Materials

Materials

1. Introduction: Material Classes
Three Material Classes:
Metals – Based on metals with some additions, high electrical conductivity, high strength
(in compression, tension, fatigue), high ductility, high thermal conductivity.
Polymers (plastics) – Compounds on non-metals, low electrical conductivity, low elastic
modulus, high friction coefficient, low thermal conductivity, high specific strength within
polymer molecule, wood (natural polymer).
Ceramics – Compounds of a metal and non-metal, high wear resistance and low friction
coefficient, high thermal stability, chemical inertness, transparency, semiconductor
industry.
Non-metals: B, C, Si, N, P, As, O, S, Se, Te, F, Cl, Br, I At
Bonds
Types of atomic bonding:
Metallic  Metals
Covalent + Secondary  Polymers
Ionic, Covalent  Ceramics
Materials with higher melting points (stronger atomic bond) have lower coefficients of
thermal expansion (CTE); the tendency of matter to change in shape, area, and volume in
response to a change in temperature, through heat transfer.
Materials with higher melting points (stronger atomic bond) have greater Modulus of
Elasticity (less strain under the same stress).
Strengths of different chemical bonds as reflected in their Heat of vaporization (kJ/mol)
Van der Waals ↓ (low); 𝑁2 12 kJ/mol
Hydrogen
↓
Metallic
↓
Ionic
↓
Covalent
↓ (high); Diamond 1180 kJ/mol
Covalent Bond – In covalent bond electrons are localized, this determines in general low
electrical and thermal conductivity, high energy is required to break covalent bonds.

Secondary bonding – Weak forces, dipole between same atoms/molecules, dipole
interaction between polar molecules, Hydrogen Bridge, this weak bonding determines:
Anisotropy in properties of polymers and softening of linear polymers with increasing
temperature.
Metallic bonding – Delocalized electrons determine high electrical and thermal
conductivities of metals, alike atoms in all directions  uniformity in properties,
deformation by slip.
Ionic bonding – Based on Coulomb Forces, electrons are immobilized, low electrical and
thermal conductivity, high energy required to break ionic bonds  high melting
temperatures, hardness, chemical inertness
Crystalline – Solid materials may be classified according to the regularity with which atoms
or ions are arranged with respect to another. A crystalline material is one in which the atoms
are situated in a repeating or periodic array over large atomic distances, repetitive threedimensional pattern, in which each atom is bonded to its nearest-neighbor atoms.
Crystal structure – The manner in which atoms, ions, or molecules are spatially arranged.
Atomic hard sphere model – When describing crystalline structures, atoms are thought of
as being solid spheres having well-defined diameters, where spheres representing nearestneighbor atoms touch one another.
Lattice – Used in the context of crystal structures, meaning a three-dimensional array of
points coinciding with atom positions (or sphere centers).
Unit cells – Small repeat entities, chosen to represent the symmetry of the crystal structure,
wherein all the atom positions in the crystal may be generated by translations of the unit
cell integral distances along each of its edges. The unit cell is the basic structural unit or
building block of the crystal structure and defines the crystal structure by virtue of its
geometry and the atom positions within.
Coordination number – For metals, each atom has the same number of nearest-neighbor
or touching atoms.
Atomic Packing Factor (APF) – The sum of the sphere volumes of all atoms within a unit cell
(assuming the atomic hard sphere model) divided by the unit cell volume. The value 0.74 is
the maximum packing possible for spheres all having the same diameter. Metals typically
have relatively large atomic packing factors to maximize the shielding provided by the free
electron cloud.
Metals

Based on Metals with some additions
Metallic bonding
Metallic crystals structures
The atomic bounding in this group of materials is metallic and thus no directional in nature.
For metals, using the hard sphere model for the crystal structure, each sphere represents
an ion core. Three relatively simple crystal structures are found for most of the common
metals: Face Centered Cubic, Body Centered Cubic, and Hexagonal Closed Packed.


Face Centered Cubic (FCC) – The crystal structure found for many metals has a unit
cell of cubic geometry, with atoms located at each of the corners and the centers of
all the cube faces.
Some metals having this crystal structure – Cooper, Aluminum, Silver, Gold
𝑎 = 2𝑅√2; N= 4; Coordination Number = 12; APF = 0.74 ≈ 74%



Body Centered Cubic (BCC) – Another common metallic crystal structure also has a
cubic unit cell with atoms located at all eight corners and a single atom at the cube
center.

Some metals having this crystal structure – Chromium, iron, tungsten
𝑎 = 4𝑅/√3; N= 2; Coordination Number = 8; APF = 0.68 ≈ 68%


Hexagonal Closed Packed (HCP) – Common metallic crystal structure with a
hexagonal unit cell. The top and bottom faces of the unit cell consist of six atoms
that form regular hexagons and surround a single atom in the center. Another plane
situated between the top and bottom planes provides three additional atoms to the
unit cell.

Some metals having this crystal structure – Cadmium, magnesium, titanium, zinc
𝑎 = 2𝑟, 𝑐 = √2/3 4𝑟; 𝑐⁄𝑎 𝑟𝑎𝑡𝑖𝑜 = 1.633;
N= 6; Coordination Number = 12; APF = 0.74 ≈ 74%
Summary
-Materials properties and, therefore, applications are determined by their internal
structures on atomic and crystallite scales.

-The materials can be divided in a simplified way into three categories: metals, polymers
(plastic) and ceramics.
-In general, metals reside in the left side or in the lower part of the periodic table as it is
conventionally presented. Polymers contain non-metallic elements located in the upper
right corner of the table. Ceramics are compounds of metals and non-metals. Some
materials fall in border areas and are not definitively categorized.
- In metals (alloys) “metallic type of atomic bonding prevails“, simplified by a lattice of
metals ions in a “sea” of valence electrons. This type of bonding determines high electrical
and thermal conductivity (by valence electrons), high ductility, tensile and impact strength
of metals.
-In polymers mostly non-metallic atoms with a molecule are tightly bonded by covalent
forces (sharing pairs of electrons).Bonds between molecules are much weaker. Plastic are
in general poor electrical and heat conductors. Their mechanical properties are anisotropic
(vary strongly depending on force application direction).
- In ceramics metallic and non-metallic elements are bonded by strong ionic forces. They
have commonly high melting points and are poor heat and electrical conductors in solid
state. Ceramics are strong under compressive but weaker under tensile loading.
- Atoms in metals are spaced ate very specific distances in a crystal lattice. Atomic radius in
metals is half of the distance between two “touching” atoms.
- Three major metal crystal structures are:
Body-Centred Cubic (BCC); Coordination No.8, packing factor 68%
Face-Centred Cubic (FCC); Coordination No.12, packing factor 74%
Hexagonal Close-Packed (HCP); Coordination No.12; Packing factor 74%
- Commercial metals contain a large number of grains, each of which is an individual crystal.
The grain size has a great effect on the materials properties.

2. Phase Diagrams
Solutions and solubility’s – When solute concentrations exceeds the solubility limit,
precipitation of a solid “phase” occurs. Solubility limit depends on temperature, typically
increases with increasing temperature.
Solubility limit – Maximum concentration of solute atoms that may dissolve in the solvent
to form a solid solution. The addition of solute in excess of this solution results in the
formation of another solid solution or compound that has a distinctly different composition.
Solid solution - The addition of impurity atoms to a metal will result in the formation of a
solid solution and/or a new second phase, depending on the kinds of impurity, their
concentrations, and the temperature of the alloy. A solid solution forms when, as the solute
atoms are added to the host material, the crystal structure is maintained, and no new
structures are formed. Compositionally homogeneous; the impurity atoms are randomly
and uniformly dispersed within the solid

Solvent and solute - Solvent represents the element or compound that is present in the
greatest amount; on occasion, solvent atoms are also called host atoms. Solute is used to
denote an element or compound present in a minor concentration.
Substitutional/ Interstitial - Impurity point defects are found in solid solutions, of which
there are two types: substitutional and interstitial.
For the substitutional type, solute or impurity atoms replace or substitute for the host atoms
 Similar atomic radii (15% or less difference), same crystal structure, similar electro
negativities, similar valences. An example of a substitutional solid solution is found for
copper and nickel. These two elements are completely soluble in one another at all
proportions.
For interstitial solid solutions, impurity atoms fill the voids or interstices among the host
atoms
Brass – A solid solution alloy, Zn/Cu, substitutional Zn, increase in strength, decrease in
electrical conductivity.
Infinite solubility – Time Independent.
Fraction of solid - 𝐴𝐵/𝐴𝐶
Fraction of Liquid – BC/AC
Summary
-Pure metal has a unique melting point, whereas an alloy melts over a temperature range.
On cooling, freezing starts at the liquidus temperature and is completed at the solidus
temperature. The liquidus curves are the solubility limits for the components in the liquid.
Exceeding solubility limits for alloying elements in solid state also results in precipitation of
new phases.
- Some alloys melt at lower temperatures than either component metal alone. The lowest
melting temperature between two solids is called the eutectic temperature. At this
temperature simultaneous precipitation of two solid phases occurs upon cooling.
- A phase diagram shows: what phases form, the composition of the phases and the relative
amounts of each phase for the ideal case of thermodynamic equilibrium.
- Alloying additions can form with the base metal, a solid solution (substitutional or
interstitial depending on atom size) or a compound (intermetallic, carbide, nitride).

- Solid-solution alloys are single phase, they retain the crystal lattice of the base metal. Most
of the commercially used alloys are multiphase. Phases are different solid solutions or
intermetallic, carbide, nitride, compounds.
3. Phase Diagrams II
Diffusion – The phenomenon of material transport by atomic motion.
Mechanism of hardening – Precipitation hardening is commonly employed with highstrength aluminum alloys
Nucleation - Involves the appearance of very small particles, or nuclei of the new phase
(often consisting of only a few hundred atoms), which are capable of growing. There are
two types of nucleation: homogeneous and heterogeneous. The distinction between them
is made according to the site at which nucleating events occur. For the homogeneous type,
nuclei of the new phase form uniformly throughout the parent phase, whereas for the
heterogeneous type, nuclei form preferentially at structural inhomogeneities, such as
container surfaces, insoluble impurities, grain boundaries, dislocations, and so on.
Heat-Treatment Procedure for Precipitation Hardening:
1) Solutioning (550°C); 2) Quenching to RT;
3) Age-hardening for short time at 200°C
Dendrites - The accumulation of solute and heat ahead of the interface can lead to
circumstances in which the liquid in front of the solidification front is supercooled. The
interface thus becomes unstable and in appropriate circumstances solidification becomes
dendritic.
Summary
Deviation of real microstructures from those predicted by phase diagrams are commonly
observed especially at low temperatures because of insufficient time to reach the
equilibrium by atomic diffusion.
Diffusion in solid state can occur by substitutional and interstitional mechanisms. Diffusion
flux (mass transfer per unit area/ time) depends on the diffusion coefficient and
concentration gradient (driving force). In order to diffuse atoms should overcome the
activation barrier. The activation Energy 𝐸𝐴 can be is therefore an important parameter for
quantitative description of the diffusion process. The activation energy can be derived from
the temperature dependence of the diffusion coefficient.
The microstructure metallic materials is largely determined by phase nucleation, which can
be homogeneous and heterogeneous. For homogeneous nucleation commonly substantial
supersaturation (supercooling) is required. In other words fast cooling rates promote

homogeneous nucleation. By very rapid cooling (quenching) it is possible to freeze the high
temperature phase, which becomes metastable at low temperature. Heterogeneous
nucleation requires less supercooling (than homogeneous), however, this is one of the
major causes for microstructure inhomogeneties, such as preferential precipitation at grain
boundaries.
Diffusion in liquids is much faster than in solids. This results in typical microstrural problems
of cast components, in particular coring, heterogeneous solidification and growth of
dendrites.
Controlled uniform precipitation is the key for high quality (high strength, high corrosion
resistance) metallic (and ceramic) materials. One method to achieve this is so called age
hardening, which consists of solution heat treatment, rapid cooling and controlled
precipitation of the strengthening phase.
Maximum strength occurs in the early stages of precipitation by tiny (coherent) particles.
During over-aging coalescence of the particles (fewer, but larger), hardness decreases.

4. Mechanical Properties
Elastic deformation – Recoverable when stress is removed.
Strain = Deformation, deformation is directly proportional to stress, linear relationship
between the strain and stress.
𝜎=

𝐹 𝑁
, 𝑀𝑃𝑎, 𝑝𝑠𝑖] = 𝐸. 𝜀
[
𝑆 𝑚𝑚
𝑆 = 𝜋𝑑2

𝜀=

∆𝑎
𝑎 (𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑠𝑖𝑧𝑒)

𝐹 = 𝑚𝑔(9.8𝑚/𝑠 2 )

Compression – Atoms move closer to each other, ∆𝑎 − 𝑎
Tension – Lattice changes size, ∆𝑎 + 𝑎
Elastic modulus – its value can be correlated with atomic bonding, decreases with increasing
temperature, materials with high strength has high young modulus
Plastic deformation – Not recoverable after the stress is removed, atoms move into new
positions and not come back, Stress-strain curve starts to deviate from the linear
relationship.
Dislocation – A linear defect in 3D crystal lattice, only limited number of atoms are
simultaneously involved in deformation by dislocation movement.

Ultimate tensile strength – Highest point of the curve, the maximum stress that a material
can withstand while being stretched or pulled before failing or breaking
Yield strength - The stress at which a material begins to deform plastically. Prior to the yield
point the material will deform elastically and will return to its original shape when the
applied stress is removed. Once the yield point is passed, some fraction of the deformation
will be permanent and non-reversible.
Ductility is another important mechanical property. It is a measure of the degree of plastic
deformation that has been sustained at fracture.
Three major methods for strengthening of metallic materials:
1) Solid solution strengthening
2) Precipitation strengthening (including age hardening)
3) Thermo-mechanical treatments (using the effects of grain size, cold work)
The material with a smaller grain size has a higher strength since grain boundaries hinder
dislocation movement. For dislocations to pass an alloy grain boundary additional energy is
required, because the other grain has a different crystallographic orientation
Strengthening by Grain Refinement
Mechanism of the effect of cold work on metal strength:
- Cold work (plastic deformation) introduces dislocations
- Deformation of cold worked material is hindered by interaction of new dislocations with
those generated during cold working
Annealing (high-temperature exposure) of cold-worked metal results in rapid annihilation
of dislocations by recovery and recrystallization (formation of new, defect-free grains from
the existing ones) by mechanism of atomic diffusion > strength decreases / ductility
increases
5. Mechanical Properties II
Hardness test is a simple way to assess the strength of materials.
𝐹

𝐻𝑉 = 𝐴 ≈

0.1891𝐹
𝑑2

Hardness is the property of a material that enables it to resist plastic deformation, usually
by penetration. However, the term hardness may also refer to resistance to bending,
scratching, abrasion or cutting.

Ductile Brittle Transition Temperature (DBTT) behavior is typical for BCC and HCP metals,
not FCC
KI shows how applied stress is intensified depending on defect size and position. By testing
samples of a given material with various defect sizes, a critical value of KI is determined,
which is called fracture toughness (KIc).
The material is going to fail by brittle fracture if KI >KIc
Fatigue mechanism for metallic materials crack
- Crack initiates in a region of high stress intensity
- Crack propagates slowly (rate depends on load cycle frequency, stress level, material
ductility, atmosphere etc.)
- Finally a sudden brittle fracture occurs
Ferritic (BCC) Steels have an endurance limit, FCC / HCP metals have NO endurance limit
Control of defects
- Reduction of impurities
- Deformation (rolling, forging to suppress casting porosity)
- Surface processing (e.g. polishing or shot peening)
6. Corrosion

Corrosion is the deterioration of materials by chemical interaction with their environment.
Anode: electrons are “produced” and metal is dissolved (anodic dissolution)
Cathode: electrons are consumed and metal is deposited (cathodic deposition)
7. Steels
Metal alloys by virtue of composition, are often grouped into two classes, ferrous and nonferrous. Ferrous alloys, those in which iron is the principal constituent, include steels and
cast irons.
Ferrous alloys – Those of which iron is the prime constituent, are produced in larger
quantities than any other metal type.
The principal disadvantage of many ferrous alloys is their susceptibility to corrosion.

Steels - They are iron-carbon alloys that may contain appreciable concentrations of other
alloying elements. The mechanical properties are sensistive to the content of carbon, which
is normally less than 1wt%.
Plain carbon steels – Contain only residual concentration of impurities other than carbon
and a little manganese.
Low carbon steels – Of all the diferent steels, those produced in the greatest quantities fall
within this classification. These generally contains less than about 0.25wt% C and are
unresponsive to heat treatments intended to form martensite; strengthening is
accomplished by cold work. Microstructures consist of ferrite and pearlite constituents.
As a consequence these alloys are relatively soft and weak but have outstanding ductility
and toughness, they are machinable, weldable and of all the steels are the least expensive
to produce. Typical applications include automobile body components, structural shapes
and sheets that are used in pipelines, buildings, bridges and tin cans.
High strength low alloy steel – Another group of low-carbon alloys, they contain other
alloying elemnts such as cooper, vanadium nickel and molybdenumin combined
concentrations as high as 10wt% and posses higher strengths than the plain low carbon
steels. Most be strengthened by heat treatment, in addition they are ductile, formable and
machinable. They are more resistant to corrosion than the plain carbon steels, which they
have replaced in many applications where structural strength is critical.
Medium carbon steels – They have carbon concentrations between about 0.25 and
0.60wt%. These alloys may be heat treated by austenitizing, quenching and then tempering
to improve their mechanical properties. They are most often utilized in the tempered
condition, having microstructures of tempered martensite. These heat treated alloys are
stronger than the low carbon steels, but at a sacrifice of ductility and toughness.
High carbon steels – Normally having carbon contents between 0.60and 1.4wt%, are the
hardest, strongest and yet least ductile of the carbon steels. They are almost always used in
hardened and tempered condition and, as such, are specialy wear resistant and capable of
holding a sharp cutting edge. The tool and die steels are high carbon alloys, usually
containing chromium, vanadium, tungsten and molybdenum. These alloying elements
combine with carbon to form very hard and wear resistant carbide compounds. These steals
are utilized as cutting tools and dies for forming and shaping materials, as well as in knives,
razors, hacksaw blades, springs and high strength wire.
Stainless steels – They are highly resistant to corrosion (rusting) in a variety of
environments, specially the ambient atmosphere. Their predominant alloying element is
Chromium; a concentration of at least 11wt% Cr is required. Corrosion resistance may also
be enhanced by nickel and molybdenum additions. They are divided on the basis of the
predominant phase constituent of the microstructure, martensitic, ferritic or austenitic.

Martensitic stainless steels are capable of being heat treated in such a way that martensite
is the prime micro constituent. For austenitic stainless steels, the austenite phase field (𝛾)
is extended to room temperature. Ferritic stainless steels are composed of the 𝛼 ferrite
(BCC) phase. Austenitic and ferritic stainless steels are hardened and strengthened by cold
work because they are not heat treatable. The austenitic stainless steels are the most
corrosion resistant because of the high chromium contents and also the nickel additions;
and they are produced in the largest quantities. Both martensitic and ferritic stainless steels
are magnetic; the austenitic stainless are not.
Cast Irons – Generically are a class of ferrous alloys with carbon contents above 2.14wt%;
in practice, however, most cast irons contain between 3.0and 4.5wt%C and, in addition,
other alloying elements. They are easily melted and amenable to casting. Furthermore,
some cast irons are very brittle, and casting is the most convenient fabrication technique.
For most cast irons, the carbon exists as graphite, and both microstructure and mechanical
behavior depend on composition and heat treatment. The most common cast iron types
are gray, nodular, white, malleable and compacted graphite.
Metal fabrication techniques
Forming Operations  Forging, Rolling, Extrusion, Drawing
Casting Sand, Die, Investment, Lost foam, Continuous
Miscellaneous  Powder metallurgy, Welding
Iron crystal structures
BCC/ 𝛼 ferrite  Stable at <912°C
FCC/𝛾 Austenite  Stable at 912°C <T<1394°C, the solubility for carbon in austenite is
higher than that in ferrite, the reason for this effect is that interstitial spaces are larger in
FCC than in BCC lattice.
Pure annealed iron has extremely low tensile strength of about 10MPa, which is not
sufficient for most practical applications. One of tge possibilities to improve strength is cold
work, by cold forging.
Iron-Cementite phase diagram
Phases present: Liquid (L), solids (𝛼, 𝛾, 𝑐𝑒𝑚𝑒𝑛𝑡𝑖𝑡𝑒)
The invariant reactions are depicted by horizontal lines (upon cooling):
Peritectic reaction: liquid phase + solid phase (𝛿)  1 solid phase (𝛾)
Eutectic reaction: liquid phase  2 solid phases (𝛾 + 𝑐𝑒𝑚𝑒𝑛𝑡𝑖𝑡𝑒)

Eutectoid reaction (Pearlite): solid phase (𝛾)  2 solid phases 𝛼 + 𝑐𝑒𝑚𝑒𝑛𝑡𝑖𝑡𝑒, from
austenite to pearlite
Effect of microstructural dimensions on hardness steel – The higher the temperature and
the longer the time available for the transformation the coarser is the microstructure, which
results in less hard but more ductile material, in practice coarser microstructure is achieved
simply by slowing down the cooling rate.
Undereutectoid steels – Have carbon contents lower than 0.77%
Alloying additions – Ni and Mn in steel add to its tensile strength and make austenite more
chemically stable, Cr increases hardness and melting temperature and V also increases
hardness while reducing the effects of metal fatigue. S and P make steel more brittle, so
these commonly found elements must be removed from the ore during processing.
Mo retards start of austenite to pearlite phase transformation. Also an increase in eutectoid
temperature.
Purposes of heat treatments:
Homogenization of material (Normalizing)
Good Machinability
Stress relief
Reanimation of ductility after cold work
Microstructure processing
Annealing – The temperature is sufficiently high to ensure complete disappearance of
ferrite. The steel is then cooled slowly to form a coarse pearlite and a relatively soft product.
Normalizing – The steel is heated to a somewhat higher temperature to promote more
rapid atom diffusion and microstructural uniformity. Excessive heating, however, would
permit undesirable grain growth. Following austenization, the normalized steel is air cooled
to produce uniformly fine pearlite.
Steel strengthening by martensitic transformation (diffusionless) - Rapidly cooling
(quenching). It occurs by simultaneous shift of atomic planes. The carbon atoms have no
time to diffuse out of the iron lattice and remain in non-equilibrium, super-saturated solid
solution. The martensite is very hard but also very brittle phase. Therefore steels in practice
are almost never used with the martensitic structure.
Hardenability – It shows to which depth the steel can be hardened. To measure
hardenability the so called end quench test is used.
Three major manufacturing steps of steel components:

Metal extraction (reduction from ores) by chemical reactions with C,H2, electrolysis and
alloying.
Shaping by casting, rolling, drawing, extrusion, forging
Optimization of properties by quenching, heat treatment, cold work