Chapter 1. INRODUCTION
1 .1 Historical Perspective
Materials are so important in the development of civilization that we associate Ages with them. In the origin
of human life on Earth, the Stone Age, people used only natural materials, like stone, clay, skins, and wood.
When people found copper and how to make it harder by alloying, the Bronze Age started about 3000 BC.
The use of iron and steel, a stronger material that gave advantage in wars started at about 1200 BC. The
next big step was the discovery of a cheap process to make steel around 1850, which enabled the railroads
and the building of the modern infrastructure of the industrial world.
1.2 Materials Science and Engineering
Understanding of how materials behave like they do, and why they differ in properties was only possible
with the atomistic understanding allowed by quantum mechanics, that first explained atoms and then solids
starting in the 1930s. The combination of physics, chemistry, and the focus on the relationship between the
properties of a material and its microstructure is the domain of Materials Science. The development of this
science allowed designing materials and provided a knowledge base for the engineering applications
• At the atomic level: arrangement of atoms in different ways. (Gives different properties for graphite
than diamond both forms of carbon.)
• At the microscopic level: arrangement of small grains of material that can be identified by
microscopy. (Gives different optical properties to transparent vs. frosted glass.)
Properties are the way the material responds to the environment. For instance, the mechanical, electrical
and magnetic properties are the responses to mechanical, electrical and magnetic forces, respectively. Other
important properties are thermal (transmission of heat, heat capacity), optical (absorption, transmission and
scattering of light), and the chemical stability in contact with the environment (like corrosion resistance).
Processing of materials is the application of heat (heat treatment), mechanical forces, etc. to affect their
microstructure and, therefore, their properties.
1.3 Why Study Materials Science and Engineering?
• To be able to select a material for a given use based on considerations of cost and performance.
• To understand the limits of materials and the change of their properties with use.
• To be able to create a new material that will have some desirable properties.
All engineering disciplines need to know about materials. Even the most "immaterial", like software or
system engineering depend on the development of new materials, which in turn alter the economics, like
software-hardware trade-offs. Increasing applications of system engineering are in materials manufacturing
(industrial engineering) and complex environmental systems.
1.4 Classification of Materials
Like many other things, materials are classified in groups, so that our brain can handle the complexity. One
could classify them according to structure, or properties, or use. The one that we will use is according to the
way the atoms are bound together:
Metals: valence electrons are detached from atoms, and spread in an 'electron sea' that "glues" the ions
together. Metals are usually strong, conduct electricity and heat well and are opaque to light (shiny if
polished). Examples: aluminum, steel, brass, gold.
Semiconductors: the bonding is covalent (electrons are shared between atoms). Their electrical properties
depend extremely strongly on minute proportions of contaminants. They are opaque to visible light but
transparent to the infrared. Examples: Si, Ge, GaAs. Ceramics: atoms behave mostly like either positive or negative ions, and are bound by Coulomb forces
between them. They are usually combinations of metals or semiconductors with oxygen, nitrogen or carbon
(oxides, nitrides, and carbides). Examples: glass, porcelain, many minerals.
Polymers: are bound by covalent forces and also by weak van der Waals forces, and usually based on H, C
and other non-metallic elements. They decompose at moderate temperatures (100 – 400 C), and are
lightweight. Other properties vary greatly. Examples: plastics (nylon, Teflon, polyester) and rubber.
Other categories are not based on bonding. A particular microstructure identifies composites, made of
different materials in intimate contact (example: fiberglass, concrete, wood) to achieve specific properties.
Biomaterials can be any type of material that is biocompatible and used, for instance, to replace human
1.5 Advanced Materials
Materials used in "High-Tec" applications, usually designed for maximum performance, and normally
expensive. Examples are titanium alloys for supersonic airplanes, magnetic alloys for computer disks,
special ceramics for the heat shield of the space shuttle, etc.
1.6 Modern Material's Needs
• Engine efficiency increases at high temperatures: requires high temperature structural materials
• Use of nuclear energy requires solving problem with residues, or advances in nuclear waste
• Hypersonic flight requires materials that are light, strong and resist high temperatures.
• Optical communications require optical fibers that absorb light negligibly.
• Civil construction – materials for unbreakable windows.
• Structures: materials that are strong like metals and resist corrosion like plastics.
Chapter 2. ATOMIC STRUCTURE AND BONDING
2.2 Fundamental Concepts
Atoms are composed of electrons, protons, and neutrons. Electron and protons are negative and positive
charges of the same magnitude, 1.6 × 10 Coulombs.
The mass of the electron is negligible with respect to those of the proton and the neutron, which form the
nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10 -2kg, and equals 1/12 the
mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A
the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu. A neutral
atom has the same number of electrons and protons, Z.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms.
Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro
number, N av = 6.023 × 10 . Note that N = 1avram/1 amu.
Calculating n, the number of atoms per cm in a piece of material of density d (g/cm ). 3
n = N × d / M
where3M is the atomic mass in am23(grams per mol). Thus, f3r graphite (carbon) with22 densi3y d = 1.8
g/cm , M =12, we get 6 × 10 atoms/mol × 1.8 g/cm / 12 g/mol) = 9 × 10 C/cm .
For a molecular solid like ice, one uses the molecular mass, M(H O) = 182 With a density of 1 g/cm , one 3
obtains n = 3.3 × 10 22 H2O/cm . Note that since the water molecule contains 3 atoms, this is equivalent to
9.9 × 10 atoms/cm .
Most solids have atomic densities around 6 × 10 atoms/cm . The cube root of that number gives the
number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that,
or 0.25 nm. This is an important number that gives the scale of atomic structures in solids. 2.3 Electrons in Atoms
The forces in the atom are repulsions between electrons and attraction between electrons and protons. The
neutrons play no significant role. Thus, Z is what characterizes the atom.
The electrons form a cloud around the neutron, of radius of 0.05 – 2 nanometers. Electrons do not move in
circular orbits, as in popular drawings, but in 'fuzzy' orbits. We cannot tell how it moves, but only say what
is the probability of finding it at some distance from the nucleus. According to quantum mechanics, only
certain orbits are allowed (thus, the idea of a mini planetary system is not correct). The orbits are identified
by a principal quantum number n, which can be related to the size, n = 0 is the smallest; n = 1, 2 .. are
larger. (They are "quantized" or discrete, being specified by integers). The angular momentum l is
quantized, and so is the projection in a specific direction m. The structure of the atom is determined by the
Pauli exclusion principle, only two electrons can be placed in an orbit with a given n, l, m – one for each
spin. Table 2.1 in the textbook gives the number of electrons in each shell (given by n) and subshells (given
2.4 The Periodic Table
Elements are categorized by placing them in the periodic table. Elements in a column share similar
properties. The noble gases have closed shells, and so they do not gain or lose electrons near another atom.
Alkalis can easily lose an electron and become a closed shell; halogens can easily gain one to form a
negative ion, again with a closed shell. The propensity to form closed shells occurs in molecules, when they
share electrons to close a molecular shell. Examples are H , N , and NaCl.
The ability to gain or lose electrons is termed electronegativity or electropositivity, an important factor in
2.5 Bonding Forces and Energies
The Coulomb forces are simple: attractive between electrons and nuclei, repulsive between electrons and
between nuclei. The force between atoms is given by a sum of all the individual forces, and the fact that the
electrons are located outside the atom and the nucleus in the center.
When two atoms come very close, the force between them is always repulsive, because the electrons stay
outside and the nuclei repel each other. Unless both atoms are ions of the same charge (e.g., both
negative) the forces between atoms is always attractive at large internuclear distances r. Since the force is
repulsive at small r, and attractive at small r, there is a distance at which the force is zero. This is the
equilibrium distance at which the atoms prefer to stay.
The interaction energy is the potential energy between the atoms. It is negative if the atoms are bound and
positive if they can move away from each other. The interaction energy is the integral of the force over the
separation distance, so these two quantities are directly related. The interaction energy is a minimum at the
equilibrium position. This value of the energy is called the bond energy, and is the energy needed to
separate completely to infinity (the work that needs to be done to overcome the attractive force.) The
strongest the bond energy, the hardest is to move the atoms, for instance the hardest it is to melt the solid,
or to evaporate its atoms.
2.6 Primary Inter atomic Bonds
This is the bond when one of the atoms is negative (has an extra electron) and another is positive (has lost
an electron). Then there is a strong, direct Coulomb attraction. An example is NaCl. In the molecule, there
are more electrons around Cl, forming Cl and less around Na, forming Na . Ionic bonds are the strongest
bonds. In real solids, ionic bonding is usually combined with covalent bonding. In this case, the fractional
ionic bonding is defined as %ionic = 100 × [1 – exp(-0.25 (X A – X B ], where X A and X aBe the
electronegativities of the two atoms, A and B, forming the molecule.
Covalent Bonding In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest
example is the H m2lecule, where the electrons spend more time in between the nuclei than outside, thus
In metals, the atoms are ionized, loosing some electrons from the valence band. Those electrons form a
electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H
atoms in the H 2olecule bind the protons.
2.7 Secondary Bonding (Van der Waals)
Fluctuating Induced Dipole Bonds
Since the electrons may be on one side of the atom or the other, a dipole is formed: the + nucleus at the
center, and the electron outside. Since the electron moves, the dipole fluctuates. This fluctuation in atom A
produces a fluctuating electric field that is felt by the electrons of an adjacent atom, B. Atom B then
polarizes so that its outer electrons are on the side of the atom closest to the + side (or opposite to the –
side) of the dipole in A. This bond is called van der Waals bonding.
Polar Molecule-Induced Dipole Bonds
A polar molecule like H 2 (Hs are partially +, O is partially – ), will induce a dipole in a nearby atom, leading
Permanent Dipole Bonds
This is the case of the hydrogen bond in ice. The H end of the molecule is positively charged and can bond
to the negative side of another dipolar molecule, like the O side of the H 2 dipole.
If molecules formed a closed shell due to covalent bonding (like H , N ) then the interaction between
molecules is weak, of the van der Waals type. Thus, molecular solids usually have very low melting points
Chapter-3: STRUCTURE OF CRYSTALS
3.2 Fundamental Concepts
Atoms self-organize in crystals, most of the time. The crystalline lattice, is a periodic array of the atoms.
When the solid is not crystalline, it is called amorphous. Examples of crystalline solids are metals, diamond
and other precious stones, ice, graphite. Examples of amorphous solids are glass, amorphous carbon (a-C),
amorphous Si, most plastics
To discuss crystalline structures it is useful to consider atoms as being hard spheres, with well-defined radii.
In this scheme, the shortest distance between two like atoms is one diameter.
3.3 Unit Cells
The unit cell is the smallest structure that repeats itself by translation through the crystal. We construct
these symmetrical units with the hard spheres. The most common types of unit cells are the faced-centered
cubic (FCC), the body-centered cubic (FCC) and the hexagonal close-packed (HCP). Other types exist,
particularly among minerals. The simple cube (SC) is often used for didactical purpose, no material has this
3.4 Metallic Crystal Structures
Important properties of the unit cells are
• The type of atoms and their radii R. • cell dimensions (side a in cubic cells, side of base a and height c in HCP) in terms of R.
• n, number of atoms per unit cell. For an atom that is shared with m adjacent unit cells, we only
count a fraction of the atom, 1/m.
• CN, the coordination number, which is the number of closest neighbors to which an atom is bonded.
• APF, the atomic packing factor, which is the fraction of the volume of the cell actually occupied by
the hard spheres. APF = Sum of atomic volumes/Volume of cell.
Unit Cell n CN a/R APF
SC 1 6 2 0.52
BCC 2 8 4Ö 3 0.68
FCC 4 12 2Ö 2 0.74
HCP 6 12 0.74
The closest packed direction in a BCC cell is along the diagonal of the cube; in a FCC cell is along the
diagonal of a face of the cube.
3.5 Density Computations
The density of a solid is that of the unit cell, obtained by dividing the mass of the atoms (n atoms atom
and dividing by Vcthe volume of the cell (a in the case of a cube). If the mass of the atom is given in amu
(A), then we have to divide it by the Avogadro number to get M . Thus, the formula for the density is:
3.6 Polymorphism and Allotropy
Some materials may exist in more than one crystal structure, this is called polymorphism. If the material is
an elemental solid, it is called allotropy. An example of allotropy is carbon, which can exist as diamond,
graphite, and amorphous carbon.
3.11 Close-Packed Crystal Structures
The FCC and HCP are related, and have the same APF. They are built by packing spheres on top of each
other, in the hollow sites (Fig. 3.12 of book). The packing is alternate between two types of sites, ABABAB..
in the HCP structure, and alternates between three types of positions, ABCABC… in the FCC crystals.
Crystalline and Non-Crystalline Materials
3.12 Single Crystals
Crystals can be single crystals where the whole solid is one crystal. Then it has a regular geometric structure
with flat faces.
3.13 Polycrystalline Materials
A solid can be composed of many crystalline grains, not aligned with each other. It is called polycrystalline.
The grains can be more or less aligned with respect to each other. Where they meet is called a grain
Different directions in the crystal have a different packing. For instance, atoms along the edge FCC crystals
are more separated than along the face diagonal. This causes anisotropy in the properties of crystals; for
instance, the deformation depends on the direction in which a stress is applied.
3.15 X-Ray Diffraction Determination of Crystalline Structure – not covered 3.16 Non-Crystalline Solids
In amorphous solids, there is no long-range order. But amorphous does not mean random, since the
distance between atoms cannot be smaller than the size of the hard spheres. Also, in many cases there is
some form of short-range order. For instance, the tetragonal order of crystalline SiO 2 (quartz) is still
apparent in amorphous SiO (sil2ca glass.)
Imperfections in Solids
Materials are often stronger when they have defects. The study of defects is divided according to their
0D (zero dimension) – point defects: vacancies and interstitials. Impurities.
1D – linear defects: dislocations (edge, screw, mixed)
2D – grain boundaries, surfaces.
3D – extended defects: pores, cracks.
4.2 Vacancies and Self-Interstitials
A vacancy is a lattice position that is vacant because the atom is missing. It is created when the solid is
formed. There are other ways of making a vacancy, but they also occur naturally as a result of thermal
An interstitial is an atom that occupies a place outside the normal lattice position. It may be the same type
of atom as the others (self interstitial) or an impurity atom.
In the case of vacancies and interstitials, there is a change in the coordination of atoms around the defect.
This means that the forces are not balanced in the same way as for other atoms in the solid, which results in
lattice distortion around the defect.
The number of vacancies formed by thermal agitation follows the law:
N V N ×Aexp(-Q /kT)V
where N isAthe total number of atoms in the solid, Q is the eneVgy required to form a vacancy, k is
Boltzmann constant, and T the temperature in Kelvin (note, not in C or F). o
When Q isVgiven in joules, k = 1.38 × 10 J/atom-K. When using eV as the unit of energy, k = 8.62 × 10
Note that kT(300 K) = 0.025 eV (room temperature) is much smaller than typical vacancy formation
energies. For instance, Q (CV) = 0.9 eV/atom. This means that N /N at roVm Aemperature is exp(-36) = 2.3
× 10 , an insignificant number. Thus, a high temperature is needed to have a high thermal concentration
of vacancies. Even so, N /NVisAtypically only about 0.0001 at the melting point.
4.3 Impurities in Solids
All real solids are impure. A very high purity material, say 99.9999% pure (called 6N – six nines) contains ~
6 × 10 impurities per cm . Impurities are often added to materials to improve the properties. For instance, carbon added in small
amounts to iron makes steel, which is stronger than iron. Boron impurities added to silicon drastically
change its electrical properties.
Solid solutions are made of a host, the solvent or matrix) which dissolves the solute (minor component).
The ability to dissolve is called solubility. Solid solutions are:
• maintain crystal structure
• contain randomly dispersed impurities (substitutional or interstitial)
Factors for high solubility
• Similar atomic size (to within 15%)
• Similar crystal structure
• Similar electronegativity (otherwise a compound is formed)
• Similar valence
Composition can be expressed in weight percent, useful when making the solution, and in atomic percent,
useful when trying to understand the material at the atomic level.
4.4 Dislocations—Linear Defects
Dislocations are abrupt changes in the regular ordering of atoms, along a line (dislocation line) in the solid.
They occur in high density and are very important in mechanical properties of material. They are
characterized by the Burgers vector, found by doing a loop around the dislocation line and noticing the extra
interatomic spacing needed to close the loop. The Burgers vector in metals points in a close packed
Edge dislocations occur when an extra plane is inserted. The dislocation line is at the end of the plane. In an
edge dislocation, the Burgers vector is perpendicular to the dislocation line.
Screw dislocations result when displacing planes relative to each other through shear. In this case, the
Burgers vector is parallel to the dislocation line.
.5 Interfacial Defects
The environment of an atom at a surface differs from that of an atom in the bulk, in that the number of
neighbors (coordination) decreases. This introduces unbalanced forces which result in relaxation (the lattice
spacing is decreased) or reconstruction (the crystal structure changes).
The density of atoms in the region including the grain boundary is smaller than the bulk value, since void
space occurs in the interface.
Surfaces and interfaces are very reactive and it is usual that impurities segregate there. Since energy is
required to form a surface, grains tend to grow in size at the expense of smaller grains to minimize energy.
This occurs by diffusion, which is accelerated at high temperatures.
Twin boundaries: not covered
4.6 Bulk or Volume Defects
A typical volume defect is porosity, often introduced in the solid during processing. A common example is
snow, which is highly porous ice. 4.7 Atomic Vibrations
Atomic vibrations occur, even at zero temperature (a quantum mechanical effect) and increase in amplitude
with temperature. Vibrations displace transiently atoms from their regular lattice site, which destroys the
perfect periodicity we discussed in Chapter 3.
Many important reactions and processes in materials occur by the motion of atoms in the solid (transport),
which happens by diffusion.
Inhomogeneous materials can become homogeneous by diffusion, if the temperature is high enough
(temperature is needed to overcome energy barriers to atomic motion.
5.2 Diffusion Mechanisms
Atom diffusion can occur by the motion of vacancies (vacancy diffusion) or impurities (impurity diffusion).
The energy barrier is that due to nearby atoms which need to move to let the atoms go by. This is more
easily achieved when the atoms vibrate strongly, that is, at high temperatures.
There is a difference between diffusion and net diffusion. In a homogeneous material, atoms also diffuse but
this motion is hard to detect. This is because atoms move randomly and there will be an equal number of
atoms moving in one direction than in another. In inhomogeneous materials, the effect of diffusion is readily
seen by a change in concentration with time. In this case there is a net diffusion. Net diffusion occurs
because, although all atoms are moving randomly, there are more atoms moving in regions where their
concentration is higher.
5.3 Steady-State Diffusion
The flux of diffusing atoms, J, is expressed either in number of atoms per unit area and per unit time (e.g.,
atoms/m -second) or in terms of mass flux (e.g., kg/m -second).
Steady state diffusion means that J does not depend on time. In this case, Fick’s first law holds that the flux
along direction x is:
J = – D dC/dx
Where dC/dx is the gradient of the concentration C, and D is the diffusion constant. The concentration
gradient is often called the driving force in diffusion (but it is not a force in the mechanistic sense). The
minus sign in the equation means that diffusion is down the concentration gradient.
5.4 Nonsteady-State Diffusion
This is the case when the diffusion flux depends on time, which means that a type of atoms accumulates in
a region or that it is depleted from a region (which may cause them to accumulate in another region).
5.5 Factors That Influence Diffusion
As stated above, there is a barrier to diffusion created by neighboring atoms that need to move to let the
diffusing atom pass. Thus, atomic vibrations created by temperature assist diffusion. Also, smaller atoms
diffuse more readily than big ones, and diffusion is faster in open lattices or in open directions. Similar to
the case of vacancy formation, the effect of temperature in diffusion is given by a Boltzmann factor: D = D 0
× exp(–Q /dT).
5.6 Other Diffusion Paths
Diffusion occurs more easily along surfaces, and voids in the material (short circuits like dislocations and
grain boundaries) because less atoms need to move to let the diffusing atom pass. Short circuits are often unimportant because they constitute a negligible part of the total area of the material normal to the
diffusion flux. .
Chapter-6: Mechanical Properties of Metals
Often materials are subject to forces (loads) when they are used. Mechanical engineers
calculate those forces and material scientists how materials deform (elongate, compress,
twist) or break as a function of applied load, time, temperature, and other conditions.
Materials scientists learn about these mechanical properties by testing materials. Results
from the tests depend on the size and shape of material to be tested (specimen), how it is
held, and the way of performing the test. That is why we use common procedures, or
standards, which are published by the ASTM.
2. Concepts of Stress and Strain
To compare specimens of different sizes, the load is calculated per unit area, also called
normalization to the area. Force divided by area is called stress. In tension and compression
tests, the relevant area is that perpendicular to the force. In shear or torsion tests, the area
is perpendicular to the axis of rotation.
s = F/A t0nsile or compressive stress
t = F/A s0ear stress
The unit is the Megapascal = 10 Newtons/m .
There is a change in dimensions, or deformation elongation, DL as a result of a tensile or
compressive stress. To enable comparison with specimens of different length, the elongation
is also normalized, this time to the length L. This is called strain, e.
e = DL/L
The change in dimensions is the reason we use A to 0ndicate the initial area since it changes
during deformation. One could divide force by the actual area, this is called true stress (see
For torsional or shear stresses, the deformation is the angle of twist, q (Fig. 6.1) and the
shear strain is given by:
g = tg q
3. Stress—Strain Behavior
Elastic deformation. When the stress is removed, the material returns to the dimension it
had before the load was applied. Valid for small strains (except the case of rubbers).
Deformation is reversible, non permanent
Plastic deformation. When the stress is removed, the material does not return to its
previous dimension but there is a permanent, irreversible deformation.
In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's
s = E e That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of
elasticity. In some cases, the relationship is not linear so that E can be defined alternatively
as the local slope:
E = ds/de
Shear stresses produce strains according to:
t = G g
where G is the shear modulus.
Elastic moduli measure the stiffness of the material. They are related to the second
derivative of the interatomic potential, or the first derivative of the force vs. internuclear
distance (Fig. 6.6). By examining these curves we can tell which material has a higher
modulus. Due to thermal vibrations the elastic modulus decreases with temperature. E is
large for ceramics (stronger ionic bond) and small for polymers (weak covalent bond). Since
the interatomic distances depend on direction in the crystal, E depends on direction (i.e., it
is anisotropic) for single crystals. For randomly oriented policrystals, E is isotropic. .
Here the behavior is elastic but not the stress-strain curve is not immediately reversible. It
takes a while for the strain to return to zero. The effect is normally small for metals but can
be significant for polymers.
5. Elastic Properties of Materials
Materials subject to tension shrink laterally. Those subject to compression, bulge. The ratio
of lateral and axial strains is called the Poisson's ratio n.
n = e lateralaxial
The elastic modulus, shear modulus and Poisson's ratio are related by E = 2G(1+n)
6. Tensile Properties
Yield point. If the stress is too large, the strain deviates from being proportional to the
stress. The point at which this happens is the yield point because there the material yields,
deforming permanently (plastically).
Yield stress. Hooke's law is not valid beyond the yield point. The stress at the yield point is
called yield stress, and is an important measure of the mechanical properties of materials. In
practice, the yield stress is chosen as that causing a permanent strain of 0.002 (strain
offset, Fig. 6.9.)
The yield stress measures the resistance to plastic deformation.
The reason for plastic deformation, in normal materials, is not that the atomic bond is
stretched beyond repair, but the motion of dislocations, which involves breaking and
Plastic deformation is caused by the motion of dislocations.
Tensile strength. When stress continues in the plastic regime, the stress-strain passes
through a maximum, called the tensile strength (s ) , TSd then falls as the material starts
to develop a neck and it finally breaks at the fracture point (Fig. 6.10).
Note that it is called strength, not stress, but the units are the same, MPa. For structural applications, the yield stress is usually a more important property than the
tensile strength, since once the it is passed, the structure has deformed beyond acceptable
Ductility. The ability to deform before braking. It is the opposite of brittleness. Ductility
can be given either as percent maximum elongation e maxor maximum area reduction.
%EL = e maxx 100 %
%AR = (A - A0)/Af 0
These are measured after fracture (repositioning the two pieces back together).
Resilience. Capacity to absorb energy elastically. The energy per unit volume is the
area under the strain-stress curve in the elastic region.
Toughness. Ability to absorb energy up to fracture. The energy per unit volume is the total
area under the strain-stress curve. It is measured by an impact test (Ch. 8).
7. True Stress and Strain
When one applies a constant tensile force the material will break after reaching the tensile
strength. The material starts necking (the transverse area decreases) but the stress cannot
increase beyond s TSThe ratio of the force to the initial area, what we normally do, is called
the engineering stress. If the ratio is to the actual area (that changes with stress) one
obtains the true stress.
8. Elastic Recovery During Plastic Deformation
If a material is taken beyond the yield point (it is deformed plastically) and the stress is then
released, the material ends up with a permanent strain. If the stress is reapplied, the
material again responds elastically at the beginning up to a new yield point that is higher
than the original yield point (strain hardening, Ch. 7.10). The amount of elastic strain that it
will take before reaching the yield point is called elastic strain recovery (Fig. 6. 16).
9. Compressive, Shear, and Torsional Deformation
Compressive and shear stresses give similar behavior to tensile stresses, but in the case of
compressive stresses there is no maximum in the s-e curve, since no necking occurs.
Hardness is the resistance to plastic deformation (e.g., a local dent or scratch). Thus, it is a
measure of plastic deformation, as is the tensile strength, so they are well correlated.
Historically, it was measured on an empirically scale, determined by the ability of a material
to scratch another, diamond being the hardest and talc the softer. Now we use standard
tests, where a ball, or point is pressed into a material and the size of the dent is measured.
There are a few different hardness tests: Rockwell, Brinell, Vickers, etc. They are popular
because they are easy and non-destructive (except for the small dent).
11. Variability of Material Properties
Tests do not produce exactly the same result because of variations in the test equipment,
procedures, operator bias, specimen fabrication, etc. But, even if all those parameters are
controlled within strict limits, a variation remains in the materials, due to uncontrolled
variations during fabrication, non homogenous composition and structure, etc. The
measured mechanical properties will show scatter, which is often distributed in a Gaussian curve (bell-shaped), that is characterized by the mean value and the standard deviation
12. Design/Safety Factors
To take into account variability of properties, designers use, instead of an average value of,
say, the tensile strength, the probability that the yield strength is above the minimum value
tolerable. This leads to the use of a safety factor N > 1 (typ. 1.2 - 4). Thus, a working value
for the tensile strength would be sW= s TS/ N.
Not tested: true stress-true stain relationships, details of the different types of hardness tests, but should
know that hardness for a given material correlates with tensile strength. Variability of material properties
Chapter 7. DISLOCATIONS AND STRENGTHENING MECHANISM
The key idea of the chapter is that plastic deformation is due to the motion of a large
number of dislocations. The motion is called slip. Thus, the strength (resistance to
deformation) can be improved by putting obstacles to slip.
2. Basic Concepts
Dislocations can be edge dislocations, screw dislocations and exist in combination of the two
(Ch. 4.4). Their motion (slip) occurs by sequential bond breaking and bond reforming (Fig.
7.1). The number of dislocations per unit volume is the dislocation density, in a plane they
are measured per unit area.
3. Characteristics of Dislocations
There is strain around a dislocation which influences how they interact with other
dislocations, impurities, etc. There is compression near the extra plane (higher atomic
density) and tension following the dislocation line (Fig. 7.4)
Dislocations interact among themselves (Fig. 7.5). When they are in the same plane, they
repel if they have the same sign and annihilate if they have opposite signs (leaving behind a
perfect crystal). In general, when dislocations are close and their strain fields add to a larger
value, they repel, because being close increases the potential energy (it takes energy to
strain a region of the material).
The number of dislocations increases dramatically during plastic deformation. Dislocations
spawn from existing dislocations, and from defects, grain boundaries and surface
4. Slip Systems
In single crystals there are preferred planes where dislocations move (slip planes). There
they do not move in any direction, but in preferred crystallographic directions (slip
direction). The set of slip planes and directions constitute slip systems.
The slip planes are those of highest packing density. How do we explain this? Since the
distance between atoms is shorter than the average, the distance perpendicular to the plane
has to be longer than average. Being relatively far apart, the atoms can move more easily
with respect to the atoms of the adjacent plane. (We did not discuss direction and plane
nomenclature for slip systems.)
BCC and FCC crystals have more slip systems, that is more ways for dislocation to
propagate. Thus, those crystals are more ductile than HCP crystals (HCP crystals are more
brittle). 5. Slip in Single Crystals
A tensile stress s will have components in any plane that is not perpendicular to the stress. These
components are resolved shear stresses. Their magnitude depends on orientation (see Fig. 7.7).
tR= s cos f cos l
If the shear stress reaches the critical resolved shear stress t CRSS, slip (plastic deformation) can start. The
stress needed is:
sy= t CRSS /cos f cos l) max
at the angles at which t CRSSis a maximum. The minimum stress needed for yielding is when f = l = 45
degrees: s = 2t . Thus, dislocations will occur first at slip planes oriented close to this angle with respect
to the applied stress (Figs. 7.8 and 7.9).
6. Plastic Deformation of Polycrystalline Materials
Slip directions vary from crystal to crystal. When plastic deformation occurs in a grain, it will
be constrained by its neighbors which may be less favorably oriented. As a result,
polycrystalline metals are stronger than single crystals (the exception is the perfect single
crystal, as in whiskers.)
7. Deformation by Twinning
This topic is not included.
Mechanisms of Strengthening in Metals
General principles. Ability to deform plastically depends on ability of dislocations to move.
Strengthening consists in hindering dislocation motion. We discuss the methods of grain-size
reduction, solid-solution alloying and strain hardening. These are for single-phase metals.
We discuss others when treating alloys. Ordinarily, strengthening reduces ductility.
8. Strengthening by Grain Size Reduction
This is based on the fact that it is difficult for a dislocation to pass into another grain,
especially if it is very misaligned. Atomic disorder at the boundary causes discontinuity in
slip planes. For high-angle grain boundaries, stress at end of slip plane may trigger new
dislocations in adjacent grains. Small angle grain boundaries are not effective in blocking
The finer the grains, the larger the area of grain boundaries that impedes dislocation motion.
Grain-size reduction usually improves toughness as well. Usually, the yield strength varies
with grain size d according to:
sy= s 0 k / y
Grain size can be controlled by the rate of solidification and by plastic deformation.
9. Solid-Solution Strengthening
Adding another element that goes into interstitial or substitutional positions in a solution
increases strength. The impurity atoms cause lattice strain (Figs. 7.17 and 7.18) which can
"anchor" dislocations. This occurs when the strain caused by the alloying element
compensates that of the dislocation, thus achieving a state of low potential energy. It costs
strain energy for the dislocation to move away from this state (which is like a potential well).
The scarcity of energy at low temperatures is why slip is hindered. Pure metals are almost always softer than their alloys.
10. Strain Hardening
Ductile metals become stronger when they are deformed plastically at temperatures well
below the melting point (cold working). (This is different from hot working is the shaping
of materials at high temperatures where large deformation is possible.) Strain hardening
(work hardening) is the reason for the elastic recovery discussed in Ch. 6.8.
The reason for strain hardening is that the dislocation density increases with plastic
deformation (cold work) due to multiplication. The average distance between dislocations
then decreases and dislocations start blocking the motion of each one.
The measure of strain hardening is the percent cold work (%CW), given by the relative
reduction of the original area, 0 to the final value d :
%CW = 100 (A –A )/A
0 d 0
Recovery, recrystallization and Grain Growth
Plastic deformation causes 1) change in grain size, 2) strain hardening, 3) increase in the
dislocation density. Restoration to the state before cold-work is done by heating through two
processes: recovery and recrystallization. These may be followed by grain growth.
Heating à increased diffusion à enhanced dislocation motion à relieves internal strain energy
and reduces the number of dislocation. The electrical and thermal conductivity are restored
to the values existing before cold working.
Strained grains of cold-worked metal are replaced, upon heating, by more regularly-spaced
grains. This occurs through short-range diffusion enabled by the high temperature. Since
recrystallization occurs by diffusion, the important parameters are both temperature and
The material becomes softer, weaker, but more ductile (Fig. 7.22).
Recrystallization temperature: is that at which the process is complete in one hour. It is
typically 1/3 to 1/2 of the melting temperature. It falls as the %CW is increased. Below a
"critical deformation", recrystallization does not occur.
13. Grain Growth
The growth of grain size with temperature can occur in all polycrystalline materials. It occurs by migration of
atoms at grain boundaries by diffusion, thus grain growth is faster at higher temperatures. The "driving
force" is the reduction of energy, which is proportional to the total area. Big grains grow at the expense of
the small ones.
Chapter 8. FAILURE
Failure of materials may have huge costs. Causes included improper materials selection or
processing, the improper design of components, and improper use. 2. Fundamentals of Fracture
Fracture is a form of failure where the material separates in pieces due to stress, at temperatures below the
melting point. The fracture is termed ductile or brittle depending on whether the elongation is large or small.
Steps in fracture (response to stress):
• track formation
• track propagation
Ductile vs. brittle fracture
deformation extensive little
track propagation slow, needs stress fast
type of materials most metals (not too cold) ceramics, ice, cold metals
warning permanent elongation none
strain energy higher lower
fractured surface rough smoother
necking yes no
• Ductile Fracture
Stages of ductile fracture
• Initial necking
• small cavity formation (microvoids)
• void growth (elipsoid) by coalescence into a crack
• fast crack propagation around neck. Shear strain at 45 o
• final shear fracture (cup and cone)
The interior surface is fibrous, irregular, which signify plastic deformation.
• Brittle Fracture
There is no appreciable deformation, and crack propagation is very fast. In most brittle materials, crack
propagation (by bond breaking) is along specific crystallographic planes (cleavage planes). This type of
fracture is transgranular (through grains) producing grainy texture (or faceted texture) when cleavage
direction changes from grain to grain. In some materials, fracture is intergranular.
5. Principles of Fracture Mechanics
Fracture occurs due to stress concentration at flaws, like surface scratches, voids, etc. If a is
the length of the void and r the radius of curvature, the enhanced stress near the flaw is:
sm» 2 s 0a/r) 1/2 where s i0 the applied macroscopic stress. Note that a is 1/2 the length of the flaw, not the
full length for an internal flaw, but the full length for a surface flaw. The stress concentration
K t s /m 0 » (a/r)
Because of this enhancement, flaws with small radius of curvature are called stress raisers.
6. Impact Fracture Testing
Normalized tests, like the Charpy and Izod tests measure the impact energy required to fracture a notched
specimen with a hammer mounted on a pendulum. The energy is measured by the change in potential
energy (height) of the pendulum. This energy is called notch toughness.
Ductile to brittle transition occurs in materials when the temperature is dropped below a transition
temperature. Alloying usually increases the ductile-brittle transition temperature (Fig. 8.19.) For ceramics,
this type of transition occurs at much higher temperatures than for metals.
Fatigue is the catastrophic failure due to dynamic (fluctuating) stresses. It can happen in bridges, airplanes,
machine components, etc. The characteristics are:
• long period of cyclic strain
• the most usual (90%) of metallic failures (happens also in ceramics and polymers)
• is brittle-like even in ductile metals, with little plastic deformation
• it occurs in stages involving the initiation and propagation of cracks.
• Cyclic Stresses
These are characterized by maximum, minimum and mean stress, the stress amplitude, and
the stress ratio (Fig. 8.20).
• The S—N Curve
S—N curves (stress-number of cycles to failure) are obtained using apparatus like the one
shown in Fig. 8.21. Different types of S—N curves are shown in Fig. 8.22.
Fatigue limit (endurance limit) occurs for some materials (like some ferrous and Ti allows).
In this case, the S—N curve becomes horizontal at large N . This means that there is a
maximum stress amplitude (the fatigue limit) below which the material never fails, no
matter how large the number of cycles is.
For other materials (e.g., non-ferrous) the S—N curve continues to fall with N.
Failure by fatigue shows substantial variability (Fig. 8.23).
Failure at low loads is in the elastic strain regime, requires a large number of cycles (typ.
4 5 4 5
10 to 10 ). At high loads (plastic regime), one has low-cycle fatigue (N < 10 - 10 cycles).
• Crack Initiation and Propagation
Stages is fatigue failure:
I. crack initiation at high stress points (stress raisers)
II. propagation (incremental in each cycle)
III. final failure by fracture N finalN initiatiopropagation
Stage I - propagation
• along crystallographic planes of high shear stress
• flat and featureless fatigue surface
Stage II - propagation
crack propagates by repetive plastic blunting and sharpening of the crack tip. (Fig. 8.25.)
• . Crack Propagation Rate (not covered)
• . Factors That Affect Fatigue Life
• Mean stress (lower fatigue life with increasing smean.
• Surface defects (scratches, sharp transitions and edges). Solution:
• polish to remove machining flaws
• add residual compressive stress (e.g., by shot peening.)
• case harden, by carburizing, nitriding (exposing to appropriate gas at high temperature)
• . Environmental Effects
• Thermal cycling causes expansion and contraction, hence thermal stress, if component is restrained.
o eliminate restraint by design
o use materials with low thermal expansion coefficients.
• Corrosion fatigue. Chemical reactions induced pits which act as stress raisers. Corrosion also
enhances crack propagation. Solutions:
o decrease corrosiveness of medium, if possible.
o add protective surface coating.
o add residual compressive stresses.
Creep is the time-varying plastic deformation of a material stressed at high temperatures. Examples:
turbine blades, steam generators. Keys are the time dependence of the strain and the high temperature.
• . Generalized Creep Behavior
At a constant stress, the strain increases initially fast with time (primary or transient deformation), then
increases more slowly in the secondary region at a steady rate (creep rate). Finally the strain increases fast
and leads to failure in the tertiary region. Characteristics:
• Creep rate: de/dt
• Time to failure.
• . Stress and Temperature Effects
Creep becomes more pronounced at higher temperatures (Fig. 8.37). There is essentially no
creep at temperatures below 40% of the melting point.
Creep increases at higher applied stresses.
The behavior can be characterized by the following expression, where K, n and Q are c
constants for a given material:
de/dt = K s exp(-Q /Rc)
• . Data Extrapolation Methods (not covered.)
• . Alloys for High-Temperature Use These are needed for turbines in jet engines, hypersonic airplanes, nuclear reactors, etc. The important
factors are a high melting temperature, a high elastic modulus and large grain size (the latter is opposite to
what is desirable in low-temperature materials).
Some creep resistant materials are stainless steels, refractory metal alloys (containing elements of high
melting point, like Nb, Mo, W, Ta), and superalloys (based on Co, Ni, Fe.)
Chapter-9: PHASE DIAGRAMS
Component: pure metal or compound (e.g., Cu, Zn in Cu-Zn alloy, sugar, water, in a syrup.)
Solvent: host or major component in solution.
Solute: dissolved, minor component in solution.
System: set of possible alloys from same component (e.g., iron-carbon system.)
Solubility Limit: Maximum solute concentration that can be dissolved at a given temperature.
Phase: part with homogeneous physical and chemical characteristics
9.2 Solubility Limit
Effect of temperature on solubility limit. Maximum content: saturation. Exceeding maximum content
(like when cooling) leads to precipitation.
One-phase systems are homogeneous. Systems with two or more phases are heterogeneous, or
mixtures. This is the case of most metallic alloys, but also happens in ceramics and polymers.
A two-component alloy is called binary. One with three components, ternary.
The properties of an alloy do not depend only on concentration of the phases but how they are arranged
structurally at the microscopy level. Thus, the microstructure is specified by the number of phases, their
proportions, and their arrangement in space.
A binary alloy may be
a. a single solid solution
b. two separated, essentially pure components.
c. two separated solid solutions.
d. a chemical compound, together with a solid solution.
The way to tell is to cut the material, polish it to a mirror finish, etch it a weak acid (components etch at a
different rate) and observe the surface under a microscope.
9.5 Phase Equilibria
Equilibrium is the state of minimum energy. It is achieved given sufficient time. But the time to
achieve equilibrium may be so long (the kinetics is so slow) that a state that is not at an energy
minimum may have a long life and appear to be stable. This is called a metastable state. A less strict, operational, definition of equilibrium is that of a system that does not change with time
Equilibrium Phase Diagrams
Give the relationship of composition of a solution as a function of temperatures and the quantities of
phases in equilibrium. These diagrams do not indicate the dynamics when one phase transforms into
another. Sometimes diagrams are given with pressure as one of the variables. In the phase
diagrams we will discuss, pressure is assumed to be constant at one atmosphere.
9.6 Binary Isomorphous Systems
This very simple case is one complete liquid and solid solubility, an isomorphous system. The example is the
Cu-Ni alloy of Fig. 9.2a. The complete solubility occurs because both Cu and Ni have the same crystal
structure (FCC), near the same radii, electronegativity and valence.
The liquidus line separates the liquid phase from solid or solid + liquid phases. That is, the solution is liquid
above the liquidus line.
The solidus line is that below which the solution is completely solid (does not contain a liquid phase.)
Interpretation of phase diagrams
Concentrations: Tie-line method
a. locate composition and temperature in diagram
b. In two phase region draw tie line or isotherm
c. note intersection with phase boundaries. Read compositions.
Fractions: lever rule
a. construct tie line (isotherm)
b. obtain ratios of line segments lengths.
Note: the fractions are inversely proportional to the length to the boundary for the particular phase. If the
point in the diagram is close to the phase line, the fraction of that phase is large.
Development of microstructure in isomorphous alloys
a) Equilibrium cooling
Solidification in the solid + liquid phase occurs gradually upon cooling from the liquidus line. The
composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line
method.) Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.
b) Non-equilibrium cooling
Solidification in the solid + liquid phase also occurs gradually. The composition of the liquid phase evolves
by diffusion, following the equilibrium values that can be derived from the tie-line method. However,
diffusion in the solid state is very slow. Hence, the new layers that solidify on top of the grains have the
equilibrium composition at that temperature but once they are solid their composition does not change. This
lead to the formation of layered (cored) grains (Fig. 9.14) and to the invalidity of the tie-line method to
determine the composition of the solid phase (it still works for the liquid phase, where diffusion is fast.)
9.7 Binary Eutectic Systems
Interpretation: Obtain phases present, concentration of phases and their fraction (%).
Solvus line: limit of solubility Eutectic or invariant point. Liquid and two solid phases exist in equilibrium at the eutectic composition and
the eutectic temperature.
• the melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt
• At most two phases can be in equilibrium within a phase field.
• Single-phase regions are separated by 2-phase regions.
Development of microstructure in eutectic alloys
Case of lead-tin alloys, figures 9.9–9.14. A layered, eutectic structure develops when cooling below the
eutectic temperature. Alloys which are to the left of the eutectic concentration (hipoeutectic) or to the right
(hypereutectic) form a proeutectic phase before reaching the eutectic temperature, while in the solid +
liquid region. The eutectic structure then adds when the remaining liquid is solidified when cooling further.
The eutectic microstructure is lamellar (layered) due to the reduced diffusion distances in the solid state.
To obtain the concentration of the eutectic microstructure in the final solid solution, one draws a vertical line
at the eutectic concentration and applies the lever rule treating the eutectic as a separate phase (Fig. 9.16).
9.8 Equilibrium Diagrams Having Intermediate Phases or Compounds
A terminal phase or terminal solution is one that exists in the extremes of concentration (0 and
100%) of the phase diagram. One that exists in the middle, separated from the extremes, is called
an intermediate phase or solid solution.
An important phase is the intermetallic compound, that has a precise chemical compositions. When
using the lever rules, intermetallic compounds are treated like any other phase, except they appear
not as a wide region but as a vertical line.
9.9 Eutectoid and Peritectic Reactions
The eutectoid (eutectic-like) reaction is similar to the eutectic reaction but occurs from one solid
phase to two new solid phases. It also shows as V on top of a horizontal line in the phase diagram.
There are associated eutectoid temperature (or temperature), eutectoid phase, eutectoid and
Solid Phase 1 à Solid Phase 2 + Solid Phase 3
The peritectic reaction also involves three solid in equilibrium, the transition is from a solid + liquid
phase to a different solid phase when cooling. The inverse reaction occurs when heating.
Solid Phase 1 + liquid à Solid Phase 2
9.10 Congruent Phase Transformations
Another classification scheme. Congruent transformation is one where there is no change in
composition, like allotropic transformations (e.g., a-Fe to g-Fe) or melting transitions in pure solids.
9.13 The Iron–Iron Carbide (Fe–Fe C) Pha3e Diagram
This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low
carbon concentrations by assuming it is the Fe—Fe C di3gram. Concentrations are usually given in weight
percent. The possible phases are:
• a-ferrite (BCC) Fe-C solution
• g-austenite (FCC) Fe-C solution
• d-ferrite (BCC) Fe-C solution • liquid Fe-C solution
• Fe 3 (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in a- ferrite is 0.022 wt%. d-ferrite is only stable at high temperatures. It is not
important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the
eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable,
decomposing into a-Fe and C when heated for several years between 650 and 770 C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with intermediate properties.
(Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)
9.14 Development of Microstructures in Iron—Carbon Alloys
The eutectoid composition of austenite is 0.76 wt %. When it cools slowly it forms perlite, a lamellar
or layered structure of two phases: a-ferrite and cementite (Fe C3.
Hypoeutectoid alloys contain proeutectoid ferrite plus the eutectoid perlite. Hypereutectoid alloys
contain proeutectoid cementite plus perlite.
Since reactions below the eutectoid temperature are in the solid phase, the equilibrium is not
achieved by usual cooling from austenite. The new microstructures that form are discussed in Ch.
9.15 The Influence of Other Alloying Elements
As mentioned in section 7.9, alloying strengthens metals by hindering the motion of dislocations. Thus, the
strength of Fe–C alloys increase with C content and also with the addition of other elements.
Chapter-10: Phase Transformations in Metals
The goal is to obtain specific microstructures that will improve the mechanical properties of a metal, in
addition to grain-size refinement, solid-solution strengthening, and strain-hardening.
10.2 Basic Concepts
Phase transformations that involve a change in the microstructure can occur through:
• Maintaining the type and number of phases (e.g., solidification of a pure metal, allotropic
transformation, recrystallization, grain growth.
• Alteration of phase composition (e.g., eutectoid reactions, see 10.5)
• Production of metastable phases (e.g., martensitic transformation, see 10.5)
10.3 The Kinetics of Solid-State Reactions
Change in composition implies atomic rearrangement, which requires diffusion. Atoms are displaced by
random walk. The displacement of a given atom, d, is not linear in time t (as would be for a straight
trajectory) but is proportional to the square root of time, due to the tortuous path: d = c(Dt) 1/2where c is a
constant and D the diffusion constant. This time-dependence of the rate at which the reaction (phase
transformation) occurs is what is meant by the term reaction kinetics. D is called a constant because it does not depend on time, but it depends on temperature as we have seen
in Ch. 5. Diffusion occurs faster at high temperatures.
Phase transformation requires two processes: nucleation and growth. Nucleation involves the formation of
very small particles, or nuclei (e.g., grain boundaries, defects). This is similar to rain happening when water
molecules condensed around dust particles. During growth, the nuclei grow in size at the expense of the
The kinetic behavior often has the S-shape form of Fig. 10.1, when plotting percent of material transformed
vs. the logarithm of time. The nucleation phase is seen as an incubation period, where nothing seems to
happen. Usually the transformation rate has the form r = A e -Q/RT(similar to the temperature dependence of
the diffusion constant), in which case it is said to be thermally activated.
10.4 Multiphase Transformations
To describe phase transformations that occur during cooling, equilibrium phase diagrams are inadequate if
the transformation rate is slow compared to the cooling rate. This is usually the case in practice, so that
equilibrium microstructures are seldom obtained. This means that the transformations are delayed (e.g.,
case of supercooling), and metastable states are formed. We then need to know the effect of time on phase
Microstructural and Property Changes in Fe-C Alloys
10.5 Isothermal Transformation Diagrams
We use as an example the cooling of an eutectoid alloy (0.76 wt% C) from the austenite (g- phase) to
pearlite, that contains ferrite (a) plus cementite (Fe C3or iron carbide). When cooling proceeds below the
eutectoid temperature (727 C) nucleation of pearlite starts. The S-shaped curves (fraction of pearlite vs.
log. time, fig. 10.3) are displaced to longer times at higher temperatures showing that the transformation is
dominated by nucleation (the nucleation period is longer at higher temperatures) and not by diffusion
(which occurs faster at higher temperatures).
The family of S-shaped curves at different temperatures can be used to construct the TTT (Time-
Temperature-Transformation) diagrams (e.g., fig. 10.4.) For these diagrams to apply, one needs to cool the
material quickly to a given temperature T bofore the transformation occurs, and keep it at that temperature
over time. The horizontal line that indicates constant temperature T inteocepts the TTT curves on the left
(beginning of the transformation) and the right (end of the transformation); thus one can read from the
diagrams when the transformation occurs. The formation of pearlite shown in fig. 10.4 also indicates that
the transformation occurs sooner at low temperatures, which is an indication that it is controlled by the rate
of nucleation. At low temperatures, nucleation occurs fast and grain growth is reduced (since it occurs by
diffusion, which is hindered at low temperatures). This reduced grain growth leads to fine-grained
microstructure (fine pearlite). At higher temperatures, diffusion allows for larger grain growth, thus leading
to coarse pearlite.
At lower temperatures nucleation starts to become slower, and a new phase is formed, bainite. Since
diffusion is low at low temperatures, this phase has a very fine (microscopic) microstructure.
Spheroidite is a coarse phase that forms at temperatures close to the eutectoid temperature. The relatively
high temperatures caused a slow nucleation but enhances the growth of the nuclei leading to large grains.
A very important structure is martensite, which forms when cooling austenite very fast (quenching) to below
a maximum temperature that is required for the transformation. It forms nearly instantaneously when the
required low temperature is reached; since no thermal activation is needed, this is called an athermal
transformation. Martensite is a different phase, a body-centered tetragonal (BCT) structure with interstitial C
atoms. Martensite is metastable and decomposes into ferrite and pearlite but this is extremely slow (and not
noticeable) at room temperature.
In the examples, we used an eutectoid composition. For hypo- and hypereutectoid alloys, the analysis is the
same, but the proeutectoid phase that forms before cooling through the eutectoid temperature is also part
of the final microstructure. 10.6 Continuous Cooling Transformation Diagrams - not covered
10.7 Mechanical Behavior of Fe-C Alloys
The strength and hardness of the different microstructures is inversely related to the size of the
microstructures. Thus, spheroidite is softest, fine pearlite is stronger than coarse pearlite, bainite