, SOLUTION MANUAL FOR Manufacturing
Engineering and Technology, 9th edition
Kalpakjian
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
,Manufacturing
Engineering
and Technology
NINTH
EDITION
Serope Kalpakjian
Illinois Institute of Technology
Steven R. Schmid
University of North Carolina at Charlotte
,This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching
their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World
Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never
be made available to students except by instructors using the accompanying text in their classes. All recipients of this
work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of
other instructors who rely on these materials.
Copyright © 2026, 2020, 2014 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request
forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department, please
visit www.pearsoned.com/permissions/.
PEARSON and Pearson+ are exclusive trademarks in the U.S. and/or other countries owned by Pearson Education,
Inc. or its affiliates.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress
are for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
, Preface
This solutions manual is intended to assist instructors in the organization of assignments and discussions
associated with courses in manufacturing engineering, and using the textbook Manufacturing Engineering
and Technology, 9th ed. In addition to these solutions, instructors can find other education resources at the
Prentice Hall maintained website, as discussed and connected with links in the e-book.
Manufacturing presents a number of challenges and opportunities to instructors. As a topic of study
it is exciting because of its breadth and unending ability to provide fascinating opportunities for research,
analysis, and creativity. Literally every discipline and sub-discipline in engineering has strong ties to man-
ufacturing, and a number of universities have used design and manufacturing as the basis of a capstone
course that culminates a mechanical engineering bachelor’s degree. To students of manufacturing, it is, at
first, a field so enormous that any semester or academic year sequence in manufacturing can do nothing
but scratch the surface of the subject. This perception is absolutely true: Manufacturing, like so many other
areas of specialization within engineering, truly is an area where lifelong learning is necessary.
As educators, we have a responsibility to prepare our students as best we can for a life of continued
education. Lifelong learning need not be restricted to formal classroom training, but it should be impressed
upon students that they need to continually and systematically examine the physical world in order to
achieve continued levels of improvement.
A challenging question, and perhaps one without any one good answer is: how should one teach
an effective manufacturing course? We have seen examples of many successful strategies, some based
solely on analytical methods, others involving surveys of manufacturing, and again others emphasizing
the impact of manufacturing on engineering design. Most instructors develop hybrid approaches that
are not restricted to any one area. We have attempted to include problems at the end of every chapter
to accommodate each of these approaches, and it is our hope that instructors will find good homework
assignments in the book.
Manufacturing is a challenge to instructors. There are a number of courses, such as statics, dynam-
ics, solid and fluid mechanics, etc., where topics for study are broken down into small enough portions
and where closed-form, quantitative problems are routinely solved by students and by faculty during lec-
tures. Such problems are important for learning concepts, and they give students a sense of security in that
absolute answers can be determined.
In manufacturing practice, such closed-form solutions do exist, but they are relatively rare. Usually,
multiple disciplines are blended, and the information available is insufficient to truly optimize a desired
outcome. In practice, manufacturing engineers need to apply good judgment after they have researched a
problem as best they can given budgetary and time restrictions. These difficult open-ended problems are
much more demanding than closed-form solutions, and require a different mindset. Instead of considering
a number as valid or invalid (usually by checking against the answer provided in the book or by the instruc-
tor), an open-ended problem can be evaluated only with respect to whether or not the result is reasonable
and if good scientific methods were used to obtain the result.
This textbook has been intentionally designed with a large number of open-ended problems. Such
problems are, in our experience, extremely valuable when teaching manufacturing engineering. However,
a solutions manual is well-suited for closed-form solutions, not open-ended problems. We have attempted
to describe the pitfalls and methods that will be valuable in solving the open-ended problems, but by their
nature, it is difficult to give a correct answer to these problems. Often, such problems have as the first
sentence in the solution “By the student”. We will describe acceptable solutions or approaches to obtaining
those solutions, but it should be recognized that many potential answers exist for these problems.
Bloom’s taxonomy of learning objectives, illustrated in Fig. 1, suggest that there is a hierarchy of skills
that students can acquire. The chapter-ending problems have been designed with Bloom’s taxonomy in
mind, with Review Questions and Qualitative Problems emphasizing lower-order thinking skills, and
, {
Creating Synthesis, Design & Projects
Higher-order Evaluating
thinking skills
Analyzing
Quantitative Problems
{
Applying
Lower-order
thinking skills Understanding Qualitative Problems
Remembering Review Questions
Figure 1: Bloom’s taxonomy of learning objectives. Source: Anderson, L.W., and Krathwold, D.R., A tax-
onomy for learning, teaching and assessing: A revision of Bloom’s Taxonomy of educational objectives: Complete
Edition, New York, Longman, 2001.
Quantitative Problems and Synthesis, Design and Projects to exercise higher-order thinking skills. It is
recognized that truly effective courses will address all Bloom levels; the chapter-ending problems have
been designed to assist instructors in this task.
A recent challenge has involved the treatment of artificial intelligence language models that are able to
respond to queries by collecting language on the Internet and formulating solutions. The language models
are impressive, and promise to become more sophisticated with time. They do represent a disruption to
the established methods of teaching engineering topics such as manufacturing. The authors recognize
that this solutions manual, and in fact the entire book, is available on the Internet, and therefore an AI
language model can formulate answers to queries based in part on the book contents. As educators, the
challenge is to teach, and avoid students obtaining AI-generated homework solutions. There are potential
approaches, but one that has been included often in the chapter-ending problems involves asking a student
to conduct a literature search and write a one-page summary of the topic; they then are asked to obtain an
AI-generated solution; they then must compare the two and explain why they are different. We have heard
of other approaches as well. Some professors (with smaller class sizes) will assign students a 5-10 minute
presentation every week, on a topic corresponding to course or book content. Students are encouraged to
use AI language models, as they still must learn the material by teaching it.
We encourage faculty to communicate with us and to give us feedback in any of the areas of the book.
Steven Schmid
ii
,Chapter 1
The Structure of Metals
Qualitative Problems
1.26. Explain your understanding of why the study of the crystal structure of metals is important.
The study of crystal structure is important for a number of reasons. Basically, the crystal structure
influences a material’s performance from both a design and manufacturing standpoint. For example,
the number of slip systems in a crystal has a direct bearing on the ability of a metal to undergo plastic
deformation without fracture. Similarly, the crystal structure has a bearing on strength, ductility
and corrosion resistance. Metals with face-centered cubic structure, for example, tend to be ductile
whereas hexagonal close-packed metals tend to be brittle. The crystal structure and size of atom
determines the largest interstitial sites, which has a bearing on the ability of that material to form
alloys, and with which materials, as interstitials or substitutionals.
1.27. What is the significance of the fact that some metals undergo allotropism?
Allotropism, also called polymorphism, is discussed in Section 1.3, and refers to a change in crystal
structure for a metal. Since properties vary with crystal structures, allotropism is useful and essential
in heat treating of metals to achieve desired properties (Chapter 4). A major application is hardening
of steel, which involves the change in iron from the fcc structure to the bcc structure (see Fig. 1.3). By
heating the steel to the fcc structure and quenching, it develops into martensite, which is a very hard,
hence strong, structure.
1.28. Is it possible for two pieces of the same metal to have different recrystallization temperatures? Is it
possible for recrystallization to take place in some regions of a part before it does in other regions of
the same part? Explain.
Two pieces of the same metal can have different recrystallization temperatures if the pieces have
been cold worked to different amounts. The piece that was cold worked to a greater extent (higher
strains), will have more internal energy (stored energy) to drive the recrystallization process, hence
its recrystallization temperature will be lower. Recrystallization may also occur in some regions of the
part before others if it has been unevenly strained (since varying amounts of cold work have different
recrystallization temperatures), or if the part has different thicknesses in various sections. The thinner
sections will heat up to the recrystallization temperature faster.
1.29. Describe your understanding of why different crystal structures exhibit different strengths and ductili-
ties.
Different crystal structures have different slip systems, which consist of a slip plane (the closest
packed plane) and a slip direction (the close-packed direction). The fcc structure has 12 slip sys-
tems, bcc has 48, and hcp has 3. The ductility of a metal depends on how many of the slip systems can
be operative. In general, fcc and bcc structures possess higher ductility than hcp structures, because
1
,2 Chapter 1 The Structure of Metals
they have more slip systems. The shear strength of a metal decreases for decreasing b/a ratio (b is
inversely proportional to atomic density in the slip plane and a is the plane spacing), and the b/a ratio
depends on the slip system of the chemical structure (see Section 1.4).
1.30. A cold-worked piece of metal has been recrystallized. When tested, it is found to be anisotropic.
Explain the probable reason.
The anisotropy of the workpiece is likely due to preferred orientation remaining from the recrystal-
lization process. Copper is an example of a metal that has a very strong preferred orientation after
annealing. Also, it has been shown that below a critical amount of plastic deformation, typically 5%,
no recrystallization occurs.
1.31. What materials and structures can you think of (other than metals) that exhibit anisotropic behavior?
This is an open-ended problem and the students should be encouraged to develop their own answers.
However, some examples of anisotropic materials are wood, polymers that have been cold worked,
bone, any woven material (such as cloth) and composite materials.
1.32. Two parts have been made of the same material, but one was formed by cold working and the other
by hot working. Explain the differences you might observe between the two.
There are a large number of differences that will be seen between the two materials, including:
1. The cold worked material will have a higher strength than the hot worked material, and this will
be more pronounced for materials with high strain hardening exponents.
2. Since hardness (see Section 2.6.2) is related to strength, the cold worked material will also have
a higher hardness.
3. The cold worked material will have smaller grains and the grains will be elongated.
4. The hot worked material will probably have fewer dislocations, and they will be more evenly
distributed.
5. The cold worked material can have a superior surface finish when in an as-formed condition.
Also, it can have better tolerances.
6. A cold worked material will have a lower recrystallization temperature than a hot worked ma-
terial.
1.33. Explain the importance of homologous temperature.
The homologous temperature is defined as the ratio of a metal’s current temperature to its melting
temperature on an absolute scale (Kelvin or Rankine, not Celsius or Fahrenheit). This is important for
determining whether or not the metal will encounter recrystallization or grain growth. The homolo-
gous temperature is more important than actual temperature, because recrystallization occurs at very
different temperatures for different metals, but the homologous temperature effects are fairly consis-
tent. The homologous temperature therefore allows one to distinguish between cold, warm, and hot
working, as discussed in Table 1.2.
1.34. Do you think it might be important to know whether a raw material to be used in a manufacturing
process has anisotropic properties? What about anisotropy in the finished product? Explain.
Anisotropy is important in cold-working processes, especially sheet-metal forming where the mate-
rial’s properties should preferably be uniform in the plane of the sheet and stronger in the thickness
direction. As shown in Section 16.7, these characteristics allow for deep drawing of parts (like bev-
erage cans) without earing, tearing, or cracking in the forming operations involved. In a finished
part, anisotropy is important so that the strongest direction of the part can be designed to support the
largest load in service. Also, the efficiency of transformers can be improved by using a sheet steel with
anisotropy that can reduce magnetic hysteresis losses. Hysteresis is well known in ferromagnetic ma-
terials. When an external magnetic field is applied to a ferromagnet, the ferromagnet absorbs some
,Qualitative Problems 3
of the external field. When sheet steel is highly anisotropic, it contains small grains and a crystal-
lographic orientation that is far more uniform than for isotropic materials, and this orientation will
reduce magnetic hysteresis losses.
1.35. What is the difference between an interstitial atom and a substitutional atom?
The difference can be seen in Fig. 1.8. A substitutional atom replaces an atom in the repeating lattice
without distortion. An interstitial does not fit in the normal lattice; it can fit in the gap between
atoms, or else it distorts the lattice. Examples of substitutionally are copper-nickel, gold-silver, and
molybdenum-tungsten. Interstitials can be self-interstitials, but common other examples are carbon,
lithium, sodium, and nitrogen.
1.36. Explain why the strength of a polycrystalline metal at room temperature decreases as its grain size
increases.
Strength increases as more entanglements of dislocations occur with grain boundaries (Section 1.4.2).
Metals with larger grains have less grain-boundary area per unit volume, and hence will not be as
able to generate as many entanglements at grain boundaries, thus the strength will be lower.
1.37. Describe the technique you would use to reduce the orange-peel effect on the surface of workpieces.
Orange peel is surface roughening induced by plastic strain. There are a number of ways of reducing
the orange peel effect, including:
• Performing all forming operations without a lubricant, or else a very thin lubricant film (smaller
than the desired roughness) and very smooth tooling. The goal is to have the surface roughness
of the tooling imparted onto the workpiece.
• Large grains exacerbate orange peel, so the use of small grained materials would reduce orange
peel.
• If deformation processes can be designed so that the surfaces see no deformation, then there
would be no orange peel. For example, upsetting beneath flat dies can lead to a reduction in
thickness with very little surface strains beneath the platen (see Fig. 14.3).
• Finishing operations can remove orange peel effects.
1.38. What is the significance of the fact that such metals as lead and tin have a recrystallization temperature
that is about room temperature?
Recrystallization around room temperature prevents these metals from work hardening when cold
worked. This characteristic prevents their strengthening and hardening, thus requiring a recrystal-
lization cycle to restore their ductility. This behavior is also useful in experimental verification of
analytical results concerning force and energy requirements in metalworking processes (see Part III
of the text).
1.39. It was stated in this chapter that twinning usually occurs in hcp materials, but Fig. 1.6b shows twinning
in a rectangular array of atoms. Can you explain the discrepancy?
The hcp unit cell shown in Fig. 1.6a has a hexagon on the top and bottom surfaces. However, an
intersecting plane that is vertical in this figure would intersect atoms in a rectangular array as depicted
in Fig. 1.6b. Thus, twinning occurs in hcp materials, but not in the hexagonal (close packed) plane
such as in the top of the unit cell.
1.40. It has been noted that the more a metal has been cold worked, the less it strain hardens. Explain why
this is the case.
This phenomenon can be observed in stress-strain curves, such as those shown in Figs. 2.2 and 2.5.
Recall that the main effects of cold working are that grains become elongated and that the average
grain size becomes smaller (as grains break down) with strain. Strain hardening occurs when dislo-
cations interfere with each other and with grain boundaries. When a metal is annealed, the grains
, 4 Chapter 1 The Structure of Metals
are large, and a small strain results in grains moving relatively easily at first, but they increasingly
interfere with each other as strain increases. This explains that there is strain hardening for annealed
materials at low strain. To understand why there is less strain hardening at higher levels of cold
work, consider the extreme case of a very highly cold-worked material, with very small grains and
very many dislocations that already interfere with each other. For this highly cold-worked material,
the stress cannot be increased much more with strain, because the dislocations have nowhere else to
go - they already interfere with each other and are pinned at grain boundaries.
1.41. Is it possible to cold work a metal at temperatures above the boiling point of water? Explain.
The metallurgical distinction between cold and hot working is associated with the homologous temper-
ature. Cold working is associated with plastic deformation of a metal when it is below one-third of
its melting temperature on an absolute scale. At the boiling point of water, the temperature is 100° C,
or 373 Kelvin. If this value is one-third the melting temperature, then a metal would have to have a
melting temperature of 1119K, or 846° C. As can be seen in Table 3.1, there are many such metals.
1.42. Comment on your observations regarding Fig. 1.14.
This is an open-ended problem with many potential answers. Students may choose to address this
problem by focusing on the shape of individual curves or their relation to each other. The instructor
may wish to focus the students on a curve or two, or ask if the figure would give the same trends for
a material that is quickly heated, held at that temperature for a few seconds, and then quenched, or
alternatively for one that is maintained at the temperatures for very long times.
1.43. Is it possible for a metal to be completely isotropic? Explain.
This answer can be answered only if isotropy is defined within limits. For example:
• A single crystal of a metal has an inherent an unavoidable anisotropy. Thus, at a length scale that
is on the order of a material’s grain size, a metal will always be anisotropic.
• A metal with elongated grains will have a lower strength and hardness in one direction than in
others, and this is unavoidable.
• However, a metal that contains a large number of small and equiaxed grains will have the first
two effects essentially made very small; the metal may be isotropic within measurement limits.
• Annealing can lead to equiaxed grains, and depending on the measurement limits, this can es-
sentially result in an isotropic metal.
• A metal with a very small grain size (i.e., a metal glass) can have no apparent crystal structure
or slip systems, and can be essentially isotropic.
1.44. Referring to Fig. 1.1, assume you can make a ball bearing from a single crystal. What advantages
and disadvantages would such a bearing have?
This is a challenging problem, and is one that can be reintroduced at the end of Chapters 1-4. Students
should be encouraged to provide answers that are based on their understanding and experience; these
are intended to start a discussion.
The advantages of a single crystal bearing include:
• Corrosion generally starts at a grain boundary, where loosely packed atoms are more susceptible
to chemical attack; therefore, the bearing could be more corrosion resistant.
• Fatigue cracks may be more difficult to form, but with some materials are more difficult to pro-
pogate through a grain than along a grain boundary.
• The strength could be higher than a polycrystalline metal.
• Distortion of the bearing at elevated temperatures may not be an issue.
Disadvantages include:
Engineering and Technology, 9th edition
Kalpakjian
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
,Manufacturing
Engineering
and Technology
NINTH
EDITION
Serope Kalpakjian
Illinois Institute of Technology
Steven R. Schmid
University of North Carolina at Charlotte
,This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching
their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World
Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never
be made available to students except by instructors using the accompanying text in their classes. All recipients of this
work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of
other instructors who rely on these materials.
Copyright © 2026, 2020, 2014 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request
forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department, please
visit www.pearsoned.com/permissions/.
PEARSON and Pearson+ are exclusive trademarks in the U.S. and/or other countries owned by Pearson Education,
Inc. or its affiliates.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress
are for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
, Preface
This solutions manual is intended to assist instructors in the organization of assignments and discussions
associated with courses in manufacturing engineering, and using the textbook Manufacturing Engineering
and Technology, 9th ed. In addition to these solutions, instructors can find other education resources at the
Prentice Hall maintained website, as discussed and connected with links in the e-book.
Manufacturing presents a number of challenges and opportunities to instructors. As a topic of study
it is exciting because of its breadth and unending ability to provide fascinating opportunities for research,
analysis, and creativity. Literally every discipline and sub-discipline in engineering has strong ties to man-
ufacturing, and a number of universities have used design and manufacturing as the basis of a capstone
course that culminates a mechanical engineering bachelor’s degree. To students of manufacturing, it is, at
first, a field so enormous that any semester or academic year sequence in manufacturing can do nothing
but scratch the surface of the subject. This perception is absolutely true: Manufacturing, like so many other
areas of specialization within engineering, truly is an area where lifelong learning is necessary.
As educators, we have a responsibility to prepare our students as best we can for a life of continued
education. Lifelong learning need not be restricted to formal classroom training, but it should be impressed
upon students that they need to continually and systematically examine the physical world in order to
achieve continued levels of improvement.
A challenging question, and perhaps one without any one good answer is: how should one teach
an effective manufacturing course? We have seen examples of many successful strategies, some based
solely on analytical methods, others involving surveys of manufacturing, and again others emphasizing
the impact of manufacturing on engineering design. Most instructors develop hybrid approaches that
are not restricted to any one area. We have attempted to include problems at the end of every chapter
to accommodate each of these approaches, and it is our hope that instructors will find good homework
assignments in the book.
Manufacturing is a challenge to instructors. There are a number of courses, such as statics, dynam-
ics, solid and fluid mechanics, etc., where topics for study are broken down into small enough portions
and where closed-form, quantitative problems are routinely solved by students and by faculty during lec-
tures. Such problems are important for learning concepts, and they give students a sense of security in that
absolute answers can be determined.
In manufacturing practice, such closed-form solutions do exist, but they are relatively rare. Usually,
multiple disciplines are blended, and the information available is insufficient to truly optimize a desired
outcome. In practice, manufacturing engineers need to apply good judgment after they have researched a
problem as best they can given budgetary and time restrictions. These difficult open-ended problems are
much more demanding than closed-form solutions, and require a different mindset. Instead of considering
a number as valid or invalid (usually by checking against the answer provided in the book or by the instruc-
tor), an open-ended problem can be evaluated only with respect to whether or not the result is reasonable
and if good scientific methods were used to obtain the result.
This textbook has been intentionally designed with a large number of open-ended problems. Such
problems are, in our experience, extremely valuable when teaching manufacturing engineering. However,
a solutions manual is well-suited for closed-form solutions, not open-ended problems. We have attempted
to describe the pitfalls and methods that will be valuable in solving the open-ended problems, but by their
nature, it is difficult to give a correct answer to these problems. Often, such problems have as the first
sentence in the solution “By the student”. We will describe acceptable solutions or approaches to obtaining
those solutions, but it should be recognized that many potential answers exist for these problems.
Bloom’s taxonomy of learning objectives, illustrated in Fig. 1, suggest that there is a hierarchy of skills
that students can acquire. The chapter-ending problems have been designed with Bloom’s taxonomy in
mind, with Review Questions and Qualitative Problems emphasizing lower-order thinking skills, and
, {
Creating Synthesis, Design & Projects
Higher-order Evaluating
thinking skills
Analyzing
Quantitative Problems
{
Applying
Lower-order
thinking skills Understanding Qualitative Problems
Remembering Review Questions
Figure 1: Bloom’s taxonomy of learning objectives. Source: Anderson, L.W., and Krathwold, D.R., A tax-
onomy for learning, teaching and assessing: A revision of Bloom’s Taxonomy of educational objectives: Complete
Edition, New York, Longman, 2001.
Quantitative Problems and Synthesis, Design and Projects to exercise higher-order thinking skills. It is
recognized that truly effective courses will address all Bloom levels; the chapter-ending problems have
been designed to assist instructors in this task.
A recent challenge has involved the treatment of artificial intelligence language models that are able to
respond to queries by collecting language on the Internet and formulating solutions. The language models
are impressive, and promise to become more sophisticated with time. They do represent a disruption to
the established methods of teaching engineering topics such as manufacturing. The authors recognize
that this solutions manual, and in fact the entire book, is available on the Internet, and therefore an AI
language model can formulate answers to queries based in part on the book contents. As educators, the
challenge is to teach, and avoid students obtaining AI-generated homework solutions. There are potential
approaches, but one that has been included often in the chapter-ending problems involves asking a student
to conduct a literature search and write a one-page summary of the topic; they then are asked to obtain an
AI-generated solution; they then must compare the two and explain why they are different. We have heard
of other approaches as well. Some professors (with smaller class sizes) will assign students a 5-10 minute
presentation every week, on a topic corresponding to course or book content. Students are encouraged to
use AI language models, as they still must learn the material by teaching it.
We encourage faculty to communicate with us and to give us feedback in any of the areas of the book.
Steven Schmid
ii
,Chapter 1
The Structure of Metals
Qualitative Problems
1.26. Explain your understanding of why the study of the crystal structure of metals is important.
The study of crystal structure is important for a number of reasons. Basically, the crystal structure
influences a material’s performance from both a design and manufacturing standpoint. For example,
the number of slip systems in a crystal has a direct bearing on the ability of a metal to undergo plastic
deformation without fracture. Similarly, the crystal structure has a bearing on strength, ductility
and corrosion resistance. Metals with face-centered cubic structure, for example, tend to be ductile
whereas hexagonal close-packed metals tend to be brittle. The crystal structure and size of atom
determines the largest interstitial sites, which has a bearing on the ability of that material to form
alloys, and with which materials, as interstitials or substitutionals.
1.27. What is the significance of the fact that some metals undergo allotropism?
Allotropism, also called polymorphism, is discussed in Section 1.3, and refers to a change in crystal
structure for a metal. Since properties vary with crystal structures, allotropism is useful and essential
in heat treating of metals to achieve desired properties (Chapter 4). A major application is hardening
of steel, which involves the change in iron from the fcc structure to the bcc structure (see Fig. 1.3). By
heating the steel to the fcc structure and quenching, it develops into martensite, which is a very hard,
hence strong, structure.
1.28. Is it possible for two pieces of the same metal to have different recrystallization temperatures? Is it
possible for recrystallization to take place in some regions of a part before it does in other regions of
the same part? Explain.
Two pieces of the same metal can have different recrystallization temperatures if the pieces have
been cold worked to different amounts. The piece that was cold worked to a greater extent (higher
strains), will have more internal energy (stored energy) to drive the recrystallization process, hence
its recrystallization temperature will be lower. Recrystallization may also occur in some regions of the
part before others if it has been unevenly strained (since varying amounts of cold work have different
recrystallization temperatures), or if the part has different thicknesses in various sections. The thinner
sections will heat up to the recrystallization temperature faster.
1.29. Describe your understanding of why different crystal structures exhibit different strengths and ductili-
ties.
Different crystal structures have different slip systems, which consist of a slip plane (the closest
packed plane) and a slip direction (the close-packed direction). The fcc structure has 12 slip sys-
tems, bcc has 48, and hcp has 3. The ductility of a metal depends on how many of the slip systems can
be operative. In general, fcc and bcc structures possess higher ductility than hcp structures, because
1
,2 Chapter 1 The Structure of Metals
they have more slip systems. The shear strength of a metal decreases for decreasing b/a ratio (b is
inversely proportional to atomic density in the slip plane and a is the plane spacing), and the b/a ratio
depends on the slip system of the chemical structure (see Section 1.4).
1.30. A cold-worked piece of metal has been recrystallized. When tested, it is found to be anisotropic.
Explain the probable reason.
The anisotropy of the workpiece is likely due to preferred orientation remaining from the recrystal-
lization process. Copper is an example of a metal that has a very strong preferred orientation after
annealing. Also, it has been shown that below a critical amount of plastic deformation, typically 5%,
no recrystallization occurs.
1.31. What materials and structures can you think of (other than metals) that exhibit anisotropic behavior?
This is an open-ended problem and the students should be encouraged to develop their own answers.
However, some examples of anisotropic materials are wood, polymers that have been cold worked,
bone, any woven material (such as cloth) and composite materials.
1.32. Two parts have been made of the same material, but one was formed by cold working and the other
by hot working. Explain the differences you might observe between the two.
There are a large number of differences that will be seen between the two materials, including:
1. The cold worked material will have a higher strength than the hot worked material, and this will
be more pronounced for materials with high strain hardening exponents.
2. Since hardness (see Section 2.6.2) is related to strength, the cold worked material will also have
a higher hardness.
3. The cold worked material will have smaller grains and the grains will be elongated.
4. The hot worked material will probably have fewer dislocations, and they will be more evenly
distributed.
5. The cold worked material can have a superior surface finish when in an as-formed condition.
Also, it can have better tolerances.
6. A cold worked material will have a lower recrystallization temperature than a hot worked ma-
terial.
1.33. Explain the importance of homologous temperature.
The homologous temperature is defined as the ratio of a metal’s current temperature to its melting
temperature on an absolute scale (Kelvin or Rankine, not Celsius or Fahrenheit). This is important for
determining whether or not the metal will encounter recrystallization or grain growth. The homolo-
gous temperature is more important than actual temperature, because recrystallization occurs at very
different temperatures for different metals, but the homologous temperature effects are fairly consis-
tent. The homologous temperature therefore allows one to distinguish between cold, warm, and hot
working, as discussed in Table 1.2.
1.34. Do you think it might be important to know whether a raw material to be used in a manufacturing
process has anisotropic properties? What about anisotropy in the finished product? Explain.
Anisotropy is important in cold-working processes, especially sheet-metal forming where the mate-
rial’s properties should preferably be uniform in the plane of the sheet and stronger in the thickness
direction. As shown in Section 16.7, these characteristics allow for deep drawing of parts (like bev-
erage cans) without earing, tearing, or cracking in the forming operations involved. In a finished
part, anisotropy is important so that the strongest direction of the part can be designed to support the
largest load in service. Also, the efficiency of transformers can be improved by using a sheet steel with
anisotropy that can reduce magnetic hysteresis losses. Hysteresis is well known in ferromagnetic ma-
terials. When an external magnetic field is applied to a ferromagnet, the ferromagnet absorbs some
,Qualitative Problems 3
of the external field. When sheet steel is highly anisotropic, it contains small grains and a crystal-
lographic orientation that is far more uniform than for isotropic materials, and this orientation will
reduce magnetic hysteresis losses.
1.35. What is the difference between an interstitial atom and a substitutional atom?
The difference can be seen in Fig. 1.8. A substitutional atom replaces an atom in the repeating lattice
without distortion. An interstitial does not fit in the normal lattice; it can fit in the gap between
atoms, or else it distorts the lattice. Examples of substitutionally are copper-nickel, gold-silver, and
molybdenum-tungsten. Interstitials can be self-interstitials, but common other examples are carbon,
lithium, sodium, and nitrogen.
1.36. Explain why the strength of a polycrystalline metal at room temperature decreases as its grain size
increases.
Strength increases as more entanglements of dislocations occur with grain boundaries (Section 1.4.2).
Metals with larger grains have less grain-boundary area per unit volume, and hence will not be as
able to generate as many entanglements at grain boundaries, thus the strength will be lower.
1.37. Describe the technique you would use to reduce the orange-peel effect on the surface of workpieces.
Orange peel is surface roughening induced by plastic strain. There are a number of ways of reducing
the orange peel effect, including:
• Performing all forming operations without a lubricant, or else a very thin lubricant film (smaller
than the desired roughness) and very smooth tooling. The goal is to have the surface roughness
of the tooling imparted onto the workpiece.
• Large grains exacerbate orange peel, so the use of small grained materials would reduce orange
peel.
• If deformation processes can be designed so that the surfaces see no deformation, then there
would be no orange peel. For example, upsetting beneath flat dies can lead to a reduction in
thickness with very little surface strains beneath the platen (see Fig. 14.3).
• Finishing operations can remove orange peel effects.
1.38. What is the significance of the fact that such metals as lead and tin have a recrystallization temperature
that is about room temperature?
Recrystallization around room temperature prevents these metals from work hardening when cold
worked. This characteristic prevents their strengthening and hardening, thus requiring a recrystal-
lization cycle to restore their ductility. This behavior is also useful in experimental verification of
analytical results concerning force and energy requirements in metalworking processes (see Part III
of the text).
1.39. It was stated in this chapter that twinning usually occurs in hcp materials, but Fig. 1.6b shows twinning
in a rectangular array of atoms. Can you explain the discrepancy?
The hcp unit cell shown in Fig. 1.6a has a hexagon on the top and bottom surfaces. However, an
intersecting plane that is vertical in this figure would intersect atoms in a rectangular array as depicted
in Fig. 1.6b. Thus, twinning occurs in hcp materials, but not in the hexagonal (close packed) plane
such as in the top of the unit cell.
1.40. It has been noted that the more a metal has been cold worked, the less it strain hardens. Explain why
this is the case.
This phenomenon can be observed in stress-strain curves, such as those shown in Figs. 2.2 and 2.5.
Recall that the main effects of cold working are that grains become elongated and that the average
grain size becomes smaller (as grains break down) with strain. Strain hardening occurs when dislo-
cations interfere with each other and with grain boundaries. When a metal is annealed, the grains
, 4 Chapter 1 The Structure of Metals
are large, and a small strain results in grains moving relatively easily at first, but they increasingly
interfere with each other as strain increases. This explains that there is strain hardening for annealed
materials at low strain. To understand why there is less strain hardening at higher levels of cold
work, consider the extreme case of a very highly cold-worked material, with very small grains and
very many dislocations that already interfere with each other. For this highly cold-worked material,
the stress cannot be increased much more with strain, because the dislocations have nowhere else to
go - they already interfere with each other and are pinned at grain boundaries.
1.41. Is it possible to cold work a metal at temperatures above the boiling point of water? Explain.
The metallurgical distinction between cold and hot working is associated with the homologous temper-
ature. Cold working is associated with plastic deformation of a metal when it is below one-third of
its melting temperature on an absolute scale. At the boiling point of water, the temperature is 100° C,
or 373 Kelvin. If this value is one-third the melting temperature, then a metal would have to have a
melting temperature of 1119K, or 846° C. As can be seen in Table 3.1, there are many such metals.
1.42. Comment on your observations regarding Fig. 1.14.
This is an open-ended problem with many potential answers. Students may choose to address this
problem by focusing on the shape of individual curves or their relation to each other. The instructor
may wish to focus the students on a curve or two, or ask if the figure would give the same trends for
a material that is quickly heated, held at that temperature for a few seconds, and then quenched, or
alternatively for one that is maintained at the temperatures for very long times.
1.43. Is it possible for a metal to be completely isotropic? Explain.
This answer can be answered only if isotropy is defined within limits. For example:
• A single crystal of a metal has an inherent an unavoidable anisotropy. Thus, at a length scale that
is on the order of a material’s grain size, a metal will always be anisotropic.
• A metal with elongated grains will have a lower strength and hardness in one direction than in
others, and this is unavoidable.
• However, a metal that contains a large number of small and equiaxed grains will have the first
two effects essentially made very small; the metal may be isotropic within measurement limits.
• Annealing can lead to equiaxed grains, and depending on the measurement limits, this can es-
sentially result in an isotropic metal.
• A metal with a very small grain size (i.e., a metal glass) can have no apparent crystal structure
or slip systems, and can be essentially isotropic.
1.44. Referring to Fig. 1.1, assume you can make a ball bearing from a single crystal. What advantages
and disadvantages would such a bearing have?
This is a challenging problem, and is one that can be reintroduced at the end of Chapters 1-4. Students
should be encouraged to provide answers that are based on their understanding and experience; these
are intended to start a discussion.
The advantages of a single crystal bearing include:
• Corrosion generally starts at a grain boundary, where loosely packed atoms are more susceptible
to chemical attack; therefore, the bearing could be more corrosion resistant.
• Fatigue cracks may be more difficult to form, but with some materials are more difficult to pro-
pogate through a grain than along a grain boundary.
• The strength could be higher than a polycrystalline metal.
• Distortion of the bearing at elevated temperatures may not be an issue.
Disadvantages include:
