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Construction Materials
LECTURE 01 – Intro to material science
Civil Engineering and material science
1. Civil Engineer:
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designs and maintains roads, bridges dams and similar structures.
Design MATERIALS, structures, machines and systems while considering
limitations imposed by practicality, safety and cost.
2. Material Science: investigating the relationships that exist between material
structures and properties of materials.
3. Material Engineering: creates systems and structures based on the Material
Science.
4. Why study material science?
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Learn to describe materials behaviour accurately and objectively
These behaviours are dictated by chemical and physical properties of materials.
Studying materials helps understand fundamentals and enables us to design and
improve durable (construction) materials
5. Engineers job
Make sure the structure:
- functions properly
- is durable against various external influences
- is economical & sustainable
Material selection
1. Properties of materials (zoek voorbeelden!)
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physical
thermal
mechanical
chemical
optical
electrical
2. Material selection
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Use the right material for the job. The material that is most economical and the
‘Greenest’ when life usage is considered
Understand the relation between properties, structure, processing and
performance.
Recognize new design opportunities offered by Materials Selection.
3. Economy
Choose the cheap & available materials, consider:
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Initial cost
Useful life
Frequency of maintenance
Cost of maintenance
Levels and units
1. Structural levels
a. Subatomic level:
electronic structure which defines interatomic
bonding. (binnen het atom)
arrangement of atoms, crystal structures
(atomen onderling)
arrangement of small grains that can only be
seen under a microscope.
anything you can see with your eyes.
b. Atomic level:
c. Microscopic level:
d. Macroscopic level:
2. Length scales
a.
b.
c.
d.
Angstrom
Nanometer
Micrometer
Millimeter
= 1Å (not SI)
= 1nm
= 1μm
= 1mm
= 10-10 m
= 10-9 m
= 10-6 m
= 10-3 m
3. Important derived SI units
Name
Newton
Pascal
Joule
Watt
Symbol
N
Pa
J
W
Quantity
Force, weight
Pressure, stress
Energy, work
power
In other SI units In SI base units
kg*m*s-2
N/m2
kg*m-1*s-1
N*m
kg*m2*s-2
J/s
kg*m2*s-3
LECTURE 02 – Atoms, Crystals and Dislocations
The Performance of large structures depends upon chemical and physical events at a
molecular scale.
Material Science is Interdisciplinary, since we need to jump back- and forwards from
chemistry to engineering.
Atoms, Ions and Interatomic bonds
1. Atoms
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The nucleus: Protons and Neutrons
Protons are positively charged (+1) and neutrons are uncharged. Number of
protons of element are constant, number of neutrons may vary.
Electrons
Electrons are negatively charged (-1), a neutral atom has an equal amount of
protons and electrons.
Atomic number and mass
o Atomic number: number of protons
o Atomic mass:
sum of the masses of the protons and neutrons
o Isotopes:
atoms of 1 element with different numbers of neutrons
Electron orbitals
o There are several orbital spheres around a nucleus. Each sphere can
contain a certain number of electrons. A sphere needs to be filled in order
for the atom to be stable
o Dormitory Analogy:
the building can
only be stable when all double rooms are
occupied up to any floor. If the highest
floor is half occupied than the floor
should be completely filled OR entirely
emptied in order to ensure the stability.
o Number of electrons Natrium is
1s22s22p63s1 is 11 electrons spread
over three spheres.
Atomic radius
o The radius of an atom is the distance from the nucleus to the outermost
electrons.
o There is a general decrease in radii from left to right in de PT, and an
increase in radii down a group.
2. Ions
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Atom to Ion
Atoms gain or lose electrons to reach a lower energy level. The atom is no longer
neutral but charged and is now called an ION.
Ionization energy (I.E.)
The energy needed to remove an electron from a
gaseous atom to form a gaseous ion. M(g) ->
M+(g) + eo The energy decreases to the left end down
in the PT. The metallic properties increase.
o Metals lose electrons relatively easily to
form cations in compounds  high IE!
Ionic radii
o Positive ions are smaller than the original neutral atom (less electrons).
o Negative ions are larger than the original neutral atom (more electrons).
3. Chemical Bonds
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Strong Bonds (Inter-atomic)
o Metallic bonds: metallic atoms (strong tendencies to lose
electrons) pack together as cations where the electrons are shared
and dispersed freely among the ions. (e.g. iron, gold)
o Covalent Bonds: elements that do not gain/lose electrons but
form compounds by sharing electrons. (e.g. diamond, water)
o Ionic Bonds:
Simplest form of chemical bonds, where ions of
opposite charge are attracted to each other and give/take
electron(s) to form a bond. 90% of all minerals are ionic
compounds. (e.g. NaCl)
Weak Bonds (inter-molecular)
Van der Waals bonds
o bonding caused by the Coulombic attraction
between positive and negative ends of dipole
molecules.
o Intermolecular attractive forces
 Hydrogen bond:
between Hydrogen and N, O or F

Dipole-dipole forces

London dispersion forces (e.g. 2 hydrogen molecules)
Electronegativity (EN)
The power of an atom in a molecule to attract electrons to itself.
Chemical Polarity
separation of electric charge leading to a molecule or its chemical
groups having an electric dipole or multipole moment.
EN and bond type
Electronegativity difference = ΔEN
ΔEN < 0,5
0,5 < ΔEN < 1,6
1,6 < ΔEN < 2,0
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2,0 < ΔEN
Fraction covalent
Non-polar covalent
Polar covalent
When metal involved: Ionic
Only non-metals: Polar covalent
Ionic
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Ceramic and semiconducting compounds (combination of metallic and nonmetallic elements)  MIXTURE of Covalent and Ionic bonds!
The fraction that is covalent can be estimated
Fraction covalent = exp(-0,25*ΔEN2) * 100%
Bonding forces and energies
o Erepulsion = B/rn
o Eattraction = ƙ*(qQ/r)
r= interatomic spacing, q and Q are atomic charges
The attractive force FA depends on the bonding that exists
between two atoms. Repulsive forces arise from
interactions between negatively charged electron clouds
for two atoms and are only important for small r as the
outer electron shells begin to overlap.
Relationship with E-modulus
o The force-distance curve for two materials 
showing the relationship between atomic bonding
and the modulus of elasticity.
o Steeo dF/dA slope gives a high modulus.
o Coulomb attraction force Fe = (kq1q2)/r2
Thermal expansion coefficient
The deeper the energy curve, the higher the melting point.
o Asymmetric curve:
 the average position in which the atom
sits shifts with temperature.
 Bond lengths therefore change (usually
get bigger for increased T)
 Thermal expansion coefficient is nonzero.
o Symmetric curve:
 No shift in the average position of the atom
 The coefficient of thermal expension is
negligible for symmetric energy wells.
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Variations in radius
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Binding Energy
Binding energies for the four bonding mechanisms
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Bond
Ionic
Covalent
Metallic
Van der Waals
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Binding Energy (kcal/mol)
150-370
125-300
25-200
<10
Types of Bonding
Atomic Arrangements
1. Orders
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No order (e.g. in monoatomic gasses, Ar)  a
Short Range Order (SRO) (e.g. silicate glass,
water vapour)  b and c
Long Range Order (LRO) (e.g. metals, alloys,
minerals)  d
2. Amorphous materials (non-crystal)
- Any material that exhibits only a short-range
order of atoms or ions is an amorphous
material.
3. Lattice and Unit Cells
- Lattice is a collection of points called lattice points that are arranged in a periodic
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pattern so that the surroundings of each point in the lattice are identical.
Arrangements of atoms or ions
The unit cell is the subdivision of a lattice that still retains the overall
characteristics of the entire lattice
4. Crystalline material
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- A Crystalline material is one in which the atoms are situated in a repeating or
periodic array over large atomic distances.
When becoming a solid, the atoms will position themselves in a repetitive threedimensional pattern (all atoms bonded).
- Metallic crystal structures
Three crystal structures for most of the common metals
R=atomic radius
o Face-Centered Cubic (FCC)  atom in each corner + on each face
𝑎 = 2𝑅√2
o Body-Centered Cubic (BCC)  atom in each corner + one in the middle
𝑎=
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4𝑅
√3
o Hexagonal Clos-Packed (HCP)  c=height of the hexagon
𝑐/𝑎 = 1.633
Atomic packing factor
Two important characteristics of a crystal structure.
o Coordination number
 For metals, each atom has the same number of nearest neighbour
or touching atoms.
 For face-centered cubics the coordination number is 12
o Atomic packing factor (APF)
𝐴𝑃𝐹 =
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𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑖𝑛 𝑎 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙
𝑡𝑜𝑡𝑎𝑙 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 𝑣𝑜𝑙𝑢𝑚𝑒
Density computation
n = number of atoms associated with each unit cell
A = atomic weight
VC = volume of the unit cell
NA = Avogadro’s number (6.022 x 1023 atoms/mol)
5. Crystallography
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Crystallography is the science of the arrangement of atoms in solids.
Crystallography history
o Robert Hooke (1660)
 Research on how to stack cannonballs
 Crystals must have spheres packed in regular order
o Nicolas Steno (1669)
 Measured quartz crystals
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 All crystals have the same angle between same faces
o Christiaan Huygens (1669)
 Measured calcite crystals
 Drawings of atomic packing and bulk shape
o René Just Haüy (1781)
 Mathematically proved that there are only 7 distinct space-filling
volume elements.
o Auguste Bravais (1848)
 Mathematically proved that there are only 14 distinct ways to
arrange points in space.
 14 Bravais lattices
- Filling shapes
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o Perfect area filling shapes (square, rectangle, triangle, etc.)
o Imperfect area filling shapes (cirkel, oval, etc.)
Seven crystal systems
o Cubic
a=b=c
e.g. Halite
o Hexagonal
a=b≠c
e.g. Beryl
o Tetragonal
a=b≠c rectangular
e.g. Zircon
o Rhombohedral a=b=c tilted cubic
e.g. Calcite
o Orthorhombic
a≠b≠c rectangular
e.g. Anhydrite
o Monoclinic
a≠b≠c tilted Orthorhombic
e.g. Augite
o Triclinic
a≠b≠c tilted Monoclinic
e.g. Feldspar
14 Bravais lattices
Set of Points in Space
Crystallographic parameters
o Coordinates of Points
Certain points (such as atom positions) can be located in
the lattice by constructing the right-handed coordinate
system.
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o A crystallographic direction
defined as a line between two points (a vector).
 Crystallographic planes are specified by three
Miller indices as (hkl). These are a method of
describing the orientation of a plane or set of
planes within a lattice in relation to the unit cell.
They were developed by William Hallowes Miller.
 Defining the vector:
1. If the plane passes through the origin, another parallel
plane must be constructed within the unit cell OR a new
origin must be established at the corner of another unit
cell.
2. The crystallographic plane either intersects or parallels
each of the three axes. The length of planar intercept
for each axis is determined in terms of lattice
parameters a, b and c.
3. The reciprocals of these numbers are taken. A plane
that parallels an axis may be considered to have an
infinite intercept and a zero index.
4. These numbers are changed to the set of smallest
integers by multiplication or division by a common
factor.
5. The integer indices are enclosed within parentheses
(hkl)
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Linear and planar densities
o Linear density (LD) is defined as the number of atoms per unit length
whose centers lie on the direction vector for a specific crystallographic
direction.
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𝐿𝐷 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑐𝑒𝑛𝑡𝑒𝑟𝑒𝑑 𝑜𝑛 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑣𝑒𝑐𝑡𝑜𝑟
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑣𝑒𝑐𝑡𝑜𝑟
o Planar density (PD) is taken as the number of atoms per unit area that are
centered on a particular crystallographic plane.
𝑃𝐷 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑐𝑒𝑛𝑡𝑒𝑟𝑒𝑑 𝑜𝑛 𝑎 𝑝𝑙𝑎𝑛𝑒
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑝𝑙𝑎𝑛𝑒
6. X-Ray diffraction
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X-Ray diffraction
helps us to identify materials by computing dhkl which is characteristic for crystals.
o Inter-planar spacing (d): distance between adjacent planes of identical
Miller index (hkl). (a=lattice constant)
𝑎
𝑑ℎ𝑘𝑙 √ℎ2 2 2
+𝑘 +𝑙
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o Bragg’s Law (λ=X-Ray wave length, ϴ=incident beam angle)
𝜆 = 2𝑑ℎ𝑘𝑙 𝑠𝑖𝑛𝛳
X-Ray diffractometer
X-Ray diffractogram
The d-spacing (ds) of each peak is obtained by solution of the Bragg equation for
the appropriate value of λ. Once all d-spacings have been determined, automated
search/match routines compare the ds of the unknown to those of known
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materials.
7. Crystals
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Single crystals
o For a crystalline solid, the periodic and repeated arrangement of atoms is
perfect or extends throughout the entire specimen without interruption.
o All unit cells interlock in the same way and have the same orientation.
o Single crystals exist in nature. They are ordinarily difficult to grow,
because the environment must be carefully controlled.
Polycrystalline materials
o Polycrystalline materials are composed of a collection of many small
crystals or grains.
o Grain boundary is where two grains meet.
Anisotropy
o Different directions in the material have different properties.
o Substances in which measured properties are independent of the
direction of measurement are isotropic.
Imperfections in solids
1. Lattice irregularity
Imperfections are NOT amorphous!
- Point Defects (0-Dimensional)
these defects disrupt the arrangement of the surrounding atoms and create a
strain in the crystal structure.
o Vacancy: an atom disappeared
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o Interstitial atom: an extra atom in the crystal  deforms the crystal 
changes the properties.
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Dislocations (1-Dimensional)
Line imperfections!
o They are introduced typically into the crystal
 During solidification of the material
 When the material is deformed permanently: plastic deformation.
b: Burgers Vector
o Screw dislocation
o The edge dislocation
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o The mixed dislocation
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2-Dimensional Defects
o Grain Boundaries
The planes in between crystals (grains)
 Small grain structure:
 High strength
 High brittleness (immediate failure)
 Large grain structure:
 Low strength
 Low brittleness
 High Ductility
o External Surfaces
The edge (surface) is also an imperfection.
 High energy – ready to react
 Atoms have less neighbours at the surface so they have more
energy. Atoms in the body are far more stable (neighbours all
around) so they are less energetic for reaction.
Significance of dislocations
o Dislocations are most significant in metals and alloys since they
contribute to a mechanism for plastic deformation.
o Plastic deformation is an irreversible deformation. The applied stress
causes dislocation motion that causes permanent deformation.
o Elastic deformation is a temporary change in shape that occurs while a
force or stress remains applied to a material.
Slip
The movement of large numbers of dislocations to produce plastic deformation.
o Atoms slip!
o Dislocation glide!
o Dislocations make slip significantly easier  less force needed
o The slip planes are those of highest packing density  search for plane
with highest density.
Summary – Dislocations
o Defects arise in solids
o The number and type of defects can be varied and controlled
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o Defects affect material properties
o Defects may be desirable or undesirable
LECTURE 03 – Mechanical Properties of Materials
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Mechanics and Chemistry
o Solids are held together by chemical and physical bonds and can be
destroyed, e.g. by mechanical fracture, melting or a chemical attack.
Nature of Material Science
o Describing the behaviour of things accurately and objectively (business of
engineers)
Response of materials to stress
o When solid material is subjected to external loading, it deforms
instantaneously. As long as these stresses are small, the deformation is
reversible.
o There is no truly rigid material, everything gives to some extent.
1. Stress and Strain
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Stress
the relationship between applied load and the cross sectional area of the
material. 𝜎 =
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𝐹
𝐴0
Strain
the ratio between longitudinal deformation to the original length of a material.
𝜖=
𝑙𝑖 −𝑙0
𝑙0
=
∆𝑙
𝑙0
o Strain is unit-less, but meter/meter is often used or strain is expressed as
a percentage (when multiplied by 100)
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Elastic stress-strain diagrams
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2. E-modulus
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Hooke’s law
Young’s modulus
Thomas Young, 1800: if we consider the stresses and strains in the material rather
than the gross deflections of the structure, Hooke’s law can be rewritten: 𝐸 =
𝑠𝑡𝑟𝑒𝑠𝑠
𝑠𝑡𝑟𝑎𝑖𝑛
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= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
o This is called the E-modulus!
Importance of E-modulus
o First, the deflections in a structure when loaded need to be known.
o Secondly, we need to know the E-modulus of various structural materials
so we can calculate their deflections and arrange that the deflections of
different materials in a structure are compatible and share the load in the
way we want them to.
The E-modulus
o The E-modulus is the stress (e.g. in MPa or GPa) needed to double the
length of a specimen, if it did not break first!
o The E-modulus is the stress to produces 100% strain
o Strength ≠ Stiffness
 E-modulus is concerned with how stiff, flexible, springy or floppy a
material is.  related to atomic bonding quality!
 Strength is the stress needed to break a material.  not related to
atomic bond strength!
 Steel is stiff and strong, nylon is flexible (low E) and strong.
E and 𝜎 − 𝜀 diagram
o Linear elastic materials
the slope of the stress-strain diagram
gives the E-modulus. 𝐸 =
𝜎
𝜀
 e.g. steel, carbon fiber, glass.
o Non-linear elastic materials
Hooke’s law does NOT APPLY!
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
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Initial tangent modulus
used for very small stresses and strains (O)
Tangent modulus
Useful if additional strain upon additional stress is of interest.
Difficult to measure correctly. (A)
Secant modulus
The slope of a line connecting the origin with an arbitrary point.
Stress/strain ratio!
Depends on the applied stress. (O-Z)
Chord modulus
The slope of the line between two arbitrary points (X-Y)
E.g. rubber, concrete, cast iron
3. Poisson’s ratio
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μ or v relates the longitudinal elastic deformation
produced by a simple tensile or compressive stress to
the lateral deformation that occurs simultaneously.
𝑣=
-
−𝜀𝑙𝑎𝑡𝑒𝑟𝑎𝑙
𝜀𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙
𝑉1 −𝑉0
𝑉0
(the – indicates contraction)
= 𝜀𝑥 (1 − 2𝑣)
o v < 0.5 tensile stress  Volume increase
o v = 0.33  for most metals
o 0.16 < v < 0.5 for other materials (e.g. v = 0.16  wood, v = 0.50 
elastomer)
4. Plastic deformation
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Plastic strain
o Permanent/plastic deformation in a material (materials don’t go back to
original shape when stress is removed).
Plastic behaviour
o Elastic behaviour ends by fracture or yielding
o Fracture
 Occurs in brittle materials due to highly raised local stresses raised
by flaws and imperfections
 Fracture strength has a high scatter due to random nature of flaw
distribution  size effect is important (the larger the specimen,
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the lower the strength).
Important for materials such as wood and concrete.
o Yielding
 Involves plastic deformation of the materials
 Mostly seen in crystalline or polycrystalline materials, typically in
metals
 = Permanent rearrangement of atoms
 Ductility: yielding enables some strain before fracture
o Yield strength
 When elastic limit is difficult to observe, we define it at the yield
point (typically at the strain of 0.002 or 0.2%).
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Yield strength preferred for design purposes
Little or no plastic deformation preferred  select
material such that design stress is lower than yield
strength.
o Yield mechanism
 Shear stress
𝜏 = 𝜎𝑡𝑒𝑛𝑠𝑖𝑙𝑒 ∗ 𝑐𝑜𝑠𝜆 ∗ 𝑐𝑜𝑠𝜙
 𝜙: Angle between tensile axis and
normal slip plane
 𝜆: the angle between tensile force
and the direction of slip
 𝜆 = 𝜙 = 45°  then 𝜏 is maximum
at 𝜏𝑀𝐴𝑋
𝜎𝑡𝑒𝑛𝑠𝑖𝑙𝑒
2
o Strain hardening
 Strain Hardening: additional stress needed for additional strain
after yielding
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
Occurs because of an increased dislocation density at the grain
boundary
o Grain size VS Strength
 Hall-Petch equation: describes the relation between yield strength
(ơy) and grain size.
𝜎𝑦 = 𝜎0 +
𝑘𝑦
√𝑑
 ơ0 = starting stress for dislocation
movement
 ky = strengthening coefficient
 d = average grain diameter
o Ductile VS Brittle
 Ductility: measure of the degree of
plastic deformation that has been
sustained at fracture
 Brittle: with very little or no plastic
deformation upon fracture
%𝐸𝐿 =
𝑙𝑓 −𝑙0
𝑙0
∗ 100 (percent
elongation %EL is the percentage of
plastic strain at fracture).
o Resilience
 Resilience is the capacity of a material to absorb
energy when it is deformed plastically and then
(upon unloading) to have this energy recovered.
 Modulus of resilience Ur  strain energy per
unit volume required to stress a material from
an unloaded state up to the point of yielding.
1
1
𝜎𝑦
𝜎𝑦2
𝑈𝑟 = 𝜎𝑦 𝜖𝑦 = 𝜎𝑦 ( ) =
2
2
𝐸
2𝐸

The area under the stress-strain curve represents
energy absorption per unit volume (in m3) of
material.
o Toughness
 The ability of a material to absorb energy and plastically deform
before fracturing.
o Engineering stress
 Under tensile loading yielding eventually
creates necking.
 Yielding becomes localized and continuation
of strain creates failure at the necking.
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
M and M’ are the points where necking starts
o Shear stress
 𝜏=

𝐹
𝐴0
F is the load or Force imposed
parallel to the upper and lower
faces with areas of A0.
 The shear strain ϴ is defined as
the tangent of the strain angle u.
o Shear modulus
 Compressive, shear or torsional stresses
also evoke elastic behaviour
 Shear stress and strain are proportional to each other through
𝜏 = 𝐺𝑦
𝑦 = 𝑡𝑎𝑛𝜃
 G is the Shear modulus  the slope of linear elastic region
of the shear stress-strain curve.
 For Isotropic materials, shear and elastic moduli are related to
each other and to Poisson’s ratio according to 𝐸 = 2𝐺(1 + 𝑣)
5. Testing
-
Experimental Determination of Tensile Properties
o For metals it is ok to use ends to grip without having stress concentration
problems.
o For brittle materials direct tensile test is NOT the best choice due to the
stress concentrations at the grip  indirect methods are preferred.
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-
Tensile testing
o 𝑇=
-
2𝑃
𝜋𝑙𝑑
 T = tensile strength
 P = failure load
 l = length
 d = diameter of the specimen
o Effect of testing parameters
 Surface imperfections stress concentrations in those
imperfections
 Rate of loading  rapid loading leads to higher strength
 Temperature  high temperature leads to high ductility but lower
yield strength, lower fracture strength and lower E-modulus
 Specimen size  Bigger sample gives lower strength
Compressive testing
o It is difficult to test ductile materials under
compression. They are better characterized
under tension.
o Brittle materials are suitable for
compression testing.
o Higher stresses are needed to break brittle
materials under compression due to the
closure of defects and flaws rather than
being stress raisers.
o Under compression the true stress-strain
curve lies under the engineering curve.
6. Hardness
- Hardness
o Hardness is a measure of a material’s resistance to localized
plastic deformation.
- Hardness tests
o Hardness tests are performed the most, because:
 They are simple and inexpensive
no special specimen needs to be prepared and the
testing equipment is relatively inexpensive.
 The test is non-destructive
the specimen is neither fractured nor excessively
deformed. (only a small indentation)
 Other mechanical properties often may be estimated
from hardness data (such as tensile strength).
o Hardness tests
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 Early tests were based on natural minerals with a scale
constructed solely on the ability of one material to
scratch another that was softer (Mohs scale).
 New developed technique:
Small indenter is forced into the surface of a material to
be tested, under controlled conditions of load and rate of
application. (Rockwell, Brinell, Vickers, Nano
indentation)
 Nano-indentation
 Mechanical probing of a material surface to nmscale depths (while monitoring load an depth)
 Material surface must be flat and polished
 Schmidt hammer
 Measures the rebound of a spring-loaded mass
impacting against the surface of the sample.
 Test hammer hits the concrete at a
defined energy
 Rebound depends on hardness of
concrete (measured by hammer).
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LECTURE 04 –Fracture
Fracture
1. Fracture
-
-
-
-
Simple fracture
the separation of a body into two or more pieces
o Response due to an imposed stress that is static and at low temperatures
(relative to the melting point of the material).
o Can occur from fatigue (cyclic stresses imposed) and creep (timedependent deformation).
Ductile & Brittle fractures
o Ductile fracture is preferred to brittle
 Brittle fracture occurs suddenly, catastrophically and without
warning.
 More strain energy required to induce ductile fracture (generally
tougher materials)
o Highly ductile fracture (a)
Specimen necks down to a point. (e.g. extremely soft
materials like Au)
o Moderately ductile fracture (b)
Fracture after some necking, small cavities and voids
are typical.
o Brittle fracture (c)
without any plastic deformation (immediate fracture).
o Cup-and-cone fracture
 (a) initial necking
 (b) small cavity formation
 (c) Coalescence of cavities to form crack
 (d) Crack propagation
 (e) Final fracture at 45 degrees angle relative
to the tensile direction.
Fracture Mechanics
Understanding of mechanics of fractures
o Allows quantification of the relationships between material properties,
stress level, presence of crack-producing flaws and propagation
mechanisms.
Griffith and material strength
o Energy and strength
 Relate the surface energy of the fracture surfaces to the strain
energy in the material before it breaks.
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
Total Strain energy per unit volume times the volume in both
triangular regions (when material is linear elastic, 𝜎 = 𝐸𝜖)
𝑈=−

𝜎2
∗ 𝜋𝑎2
2𝐸
The Surface energy with a crack of length a (and unit depth)is:
𝑆 = 2𝛾𝑎 (ƴ=surface energy, and 2 free surfaces have been formed)

The Griffith Equation
𝝈𝒇 = √
-
𝑬𝑮𝒄
𝝅𝒂
 Critical strain energy release rate Gc (J/m2)
 Stress level ơf
 Size of the flaw a
Stress concentrations
o Tensile loading, computation of maximum stress at a crack tip
𝑎
1⁄
2
𝜎𝑚 = 2𝜎0 ( )
𝜌
𝑡
o
𝜎𝑚
⁄𝜎0 is denoted as the stress concentration factor Kt.
𝐾𝑡 =
-
𝜎𝑚
𝜎0
𝑎
1⁄
2
= 2( )
𝜌
𝑡
Fracture toughness
o Fracture toughness Kc (MPa(m)0.5)
a measure of a material’s resistance to brittle
fracture when crack is present.
𝐾𝑐 = 𝑌𝜎𝑐 √𝜋𝑎



-
-
ơc : critical stress for crack propagation
a : crack length
Y : dimensionless parameter depending
on crack and specimen sizes, geometries
and loading.
Fracture modes
o Tensile mode (a)
o Sliding mode (b)
o Tearing mode (c)
o Plane strain fracture toughness 𝐾𝐼𝑐 = 𝑌𝜎√𝜋𝑎
Design strategy
o 3 variables that must be considered:
 Fracture toughness, Kc OR Plane strain fracture toughness, KIc
 The imposed stress, ơ
 Flaw size, a
o First, decide which variables are constrained by application and which are
subject to design control.
e.g. material selection (and hence Kc or KIc) is often dictated by factors such as density or
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corrosion characteristics. OR the allowable flaw size is either measured or specified by
limitations.
o Once 2 parameters are prescribed, the third becomes fixed
o Computation of design stress
𝜎𝑐 =
𝐾𝐼𝑐
𝑌√𝜋𝑎
o Computation of maximum allowable flaw length
-
1 𝐾
𝑎𝑐 = ( 𝐼𝑐)
𝜋 𝜎𝑌
2
Testing
o List of Non-destructive Testing (NDT) Techniques
o Fracture Toughness Testing
 Structures constructed from alloys that
exhibit this ductile-to-brittle transition
should be used at temperatures above
the transition temperature to avoid
brittle and catastrophic failure.
2. Fatigue
-
-
o Form of failure that occurs in structures subjected to dynamic and
fluctuating stresses (bridges, aircraft, etc.)
o Failure can occur at stress levels lower than the tensile or yield strength
for a static load.
o Fatigue is the single largest cause of failure in metals (90%).
Fatigue
o Occurring very suddenly without warning
Fatigue fracture
o Crack formed at the top edge
o Smooth area (near the top) is the area over which
crack propagated slowly
o Rapid failure occurred over the area with a dull an
fibrous texture (largest area).
S-N curve (Wöhler curve)
o After sufficient cycles in a fatigue test, the specimen may fail.
o Results of fatigue tests are presented as an S-N curve
o The stress (S) plotted versus the number of cycles (N) till failure.
o Fatigue tests can
 Tell how long a part may survive
 The maximum allowable loads that can be applied
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-
o Endurance Limit: Stress below which failure due to fatigue will never
occur.
o Fatigue life: Number of cycles at which the metal will fracture (for known
stress level)
o Fatigue strength: value of stress that causes material to fracture (for
known number of cycles)
Fatigue Testing
o Rotating cantilever beam test
 Cylindrical specimen is
mounted on a motor driven
chuck with a weight suspended
from one end.
 As the specimen rotates each
side is periodically stressed in
tension and compression under the force of gravity.
 As the specimen rotates the stress at any given point goes through
a complete cycle from maximum tension to maximum
compression.
3. Rheology Of Solids
-
Elastic and Viscous behaviour
o Most materials will exhibit a time-dependent component in response to
stress (viscous behaviour).
o Viscoelastic material: solid which exhibits response to both immediate
elastic stress AND time-dependent viscous stress.
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o Elastic behaviour
o Viscoelastic behaviour
 Viscosity (fluid): measure of its resistance to deformation by shear
and tensile stress [Pa.s]
-
Rheological models
o Simple models
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
Maxwell model
Simulates fluid properties of
materials
 Conditions:
o 𝜎 = 𝐸 ∗ 𝜀1 = 𝜂 ∗
𝜀̇2
o 𝜀 = 𝜀1 + 𝜀2
𝜎
𝜎
𝐸
𝜂
 𝜀= + 𝑡

Kelvin-Voigt material
Simulates solid materials
 Conditions:
o 𝜎 = 𝜎1 + 𝜎2
o 𝜀 = 𝜀1 = 𝜀2
𝜎
𝜀 = (1 − 𝑒
𝐸

−𝐸𝑡⁄
𝜂)
o Complex models
 Burgers model
simulate the stress-strain time
behaviour of concrete

𝜀=
𝜎
𝐸2
+
𝜎
𝐸1
(1 − 𝑒
−𝐸𝑡⁄
𝜂1 ) 𝜎 𝑡
𝜂2
LECTURE 05 –Phase Diagrams
1. Diagrams
- Importance of Phase Diagrams for alloy systems
o There is a strong correlation between microstructure and
mechanical properties.
o Development of microstructure of an alloy is related to the
characteristics of its phase diagram.
- Material Processing
o Material properties reflect their microstructure
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o Microstructures are controlled by the composition of the
material and how it is processed.
o Phase diagrams provide fundamental knowledge of what the
equilibrium structure of a metallic alloy is.
- Definitions/Terminology
o Metallic alloy mixture of a metal with other metals or nonmetals. (Ceramic alloys can be mixed from ceramics)
o Binary alloy
contains two components. (ternary alloy=3)
o Component, c:
pure metals and/or compounds of which
an alloy is composed (e.g. Au-Ag-Ni, NaCl-H2O)
o Phase, p:
a homogeneous portion of a system that has
uniform physical and chemical characteristics
 Suger+water: 2 components – 2 phases
 Sugar syrup: 2 components – 1 phase
- Solubility limit
- One-Component Phase Diagrams
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2. Binary Phase Diagrams
-
o Very important for 2 component alloys (e.g. steel)
o Diagram in which temperature and composition are variable parameters,
pressure is held constant (1 atm).
o Represent the relationships between temperature and the compositions
and quantities of phases at equilibrium (which influences the
microstructure of an alloy).
Binary Isomorphous System
- Lever Rule
- Mechanical properties of Isomorphous alloys
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