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Chapter 4
Properties and Behavior of Materials
4.1
4.2
4.3
4.4
4.5
4.6
Introduction
Physical Properties of Materials
Structure of Metals
Mechanical Properties of Materials
Comparison of the Properties of Materials
Relative Cost of Engineering Materials
4.7 Case Study
4.8 Summary
4.9 Questions
4.10 Problems
4.11 Suggested Reading
In this chapter we will review the structure and properties of engineering materials. We
will focus on the physical, electrical and mechanical properties of materials that influence their
selection for a design application and subsequent processing. Examples of the importance of
these properties with respect to manufacturing process applications will also be given. The
treatment given is a review of material you have most likely had in prerequisite courses in
physics or material science.
4.1
Introduction
Designers and engineers are usually more interested in the behavior of materials under
load or when in a magnetic field than in why they behave as they do. Yet the better we
understand the nature of materials and the reasons for their physical and mechanical properties
the more quickly and wisely you will be able to choose the proper material for a given design.
Generally, a material property is the measured magnitude of its response to a standard test
performed according to a standard procedure in a given environment. In engineering materials
the loads are mechanical or physical in nature and the properties are recorded in handbooks or,
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for new materials, are made available by the supplier. Frequently we tabulate such information
for room-temperature conditions only, so when the actual service conditions are at subfreezing or
elevated temperatures, more information is needed.
The properties of materials are sometimes referred to as structure-sensitive, as compared
to structure-insensitive properties. In this case structure-insensitive properties include the
traditional physical properties: electrical and thermal conductivity, specific heat, density, and
magnetic and optical properties. The structure-sensitive properties include the tensile and yield
strength, hardness, and impact, creep, and fatigue resistance. It is recognized that some sources
maintain that hardness is not a true mechanical property, because it varies somewhat with the
characteristics of the indentor and therefore is a technological test. It is well known that other
mechanical properties vary significantly with rate of loading, temperature, geometry of notch in
impact testing, and the size and geometry of the test specimen. In that sense all mechanical tests
of material properties are technological tests. Furthermore, since reported test values of materials
properties are statistical averages, a commercial material frequently has a tolerance band of 5
percent or more deviation from a given published value.
In the solid state, materials can be classified as metals, polymers, ceramics, and
composites. Any particular material can be described by its behavior when subjected to external
conditions. Thus, when it is loaded under known conditions of direction, magnitude, rate, and
environment, the resulting responses are called mechanical properties. There are many possible
complex interrelationships among the internal structure of a material and its service performance
(Fig. 4.1). Mechanical properties such as yield strength, impact strength, hardness, creep, and
fatigue resistance are strongly structure-sensitive, i.e., they depend upon the arrangement of the
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atoms in the crystal lattice and on any imperfections in that arrangement, whereas the physical
properties are less structure-sensitive. These include electrical, thermal, magnetic, and optical
properties and do depend in part upon structure; for example, the resistivity of a metal increases
with the amount of cold work. Physical properties depend primarily upon the relative excess or
deficiency of the electrons that establish structural bonds and upon their availability and mobility.
Between the conductors with high electron mobility and the insulators with no free electrons,
precise control of the atomic architecture has created semiconductors that can have a planned
modification of their electron mobility. Similarly, advances in solid-state optics have led to the
development of the stimulated emission of electromagnetic energy in the microwave spectrum
(masers) and in the visible spectrum (lasers).
Figure 4.1
Standard material shapes.
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In studying the general structure of materials, one may consider three groupings: first,
atomic structure, electronic configuration, bonding forces, and the arrangement of the
aggregations of atoms; second, the physical aspect of materials, including properties such as
electrical and thermal conductivity, specific heat, and magnetism; and third, their macroscopic
properties, such as their mechanical behavior under load, which can be explained in terms of
impurities and imperfections in the lattice structure and the procedures used to modify that
behavior.
4.2
Physical Properties of Materials
In the selection of materials for industrial applications, many engineers normally refer to their
average macroscopic properties, as determined by engineering tests, and are seldom concerned
with microscopic considerations. Others, because of their specialty or the nature of their
positions, have to deal with microscopic properties.
The average properties of materials are those involving matter in bulk with its flaws, variations
in composition, and variations in density that are caused by manufacturing fluctuations.
Microscopic properties pertain to atoms, molecules, and their interactions. These aspects of
materials are studied for their direct applicability to industrial problems and also so that possible
properties in the development of new materials can be estimated.
In order not to become confused by apparently contradictory concepts when dealing with the
relationships between the microscopic aspects of matter and the average properties of materials,
it is wise to consider the principles that account for the nature of matter at the different levels of
our awareness. These levels are the commonplace, the extremely small, and the extremely large.
The commonplace level deals with the average properties already mentioned, and the principles
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involved are those set forth by classical physics. The realm of the extremely small is largely
explained by means of quantum mechanics, whereas that of the extremely large is dealt with by
relativity.
Relativity is concerned with very large masses, such as planets or stars, and large velocities that
may approach the velocity of light. It is also applicable to smaller masses, ranging down to
subatomic particles, when they move at high velocities. Relativity has a definite place in the tool
boxes of nuclear engineers and electrical engineers who deal with particle accelerators. For
production engineers, relativity is of only academic interest and is mentioned here for the sake of
completeness.
4.2.1 Application of Concepts from Quantum Mechanics
Quantum mechanics, once restricted to the academic halls, has now become a
bread-and-butter topic. It generally deals with particles of atomic or subatomic sizes. But from
the understanding of the behavior of these particles comes a better understanding of such
phenomena as thermal conductivity, heat capacity, electric conductivity . . . and the very
existence of transistors and thermistors.
Quantum mechanics is a complex subject, largely outside the scope of this text, yet a brief
mention of two of its most important concepts may aid the production-design engineer in the
study of the basic characteristics of materials. One of these is Planck's quantum hypothesis, later
extended by Einstein and others. The other is Pauli's exclusion principle.
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The quantum hypothesis postulates that the bound energy state of particles of very small
size cannot be represented by a continuous function but is discrete in nature. Thus, between any
two permissible energy states of a bound particle there exists a region of states that are forbidden.
Each of the electrons of any atom has a particular energy level, E1, E2 , E3 , etc. For an
electron to go from one energy state to a higher one, it must receive sufficient energy to jump
through the forbidden-energy regions. Thus if an electron at energy level E2 is to go to the
higher-energy level E3 , it must receive an energy E2 (Fig. 4.2).
For it to go to energy level E4 it must receive an energy of E2  E3 . If an electron
receives insufficient energy to jump a forbidden energy region, it will get rid of its extra energy
in the form of electromagnetic radiation and remain in its original energy state. By the same
token, if an electron at, say, energy level E1 receives energy greater than E1 but smaller than
E1  E2 , it will be able to go to E2 and the excess energy over E1 will be emitted as
electromagnetic radiation.
All matter has a spontaneous tendency to be in the lowest possible energy state.
Consequently, the electrons of any atom fill the lowest permissible energy levels and are only
excited to upper empty levels when they are given energy by means of interaction with
electromagnetic radiation, particle bombardment (by electrons, protons, etc.), or an electric field,
or by thermal excitation (collision with neighboring atoms brought about by an increased
amplitude of atomic vibration caused by an increase in temperature).
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Figure 4.2
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The iron-carbon diagram for carbon contents up to 5 percent.
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Thus, if an electron is dislodged from its initial energy level it can only go to a higher
unoccupied level or entirely out of the atom. On doing this, it leaves an empty state that will be
immediately occupied either by the original dweller or by any of the electrons at a higher energy;
in any case, the electron that drops down will release its excess energy in the form of
electromagnetic radiation. This in turn will leave its own original level vacant and there will be
more transitions until all the normally filled levels are filled again.
It may be recalled that the number of electrons in any atom is equal to the number of
protons in the nucleus. If for any reason an atom is stripped of some or all of its electrons, free
electrons in the vicinity of the ion will rapidly fall into the empty energy levels, emitting their
excess energy in the form of radiation.
The preceding discussion states that each electron in an atom is associated with a
particular energy state–but there can be only one electron at each particular energy level. This is
explained by Pauli’s exclusion principle, which states that no two bound particles in an
interacting system can exist at exactly the same energy state. Thus, when there are two electrons
in one of the electron “shells” of an atom (principal quantum numbers), that normally could be
considered to be at the same energy, their actual individual energy levels are different although
rather close to one another. By the same token, when there are 8 electrons in a “shell,” they have
eight separate energy levels. When two or more atoms are brought together, there is a further
shift and splitup of energy levels.
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Figure 4.3
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The maximum permissible number of electrons in the first “shell” (principal quantum
number) is 2, in the second 8, in the third 18, in the fourth 32, etc. Then for an isolated atom
there will be 2 individual levels at the first principal level, 8 at the second, and so on (Fig. 4.3). If
two atoms are brought together (Fig. 4.4), then the first principal level will have 4 energy states,
the second 16, and so forth. When many atoms are brought together, there will be many electrons
at any principal quantum level and the spacing between individual energy levels will be so small
that there will in effect be energy bands rather than individual levels. Note that there are 6.023 x
1023 atoms in one gram-atom, which is Avogadro's number. It must be understood that each kind
of atom has its own particular energy-level arrangement and that energy splits and band
formations only take place where there would be a coincidence of energy levels, such as is
illustrated in Fig. 4.4. But if there are two different atoms, A and B. and their energy levels do
not coincide, the energy-level arrangement of their combination will be a superposition rather
than a level shifting (Fig. 4.5).
Figure 4.4
Idealized fatigue curves for ferrous and nonferrous alloys. For ferrous
alloys an endurance limit, below which stress failure does not occur, is
reached near 106 - 107 cycles. For nonferrous alloys a fatigue limit is not
reached, even beyond 108 cycles.
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Figure 4.5
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Effect of surface quality on endurance limit and fatigue strength (Serope
Kalpakjian, Manufacturing Processes for Engineering Materials, Addison
Wesley, 1984).
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In the same way, if there is a large group of atoms of the same kind and one different
atom (as an impurity atom) is brought into the group, there will be a shift in the levels that
coincide and a superposition where there is no coincidence (Fig. 4.6). It is to be noted that this
type of superposition is the same as introducing permissible steps in the forbidden energy
regions. By means of these steps the electrons may jump to higher-energy levels without
requiring as much energy at any one time.
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Figure 4.6
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Variations in average mechanical properties of as-rolled 1-in. diameter
bars of plain carbon steels, as a function of carbon content.
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If the bound arrangement of a given solid is such that all the energy levels in a certain
band are filled, whereas the energy levels in the next band higher up are entirely empty, the
material is an insulator. For this material to conduct, the valence electrons would require
acceleration to gain some energy above the ground state—but in such a case there are no
immediately adjacent empty higher-energy levels, only a wide forbidden energy gap. To jump
that energy gap would require considerably more energy than is provided in the normal mode of
excitation, and therefore the material is an insulator––but it could conduct if a sufficient input of
energy were supplied.
If the valence electrons of a solid occupy a partially empty band, these electrons can be
accelerated with very little energy and the material is classed as a conductor.
When the valence electrons of a solid occupy a filled band but the forbidden energy gap is
small, of the order of kT (where k is Boltzmann's constant, 1.3810-9 J/K and T is absolute
temperature in Kelvins (K)) at ordinary temperatures, then it is not difficult for the valence
electrons to jump to the empty band. Such a material is known as an intrinsic semiconductor.
In the case of insulators and semiconductors, the top filled band is known as the valence
band and the higher adjacent empty band is known as the conduction band.
In conductors, the higher-energy electrons are already in the conduction band and can
move freely at the least excitation. On the other hand, insulators require considerable energy for
an electron in the valence band to go to the conduction band. Any insulator may be made to
conduct electricity if its electrons are sufficiently energized. The electrons that can move about
freely in the conduction band are viewed as “free electrons” that are not associated with any atom
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in particular. These electrons are considered principally responsible for the electrical and thermal
conductivity of matter.
Before entering into a detailed discussion of the physical properties of materials, it is
convenient to review another mechanism that also intervenes in the evaluation of these
properties. This is the oscillatory motion of atoms or molecules that are bound in a solid. In gases
and liquids the atoms are free to move about, to a greater or lesser extent, respectively, but in a
solid the atoms or molecules are restricted to oscillation about fixed points.
The atoms or molecules of a solid above absolute zero always vibrate about fixed centers.
The higher the temperature, the greater the amplitude of the oscillation, and this amplitude of
oscillation has a direct effect on the conductivity of solids. The oscillation stores energy and this
energy is directly related to the heat capacity of solid materials.
De Broglie’s relationship between moving particles and wave motion is not only
applicable to the theory of relativity and quantum physics but also to modern physics as a whole.
De Broglie conceived that a moving particle can be associated with a wave motion and that
propagation of a wave can be considered as a particle. This viewpoint can account for the
diffraction of particles such as electrons and neutrons––a phenomenon that was formerly
considered an exclusive property of wave motion. It also accounts for the particle-like collision
of photons.
4.2.2 Heat Capacity
Heat capacity is the amount of heat that is transferred in raising the temperature of a unit
mass of material by one degree. The heat capacity of a solid depends upon the amplitude of
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oscillation of the particles about their centers of equilibrium. The greater the temperature, the
greater the amplitude, and consequently the greater will be the heat capacity. It is measured in
terms of energy per unit mass. (Recall that the specific heat of a substance is the ratio of its heat
capacity to the heat capacity of water; it is a dimensionless quantity.) This variation is
represented as a continuous function in different ranges; however, it is actually a discrete
function, since the particles cannot vibrate in a continuous mode but in quantized ones. For the
majority of engineering applications, heat capacities may be considered to be numerically equal
to specific heats. We will find that heat capacity is very important to understanding the metal
casting and welding processes since metal in the molten state cools and solidifies. Additionally,
in machining and forming specific heats can be used to estimate the average temperature of the
part or in the case of a machining the chip and tool. We will also find that materials with small
heat capacities (like titanium) are generally difficult to machine.
Starting from a very low temperature the heat capacity increases proportionally to the
third power of the temperature and tapers off to a constant value of 6 Cv [about 6 cal/(mol°K)]
for any substance after passing a critical temperature called the Debye temperature,  (Fig. 4.7
and Table 4.1).
As the gram-molar values for different substances vary, their heat capacity per pound will
vary even though their heat capacities per gram-mole are the same.
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Figure 4.7
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Average properties of 1-in. commercial carbon-steel bars, as they vary
with carbon content and with treatment subsequent to final rolling.
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4.2.3 Thermal Conductivity
The thermal conductivity of a solid may be viewed from the standpoint of the free-electron
theory. As these electrons drift because of a difference of thermal potential, they may travel along
until they interact with an atom. This travel is denoted as the mean free path. When the atoms are
lined up with low amplitude of oscillation (at low temperatures), the electrons may travel a fairly
long distance without interference (a large mean free path); but as the temperature of the solid
increases so does the amplitude of oscillation and the electrons interact with the atoms more
often (a small mean free path). The larger the mean free path, the larger the thermal conductivity
of the material. Thus, at low temperatures the thermal conductivity of conductors is usually larger
than at higher temperatures (Fig. 4.8). The mean thermal conductivity is defined by
km 
t0
1
k dt

t0  t1 t1
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where k is thermal conductivity, Btu/h/ft2/unit temperature gradient °F/ft.
Figure 4.8
True proportional limit is reached by cold drawing, although the steel can
be more heavily loaded without taking a permanent set. Stress relief at 900oF will restore
and increase the proportional limit to a high figure.
In the case of a thermal insulator, the electrons have to be given considerable energy
before they can jump into the conduction band and act as conductors. Therefore, insulators gain
in conductivity as the temperature increases, despite the interference caused by the increased
oscillation of the atoms.
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Another way to look at thermal conductivity is on the basis of wave propagation. It has
been determined that the transport of heat through a body can be considered as the propagation of
waves. From De Broglie’s relationship these waves may be treated as particles and the whole
phenomenon can be studied as the scattering of these particles, which are called phonons. Using
this model of phonon scattering, it has been determined that the isotope distribution in a material
has a bearing on the scattering of the phonons, for the minority isotopes act as scattering centers
thus reducing the thermal conductivity of the material.
Thermal conductivity is a key property for many manufacturing processes. In
deformation processing thermal conductivity is used to theoretically calculate temperature rise.
In machining materials with poor thermal conductivity such as titanium are difficult to machine
since the heat is not dispersed throughout the workpiece. Peak temperatures therefore are close
to the tool tip and thermal residual stresses are possible.
4.2.4 Electrical Resistivity
The phenomenon of electrical conductivity is similar to that of thermal conductivity.
They are both related to the drift of free electrons. The electrical conductivity is often replaced by
its inverse, resistivity for practical engineering calculations. Thus the resistance R in ohms of a
conductor at a given temperature is calculated by
R
l
A
where r is the resistivity of conductor material,  · cm, l is the length of conductor in cm, A is the
cross-sectional area in cm2.
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Table 4.2 gives the resistivity of various metallic elements and semiconductors at room
temperature arranged in order of increasing resistivity. Note that semiconductors have high
resistivity in the unaltered state.
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The resistance of pure metals increases with temperature. It may be calculated at any
temperature below the melting point by means of the relationship
R  R11  1 t  t1 
where  is the temperature coefficient of resistance and t is the temperature. The subscript 1
refers to the reference-temperature values. Thus, if the resistance R1 and the temperature
coefficient 1 have been evaluated at temperature t1 the resistance R at temperature t can be
calculated (Table 4.3).
Electrical resistivity between the surfaces of two metal components produces the heat necessary
for resistance welding when an electrical current is passed through them. The most common
form of this, spot welding, is much used in the automotive industry to weld car bodies. This
process is frequently automated using robots and has enhanced line productivity significantly.
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4.2.5 Semiconductors
In the case of conductors, the electrons are already in the conduction band and can drift at
the least excitation. In contrast, the electrons of insulators have to receive considerable energy
before their electrons can jump from the valence band to the conduction band. When this
happens it is referred to as a breakdown of the insulator.
When some impurity atoms are included in some materials, this introduces intermediate
permissible steps in the forbidden band and then the valence electrons can jump out of the
valence band with much less excitation than in the pure insulator. Materials arranged in this
manner are known as extrinsic semiconductors
The motion of the positive hole that remains in the valence band contributes to the
conductivity of the material as well as the motion of the electrons that have reached the
conduction band. When the impurity atoms introduce vacant levels close to the valence band,
electrons can jump from the valence band to these levels, leaving behind their positive holes. The
free levels are called acceptor levels. Materials arranged in this way are called p-type
semiconductors for the positive hole responsible for the electrical conductivity (Fig. 4.9).
Figure 4.9
Three-dimensional representation of the structure of flake granite in gray
iron, made from a specimen from which the matrix was dissolved by
hydrochloric acid.
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The n-type semiconductors are those in which the impurity atoms introduce filled energy
levels close to the lower edge of the conduction band. In this case, the electrons from these levels
can be easily expelled into the conduction band. The interposed levels are called donor levels.
The n designation results from the negative charge introduced into the conduction band.
Impurities with loosely bonded electrons introduce donor levels in semiconductors; that
is, they can easily contribute negative charges to the empty conduction band of the parent
material, and thus produce n-type semiconductors. Common “impurities” used to produce n-type
semiconductors are arsenic, phosphorus, and antimony. The typical parent material for n -type
semiconductors is germanium. The p-type impurities are those that introduce acceptor levels in a
semiconductor—and permit the production of positive “holes” in the valence band. Examples of
these elements are gallium, boron, and iridium. Typical parent materials are silicon and
germanium.
The calculation of resistances or conductivities of semiconductors is outside the scope of
this book. It is suggested that interested students consult standard works concerning the physics
of electrical engineering.
4.2.6 Magnetic Properties of Materials
A moving electric charge produces a magnetic field that is concentric with its direction of
motion. If the charge moves in a circle, the magnetic field concentrates in the center of the circle
and produces a magnetic dipole (Fig. 4.10). A moving charge within an atom contributes to the
magnetic behavior of a material. The magnetic flux B induced in a material depends on how well
the tiny dipoles line up when an external magnetic field H is applied. The ratio of B to H is
known as the magnetic permeability, M of the material:
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M
Figure 4.10
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B
H
Pearlitic microstructures found in the matrix of pearlitic gray, malleable,
and ductile cast irons. Nital etch; 1000x. (Courtesy of John Hoke,
Pennsylvania State University.)
Solids exhibit three major types of magnetic behavior: diamagnetism, paramagnetism,
and ferromagnetism. Diamagnetism is observed in materials that have complete outer electron
rings, such as the elements in the eighth column of the periodic table. Such elements normally
have zero net magnetic moment. The presence of an external field induces an opposite weak
magnetism. The magnetic permeability of diamagnetic materials is less than unity.
Paramagnetic materials have permanent microscopic magnetic moments caused by the
spin and orbital motions of the electrons. Paramagnetism is found in all atoms with partially
filled inner shells. It is also produced from the spin of the free electrons that are present in
metals. The microscopic magnets readily line up when the material is placed in a magnetic field.
The permeability of paramagnetic substances is greater than unity.
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Paramagnetic and diamagnetic behavior are briefly mentioned only for the sake of
completeness, since the magnitude of the effects is so small when compared with its magnitude
for ferromagnetic materials. Ferromagnetism is the important magnetic property of an
engineering material. It stems from the spontaneous alignment of the small atomic magnets into
magnetic domains. The permeability of ferromagnetic material is much greater than unity. This
magnetic behavior is not obvious in soft magnetic materials, such as pure iron, because all their
magnetic domains are oriented at random. In permanent magnets there is a greater number of
domains with a particular orientation than there is without a domain. The magnetic domains can
be aligned in the presence of a magnetic field H, thus producing a magnetic flux B. The rotation
of the magnetic domains must overcome internal friction within the magnetic field, therefore B
and H are not linearly proportional. If H is cycled and B and H are plotted, a hysteresis curve
whose internal area is proportional to the energy consumed per cycle is obtained. Engineers
considering materials for use in electromagnetic circuits should select ferromagnetic materials
having a narrow hysteresis loop.
Most materials are nonmagnetic. Only iron, nickel, cobalt, ferric oxide, and alloys
containing chromium, nickel, manganese, or copper are magnetic to any extent. High-silicon iron
is the most permeable material and is widely used in magnetic circuits such as those in
transformers. While magnetic properties are not frequently used to process materials, they are
used in many other nondestructive evaluation techniques to inspect materials and their integrity
after processing.
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Structure of Metals
The atomic arrangement or structure of metals greatly influences their behavior and
properties. It can control hardness, ductility (ability to plastically deform prior to fracture),
strength, and other properties. These properties can be very important in selecting and
controlling manufacturing processes for efficiency and quality.
4.3.1 Crystal Structure
When metals solidify they arrange themselves into orderly configurations known as
crystals. There are 14 crystalline structures or lattices that are possible. However, commercially
useful metals and alloys fall into only three types of lattices: body-centered cubic, face-centered
cubic, and hexagonal closed-packed. Figure 4.11 shows these lattice types by illustrating its unit
cell or smallest building block of the lattice, which is repeated throughout. The atomic spacing
on the unit cell varies by material but is on the order of 10-8 in.
You can think of this packing
structure as the stacking of rigid balls into the appropriate pattern.
Figure 4.11
Microstructure of ductile iron showing the spheroidal graphite in a
pearlitic matrix. Nital etch; 230x. (Courtesy of John Hoke, Pennsylvania
State University.)
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In the case of the body-centered cubic structure atoms are placed in each corner and in the
center of the unit cell. Each atom has eight nearest neighbors in this case and only about 68% of
the volume of the cube, or unit cell, is occupied. Metals such as iron, chromium, titanium and
vanadium have a body-centered cubic (bcc) structure at room temperature. It is possible that a
metal can change packing structure depending on the temperature of pressure applied. Such
materials are terms allotropic (or polymorphic). Iron is a good example of an allotropic material
and transforms to a face-centered cubic packing structure above 1674F and transforms again
back to body-centered cubic above 2541F.
In a face-centered cubic structure (fcc) atoms reside at the corners and at the center of
each face (instead of the center of the entire cell). Thus each atom has twelve nearest neighbors.
The neighbors include six within the plane and three each from the layers above and below. This
packing configuration occupies 74% of the volume of the unit cell. Some typical face-centered
cubic metals include aluminum, copper, nickel and gold.
As shown in Figure 4.11 and Table 4.4 hexagonal close-packed (hcp) materials also
have 12 nearest neighbors while occupying 74% of its unit cell. Metals such as magnesium and
zinc have the hexagonal close-packed structure.
Table 4.4
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Crystal structure is important to plastic deformation-based processes since it can limit slip
and ductility. For example, hexagonal close packed materials such as magnesium and titanium
have limited ductility. This can affect its ability to bend without fracture when used in sheet
form.
4.3.2 Imperfections and Deformation
The actual strength of metals is considerably lower than predicted theoretically. Theoretical
predictions consider the material to be “perfect” while in actuality they are imperfect. Were this
not the case, we would most likely use a very different set of engineering materials since the
difference is a factor of one hundred. These imperfections or defects in crystal structure include:
1) point defects, 2) line defects, and 3) planar defects.
Illustrated in Figure 4.12 point defects include vacancies where an atom is missing. Interstitial
atoms where an extra atom is in the lattice, but not at expected sites, also can cause difference
behavior of the material. Similarly an impurity (atom of a different type) can also be found at an
unexpected lattice site.
Figure 4.12
Microstructure of malleable iron showing the typical carbon with (left) a
ferritic matrix and (right) a pearlitic matrix. (Courtesy of John Hoke,
Pennsylvania State University.)
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It is also possible that bulk (or volume) imperfections. A void or inclusion (such as
oxides and sulfides) can alter a material’s behavior. For example, in machining a sulfide
inclusion can greatly alter the ease with which steel (MnS inclusion) or copper (Cu2S) can be
machined by changing the flow pattern of the chip on the tool. This is described in detain in
Chapter 17.
Dislocations, or line defects are localized disruptions in the crystal lattice. These defects are the
most significant in explaining the large difference between the theoretical and actual strength of
metals. There are two types or geometries for dislocations. The edge dislocation (see Figure
4.13 a) is easily identified by generating a circuit on the plane presented. By moving say, four
atomic spaces in all directions the circuit fails to close as we would expect. We are one atomic
distance away from closure in the plane in which we started. Therefore a defect must be present.
Closer inspection of the crystal lattice reveals an extra half plane of atoms which causes this. An
edge dislocation is pictured in Figure 4.13(b). If we apply the same logic to this lattice (e.g.
moving four atomic distances in four orthogonal directions we again are unable to close the
circuit and wind up one atomic space below where we started. This subtle difference
differentiates these two types of dislocations. Dislocation aid plastic deformation by their ability
to move through the crystal lattice. This ability of atoms to slip decreases strength of the material
and will be described in more detail in Chapter 5.
Theoretical calculations reveal a yield stress 50 to 100 times greater than what we find in
practice. The reason for this discrepancy lies in the presence of defects that allow for movement
at considerably lower stresses. Without this we would likely use far less metal since the
equipment required would be so large.
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Figure 4.13
03/06/16
Tensile strength and hardness as a function of section thickness for various
grades of cast iron.
4.3.3 Grains and Grain Boundaries
Previously in this section we discussed unit cells as the building blocks of crystalline
materials. With the exception of highly specialized components, most are composed of many
crystals, each with a different orientation. Each of these crystals is referred to a grain.
Grains form as liquid metal cools and begins to solidify. At various sites crystals begin to
solidify independently of each other and atoms attach themselves in the patterns (or packing
structures) discussed previously in this section and illustrated in Figure 4.14 . Eventually these
randomly oriented crystals grow until they interfere with other crystals. Each crystal then borders
other crystals with these borders known as grain boundaries.
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Figure 4.14
03/06/16
Tensile strength properties of cast irons.
The number and size of the grains developed depends on the rate at which new crystal
sites are nuleated. A low nucleation rate there will be comparatively fewer grains but they will
be larger in size. The size or grains has a large impact on mechanical properties with larger
grains having lower hardness and strength. However, larger grained materials will also have
greater ductility, or ability to deform prior to failure. All of these properties are important not
only in the functionality of the component produced but in how efficiently they can be processed.
During solidification we can control grain size by adjusting the cooling rate. As you will see in
Chapter __ (note- must wait to see where the material falls) on casting, the mold material (e.g.
material against which the metal solidifies) and its thermal properties will dictate grain size.
It is important to note that the random orientation of grains produces a material that is
isotropic, having the same properties in all directions. However, processing of the material
mechanically can orient the grains. This preferred orientation can cause directionalized
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properties in the material. A good example of this comes from examining sheet metal. The sheet
has been placed between large rollers and thinned, causing the grains to elongate in the direction
of the deformation. Upon later bending (such as for a car body or outer panel of a kitchen
appliance) the properties will not be the same in all directions with a subsequent difference in
response. This problem is becoming acute for connectors used in computers and other
instrumentation. The downsizing of chips and other components necessitates the downsizing of
connectors. As we continue to require smaller connectors the bend may occur in a small number
of similarly oriented grains and directional differences will be greatly magnified in importance.
4.4 Mechanical Properties of Materials
Once the important physical properties of a material have been established, mechanical
properties such as yield strength and hardness must be considered. Mechanical properties are
structure- sensitive in the sense that they depend upon the type of crystal structure and its
bonding forces, and especially upon the nature and behavior of the imperfections that exist within
the crystal itself or at the grain boundaries. Mechanical properties are important in processes that
employ plastic deformation such as forming of bulk or sheet, as well as machining. Modulus of
elasticity is also important in assembly.
An important characteristic that distinguishes metals from other materials is their ductility
and ability to be deformed plastically without loss in strength. In design, 5 to 15 percent
elongation provides the capacity to withstand sudden dynamic overloads. In order to
accommodate such loads without failure, materials need dynamic toughness, high moduli of
elasticity, and the ability to dissipate energy by substantial plastic deformation prior to fracture.
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To predict the behavior of a material under load, engineers require reliable data on the
mechanical properties of materials. Handbook data is available for the average properties of
common alloys at 68°F. In design, the most frequently needed data are tensile yield strength,
hardness, modulus of elasticity, and yield strengths at temperatures other than 68°F. Designers
less frequently use resistance to creep, notch sensitivity, impact strength, and fatigue strength.
Suppliers' catalogs frequently give more recent or complete data.
Production-engineering data that is seldom found in handbooks include
strength-to-weight ratios, cost per unit volume, and resistance to specific service environments.
A brief review of the major mechanical properties and their significance to design is
included to ensure that the reader is familiar with the important aspects of each test.
4.4.1 Tensile Properties of Materials
When a material is subjected to a tensile or compressive load of sufficient magnitude, it
will deform, at first elastically and then plastically. The deformation is elastic if after the load is
removed the material returns to its original shape and dimensions; if it does not, the material has
undergone plastic in addition to elastic deformation. The engineering stress-strain diagram
presents the elastic data for a material, whereas the natural (or true) stress-strain diagram can
present both elastic and plastic properties in a form that is useful to the designer and the engineer.
Engineering Stress-Strain Relationships
In the elastic range, deformation is proportional to the load that causes it. The proportionality is
stated by Hooke's law in terms of the stress S and strain e:
S  Ee
(4.1)
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where E is Young's modulus, the constant of proportionality between stress and strain, lb/in.2, S
is the stress = P/A = load/initial cross-sectional area, lb/in.2, e is the engineering strain = l/l0 =
change in length/original length, in./in.
If, in the process of pulling a tensile specimen to failure, the stress is plotted as a function of the
strain at selected strains, the engineering stress-strain curve results (Fig. 4.15). Note that the
stress is plotted as a function of the strain, contrary to the usual procedure of plotting the
dependent variable as a function of the independent variable.
Figure 4.15
Stress-strain relationships of the principal cast irons in tension.
The straight part of the stress-strain curve is the proportional range described by Hooke's law.
The upper limit L of this range is known as the proportional limit. In the case of annealed
low-carbon steel there follows a region, the yield point, where the strain increases without any
significant increase in stress. As indicated in the diagram, there can be an upper yield point, UY,
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and a lower yield point, LY. The maximum stress to which a material may be subjected is labeled
U and the breaking point is denoted by B.
When a material is stressed beyond the elastic limit a permanent deformation results. However,
this permanent deformation is associated with an elastic one. Notice that if the material of Fig.
4.15 is stressed to point P. upon the removal of the load so that the stress returns to zero, the
plastic (permanent) strain is obtained by following downward from point P along a line parallel
to the proportional line. Here we have at point P the total strain t, composed of an elastic
component e and a plastic one p.
The area under the curve in Fig. 4.15, up to the proportional limit, represents the potential energy
per unit volume (resilience) stored in an elastically deformed body; on the other hand, the total
area under the curve up to point B represents the total energy per unit volume (modulus of
toughness) required to break the specimen.
The engineering properties of commercial plastics vary considerably. For any given plastic, the
stress-strain curve depends upon both the temperature and the rate of strain. Slow straining and
higher temperatures result in larger ultimate elongations and lower moduli (slopes). Figure 4.16
illustrates typical load-elongation curves for three classes of plastics. Those plastics characterized
by curve C have a high initial modulus and a small area under the stress-strain curve (they are
brittle). These plastics characteristically fail by catastrophic crack propagation at strains of about
2 percent.
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Figure 4.16
03/06/16
Tensile modulus of elasticity (million lb/in2) (secant modulus of 25
percent of ultimate strength).
Those plastics following curve B are usually referred to as engineering thermoplastics. These
plastics have good tensile strength and hardness and will deform or draw beyond the yield point,
which is evidence of much molecular orientation prior to failure. Thus, these plastics have impact
resistance or toughness as well as good strength. They will withstand shock without brittle
failure.
Curve A illustrates those plastics that are both tough and flexible. In these plastics, ductile
deformation results from converting a material of low crystallinity to one of high crystallinity.
These plastics have low tensile strength and moduli. The reader should understand that polymers
are much more sensitive to temperature than either metals or ceramics in connection with their
response to an applied stress. Figure 4.17 illustrates the relationship between temperature and
elastic modulus of a typical thermoplastic material.
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Figure 4.17
03/06/16
Yield strength, 0.2 percent offset (1000 lb/in2)
Natural (True) Stress-Strain Relationships
In many engineering designs, only the elastic behavior of a material is significant, so the
engineering stress-strain curve was commonly used to depict the behavior of a material up to its
yield point. The yield strength of a material is calculated by dividing the load at the yield point by
the original cross-sectional area of the test specimen. However, when dealing with a material that
is stressed beyond the elastic range, as in plasticity or metal forming, it is apparent that we should
find a way to define the relationships in terms of the changing cross-sectional area. This is a
considerably more accurate way to obtain property information. Thus, the natural or true stress,
 , is defined as the load at any instant divided by the cross-sectional area at that instant. Thus,

Pi
Ai
(4.2)
Similarly we may define the true strain as the change in linear dimension divided by the
instantaneous value of the length. Thus:
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Chapter 4
 
li
t0
03/06/16
dl
l
 ln i
l
l0
(4.3)
Typical natural stress-strain curves for steel and brass are given in Fig. 4.18.
The plastic region of the true stress-strain diagram may be expressed by
   o tm   0  e   p m
(4.4)
where a is the true stress, 0 is the work-hardening constant (a constant of the material), t is the
total strain = elastic strain e + plastic strain p, m is a constant of the material.
Figure 4.18
Endurance limit (1000 lb/in2)
Equation (4.4) is known as the strain-hardening equation. If both Eqs. (4.1) and (4.4) are
expressed in logarithmic form, the result is:
ln S  ln E  ln  e
(4.5)
ln   m ln  t  ln  0  e   p   ln  0
(4.6)
These two equations plotted on log-log paper yield two straight lines with a discontinuity about
the region of the yield point (Fig. 4.18). It will be noted that Eq. (4.5), for the elastic zone, is the
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equation of a straight line with a slope of unity (45) and an intercept of ln E. Equation (4.6) is
also a straight line but with intercept ln 0 and slope m.
Example 4.1
An AISI 1020 steel is machined into a tensile specimen. The tensile test is run until a total strain
of 10-2 in/in is achieved. Determine the instantaneous length and normal stress.
Solution:
The instantaneous length is determined from the definition of the natural (true) strain as follows:
li

l
ll
dl
dl
 
 ln li  10  2
l 2.00 l
2.00
l i  2.020"
The normal stress can be obtained using the flow curve information in Figure 4.14. From the
figure 0=115,000 psi and m=0.22. The stress can be computed as follows:
   0  m  (115000)(0.01) 0.22  41,750 psi
Correlation of Engineering and Natural Stresses and Strains
Hooke’s law applies for the elastic range of the true stress-strain diagram as well. The
relationship is expressed in this case by
S  Ee
(4.7)
S  engineering stress  P A0  loading force / original cross - sectional area
(4.8)
where E is Young’s modulus, and
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e  engineerin g strain  li  l0  l0  change of length/ori ginal length
(4.9)
It is convenient to derive a relationship between the true stress-strain curve and the engineering
stress-strain curve. For true stress, there is the relationship

P
Ai
[see Eq. (4.4)]
As the volume of the material remains constant during the loading Ali i  A0l0 ; thus
l0
li
(4.10)
P li
A0 l0
(4.11)
li
l0
(4.12)
Ai  A0
Consequently,

Substituting Eq. (4.6) into Eq. (4.9) results in
S
which is the relationship between true stress and engineering stress.
On the other hand, true strain is defined as
 
li
l0
A 
dl
l
l
 ln l li0  ln i  ln  0 
l
l0
 Ai 
(4.13)
Recalling from Eq. (4.7) that the engineering strain is
li  l0 li
 1
l0
l0
(4.14)
li
 e 1
l0
(4.15)
  ln e  1
(4.16)
e
there results
Substituting Eq. (4.15) into Eq. (4.13) gives
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the relationship between true strain and the engineering strain.
It is to be noted that the strain corresponding to the elastic limit of most engineering materials is
very small, usually smaller than 0.005; consequently,
li
 1, and, ln e  1  e
l0
(4.17)

S li l0  S


 ln e  1 e
(4.18)
Therefore,
E
It is worthwhile for the practical engineer to be conscious of the differences between the
basic stress-strain diagrams for different materials, and also of how the stress-strain diagram for
one material varies according to its mechanical or thermal treatment. Also, we emphasize again
that the strain at the elastic limit for most engineering materials is very small. Many textbook
presentations represent the elastic part of the stress-strain curve tilted completely out of
proportion for ease of illustration.
While the true stress-true strain representation is clearly the more accurate it is not
generally used in engineering design since obtaining real-time data on length and area is quite
difficult and most engineering designs consider the yield (where the difference is modest) to be
failure. The flow curve representation of deformation is used for complex models in the metal
forming area since the deformation of the workpiece is considerable for flow into a desired
shape.
Example 4.2
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Consider a tensile test with the following length engineering strain measurements: 0.01, 0.03,
0.05, .100, .150, .200, .250, .300
Calculate the natural (true) strain and determine the error in the engineering strain.
Solution:
Consider the engineering strain of 0.001. The natural strain may be calculated as:
  ln( e  1)  ln( 0.001  1)  0.00995
And the percent error determined to be:
%error 
e

x100 
0.01  0.00995
x100  0.5%
0.00995
Performing this calculation for all strains:
e
0.01
0.03
0.05
0.10
0.15
0.20
0.25
0.30

0.00995
0.0296
0.0488
0.095
0.140
0.182
0.223
0.262
% error
0.5%
1.4%
4.1%
5.26%
7.1%
9.9%
12.1%
14.5%
Note that the error is small at low strains but increases rapidly thereafter.
4.4.2 Combined Stresses
Stresses in solids can be described in several ways. The simplest method, using principal stresses,
is the most practical procedure for the manufacturing engineer. Principal stresses are a set of
three direct stresses, mutually at right angles, acting on planes of zero shear stress. The
directions along which principal stresses act are principal axes, and the planes normal to the
principal directions are principal planes.
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The technique for finding principal stresses and principal directions is to sum components
of force on an arbitrary free body (of the solid under stress) in three noncoplanar directions, to set
the shear stresses to zero on a plane whose direction is to be determined, and to solve for the
three unknowns: the magnitude of the principal stress and two of the direction cosines of the
principal plane. The process is repeated in two dimensions to obtain a second principal plane.
The third principal plane is at right angles to each of the two planes so determined. Usually, for
simplicity, the arbitrary free body is a tetrahedron containing the given stresses.
In practice, the principal planes are often apparent. Not only are the principal planes free from
shear stress, but the principal stresses include both the maximum and the minimum normal
stress. Figure 4.19 provides examples in which the direction of principal stress is obvious. A ram
pressing on metal in a closed die would have the direction of ram motion as a principal axis. The
reader should note, however, that if very high pressures are involved, so that the metal tends to
flow laterally beneath the ram face, the ram axis would not necessarily be a principal axis. A
cylinder pressurized by a fluid would have principal axes normal to the cylinder wall, parallel to
the cylinder axis, and circumferentially. The reader should understand that the directions of the
principal axes can change from point to point in a metal that is not under uniform stress. Note in
Figure 4.19 that the axis of wire drawing is a principal axis In three-point bending, a principal
axis (in the absence of friction) at the plane of the sheet is normal to the sheet. This is not true at
the center of the sheet, since there is a parabolic distribution of horizontal shear, which is a
maximum at the center and zero at the edges.
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Figure 4.19
03/06/16
Typical Brinell hardness numbers.
It can be shown that the maximum shear stress in a body under stress is equal in
magnitude to half the algebraic difference of the maximum and minimum shear stresses, and lies
in planes at 45° angles to these principal shear stresses. Figure 4.20 shows the location of planes
of maximum shear stress from the position of planes of maximum and minimum principal
stresses.
Figure 4.20
Relative damping capacities of several engineering materials.
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The average normal stress S is of importance in metal working under pressure. It is defined as the
algebraic average of the three principal stresses. See Figure 4.21. Thus
S
Figure 4.21
S1  S2  S3
3
Interaction of tolerance, component size, and various manufacturing
process.
Compression here is taken as positive and tension as negative. For examples, let the three
principal stresses be 16,000 psi compression, 6000 psi tension and zero. The maximum shear
stress is (16,000 + 6000)/2 = 11,000 psi, and the average normal stress is (16,0006000 + 0)/3 =
3333 psi.
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The average normal stress S is related to the ductility or brittleness of a material. It does not
indicate whether plastic flow will take place. Two commonly used criteria for determining the
beginning of yielding or plastic flow are:
1. Distortion energy theory, sometimes referred to as octahedral shear stress theory or the
Huber-von Mises-Hencky theory (or simply von-Mises theory).
2. Maximum shearing stress, or Tresca, theory.
Both of these criteria are intended for use only with materials that are isotropic (having the same
physical properties in all directions) and homogeneous (having the same physical properties at
every point).
The distortion energy theory states that plastic flow occurs in a material when a quantity J equals
the value of J at onset of plastic flow in a uniaxial tensile test. Here we have the relationship:
S1  S2 2  S2  S3 2  S2  S1 2  2S ys 2
where S1, S2, and S3 are the principal normal stresses (see Fig. 4.22).
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Figure 4.22
03/06/16
Surface finish and tolerances obtainable from various processes. These are
compared to requirements for some sample components.
The maximum shear stress theory states that yielding occurs in a specimen when the
uniaxial tensile yield strength of the material equals the largest principal stress minus the smallest
principal stress. Thus
Smax  Smin  Sys
Failure is predicted by this theory if S1  S2  S f (fracture stress).
The question arises of which criterion of plastic flow is the more exact, the distortion
energy criterion or the maximum shear stress criterion. It has been found that one criterion may
be better for one material while another criterion is better for a different material.
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It is thus apparent that for some materials a simple tension test suffices to determine the
onset of plastic flow; such materials possess a known criterion. As a rule of thumb, the distortion
energy criterion is suitable for heat-treated (normalized or hardened) ferrous alloys, the
maximum shear stress criterion for annealed ferrous alloys, and neither for highly hardened
ferrous alloys and for magnesium alloys. In all cases, one can assess the onset of plastic flow
from scale experiments.
4.4.3 Hardness
Hardness is an engineering property that is related to the wear resistance of a material, its
ability to abrade or indent another material, or its resistance to permanent or plastic deformation.
The selection of the appropriate hardness test is dependent upon the relative hardness of the
material being tested and the amount of damage that can be tolerated on the surface of the test
specimen. Table 4.5 provides information relative to the most used hardness standards, each
having application for certain types of materials. Hardness can be measured by three types of
tests: (1) indentation—Brinell, Rockwell, Knoop, Durometer; (2) rebound or dynamic—
Scleroscope; (3) scratch—Moh. These standards together with the materials to which they apply
are as follows:
1. Brinell—ferrous and nonferrous metals, carbon and graphite
2. Rockwell B—nonferrous metals or sheet metals
3. Rockwell C—ferrous metals
4. Rockwell M—thermoplastic and thermosetting polymers
5. Rockwell R—thermoplastics and thermosetting polymers
6. Knoop—hard materials produced in thin sections or small parts
7. Vickers diamond pyramid hardness—all metals
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8. Durometer—rubber and rubber-like materials
9. Scleroscope—primarily used for ferrous alloys
10. Moh—minerals
Table 4.5
We compare the characteristics of these various hardness tests in Fig. 4.23.
The Brinell hardness test is applicable to most metals and their alloys. This test provides a
number related to the area of the permanent impression made by a ball indentor, usually 10 mm
in diameter, pressed into the surface of the material under a specified load. The larger the Brinell
number, the harder the material. The Brinell hardness number (BHN) is computed as follows:
BHN =
P
D 2D 
D2  d 2

where P is the applied load in kg, D is the diameter of ball in mm, d is the diameter of impression
the ball makes in the material measured in mm and BHN is the Brinell hardness in kg/mm2.
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Rockwell hardness is also an indentation test used on both metals and plastics. The
Rockwell method makes a smaller indentation compared with the Brinell test, is more applicable
to thin materials and is more rapid. The Rockwell number is derived from the net increase in
depth of an impression of a standard indentor as the load is increased from a fixed minor load to
a major load and then returned to the minor load. The Rockwell C test (using a brale as indentor
and a major load of 150 kg) is used primarily for ferrous alloys, whereas the Rockwell B
procedure (using as indentor a 1/16 in. ball and a major load of 100 kg) is used for softer or
thinner alloys for which a minimum indentation is preferred. Rockwell M numbers are applied to
hard plastics.
The Knoop and Vickers hardness tests measure the microhardness of small areas of a
specimen. They are especially suited for measuring the hardness of very small parts, thin
sections, and individual grains of a material, using a microscope equipped with a measuring
eyepiece. Both tests impose a known load on a small region of the surface of a material for a
specified time. In the case of the Knoop test, the indentor is a diamond with a length-to-width
ratio of about 3:1, whereas the Vickers indentor is a square diamond pyramid with an apical
angle of 136°. Both values of hardness are calculated by dividing the applied load by the
projected area of the indentation. For the Vickers method, V = P/0.5393d2, where V is the
Vickers hardness number, P is the imposed load (1 to 120 kg), and d the diagonal of indentation
in mm.
The Shore Scleroscope is a rebound device that drops a ball of standard mass and
dimensions through a given distance. The height of the rebound is measured. As the hardness of
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the test surface increases, the rebound height increases because less energy is lost in plastic
deformation of the test surface.
The Durometer hardness test is used in conjunction with elastomers (rubber and
rubberlike materials). Unlike other hardness tests, which measure plastic deformation, this test
measures elastic deformation. Here an indentor of hardened steel is extended into the material
being tested. A hardness value of 100 represents zero extension of the indentor; at zero reading,
the indentor extends 0.10000..000
003 in. beyond the presser foot that surrounds the area being
measured.
Moh hardness values are used principally in the designation of hardness of minerals. The
Moh scale is so arranged that each mineral will scratch the mineral of the next lower number.
Ten selected minerals have been used in the development of this scale. The scale, along with the
values for these ten minerals are: talc, 1; rock salt or gypsum, 2; calcite, 3; fluorite, 4; apatite, 5;
feldspar, 6; quartz, 7; topaz, 8; corundum, 9; diamond, 10. According to the Moh hardness scale,
a human fingernail has a hardness of 2, annealed copper 3, and martensite 7. The Moh scale has
too few values to be of practical use in the metal-working field, since four values cover the range
of the softest to the hardest metals.
In view of the wide variation in the characteristics of engineering materials, one hardness
test for all materials is not practical, but conversion from one hardness scale to another can be
done in some cases. The Brinell and Rockwell B and S scales can be converted from one to the
other. To approximate equivalent hardness numbers, the alignment chart shown in Table 4.5 can
be used. This chart does not included a Durometer scale, since correlation between Durometer
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and Brinell values is inconsistent. The Durometer test measures the elastic properties of a
material, whereas all other indentation hardness tests measure the plastic properties of a material.
4.4.4 Impact Properties
In some designs, dynamic forces are likely to cause failure. For example an alloy may be
hard and have high compressive strength and yet be unable to withstand a sharp blow. In
particular, low-carbon steels are susceptible to brittle failure at certain temperatures (Fig. 4.24).
Experience has demonstrated that the impact test is sensitive to the brittle behavior of such
alloys. Most impact tests use a calibrated hammer to strike a notched or unnotched test specimen.
In the former, the test result is strongly dependent on the base of the notch, where there is a large
concentration of biaxial stresses that produce a fracture with little plastic flow. The impact test is
particularly sensitive to internal stress producers such as inclusions, flake graphite, second
phases, and internal cracks.
The results from an impact test are not easily expressed in terms of design requirements
because it is not possible to determine the biaxial stress conditions at the notch. There also seems
to be no general agreement on the interpretation or significance of the result. Nonetheless the
impact test has proved especially useful in defining the temperature at which steel changes from
brittle to ductile behavior. Low-carbon steels are particularly susceptible to brittle failure in a
cold environment such as the North Atlantic. There were cases of Liberty ships of World War II
vintage splitting in two as a result of brittle behavior when traveling in heavy seas during the
winter.
In a particular design having a notch or any abrupt change in cross section, the maximum
stress occurs at this location and may exceed the stress computed by typical formulas based upon
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simplified assumptions in connection with stress distribution. The ratio of this maximum stress
to the nominal stress is known as a stress concentration factor, usually denoted by K. Stress
concentration factors may be determined experimentally or by calculations based on the theory of
elasticity. Figure 4.24 illustrates stress concentration factors for fillets of various radius divided
by the thickness of castings subjected to torsion, tension, and bending stresses.
Impact properties are an important consideration in developing tooling for many
applications. Processes that impart high impact loads may limit the range of appropriate tool
materials since chipping or fracture may occur. In stamping a punch that that removes material
by driving through the sheet, sometimes thousands of times per minute, sees high impact loads
and chipping may occur if a tool material is used that cannot absorb sufficient energy. Cutting
tools also can see impacts where the tool is periodically engaged and then disengaged in the
cutting due to the geometry of the part being cut. In both cases care must be taken in selecting
the right material and material grade.
4.4.5 Fatigue Properties and Endurance Limit
Although yield strength is a suitable criterion for designing components that are to be
subjected to static loads, for cyclic loading the behavior of a material must be evaluated under
dynamic conditions. The fatigue strength or endurance limit of a material should be used for the
design of parts subjected to repeated alternating stresses over an extended period of time. As
would be expected, the strength of a material under cyclic loading is considerably less than it
would be under a static load (Fig. 4.25). The plot of stress as a function of the number of cycles
to failure is commonly called an S-N curve. It is interesting to note that for specimens of SAE
1047 steel there is a stress called the endurance or fatigue limit below which the material has an
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infinite life (>108 cycles), i.e., the steel would not fail regardless of exposure time (Fig. 4.26). In
contrast, the 2014-T6 aluminum alloy has no limiting stress value.
Fatigue data are inherently more variable than tensile test data. In part the scatter is
caused by variation in surface finish and environment (Fig. 4.28). Polished specimens of the
same material give significantly better life than machined or scaly surfaces. Since most fatigue
failures initiate at surface notches, fatigue behavior and notch sensitivity are closely related. Thus
mechanical or other treatments that improve the integrity of the surface, or add residual
compressive stresses to it, improve the endurance limit of the specimen.
Overstressing above the fatigue limit for cycles fewer than necessary to produce failure at
that stress reduces the fatigue limit. Also, understressing below the fatigue limit may increase the
fatigue limit. Thus, cold working and shot peening usually improve fatigue properties.
Several standard types of fatigue-testing machines are commercially available. The results
of extensive fatigue-life testing programs are now available in the form of S-N curves that are
invaluable for comparing the performance of a material that is expected to be subjected to
dynamic loads.
While of critical importance in the service life of a component, tooling can also fatigue
and fracture from cyclic mechanical and thermal loading. A good example is in the deployment
of carbide or ceramic inserts for the milling process. A rotating cutter ensures that all inserts cut
for a small portion of the rotation. Thus the tool heats up while cutting and cools when out of cut
and rotating at high speeds. Dimensional changes in the tool from this thermal cycling can cause
the tool to fail via fatigue.
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4.4.6 Creep and Stress Rupture
As metals are exposed to temperatures within 40 percent of their absolute melting point,
they begin to elongate continuously at low constant load (stresses beyond the proportional limit).
A typical creep curve is a plot of the elongation against time of a wire subjected to a tensile load
at a given temperature (Fig. 4.29). Creep is explained in terms of the interplay between
work-hardening and softening from recovery processes such as dislocation climb, thermally
activated cross slip, and vacancy diffusion. During primary creep the rate of work-hardening
decreases because the recovery processes are slow, but during secondary creep both rates are
equal. In the third stage of creep, grain-boundary cracks or necking may occur that reduce the net
cross-sectional area of the test specimen. Creep is sensitive to both the test temperature and the
applied load. Increases in temperature speed up recovery processes and an increased load raises
the whole curve.
The region of constant strain rate or secondary creep (stage 2—steady state in Fig. 4.29)
is usually used to estimate the probable deformation throughout the life of the component. The
working stress is then chosen so that the total predicted deformation is within tolerance.
In the stress rupture test, the specimen is held under an applied load at a given
temperature until it fails. A series of curves are plotted that can be helpful to the designer who
must consider high-temperature applications.
4.5 Comparison of the Properties of Materials
The materials commonly used in manufacturing can be divided into four groups for the
purpose of contrasting their properties: ferrous, nonferrous, thermosetting, and thermoplastic. In
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some cases these four groups are not particularly appropriate, since, for example, dielectric
strength is not applicable to metals. On the other hand, polymers have such low yield strengths
that they fare poorly when compared with even the weakest metal on the basis of strength.
The bar charts in Fig. 4.30 compare selected physical properties of the four classes of
materials, including dielectric strength, resistivity, coefficient of thermal expansion, thermal
conductivity, and specific weight. It can be readily seen that mica and glass have up to four times
the breakdown strength of polymers or rubber. Some thermoplastics exceed all other materials in
electrical insulation, with most other materials fairly close to second place. The coefficient of
thermal expansion of polymers is an order of magnitude greater than that of metals, whereas the
thermal conductivity of metals far exceeds that of all plastics. The specific weight of ferrous
alloys is four to five times that of polymers and three times that of aluminum alloys.
The same groups of materials were compared with respect to their mechanical properties,
including ultimate strength, yield strength, modulus of elasticity, hardness, and useful
temperature range (Fig. 4.31). The ultimate tensile strength of metals far exceeds that of
polymers—by a factor of 25 for unreinforced materials and a factor of 8 for the woven
glass-reinforced resins. In the case of the modulus of elasticity, the best thermosets are below the
lowest nonferrous materials with a maximum of 5106 lb/in.2 (Fig. 4.32). The ferrous materials
range from 12106 for class 25 gray iron to 30106 for most steels. Tungsten carbides are off the
graph with values up to 90 to 95106 lb/in.2 Tungsten carbide, therefore, despite its cost and
weight, is useful for long, cantilever-beam, boring-tool holders because of its low deflection
under load. In the comparison of yield strengths, metals are far superior to polymers. Nonferrous
materials range from a few hundred to 80,000 lb/in.2 for aluminum and 175,000 lb/in.2 for certain
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copper- and nickel-based alloys. Ferrous alloys range from 20,000 lb/in.2 for certain gray irons to
280,000 lb/in.2 or more for particular alloy steels.
The usable range of temperature for steel ranges from -460°F to almost 2000°F for
specific stainless steels. Aluminum alloys can withstand temperatures from 300 to 500°F, and
some titanium-reinforced polymers are useful up to 400 to 900°F, but the vast majority are good
only to 200°F. Hardness is the most difficult property to use for making valid comparisons,
because the deformation of plastics and elastomers under an indentor is different from that of
metals. As a group, polymers are far softer than metals. Ferrous and nickel-base alloys range
from 100 to 600 Bhn, which is a tremendous range of values.
4.6 Relative Cost of Materials Engineering
The design engineer is responsible for the initial specification of a material, yet in many
cases he spends little time checking alternatives. Many designers feel that their obligation ends
with the functional design, so they tend to minimize the importance of material selection. The
reasons are many, but two are likely to be (1) lack of proper education in their engineering
courses and (2) inadequate time because of the need to meet a deadline.
In over 90 percent of all designs a material is selected primarily on the basis of yield
strength and ability to fill space at the lowest cost. In some cases, other criteria, depending
primarily on physical properties such as electrical conductivity or chemical properties such as
corrosion resistance, are dictated by the end-use of the design and form the basis for the material
specification.
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It is the designer's responsibility to match the functional and esthetic requirements of his
design with the behavior of a particular material so that the total cost after manufacture is
minimized. In a large organization, this undertaking is a team effort in which design engineers,
production engineers, and materials specialists all play an important role. In a small company, the
designer may handle the entire assignment.
The costs of engineering materials are in a constant state of flux. Three components may
be recognized: first, the general price changes that follow the ebb and flow of the national
economy; second, the supply-and-demand effect on the price of some metals, specifically copper
and nickel; and finally, the effect of rising production capacity and strong competition, as found
in the polymer industry since the 1950s. In general the polymers have dropped in price in the past
two decades, whereas the cost of all metals but aluminum has increased. Inflation has also led to
increasing prices.
Materials cannot be compared on the basis of cost alone because they have widely
varying densities and strengths. If the cost per pound is converted to cost per unit volume, a more
meaningful comparison can be made. When the same materials are compared on the basis of cost
per unit of strength per unit of volume it is evident that not only do most materials become
strongly competitive, but that in the future, if stronger polymers are created, the 4000-year
dominance of metals may be severely challenged (Fig. 4.33).
4.7
Case Study
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Your company is using steel stampings that are subsequently bent as a cover for its new lawn
tractor. Several materials are currently under consideration with the following flow curve
information:
Metal
Condition
n
K (MPa)
Fracture Strain
1020
Annealed
0.26
530
1.38
1045
Hot rolled
0.14
965
0.63
1112
Annealed
0.19
760
0.99
1112
Cold rolled
0.08
760
0.65
4135
Annealed
0.17
1015
0.95
4135
Cold rolled
0.14
1100
0.69
4340
Annealed
0.15
640
1.00
52100
Annealed
0.07
1450
0.51
From a design standpoint it has been determined that the minimum strength coefficient
should be 605 MPa and that maximum toughness is needed to reduce potential customer
dissatisfaction. In working with the manufacturing engineers you have determined that the
maximum equivalent true normal strain in the bends to be 0.165. You do not want a plastic
instability that will compromise integrity in these locations. Select the most appropriate
material.
Solution. The minimum strength coefficient constraint eliminates the 1020 steel. The
manufacturing constraint on strain is evaluated by examining the strain hardening coefficient, n.
This quantity represents the strain where plastic instability will occur that can demean
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performance in this application. This eliminates: 1045 hot rolled, 1112 cold rolled, 4135 cold
rolled, 4135 annealed, and 52100 annealed. We will now evaluate the remaining materials on
their toughness:
For 1112 annealed:
T   760 0.19 d  631
For 4135 annealed:
T   1015 0.17 d  817
Based on the toughness the 4135 annealed steel would be the best choice of material.
4.8

Summary
The heat capacity of a solid depends upon the amplitude of oscillation of the particles about
their centers of equilibrium. The greater the temperature, the greater the amplitude, and
consequently the greater will be the heat capacity.

A material that can change packing structure is said to be allotropic.

Dislocations are localized disruptions in the crystal lattice. Edge and screw dislocations are
capable of lowering the theoretical strength of a crystal.

Hooke’s Law states that the engineering stress and strain are proportional.

The natural (or true) stress differs from the engineering stress since it uses the instantaneous
area rather than the original cross-sectional area.

Brinell and Rockwell hardness tests relate to the ability of a material to resist indentation.
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The endurance or fatigue limit is the stress below which a material has an infinite life (>108
cycles).
4.9
Questions
1.
Explain clearly the difference between the physical properties and mechanical properties
of a material. Give several examples.
2.
Why is a designer or production engineer interested in the properties of materials?
3.
Would a designer and a production engineer be equally interested in the same properties
of a material to be used, for example, in an electric motor frame? Explain your answer.
4.
What is the difference between the structure-sensitive and structure-insensitive properties
of a material?
5.
Give several distinguishing characteristics of the four major classes of solid materials.
6.
What are three general groupings that can be used in the study of the structure of
materials?
7.
What is the major feature of Planck's quantum hypothesis? What physical property of a
material does it help us to understand?
8.
What is the basic factor that affects the value of the heat capacity of a solid?
9.
How would the heat capacity of two metals vary, in general?
10.
What is the specific heat of a substance?
11.
What property of two materials would lead to a difference in the magnitude of their heat
capacities?
12.
How does the thermal conductivity of any material vary with temperature?
13.
Why does the thermal conductivity of a metal exceed that of a plastic?
14.
Make a sketch of the stress-strain diagram of a typical "engineering thermoplastic."
15.
What is the relationship between true strain and engineering strain?
16.
What is the advantage of the true stress-true strain relationship for a design engineer?
17.
Why does the elastic region of the true stress-true strain graph plot as a 45° slope?
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18.
At what point will the compression stress-strain curve diverge from the tensile
stress-strain curve?
19.
How is hardness determined? Give the nature of the various hardness tests.
20.
Why is the Moh hardness test seldom used in connection with checking the hardness of
metals?
21.
What is the relationship between hardness and tensile strength for steel? Is this
relationship also found for other alloys?
22.
How do fatigue tests aid the design engineer?
23.
In a casting having a radius of fillet to thickness ratio of 1, what stress concentration
factor would apply to tensile stresses?
24.
What is the value of a creep test in a production design?
25.
In a production design, what are the principal advantages of thermosets and
thermoplastics compared to metals?
26.
What is the value of “shot peening” a particular part?
27.
What are the major advantages of ferrous alloys compared with plastics and other
metallic alloys?
28.
What material is strongest on a strength-to-weight basis?
29.
How does cost affect the choice which material to use for a given situation?
30.
What is a unit cell?
31.
Define the term slip system.
32.
Draw the face-centered cubic unit cell. Illustrate the 12 slip systems.
multiple unit cells).
33.
Draw both screw and edge dislocations, labeling the Burger's vector and showing the
Burger's circuit.
34.
Define work hardening (or strain hardening).
35.
What are grain boundaries and what influence do they have on the strength and ductility of
metals.
36.
What is the difference between preferred orientation and mechanical fibering.
37.
How does plastic deformation influence anisotropy in metals?
(You may use
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38.
What effects does recrystalization have on properties of metals?
39.
For a given strain what affect does increasing the strain rate or temperature have on the
stress developed?
40.
Define the term hardness.
41.
What are residual stresses and by what means (mechanisms) are they imparted to a
material?
42.
What is a fatigue failure and how does it occur?
4.10 Problems
1.
Explain the behavior of electrical and thermal insulators and conductors as a function of
temperature in terms of the band theory of solids and free electrons. Show by an
appropriate sketch how a semiconductor can become a conductor or an insulator.
2.
A standard tensile test on a specimen 0.505 in. diameter with a 2-in. gauge length yielded
the following data: yield load, 11,700 lb.; maximum load, 65,000 lb; gauge length at the
maximum load, 3.018 in.; reduction in area at fracture, 35 percent. Determine the yield
strength, the engineering fracture stress, the natural fracture stress, the strain-hardening
equation, and its constants.
3.
Given the strain-hardening equation for an annealed material as = 95,0000.25 estimate its
yield and tensile strengths as annealed and after 60 percent cold work.
4.
If the value for the BHN of AISI 1040 steel as water-quenched and tempered at 400°F is
560, what would be its probable tensile strength?
5.
From a long time-creep test of Inconel X at 1500°F carried out in a nonoxidizing
atmosphere, the following data were obtained:
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(a) Elongation after 10 h, 1.2 percent
(b) Elongation after 200 h, 2.3 percent
(c) Elongation after 2000 h, 4.5 percent
(d) Elongation after 4000 h, 6.8 percent
(e) After 5000 h, neckdown began
(f) At 5500 h, rupture occurred
Determine the creep rate of Inconel X at 1500 h.
6.
A specimen of 60-40 brass was cold-rolled so that it received a 63 percent reduction,
what is the magnitude of the true strain in the material?
7.
A cast iron bearing plate 10 x 10 x 2.5 in. is subjected to a uniformly compressive load.
The compressive strength of gray iron is 100,000 Ib/in.2 and the strain at fracture was
found to be 0.002 in./in. What was
(a) The compressive fracture load?
(b) The total contraction at fracture?
(c) The total strain energy corresponding to fracture?
8.
Show that the lattice constant a in Figure 1.3(a) from the text (i.e. a fcc packing structure) is
related to the atomic radius by a = 2 2 R 1 where R is the radius of the atom as depicted in
the tennis-ball model.
9.
Consider a tensile specimen with gage length of 2.00" and original diameter of 0.2". Upon
fracture the diameter is 0.08" and length 3.21". The loading of the specimen is as follows:
Condition
Load (lbs.)
yield
3000
maximum
4540
fracture
3890
(a)
Determine the (engineering) yield stress.
(b)
Find the (engineering) ultimate tensile strength.
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(c)
What is the (engineering) stress at fracture.
(d)
Determine the (engineering) strain at fracture.
(e)
Find the ductility of the specimen (both % change in area and length).
Consider a tensile specimen with gage length of 4.00" and original diameter of 0.3". Upon
fracture the diameter is 0.25" and length 4.65". The loading of the specimen is as follows:
Condition
Load (lbs.)
yield
3150
maximum
3990
fracture
11.
3800
(a)
Determine the (engineering) yield stress.
(b)
Find the (engineering) ultimate tensile strength.
(c)
What is the (engineering) stress at fracture.
(d)
Determine the (engineering) strain at fracture.
(e)
Find the ductility of the specimen (both % change in area and length).
Consider a tensile specimen with gage length of 2.00" and original diameter of 0.2". Upon
fracture the diameter is 0.09" and length 3.11". The loading of the specimen is as follows:
Condition
Load (lbs.)
yield
2420
maximum
3100
fracture
2820
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13.
14.
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(a)
Determine the (engineering) yield stress.
(b)
Find the (engineering) ultimate tensile strength.
(c)
What is the (engineering) stress at fracture.
(d)
Determine the (engineering) strain at fracture.
(e)
Find the ductility of the specimen (both % change in area and length).
For problem 9 find:
(a)
True strain at fracture
(b)
True stress at fracture
For problem 10 find:
(a)
True strain at fracture
(b)
True stress at fracture
For problem 11 find:
(a)
True strain at fracture
(b)
True stress at fracture
Show that for small strains that the following relationship is true:
 = ln (e + 1)
16.
A steel has the following flow curve:
 = 80,000 0.45 psi
17.
(a)
Determine the strain where necking is initiated.
(b)
What is the true ultimate tensile strength?
(c)
Determine the engineering ultimate tensile strength.
A steel has the following flow curve:
 = 75,000 0.4 psi
(a)
Determine the strain where necking is initiated.
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(b)
What is the true ultimate tensile strength?
(c)
Determine the engineering ultimate tensile strength.
03/06/16
18.
A 2.00" long aluminum specimen is elastically stressed to 10,000 psi and elongated by
0.002". Determine its modulus of elasticity.
19.
A 2.00" long copper specimen is elastically stressed to 7,500 psi and elongated by 0.001".
Determine its modulus of elasticity.
20.
When a load of 100 kg is used in Rockwell hardness test, determine HRA when the
differential penetration depth (t) is 0.08 mm.
21.
A material with the flow curve  = 60,000 .42 psi fractures at a strain of f = 1.29.
Determine its toughness.
22.
A material with the flow curve  = 45,000 .30 psi fractures at a strain of f = 2.75.
Determine its toughness.
4.11 Suggested Reading
American Society for Metals: Metals Handbook, Metals Park, Ohio, 1985.
Brophy, J. H., Rose, R. M., and Wulff, J. "The Structure and Properties of Materials," Vol. 11.
Thermodynamics of Structure, Wiley, New York, 1964.
Cahners, Inc.: Ceramic Data Book, Cahners, Chicago [published annually].
Carter, G.F., and Paul, D.E., Material Science and Engineering, ASM, 1990.
Chapman-Reinhold: Materials Selector Issue, Materials Engineering Series, Chapman Reinhold,
New York [published annually].
Courtney, T.H., The Mechanical Behavior of Materials, McGraw-Hill, 1990.
Dieter, G.E., Mechanical Metallurgy, 3rd Edition, McGraw-Hill Inc., New York, 1988.
Flinn, R.A., and Trojan, P.K., Engineering Materials and Their Applications, 4th Edition,
Houghton Mifflin Co., Boston, MA 1990.
Leslie, W. C.: The Physical Metallurgy of Steels, McGraw-Hill, New York, 1981.
Maki, T., Tsuzaki, K., and Tamura, I.: "The Morphology of Microstructure Composed of Lath
Martensite in Steels," Transactions of the Iron and Steel Institute of Japan vol. XX 1980.
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Mcclintock, F. A., and Argon, A. S.: Mechanical Behavior of Materials, Addison Wesley
Reading, Mass., 1966.
McLean, D.: Mechanical Properties of Metals, Wiley, New York, 1962.
Meshil, M.: Mechanical Properties of BBC Metals, TMS-AIME, Warrendale, Pa., 1982
Parker, E. R.: Materials Data Book for Engineers and Scientists, McGraw-Hill, New York 1967.
Rosenthal, D.: Introduction to Properties of Materials, Van Nostrand, Princeton, N.J., 1964.
Samaus, C. H.: Metallic Materials in Engineering, Macmillan, New York, 1963.
Shackelford, J.F., Introduction to Materials Science for Engineers, 4th Edition, MacMillan, 1995.
Smith, W.F., Principles of Material Science and Engineering, 3rd Edition, MacGraw-Hill, 1996.
Smithells, C. J.: Metals Reference Book, 3d ea., Butterworths, London, 1962.
Van Vlack, L.H., Elements of Material Science and Engineering, 6th Edition, Addison-Wesley
Publishing Co., Reading, MA, 1989.
Winchell Symposium on Tempering of Steel: Metallurgical Transactions, vol. 14A, pp.
985-1146, 1983.
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