UNIT 1 Elastic and Plastic Behaviour

MATERIALS TECHNOLOGY

V.G.UMASEKAR A.P(O.G)SCHOOL OF MECHANICAL ENGG.,

SRM UNIVERSITY

INSTRUCTIONAL OBJECTIVES

This course will enable the students to know more about Different materials with their properties Various production techniques and applications Various production techniques and applications Fracture analysis for different metals Strengthening mechanisms and Applications of metallic and non metallic materials

Unit Title Details

Unit 1 - ELASTIC AND PLASTIC BEHAVIOUR Unit 2 - FRACTURE BEHAVIOUR Unit 3 - PHASE DIAGRAMS Unit 4 - MODERN METALLIC MATERIALS Unit 4 - MODERN METALLIC MATERIALS Unit 5 - NON METALLIC MATERIALS

Unit 1 - ELASTIC AND PLASTIC BEHAVIOURBEHAVIOUR

Materials classification

Solid materials have been conveniently grouped into three basic classifications metals, ceramics, and ceramics, and polymers.

Metals

Metallic materials are combinations of metallic elements.

They have large numbers of nonlocalized electronselectrons

Metals are extremely good conductors of electricity and heat.

They are not transparent to visible light. Metals are quite strong.A polished metal

surface has a lustrous appearance.

Ceramics

Ceramics are compounds between metallic and nonmetallic elements

They are insulative to the passage of electricity and heat.and heat.

They are more resistant to high temperatures and harsh environments than metals and polymers.

ceramics are hard but very brittle. Example : oxides, nitrides, and carbides.

Polymer

Polymers are organic compounds that are chemically based on carbon, hydrogen, and other nonmetallic elements

It includes the familiar plastic and rubber It includes the familiar plastic and rubber materials.

They have very large molecular structures. They have low densities and may be

extremely flexible

Crystalline material

A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances.

All metals, many ceramic materials, and certain All metals, many ceramic materials, and certain polymers form crystalline structures under normal solidification conditions.

Some of the properties of crystalline solids depend on the crystal structure of the material

Example: Al, Cu, Cd, gold, Cr

Non-Crystalline material

Non-crystalline solids lack a systematic and regular arrangement of atoms over relatively large atomic distances.

Sometimes such materials are also called Sometimes such materials are also called amorphous or supercooled liquids

Example : Fused silica,

Crystalline Vs Non-crystalline Structure

Single crystal material

For a crystalline solid, when the periodic and repeated arrangement of atoms is perfect the result is a single crystal.

All unit cells interlock in the same way and have the same orientation.the same orientation.

Single crystals exist in nature, but they may also be produced artificially.

single crystals of silicon and other semiconductors are used in electronic micro circuit.

Poly Crystalline material Most crystalline solids are composed of a

collection of many small crystals or grains Such materials are termed polycrystalline. the crystallographic orientation varies from

grain to grain.grain to grain. The region where two grains meet is called a

grain boundary. some atomic mismatch exists in the grain

boundary.

Polycrystalline material

Crystalline defects

A lattice irregularity having one or more of its dimensions on the order of an atomic diameter is called crystalline defect. Point defect Point defect One dimensional defect or linear defect Two dimensional defect Bulk or volume defect

Point Defect

1.Vacancy2. Self interstitial

Two dimensional representation of vacancy and self interstitial

Linear or one-dimensional defect

Linear defect Dislocation

A dislocation is a one dimensional defect around which atoms are misaligned.

Types of dislocation Edge dislocation Edge dislocation Screw dislocation

Edge Dislocation

An extra portion of a plane of atoms, or half-plane, the edge of which terminates within the crystal. This is termed an edge dislocation

In an edge dislocation, localized lattice In an edge dislocation, localized lattice distortion exists along the end of an extra half-plane of atoms.

This extra half plane of atom defines the dislocation line.

Elasticity in metals

Elastic deformation: Deformation in which the stress and strain is proportional is called elastic deformation.

As per Hooks law within the elastic limit the As per Hooks law within the elastic limit the stress is proportional to the strain.

= E ------------ eqn 1 The constant of proportionality is called as

Modulus of Elasticity or young's modulus (E).


Stress strain curve that show the linear elastic deformation


The plot of stress and strain with in the elastic limit yield a linear relationship.

The slope of this linear segment corresponds to The slope of this linear segment corresponds to the modulus of elasticity E.

Modulus of elasticity is also referred as stiffness Stiffness is a materials resistance to elastic

deformation. The greater the modulus, the material is stiffer.


Elastic deformation is temporary or nonpermanent.

when the load is removed the material returns to its original shape.to its original shape.

In the atomic level, the elastic deformation occurred because of small change in the inter atomic spacing and the stretching of inter atomic bonds.


The magnitude of the modulus of elasticity is a measure of the resistance to separation of adjacent atoms.

This elasticity is proportional to the slope of This elasticity is proportional to the slope of the inter-atomic force-separation curve.


When the temperature increases, the modulus of elasticity of the metal reduces. Refer the graph for 3 metals.

Plastic Deformation

When the material is deformed beyond the elastic point, the stress is no longer proportional to strain and plastic deformation occurs.to strain and plastic deformation occurs.

Upon removal of the stress they do not return to their original position.

This permanent deformation for metals is accomplished by means of a process called slip.

Plastic Deformation

Plastic Deformation

Slip involves the motion of dislocations During this process, inter-atomic bonds must

be ruptured and then reformedbe ruptured and then reformed On a microscopic scale, plastic deformation

corresponds to the net movement of large numbers of atoms in response to an applied stress.

Mechanism of Plastic deformation

Two mechanisms that cause the plastic deformation are1. Slip2. Twinning2. Twinning

Plastic deformation - Motion of large

PlasticDeformation by Slip

Plastic deformation - Motion of large numbers of dislocations in a crystal

Plastic Deformation by Slip

Slip is a plastic deformation mechanism in which one part of the crystal moves or glides over another part along slip planes.

The movement of large number of dislocations The movement of large number of dislocations within the crystal are responsible for slip.

An edge dislocation moves in response to a shear stress applied in a direction perpendicular to its line (dislocation line).

Mechanics of Dislocation Motion

Formation of a step on the surface of a crystal by the motion of an edge dislocation

Slip System

There is a preferred plane, and in that plane there are specific directions along which dislocation motion occurs.

The crystallographic plane along which the The crystallographic plane along which the dislocation line traverses is the slip plane.

In that slip plane the dislocation travel in a particular direction. It is called slip direction.

This combination of the slip plane and the slip direction is termed the slip system

Slip System

Metals with FCC or BCC crystal structures have a relatively large number of slip systems (at least 12)

These metals are quite ductile because These metals are quite ductile because extensive plastic deformation is normally possible along the various systems.

Conversely, HCP metals, having few active slip systems, are normally quite brittle.

Slip System

The slip system depends on the crystal structure of the metal.

For a particular crystal structure, the slip plane is that plane having the most dense atomic is that plane having the most dense atomic packing, that is, has the greatest planar density.

The slip direction corresponds to the direction, in this plane, that is most closely packed with atoms, that is, has the highest linear density

Plastic Deformation by Slip

In slip the crystal lattice move by multiple of unit spacing between the atoms.

Slip results in visible step on the surface of the crystal.crystal.

Slip System for FCC unit cell

Dislocation

The number of dislocations, or dislocation density in a material, is expressed as the total dislocation length per unit volume.

The units of dislocation density are millimeters of dislocation per cubic millimeter or just per square millimeter.

10-3 mm2 are typically found in carefully solidified metal crystals

Dislocation

All metals and alloys contain some dislocations that were introduced during Solidification Plastic deformation and Plastic deformation and as a consequence of thermal stresses that result

from rapid cooling

Twin Boundary

A twin boundary is a special type of grain boundary across which there is a specific mirror lattice symmetry.

Atoms on one side of the boundary are Atoms on one side of the boundary are located in mirror image positions of the atoms on the other side

Twin Boundary

Plastic Deformation by Twinning

Twinning is a plastic deformation mechanism. In twinning, each plane of atoms moves in the

same direction, a definite distance, such that the extent of the movement of each plane is the extent of the movement of each plane is proportional to its distance from the twinning plane.


The movement of the planes alters the direction of the lattice and thus a twinned region forms.region forms.

After twinning it appears as if two parts of a crystal having same orientation are joined by a twin band of the crystal having a markedly different orientation.


Twinning occurs on a definite crystallographic plane and in a specific direction, both of which depend on the crystal structure.

Zinc, tin and iron deform by twinning. Zinc, tin and iron deform by twinning. Twinning may be caused by

impact thermal treatment plastic deformation.

Comparison of slip & twinning in single crystal

Comparison of slip & twinning in single crystal

S.NO SLIP TWINNING

1 All atoms in one block move the same distance

Atoms in each successive plane within a block move different distance

2 Slip appears as thin lines Twinning appears as broad lines or bands

3 There is very little change in lattice orientation, of slipped region

There is a markedly different lattice orientation in the twinned region.

4 Requires less shear stress Requires higher shear stress

Strengthening Mechanisms

All strengthening techniques rely on this simple principle

Restricting or hindering dislocation motion makes a material harder and motion makes a material harder and stronger.

Strengthening Mechanisms

Different types of strengthening Mechanisms arev Grain boundary strengtheningv Solid-solution strengtheningv Solid-solution strengtheningv Work hardening v Dispersion strengthening v Particle strengthening v Fiber strengthening

Grain boundary

Grain Boundary Strengthening

The size of the grains, in a polycrystalline metal influences the mechanical properties.

Adjacent grains have different crystallographic Adjacent grains have different crystallographic orientations and, a common grain boundary.

During plastic deformation, dislocation motion must take place across this common boundary, say, from grain A to grain B.


The grain boundary acts as a barrier to dislocation motion for two reasons:

1. Since the two grains are of different orientations, a dislocation passing into grain B orientations, a dislocation passing into grain B will have to change its direction of motion; this becomes more difficult as the crystallographic misorientation increases.

2. The atomic disorder within a grain boundary region will result in a discontinuity of slip planes from one grain into the other.


A fine-grained material is harder and stronger than one that is coarse grained.

The reason is the fine grain material has a greater total grain boundary area to impede greater total grain boundary area to impede dislocation motion.


Grain size may be regulated by the rate of solidification from the liquid phase,

and also by plastic deformation followed by an appropriate by plastic deformation followed by an appropriate

heat treatment.

grain size reduction improves not only strength, but also the toughness of many alloys.

Hall-Petch Equation

For many materials, the yield strength y varies with grain size according to

Above equation is called as Hall-petch equation d is the average grain diameter 0 and ky are constants for a particular material

Problem based on Hall-Petch Equation

The lower yield point for an iron that has an average grain diameter of 5 x10-2 mm is 135 MPa. At a grain diameter of 8 x 10-3 mm, the yield point increases to 260MPa. At what grain yield point increases to 260MPa. At what grain diameter will the lower yield point be 205 Mpa? (d = 1.48x10-2 mm)

Solid-Solution Strengthening In Solid-solution strengthening, impurity atoms

added to the pure metal. These atoms substitute the base metal atoms or go

and occupy the interstitial space between them.Pure metals generally soft and weak in nature than Pure metals generally soft and weak in nature than alloys.

When impurity atoms is added with pure metal, they go inside the solid solution and induce lattice strains on the surrounding host atoms.

Solid Solution

A solid solution forms when, as the solute atoms are added to the host material, the crystal structure is maintained, and no new structures are formed.structures are formed.

the impurity atoms are randomly and uniformly dispersed within the solid.

Solid Solution - Types

Substitutional solid solution In substitutional solid solution, solute atoms

substitute for the solvent atoms. Example Brass. It is an alloy of copper and zinc. Example Brass. It is an alloy of copper and zinc. Pure copper is a soft &ductile metal. When zinc is

added to copper, its strength increases. Here zinc is the solute atoms and copper is the

solvent atoms.

Substitutional solid solution

Solute atom

Solvent atoms

Substitutional solid solutionSolvent atoms

Solute atom


The increase in strength of an alloy depends upon the following factors. Amount of solute atoms (solute concentration) Atomic size difference ( difference in size between Atomic size difference ( difference in size between

the solute and solvent)


Interstitial solid solution In interstitial solid solution, solute atoms fill the

interstices among the solvent atoms Carbon forms an interstitial solid solution when Carbon forms an interstitial solid solution when

added to iron.

Solid Solution

Solid-Solution Strengthening

During plastic deformation, dislocation travel inside the solid solution.

Lattice strain field of moving dislocation interact with the strain field induced by the interact with the strain field induced by the impurity atoms.

These interaction restrict the free movement of the dislocation and in turn raises the strength needed to deform the metal.


An impurity atom that is smaller than a host atom for which it substitutes exerts tensile strains on the surrounding crystal lattice.

Conversely, a larger substitutional atom Conversely, a larger substitutional atom imposes compressive strains in its vicinity.

Strain Hardening or Work Hardening

Strain hardening is the phenomenon whereby a ductile metal becomes harder and stronger as it is plastically deformed.

Strain hardening can be explain with the help Strain hardening can be explain with the help of stress strain curve.


Initially, the metal with yield strength y0 is plastically deformed to point D.

The stress is released, then reapplied with a resultant new yield strength, y . resultant new yield strength, yi .

The metal has thus become stronger during the process because yi is greater than y0 .

Strain Hardening Based on dislocation concept

The dislocation density in a metal increases with deformation , due to dislocation multiplication or the formation of new dislocations.

Consequently, the average distance of Consequently, the average distance of separation between dislocations decreases. The dislocations are positioned closer together.

On the average, dislocationdislocation strain interactions are repulsive.


The net result is that the motion of a dislocation is hindered by the presence of other dislocations.

As the dislocation density increases, this As the dislocation density increases, this resistance to dislocation motion by other dislocations becomes more pronounced.

Thus, the imposed stress necessary to deform a metal increases with increasing cold work.


Strain hardening is utilized to enhance the mechanical properties of metals during fabrication procedures.

The effects of strain hardening may be The effects of strain hardening may be removed by an annealing heat treatment.

Dispersion Strengthening

The strength of metal can be increased by finely dispersing small, hard and inert particles in the matrix metal.

These particles act as an obstacle for moving These particles act as an obstacle for moving dislocations.


In this method, finely divided hard insoluble particles (10-7 cm diameter) are added into the soft metal matrix.

The dispersed hard insoluble particles are The dispersed hard insoluble particles are called as despersoid.

The hard particles are carbides, oxides & nitrides or intermetallic compounds.


These hard particles provide obstruction to the moving dislocation.

Also the interaction of the stress field of dislocation and stress field around particles dislocation and stress field around particles offer resistance.

These resistance to dislocation raises the stress needed for the dislocation movement.


These particles neither dissolve at high temperature nor grow in size.

Hence dispersion strengthened materials maintain their strength even at high maintain their strength even at high temperatures.

Dispersion strengthened alloys are produced by powder metallurgy technique(mechanical alloying).

Dispersion Strengthening Dislocation movement against the Particles


In this method, the increase in strength of the material depends on 1. The amount of particles2. The size of the particles2. The size of the particles3. The shape of the particles4. The distribution of the particles in the metal matrix


To obtain most effective dispersion strengthening, the particles need to be Hard Small Small Round and numerous

Dispersion Strengthening by Hard Insoluble Particles - Example

Sintered Aluminium Powder (SAP) is strengthened by Al2O3 particles by 6-14%.

Its strength is 5 times greater than the Aluminium and withstand temperature of Aluminium and withstand temperature of upto 400C without loss of strength.

Thoria dispersed nickel is strengthened by ThO2 2% in nickel and can withstand 1000C

Fiber Strengthening

Materials are strengthened by adding fine fibers into a ductile matrix material.

Fiber strengthened materials are called as composite materials.composite materials.

Example: Glass-fiber reinforced polymer.

Fiber Strengthening - Fiber

Fibers are fine filaments, wires or whiskers which have diameters ranging from 1m to 250 m.

Properties of fiber Properties of fiber High strength High elastic modulus

Function of fiber Carry all of the tensile load

Fiber Strengthening Fiber Materials

Metallic fiber Tungsten Stainless steel

Non metallic fiber Non metallic fiber Boron Boron nitride Graphite Glass Silicon carbide Kevlar

Fiber Strengthening Matrix Material

Matrix material is a material that binds the fibers together and also transfer the stress to them.

Different matrix materials are Different matrix materials are Metals Polymer Ceramics

Fiber Strengthening Matrix Material

Functions of the matrix material Transmit the load to the fibers Protect the fibers from surface damage Separate the individual fibers Separate the individual fibers Blunt the crack which arises from fiber damage.

Fiber Strengthening

Superplasticity

Super plasticity is a property of some alloys in which very great plastic elongations of upto2000% or more can be obtained under the action of quite low tensile stress.action of quite low tensile stress.

Such a state is usually achieved at high homologous temperature, typically half the absolute melting point (0.5Tm)

Superplasticity

Important elements in super plastic properties High strain rate sensitivity (>0.5) Small grain Nature of secondary phase Nature of secondary phase Resistance to tensile separation at grain

boundaries Grain shape

Ductility

Ductility is a mechanical property. Ductility is a measure of the degree of plastic

deformation that has been sustained at fracturefracture

Percentage Elongation

Ductility may be expressed quantitatively as either percent elongation.

The percent elongation %EL is the percentage of plastic strain at fracture.of plastic strain at fracture.

lf is the length of the specimen at fracture. Lo is the original gauge length of the specimen.

Strain Rate

Strain rate is the rate of change in strain of a material with respect to time.

In physics the strain rate is generally defined as the derivative of the strain with respect to as the derivative of the strain with respect to time.

Strain rate is measured in reciprocal of seconds (s1).

It is denoted by the symbol

Strain Rate

L(t) length of the specimen at time t. L0 is the original length of the specimen.v is the velocity with which the two ends of the specimen moves

Strain Rate Sensitivity Index

A power relationship can be used to express the true stress at a given strain , in terms of the strain rate

= A ()m = A () A is a constant and m is the index of strain rate

sensitivity. If m=0, the stress is independent of the strain

rate and the stress-strain curve would be the same for all strain rates.

Stress Strain curve

Strain Rate Sensitivity Index

m = 0.2 for common metals. If m=0.4 0.9 the material may exhibit super

plastic behaviour, that is deform by several hundred percent of strain without necking.hundred percent of strain without necking.

Superplasticity

Superplasticity can be defined as an ability of a polycrystalline material to exhibit extraordinarily large elongation at elevated temperatures and at relatively low stresses.

It is a property commonly found in many metals, alloys, intermetallics and ceramics when the grain size is very small.

Less than several micrometers for metals and less than one micrometer for ceramics.

Superplasticity The superplasticity behavior makes

superplastic forming an attractive option for the manufacture of complex shaped components in the metal industry.

Ceramics are hard, strong and stiff materials. Ceramics are hard, strong and stiff materials. They are brittle and lack the ductility of metal at ambient temperature.

The application of superplasticity makes it possible to fabricate ceramic components just like superplastic metals.

Superplasticity

Part made from super plastic forming

Superplasticity

Reference from Bonding Theory for Metals and AlloysBy Frederick E. Wang

Superplasticity

The requirements for a material to become superplastic include Fine grain size typically below 10 m. Fine dispersion of thermally stable particles that Fine dispersion of thermally stable particles that

act to pin the grain boundaries and maintain the fine grain structure at the high temperature.

High strain rate sensitivity (>0.5) which prevents localized deformation at a reduced cross section (necking)

Effect of Temperature on Plastic Behaviour

When the temperature of the material increases, its modulus of elasticity, yield strength and tensile strength decreases.

The ductility of the material increases when The ductility of the material increases when the temperature rises.

The graph shows how the stress-strain behaviour of iron varies with temperature.

Effect of Temperature on Plastic Behaviour

Deformation of Non Crystalline Materials (Ceramics)

Plastic deformation does not occur by dislocation motion for noncrystalline ceramics

These materials do not have regular atomic structure. structure.

Noncrystalline materials deform by viscous flow, the same manner in which liquids deform.

The rate of deformation is proportional to the applied stress.

Deformation of Non Crystalline Materials (Ceramics)

Deformation of Non Crystalline Materials

In response to an applied shear stress, atoms or ions slide past one another by the breaking and reforming of interatomic bonds.

However, there is no prescribed direction in However, there is no prescribed direction in which this occurs, as with dislocations.

UNIT 1 Elastic and Plastic Behaviour

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