7217405-Material-Science

8/7/2019 7217405-Material-Science

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Material Science Syllabus

Satish Kailash Vasu/IISc, Bangalore V1/1-6-04/2

Module 10: Applications and Processing of Ceramics (1)Types and applications of ceramics. Fabrication and processing of ceramics.Module 11: Applications and Processing of Polymers (2)Mechanical behavior of polymers. Mechanisms of deformation and strengthening of polymers. Crystallization, melting and glass transition. Polymer types. Polymersynthesis and processing.

Module 12: Composites (1)Particle reinforced composites. Fiber reinforced composites. Structural compositesModule 13: Corrosion and Degradation of Materials (1)Corrosion of metals. Corrosion of ceramics. Degradation of polymers

Module 14: Electrical Properties (1)

Electrical conduction. Semi conductivity. Super conductivity. Electrical conduction inionic ceramics and in polymers. Dielectric behavior. Ferroelectricity. Piezoelectricity

Module 15: Thermal Properties (1)

Heat capacity. Thermal expansion. Thermal conductivity. Thermal stresses

Module 16: Magnetic Properties (1)

Diamagnetism and paramagnetism. Ferromagnetism.Antiferromagnetism andferrimagnetism. Influence of temperature on magnetic behavior. Domains andHysteresis

Module 17: Optical Properties (1)

Basic concepts. Optical properties of metals. Optical properties of nonmetals.Application of optical phenomena.

Module 18: Economic, Environmental and Social Issues of Material Usage (2)

Economic considerations. Environmental and societal considerations. Recyclingissues. Life cycle analysis and its use in design


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Lecture PlanModule Learning Units Hours

per topicTotalHours

1. Historic perspective and Materials Science 12. Why study properties of materials.

Classification of materials1

1) Introduction

3. Advanced materials, Future materials andModern materials

13

. Atomic Structure and atomic bonding insolids

1

5. Crystal structures, Crystalline and non-crystalline materials

1

6. Miller indices, Anisotropic elasticity andelastic behavior of composites

1

7. Structure and properties of polymers 1

2) Atomic Structure,Interatomic Bondingand Structure of Crystalline Solids

8. Structure and properties of Ceramics 1

5

9. Pint defects, theoretical yield point, line

defects and dislocations

13) Imperfections in

Solids 10. Interfacial defects, bulk or volume defectsand atomic vibrations

1 2

11. Elastic deformation and plastic deformation 112. Interpretation of tensile stress-strain curves 1

4) MechanicalProperties of Metals

13. Yielding under multiaxial stress, Yieldcriteria and macroscopic aspects of plasticdeformation and property variability anddesign factors

1 3

14. Diffusion Mechanisms and steady state andnon-steady state diffusion

15) Diffusion

15. Factors that influence diffusion and non-equilibrium transformation andmicrostructure

1 2

16. Dislocation and plastic deformation andmechanisms of strengthening in metals

1

17. Recovery, recrystallization and grain growth 1

6) Dislocations andStrengtheningMechanisms

18. Strengthening by second phase particles,optimum distribution of particles and latticeresistance to dislocation motion

1 3

19. Equilibrium phase diagrams, Particlestrengthening by precipitation andprecipitation reactions

1

20. Kinetics of nucleation and growth 121. The iron-carbon system, phasetransformations

1

7. Phase Diagrams

22. Transformation rate effects and TTTdiagrams, Microstructure and propertychanges in iron-carbon system

1

4

23. Fracture, ductile and brittle fracture 124. Fracture mechanics 1

8. Failure

25. Impact fracture, ductile brittle transition 1


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26. Fatigue, crack initiation and propagation,crack propagation rate

1

27. Creep, generalized creep behavior, stress andtemperature effects

15

28. Types on metals and alloys, fabrication of metals, thermal processing of metals

19. Applications andProcessing of Metalsand Alloys 29. Heat treatment and precipitation hardening 1

2

10. Applications andProcessing of Ceramics

30. Types and applications of ceramics,fabrication and processing of ceramics 1 1

31. Mechanical Behavior of polymers,Mechanisms of deformation andstrengthening of polymers

111. Applications andProcessing of Polymers

32. Crystallization, melting and glass transition,polymer types and polymer synthesis andprocessing

1

2

12. Composites 33. Particle reinforced composites, fiberreinforced composites, structural composites 1 1

13. Corrosion andDegradation of Materials

34. Corrosion of metals, Corrosion of ceramics,Degradation of polymers 1 1

14. ElectricalProperties

35. Electrical conduction, Semi conductivity,Super conductivity, Electrical conduction inionic ceramics and in polymers, Dielectricbehavior, Ferroelectricity, Piezoelectricity

2 1

15. ThermalProperties

36. Heat capacity, Thermal expansion, Thermalconductivity, Thermal stresses

1 1

16. Magnetic

Properties

37. Diamagnetism, paramagnetism,

ferromagnetism, antiferromagnetism, andferrimagnetism. Influence of temperature onmagnetic behavior, domains and hysteresis

1 1

17. OpticalProperties

38. Basic concepts, Optical properties of metals,Optical properties of nonmetals, Applicationof optical phenomena

1 1

39. Economic considerations, Environmentaland societal considerations, Recycling issues 1

18. Economic,Environmental andSocial Issues of Material Usage

0. Life Cycle analysis and its use in design 12


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Material Science/Introduction Learning Material

Introduction

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 naturalmaterials, like stone, clay, skins, and wood. When people found copper and how to makeit harder by alloying, the Bronze Age started about 3000 BC. The use of iron and steel, astronger material that gave advantage in wars started at about 1200 BC. The next big stepwas the discovery of a cheap process to make steel around 1850, which enabled therailroads and the building of the modern infrastructure of the industrial world.

Materials Science and Engineering

Understanding of how materials behave like they do, and why they differ in propertieswas 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 itsmicrostructure is the domain of Materials Science. The development of this scienceallowed designing materials and provided a knowledge base for the engineeringapplications (Materials Engineering).

Satish V. Kailas/IISc M1/L1/V1/Aug 2004/1


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Why Study Materials Science and Engineering?

To be able to select a material for a given use based on considerations of cost andperformance.

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, whichin turn alter the economics, like software-hardware trade-offs. Increasing applications of system engineering are in materials manufacturing (industrial engineering) and complexenvironmental systems.

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. Theone 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 andare opaque to light (shiny if polished). Examples: aluminum, steel, brass, gold.

Semiconductors: the bonding is covalent (electrons are shared between atoms). Theirelectrical 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 byCoulomb forces between them. They are usually combinations of metals orsemiconductors 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, andusually based on H, C and other non-metallic elements. They decompose at moderatetemperatures (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 materialthat is biocompatible and used, for instance, to replace human body parts.



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Advanced Materials

Materials used in "High-Tec" applications, usually designed for maximum performance,and normally expensive. Examples are titanium alloys for supersonic airplanes, magneticalloys for computer disks, special ceramics for the heat shield of the space shuttle, etc.

Modern Material's Needs

Engine efficiency increases at high temperatures: requires high temperaturestructural materials

Use of nuclear energy requires solving problem with residues, or advances innuclear waste processing.

Hypersonic flight requires materials that are light, strong and resist hightemperatures.

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.


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Satish V. Kailas ME/MS

Module-1

Introduction


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1. Historic perspective and Materials Science

2. Why study properties of materials, Classifica

materials

3. Advanced materials, Future materials and

materials needs

Contents


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Historic Perspective

Materials are very important in development of

civilization. In respect, their names are assoc

history, e.g. stone age, Bronze age, Iron age, etc.

With time humans discovered new materials a

techniques to produce known materials. Thi

ongoing process for coming centuries, i.e. no end i


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Materials Science

It can be defined as science dealing the relationshexist between the structures and properties of mwhich are useful in practice of engineers profession

Basic components and their interrelationship:

Structure

Properties Process

Performance


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Properties Of Materials

All solid engineering materials are characterized properties.

Engineering use of a material is reflection of its p

under conditions of use.

All important properties can be grouped into six caMechanical, Electrical, Thermal, Magnetic, Opt

Deteriorative.

Each material possess a structure, relevant propertie

dependent on processing and determines the perform


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Why Study Properties Of Materials? -

Since there are thousands of materials available it

impossible to select a material for a specific tas

otherwise its properties are known.

There are several criteria on which the final de

based on.

There are less chances of material possessing optim

combination of properties.

A need to trade off between number of factors!


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The classic example involves strength and ductility:

Normally material possessing strength have

ductility.In such cases a reasonable comprise betw

or more properties are important.

A second selection consideration is any deterio

material properties during service operations.

Finally the overriding consideration is economics.

Why Study Properties Of Material


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Classification Of MaterialsThree basic groups of solid engineering materials atomic bonds and structures:

MetalsCeram

Classification can also be done based on either p(mechanical, electrical, optical ), areas of (structures, machines, devices ). Further we cathese groups.

According to the present engineering needs:Composites, Semiconductors, Biomatrials


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Metals

Characteristics are owed to non-localized electrons bond between atoms) i.e. electrons are not bouparticular atom.

They are characterized by their high thermal and conductivities.

They are opaque, can be polished to high luster. Theand reflectivity of a metal arise from the responunbound electrons to electromagnetic vibrationsfrequencies.

Relatively heavier, strong, yet deformable.

E.g.: Steel, Aluminium, Brass, Bronze, Lead, Titan


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Ceramics

They contain both metallic and nonmetallic elementCharacterized by their higher resistance to high tempand harsh environments than metals and polymers.

Typically good insulators to passage of both electricity.

Less dense than most metals and alloys.

They are harder and stiffer, but brittle in nature.

They are mostly oxides, nitrides, and carbides of me

Wide range: traditional (clay, silicate glass, ce

advanced (carbides, pure oxides, non-silicate glasseE.g.: Glass, Porcelain, Minerals, etc.


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Polymers

Commercially called plastics ; noted for their lflexibility and use as insulators.

Mostly are of organic compounds i.e. based onoxygen and other nonmetallic elements.

Consists large molecular structures bonded by covavander Waals forces.

They decompose at relatively moderate temperatur400 C).

Application: packaging, textiles, biomedical device

devices, ceramics household items, toys, etc.E.g.: Nylon, Teflon, Rubber, Polyester, etc.


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CompositesConsist more than one kind of material; tailor benefit from combination of best characteristicsconstituent.

Available over a very wide range: natural (synthetic ( fiberglass ).

Many are composed of two phases; one is matrix continuous and surrounds the other, dispersed phase

Classified into many groups: (1) depending on orienphases; such as particle reinforced, fiber reinforceddepending on matrix; metal matrix, polymer matrix

matrix.E.g.: Cement concrete, Fiberglass, special refractory bricks, plywood, etc.


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Semiconductors

Their electrical properties are intermediate when c

with electrical conductors and electrical insulators.

These electrical characteristics are extremely sensiti

presence of minute amounts of foreign atoms.

Found very many applications in electronic devi

decades through integrated circuits. In can be

semiconductors revolutionized the electronic ind

last few decades.


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Biomaterials

Those used for replacement of damaged or diseasparts.

Primary requirements: must be biocompatible wtissues, must not produce toxic substances.

Important materials factors: ability to support the for

friction and wear, density, reproducibility and cost.All the above materials can be used dependingapplication.

A classic example: hip joint.

E.g.: Stainless steel, Co-28Cr-6Mo, Ti-6Al-4V, ulmolecular weight polyethylene, high purity dense Aetc.


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Advanced MaterialsCan be defined as materials used in high-tech dewhich operates based on relatively intricsophisticated principles (e.g. computers, air/spaelectronic gadgets, etc.).

These are either traditional materials with properties or newly developed materials wiperformance capabilities. Thus, these are expensive.

Typical applications: integrated circuits, lasers, LCoptics, thermal protection for space shuttle, etc.

E.g.: Metallic foams, inter-metallic compoundcomponent alloys, magnetic alloys, special ceramhigh temperature materials, etc.


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Future Materials - 1

Group of new and state-of-the-art materials nodeveloped, and expected to have significant influpresent-day technologies, especially in the medicine, manufacturing and defense.

Smart/Intelligent material system consists somesensor (detects an input) and an actuator responsive and adaptive function).

Actuators may be called upon to change shape, natural frequency, mechanical characteristics in reschanges in temperature, electric/magnetic fields, mpH, etc.


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Four types of materials used as actuators:Shape memory alloysPiezoelectric ceramicsMagnetostrictive materials

Electro-/Magneto-rheologic fluids

Materials / Devices used as sensors:Optical fibersPiezoelectric materials

Micro-electro-mechanical systems (MEMS)- etc.


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Typical applications:1. By incorporating sensors, actuators and chip processystem, researchers are able to stimulate biologicalike behavior.

2. Fibers for bridges, buildings, and wood utility poles

3. They also help in fast moving and accurate robot paspeed helicopter rotor blades.4. Actuators that control chatter in precision machine t5. Small microelectronic circuits in machines rang

computers to photolithography prints.

6. Health monitoring detecting the success or failproduct.


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Modern Materials Needs

Engine efficiency increases at high temperatures; high temperature structural materials.

Use of nuclear energy requires solving problems withor advance in nuclear waste processing.

Hypersonic flight requires materials that are light, stresist high temperatures.

Optical communications require optical fibers thalight negligibly.

Civil construction materials for unbreakable windo

Structures: materials that are strong like metals acorrosion like plastics.


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Material Science/Atomic Structure, Inter atomic bonding Learning Materialand structure of crystalline solids and atomic bonding in solids


Atomic Structure and atomic Bonding in solids

Atomic Structure :

Atoms are composed of electrons, protons, and neutrons. Electron and protons arenegative and positive charges of the same magnitude, 1.6 10 -19 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 -27 kg, 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 andprotons have very similar masses, roughly equal to 1 amu. A neutral atom has the samenumber of electrons and protons, Z.

A mole is the amount of matter that has a mass in grams equal to the atomic mass in amuof the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in amole is called the Avogadro number, N av = 6.023 10 23. Note that N av = 1 gram/1 amu.

Calculating n, the number of atoms per cm 3 in a piece of material of density (g/cm 3).

n = N av / M

where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with adensity = 1.8 g/cm 3, M =12, we get 6 10 23 atoms/mol 1.8 g/cm 3 / 12 g/mol) = 9 1022 C/cm 3.

For a molecular solid like ice, one uses the molecular mass, M(H 2O) = 18. With a densityof 1 g/cm 3, one obtains n = 3.3 10 22 H2O/cm 3. Note that since the water moleculecontains 3 atoms, this is equivalent to 9.9 10 22 atoms/cm 3.

Most solids have atomic densities around 6 10 22 atoms/cm 3. The cube root of thatnumber gives the number of atoms per centimeter, about 39 million. The mean distancebetween atoms is the inverse of that, or 0.25 nm. This is an important number that givesthe scale of atomic structures in solids.


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Atomic bonding in solids:

Primary Interatomic Bonds

Ionic Bonding

This is the bond when one of the atoms is negative (has an extra electron) and another ispositive (has lost an electron). Then there is a strong, direct Coulomb attraction. Anexample is NaCl. In the molecule, there are more electrons around Cl, forming Cl - andless around Na, forming Na +. Ionic bonds are the strongest bonds. In real solids, ionicbonding is usually combined with covalent bonding.

Covalent Bonding

In covalent bonding, electrons are shared between the molecules, to saturate the valency.The simplest example is the H 2 molecule, where the electrons spend more time inbetween the nuclei than outside, thus producing bonding.

Metallic Bonding

In metals, the atoms are ionized, loosing some electrons from the valence band. Thoseelectrons form an electron sea , which binds the charged nuclei in place, in a similar waythat the electrons in between the H atoms in the H 2 molecule bind the protons.

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 dipolefluctuates. This fluctuation in atom A produces a fluctuating electric field that is felt bythe electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons areon 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 2O (Hs are partially +, O is partially ), will induce a dipole in a

nearby atom, leading to bonding.

Permanent Dipole Bonds

This is the case of the hydrogen bond in ice. The H end of the molecule is positivelycharged and can bond to the negative side of another dipolar molecule, like the O side of the H 2O dipole


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Crystal Structures:

Atoms self-organize in crystals , most of the time. The crystalline lattice is a periodicarray 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. Examplesof 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, withwell-defined radii. In this scheme, the shortest distance between two like atoms is onediameter.

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 4 3 0.68

FCC 4 12 2 2 0.74

HCP 6 12 0.74


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Crystalline and Non-crystalline materials:

Single Crystals

Crystals can be single crystals where the whole solid is one crystal. Then it has a regulargeometric structure with flat faces.

Polycrystalline Materials

A solid can be composed of many crystalline grains, not aligned with each other. It iscalled polycrystalline . The grains can be more or less aligned with respect to each other.Where they meet is called a grain boundary .

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 tetragonalorder of crystalline SiO 2 (quartz) is still apparent in amorphous SiO 2 (silica glass.)


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Miller Indices:Rules for Miller Indices:

Determine the intercepts of the face along the crystallographic axes, in terms of unit cell dimensions.

Take the reciprocals Clear fractions Reduce to lowest terms

For example, if the x-, y-, and z- intercepts are 2, 1, and 3, the Miller indices arecalculated as:

Take reciprocals: 1/2, 1/1, 1/3 Clear fractions (multiply by 6): 3, 6, 2 Reduce to lowest terms (already there)

Thus, the Miller indices are 3,6,2. If a plane is parallel to an axis, its intercept is atinfinity and its Miller index is zero. A generic Miller index is denoted by (hkl) .

If a plane has negative intercept, the negative number is denoted by a bar above thenumber. Never alter negative numbers. For example, do not divide -1, -1, -1 by -1 to get1,1,1. This implies symmetry that the crystal may not have!


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Some General Principles

If a Miller index is zero, the plane is parallel to that axis. The smaller a Miller index, the more nearly parallel the plane is to the axis. The larger a Miller index, the more nearly perpendicular a plane is to that axis. Multiplying or dividing a Miller index by a constant has no effect on the

orientation of the plane Miller indices are almost always small.

Why Miller Indices?

Using reciprocals spares us the complication of infinite intercepts. Formulas involving Miller indices are very similar to related formulas from

analytical geometry. Specifying dimensions in unit cell terms means that the same label can be applied

to any face with a similar stacking pattern, regardless of the crystal class of thecrystal. Face 111 always steps the same way regardless of crystal system.

Anisotropy

Different directions in the crystal have different packing. For instance, atoms along theedge FCC crystals are more separated than along the face diagonal. This causesanisotropy in the properties of crystals; for instance, the deformation depends on the

direction in which a stress is applied.

Elastic Behavior of Composites:

The idea is that by combining two or more distinct materials one can engineer a newmaterial with the desired combination of properties (e.g., light, strong, corrosionresistant). The idea that a better combination of properties can be achieved is called theprinciple of combined action.

A type of composite that has been discussed is perlitic steel, which combines hard, brittle

cementite with soft, ductile ferrite to get a superior material.

Natural composites: wood (polymer-polymer), bones (polymer-ceramics).

Usual composites have just two phases:


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matrix (continuous) dispersed phase (particulates, fibers)

Properties of composites depend on

Properties of phases Geometry of dispersed phase (particle size, distribution, orientation) Amount of phase

Classification of composites: three main categories:

Particle-reinforced (large-particle and dispersion-strengthened) Fiber-reinforced (continuous (aligned) and short fibers (aligned or random) Structural (laminates and sandwich panels)

In many applications, like in aircraft parts, there is a need for high strength per unitweight (specific strength). This can be achieved by composites consisting of a low-density (and soft) matrix reinforced with stiff fibers.

The strength depends on the fiber length and its orientation with respect to the stressdirection.

The efficiency of load transfer between matrix and fiber depends on the interfacial bond.


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Structure and properties of polymers :

Polymers are common in nature, in the form of wood, rubber, cotton, leather, wood, silk,proteins, enzymes, starches, cellulose. Artificial polymers are made mostly from oil.Their use has grown exponentially, especially after WW2. The key factor is the very lowproduction cost and useful properties (e.g., combination of transparency and flexibility,long elongation).

Hydrocarbon Molecules

Most polymers are organic, and formed from hydrocarbon molecules. These moleculescan have single, double, or triple carbon bonds. A saturated hydrocarbon is one whereall bonds are single, that is, the number of atoms is maximum (or saturated). Among thistype are the paraffin compounds, C nH2n+2 (Table 15.1). In contrast, non-saturated

hydrocarbons contain some double and triple bonds.

Isomers are molecules that contain the same molecules but in a different arrangement.An example is butane and isobutane.

Polymer molecules are huge, macromolecules that have internal covalent bonds. For mostpolymers, these molecules form very long chains. The backbone is a string of carbonatoms, often single bonded.

Polymers are composed of basic structures called mer units. A molecule with just onemer is a monomer.

The Chemistry of Polymer Molecules

Examples of polymers are polyvinyl chloride (PVC), poly-tetra-chloro-ethylene (PTFE orTeflon), polypropylene, nylon and polystyrene. Chains are represented straight but inpractice they have a three-dimensional, zig-zag structure (Fig. 15.1b).

When all the mers are the same, the molecule is called a homopolymer. When there ismore than one type of mer present, the molecule is a copolymer .

Molecular Weight

The mass of a polymer is not fixed, but is distributed around a mean value, since polymermolecules have different lengths. The average molecular weight can be obtained byaveraging the masses with the fraction of times they appear (number-average) or with themass fraction of the molecules (called, improperly, a weight fraction).


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The degree of polymerization is the average number of mer units, and is obtained bydividing the average mass of the polymer by the mass of a mer unit.

Polymers of low mass are liquid or gases, those of very high mass (called high-polymers,are solid). Waxes, paraffins and resins have intermediate masses.

Molecular Shape

Polymers are usually not linear; bending and rotations can occur around single C-C bonds(double and triple bonds are very rigid) (Fig. 15.5). Random kings and coils lead toentanglement, like in the spaghetti structure shown in Fig. 15.6.

Molecular Structure

Typical structures are :

linear (end-to-end, flexible, like PVC, nylon) branched cross-linked (due to radiation, vulcanization, etc.) network (similar to highly cross-linked structures).

Molecular Configurations

The regularity and symmetry of the side-groups can affect strongly the properties of polymers. Side groups are atoms or molecules with free bonds, called free-radicals, like

H, O, methyl, etc.

If the radicals are linked in the same order, the configuration is called isostatic

In a stereoisomer in a syndiotactic configuration, the radical groups alternative sides inthe chain.

In the atactic configuration, the radical groups are positioned at random.

Copolymers

Copolymers, polymers with at least two different types of mers can differ in the way themers are arranged. Fig. 15.9 shows different arrangements: random, alternating, block,and graft.

Polymer Crystallinity


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Crystallinity in polymers is more complex than in metals (fig. 15.10). Polymer moleculesare often partially crystalline ( semicrystalline ), with crystalline regions dispersed withinamorphous material. .

Chain disorder or misalignment, which is common, leads to amorphous material sincetwisting, kinking and coiling prevent strict ordering required in the crystalline state.Thus, linear polymers with small side groups, which are not too long form crystallineregions easier than branched, network, random copolymers, or polymers with bulky sidegroups.

Crystalline polymers are denser than amorphous polymers, so the degree of crystallinitycan be obtained from the measurement of density.

Polymer Crystals

Different models have been proposed to describe the arrangement of molecules insemicrytalline polymers. In the fringed-micelle model, the crystallites (micelles) areembedded in an amorphous matrix (Fig.15.11). Polymer single crystals grown are shapedin regular platelets (lamellae) (Fig. 15.12). Spherulites (Fig. 15.4) are chain-foldedcrystallites in an amorphous matrix that grow radially in spherical shape grains.


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Structure and properties of ceramics:

Ceramics are inorganic and non-metallic materials that are commonly electrical andthermal insulators, brittle and composed of more than one element (e.g., two in Al 2O3)

Ceramic Structures

Ceramic bonds are mixed, ionic and covalent, with a proportion that depends on theparticular ceramics. The ionic character is given by the difference of electronegativitybetween the cations (+) and anions (-). Covalent bonds involve sharing of valenceelectrons. Very ionic crystals usually involve cations which are alkalis or alkaline-earths(first two columns of the periodic table) and oxygen or halogens as anions.

The building criteria for the crystal structure are two:

maintain neutrality charge balance dictates chemical formula achieve closest packing

the condition for minimum energy implies maximum attraction and minimum repulsion.This leads to contact, configurations where anions have the highest number of cationneighbors and viceversa.

Silicate Ceramics

Oxygen and Silicon are the most abundant elements in Earths crust. Their combination(silicates) occur in rocks, soils, clays and sand. The bond is weekly ionic, with Si 4+ as thecation and O 2- as the anion. r Si = 0.04 nm, r O.= 0.14 nm, so r C /rA = 0.286.

The tetrahedron is charged: Si 4+ + 4 O 2- (Si O 4)4-. Silicates differ on how thetetrahedra are arranged. In silica, (SiO 2), every oxygen atom is shared by adjacenttetrahedra. Silica can be crystalline (e.g., quartz) or amorphous, as in glass.

Soda glasses melt at lower temperature than amorphous SiO 2 because the addition of Na 2O (soda) breaks the tetrahedral network. A lower melting point makes it easy to formglass to make, for instance, bottles.

Carbon


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Carbon is not really a ceramic, but an allotropic form, diamond, may be thought as a typeof ceramic. Diamond has very interesting and even unusual properties:

diamond-cubic structure (like Si, Ge) covalent C-C bonds highest hardness of any material known very high thermal conductivity (unlike ceramics) transparent in the visible and infrared, with high index of refraction semiconductor (can be doped to make electronic devices) metastable (transforms to carbon when heated)

Synthetic diamonds are made by application of high temperatures and pressures or bychemical vapor deposition. Future applications of this latter, cheaper production method

include hard coatings for metal tools, ultra-low friction coatings for space applications,and microelectronics.

Graphite has a layered structure with very strong hexagonal bonding within the planarlayers (using 3 of the 3 bonding electrons) and weak, van der Waals bonding betweenlayers using the fourth electron. This leads to easy interplanar cleavage and applicationsas a lubricant and for writing (pencils). Graphite is a good electrical conductor andchemically stable even at high temperatures. Applications include furnaces, rocketnozzles, electrodes in batteries.

A recently (1985) discovered formed of carbon is the C 60 molecule, also known as

fullerene or bucky-ball (after the architect Buckminster Fuller who designed the geodesicstructure that C 60 resembles.) Fullerenes and related structures like bucky-onions amdnanotubes are exceptionally strong. Future applications are as a structural material andpossibly in microelectronics, due to the unusual properties that result when fullerenes aredoped with other atoms.

Imperfections in Ceramics

Imperfections include point defects and impurities. Their formation is strongly affectedby the condition of charge neutrality (creation of unbalanced charges requires theexpenditure of a large amount of energy.

Non-stoichiometry refers to a change in composition so that the elements in the ceramicare not in the proportion appropriate for the compound (condition known asstoichiometry). To minimize energy, the effect of non-stoichiometry is a redistribution of the atomic charges (Fig. 13.1).


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Charge neutral defects include the Frenkel and Schottky defects. A Frenkel-defect is avacancy- interstitial pair of cations (placing large anions in an interstitial position requiresa lot of energy in lattice distortion). A Schottky-defect is the a pair of nearby cation andanion vacancies.

Introduction of impurity atoms in the lattice is likely in conditions where the charge ismaintained. This is the case of electronegative impurities that substitute a lattice anionsor electropositive substitutional impurities. This is more likely for similar ionic radiisince this minimizes the energy required for lattice distortion. Defects will appear if thecharge of the impurities is not balanced.

Brittle Fracture of Ceramics

The brittle fracture of ceramics limits applications. It occurs due to the unavoidablepresence of microscopic flaws (micro-cracks, internal pores, and atmosphericcontaminants) that result during cooling from the melt. The flaws need to crack formation, and crack propagation (perpendicular to the applied stress) is usuallytransgranular, along cleavage planes. The flaws cannot be closely controlled inmanufacturing; this leads to a large variability (scatter) in the fracture strength of ceramicmaterials.

The compressive strength is typically ten times the tensile strength. This makes ceramicsgood structural materials under compression (e.g., bricks in houses, stone blocks in thepyramids), but not in conditions of tensile stress, such as under flexure.

Plastic deformation in crystalline ceramics is by slip, which is difficult due to thestructure and the strong local (electrostatic) potentials. There is very little plasticdeformation before fracture.

Non-crystalline ceramics, like common glass deform by viscous flow (like very high-density liquids). Viscosity decreases strongly with increases temperature.


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Atomic Structures, Interatomic Bonding of Crystalline Solids

Module 2


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1. Atomic Structure and Atomic bonding in sol

2. Crystal structures, Crystalline and Non-cryst

3. Miller indices, Anisotropic elasticity and Eof Composites

4. Structure and properties of polymers

5. Structure and properties of ceramics

Contents


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Atomic Structure -1Every atom consists of a small nucleus protons and neutrons, which is encirclelectrons in their orbitals , specific energy levThe top most ortibal electrons,valence electrmost material properties that are of intereE.g.: chemical properties, nature of bondingoptical/magnetic/electrical properties.Electrons and protons are negative and posithe same magnitude being 1.60x10-19 coulomb Neutrons are electrically neutral.

Protons and neutrons have approximate1.67x10-27 kg, which is larger than that o9.11x10-31 kg.


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Atomic number ( Z ) - is the number of protonAtomic mass ( A) - is the sum of the massand neutrons within the nucleus.Atomic mass is measured in atomic mawhere 1amu=(1\12) the mass of most commcarbon atom, measured in grams.

A Z+N , where N is number of neutrons.Isotopes - atoms with same atomic numbeatomic masses.

A mole is the amount of matter that has a equal to the atomic mass inamu of the atmole of carbon has a mass of 12 grams.

Atomic Structure -2


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The number of atoms or molecules in a molcalled the Avogadros number, Nay. Nay=16.023x1023.E.g.: Calculating the number of atoms per c3of material of densityd (g/cm3)n = N av d / M , where M is the atomic massThus, for graphite (carbon) with a densityd =

M =12, n = 6.023 1023 atoms/mol 1.8 g/c= 9 1022 atoms/cm3.Most solid materials will have atomic densit6x1022, thats about 39 million atoms per centMean distance between atoms is in the ranggives an idea about scale of atomic structures

Atomic Structure -3


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Atomic Bonding In Solid

Two questions need to be answered: whyclustered together?, and how they are arrange

Bonds are two kinds Primary, and Seconda

Primary bonds relatively stronger. Exists inmaterials.

E.g.: Ionic, Covalent, and Metallic bonds.

Secondary bonds relatively weaker bonds

substances like water along with primary bonE.g.: Hydrogen, and Vander Waals forces.


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Atomic bonding

Primary bonding

Secondaryionic covalent metallic

Fluctuatinginduced

Polindu

Atomic Bond In Solids


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Primary Inter-Atomic Bon

These bonds invariably involves valence elec

Nature of bond depends on electron respective atoms.

Atoms tend to acquire stable electron arranvalence orbitals by transferring (ionic), shand metallic) valence electrons. This leads bonds.

Bond energies are in order of 1000 kJ/mol.


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Ionic BondThis primary bond exists between two atomof electron(s) results in one of the atoms to b(has an extra electron) and another positielectron).This bond is a direct consequence of s

attraction between charged atoms.Basically ionic bonds are non-directional in nIn real solids, ionic bonding is usually excovalent bonding.

E.g.: NaCl. In the molecule, there are more Cl, forming Cl- and fewer electrons around N


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Covalent Bond

This bond comes into existence if valencshared between a pair of atoms, thus acqusaturating the valence configuration.

Covalent bonds are stereo specific i.e. each

a specific pair of atoms, which share a pair opposite magnetic spins).

Typically, covalent bonds are very strong, annature.

E.g.: H2 molecule, where an electron from eshared by the other atom, thus producing the


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Metallic Bond

This bond comes into existence if valencshared between number of atoms, i.e. arnucleuses are surrounded by electron pool.

Shared electrons are not specific to a pacontrast to Covalent bond, i.e. electrons are d

As shared electrons are delocalized, metallicdirectional.

Very characteristic properties of metals like helectrical conductivities are result of presencelectron pool.


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Secondary Inter-Atomic Bon

These bonds involves atomicor molecular dipo

Bonds can exists between induced and pe

(polar molecules).

Bond comes into existence because of Colu

between positive end of one dipole and

another dipole.

Bond energies are in order of 10 kJ/mol


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Secondary Inter-Atomic Bon

Existence of these depends on three kindfluctuating dipoles, Polar-molecule dipoles dipoles.

Permanent dipole bonds are also called Hyd

covalently bonded hydrogen atoms for exaF-H share single electron becomes pos proton that is capable of strong attractivenegative end of an adjacent molecule.

Hydrogen bonds is responsible for water t exat room temperature.


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Crystal Structures

All solid materials are made of atoms/molearranged in specific order in some mcrystalline solids . Otherwise non-crystallinesolids .

Groups of atoms/molecules specifically arran Lattice is used to represent a three-dimenarray of points coinciding with atom position

Unit cell is smallest repeatable entity that

completely represent a crystal structure. It block of crystal structure.


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Unit Cell

It is characterized by:

Type of atom and their radii, R

Cell dimensions,a and c (for hexagonal structu

Number of atoms per unit cell,n

Coordination number (CN ) closest neighbors

Atomic packing factor, APF

Most common unit cells Face-centerecentered cubic and Hexagonal.


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Common Crystal Structu

126Hexagonal Close Packed

4/124Face-Centered Cubic

4/82Body-Centered Cubic

4/61Simple Cubic

a / RCN nUnit Cell


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Schematic Unit Cells


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Miller Indices

A system of notation is required to iddirection(s) or plane(s) to characterize theatoms in a unit cellFormulas involving Miller indices are very

formulas from analytical geometry simple tUse of reciprocals avoids the complicainterceptsSpecifying dimensions in unit cell terms melabel can be applied to any plane with a pattern, regardless of the crystal class of (111) always steps the same way regardless o


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Miller Indices - Directio

A vector of convenient length is placed required direction

The length of the vector projection on each

measuredin terms of unit cell dimensionsThese three numbers are made to smallestknown as indices, by multiplying or dividinfactor

The three indices are enclosed in square bracA family of directions is represented by


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Miller Indices - Example


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Miller Indices Useful ConIf a plane is parallel to an axis, its intercept its Miller index will be zero

Never alter negative numbers. This implies the crystal may not have! Use bar over represent negative numbers.A plane or direction of family is not necessother planes or directions in the same familyThe smaller the Miller index, more nearly pto that axis, and vice versaMultiplying or dividing a Miller index by effect on the orientation of the planeWhen the integers used in the Miller indicthan one digit, the indices must be separatE.g.: (3,10,13)


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Useful Conventions For Cub[uvw] is normal to (hkl) if u = h, v = k , and w = [111][uvw] is parallel to (hkl) if hu + kv + lw = 0Two planes (h1k1l1 ) and (h2k2l2 ) are normal + l1l2 =0Two directions (u1v1w1 ) and (u2v2w2 ) are norv1v2 + w1w2 =0Inter-planar distance between family of plane by:Angle between two planes is given by:

222}{ lk h

ad hkl ++

=

21

21

21

2121coshlk h

k k hh

++

+=


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Miller-Bravis Indices

Miller indices can describe all possible planeany crystal.However, Miller-Bravis indices are used in hesystems as they can reveal hexagonal symmeIndices are based on four axes three are cop

plane at 120

apart, fourth axis is perpendicula planeBoth for planes/directions, extra index is give

t = -(u+v), i = -(h+k )

where plane is represented as [uvtw], and a direrepresented by (hkil )E.g.: Basal plane (0001), Prismatic plane


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Polymers - DefinitionPolymers are made of basic units calledmers

These are usually Hydrocarbons where matoms are Hydrogen and CarbonWhen structure consists of only onemer , it is mcontains more than onemer , it is called polym

Isomers are molecules those contain same numers but arrangement will be differentE.g.: Butene and IsobuteneWhen a polumer has ONE kind of mers in its called homopolymer Polymer made with more than one kind ofmcopolymer


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Polymer Structures

Linear , where mer units are joined togethersingle chains. E.g.: PVC, nylon.

Branched , where side-branch chains are conones. Branching of polymers lowers polymer

of lower packing efficiencyCross-linked , where chains are joined onevarious positions by covalent bonds. This usually achieved at elevated temperatures byE.g.: vulcanization of rubber

Network , trifunctional mer units with 3-D nunder this category. E.g.: epoxies, phenol-for


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Polymer Structures

Schematic presentation of polymer structuresIndividualmers are represented by solid circle


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Thermo-Sets Thermo-PPolymers mechanical response at elevatestrongly depends their chain configurationBased on this response polymers are groupthermo-sets and thermo-plastsThermo-sets: become permanently hard when

not soften during next heat cycle. Durincovalent bonds forms thus extensive cros place. Stronger and harder than thermo-plastsE.g.: Vulcanized rubber, epoxies, some polyeThermo-plasts: softens at high temperature

hard at ambient temperatures. The procesUsually made of linear and branched structurE.g.: Polystyrene, Acrylics, Cellulosics, Viny


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Polymer Crystallinity

Crystallinity in polymers is more complex thaPolymer crystallinity range from almost crystamorphous in nature

It depends on cooling path and on chain conf

Crystalline polymers are more denser than am polymers

Many semicrystalline polymers formspherulitesspherulite consists of collection of ribbon likelamellar crystallites.

E.g.: PVC (Poly Vinyl Chloride)


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Polymer Properties


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Ceramics

Ceramics are inorganic and non-metallic mate

Atomic bonds in ceramics are mixed covale

Proportion of bonds is specific for a ceramic

Ionic bonds exists between alkalis/alkaline-e

oxygen/halogens.

Mostly oxides, carbides, nitrides of metals arE.g.: Sand, Glass, Bricks, Marbles


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Ceramic Structures

Building criteria for ceramic structures:- maintain neutrality- closest packing

Packing efficiency can be characterized bnumber which depends on cation-anion radius

6432Coordination

number

0.414 0.732

0.225 0.414

0.155 0.225

1. Thus, a working value forthe tensile strength would be W = TS / N .

Utilization of design stress is usually preferred since it is based on the anticipatedmaximum applied stress instead of the yield strength of the material. The choice of anappropriate value of N is necessary. If N is too large, then component over design willresult; that is , either too much material or an alloy having a higher than necessary

strength will be used. Values normally range between 1.2 and 4.0. Selection of N willdepend on a number of factors, including economics, previous experience, the accuracywith which mechanical forces and material properties may be determined and mostimportant, the consequences of failure in terms of loss of life or property damage.


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Material Science/Mechanical Properties of Metals Lecture Notes

Satish Kailash Vasu/IISc, Bangalore M4/L2/V1/dec2004/ 1

4.3 Interpretation of tensile stress-strain curves:

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 pointis 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

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 andreforming bonds.

Plastic deformation is caused by the motion of dislocations.

Tensile strength . When stress continues in the plastic regime, the stress-strain passesthrough a maximum, called the tensile strength ( TS) , and then falls as the material startsto develop a neck and it finally breaks at the fracture point .

For structural applications, the yield stress is usually a more important property than thetensile strength, since once the it is passed, the structure has deformed beyond acceptable

limits.

Ductility . The ability to deform before braking. It is the opposite of brittleness . Ductilitycan be given either as percent maximum elongation max or maximum area reduction.

%EL = max x 100 %

%AR = ( A 0 - A f )/ A 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 thetotal area under the strain-stress curve . It is measured by an impact test .


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True Stress and Strain

When one applies a constant tensile force the material will break after reaching the tensilestrength. The material starts necking (the transverse area decreases) but the stress cannotincrease beyond TS . The 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.


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4.4 Yielding under multiaxial stress-strain curves

4.5 Yield criteria and macroscopic aspects of plastic deformation

Gross plastic deformation of a polycrystalline specimen corresponds to the comparable

distortion of the individual grains by means of slip. During deformation, mechanicalintegrity and coherency are maintained along the grain boundaries; that is, the grainboundaries is constrained, to some degree, in the shape it may assume by its neighboringgrains. Before deformation the grains are equiaxed, or have approximately the samedimension in all directions. For this particular deformation, the grains become elongatedalong the directions. For this particular deformation, the grains become elongated alongthe direction in which the specimen was extended.

4.6 Property variability and design 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 minimumvalue tolerable. This leads to the use of a safety factor N > 1. Thus, a working value forthe tensile strength would be W = TS / N .

Utilization of design stress is usually preferred since it is based on the anticipatedmaximum applied stress instead of the yield strength of the material. The choice of anappropriate value of N is necessary. If N is too large, then component over design willresult; that is , either too much material or an alloy having a higher than necessarystrength will be used. Values normally range between 1.2 and 4.0. Selection of N willdepend on a number of factors, including economics, previous experience, the accuracywith which mechanical forces and material properties may be determined and most

important, the consequences of failure in terms of loss of life or property damage.


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Mechanical Properties Of Metals

Module - 4


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1. Elastic deformation and Plastic deformation

2. Interpretation of tensile stress-strain curves

3. Yielding under multi-axial stress, Yield

Macroscopic aspects of plastic deformation and

variability & Design considerations

Contents


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Mechanical Loads - Deformatio

ObjectExternal load

translation rotation deformation

distortion change in

dilatation change in


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Temporary / recoverable Permanent

time independent elastic

time dependent anelastic (under load),

elastic aftereffect (after removalof load)

Deformation Function Of Time

time independe

time dependen(under load),

combination of recoverable and permanent, but timdependent visco-elastic


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Engineering Stress Engineering

Load applied acts over an area.Parameter that characterizes the load effect is load divided by original area over which the loadis called conventional stress or engineering ssimply stress. It is denoted by s.

Corresponding change in length of the ocharacterized using parameter given as per cenin the length known as strain. It is denoted by e.

As object changes its dimensions under appliengineering stress and strain are not be representatives.

0

0

0

, L

L Le

A P

s==


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True Stress True Strain

True or Natural stress and strain are defined to g picture of the instantaneous conditions.

True strain:

True stress:

+

+

+

= ...223

1

12

0

01

L L L

L L L

L L L

0

L

L=

)1(0

0 +=== e s A A

A P

A P


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Different Loads Strains


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Elastic Deformation - 1

A material under goes elastic deformation first f by plastic deformation. The transition is not many instances.For most of the engineering materials, completdeformation is characterized by strain proport

stress. Proportionality constant is called elastic or Youngs modulus, E.

Non-linear stress-strain relation is applimaterials. E.g.: rubber.

E =


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For materials without linear stress-strain portion, eior secant modulus is used in design calculations.


The tangent modulus istaken as the slope of

stress-strain curve atsome specified level.

Secant modulerepresents the slope of secant drawn from theorigin to some given

point of the - curve.


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Theoretical basis for elastic deformation revdisplacements of atoms from their equilibrium po stretching of atomic bonds.Elastic moduli measures stiffness of material. It c

be a measure of resistance to separation of atoms.Elastic modulus = fn (inter-atomic forces)

= fn (inter-atomic distance)= fn (crystal structure, orientation

=> For single crystal elastic moduli are not isoFor a polycrystalline material, it is conside

isotropic.Elastic moduli slightly changes with temp(decreases with increase in temperature).


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Linear strain is always accompanied by lateral smaintain volume constant.The ratio of lateral to linear strain is called Poisso( ).Shear stresses and strains are related as = G

shear modulus or elastic modulus in shear.Bulk modulus or volumetric modulus of elasdefined as ratio between mean stress to volumetri

K = m / All moduli are related through Poissons ratio.

)1(2 += E G

1(3 == K

m


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Plastic Deformation - 1Following the elastic deformation, material un

plastic deformation.Also characterized by relation between stress and constant strain rate and temperature.Microscopicallyit involves breaking atomic

moving atoms, then restoration of bonds.Stress-Strain relation here is complex because o plane movement, dislocation movement, and the othey encounter.Crystalline solids deform by processes slip and t

in particular directions.Amorphous solids deform by viscous flow mewithout any directionality.


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Plastic Deformation - 2

Because of the complexity involved, theory of pneglects the following effects:- Anelastic strain, which is time dependent recstrain.- Hysteresis behavior resulting from loading

loading of material.- Bauschinger effect dependence of yield sloading path and direction.Equations relating stress and strain are called conequations.

A true stress-strain curve is called flow curvethe stress required to cause the material to flow plto certain strain.


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Plastic Deformation - 3

Because of the complexity involved, there hamany stress-strain relations proposed.

),,,( turemicrostrucT fn &=

n

K =

m K &=

n K )( 0 +=

no K +=

Strain hardening exponent

Strain-rate sensitivity, m =

Yield strength 0

Strain from previous work


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Tensile Stress-Strain Curve - 1

A Starting point E TensiE Corresponding to E on flow curveF Fracture point I Fractu


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A Starting point B ProportioC Elastic limit D Yield limG 0.2% offset strain H Yield stra


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Apart from different strains and strength points, twimportant parameters can be deduced from the curresilience and toughness.Resilience (U r ) ability to absorb energy unddeformation

Toughness (U t) ability to absorb energy undeinvolving plastic deformation. Represents combin

both strength and ductility.

E s

E s

se sU r 221

21 200

000===

f u

f ut e s s

e sU 2

0+

f ut e sU 32

area ADH

area AEFI


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Yielding Under Multi-Axial Stre

With on-set of necking, uni-axial stress conditiointo tri-axial stress as geometry changes tales placflow curve need to be corrected from corresponding to tensile strength. Correction h

proposed by Bridgman.

[ ])2/1ln()/21()(

Raa Ravg x

++=

where

( x)avg measured stress in the axial direction,

a smallest radius in the neck region,

R radius of the curvature of neck


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Yield Criteria - 1Von Mises or Distortion energy criterion:yielding occurs once second invariant of stress

(J2) reaches a critical value. In other terms, yieonce the distortion energy reaches a critical value.

22 k J = [ 32322212 ()()(6

1 ++= J

Under uni-axial tension, 1 = 0 , and 2= 3= 0

[ ]12132322210

022

020

)()()(2

1

3)(61

++=

==+ k k

00 577.03

1 ==k where k yield stress und


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Yield Criteria - 2Tresca or Maximum shear stress criterionyielding occurs once the maximum shear stress ostress system equals shear stress under uni-axial

231

max

=

Under uni-axial tension, 1 = 0 , and 2= 3= 0

0310

031

max 22

====

031

21

2

==k

Under pure shear stress conditions ( 1 =- 3 = k


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Macroscopic Aspects PlasDeformation - 1

As a result of plastic deformation (Dislocation genmovement and (re-)arrangement ), following obsecan be made at macroscopic level:dimensional changeschange in grain shapeformation of cell structure in a grain


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Macroscopic Aspects PlasDeformation- 2


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n

x x

n

ii

== 11

1

(

=

=

n

x s

n

ii

Property VariabilityScatter in measured properties of engineering matinevitable because of number of factors such as:test methodspecimen fabrication procedureoperator biasapparatus calibration, etc.

Average value of x over nsamples.

Property variabiliStandard deviatio

Scatter limits:

x - s, +s x


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Design Consideration - 1To account for property variability and unfailure, designers need to consider tailored values. Parameters for tailoring: safety factor design factor ( N ). Both parameters take valuthan unity only.E.g.: Yield strength

w = y / N d = N c

where w working stress

y yield strength

d design stress

c calculated stress


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Design Consideration - 2Values for N ranges around: 1.2 to 4.0.Higher the value of N, lesser will the design efficieither too much material or a material havinthan necessary strength will be used.Selection of N will depend on a number o

Economics.Previous experienceThe accuracy with which mechanical forcesMaterial propertiesThe consequences of failure in terms of loss o

property damage.


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Material Science/Diffusion Lecture Notes

Satish Kailash Vasu/IISc, Bangalore M5/L1/V1/dec2004/1

Chapter 5. Diffusion

5.1 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 moveto let the atoms go by. This is more easily achieved when the atoms vibrate strongly, thatis, 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 randomlyand there will be an equal number of atoms moving in one direction than in another. Ininhomogeneous materials, the effect of diffusion is readily seen by a change inconcentration with time. In this case there is a net diffusion. Net diffusion occursbecause, although all atoms are moving randomly, there are more atoms moving inregions where their concentration is higher.

5.2 Steady-State Diffusion

The flux of diffusing atoms, J , is expressed either in number of atoms per unit area andper unit time (e.g., atoms/m 2-second) or in terms of mass flux (e.g., kg/m 2-second).

Steady state diffusion means that J does not depend on time. In this case, Ficks first lawholds 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. Theconcentration gradient is often called the driving force in diffusion (but it is not a force inthe mechanistic sense). The minus sign in the equation means that diffusion is down theconcentration gradient.

5.3 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 themto accumulate in another region).


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Material Science/Diffusion Lecture Notes

Satish Kailash Vasu/IISc, Bangalore M5/L2/V1/dec2004/1

5.4 Factors that influence diffusion

As stated above, there is a barrier to diffusion created by neighboring atoms that need tomove to let the diffusing atom pass. Thus, atomic vibrations created by temperature assistdiffusion. 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 effectof temperature in diffusion is given by a Boltzmann factor: D = D 0 exp(Q d /kT).

5.5 Non-equilibrium transformation and microstructure:

Non-equilibrium solidification

Conditions of equilibrium solidification and the development of microstructures arerealized only for extremely slow cooling rates. The reason for that is that with changes intemperature, there must be readjustments in the compositions of liquids and solid phasesin accordance with the phase diagram. These readjustments are accomplished by

diffusional processes- that is, diffusion in both solid and liquid phases and also across thesolid-liquid interface.

Non-equilibrium cooling

During cooling metastable equilibrium have been continuously maintained, that issufficient time has been allowed to each new temperature for any necessary adjustment inphase compositions and relative amounts as predicted from iron-iron carbide phasediagram. In most situations these cooling rates are impractically slow and reallyunnecessary; in fact, on many occasions non-equilibrium conditions are desirable. Twonon equilibrium effects of practical importance are (1) the occurrence of phase changes

or transformations at temperatures other than those predicted by phase boundary lines onthe phase diagram, and (2) the existence at room temperature of non-equilibrium phasesthat do not appear on the phase diagram.


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Diffusion

Module 5


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1. Diffusion mechanisms and steady-state & non-stead

diffusion

2. Factors that influence diffusion and non-equilibrium

transformation & microstructure

Contents


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Diffusion Phenomenon

Definition Diffusion is the process of mass which atoms change their positions relative to nein a given phase under the influence of thermagradient.The gradient can be a compositional gradient, an or magnetic gradient, or stress gradient.Many reactions in solids and liquids are d

dependent.Diffusion is very important in many industdomestic applications.E.g.: Carburizing the steel, annealing homogeafter solidification, coffee mixing, etc.


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Diffusion Mechanisms - 1

From an atomic perceptive, diffusion is a stmigration of atoms from one lattice position to ano

Migration of atoms in metals/alloys can occur iways, and thus corresponding diffusion mechadefined.


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Diffusion Mechanisms - 2Most energetically favorable diffusion mechavacancy mechanism. Other important mechainterstitial mechanism by hydrogen/nitrogen/oxygen diffuse into many metalIn ionic crystal, Schottky and Frankel defects asdiffusion process.When Frenkel defects dominate in an ionic crycation interstitial of the Frenkel defect cardiffusion flux. If Schottky defects dominate, thevacancy carries the diffusion flux.In thermal equilibrium, in addition to above defeccrystal may have defects generated by impuritiesdeviation from stochiometry.


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Diffusion Mechanisms - 3

Diffusion that occurs over a region is volume diffuDiffusion can occur with aid of linear/surface which are termed as short-circuit paths. These ethe diffusivity.

However, diffusion by short-circuit (E.g.:dislocaions, grain boundaries) is small becaeffective cross-sectional area over which thoperative is small.Diffusion can occur even in pure metals thatnoticeable. Diffusion that occurs in alloys wnoticeable called net diffusion as there occurs a noconcentration gradient.


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Diffusion Time Function? - 1

Steady-state and Non-steady-state diffusion procedistinguished by the parameter diffusion flux, J.

Flux is defined as number of atoms crossing a uperpendicular to a given direction per unit time.

Thus flux has units of atoms/m 2.sec or moles/m

If the flux is independent of time, then the dprocess is called steady-state diffusion. On the othfor non-steady-state diffusion process, flux is de

on time.


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Diffusion Time Function? - 2


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Steady-State DiffusionSteady-state diffusion processes is characterized by first law, which states that diffusion flux is proporticoncentration gradient.

The proportionality constant, D, is called diffusioncoefficient or diffusivity. It has units as m 2 /sec.For one-dimensional case, it can be written as

where D is the diffusion constant, dc/dx is the gradithe concentration c, dn/dt is the number atoms cross

unit time a cross-sectional plane of area A.E.g.: Hydrogen gas purification using palladium mesheet.

dt dn

Adxdc

D J x1== ),( t x f J x


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Non-Steady-State Diffusion 1Most interesting industrial applications are non-steaddiffusion in nature.

Non-steady-state diffusion is characterized by Fickslaw, which can be expressed as

where dc/dt is the time rate of change of concentratiparticular position, x.A meaningful solution can be obtained for the above

second-order partial equation if proper boundary concan be defined.

== dxdc

Ddxd

dxdJ

dt dc

2

2

dxcd

Ddt dc

=


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Non-Steady-State Diffusion 2One common set of boundary conditions and the soluFor t = 0, C = C 0 atFor t > 0, C = C s at x=0

C = C 0 atThe solution is

where C x represents the concentration at depth xThe term erf stands for Gaussian error function, whvalues can be obtained from standard mathematical

E.g.: Carburization and decarburization of steel, corrresistance of duralumin, doping of semi-conductors,

= x

x0

=

Dt

xerf C C

C C

s

x

2100


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Influencing Factors For DiffusionDiffusing species: Interstitial atoms diffuse easily tsubstitution atoms. Again substitution atoms with difference in atomic radius with parent atoms diffuwith ease than atoms with larger diameter.Temperature: It is the most influencing factor. Therelations can be given by the following Arrheniusequation

where D 0 is a pre-exponential constant, Q is thactivation energy for diffusion, R is gas consta(Boltzmanns constant) and T is absolute tempe

=

RT Q

D D exp0


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Influencing Factors For DiffusioFrom the temperature dependence of diffusivity, it is

experimentally possible to find the values of Q

Lattice structure: Diffusivity is high for open lattice strand in open lattice directions.

Presence of defects: The other important influencing fadiffusivity is presence of defects. Many atomic/voldiffusion processes are influenced by point defectsvacancies, interstitials.

Apart from these, dislocations and grain boundaries, i.e

short-circuit paths as they famously known, greatlyenhances the diffusivity.


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Non-Equilibrium TransformatiMicrostructure 1

Non-equilibrium transformation occurs, usually, dumany of the cooling processes like casting processEquilibrium transformation requires extremely largwhich is in most of the cases impractical and notnecessary.

Alloy solidification process involves diffusion in liphase, solid phase, and also across the interface betliquid and solid.As diffusion is very sluggish in solid, and time avafor it is less, compositional gradients develop in ca

components.These are two kinds: coring and segregation.


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Non-Equilibrium TransformatioMicrostructure 2

Coring: It is defined as gradual compositional chanacross individual grains.Coring is predominantly observed in alloys havingmarked difference between liquidus and solidustemperatures.

It is often being removed by subsequent annealing hot-working.It is exploited in zone-refining technique to producpurity metals.Segregation: It is defined as concentration of particusually impurity elements, along places like grainboundaries, and entrapments.Segregation is also useful in zone refining, and alsoproduction of rimming steel.


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Non-Equilibrium TransformatioMicrostructure 3

Micro-segregation is used to describe the differencescomposition across a crystal or between neighboringMicro-segregation can often be removed by prolongeannealing or by hot-working.Macro-segregation is used to describe more massive

heterogeneities which may result from entrapment ofpockets between growing solidifying zones.Macro-segregation persists through normal heating aworking operations.Two non equilibrium effects of practical importance:occurrence of phase changes or transformations aother than those predicted by phase boundary lines odiagram, and (2) the existence of non-equilibrium phroom temperature that do not appear on the phase dia


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Material Science/Dislocations and Strengthening Mechanisms Lecture Notes


Chapter 6. Dislocations and Strengthening Mechanisms

6.1 Basic Concept of dislocation

Dislocations can be edge dislocations, screw dislocations and exist in combination of thetwo. Their motion (slip) occurs by sequential bond breaking and bond reforming . Thenumber of dislocations per unit volume is the dislocation density , in a plane they aremeasured per unit area.

Characteristics of Dislocations

There is strain around a dislocation which influences how they interact with otherdislocations, impurities, etc. There is compression near the extra plane (higher atomicdensity) and tension following the dislocation line.

Dislocations interact among themselves. When they are in the same plane, they repel if they have the same sign and annihilate if they have opposite signs (leaving behind aperfect crystal). In general, when dislocations are close and their strain fields add to alarger value, they repel, because being close increases the potential energy (it takesenergy 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 andsurface irregularities.

Plastic Deformation

Slip directions vary from crystal to crystal. When plastic deformation occurs in a grain, itwill 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 perfectsingle crystal, as in whiskers.)

6.2 Mechanisms of Strengthening in Metals

General principles. Ability to deform plastically depends on ability of dislocations tomove. Strengthening consists in hindering dislocation motion. We discuss the methods of grain-size reduction, solid-solution allo

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