve these
martensitic structures.
Jominy End Quench Test
A commonly used measure of the cooling rates required to achieve this martensitic
structure is the depth to which steel can be transformed to martensite. This is called the
hardenability of the steel. The cooling rate at the surface of a steel plate is very fast but
becomes slower as the distance from the surface increases. Therefore, the distance from the
surface is an equivalent measure of the cooling rate, and can be used to give the hardenability
of the steel.
The depth is usually measured by the Jominy End Quench Test. In this test one end of
a round bar is quenched in a water stream and the other end cools in air. Thus, various
cooling rates are obtained in the specimen. By measuring the hardness as a function of the
distance from the quenched end, the cooling rates necessary to form martensite can be
determined. Thus the greater this distance, the greater the hardenability of the steel. (Since
martensite is much harder than the other phases in steel, it is easy to find with hardness
measurements. The cooling rates in the specimen can be found experimentally using
thermocouples.)
In the lab you will be measuring the hardenability of two steels using the Jominy End
Quench Test. In addition, you will examine the microstructures of several different
transformation products, e.g. pearlite, martensite, etc.
35
EXPERIMENTAL PROCEDURE
In this test the hardenability of low-alloy steel, AISI 4140 is compared to that of a
plain 0.4% C carbon steel, AISI 1040. The experimental procedure is as follows:
(1) Lay a Jominy specimen on the tray and push the tray into the furnace set at 860°C using
tongs and heat resisting gloves. Do not attempt to stand the specimen in the tray since it will
topple over.
(2) Adjust the water column height in the Jominy end quenching tank to 2-1/2 inches above
the 1/2 inch orifice with the quick opening valve wide open. Close the quick opening valve
without changing the water column height adjustment so that when the quick opening valve
is opened later the water column will rise immediately to 2-1/2 inches. The water
temperature should lie between 40 to 85°F (not usually a problem). (At this point you should
start on the microstructural examination part of the laboratory.)
(3)
After 30 minutes in the furnace, transfer the Jominy specimen to the specimen holder of
the Jominy end quenching tank. After the Jominy specimen is in place, turn on the water and
quench the bottom end of the specimen. Transfer from furnace to quench should be rapid
(not more than 5 seconds) and students are advised to practice the motions in advance. A
second student with heat resisting gloves and a second pair of tongs or large pliers may assist
the placement of the Jominy specimen, while a third operates the quick opening valve. Care
should be taken to position the specimen so that it hangs straight down and a uniform
umbrella pattern of water rebounds from the specimen bottom. Lopsided quenching can
result from a piece of scale under the rim supporting the specimen.
(4)
Leave the specimen in place with the water flowing for at least 10 minutes.
(5)
While the first specimen is cooling, lay the second specimen into the tray and push the
tray into the furnace. Remember to record the time as you need to heat the specimen for 30
minutes.
(6)
Remove the first specimen from the specimen holder and cool it in water.
(7)
Grind a flat on the side of the specimen at least 0.015 inch deep. Use the belt grinder
with 80 grit paper. Grind gently with coolant water flowing on the surface of the grinding
paper. Remove any loose scale on both side of the specimen with grinding paper.
36
(8) Mark a scale on the flat as follows. Divide the first inch from the quenched end into
1/16 inch increments. Divide the next inch into 1/8 inch increments.
(9) Measure the Rockwell hardness on the C scale (use Table I). Start in the middle and
work towards the quenched end. The first measurement should be taken beyond the two inch
mark and discarded. It is expected to be low due to the “seating” of the specimen in the
anvil. Thereafter, record the hardness at each increment that you have marked off. It is
important to keep the indentations in the center of the flat, since errors will arise if they are at
the edges of the flat. Note that any bits of scale remaining between the specimen and the
anvil will crush during the indentation process, resulting in an erroneously low measurement.
(10) After the second specimen has been heated for 30 minutes, return to step 3.
Microstructural Examination
The lab assistant will give you a number of specimens which are already prepared for
light optical microscopy. All specimens are made from a 0.4% plain carbon steel (AISI
1040) and have been austenitized and subsequently cooled to room temperature. The cooling
rates are not the same for each specimen. Examine the specimens in the microscope and
describe with words what structural features you can see. Also make a sketch of the
microstructure of each specimen, including the magnification of the microscope. The camera
objective has a magnification of about 30x. If necessary polish the specimens again and etch
in nital, 2% nitric acid in alcohol. This part of the experiment should be done while the
Jominy specimens are being heated. You may wish to take photographs of the
microstructures that are difficult to sketch.
ANALYSIS
(1) Make a plot of the hardness (y-axis) versus the distance from the quenched end (x-axis).
The distance scale should be in 1/16 inch increments. Use Rockwell hardness numbers in the
plot.
(2)
Using the conversion table in this handout, determine the Brinell hardness number
(BHN) corresponding to each of your hardness measurements. Use the 10 mm standard ball.
37
If the hardness is greater than Rockwell C-52, use the 10 mm carbide ball for all of your
conversions.
(3) The tensile strength of steel is approximately equal to 500 times the BHN, where the
strength is in psi. Calculate the tensile strength at each position on the Jominy specimen.
(Although martensite has a very high tensile strength, it is too brittle for most engineering
applications.)
(4)
The cooling rate at 700 °C as a function of the distance from the quenched end is given
in Figure. 6. For each of your hardness measurements, determine the cooling rate at 700 °C.
(5)
Answers to 2, 3 and 4 must be presented in a table giving the distance from the
quenched end, the Rockwell hardness, the BHN, the tensile strength and the cooling rate.
This will be Table 1.
(6) Make a plot of the BHN (y-axis) versus the logarithm of the cooling rate. The cooling
rate should be shown explicitly as degrees C per second. Note the difference in cooling rate.
(7) Include your sketches of the microstructures at this point.
observed in the microstructures.
Identify the features
QUESTIONS
(1) The hardenability of a steel may be designated by a code indicating the distance from
the quenched end (in 16ths of an inch) within which the desired hardness is attained. For
example, if a Rockwell C Hardness of 45 or higher is obtained out to 9/16" from the
quenched end, we can write that the hardenability J-45 is 9. Find J-40 and J-35 for the 1040
and the 4140 steels.
(2)
What microstructures would you expect for the 1040 steel at:
(a) 1/16 from the quenched end
(b) 4/16 inch from the quenched end
(c) 2 inches from the quenched end
38
To answer these questions use the continuous cooling transformation curve in Fig. 5. Plot the
temperature vs. time curve on this graph for each of the cooling times, a, b and c. Assume
that the cooling rate at 700 °C is constant at all temperatures and that cooling starts at 860 °C.
For times less than 1 second, extend the axis to the left to 0.1 second and plot the cooling
rates to the left of the y-axis.
(3) Describe the probable heat treatment that produced each of the microstructures that you
examined. Be sure to explain why these heat treatments produced these microstructures.
(4)
Is high hardenability desirable in steels? Explain your answer briefly.
(5) Briefly explain the difference between hardness and hardenability.
(6) (a) Name the three factors that influence the degree to which martensite is formed
throughout the cross section of a steel specimen.
(b) For each, tell how the extent of martensite formation may be increased.
FIGURES
39
40
41
42
REFERENCES
D. R. Askeland, The Science and Engineering of Materials, Alt. Ed., PWS Engineering,
1984, pp. 288-303, 351-376.
L. H. Van Vlack, Elements of Materials Science and Engineering, 5th ed., 1985, pp. 402-415,
431-435,439-445, 455-463, 469-478.
L. H. Van Vlack and C. J. Osborn, Study Aids for Introductory Materials Courses, pp. 135140, 157-208.
43
G. L. Kehl, Principles of Metallographic Laboratory Practice, McGraw-Hill, 1949, pp. 303310, 229-240.
J. Wulff, et. al., Structure and Properties of Materials, Vol. 1, pp. 184-197; Vol. 2, pp. 123128.
A. G. Guy, Physical Metallurgy for Engineers, 1962, Addison-Wesley, 1962, pp. 122-124,
294-298, 301-311.
44
HEAT TREATMENT OF STEELS
INTRODUCTION
Pure iron has three solid phases. At temperatures from 1394 °C to 1538 °C, it exists
as a bcc structure called delta iron. From 912 °C to 1394 °C, it has an FCC structure called
gamma iron or austenite. And from -273 °C to 912 °C, it resumes a BCC structure and is
called alpha iron or ferrite.
Austenite can dissolve a maximum of 2.11% carbon, but ferrite can only dissolve
0.02% carbon. This is shown in Fig. 1, which is the phase diagram of the iron-carbon
system. When austenite is cooled and changes phase to ferrite, this excess carbon combines
with iron to form a compound called Cementite, Fe3C.
At a composition of 0.77% carbon and a temperature of 727 °C, austenite changes
directly to ferrite and cementite. This is called the eutectoid reaction and occurs at particular
temperature and composition, called the eutectoid temperature and eutectoid composition.
The ferrite and cementite form a unique, lamellar structure in which plates of ferrite are
interleaved with plates of cementite, as shown in Fig. 2. This structure is called Pearlite.
For carbon contents less than 0.77% C, ferrite forms at temperatures above 727 °C in
the form of two phase field -- ferrite plus austenite, (shown in Fig. 1). This ferrite is called
free ferrite, or primary ferrite, since it is not bound up in the pearlite structure. Upon cooling
from this two phase field, the austenite which has not transformed to free ferrite will
transform to pearlite at a temperature of 727 °C.
If the cooling rate is very high, these transformations may be suppressed and a
metastable phase called martensite is formed. Martensite consists of excess carbon atoms
trapped in the bcc crystal. These excess atoms greatly strain the crystal and cause it to stretch
into a body-centered-tetragonal crystal structure in which one side is longer than the other
two. The martensite is very hard but brittle. For most engineering purposes, it is too brittle
to be used. The brittleness can be substantially reduced without too much loss in hardness by
heating the martensite for a period of time. This is called tempering and produces tempered
33
martensite. Tempered martensite is of great commercial importance because of its high
strength and reasonable ductility.
The transformation from austenite to pearlite does not occur instantaneously, as does
the transformation to martensite. Instead, time is required for the reaction to begin and for
the carbon atoms to diffuse through the austenite to form cementite. This time dependence is
shown by means of diagrams called Isothermal Transformation (IT) Diagrams. They are
constructed by holding the temperature constant and observing the phase changes as a
function of time.
An IT diagram is shown in Fig. 3 for a steel having 0.8% C, which is essentially the
eutectoid composition. In this figure the line labeled ts gives the time required to start the
phase transformation as a function of temperature. The line labeled tf gives the time required
to finish the transformation. The dotted line labeled Ms gives the temperature at which the
martensite transformation starts, and the dotted line labeled Mf gives the temperature this
transformation is finished. Since the martensite transformation is instantaneous, time is not a
variable. The amount of martensite formed depends only on the temperature. Between Ms
and Mf not all of the austenite transforms to martensite. The austenite that does not
transform remains as austenite and is called retained austenite.
In Fig. 3, Carbide refers to cementite, α stands for ferrite, γ for austenite and M for
martensite. If we were to hold the temperature at 600 °C for 100 seconds, we would still
have these same phases. Martensite could not form because all of the austenite has already
been transformed to ferrite and cementite.
Figure 3 has a pronounced "nose" at about 575 °C and 1 second. At this point the
transformation occurs in the shortest time. Above this nose pearlite is formed. Below this
nose and above the martensite start line, another arrangement of ferrite and cementite is
formed. This arrangement is called Bainite, and is composed of fine particles of cementite in
a ferrite matrix. For steel that has less than 0.77% C, an additional line has to be added to the
IT diagram. This is the line showing the formation of free ferrite. This line is shown in Fig.4
as the top most line. Figure 4 is for a steel having 0.45% C.
The IT diagram is constructed by holding the temperature constant. In many
applications, the steel cools continuously over time. To show the transformations for this
case, another diagram is used. This is called the Continuous Cooling Transformation (CCT)
Diagram and is shown in Fig. 5 for a steel containing 0.4% C. In this diagram the primary
34
alpha is the same as the free ferrite, and no martensite finish line is shown. It is difficult in
practice to find this finish temperature. The lines on the CCT are displaced to lower
temperatures and longer times relative to the IT diagram. Also, the bainite transformation is
not as strongly affected by continuous cooling as is the pearlite reaction. Therefore, the
bainite reaction occurs at shorter times than the pearlite reaction.
As can be seen from Fig. 3, extremely rapid cooling rates are required to achieve
martensitic structures. These structures are desired because they can be tempered to high
strengths with reasonable ductilities (called tempered martensite). One of the main effects of
adding alloying elements to steels is to permit slower cooling rates to achieve these
martensitic structures.
Jominy End Quench Test
A commonly used measure of the cooling rates required to achieve this martensitic
structure is the depth to which steel can be transformed to martensite. This is called the
hardenability of the steel. The cooling rate at the surface of a steel plate is very fast but
becomes slower as the distance from the surface increases. Therefore, the distance from the
surface is an equivalent measure of the cooling rate, and can be used to give the hardenability
of the steel.
The depth is usually measured by the Jominy End Quench Test. In this test one end of
a round bar is quenched in a water stream and the other end cools in air. Thus, various
cooling rates are obtained in the specimen. By measuring the hardness as a function of the
distance from the quenched end, the cooling rates necessary to form martensite can be
determined. Thus the greater this distance, the greater the hardenability of the steel. (Since
martensite is much harder than the other phases in steel, it is easy to find with hardness
measurements. The cooling rates in the specimen can be found experimentally using
thermocouples.)
In the lab you will be measuring the hardenability of two steels using the Jominy End
Quench Test. In addition, you will examine the microstructures of several different
transformation products, e.g. pearlite, martensite, etc.
35
EXPERIMENTAL PROCEDURE
In this test the hardenability of low-alloy steel, AISI 4140 is compared to that of a
plain 0.4% C carbon steel, AISI 1040. The experimental procedure is as follows:
(1) Lay a Jominy specimen on the tray and push the tray into the furnace set at 860°C using
tongs and heat resisting gloves. Do not attempt to stand the specimen in the tray since it will
topple over.
(2) Adjust the water column height in the Jominy end quenching tank to 2-1/2 inches above
the 1/2 inch orifice with the quick opening valve wide open. Close the quick opening valve
without changing the water column height adjustment so that when the quick opening valve
is opened later the water column will rise immediately to 2-1/2 inches. The water
temperature should lie between 40 to 85°F (not usually a problem). (At this point you should
start on the microstructural examination part of the laboratory.)
(3)
After 30 minutes in the furnace, transfer the Jominy specimen to the specimen holder of
the Jominy end quenching tank. After the Jominy specimen is in place, turn on the water and
quench the bottom end of the specimen. Transfer from furnace to quench should be rapid
(not more than 5 seconds) and students are advised to practice the motions in advance. A
second student with heat resisting gloves and a second pair of tongs or large pliers may assist
the placement of the Jominy specimen, while a third operates the quick opening valve. Care
should be taken to position the specimen so that it hangs straight down and a uniform
umbrella pattern of water rebounds from the specimen bottom. Lopsided quenching can
result from a piece of scale under the rim supporting the specimen.
(4)
Leave the specimen in place with the water flowing for at least 10 minutes.
(5)
While the first specimen is cooling, lay the second specimen into the tray and push the
tray into the furnace. Remember to record the time as you need to heat the specimen for 30
minutes.
(6)
Remove the first specimen from the specimen holder and cool it in water.
(7)
Grind a flat on the side of the specimen at least 0.015 inch deep. Use the belt grinder
with 80 grit paper. Grind gently with coolant water flowing on the surface of the grinding
paper. Remove any loose scale on both side of the specimen with grinding paper.
36
(8) Mark a scale on the flat as follows. Divide the first inch from the quenched end into
1/16 inch increments. Divide the next inch into 1/8 inch increments.
(9) Measure the Rockwell hardness on the C scale (use Table I). Start in the middle and
work towards the quenched end. The first measurement should be taken beyond the two inch
mark and discarded. It is expected to be low due to the “seating” of the specimen in the
anvil. Thereafter, record the hardness at each increment that you have marked off. It is
important to keep the indentations in the center of the flat, since errors will arise if they are at
the edges of the flat. Note that any bits of scale remaining between the specimen and the
anvil will crush during the indentation process, resulting in an erroneously low measurement.
(10) After the second specimen has been heated for 30 minutes, return to step 3.
Microstructural Examination
The lab assistant will give you a number of specimens which are already prepared for
light optical microscopy. All specimens are made from a 0.4% plain carbon steel (AISI
1040) and have been austenitized and subsequently cooled to room temperature. The cooling
rates are not the same for each specimen. Examine the specimens in the microscope and
describe with words what structural features you can see. Also make a sketch of the
microstructure of each specimen, including the magnification of the microscope. The camera
objective has a magnification of about 30x. If necessary polish the specimens again and etch
in nital, 2% nitric acid in alcohol. This part of the experiment should be done while the
Jominy specimens are being heated. You may wish to take photographs of the
microstructures that are difficult to sketch.
ANALYSIS
(1) Make a plot of the hardness (y-axis) versus the distance from the quenched end (x-axis).
The distance scale should be in 1/16 inch increments. Use Rockwell hardness numbers in the
plot.
(2)
Using the conversion table in this handout, determine the Brinell hardness number
(BHN) corresponding to each of your hardness measurements. Use the 10 mm standard ball.
37
If the hardness is greater than Rockwell C-52, use the 10 mm carbide ball for all of your
conversions.
(3) The tensile strength of steel is approximately equal to 500 times the BHN, where the
strength is in psi. Calculate the tensile strength at each position on the Jominy specimen.
(Although martensite has a very high tensile strength, it is too brittle for most engineering
applications.)
(4)
The cooling rate at 700 °C as a function of the distance from the quenched end is given
in Figure. 6. For each of your hardness measurements, determine the cooling rate at 700 °C.
(5)
Answers to 2, 3 and 4 must be presented in a table giving the distance from the
quenched end, the Rockwell hardness, the BHN, the tensile strength and the cooling rate.
This will be Table 1.
(6) Make a plot of the BHN (y-axis) versus the logarithm of the cooling rate. The cooling
rate should be shown explicitly as degrees C per second. Note the difference in cooling rate.
(7) Include your sketches of the microstructures at this point.
observed in the microstructures.
Identify the features
QUESTIONS
(1) The hardenability of a steel may be designated by a code indicating the distance from
the quenched end (in 16ths of an inch) within which the desired hardness is attained. For
example, if a Rockwell C Hardness of 45 or higher is obtained out to 9/16" from the
quenched end, we can write that the hardenability J-45 is 9. Find J-40 and J-35 for the 1040
and the 4140 steels.
(2)
What microstructures would you expect for the 1040 steel at:
(a) 1/16 from the quenched end
(b) 4/16 inch from the quenched end
(c) 2 inches from the quenched end
38
To answer these questions use the continuous cooling transformation curve in Fig. 5. Plot the
temperature vs. time curve on this graph for each of the cooling times, a, b and c. Assume
that the cooling rate at 700 °C is constant at all temperatures and that cooling starts at 860 °C.
For times less than 1 second, extend the axis to the left to 0.1 second and plot the cooling
rates to the left of the y-axis.
(3) Describe the probable heat treatment that produced each of the microstructures that you
examined. Be sure to explain why these heat treatments produced these microstructures.
(4)
Is high hardenability desirable in steels? Explain your answer briefly.
(5) Briefly explain the difference between hardness and hardenability.
(6) (a) Name the three factors that influence the degree to which martensite is formed
throughout the cross section of a steel specimen.
(b) For each, tell how the extent of martensite formation may be increased.
FIGURES
39
40
41
42
REFERENCES
D. R. Askeland, The Science and Engineering of Materials, Alt. Ed., PWS Engineering,
1984, pp. 288-303, 351-376.
L. H. Van Vlack, Elements of Materials Science and Engineering, 5th ed., 1985, pp. 402-415,
431-435,439-445, 455-463, 469-478.
L. H. Van Vlack and C. J. Osborn, Study Aids for Introductory Materials Courses, pp. 135140, 157-208.
43
G. L. Kehl, Principles of Metallographic Laboratory Practice, McGraw-Hill, 1949, pp. 303310, 229-240.
J. Wulff, et. al., Structure and Properties of Materials, Vol. 1, pp. 184-197; Vol. 2, pp. 123128.
A. G. Guy, Physical Metallurgy for Engineers, 1962, Addison-Wesley, 1962, pp. 122-124,
294-298, 301-311.
44
