defect: the beauty grains of metals hafid aourag university of tlemcen 1annaba 10-12 may 2010

Defect: the Defect: the Beauty Grains Beauty Grains

of Metalsof Metals

Hafid AouragHafid Aourag

University of TlemcenUniversity of Tlemcen1Annaba 10-12 May 2010

Why is there something Why is there something rather than nothing?rather than nothing?

Why should nothing be Why should nothing be more natural more natural than than something?something?

How could How could “nothing” “nothing” even exist?even exist?

Why is there God Why is there God rather than nothing?rather than nothing?

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Out of the voidOut of the void

Physics of the Void:Physics of the Void:

No No mattermatter or or energy.energy. “Nothing?”“Nothing?”

Perfect Perfect symmetry.symmetry.

No No order.order.

Yet, described by Yet, described by laws laws of physicsof physics that follow that follow from symmetries.from symmetries.

““Nothing is unstable”Nothing is unstable”--Frank Wilcsek--Frank Wilcsek


Where do the laws of physics Where do the laws of physics come from? (To be come from? (To be published.)published.)NotNot handed down from above. handed down from above.

NotNot restrictions on the restrictions on the behavior of matter.behavior of matter.

Restrictions on the way Restrictions on the way physicistsphysicists can formulate their can formulate their mathematical statements about mathematical statements about observations.observations.


Noether’s theoremNoether’s theorem

For every continuous symmetry of the laws of physics there exists a conservation law and vice versa.

-Emmy Noether (1915)


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The basic “laws” of physics are mathematical statements that The basic “laws” of physics are mathematical statements that have the form they do in an attempt to describe reality in an have the form they do in an attempt to describe reality in an objectiveobjective way. way.

They must be They must be point-of-view invariant.point-of-view invariant.

Conservation laws follow from Conservation laws follow from space-time symmetries.space-time symmetries.

ForcesForces are introduced to preserve invariance. are introduced to preserve invariance.

However, complex structures exist that However, complex structures exist that violateviolate some invariance some invariance principles.principles.

The mechanism is The mechanism is spontaneous (random) symmetry breaking.spontaneous (random) symmetry breaking.

Underlying “laws” Underlying “laws” stillstill invariant. invariant.

The laws of physics are human inventions that follow The laws of physics are human inventions that follow from the from the symmetries of the void.symmetries of the void.

They are not arbitrary, but must agree with They are not arbitrary, but must agree with observations.observations.

They look as they should look if there is They look as they should look if there is no God.no God.

Structure results from Structure results from spontaneousspontaneous (accidental) (accidental) symmetry breaking.symmetry breaking.

The void is The void is unstableunstable and so expect “something” rather and so expect “something” rather than “nothing.”than “nothing.”

The universe can have come from The universe can have come from “nothing.”“nothing.”


Natural complexityNatural complexity

Complexity is Complexity is generated naturally generated naturally all the timeall the time

Snowflakes and other Snowflakes and other crystalscrystals

FerromagnetsFerromagnets

Polarized lightPolarized light

MicrostrutureMicrostruture

Evolution!Evolution!


Spontaneous symmetry Spontaneous symmetry breakingbreaking

Ball of iron at Ball of iron at highhigh temperature temperatureBall of iron at Ball of iron at lowlow temperature temperature

Magnetic fieldMagnetic field

Tc

No magnetic fieldNo magnetic field

TTcc


Broken symmetry in natureBroken symmetry in nature- self organization- self organization

SunflowerSunflowerSimulation based onSimulation based onminimizing minimizing symmetricsymmetric potential energypotential energy

Spirals very common in plantsSpirals very common in plantsExhibit Fibonacci series: 0,1,1,2,3,5,8,13,21,34,…Exhibit Fibonacci series: 0,1,1,2,3,5,8,13,21,34,…

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Fractal DimensionFractal Dimension

Fractal Dimension (Sierpinski Triangle)

3=2? 1 Dimension1 Dimension 2=22=211

F DimensionF Dimension 3=23=2??

2 Dimensions2 Dimensions 4=24=222

3 Dimensions3 Dimensions 8=28=233

d Dimensionsd Dimensions n=2n=2dd

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Formation of GrainsFormation of Grains

from a molten state:from a molten state: The growth starts from the The growth starts from the

nuclei of crystallization, and the nuclei of crystallization, and the crystals grow toward each other crystals grow toward each other ((A-EA-E).).

When two or more crystals When two or more crystals collide, their growth is stopped.collide, their growth is stopped.

Finally, the entire space is filled Finally, the entire space is filled with crystals (with crystals (FF).).

Each growth crystal is Each growth crystal is called a “called a “graingrain”. Grains ”. Grains contact each other at “contact each other at “grain grain boundariesboundaries”.”.

Grain

Grain boundary

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Grain SizeGrain Size

In general, the smaller the grain size of the In general, the smaller the grain size of the metal, the better its physical properties.metal, the better its physical properties.

Control of Grain SizeControl of Grain Size Number of nuclei of crystallization Number of nuclei of crystallization

The more rapidly the liquid state can be changed to the The more rapidly the liquid state can be changed to the solid state, the smaller or finer the grains will be.solid state, the smaller or finer the grains will be.

Rate of crystallizationRate of crystallization If the crystals form faster than do the nuclei of If the crystals form faster than do the nuclei of

crystallization, the grains will be larger.crystallization, the grains will be larger.

Slow cooling results in large grains.Slow cooling results in large grains.


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The shape of the grains The shape of the grains may be influenced by may be influenced by the shape of the mold the shape of the mold in which the metal in which the metal solidifies.solidifies.

Square mold


Is the sliding easy to occur in perfect metallic crystals?

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No….if they were really “perfect”.

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Lattice imperfectionsLattice imperfections

Several types exist on various atomic Several types exist on various atomic levels:levels:

Point defectsPoint defects

Line defects (Line defects (DislocationsDislocations))

Grain BoundariesGrain Boundaries

Macroscopic DefectsMacroscopic Defects


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Whenever the dislocation Whenever the dislocation motions are impeded, the motions are impeded, the material becomes more material becomes more resistant to slip, making it resistant to slip, making it stronger.stronger.

The presence of other The presence of other defects such as point and defects such as point and other line defects helps to other line defects helps to immobilize the movement immobilize the movement of these dislocations of these dislocations during stress.during stress.


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Grain boundaries are Grain boundaries are defects which have defects which have higher energy than the higher energy than the grains and are more grains and are more active with chemicals.active with chemicals.

Help to stop the Help to stop the dislocation.dislocation.


OIM Analysis of Grain Boundary Microstructure in -SiC Polycrystal

(a) SEM Observation (b) Grain Orientation , Grain Boundary Character Distribution (GBCD)

(S.Tsurekawa, T.Watanabe, H.Watanabe and T.Tamari, Key Eng. Mater., Vol. 247 (2003), 327 ~330. )26Annaba 10-12 May 2010

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Macroscopic DefectsMacroscopic Defects

Holes, bubbles, surface imperfections, Holes, bubbles, surface imperfections, cracks, and macroscopic impuritiescracks, and macroscopic impurities


The examination of microstructure may be done over a wide range of length scales or magnification levels, ranging from a visual or low-magnification (~20×) examination to magnifications over 1,000,000× with electron microscopes. Metallography may also include the examination of crystal structure by techniques such as x-ray diffraction. However, the most familiar tool of metallography is the light microscope, with magnifications ranging from ~50 to 1000× and the ability to resolve microstructural features of ~0.2 μm or larger.

Microstructural investigations

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Microstructures of carbon steels

Ferrite AustenitePearlite

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Ferrite and pearlite grainsat 0.1 % C

Ferrite and pearlite grainsat 0.4 % C

Pearlite and cemetite grainsat 1.3 % C

Microstructures of carbon steels

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Microstructure of 0.4 wt % C steel

Ferrite

Pearlite

phasediagram1.swf

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Microstructure of 1.3 wt % C steel

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Cast MicrostructureCast Microstructure

Grains are usually visible.Grains are usually visible.

Size of grains Size of grains cooling rate (fast rate cooling rate (fast rate small grains) small grains)

Fine-grained Fine-grained (“equiaxed” = uniform in size (“equiaxed” = uniform in size and shape)and shape) alloys are generally more alloys are generally more desirable for dental applications. desirable for dental applications. more uniform propertiesmore uniform properties


a) Gray iron: the dark graphite flakes are embedded in ferrite matrix. 500x. b) Malleable (nodular) iron: the dark graphite nodules are surrounded by ferrite

matrix. 200xc) White iron: the light cementite regions are surrounded by pearlite, which has

the ferrite–cementite layered structure. 400x.d) Ductile iron: dark graphite rosettes (temper carbon) in ferrite matrix.

Microstructure of cast iron

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Wrought MicrostructureWrought Microstructure

Metal ingots Metal ingots hot/cold working (rolling, hot/cold working (rolling, swaging, or wire-drawing) swaging, or wire-drawing) produce severe produce severe mechanical deformation of the metalmechanical deformation of the metal E.g. orthodontic wires and bandsE.g. orthodontic wires and bands

Grains are broken down, entangled in each Grains are broken down, entangled in each other, and elongated to develop a fibrous other, and elongated to develop a fibrous structure.structure.

In general, mechanical properties are In general, mechanical properties are superior to those of the same cast alloys.superior to those of the same cast alloys.


Microstructure of an aluminum casting alloy reinforced with silicon carbide particles. In this case, the reinforcing particles have segregated to interdendritic regions of the casting ( 125). (Courtesy of David Kennedy, Lester B. Knight Cost Metals Inc.)

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Microstructure of tungsten carbide—20% cobalt-cemented carbide (1300). (From Metals Handbook, Vol. 7, 8th Ed., American Society for Metals, 1972.)

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Recrystallization and Recrystallization and Grain GrowthGrain Growth

The reappearance of the grain or The reappearance of the grain or crystalline structure when heated or crystalline structure when heated or annealed (usually more obvious in the annealed (usually more obvious in the wrought mass).wrought mass).

Degree of recrystallization is related to:Degree of recrystallization is related to:

Alloy composition and mechanical treatmentAlloy composition and mechanical treatment

Temperature and the duration of the heating Temperature and the duration of the heating operationoperation


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A,A, the fibrous the fibrous microstructure and arrows microstructure and arrows indicate residual stresses.indicate residual stresses.

B,B, Minimal heat leaves the Minimal heat leaves the fibrous structure intact but fibrous structure intact but relieves the stresses. The relieves the stresses. The lattice remains distorted.lattice remains distorted.

C,C, Annealing with more Annealing with more heat allows the lattice heat allows the lattice deformation to be relieved.deformation to be relieved.

D D andand E, E, Further heating Further heating causes a loss of the fibrous causes a loss of the fibrous structure and growth of the structure and growth of the grains, which increase in grains, which increase in size with increasing size with increasing application of heat.application of heat.

gross view microstructure crystal view


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Strengthening of Strengthening of Metals and AlloysMetals and Alloys

Principle: Increased interaction of dislocations Principle: Increased interaction of dislocations will increase the strength of the materials.will increase the strength of the materials. (1) Grain size alterations(1) Grain size alterations

Small grains Small grains reducedreduced ductility but ductility but increasedincreased strength, strength, toughness and polishability. toughness and polishability.

Can be achieved from:Can be achieved from:

QuenchingQuenching (quick cooling) (quick cooling)

Use of nucleating agentsUse of nucleating agents

Use of Use of grain refinersgrain refiners e.g. Ir e.g. Ir encourage even nucleation (without encourage even nucleation (without sacrificing ductility)sacrificing ductility)

Plastic deforming (cold working)Plastic deforming (cold working)


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(2) Cold-working(2) Cold-working Work-hardening or strain-hardening: rolling, wire drawing Work-hardening or strain-hardening: rolling, wire drawing

mechanically deform the alloy mechanically deform the alloy

The shape of the grain is changed from equiaxed to long The shape of the grain is changed from equiaxed to long and thin.and thin.

Increases hardness and yield strength as well as Increases hardness and yield strength as well as chemical reactivitychemical reactivity

Decreases ductility and corrosion resistanceDecreases ductility and corrosion resistance

The harmful effect of cold-working may be removed by The harmful effect of cold-working may be removed by heat treatment, recrystallization, and grain growth.heat treatment, recrystallization, and grain growth.


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(3) Annealing(3) AnnealingHeating the alloy to temperatures sufficient to Heating the alloy to temperatures sufficient to

alter grain size (1/3 - 1/2 melting temperature)alter grain size (1/3 - 1/2 melting temperature) Recrystallization and grain growthRecrystallization and grain growth

The grains convert from long and thin to equiaxed The grains convert from long and thin to equiaxed (convert the cold working result)(convert the cold working result)

(4) Solute-hardening(4) Solute-hardeningAdding solute or impurity atoms which will Adding solute or impurity atoms which will

interact with dislocations.interact with dislocations.


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(5) Precipitation or age hardening(5) Precipitation or age hardening Relies on the ability of an alloy to be Relies on the ability of an alloy to be

converted from a single solid phase converted from a single solid phase structure to one that exhibits two phases.structure to one that exhibits two phases.

When heated at temperature < melting When heated at temperature < melting point, diffusion of foreign atoms occurs point, diffusion of foreign atoms occurs resulting a highly strained lattice resulting a highly strained lattice exhibiting enhanced mechanical exhibiting enhanced mechanical properties.properties.

The rate and length of aging (time and The rate and length of aging (time and temperature) can be manipulated to temperature) can be manipulated to create material with the desired create material with the desired combination of properties.combination of properties.

Interactions between dislocations and Interactions between dislocations and precipitates result in higher strength and precipitates result in higher strength and toughness but moderate ductility.toughness but moderate ductility.

Tem

pera

ture

Metal C(100%)

Metal D(100%)

%composition

Liquid +Solid

liquidus

solidus

Two-PhasedStructure


Theory of Theory of Topology and Topology and the Design of the Design of

MaterialsMaterials

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Case StudyCase Study

THE TITANICTHE TITANIC

Why did it sink so quickly?Why did it sink so quickly?46Annaba 10-12 May 2010

OverviewOverview Case StudyCase Study

The TitanicThe Titanic

• Fracture Mechanisms• Types of Fracture

• Metals/Ceramics/Polymers

• Composites

• Brittle/Ductile Transition

• Charpy Impact Test

• Fatigue• Fatigue Life

• Environmental Effects• Stress Corrosion• Creep 47Annaba 10-12 May 2010

Fracture MechanismsFracture Mechanisms

Fracture Mechanisms are differentFracture Mechanisms are differentin different materials.in different materials.

It’s important to understandIt’s important to understand

ductileductile and and brittlebrittle failurefailure, and , and

ductileductile and and brittlebrittle fracturefracture mechanismsmechanisms..DUCTILE FAILURE : HIGH ENERGYBRITTLE FAILURE : LOW ENERGY

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Case Study - The Case Study - The TitanicTitanic

Maiden VoyageMaiden Voyage April 10th 1912April 10th 1912

• Struck an Iceberg• 11.40pm, April 14th 1912

• Sank with over 1500 lives lost• 2.20am, April 15th 1912

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Case Study - The Case Study - The TitanicTitanic

The Iceberg

The Damage

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The iceberg caused damage The iceberg caused damage over a distance of 100m over a distance of 100m along the side of the Titanic.along the side of the Titanic.

The damage area was 1.1mThe damage area was 1.1m22

This flooded 6 compartmentsThis flooded 6 compartments

This damage was sufficient to sink the Titanic

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The TitanicThe Titanic Titanic SteelTitanic Steel 0.2% Carbon Steel0.2% Carbon Steel

Yield Strength: 190 MPaYield Strength: 190 MPa

Tensile Strength: 420 Tensile Strength: 420 MPaMPa

Elongation: 29%Elongation: 29%

Modern SteelModern Steel 0.2% Carbon Steel0.2% Carbon Steel

Yield Strength: 205 MPaYield Strength: 205 MPa

Tensile Strength: 380 Tensile Strength: 380 MPaMPa

Elongation: 26%Elongation: 26%

150 µm 20 µm Modern steel has smaller

grain structure

Averagegrain size 26 µm

Averagegrain size 42 µm

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-100 0 100 200

Temperature (ºC)

200

150

100

50

0

Modern Steel

Titanic SteelC

harp

y Im

pact

Ene

rgy

(J)

Titanic Steel, 0ºC

Seawater temperature(14th April 1912)-2ºC

Titanic SteelTitanic Steel Low toughnessLow toughness

Large grainsLarge grains

Low purity steelLow purity steel (High Phosphorus (High Phosphorus

and Sulphur and Sulphur content)content)

Would a modern ship survive?

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SummarySummary The Titanic Steel was brittle at low temperature.The Titanic Steel was brittle at low temperature.

This This probablyprobably increased the amount of damage increased the amount of damage when the iceberg collided.when the iceberg collided.

A modern ship A modern ship mightmight survive! survive!less damageless damage

better design (water-tight bulkheads)better design (water-tight bulkheads)

better navigation equipmentbetter navigation equipment

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Was the Titanic Steel Was the Titanic Steel Brittle?Brittle?

New evidence New evidence suggests another suggests another cause for the sinking cause for the sinking of the Titanic…...of the Titanic…...

RMS Olympic and HMS Hawke(collided 1911)

Evidence for brittle fracture under impact, but ductile tearing at lower speeds

Splitting of the steel hull unlikely…..55Annaba 10-12 May 2010

Was the Titanic Steel Was the Titanic Steel Brittle?Brittle?

The Titanic steel was brittle, but no more so than any other ship of its time…..

Failed Titanic Rivet

MnS inclusionsParamagnetic susceptibility of ferrite and cementite obtained from ab initio calculations , Journal of Magnetism and Magnetic Materials, Volume 299, Issue 1, April 2006, Pages 64-69 Y.D. Zhang, H. Faraoun, C. Esling, L. Zuo and H. Aourag 56Annaba 10-12 May 2010


Atomic mismatch in the transition from crytalline Atomic mismatch in the transition from crytalline orientation of one grain to that of the adjacent oneorientation of one grain to that of the adjacent one

Small angle grain boundarySmall angle grain boundary

Interstitial or grain boundary energy similar to surface Interstitial or grain boundary energy similar to surface energy energy

more chemically reactivemore chemically reactive

impurity atoms tend to segregate hereimpurity atoms tend to segregate here

lower in large or coarse-grained materials than in fine-lower in large or coarse-grained materials than in fine-grained materialsgrained materials

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Boron, SulfurBoron, Sulfur

Intermetallics, Volume 14, Issue 2, February 2006, Pages 142-148 A. Kellou, T. Grosdidier and H. Aourag

Acta Materialia, Volume 52, Issue 11, 21 June 2004, Pages 3263-3271 A. Kellou, H. I. Feraoun, T. Grosdidier, C. Coddet and H. Aourag

Study of stability of twist grain boundaries in hcp zinc • ARTICLEScripta Materialia, Volume 54, Issue 5, March 2006, Pages 865-868 H. Faraoun, G. Vincent, C. Esling and H. Aourag

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Quantum mechanics and Quantum mechanics and metallurgymetallurgy

Hume-Rothery RulesHume-Rothery Rules

- - Solid Solubility is described as a continuous function of two Solid Solubility is described as a continuous function of two quantum mechanically derived parameters: Electronegativity and quantum mechanically derived parameters: Electronegativity and atomic sizeatomic size

- - Introduction of the concept of distance in this parameter space Introduction of the concept of distance in this parameter space ( metric space) ( metric space)

- - distance between points is represented as measuring the distance between points is represented as measuring the differences between properties of the relevant metals and alloysdifferences between properties of the relevant metals and alloys

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Single metric Space and Single metric Space and Metallic PropertiesMetallic Properties

Energy Space, where E is solution Energy Space, where E is solution HH==EEfor a particular configurationfor a particular configuration

Differences between two points give the Differences between two points give the difference in energy between two difference in energy between two configurations (measured) (Metric has a configurations (measured) (Metric has a meaning)meaning)

Problem : SE, no extrapolation so Problem : SE, no extrapolation so appealing to additionnal constructsappealing to additionnal constructs

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Forced to construct new Forced to construct new parameter space (no parameter space (no physical)physical) KS equations, charge density, KS equations, charge density,

Charge densities is measurable quantitiesCharge densities is measurable quantities

Construct a parameter space based on Construct a parameter space based on charge densitycharge density

So seek a metric which measures the So seek a metric which measures the distance between two densitiesdistance between two densities

We hope that this distance correlates with We hope that this distance correlates with propertiesproperties

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Why NotWhy Not This choice , possible to predict the This choice , possible to predict the

direction of change in the Charge density direction of change in the Charge density upon changing configuration of alloyingupon changing configuration of alloying

Changes in charge density are second Changes in charge density are second order in the energy ( order in the energy ( So rather large So rather large changes in charge density are changes in charge density are necessary to produce changes in necessary to produce changes in energyenergy))

So it could be a tool this metricSo it could be a tool this metric62Annaba 10-12 May 2010

Bader Topological Theory Bader Topological Theory of Molecular Bondingof Molecular Bonding

(r )(r ) is a scalar field is a scalar field

We may represent a topology of a We may represent a topology of a scalar field in terms of its critical pointsscalar field in terms of its critical points

grad grad (r ) =0(r ) =0

There is 4 kinds of critical points in 3DThere is 4 kinds of critical points in 3D

Local minimum, local maximum and two Local minimum, local maximum and two saddle pointssaddle points

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RéalitéRéalité

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Concepts : chimistesConcepts : chimistes

Bader Bader

Molécules Molécules organiqueesorganiquees

EberhartEberhart

Solides métalliquesSolides métalliques

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Critical Points CpCritical Points Cp

CP (3,3)CP (3,3)

Number of positive curves minus the Number of positive curves minus the number of negative curvesnumber of negative curves

Minimum cp (3,3)Minimum cp (3,3)

Maximum cp (3,-3)Maximum cp (3,-3)

Saddle with the two of the three curvatures Saddle with the two of the three curvatures negative is (3,-1) while the other id (3,1)negative is (3,-1) while the other id (3,1)

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Polyhedra topologyPolyhedra topology

These bonds are the edges of two polyhedra These bonds are the edges of two polyhedra or cages; tetrahedra and octahedraor cages; tetrahedra and octahedra

Packing of which gives rise to the FCCPacking of which gives rise to the FCC Number of corners, edges and faces (c,e,f)Number of corners, edges and faces (c,e,f) Tetrahedron: (4,6,4), Octahedra ( 6,12,8)Tetrahedron: (4,6,4), Octahedra ( 6,12,8) Total charge density will reflect these features Total charge density will reflect these features

with a (3,-3) cp (an atom) at each corner, a with a (3,-3) cp (an atom) at each corner, a (3,-1) cp along each edge, a (3,1)cp in each (3,-1) cp along each edge, a (3,1)cp in each face, and a (3,3)cp within this polyhedraface, and a (3,3)cp within this polyhedra

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Topologies of the B2 Topologies of the B2 Structure Structure

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http://cst-www.nrl.navy.mil/lattice/struk.picts/b2.s.png

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Thanks

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defect: the beauty grains of metals hafid aourag university of tlemcen 1annaba 10-12 may 2010

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