FE ReviewMaterials Properties

Jeffrey W. FergusMaterials EngineeringOffice: 284 Wilmore

Phone: 844-3405email: jwfergus@eng.auburn.edu

Electrical Properties

• Electrical resistance– resistance (R) = resistivity (ρ) length (l) / area (A)– resistivity is a material property– conductivity (σ) = 1 / resistivity (ρ)

l

A– conductivity (σ) = 1 / resistivity (ρ)

• Temperature dependence – with increasing temperature…– metals: resistance increases (conductivity decreases)– semiconductors: conductivity increases (resistivity decreases)

• extrinsic: like metals in intermediate temperatures

– insulators: conductivity increases (resistivity decreases)

A

Mechanical Properties

• Stress-strain relationships– engineering stress and strain– stress-strain curve

• Testing methods• Testing methods– tensile test– endurance test– impact test

Stress

AF=σ=Normal

AF=τ=Shear

F F FA A A

Tension: σ>0 Compression: σ<0

Strain

oo

ol

ll

ll ∆=−=ε=Strain θ==γ= tanha

strain Shear

a

lol lo l hθ

Tensile Test

thickness

Control length (l)

Measure force (F) with load cell

oo

ol

ll

ll ∆=−=ε=Strain

lengthwidth

Measure force (F) with load cell

twF

AF

⋅==σ=Stress

Reduced section used to limit portion of sample undergoing deformation

Stress-Strain Curve

Ultimate Tensile Strength

Yield Point

Elastic Limit

Force decreases due to neckingS

tres

s

Strain

Slope = E (Young’s Modulus)

Percent Elongation(total plastic deformation)

Elastic Limit

Proportionality Limit

0.2% Offset Yield Strength

0.2% offsetyield strength

Str

ess

Strain0.2% strain

yield strength

True/Engineering Stress/Strain

oE A

F=σoo

oE l

ll

ll ∆=−=εEngineering

(initial dimensions)

Stress Strain

iT A

F=σ ∫

==ε

i

o

l

l o

iT l

lln

ldl

( )1+ε=ε ET ln

( )EET ε+σ=σ 1ooii lAlA ⋅=⋅

True(instantaneous

dimensions)

Usingand

True/Engineering Stress/Strain

True

True stress does not decrease

Str

ess

Strain

Engineering

Decrease in engineering stress due to decreased load required in the reduces cross-sectional area of the neck.

Strain Hardening

Str

ess

Plastic deformation require larger load after deformation.

Str

ess

Strain

Onset of plastic deformation after

reloading

after deformation.Sample dimensions are decreased, so stress is even higher

Bending Test

Four-point Three-point

h

wFF/2F/2

LL/2

By summing moment in cantilever beam

22

3

wh

FLmax =σ

Tension at bottom, compression at top

Hardness

• Resistance to plastic deformation• Related to yield strength• Most common indentation test

– make indentation– make indentation– measure size or depth of indentation– macro- and micro- tests

• Scales: Rockwell, Brinell, Vickers, Knoop

Impact

Toughness: combination of strength and ductility -energy for fracture

hi

hf

Fracture energy = mghi -mghf

Charpy V-notch

Ductile-Brittle Failure

• Ductile– plastic deformation– cup-cone / fibrous

fracture surface

Ductile-Brittle Transition Temperature

(DBTT)• Brittle

– little or no plastic deformation

– cleaved fracture surface

Temperature

Fra

ctur

e E

nerg

y

(DBTT)

Creep / Stress Relaxation

• Load below yield strength - elastic deformation only• Over long time plastic deformation occurs• Requires diffusion, so usually a high-temperature

processprocess• Activation energy, Q (or EA)

−⋅=

−⋅=ε=kTE

expART

QexpA A

ɺratecreep

Creep /Stress Relaxation

CreepFF Stress Relaxation

FF

time

fixed strain

fixed load

time

Permanent deformation

Fatigue

Fatigue Limit(ferrous metals)

Repeated application of load - number of cycles, rather than time important.

σmax

0

Number of Cycles to Failure

Str

ess (ferrous metals)

σmin

σave ∆σ

σmax

σmin

0

Corrosion Resistance

• Thermodynamics vs. Kinetics– thermodynamics - stable phases– kinetic - rate to form stable phases

• Active vs. Passive– active: reaction products ions or gas - non protective– passive: reaction products - protective layer

• Corrosion resistance– inert (noble): gold, platinum– passivation: aluminum oxide (alumina) on aluminum,

chromia on stainless steel

Electrode Potential

• Tendency of metal to give up electron• Oxidation (anode)

– M = M2+ + 2e- (loss electrons)

• Reduction (cathode)• Reduction (cathode)– M2+ + 2e- = M (gain electrons)

• LEO (loss electrons oxidation) goes GER (gain electrons reduction)

Corrosion Reactions• Oxidation - metal (anode)

– M = M2+ + 2e-

• Reduction - in solution (cathode)– 2H+ + 2e- = H2

– 2H+ + ½O2 + 2e- = H2O– H O + ½O + 2e- = 2OH-– H2O + ½O2 + 2e- = 2OH-

• Overall Reactions– M + 2H+ =M2+ + H2

– M + 2H+ + ½O2 = M2+ + H2O– M + H2O + ½O2 = M2+ + 2OH- = M(OH)2

Electromotive Force

• Gibbs Free Energy (∆G) =-nFE (Electromotive Force)– n = number of electrons, F = Faraday’s Constant– favorable: energy decrease (-) = positive voltage

• Fe2+ + 2e- = Fe: Ered = +0.440 V• Fe2+ + 2e- = Fe: Ered = +0.440 V• Fe = Fe2+ + 2e-: Eox = -0.440 V• H2O = 2H+ + ½O2 +2e-: Ered = +1.229 V• Fe + 2H+ + ½O2 = Fe2+ + H2O: E = 0.789 V

– E does not change with number of moles (∆G does)– E must be corrected for non-standard state

• concentration of H+ (i.e. pH), oxygen pressure…

Galvanic Corrosion / Protection

• At joint between dissimilar metals– reaction rate of active metal increases– reaction of less active metal decreases

• Galvanic corrosion– high corrosion rate at galvanic couple

• presence of Cu increase the local corrosion rate of Fe

• Galvanic protection– galvanized steel

• presence of Zn decreases the local corrosion rate of Fe

– galvanic protection• Mg or Zn connected to Fe decrease corrosion rate

Zn

Fe

Fe Cu

Waterline Corrosion

• Oxygen concentration in water leads to variation in local corrosion rates

Higher corrosion rate near oxygen accessoxygen access

Rings of rust left from water drops

Rust just below water surface

Materials Processing

• Diffusion• Phase Diagrams

– Gibb’s phase rule– lever rule– lever rule– eutectic system / microconstituents– Fe-Fe3C diagram (ferrous metals)

• Thermal-mechanical processing

Diffusion

• Atoms moving within solid state• Required defects (e.g. vacancies)• Diffusion thermally activated• Diffusion constant follows Arrhenius relationship

−=

−=kTE

expDRT

QexpDD A

oo

Gas constant

Boltzman’s constant Temperature

Activation Energy

Steady-State Diffusion

• Fick’s first law (1-D)• J = flux (amount/area/time)• For steady state

∂∂−=

xC

DJ

∆∆−=

xC

DJ ∆x

∆C

∆x

sm

massm

m

mass

sm

J2

32=

−=

Phase Equilibria

• Gibb’s Phase Rule• P + F = C + 2 (Police Force = Cops + 2)

– P = number of phases– F = degrees of freedom– C = number of components (undivided units)– 2: Temperature and Pressure– 2: Temperature and Pressure

• One-component system– F = 1 + 2 - P = 3 - P

• Two-component system– F = 2 + 2 - P = 4 - P

• Two-component system at constant pressure– F = 2 + 1 - P = 3 - P

“2” becomes “1” at constant pressure

Pressure-Temperature Diagram

Single-phase area: can change T

Two-phase line: Change T (P) require specific change in P (T)

(F=1)

One component: H2OIf formation of H2 and O2 were considered there would be two

components (H and O)

water

ice

watervapor

Temperature

Pre

ssur

e

Single-phase area: can change T and P independently

(F=2)

Three-phase point: One occurs at specific T and P (triple point)

(F=0)

Phase Diagrams

L

δ

δ + γ δ + L

Two-component @ constant pressureThree-phase - horizontal line

Eutectic

PeritecticL +solid (δ) → solid (γ)

α

γ

β (pure B, negligible

solubility of A)

α + γ

γ + β

α + β

γ + L β + L

Composition (%B)

Tem

pera

ture Eutectic

L → 2 solids (γ + β)

Eutectoidsolid (γ) → 2 solids (α + β)

BA

Lever Law• Phase diagram give compositions of phases

– two-phase boundaries in 2-phase mixture

• Mass balance generate lever law

LiquidComp.

(XL)

SolidComp.

(XS)

AlloyComp.(Xalloy)

Opposite arm over total length

Right arm for solid

L

S

Composition (%B)A B

Tem

pera

ture

(XL)(XS) (Xalloy)

SL

alloyL

XX

XXsolid%

−−

=

SL

Salloy

XX

XXliquid%

−−

=

Right arm for solid

Left arm for liquid

70 wt% Pb - 30 wt% Sn

256°C

First solid

( ) %27)(%3.18.)(%8.61)(%3.18)(%30

%8.61.% =−−=

PbSnliqSnPbSnalloySn

Snliq

At 183.1°C

(Pb)L

12.8 wt% Sn

( ) %73)(%3.18.)(%8.61)(%30.)(%8.61

%3.18.% =−−=

PbSneutSnalloySneutSn

SnPbprim

(Pb)L

70 wt% Pb - 30 wt% Sn

256°C

First solid

( ) %15)(%3.18.)(%8.97)(%3.18)(%30

%8.97% =−−=

PbSnliqSnPbSnalloySn

Snβ

At 182.9°C

(Pb)

12.8 wt% Sn

( ) %85)(%3.18.)(%8.97)(%30.)(%8.97

%3.18% =−−=−

PbSnliqSnalloySnliqSn

SnphasePb

(Pb)

Eutectic(Pb)+β

Microconstituents

( ) )(%3.18)(%30 =−= PbSnalloySn

( ) %73)(%3.18.)(%8.61)(%30.)(%8.61

%3.18.Prim% =−−=

PbSneutSnalloySneutSn

SnPb

Eutectic Microsconstituent ((Pb)+βSn)

Primary Pb

( ) %27)(%3.18.)(%8.61)(%3.18)(%30

%8.61% =−−=

PbSnliqSnPbSnalloySn

SnL

( ) %55)(%3.18.)(%8.97)(%3.18.)(%8.61

%8.97% . =−−=

PbSnliqSnPbSneutSn

Sneutinβ

( ) %45)(%3.18.)(%8.97.)(%8.61.)(%8.97

%3.18% . =−

−=PbSnliqSneutSnliqSn

SnPb eutin

Phases in Eutectic Microsconstituent

Phases in Microconstituents

(Pb) 73 g primary (Pb)

27 g eutecticβ

12 g (Pb) (45% of 27 g)

(Pb) + βSn15 g βSn (55% of 27 g)

Total amounts in 100 g sampleTotal (Pb) = 73 + 22 = 85 g Total βSn = 15 g(same as directly from the lever law)

Fe-Fe3C Phase Diagram

Austenite Cementite

Ferrite

Pearlite (ferrite + cementite)%C = 0.77%

HypereutectoidHypoeutectoid

Cast Irons

Steels

Time-Temperature-Transformation (TTT) Diagram

fs727°C

800°C

Decomposition of Austenite at fixed temperature Pearlite: High Temp

slow nucleation

Coarse pearliteps

bs

ms

mf

pf

bf

200°C

100°C

KeyMain symbolf = ferritep = pearliteb = bainitec = cementite

(Fe3C)Subscriptss = startf = finish

Tem

per

atu

re

Log TimeMartensite

athermal (diffusionless)

Bainite: Diffusion slow

for pearlite

Coarse pearlite

Fine pearlite

Quench / Hardenability / Tempering

• Quench - rapidly cool– in steel: cool fast enough to Ms to prevent pearlite / bainite

formation

• Hardenability• Hardenability– ease of forming martensite in steels– alloying elements inhibit pearlite / bainite formation, promote

martensite formation

• Tempering of steels– reheating martensite to form transition carbides– improve toughness

Cold Working• Plastic deformation creates dislocations, which

increases strength / decreases ductility• Reduction in Area used to quantify degree of cold

working%

AAfA

RA%CW%i

i 100⋅−==

lwlw ⋅−⋅%

lwlwlw

RA%ii

ffii 100⋅⋅

⋅−⋅=

%l

llRA%

i

fi 100⋅−=

if wwfor ≅

%d

dd%

d

dd

RA%

i

fi

i

fi

100100

4

442

22

2

22

⋅−

=⋅⋅π

⋅π−

⋅π

=

Cold Worked Properties

400

500

600

Str

ess

(MP

a) 10

12

14

16

Percen

t Elo

ng

ation

Yield StrengthTensile Strength

0

100

200

300

0 10 20 30 40 50 60 70 80

Percent Cold Work

Str

ess

(MP

a)

0

2

4

6

8

Percen

t Elo

ng

ation

Tensile StrengthPercent Elongation

Balancing Strength / Ductility

300

400

500

600

Str

ess

(MP

a)

20

25

30

35

Percen

t Elo

ng

ation

Yield Strength

Tensile Strength

Percent Elongation

0

100

200

0 10 20 30 40 50 60 70 80

Percent Cold Work

Str

ess

(MP

a)

0

5

10

15

Percen

t Elo

ng

ation

Sy > 310 MParequires

%CW > 22%Elongation > 10%

requires%CW < 31%

Both Propertiesrequires

22% < %CW < 31%

Balancing Strength / Toughness

400

450

500

550

600

Str

ess

(MP

a)30

35

40

45

50Yield Strength

Tensile Strength

Fracture Toughness Fractu

re To

ug

hn

ess (K

σy = 250 MPa13% CW

Sy > 250 MPaand

KIc > 16 MPa m½

requires13% < %CW < 39%

100

150

200

250

300

350

0 10 20 30 40 50 60 70Percent Cold Work

Str

ess

(MP

a)

0

5

10

15

20

25

Fractu

re To

ug

hn

ess (KIc ) (M

Pa m

0.5)

KIc = 16 MPa m0.5

39% CW

31% CWSy = 364 MPa

KIc = 22 MPa m0.5

13% < %CW < 39%

Examplefor 31% CW

Sy = 364 MPaKIc = 22 MPa m½

Cold Work / Anneal / Hot Work• Annealing can eliminate effect of cold work

– recovery - stress relief, little change in properties– recrystallization - elimination of dislocations, decrease in

strength, increase in ductility– grain growth - increase in grain size, decreases both

strength and ductility

• Hot working• Hot working– deforming at high enough temperature for immediate

recrystallization– list cold-working and annealing at the same time– no increase in strength– used for large deformation– poor surface finish - oxidation– after hot working, cold working used to increase strength and

improve surface finish

Organization from 1996-7 Review Manual(same topics in 2004 review manual)

• Crystallography• Materials Testing• Metallurgy

Crystallography

• Crystal structure– atoms/unit cell– packing factor– coordination number– coordination number

• Atomic bonding• Radioactive decay

Bravais Lattice

Crystal System Centering

P: Primitive: (x,y,z)

(x,y,z): Fractional coordinates -proportion of axis length, not absolute distanct

a

b

c

β α

γ

P: Primitive: (x,y,z)

I: Body-centered: (x,y,z); (x+½,y+½,z+½)

C: Base-centered: (x,y,z); (x+½,y+½,z)

F: Face-centered: (x,y,z); (x+½,y+½,z)(x+½,y,z+½); (x,y+½,z+½)

Centering must apply to all atoms in unit cell.

Bravais Lattices (14)

Crystal System Parameters Primitive

(Simple) Body-

Centered Face-

Centered Base-

Centered

Cubic a=b=c

α=β=γ=90° X X X

Tetragonal a=b≠c

α=β=γ=90° X X

α=β=γ=90°

Orthorhombic a≠b≠c

α=β=γ=90° X X X X

Rhombohedral a=b=c

α=β=γ≠90° X

Hexagonal a=b≠c

α=β=90°, γ=120° X

Monoclinic a≠b≠c

α=γ=90°, β≠120° X X

Triclinic a≠b≠c

α≠β≠γ≠90° X

Atoms Per Unit Cell

• Corners - shared by eight unit cells (x 1/8)– (0,0,0)=(1,0,0)=(0,1,0)=(0,0,1)=(1,1,0)

=(1,0,1)=(0,1,1)=(1,1,1)

• Edges - shared by four unit cells • Edges - shared by four unit cells (x 1/4)– (0,0,½)= (1,0,½)= (0,1,½)= (1,1,½)

• Faces - shared by two unit cells (x 1/2)– (½,½,0)= (½,½,1)

Common Metal Structures

• Face-Centered Cubic (FCC)– 8 corners x 1/8 + 6 faces x 1/2 – 1 + 3 = 4 atoms/u.c.

• Body-Centered Cubic (BCC)– 8 corners x 1/8 + 1 center – 8 corners x 1/8 + 1 center – 1 + 1 = 2 atoms/u.c.

• Hexagonal Close-Packed (HCP)– 8 corners x 1/8 + 1 middle – 1 + 1 = 2 atoms/u.c.– 12 hex. Corner x 1/6 +2 face x 1/2 + 3

middle = 6 atoms/u.c.

Packing Factor

• Fraction of space occupied by atoms• For FCC

cba

rFP i

⋅⋅= ∑

334 π

..

ar

raraa2

44diagonalface 22 =⇒⋅=+=

( ) ( )3434

• For BCCa

r ( ) ( )740

23

24

443

334

3

334

.r

a

r.F.P =π=

π⋅=

π⋅=

r3

4ar4aaadiagonalbody 222 =⇒⋅=++=

( ) ( )680

83

34

223

334

3

334

.r

a

r.F.P =π=

π⋅=

π⋅=

Density

volumemass

.c.uvolume

moleatom

molemass

.c.uatom

Density =

⋅

⋅

=

For nickel:- Atomic weight = 58.71 g/mole

( ) 338249158

1052393106020

71584

cm

g.

cmx.moleatom

x.

moleg

..c.u

atom

Density =⋅

⋅

=−

- Atomic weight = 58.71 g/mole- Lattice parameter = 3.5239 Å=3.5239 x 10-8 cm- Avogadro’s No. = 6.02 x 1023 = 0.602 x 1024 = atoms/mole

Close Packed (CN=12)

Highest packing density for same sized spheresFCC and HCP structures

Cube Center (CN=8)

Same atoms: BCCDifferent atoms: CsCl

Octahedral Site (CN=6)

In FCC:- Center (½,½,½)- Edges (0,0,½),(0,½,0),(½,0,0)- 4 per unit cell- All filled - NaCl structure

8-sided shape

Tetrahedral Site (CN=4)In FCC:- Divide cell into 8 boxes - center of small box- (¼,¼,¼),(¾,¼,¼),(¼,¾,¼),(¾,¾,¼)(¼,¼, ¾)(¾,¼, ¾),(¼,¾, ¾)(¾,¾, ¾)-8 per unit cell-All filled - CaF2 structure; half-filled - ZnS-All filled - CaF2 structure; half-filled - ZnS

4-sided shape

Radius Ratio Rules

Critical Radius for CN 8 = 0.732CN 8

Critical radius is size of atom which just fits in siteDefine minimum for bonding (i.e. atoms must touch to bond)

Critical Radius for CN 8 = 0.732

Critical Radius for CN 6 = 0.414

Critical Radius for CN 4 = 0.225

CN 6

CN 4

CN 3planar

Close Packed Plane

A BA BA C

HCP: ABABABABABABABABFCC: ABCABCABCABCABCSame packing density (0.74)Same coordination (CN=12)

Miller Indices

Planes

Directions

(hkl)

{hkl}

[hkl]

<hkl>

specific

family

specific

family

- No commas- No fractions- Negative indicated by bar over number<hkl> family

A family of planes includes all planes which are equivalent by symmetry - depends on crystal system.- For cubic: (110),(011) and (101) are all {110}- For tetragonal: (011) and (101) are {101}

but (110) is not (c≠a)

over number

Miller Indices - Directions

ba

c

-1/3

1/2-1

x1/2

y-1

z-1/3 (x 6)

[ ]263

1

1/4

1/2

x1

y1/4

z1/2 (x 4)

[ ]214

[ ]263

Miller Indices - Planes

41

21

ba

c

41

21

ba

c

x1/44

y∝0

z-1/2-2

( )204

interceptreciprocal

Miller Indices - Planes

31

21

ba

c

41

31

21

ba

c

41

x1/44

y-1/3-3

z-1/2-2

( )234

interceptreciprocal

Atomic Bonding

• Covalent– sharing electrons– strong– directional

• Metallic– metal ions in sea or

electrons– moderately strong– directional

• Ionic– trading of electrons– electrostatic attraction or

ions– strong– non-directional

– non-directional

• Secondary– Van der Waals– H-bonding– electrostatic attraction of

electric dipole (local charge distribution

– weak

Radioactive Decay

• Loss of electrons/protons/neutrons– alpha - 2 protons / two neutrons (i.e He nucleus)– beta - electrons– gamma - energy

• Exponential decay

−= t

expNNtime

• Exponential decay

τ

−= texpNN o

( ) ( )22 2

121

21

21

ln

tln

N

Nln

texpNNN

o

ooo −=τ⇒=

−=

τ⇒==

( )

⋅−=

⋅−=21

21

69302t

t.expN

tlnt

expNN oo half life

amount

original amount

time constant