MET 205�Metallurgy and Material Science

Preamble:

Understanding of the correlation between the chemical bonds and crystal structure of metallic

materials to their mechanical properties.

Recognize the importance of crystal imperfections including dislocations in plastic deformation.

Learning about different phases and heat treatment methods to tailor the properties of Fe-C

alloys.

Examine the mechanisms of materials failure through fatigue and creep.

To determine properties of unknown materials and develop an awareness to apply this

knowledge in material design

Metallurgy and Material Science. Dr. S Jose

Introduction

• Material Science : Study of the structure & properties of materials
• Investigation of structure- properties relationship.
• Properties of materials is depend on structure
• Structure: Arrangement of internal component of matter in materials
• Property : Response of the materials when exposed to an external stimulus
• Properties are the way the material responds to the environment and external forces
• Strength
• Toughness
• Hardness
• Ductility
• Elasticity,
• Fatigue,
• Creep…etc

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Why study Materials Science ?

• Important to understand capabilities and limitation of materials
• Lack of fundamental understanding of materials and their properties will cause catastrophic failure

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• An understanding of Materials Science helps us to design better components, parts , devices, etc.
• How do you make something stronger or lighter?
• How do elements come together to form alloys ?

METALLURGY

• Metallurgy, art and science of extracting metals from their ores and modifying the metals for use.
• It also concerns the chemical, physical, and atomic properties and structures of metals and the principles whereby metals are combined to form alloys.
• Metallurgy encompasses both the science and the
• technology of metals.

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CLASSES OF MATERIALS

• There are 3 major classes

Metal

• Strong, ductile, High thermal & electrical conductivity, Opaque, reflective
• Pure metallic elements or combination of metallic elements (alloys) . Air frame, landing gear, engine components

Ceramic

• Brittle, glassy, elastic, Non-conducting (insulators)
• Molecules based on bonding between metallic and non-metallic elements. Typically insulating and refractory – coating on high temp engine components

Polymers

• Ductile, low strength, low density, Thermal & electrical insulators Optically translucent or transparent
• Many are organic compound Chemically based on C , H other non-metals
• – windows , cabin interior

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Sub-classes of Materials

1. Semiconductor (ceramics), Intermediate electrical properties
2. Composite (all three classes), combination
3. Bio Materials (all three classes), Compatible with body tissue

Ceramics

Glass Graphite Diamond

Composites

PMC MMC CMC

Engineering Materials

Metals

Non-Metals

Ferrous

Irons Carbon Steel Alloy Steel

Non ferrous

Aluminium Copper Titanium

Polymers

Thermoplastics Thermosetting Elastomers

Jasmi 2011

Metal

Introduction

Ceramic

Polymer

Introduction

Composite

Semiconductor

Atomic Structure

x

Atoms

= nucleus (protons and neutron)

+ electrons

Electrons, protons have negative and positive charges of the same magnitude

Neutron are electrically neutral

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Proton and neutron have the same mass

1.67 x 10 ^–27 kg

Mass of an electron is much smaller (9.11 10 ^–31 kg and can be neglected in calculation

The atomic mass (A) = mass of proton mass of neutron

Atomic number (Z) = number of proton

Atomic Bonding

1. Ionic bonding

Strong interaction among negative atom (have an extra electron ) and positive atom (lost an electron)

Strong atomic bonds due to transfer of electrons

2. Covalent bonding

Electrons are shared between the molecules to saturate the valence

Large interactive force due to sharing of electrons

3. Metallic bonding

The atoms are ionized, loosing some electrons from the valence

band.

Those electrons form an electron sea, which binds the charged nuclei in place.

Atomic Bonding

• Occurs between + and - ions.
• Requires electron transfer.
• Large difference in electronegativity required.
• Example: NaCl

1. Ionic Bonding

Non-metal

accepts electrons

Ionic bond : Metal +

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donates

electrons

Atomic Bonding

Electrons are shared between the molecules to saturate the valence

2. Covalent Bonding

H + H

1s¹ Electrons

Electron Pair

H H

Hydrogen Molecule

Atomic Bonding

Requires shared electrons

Example : CH₄

C : has 4 valence e, needs 4 more H : has 1 valence e, needs 1 more

Si with electron valence : 4

Four covalent bonds must be formed

Atomic Bonding

Arises from a sea of donated valence electrons (1, 2, or 3 from each atom).

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Primary bond for metals and their alloys

3. Metallic Bonding

Valence electrons are detached from atoms, and spread in an electron sea that “glues’ the ions together

Space lattice & unit cell

• The three-dimensional network of imaginary lines connecting atoms is called the space lattice.
• A crystal is an arrangement in three dimensions of atoms or molecules in repetitive patterns.
• The smallest unit having the full symmetry of the crystal is called the unit cell, the edges of which form three axes: a, b, and c.

Body centered cube(BCC)

• a cubic unit cell with atoms located at all eight corners and a single atom at the cube center.

Face centered cube

Hexagonal closed packing

No of atoms per unit cell

No of atoms per unit cell

Each atom in contact with 4 atom in same plane and one each in top and bottom plane.

Coordination number=6

Atomic packing factor

• Simple cubic
• a=2r
• No of atoms= 1
• Volume of unit cell= a³

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APF= 4/3 ∏ r ³

^{--------------------- = 0.52}

a³

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^{52 % filled with atoms, other empty}

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Face centered cube

No of atoms in unit cell

Coordination number

• 4 atoms in same plane
• 4 atoms each in plane top and bottom

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• Coordination number =12

• No of atoms per unit cell

Body centered cube(BCC)

• 4 atoms each in plane top and bottom
• Coordination number= 8

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Hexagonal closed packing

• Six atoms in same plane
• 3 atoms each in plane top and bottom

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• Coordination number= 12

Volume of unit cell= cross sectional area x height

there are six triangles

a= 2r

Area of hexagon = area of triangle x 6

= 6 x a x h /2

= 3ah

Triangle AOG, a² = (a/2) ² + h²

h =√(a²-(a/2)² ) =a√3/2

Area of hexagonal face= 3a²√3/2

The lattice parameter a and c for HCP is related as c=1.633a

Volume of hexagonal unit cell = 3a²√3/2 x 1.633a

= 4.24 a³

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APF= 6 x 4/3 ∏ r ³

^{--------------------- =} 0.74

4.24 a³

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Miller indices

Miller planes

DEFORMATION OF METALS

• When a material is subjected to an external force or load, the material suffers a change in shape, which is called deformation.
• If the deformation is temporary,(if the deformation disappears on removal of the load) it is elastic deformation and if permanent, (if the deformation persists even after removal of the load), it is called plastic deformation.
• Both deformation take place due to adjustment or displacement in atomic arrangement within the crystal.
• The load may be tensile, compressive or shear, and its magnitude may be constant with time or it may fluctuate.
• Application time may be for only a fraction of a second or may extend over a period of years.
• Temperature or corrosive atmosphere are environmental factors.

Elastic Deformation

• When a solid material is subjected to an applied force, the atoms within the crystal are displaced from their normal position of equilibrium.
• This displacement will be just enough to develop attractive forces between the atoms to balance the applied load.
• When the atoms are so displaced, the material is said to have undergone a deformation.
• Thus, when a solid bar is loaded axially in tension, it becomes slightly longer.
• If, on removal of the load, the bar returns to its original dimensions, the deformation is elastic in nature.
• This is because the displacement of the atoms is by relatively small amounts and the removal of the applied load allows the atoms to return to their normal equilibrium positions.
• Thus the elastic deformation is reversible.

Poisson effect

• Consider a group of four atoms with centres at p, q, m and n as shown in figure.
• When the bar is subjected to an axial load along mn, the distance mn will increase.
• If p and q remain fixed; pm, pn, qm and qn would all be lengthened.
• Since p and q are also free to move, what really happens is that p and q move to positions p’ and q’ such that p’m’ = pm, p’n' = pn and so on.
• This results in mn elongating and pq contracting correspondingly.
• Any elongation or compression of the crystal in one direction due to a uniaxial force produces adjustment in the dimensions at right angle to the force.
• That means when an elongation is produced in the tensile direction, a small contraction is indicated at right angles to the tensile force and vice-versa.
• This is known as Poisson effect.
• As the applied load increases and the atoms are displaced further apart, a point is reached at which elastic range ends.
• Deformation is no longer a simple separation of atoms, and the behaviour is said to be inelastic.
• There are two possible ways for the elastic stage to end-by fracture or by yielding.
• When the elastic range is immediately followed by fracture, the material is said to be brittle.

Plastic deformation by slip

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• Consider an atom A in the upper layer of the crystal occupying a position of equilibrium in the valley of atoms C and D at the lower layer.
• Under the influence of an applied force P, the atom A is moved to another similar position of equilibrium in the valley of atoms D and E Atoms ahead of A are also moved in similar fashion.
• If the applied force persists, the atom A moves further forward to another position of equilibrium.
• Since, after every displacement, the atom A occupies a position of equilibrium, it has no tendency to move back to its original position,
• Thus the displacement is permanent or irrevocable.
• Thus it is seen that under the influence of a shear force, atoms move relative to each other on certain planes from one position of equilibrium to another position of equilibrium, causing a permanent deformation some atoms are said to have slipped past the other atoms on a certain plane in a certain direction.
• This process is called slip, the plane on which slip takes place is known as the slip plane and the direction along which the atoms move is known as the slip direction.

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Schmid’s law

• The above equation is known as Schmid's law.
• The critical resolved shear stress is the shear stress required to break enough metallic bonds in order for slip to occur.
• This means plastic deformation occurs only when the applied stress (σ) produces a resolved shear stress (Ʈ_r) which is equal to the critical resolved shear stress.
• This value of shear stress is the minimum value for a particular crystal to initiate slip along a slip plane.

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Plastic Deformation by Twinning

• In certain materials, when a shear stress is applied, planes of atoms in the lattice move parallel to a specific plane so that the lattice is divided into two symmetrical parts which are differently oriented.
• This phenomenon is known as twinning and the planes parallel to which atomic movement has taken place are known as twinning planes.

• The differently oriented region within the crystal and between the twinning planes is known as the twinned region.
• The amount of movement of each plane of atoms in the twinned region is proportional to its distance from the twinning plane, so that a mirror image is formed across the twin plane.
• Twinning is not a significant deformation mechanism for cubic metals. However, it is a significant mode of deformation in HCP crystals.

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Solidification of Crystallisation Materials

• For a crystalline solid, when the periodic and repeated arrangement of atoms is perfect and extends throughout the entirety of the material without any interruptions, the result will be what is known as single crystal.
• All the unit cells interlock in the same way and have the same orientation.
• Single crystals exist in nature but are very rare.
• Under carefully controlled environment, single crystals can be grown artificially - but with considerable difficulty.
• Virtually all the familiar crystalline solids are composed of a collection of many small crystals known as grains.
• Such materials are termed polycrystalline.
• Also it is observed that the individual grains are not perfect in the arrangement of atoms in the crystal lattice and that many interruptions exist. They are known as crystal imperfections or defects.
• Grain structure and the defects develop during solidification of the liquid material.
• Solidification of pure metals, also known as crystallisation is the transition from liquid state to solid state.
• In the liquid state, atoms of any material will be in constant motion due to their high kinetic energy owing to the high temperature.

• The atoms do not have any definite arrangement.
• However, when the temperature of the molten metal is brought down, it is possible that some atoms at any given instant, may group together in positions exactly corresponding to the space lattice they assume when solidified.
• These chance aggregates or groups are not permanent; but continually, break up and regroup at other points.

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• How long they last is determined by the temperature and the size of the group.
• The higher the temperature, the greater the kinetic energy of atoms and hence the shorter the life of the group.
• When the temperature of liquid is sufficiently decreased, atomic movement also decreases.
• This lengthens the life of the group and also promotes the formation of more groups within the liquid. Such groups are known as embryos.

Undercooling

• As the temperature of the liquid metal drop, a stage is reached where the embryos (more like solid) and the surrounding liquid coexist.
• This temperature is known as the solidification point or freezing point.
• At this point, both the liquid and solid states are at the same temperature and hence have the same kinetic energy for the respective atoms.
• But there is significant difference in the potential energy.
• The atoms in the solid are much closer together resulting in lowering of potential energy.
• Thus, solidification occurs with release of energy.
• The difference in potential energy between the liquid and solid states is known as latent heat (heat of fusion or heat of solidification).
• However, at the freezing point, energy is required to establish a surface between the solid and the liquid.
• In pure materials, at freezing point, insufficient energy is released by the heat of fusion to create a stable boundary surface.
• Hence some undercooling (super cooling) is necessary to form a stable solid region.

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Homogenous & Heterogeneous Nucleation

Homogenous Nucleation

• At sufficiently low temperatures, nucleation occurs by the grouping of a few atoms from the liquid.
• Nucleation of this type, originated with the support of undercooling is known as homogenous nucleation.
• This kind of nucleation occur uniformly throughout the liquid.
• The nucleus grows further by adding more and more atoms to it which leads to a small solid region.
• Such stable solid regions within the liquid are known as nuclei.
• Subsequent to the formation of nuclei, release of heat of fusion takes place and the temperature will be raised to the freezing point again.
• But loss of heat to the surroundings lowers the temperature again making more atoms to freeze.
• These atoms may attach themselves to already existing nuclei or form new nuclei of their own.
• Thus the process of solidification continues apparently at constant temperature till the entire liquid is transformed into solid.

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Heterogeneous Nucleation

• Nucleation is also facilitated by the presence of some impurity atoms, an inoculant (grain refiner), an imperfection or a grain boundary.
• This type of preferential nucleation is called heterogeneous nucleation.

Dendritic Growth

• During the process of solidification, each nucleus grows by attracting atoms from the liquid into the space lattice.
• Crystal growth continues in three dimensions, the atoms attaching themselves in certain preferred directions, usually along the axes of the crystal.
• This gives rise to the characteristic tree-like structure which is called a dendrite.
• This is a sort of crystal skeleton from which arms begin to grow in all directions depending upon the lattice pattern.
• From the primary arms, secondary, tertiary etc. arms begin to sprout, somewhat similar to branches and twigs growing out of the trunk of a tree, leading to the formation of a rather elongated skeleton.
• In the case of metallic dendrites, these branches and twigs conform to a rigid geometrical pattern.
• The dendritic arms continue to grow and thicken at the same time, until ultimately the space between them will become filled with solid.
• Meanwhile the outer arms of one dendrite begin to make contact with those of neighbouring dendrites, which have been developing independently at the same time.

• If the material is pure, there shall be no evidence of dendritic growth once the solidification is complete, since all the atoms are identical.
• If the material is impure, dissolved impurities will often tend to remain in the molten portion of the metal, which ultimately solidifies in the spaces between the dendrites.
• Since their presence will often cause a slight alteration in colour of the parent metal, the dendritic structure will be easily revealed on microscopical examination.
• The areas containing impurity will appear as patches between the dendrite arms.

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Grains

• The randomly formed nuclei will be having different crystallographic orientations.
• The nuclei grow into crystals by the successive addition of atoms from the surrounding liquid.
• All these neighbouring crystals (or grains) will be oriented differently due to their independent formation
• As these grow, the outer arms of the neighbouring crystals meet similar extremities of other neighbouring grains.
• Finally at a certain stage, further growth outwards becomes impossible, the remaining of the crystal.
• These crystals are commonly called grains.
• A grain is a portion of the material within which the atomic arrangement is nearly identical. But the orientation of the atomic arrangement may be different for adjoining grains.
• The area along which the grains meet is known as grain boundary is a region of mismatch.

• The grain boundary in a polycrystalline material is a region of disturbed lattice of a few atomic diameter wide.
• At some locations along the grain boundary, the atoms are so closer that they cause a region of compression.
• In some other areas, the atoms are so far apart and lead to regions of tension.
• On moving from one grain to another, the crystallographic orientation changes abruptly.
• This misalignment between adjacent grains can be quantified by the angle between the respective crystallographic orientations
• When this misalignment is of the order of a few degrees (upto 10°) it is called as low-angle grain boundary (tilt boundary).
• The high-angle grain boundary will have more mismatch in the orientation.

Single Crystal and Polycrystal

• When a liquid is cooled slowly in equilibrium with the surroundings, the solid that form contains tiny crystals called grains.
• The number of grains formed during solidification depends on the number of nuclei formed.
• If all nucleation sites except one are suppressed, the liquid solidifies into a single grain.
• Even the orientation of grain can be engineered to be in a specific direction.
• Single crystals show excellent high temperature properties because of the absence of grain boundaries.
• When the liquid is normally cooled under equilibrium condition, there would be abundant nucleation sites and the liquid solidifies into a large number of small grains.
• Though these grains look alike, the crystallographic orientations are different and the orientation changes randomly from one grain to other.
• Such a solid is called polycrystalline

Grain Size

• The rate at which a molten metal is cooled when it reaches the freezing point affects the size of the crystal which forms.
• A slow fall in temperature, which leads to a small degree of undercooling at the onset of solidification, promotes the formation of relatively few nuclei, so that the resultant crystal size will be large.
• Rapid cooling on the other hand, leads to high degree of supercooling, and the onset of solidification results in the formation of a large number of nuclei and hence a large number of crystals or grains smaller in size will be formed.
• As the grain size is having effect on material properties, there are methods to control the nucleation process and thereby the material properties.
• Grain size in materials is also controlled by the combination of controlled deformation and thermal treatments, called thermo mechanical treatment.
• A well designed thermo mechanical process gives a microstructure with a preferred orientation of grains and tailored material properties.

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Grain Shape

• Nature of the container in which the liquid metal cools, will also affect the shape and number of grains.
• When the molten grains formed, metal first strike the mould, the mould is cold and has a chilling effect.
• This results in the formation of a large number of nuclei and consequently large number of fine grains along the surface of the solidifying metal.
• As the mould is warmed up. the chilling effect is reduced, so that nuclei formation is retarded as the solidification progresses.
• Thus the crystals formed towards the centre of the mould will be larger in size.
• In the intermediate portion, the rate and nature of cooling are favourable to the formation of elongated columnar grains.
• Thus, ordinarily, three separate zones can be distinguished in an ingot solidified in a large mould.
• First zone is near to the mould walls where fine grains are observed, followed by a zone of long columnar grains and the third zone towards the centre of mould having coarse, equiaxed grains.
• If the mould is narrow, or longer, the equiaxed zone may be absent.
• Similarly, metallic mould tends to produce a fine grained structure, while sand mould a coarse grained structure.
• Also thin Sections are subjected to relatively larger rate of cooling, resulting in fine grains.
• A grain is called equiaxed when it is having the same dimensions along the three co-ordinate directions.

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Hall- Petch Equation

• Relationship between the yield stress and grain size of a material.

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• σ_o - yield strength (stress needed to cause plastic deformation.
• D – average diameter of grains
• σ_i and k are constants for materials

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• The yield strength of mild steel with an average grain size of 0.05mm is 138MPa. The yield strength of the same steel with a grain size of 0.007mm is 276MPa. What will be the grain size of the same steel with a yield stress of 207 MPa. Assume the Hall-Petch equation is valid and that the changes in yield stress are due to changes in grain size.

Identify the crystal structure

1 A^o= 10 ^-8 cm

2.6g/cm³

Question

• Nickel has FCC crystal structure, Determine its density if the atomic weight is 58.71 and the atomic radius is 1.25A^o