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Lecture 1
Introduction
The goal of this course is to provide a basic introduction to the mechanical properties of materi-
als at an introductory graduate level. As we will see throughout the course, it is the microscopic
structure of a material that determines its mechanical properties. Thus, this course focuses on the
relationships between structure and mechanical properties of materials.
In this lecture, we will define what constitutes mechanical properties and, after a little
motivation, discuss some important classifications of materials, and start to describe some basic
concepts of structure of materials. We will develop some basic vocabulary, and will begin to
discuss why it is so important to understand the relationship between microstructure and
mechanical properties.

Mechanical Properties
So what are mechanical properties? The mechanical properties of a material characterize its
response to mechanical forces. In general, when we apply a load to a solid, its dimensions
change and we call this response “deformation.” Deformation, and thus mechanical properties,
can be divided into three categories (Figure 1.1):
Elastic: If the material eventually returns to its original dimensions when we remove the
load, we refer to the deformation as “elastic.” Elastic deformations are said to be recoverable.
Plastic: If the material retains some permanent deformation when we remove the load, we
refer to the deformation as “plastic.” Plastic deformations are not recoverable.
Fracture: If the material separates into two or more pieces under the applied load, its
dimensions can change dramatically and we call this dimension-changing process “fracture.”
Any process that involves propagation of a crack (even before the part separates completely)
is a fracture process. Deformations due to fracture are also not recoverable.
It turns out that there is a hierarchy in understanding these properties. Although one can
understand the fundamentals of elastic deformation without knowing much about plastic defor-
mation or fracture, background knowledge about elastic properties is necessary to understand
plastic deformation, and knowledge of both elastic and plastic properties is necessary to under-
stand fracture. Thus, we will focus first on elastic properties, then on plastic properties and
finally on fracture properties.

Motivation
Understanding the mechanical behavior of materials is very important. Regardless whether its
function is mechanical, electrical, optical, chemical, or biological, every object must be able to
maintain its structural integrity, or at least to fail in a forgiving way, if it is to be useful and safe.
Knowing how a material reacts to mechanical loads, enables us to design and build safer, more
effective products of every kind. Conversely, failure to understand mechanical behavior can lead
to components that fail in unexpected ways —sometimes with fatal and expensive consequences.
We will see many examples of both successful and unsuccessful materials in this class.
Mechanical behavior is so important that the “ages” of human history—“stone age,” “bronze
age,” “iron age,” etc.—are named for the materials that made the “high technology” of each of

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those eras possible. Then, as now, the level of civilization that was possible depended on the
technology that was available, which, in turn, depended on the materials that people understood
and knew how to use. For most of history, the main uses of materials were mechanical. But even
today, when we routinely make use of the electrical, magnetic, optical, chemical, and biological
properties of materials as well, we must always be concerned about the mechanical integrity of
every object that we use, and thus about mechanical properties.

original object

apply load

remove load

elastic: plastic: fracture:

original permanent separation
dimensions deformation
recovered

Figure 1.1: Types of deformation

In some cases, the mechanical function is obvious. In civil infrastructure such as bridges and
buildings, or in machine components such as pressure vessels, gears, and levers, design is
dominated by calculations of load bearing ability. In other cases, a device may not have an
explicit mechanical function, yet its performance is nonetheless dominated by mechanical
considerations. For example, the central processing unit (CPU), the main “computer chip” in
your computer, laptop, or cell phone, will eventually fail, most likely by processes controlled by
the internal stresses that arise due to differential thermal expansion between the different
constituent materials. Even the mechanical properties of naturally occurring materials that we did
not engineer are important. For example, we need to know how to fracture different types of rock
in order to extract resources (metals, minerals, hydrocarbons), build roads, and excavate for
foundations; we use wood for furniture and as a primary residential structural material; and we
depend on bone—a complex composite that has an amazing ability to modify itself in response
to loads—for our own structural integrity.

A Basic Vocabulary of Mechanical Properties

We need a basic vocabulary to talk about mechanical properties. We will define these terms
more precisely later. For now, you should know:

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Stiffness is a measure of a material’s ability to resist elastic deformation. The opposite of

stiffness is compliance. A rubber band is very compliant (not very stiff). A diamond is very
stiff (not very compliant).
Strength is a measure of a material’s ability to resist permanent deformation, whether due to
plastic deformation or fracture. The opposite of strong is weak. The words hard and soft are
equivalent to strong and weak, respectively, with respect to plastic deformation. Some steels
can be very strong, styrofoam is very weak.
Ductility is a measure of how much a material can deform plastically before fracture. The
opposite of ductile is brittle. Many metals are ductile. Silicate glasses (most ceramics) are
generally quite brittle.
Toughness is a measure of how much energy (work) it takes to fracture a material. For
maximum toughness, we need materials that show lots of deformation at very high loads (i.e.
high ductility and high strength). Brittle materials (like window glass) are not very tough
because they don’t deform very much. Ductile weak materials (like lead) are not very tough
because they don’t support high loads.
Be careful with these definitions! In particular, people often mix up strength, stiffness, and
hardness. By these definitions, a spring that deforms easily (but elastically) at low loads may be
said to be compliant, but not weak or soft. Similarly, a spring with a high stiffness would not be
referred to as strong or hard.

The Relationship between Microscopic Structure and Mechanical Properties

As we will see, in order to understand mechanical properties of a material, we must first
understand the details of its internal configuration on a microscopic scale. This is traditionally
divided into three categories: At the level of atoms, atomic bonding, or the way that individual
atoms are bound to each other in a material, plays the key role in determining its stiffness and
also whether it is basically brittle or ductile. On a somewhat larger scale (about 0.1 to 10 nm),
the stiffness and strength of a material are very sensitive to the local atomic arrangements, or
how atoms are organized relative to each other to form phases, the basic building blocks of the
material. At an even larger scale (typically about 10 nm to about 10 mm), the phases, the defects
in those phases, and the way those phases are arranged (phase morphology) dominate in
determining mechanical properties. The features of the material on this scale make up what is
known as its microstructure.

Atomic Bonding
At the atomic level, the nature of interatomic bonds determines the most basic characteristics of a
material. These topics are covered in other courses and will not be covered here. It is sufficient to
remember that metallic bonds are strong but non-directional, that covalent bonds are strong and
highly directional, that ionic bonds are strong and require local charge neutrality, and that weak
bonds are so named because they are weak.
Metallic bonds arise when individual atoms give up their valence electrons to share with the
whole ensemble of atoms. Because metallic bonds are strong, metallic materials are generally
stiff and strong. Because those bonds are non-directional, it is possible for atoms to move around
relative to one another, leading to the ductility for which metals are famous. In addition, metals

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tend to be close-packed (high atomic density). Since the valence electrons are not tied to any
particular atom metals have high electrical conductivity and are optically opaque.
Covalent bonds arise when atoms share electrons in specific orbitals. These bonds specify
both interatomic distances and interatomic angles. Since covalent bonds are strong, materials
having these bonds are very stiff and strong. Furthermore, since atoms are not free to move
relative to one another covalently bonded materials are intrinsically brittle. Strict relative atom
location requirements lead to lower (than metals) atom densities. To the extent that all electrons
are tied up in bonds, covalent solids are good electrical insulators and, in the absence of defects,
can be transparent.
Ionic bonds arise when atoms donate/accept electrons creating ions that can be considered to
be electrostatically attracted. Since ionic bonds are strong, materials having ionic bonds are stiff
and strong. Ionic bonds are non-directional; however, they require that atoms with opposite
charges be arranged in a specific way so that the net local charge is zero. Thus, atoms are not
free to move relative to one another and ionically bonded materials are also intrinsically brittle.
Again, to the extent that all electrons are tied up in bonds, ionic solids tend to be insulators and
in the absence of defects are transparent.
Weak bonds (e.g. hydrogen bonds, van der Waals bonds) arise due to the inhomogeneous
distribution of charge in molecules. The somewhat positive regions of one molecule are attracted
to the somewhat negative regions of another. Such bonds are both weak and compliant.
Molecular materials like ice, graphite, and many polymers are held together by weak bonds. The
properties of such materials vary widely depending on the configurations of the molecules. For
example, ice, with its small H2O molecules, is quite brittle while long-chain polymers can have
high ductility and toughness.

Local Atomic Arrangements

Given a group of atoms with their predilections for certain types of atomic bonds, the next
question we can ask is ‘in what ways can atoms be combined to form a material?’ We will define
three broad categories. Depending on the atoms involved, we might have crystalline,
amorphous, or molecular materials.
A crystal is simply defined as a 3-D periodic array of atoms in space. The vast majority of
engineering materials are essentially crystalline, and the effects of the crystalline nature of
materials on their mechanical properties are so profound that we will devote some time to
learning about crystalline structures and, importantly, crystal defects.
An amorphous material is defined as one that has no discernable long-range order. Many
materials can be made to be amorphous, even if a crystalline form is available, by simply
cooling from the (amorphous!) melt fast enough that the atoms do not have time to organize
into a crystal structure before they are frozen into place. The ability of a material to take on
an amorphous form depends on how easily atoms can move around near the melting
temperature. Silicate glasses are amorphousa and can be formed at relatively low cooling
rates, but typical metals need extremely fast cooling rates (106–109 ˚C/s) to solidify in an
amorphous state.

a
A glass is a specific amorphous structure having a second-order phase transition between the liquid and solid
states. Glasses are a subset of amorphous materials.

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Molecular materials are formed when the basic units of the materials are molecules rather
than atoms. The most common of this group are engineering polymers (of which there are
many!), but this is a very large and growing area that includes materials as diverse and
interesting as hydrogels and materials made from peptides. Molecular materials may be
crystalline or amorphous, and are often semicrystalline, with molecules occupying crystal
lattice sites but with some deviations from the ideal positions, or consisting of crystalline
regions intermixed with amorphous regions.

Microstructure
The term “microstructure” is generally thought to describe which phases are present, their
morphological arrangement, and the defect structures in those phases. Historically, it has been
applied primarily to crystalline materials.
Although materials often are crystalline, materials composed of perfect single crystals are
exceedingly rare. Thus, when thinking about crystals, one can think of microstructure as the
deviations from the perfect crystalline state. The key elements of the microstructure of a
crystalline material may be classified into three categories:
1. Defects are “mistakes” in the crystal structure and can be categorized as follows:
• Point defects (0-D): Local mistakes in the structure without lateral extent. Examples
include vacancies (atoms missing from the periodic structure), interstitials (extra
atoms in-between periodic atom positions), and substitutionals (atoms other than the
expected ones at the expected periodic positions).
• Line defects (1-D): A specific class of defects called dislocations that are long in one
dimension but limited in the other two. Dislocations are so important that we will
devote at least two lectures to them.
• Planar defects (2-D): Defects that can be treated as an internal surface—long in two
dimensions but limited in the third. Examples include grain boundaries (boundaries
between regions having the same crystal structure but different orientations), twin
boundaries (like grain boundaries but for specific misorientations), and stacking
faults (boundaries between regions having the same crystal structure but shifted with
respect to each other in the fault plane).
2. A phase is a region possessing a unique crystal structure and properties that vary
continuously (in the mathematical sense) with position within it. The composition does not
have to be constant within a phase. In steel (an alloy of iron containing small amounts of
carbon), for example, it is possible to produce at least five phases:
• Ferrite (a-Fe): pure Fe in a body centered cubic crystal structure
• Austenite (g-Fe): Fe in a face centered cubic crystal structure
• Iron carbide (Fe3C): a compound containing Fe and C having an orthorhombic crystal
structure)
• Martensite (a’): a distorted body centered cubic-tetragonal structure containing C
• Graphite (pure carbon in a hexagonal crystal structure)

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One of the reasons steel is such a useful engineering material is that its mechanical
properties can be altered drastically by producing different combinations of these phases.
Engineers rely strongly on phase diagrams to tell them what phases will be in the
equilibrium microstructure of a material of a particular composition at a particular
temperature.
3. The phase morphology refers to the spatial arrangement and distribution of defects or
phases. For example, the two phases a-Fe and Fe3C can be produced in many morphologies
in steel, including:
• Pearlite: lamellar alternating plates of a-Fe and Fe3C. The thickness of the plates can
be changed by heat treatment.
• Spheroidite: spheres of Fe3C in a-Fe. The size and spacing of these carbide spheres
can also be changed by heat treatment
Two steels having the same amounts of the same phases in different morphologies can have
very different mechanical properties.
For a crystalline material, the specification of phases present, their morphology, and the defect
structures within those phases constitutes a complete description of the microstructure. The term
“microstructure” can also be used to refer to glassy or molecular materials, to the extent that
those materials include different phases, phase morphologies, or defect structures.
Except for changes in the relative amounts of different phases, the elastic properties of
materials are not much affected by changes in microstructure. The elastic properties are often
said to be structure insensitiveb. On the other hand, plastic deformation and fracture are very
sensitive to the microstructure and are said to be structure sensitive properties.

Deformation Mechanisms, Structure, Processing, and Mechanical Properties

It cannot be overstated that understanding the connection between microstructure and
mechanical properties is critical to understanding the mechanical behavior of materials.
For deformation to occur, atoms must move relative to one another. The way that atoms
move relative to each other for a specific type of deformation is called a deformation
mechanism. Whether a particular deformation mechanism occurs under a certain set of
conditions (load, temperature, etc.) depends on the structure, including bonding, atomic
arrangements, and microstructure. The structure, in turn, is very sensitive to the particular steps
used to make the material. By changing these processing steps, we can change the structure and
thus the mechanical properties. The heart of this course is understanding deformation
mechanisms, materials structure, materials processing, and mechanical properties and the
relationships among them.
Does an engineer building km-long bridges really need to know about details of the materials
used on the atomic scale? The answer is yes! The mechanical properties of materials are
fundamentally determined by those details and those details can be changed. These changes can
be beneficial, for example when a certain process treatment is used to dramatically strengthen the
steel girders in a bridge by intentional manipulation of the microstructure. But these changes can
also be deadly when, for example, those same girders weaken and fail due to unintended changes

b
By “structure” here, we mean “microstructure” in the classical sense.

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in microstructure caused by use or environmental factors. As engineers we must be aware of the

relationships between the microscopic structure and the mechanical properties of materials.

Classes of Materials
For convenience, we will divide the materials that we look at into four groups: metals, ceramics,
polymers, and composites. Metals, ceramics, and polymers are distinguished in a very
fundamental way by the nature of their atomic bonding and each has a characteristic set of
behaviors and uses. Composites are combinations of phases of different materials. Some general
features of these groups of materials can be summarized as follows:
Metals are characterized by metallic bonding (!) and are generally stiff and can be made very
strong. The strength of a metal depends very much on defects and can easily be controlled.
Because they are ductile, metals generally fail in a forgiving way, providing plenty of
warning (plastic deformation) that a failure is imminent. In addition, metals are usually easy
to form into desired shapes by casting, plastic deformation, cutting, welding, and fastening.
For these reasons, metals are very widely used structural materials. Disadvantages of metals
include high specific weight, poor performance at high temperatures, and corrosion.
Ceramics are characterized by ionic and covalent bonding. Ceramics are very stiff and hard
and retain these properties at high temperatures. Ceramics don’t corrode so easily and also
have lower specific weight than metals. However, ceramics are brittle and tend to fail
catastrophically by fracture without warning. Furthermore, ceramics cannot easily be made
into desired shapes by cutting, plastic deformation, or welding, and require special care in
fastening.
Polymers are made up of covalently bonded chain molecules which may be connected to
each other by weak forces, or ionic or covalent bonds. Polymers are generally very compliant
and have advantages in very low specific weights, low price, and the ability to form complex
shapes easily. Polymers can also be made to be tough. Polymers have the disadvantage of
being relatively weak, can’t be used at high temperatures, and may degrade over time.
Composites consist of two or more different materials that are combined specifically to take
advantage of certain features of each one. For example, a composite consisting of light,
strong, stiff, but brittle carbon fibers in a tough, light, compliant, but weak epoxy matrix
makes a composite which is light, stiff, tough, and strong. The mechanical properties of
composites cover a very wide range.
Note that most engineering materials can be classified according to this scheme. An
important exception is molecular materials other than polymers. We define molecular materials
as those consisting of molecules held together by weak bonds. Polymers are a subset of this
category but are both so important in engineering and unified by their long-chain molecules that
we treat them separately. As it turns out, we can treat molecular materials like graphite and ice as
ceramics due to their brittle behavior, and other long-chain molecular materials such as DNA or
collagen as polymers, again due to the similarities in their mechanical behaviors.
Other classification schemes are often used, but we will map them onto the above scheme.
For example, “semiconductors” is an important class of materials due that are classified by their
electrical behavior. From a mechanical properties point of view, semiconductors such as silicon
and germanium are ceramics. “Biomaterials” is another important class of materials lumped
together because of their origins or applications in biology. Most biological materials are

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polymeric, or ceramic. For example, bone is a composite consisting mostly of collagen (polymer)
and hydroxyapatite (ceramic).

Isotropy and Homogeneity

A material is said to be isotropic if the properties at a point are the same in all directions at that
point. As it turns out, many materials properties are anisotropic, that is, their properties are
different in different directions at a point. This concept is illustrated in Figure 1.2a and b where
the lengths of the lines indicate the magnitude of some property in the different directions
indicated by the lines themselves. If the property is the same in all directions (Fig. 1.2a), the
material is isotropic. If the property is different in different directions (Fig. 1.2b), the material is
anisotropic. For example, suppose the lengths of the lines represent stiffness. The material in Fig.
1.2a would have the same stiffness in all directions, while the material in Fig. 1.2b would be
stiffer in some directions and more compliant in others—all at the same point.
A material is said to be homogeneous if the properties are the same at all points in the
material. As it turns out, many materials properties are inhomogeneous, that is, their properties
vary from point to point in the material. This concept is illustrated in Figure 1.2c and d where the
different colors indicate different phases with different properties. In Fig. 1.2c only one phase is
present and if that phase is the same everywhere, the region we are looking at will be
homogeneous. In Fig. 1.2d two phases (black and white) are shown. If the properties of these
phases are different, the material will be inomogeneous. It is important to note that properties can
vary continuously within a phase so a single-phase material can also be inhomogeneous.

(a) (b)

(c) (d)

Figure 1.2: (a) Isotropic, (b) anisotropic, (c) homogeneous, and (d) inhomogeneous
materials.

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In fact, most materials are both anisotropic and inhomogeneous. This complicates our ability
to understand and analyze them considerably—so much so that in most elementary courses these
concepts are sidestepped completely, or at least partially. Since understanding anisotropy and
inhomogeneity are essential to understanding mechanical behavior, we will not avoid these
topics. However, we will not be able to cover them in any detail in this introductory course. Our
tactic will be to start with isotropic homogeneous materials and then illustrate the effects of
anisotropy and inhomogeneity in a basic way. To fully understand these effects, you will need
several graduate level courses in mechanical properties.

Time Dependence
An additional important complication is that all deformation is time dependent on some scale!
However, how much we care about the time dependence depends on the situation. We can use
the concept of the Deborah numberc, D, to understand this.
materials response time test rate
𝐷= or, equivalently,
observation time deformation rate
When we apply a load to a material, there are usually multiple available deformation
mechanisms (ways that atoms can move relative to each other), each of which proceeds at a
particular rate depending on the conditions (load, temperature, pressure…). These rates may vary
by many orders of magnitude. For example, consider an idealized case where we impose a load
instantaneously and hold it constant on a material with a “fast” deformation mechanism that
reaches equilibrium and stops in µs and a “slow” deformation mechanism that reaches
equilibrium over many years. The situation is shown in Figure 1.3.

Figure 1.3: Displacement as a function of time for a material with fast and slow deformation
mechanisms subjected to a constant load at time = 0.
If we apply the load over a typical laboratory test time of seconds to minutes, then for the fast
mechanism D << 1 and for the slow mechanism D >> 1. Our material appears to respond
instantaneously with the fast mechanism and the slow mechanism doesn’t appear to occur at all.
Furthermore, on this time scale the deformation appears to be time-independent. It doesn’t
matter if we hold for 1 s or for 1 hr, the answer is virtually the same. However, if we apply the
load on a typical application time of a few decades (many engineered structures are intended to

c
See M. Reiner, “The Deborah Number,” Physics Today, January 1964, p. 62.

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last this long), then for the fast mechanism D is still << 1, but now we see that the material is
deforming by the slow mechanism on the time scale of the test; that is, D ≈ 1. That is, the
deformation increases the longer the application time. On this time scale the deformation appears
to be time-dependent. We would also see time-dependent behavior if our observation time were
a few µs. For a given deformation mechanism, if D << 1 the materials response is fast relative to
the time of the test and the material will appear to respond instantaneously. If D >> 1 the
materials response is slow relative to the time of the test and that mechanism will appear to be
inactive. For D << 1 or D >> 1 the response will be time independent. For D ≈ 1, the materials
response is occurring on the same time scale as the time of the test and the behavior will be time-
dependent.
We will often see that by changing conditions (primarily test rate or temperature) we can
move between regions where the materials response is time-dependent to regions where it is
time-independent and vice versa. In fact, all three categories of deformation have common time-
dependent and time-independent regimes. Time-dependent elastic deformation is often referred
to as “anelastic” and permanent plastic deformation that accumulates over longer times
(generally anything more than a few seconds) at constant load is referred to as “creep.” Fracture
processes may also be fast, for example when a crack runs through an overloaded brittle
material, or slow. For example, in a process known as “fatigue,” a crack may move through a
material in small incremental steps due to low amplitude cyclic loading. In a process known as
“environmentally assisted cracking” (EAC), chemical process break bonds at crack tips
leading to very slow crack growth. In our study of mechanical properties, we will examine
elasticity, plasticity and fracture at both short and long timescales.

Summary
To help you organize your thoughts, in this class we will “fill in the blanks” relating
microstructure to mechanical properties in the categories shown in Table 1.1. You will have the
chance to obtain at least some basic understanding in each category, although some will
necessarily get more attention than others. For example, we won’t study plastic deformation in
ceramics much since ceramics are very brittle!

Elastic Plastic Fracture

“instanta- “anelastic” “plasticity” “creep” “fast Fatigue/
neous” fracture” EAC
Metals
Ceramics
Polymers
Composites
Table 1.1: Chart of topics to be covered in this class.

Cornell MS&E 5802 Lecture 1 Ó2024 Shefford P. Baker