micro structures & properties

8/7/2019 Micro Structures & Properties

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Microstructure

&

Mechanical Properties

V Arunkumar

Roll No 2010413002

M.Tech (II Year) - Nanoscience & Nanotechnology

V Arunkumar - Roll No 2010413002 M.Tech (II Sem) - Nanoscience & Nanotechnology

Microstructure & Mechanical Properties


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Contents


S.No TOPICS

1. Introduction to Plastic Deformation

2. Grains & Dislocation

3. Strengthening Mechanisms

4. Reference



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Material undergoes Elastic Deformation if Stress < Yield Stress

Material undergoes Plastic Deformation if Stress > Yield Stress

Plastic deformation the force to break all bonds in the slip plane is much

higher than the force needed to cause the deformation.

Theoretical yield strength predicted for perfect crystals is much greater than

the measured strength.The large discrepancy puzzled many scientists until

Orowan, Polanyi, and Taylor (1934).

The existence of defects (specifically, dislocations) explains the discrepancy.

The reason was proposed by in 1934 by Taylor, Orowan and Polyani: Plastic

deformation is due to the motion of a large number of dislocations.


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DefectsPoint defects: vacancies, interstitial atoms, substitional atoms, etc.

Line defects: dislocations(edge, screw, mixed)

Most important for plastic deformation

Surface defects: grain boundaries, phase boundaries, free surfaces,etc.


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Edge dislocations

Burgers vector: characterizes the strength of dislocations

Edge dislocations: b B dislocation line


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Screw dislocations

Burgers vector b parallel to dislocation line

Mixed dislocationHave both edge and screw

components.


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Movement of an edge dislocation

Break one bond at a time, much easier than breaking all the bondsalong the slip plane simultaneously, and thus lower yield stress.


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Dislocations allow deformation at much lower stress than in a perfect crystal

If the top half of the crystal is slipping one plane at a time then only a small fraction of

the bonds are broken at any given time and this would require a much smaller force. The

propagation of one dislocation across the plane causes the top half of the crystal tomove (toslip) with respect to the bottom half but we do not have to break all the bonds

across the middle plane simultaneously (which would require a very large force).The slip

planethe crystallographic plane of dislocation motion.


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Motion of dislocations


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Interactions of dislocationsTwo dislocations may repel or attract each other, depending on their

directions.

Repulsion Attraction


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Line tension of a dislocation

Atoms near the core of a dislocation have a higher energy due to

distortion.

Dislocation line tends to shorten to minimize energy, as if it had a line

tension.

Line tension = strain energy per unit length

T

T

2

2

1GbT }


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Dislocation multiplicationSome dislocations form during the process of crystallization.

More dislocations are created during plastic deformation.

Frank-Read Sources: a dislocation breeding mechanism.


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Strengthening mechanisms

Pure metals have low resistance to dislocation motion, thus low

yield strength.

Increase the resistance by strengthening:

Solution strengthening

Precipitate strengthening

Work hardening


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Solution strengthening

Add impurities to form solid solution (alloy)

Example: add Zn in Cu to form brass, strengthincreased by up to 10 times.

Cu Cu Cu Cu Cu Cu

Cu Cu Cu

Cu Cu Cu Cu

Zn Zn

B

igger Zn atoms make the slipplane rougher, thus increase the

resistance to dislocation motion.


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Solid solution hardening

Dissolve other elements (solute) into the parent material (solvent) to form solid solution.

Interstitial solution Substitutional solution

Steel (C in Fe) Brass (Zn in Cu)


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Solid solution hardening

Large distortion due to mismatch makes

it hard for dislocation to move.

Large population of solute atoms

obstruct dislocation motion.


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Dispersion strengthening: mix small particles(dispersoids) into a powdered metal, then compact and

sinter.

Proper heat treatments can control the formation of

precipitates (more later).

Precipitates: compound particles precipitates out from

the solution as it is cooled.

Solid solution: single-phase, random mixture of atoms

(substitutionalor interstitutional)


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Precipitates (small particles) can promote

strengthening by impeding dislocation

motion.

Dislocation bowing and looping.

Critical condition at semicircularconfiguration:

TbL 2!X

L

Gb

bL

T}!

2X

M.F. Ashby and D.R.H. Jones, Engineering Materials 1, 2nd

ed. (2002)


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Work-hardeningDislocations interact and obstruct each other.

Accounts for higher strength of cold rolled steels.

W

I

WYU

WYL

Strain hardening

WUTS

If


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Dislocation yield strength

Combine the resistance due to lattice, solid solution,

precipitates, and dislocation tangles in an additive way:


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Polycrystalline materialsDifferent crystal orientations in different grains.

Crystal structure is disturbed at grain boundaries.


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Plastic deformation in Polycrystals

Slip in each grain is constrained

Dislocations pile up at grain boundaries

Gross yield-strength is higher than single crystals (Taylor factor)

Strength depends on grain size

(Hall-Petch Relation

YYXW 3!

2/1

0

! KdY

WW


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Important features of plasticity :Stress-strain curves provide a straightforward way to measure yield stress, ultimate tensile

stress and ductility.

The maximum load and maximum uniform elongation are predictable from the stress-strain

curve (e.g. power law).

Single crystal behavior reflects the anisotropy of the crystal for both elastic and plastic

behavior.

Single crystal plastic behavior is controlled by dislocation movement; deformation twinning

can supplement dislocation glide

The presence of dislocations that can glide at low (critical resolved) shear stresses means that

metals yield plastically at stresses far below the theoretical strength.


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Strain Rate - Dependence Temperature & Grain size

The variation of mechanical behavior with temperature and strain rate depends on the kind of

obstacle that dislocations have to move past.

In fcc metals, yield is dominated by other dislocations (the "forest hardening model") such that

the strain rate/temperature variation is dominated by the (weak) variation in shear

modulus(with temperature) through the "Taylor equation", =MGb.

In bcc metals, yield at low temperatures is dominated by lattice friction (i.e. the Peierls stress)

and large strain rate/temperature sensitivities are observed. Most ceramics follow the bcc

model because they too have high lattice frictions at low temperatures (but become plastic

and ductile at elevated temperatures).

Single crystals are important because many high temperature applications require singlecrystal or coarse poly-crystals in order to maximize creep resistance, i.e. by minimizing grain

boundary area.

Microelectronic applications use single crystals ofSi where the absence of grain boundaries is

not important unless MEMS devices are being designed.


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The work hardening behavior of single crystals is summarized by fourstages: stage I is known

as "easy glide"; stage II as "linear, athermalhardening"; stage III as "dynamic recovery"; and

stage IV as "linearhardening".

For a polycrystal to exhibit ductility, it must be possible for every grain to deform plastically in

an arbitrary manner. This is summarized as vonMises criterion which states that a minimum of

five independent systems are required for ductility. This can be understood most easily by

considering that an arbitrary strain has five independent components there is an equation

(linear) that links the slip on an individual slip system (or twinning system) to the macroscopic

shape change (i.e. strain); therefore five independent systems are needed in order to satisfy

the five independent strain components


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Dislocation flow in a polycrystal is quite heterogeneous. Dislocations get entangled in one

another as they expand over their slip planes. The major consequence of this is that any

dislocation motion (over a distance larger than the mean spacing) leaves behind a certain

amount of dislocation; this is called dislocation storage and hardens the crystal. By a

combination of collapse of tangles and cross-slip (switching of slip planes by screw-

configuration segments), however, dislocations of opposite sign can meet and annihilate; this

is called dynamic recovery (because it only happens during continuing straining)and decreases

the hardening rate (i.e. the net storage rate of dislocations decreases because of dynamic

recovery). Eventually dynamic recovery balances storage and the flow stress saturates, or

nearly so


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At high temperatures, dynamic recovery occurs early on in straining and, withthe ease of non-

conservative motion (climb), the work hardening becomesnegligible. With rapid dynamic (and

static) recovery, the dislocation structurebecomes a sub-grain structure with well defined, low

angle boundaries. If single crystal is bent, then the dislocations left behind after the

deformation tendto re-arrange themselves into walls of edge dislocations of the same type

andsign. Such a recovered or polygonized structure is a clear example ofgeometrically

necessary dislocations.


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REFERENCE

1. Material Science and Engineering by William Callister

2. Material Science for Engineers by Ashby & Miller

3. Study Materials on Strengthening of Materials by University of Tennessee, Dept. of

Materials Science and Engineering

4. Study Materials on Microstructues by Carnegie Mellon University

5. Lecture Materials on Materials Science by University of Texas - Austin

6. Notes by University of Illinois on Material Science - Thermal & Mechanical Properties

of Materials (TOO GOOD HENCE ENCLOSED HEREWITH)


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