advanced high temperature alloys

Advanced High Temperature Alloys

Prof. Dr.-Ing. Uwe GlatzelgMetals and Alloys

University BayreuthSS 2010

University Bayreuth, Advanced High Temperature Alloys Uwe Glatzel, Metals and Alloys1

Lecturer:Lecturer:Prof Dr Ing habil Uwe GlatzelProf. Dr.-Ing. habil. Uwe Glatzel• born Dez. 1960• Physik-Diplom (B Sc and M Sc) in Tübingen• Physik-Diplom (B.Sc. and M.Sc) in Tübingen

(exchange year in Corvallis, Oregon, USA)• PhD thesis at the Institute for Metals Research, Technical

University Berlin, Prof. Monika Feller-Kniepmeier• post-doc (1 Jahr) at Stanford University• Habilitation TU-BerlinHabilitation TU-Berlin• Gerhard-Hess award of the German Science Foundation

(DFG) for young scientist (400.000 €)• 1996-2003 full professor for Metals and Alloys, Jena• since April 2003 Bayreuth (Chair for Metals and Alloys)postal address:

d i h b h ( )


Ludwig-Thoma-Str. 36b phone: +49 (0) 921 - 55-5555D-95447 Bayreuth, Germany e-mail: [email protected]

Literature• R Bürgel Handbuch Hochtemperatur-Werkstofftechnik Vieweg

LiteratureR. Bürgel, Handbuch Hochtemperatur Werkstofftechnik, Vieweg

• R.C. Reed, The Superalloys - Fundamentals and Applications, Cambridge Univ. Press• H. Frost, M. Ashby, Deformation-Mechanism Maps, Pergamon Press

G M th M V d V d M t i l f Hi h T t E i i• G. Meetham, M. Van der Voorde, Materials for High Temperature Engineering Applications, Springer

• J. Betten, Creep Mechanics, Springer• Askeland: Materialwissenschaften, Spektrum Lehrbuch; 1994• Callister: Materials Science and Engineering - An Introduction, Wiley, New York, 1999• H. Schumann, Metallographie, Deutscher Verlag für Grundstoffindustrie, Leipzig• F. Vollertsen, S. Vogler, Werkstoffeigenschaften und Mikrostruktur, Hauser Verlag• P. Haasen, Physikalische Metallkunde, Springer-Verlag, Berlin• H -J Bargel G Schulze Werkstoffkunde VDI-Verlag DüsseldorfH. J. Bargel, G. Schulze, Werkstoffkunde, VDI Verlag, Düsseldorf• P. Sarrazin, A. Galerie, J. Fouletier, Mechanisms of High Temperature Corrosion, Trans

Tech Publications


lecture notes: http://www.metalle.uni-bayreuth.de then "Lehre" then "Vorlesungen", you will find the link to this lecture notes and three review talks we will do at the end.

What You Should Know:What You Should Know:

• basic thermodynamics• introduction to diffusionintroduction to diffusion• introduction to dislocations• phase diagrams• theory of elasticity• theory of elasticity• ...• basic materials science courses


Contents1 Introduction Basics

Contents1. Introduction, Basics2. Stability of Microstructure3. Mechanical Properties

a) Static)b) Cyclic (Fatigue)

4 High Temperature Corrosion4. High Temperature Corrosion5. High Temperature Alloys6. Lost Wax Investment Casting7. Depending on Time: Lectures on


p ga) SX Ni-Base Superalloys b) LEK 94 c) Pt-Base Superalloys

IntroductionIntroduction

• only alloys will be looked at (no ceramics no• only alloys will be looked at (no ceramics, no polymers).

• no coatings (BUT : practically all high temperature systems are coated!), simply not enough timeenough time.


Maximum Temperatures for li i f iff i lApplications of Different Materials

i i t tGroup maximum service temperature[°C] deformation/damage mechanism

Polymer up to 300 melting, decomposing (pyrolyze)

Glass up to 800 viscous flow

Fe-Basis (coated) up to 1100Fe-ODS up to 1300

Metals

Fe ODS up to 1300Ni-base up to 1200Pt-base up to 1600

refractory metals in inert h b 1600

creep, dislocation climb,grain boundary sliding

atmosphere above 1600MoSi2 up to 1800

Ceramics SiC up to 1600viscous flow, glass transition temperature grain boundaryCeramics SiC up to 1600 temperature, grain boundary

sliding

Composits (SiC/C) up to 1600 complex


p ( ) p p

Overview MaterialsOverview Materialsen

gth

usab

le st

ru

source: Plansee AGPlansee AG, Reutte, Tirol, Austria


temperature [°C]500 1500 2000

Taking Density into AccountTaking Density into Accounten

gth

usab

le st

ru


500 1500 2000temperature [°C]

Oxidation ResistanceOxidation Resistanceen

gth

usab

le st

ru


500 1500 2000temperature [°C]

Refractory Metals:

Most common definition ofwider definition Most common definition of

refractory metals (refractory = widerspenstig, halsstarrig):

of refractory metals

two elements of the 5. and three elements of the 6. period with melting points higher

Tm of platinum

with melting points higher than Pt. Processing in general by powder metallurgy.


DensityDensity

R PtOs, IrReWTa

Pt

Au

Os, Ir

Ru, Rh, PdHf

TcMo

PdMo

NbAg


Abundance of ElementsAbundance of Elements

to find 1 atom Rh within a bunch of Si-atoms is comparable toatoms is comparable to find one individual person within the word population


population

Material ChoiceMaterial Choice

• temperature• environment• moving/non-moving part• design complexity (how to manufacture)• price constrictions (depending on applicationprice constrictions (depending on application

of system). Reduction of 1 kg in weight:car 0 5 €– car ~ 0 - 5 €

– plane ~ 100 – 500 €


– aerospace ~ 100.000 - 500.000 €

Influence of onInfluence of ... on ...• temperature:temperature:

– phase transitions, volume fractions, ...– diffusion ( recrystallization, dislocation climb, diffusional creep, ... )– thermal fatigue (TF)

• mechanical:– creep– fatigue (low cycle, LCF, high cycle fatigue, HCF)

i t• environment:– oxidation– corrosion– corrosion

• combinations:– thermo-mechanical fatigue (TMF)


thermo mechanical fatigue (TMF)– stress corrosion cracking, stress oxidation, ...

BasicsBasicsThermodynamics ↔ KineticsThermodynamics ↔ Kinetics

Boltzmann-statistics: energy ofmovement increases with temperature 3p

Tk23u Batomkin ⋅=

TRQ

0 e ⋅−

⋅ε=ε &&Tk3Tk

232u2u BBatomkinatomtotal ⋅⋅=⋅⋅=⋅=


0Arrhenius-plotTR3U

moltotal ⋅⋅= 0,33 eV, bzw. 32 kJ/mol bei 1000°C

Vacancy ConcentrationVacancy Concentration

F U T S t ti iF = U - T·S non-zero vacancy concentration is in thermodynamic equilibrium

TRQ

v

vac

ec ⋅−

= Qvacnickel = 1,36 eV (energy necessary to create one vacancy)

T[°C] 20 300 450 800 1000 1200 1454

T/Tm 0.17 0.33 0.42 0.62 0.74 0.85 1.00

cv 10-23 3·10-12 10-9 10-6 10-5 7·10-5 3·10-4


equilibrium vacancy concentration for nickel

Nickel Vacancy ConcentrationNickel Vacancy Concentration

100

10 5

entra

tion 10-5

10-10

canc

y co

nc

10-15

Nickel Vacancy Concentration

vac

10-20

Nickel Vacancy Concentration

ncen

tratio

n [

10-4

]

1,00

temperature [°C]

0 200 400 600 800 1000 1200 1400 160010-25

Tm0 200 400 600 800 1000 1200 1400 1600

vaca

ncy

con

0,100,01

T


temperature [°C] Tm

DiffusionDiffusion

cDj ∇⋅−=rv

1. Fick's law[j] ( ) 2 1[j] = (atoms) · m-2 · s-1

[D] = m2 · s-1[D] m s

[c] = (atoms) · m-3

diff ivacancy diffusion or volume diffusion


Coefficient of DiffusionCoefficient of Diffusion

Qvac energy to create a vacancyQ i ti activation energy to migrate a vacancyQmigration activation energy to migrate a vacancyQSD activation energy for volume diffusion

QSD = Qvac + Qmigration

TkQ

0Tk

)QQ(

0

SDmigrationvac

eDeDD ⋅−

⋅

+−

⋅=⋅= 00

QSD ≈ 17 ·kB ·Tm QSDnickel ≈ 2.5 eV = 244 kJ/mol


(for a perfect crystal; defects will lower the activation energies)

Dependence Melting Point and Enthalpy of Vacancy Creation

T Q t lelement Tm[°C] 17·R·Tm

Qvac[eV]

crystal structure

Pb 327 0 88 0 57 fccPb 327 0.88 0.57 fcc

Al 660 1.36 0.68 fcc

Cu 1 085 1.99 1.29 fcc

Ag 1 235 2.21 1.12 fcc

Ni 1 455 2.53 1.78 fcc

Pt 1 768 2 98 1 32 fccPt 1 768 2.98 1.32 fcc

Mo 2 623 4.23 3.00 bcc


W 3 422 5.40 4.00 bcc

QSD versus TQSD versus Tm

400 kJ/mol

0 13 k /( l )0.137 kJ/(mol·K)≈ 17 · kB ·NA


Coefficient of DiffusionCoefficient of Diffusion

Steep slope indicates a p phigh activation energy.

S ll l t diffSmall elements diffuse faster.

Diffusion in fcc crystals slower than in bcc crystals.y


Coefficient of Diffusion with DefectsCoefficient of Diffusion with Defects

Coefficient of diffusion of Th i W

surface diffusion

in W.

Overall velocity for diffusion grain boundary diffusion

depending on grain boundary thickness, grain size and volume diffusion

dislocation density.pipediffusion


Pipe DiffusionPipe DiffusionD D + a ρ DDeff = DSD + adisl. · ρ · Ddisl.

adisl. area of dislocation core( ≈ 5 b2 ≈ 0 3 nm2)ol me diff sion ( ≈ 5 b2 ≈ 0.3 nm2)

ρ dislocation density

D i diff i l

volume diffusiondominant

pipe diffusiondominant Ddisl. pipe diffusion along

dislocation core

t fl D

dominant

increasing

atom flux ~ D·area

2grainSD dD~

timeatoms

⋅⎟⎠⎞

⎜⎝⎛

nbD~i

atoms 2disl ⋅⋅⎟

⎠⎞

⎜⎝⎛

decreasing

dashed line:

diffusion in crystal by the velocity of pipe diffusion

graintime ⎠⎝

22 bDnbDdD

identical atom fluxes if:time .disl

.disl⎟⎠

⎜⎝


ρ⋅⋅=⋅⋅=⋅ 2.disl

grain

2.dislgrainSD bD

dbDdD

Grain Boundary DiffusionGrain Boundary Diffusion

Deff = DSD + π · δ / d · Dgrain bound.

with:volume diffusiondominant

grain boundary diffusion

δ effective grain boundary thickness ( ≈ 2 b ≈ 0.5 nm)

dominantfinegrain

d grain size

D pipe diffusion along

coarsegrain

Ddisl. pipe diffusion along dislocation core

dashed line: diffusion in crystal by the velocity


y y yof grain boundary diffusion

Activation Energies Indicating Mechanism Changes

~ QSD

Single crystal aluminium, oriented such that <110>{111} slip is activated.


Lytton, Shepard and Dorn, Trans. AIME 212 (1958) 220

Diffusion in Ordered Structures ( lli h )(Intermetallic Phases)

• High binding energies high activation• High binding energies high activation energies low coefficient of diffusion

• For example NiAl: very low enthalpy of ordered B2 structure low enthalpy outweighs entropyB2 structure low enthalpy outweighs entropy

ordered up to meltingt ttemperatureTm

Ni = 1454°CTm

Al = 660°CTm

NiAl = 1638°C


m

Second Fick's LawSecond Fick s LawC b l d d di tl f fi t Fi k' l

cDtc

Δ⋅=∂∂

Can be concluded directly from first Fick's law.

Similar in heat transfer systems electricalt∂ Similar in heat transfer systems, electrical potential, ... .

1( )x1)x(f1 Γ−=

⎟⎞

⎜⎛Γ

x1)(f0.6

0.8

f1(x)

⎟⎠

⎞⎜⎝

⎛Γ−=5.0

1)x(f2

⎟⎞

⎜⎛Γ

x1)x(f0.2

0.4

f2(x)

f3(x)

⎟⎠

⎜⎝

Γ−=05.0

1)x(f3

( ) ⎟⎞

⎜⎛ xsolution to these


0.5 1 1.5 2( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛Γ⋅−−=

tD2xccc)t,x(c 011

solution to these boundary conditions:

Thermal ConductivityThermal Conductivity

The most simple, stationary case: no heat radiation, constant temperatures in front and back of component.

λ … coefficient of heat (or thermal) conductivity: λ = a · cp · ρ

a … coefficient of temperature conductivity

cp … heat capacity

ρ … density

compare:

cDj ∇⋅−=rr

Tλq ∇⋅−=r

&r

c∂ T∂


cDtc

Δ⋅=∂∂ ΔTa

tT

⋅=∂∂

Temperature Distribution with h l i i ( )Thermal Barrrier Coating (TBC)

cooling aircooling air

hot air

Wärmedämm-schicht

Haftvermittlerschicht GrundwerkstoffTBC bond coat substrateschicht

In case of transients, the temperature should reach a stable distribution as fast as possible in order to reduce thermal stresses ( temperature conductrivity as high as possible).I f t ti i t h t d ti it l d t h t fl i t th lid


In case of stationary circumstances, heat conductivity leads to heat flow into the solid.

Material Parameters at RTMaterial Parameters at RT

heat cond heat cap density temp cond

⎥⎦⎤

⎢⎣⎡

⋅KmW

⎥⎦

⎤⎢⎣

⎡⋅KkgJ

⎥⎦⎤

⎢⎣⎡

3cmg

⎥⎦

⎤⎢⎣

⎡ −

sm10

26

material/property

heat cond.λ

heat cap.cp

densityρ

temp. cond.a

⎦⎣ g ⎦⎣ ⎦⎣

ferritic steel 45 460 7.8 13.0

austenite steel 15 500 8.0 3.8

Ni-base alloys 11 450 8.2 3.0

Mo 145 240 10.2 59.0

Ti alloys (α-rich) 7 530 4.5 2.9

Al 210 890 2.7 87.0

Al2O3 bei RT( Al2O3 bei 1000°C )

25( 6)

800 3.9 8.4source: Bürgel

Attention: Heat conductivity strongly depends on alloy composition see steels and pure


Attention: Heat conductivity strongly depends on alloy composition, see steels and pureNi with 91 W/(m⋅K) in comparison to Ni-base alloys with 11 W/(m⋅K)

ContentsContents1 Introduction Basics1. Introduction, Basics2. Stability of Microstructure3. Mechanical Properties

a) Staticb) Cyclic (Fatigue)



a) SX Ni-Base Superalloys b) LEK 94 c) Pt-Base Superalloys

Microstructure is NOT stableMicrostructure is NOT stable

annealed deformedannealed deformed


stress-relieved recrystallized

RecrystallizationRecrystallization

time dependence of recrystallization can berecrystallization can be approximated by Avrami Johnson MehlAvrami-Johnson-Mehl function:

n

0tt

e1f⎟⎠⎞⎜

⎝⎛−

−=r e1f


Grain CoarseningGrain Coarsening

• driving force: reduction of grain boundary energygy

• T > 0.7 · Tm

d f i• no pre-deformation necessary• self-similar systemse s sys e• Ostwald ripening d ~ t1/3 (big grains eat up

ll i )small grains)• new grains have low dislocation density


g y

Grain CoarseningGrain Coarsening

monomodal

bimodal (some grain boundaries are pinned, e.g. by precipitates)


Precipitate HardeningPrecipitate Hardening

Requirements:• solid solution at higher

t t ( bilit ttemperatures (ability to homogenization heat treatment)treatment)

• during cooling a two-phase region should be reachedg

• in general: cooling rate as high as possible, thereafter g pannealing (in the two-phase region) to let grow the

i i


precipitates

Thermodynamic ↔ KineticThermodynamic ↔ Kinetic


Example: Al-Cu AlloyExample: Al Cu Alloy

G i i P tGuinier-Preston Zones leading to θ-Precipitates (Al2Cu) have paved the way to the success of Al-alloys


Other Examples of i i h d iprecipitate hardening:

Al2Cu in AlCu alloy:


nickel-base superalloyplatinum-base superalloy

Time Dependence of Precipitation Hardening

nucleation growth coarseningnucleation, growth, coarsening

T = const.

dT precipitate size λT distance between precipitates


fT volume fraction of precipitates

Coherent - Semicoherent - IncoherentCoherent Semicoherent Incoherent

(mit Orientierungsbezug) (ohne Orientierungsbezug)

misfit ( ) aa

aaa

aaa

aaaa:

T

MT

M

MT

MT21

MT Δ≈

−≈

−≈

+−

=δ


( ) aaaaa TMMT2 +

Energy ConsiderationEnergy Consideration

ΔGtotal = ΔGvol + ΔGboundary + ΔGstrain + ΔGdefect

total change in free enthalpy

strain enthalpy (elastic energy + dislocation line energy)

enthalpy of phase boundary (scales with surface)

reduction of enthalpy by precipitation coupled with a defect

enthalpy of formation of matrix to precipitate (scales with volume)

py p y ( )


Heterogeneous NucleationHeterogeneous Nucleation


TEM-Micrograph of TiC Precipitates at Di l i i A i i S lDislocations in an Austenitic Steel


Ostwald-Ripening of PrecipitatesOstwald Ripening of Precipitates

d3 - d03 ~ D⋅t here for T/Tm ≈ 0.74

' ti l i i IN 738 LC tγ' particle size in IN 738 LC atT = 920°C.

particle coarsening constant of(50 nm)3/h(50 nm)3/h


Room Temperature (RT) versusHi h T (HT) D f iHigh Temperature (HT) Deformation

• most alloy properties at room temperature are time and rate independent (elastic constants, tension stress, ... ), tension stress experiment.

• For T > 0.4 · Tm the properties (deformation) will be time m p p ( )and rate dependent, creep experiment.

deformation hardening fine grain hardening solid solution strengthening

precipitate hardening

cold deformation (RT) strong medium medium to strong medium to strong

creep (HT)

temporary hardening, reduced creep rupture strength, may lead to

recrystallization

reduced strength with fine grain material coarse grain, ideally

single crystal

medium medium to strong


Change in Materials Properties with Temperature

Material properties of steel and Ni alloys at elevatedNi-alloys at elevated temperatures. Comparison b t h t t d lbetween short-term and long-term parameters.


Tension ↔ Creep ExperimentTension ↔ Creep Experiment


Elastic (E-)Modulus andi iPoisson's Ratio

)1(2EG

ν+⋅=shear modulus G


Anisotropy and Temperature Dependence of El i C i Ni b S llElastic Constants in Ni-base Superalloys

D. Siebörger, H. Knake, U. Glatzel, Mat. Sci. Eng. A298 (2001)

Orientation dependence of Young’s modulus E of matrixphase Distance from the center tophase. Distance from the center to the surface indicates the magnitude of the Young’s modulus i thi di ti


in this direction.

High Temperature DeformationHigh Temperature Deformation

• dislocation glide (Peierls stress, in fcc and hcp very small and for T > 0.15 Tm negligible)

li f di l ti d di l ti i t ti (f l• cross slip of screw dislocations and dislocation interactions (for a low stacking fault energy larger dislocation spacing thermal activation necessary T > 0 2 T influence on deformation rate)activation necessary, T > 0.2 Tm, influence on deformation rate)

• climb of edge dislocations to overcome obstacles:diffusion at completepdislocation line

T > 0.4 Tm


Dislocation ClimbDislocation Climb

climb of edge dislocations to annihilate each other.

arrangement in low energy configurations (sub-grain boundaries), climbing around b l (l i h lidabstacles (leaving the glide

plane)

movement of screw dislocations ith kink


dislocations with kink

Internal Back StressInternal Back Stress

i l i li b ll ihil i f di l iDislocations climb allows annihilation of dislocations and to establish a constant dislocation density, resulting in an internal back stress of:

bG ρασ ⋅⋅⋅= bG.int

1bG 1σdislocation = and

r1

2bG⋅

π⋅⋅

r1

=ρ

G shear modulus, α constant 0.3 - 1, b magnitude of Burgers vector


Creep ExperimentCreep Experiment

behavior of pure metals:

primary secondary tertiary:


primary secondary tertiary:

Creep Experimental Setup up to 1400°C

Constant temperature and stress or a d st ess oload


Creep Experimental Setup forElectrical Conductivity Materialy

up to Melting Temperature

Pyrometer from left, optical strain measurement from right, both contact-free.


g ,

Interrupted creep testsInterrupted creep tests

[001] orientation 1123K 650MPa67

single crystal (SX) nickel base superalloy (habilitation thesis Glatzel)8x10-6

[001] orientation, 1123K, 650MPa

stra

in [

%]

3456

[001] orientation, 1123K, 650MPa

in ra

te [

1/s]

4x10-6

6x10-6

0 10 20 30 40 50 60 70

s

012

0 10 20 30 40 50 60 70

stra

i

0

2x10-6

time [h]

0 10 20 30 40 50 60 70

time [h]

0 10 20 30 40 50 60 70

1123K, 650 MPa]

10-5

logarithm of strain rate versus strain,

stra

in ra

te [

1/s]

10-6

logarithm of strain rate versus strain (most valuable information for

i l i i )

University Bayreuth, Advanced High Temperature Alloys Uwe Glatzel, Metals and Alloys61strain [%]

0 1 2 3 4 5 610-7

materials scientist)

Different Creep StagesDifferent Creep Stages

• primary creep: strain rate dε/dt decreases material hardens

• secondary creep stage: strain rate constant hardening and softening are in equilibriumhardening and softening are in equilibrium dislocation multiplication and annihilation in equilibrium disl. density ρ = const.

• tertiary creep: necking (creep pores) developtertiary creep: necking (creep pores) develop local stress and strain rate increases

drasticallyUniversity Bayreuth, Advanced High Temperature Alloys Uwe Glatzel, Metals and Alloys62

drastically.

Modelling of Primary and dSecondary Creep Stage

l idensity velocity

vb= ρε& vb ⋅⋅= ρε


Problem with Low Creep RatesProblem with Low Creep Rates

Life time of stationary gas turbines > 20 years Assuming aLife time of stationary gas turbines > 20 years. Assuming a maximum deformation of 3%, this leads to an assumed

d i ( l i i d isteady state strain rate (neglecting primary and tertiary creep) of about = 5·10-11 s-1. Reliable data in labs statesteadyε&can only be obtained down to 1·10-9 s-1 (1 μm change with l0 = 25 mm after 10 h one creep experiment with 3.5%l0 25 mm after 10 h one creep experiment with 3.5% strain per year!).Th f ithi i it l b t dTherefore within university labs we are two and more orders of magnitude too fast than real life in a stationary


gas turbine!

Engineering Creep CurvesEngineering Creep Curves

raw data creep curves:raw data creep curves:

time to failure: time - strain

isochrone time to failure: isochrone strain


Natural Creep LawNatural Creep Law

b& vbstatesteady ⋅⋅ρ=ε&

2external

bG⎟⎠⎞

⎜⎝⎛

⋅σ

≈ρbG ⎠⎝ ⋅

1v σexternal~v σ

natural creep lawbG

~ 2

3external

⋅σ

ε&


bG

Norton Creep Law (Empirical)Norton Creep Law (Empirical)

TRQ

nexternal

creep

eA ⋅

−

⋅σ⋅=ε&with the Norton creep exponent "n" and

Qcreep ≈ Qself diffusionQcreep Qself diffusion

l b kpower law break down (plb) stress dependence

of the stationary T = const.

dislocation

creep rate of the austenitic steel 800 H at 900°C and

climbH at 900°C and 1000°C:


diffusional creep

Diffusional CreepDiffusional Creep

• Nabarro-Hering creep (pure volume diffusion)

D ΩTkh

D2 2

diffusionselfNH ⋅

Ω⋅σ=ε&

• Coble creep (grain boundary diff.)

TkhD

2 3boundarygrain

C ⋅Ω⋅σ⋅δ

=ε&

h grain size, δ thickness of grain boundary


Combined NH and Coble Creep:Combined NH and Coble Creep:

2eff

3boundarygrain

2diffusionself

CNHdiff iD~

DD2 ⋅

Ωσ⎟⎟⎞

⎜⎜⎛ ⋅δ⋅π

+⋅Ω⋅σ

⋅=ε+ε=ε &&&232CNHcreepdiffusion hTkhhTk

2 ⎟⎟⎠

⎜⎜⎝

+⋅

ε+εε

hD

DD boundarygraindiffusionselfeff

⋅δ⋅π+=

real geometry (non-cuboidal grains)


Temperature Dependence of iStationary Creep Rate

σ = 28 MPA = const.

fcc alloys:

TRQcn

53A−

⎟⎞

⎜⎛ σ& TR5,3

SFs eE

A ⋅⋅⎟⎠⎞

⎜⎝⎛ σ⋅γ⋅=ε&


Austenitischer Stahl 800H

Activation Energy for CreepActivation Energy for Creep

slope = 1


Constant Load ↔ Constant StressConstant Load ↔ Constant Stress

( )nn )1(FF ⎟⎞

⎜⎛ ε+⋅⎞⎛ ( )nn

000

00n

0 1A

)1(FAF

ε+⋅σ⋅ε=⎟⎟⎠

⎞⎜⎜⎝

⎛ ε+⋅⋅ε=⎟

⎠⎞

⎜⎝⎛⋅ε=σ⋅ε=ε &&&&&

failure

in case the gauge length deforms uniform with constant volume

This method is applicable to determine the stress exponent "n" only, if the secondary creep state y, y plasts to at least 10%


ln = ln + n · ln σ0 + n · ln (1+ε) = const. + n · ln (1+ε)ε& 0ε&

Ashby Deformation Mechanism Maps

n = 3


Ashby Deformation Mechanism Maps

Versetzungsklettern !dislocation climb !


Deformation Mechanisms:Deformation Mechanisms:

Elastic Deformation: Spontaneous and reversible deformation. In the elastic region: σ = E·ε (rule of thumb: εe, max ≈10-3, but definitely << 1%). Plastic or non-reversible deformation achieves way higher strains. Coble-creep (grain boundary diffusion) is in theory possible even at 0 K.p (g y ) y p

Dislocation Glide: … without significant time dependent recovery (climb). Is dominant in the complete temperature regime from 0 K up to the melting point Tm at moderate and higher stress levels. At low temperatures (< 0 4 T ) dislocation glide has the lower boundary in the range of the elastic stress limittemperatures (< 0.4⋅Tm) dislocation glide has the lower boundary in the range of the elastic stress limit (typically 10-3⋅E).

Dislocation Climb: At higher temperatures (> 0.4⋅Tm) and lower stress levels dislocation climb plays the major role => time dependent constant strain rate (dε/dt)ss ~ σn, with a Norton stress exponent in-between 3 und 8.

Diffusional Creep: In-between 0 K und 0.8⋅T and very low stress levels: Coble-creep (grain boundaryDiffusional Creep: In between 0 K und 0.8 Tm and very low stress levels: Coble creep (grain boundary diffusion). Below 0.4⋅Tm not measurable. For geological times a time dependent deformation can be determined. Transition to Nabarro-Herring creep (volume diffusion) is dependent on grain size and grain boundary thickness The transition temperature from coble to Nabarro Herring creep can be explained by


boundary thickness. The transition temperature from coble to Nabarro-Herring creep can be explained by the different activation energies of volume and grain boundary diffusion.

Creep of AlloysCreep of Alloys

a) interaction dislocationand impurity (low temp.)

solutionsolidi bG σ+ρ⋅⋅⋅α=σ

b) stationary dislocationpinned by impurities(C ll l d )(Cottrell clouds)

c) pulled off Cortrell clouds(Lüd b d )(Lüders bands)

d) gliding dislocation trailsi iti b hi d ( i lid )impurities behind (viscous glide)

e) impurities faster than dislocation (very high temp., no hardening)


f) annihilation due to dislocation climb

Precipitation HardeningPrecipitation Hardening

eprecipitatsolutionsolidi bG σ+σ+ρ⋅⋅⋅α=σ

threshold stress concept (with n ≈ 3 - 4 and Qcreep = Qself diffusion):

TRQcn

0ss e

EA ⋅

−

⋅⎟⎠⎞

⎜⎝⎛ σ−σ⋅=ε&

mechanism temperaturecoherent and semi-

coherent phase boundaries

in-coherent phase boundaries

cutting 0 K up to Ts yes no

bypass by Orowan 0 K up to Ts yes yes

li b b l 0 4 T


climb over obstacles > 0.4⋅Ts yes no

Hardening Mechanisms as Function of Precipitate Size

dT0 initial precipitate sizedT0 initial precipitate size

σ1 and σ2 arbitrary external stress levels

passing by:

li bi

Td~ε&

1&

= cutting

climbing:

Cutting is relevant only for coherent

2Td

~ε

precipitates

Dependence of stationary creep rate on initial precipitate size for two different


p pexternal stress levels

Pinning of Dislocations by bid i i i lCarbides in Austenitic Steel

T 1000°C 25 MP bid f th t TiC d M C


T = 1000°C, σ = 25 MPa, carbides of the type TiC und M23C6

Very High Volume FractionsVery High Volume Fractions

Volume fractions of 70% are only achievable with non spherical precipitatesVolume fractions of 70% are only achievable with non-spherical precipitates. Spacing between precipitates is getting smaller Orowan stressσO ≈ G·b/L necessary. For small strains precipitates are not cut byσOrowan G b/L necessary. For small strains precipitates are not cut by dislocations. With G = 90 GPa, b = 0.25 nm, L ≈ 75 nm => σOrowan ≈ 300 MPa

nickel base superalloys

ODS llODS alloys:

σOrowan ≈ .vol

dfbG ⋅⋅


.partd

Dispersion Hardening(oxide dispersion strengthened alloys (ODS-alloys))

precipitate strengthenedyield precipitate strengthened

dispersion strengthened

stress

temperature

back-side pinning of dislocation by


p g yODS-particle (Rössler + Arzt)

Summary:d i h iHardening Mechanisms

Internal back stress in steady state regime: ρασ ⋅⋅⋅= bGi

Orowan stress in case of precipitates or particles: σOrowan ≈ G·b/L

Solid solution strengthening: ΩΔΩ⋅≈ .constsolutionsolidσ

ΔIn case of coherent precipitates: E

aa

coherencyΔ

≈σ


Creep DamageCreep Damage

creation of a creep pore in poly-crystalline material due to disloction glide:


a) cracks at grain boundaries b) cavities (micropores) at grain boundaries

Creep DamageCreep Damage

nucleation, not detectable with OMfracture

micropore, difficult to detectmicro cracks

pear necklace like chain of micropores (easy detectable)


Extrapolation of Time-to-Fracture Data(L Mill l L Mill )(Larson-Miller plot, Larson-Miller parameter)

M k G t l ti ith t t K d t 1

Kt =

Monkmann-Grant relation with constant K and exponent m ≈ 1:

or: ( )lnmK)tln( ε&mss

ftε

=&

or: ( )ssf lnmK)tln( ε⋅−=

TRQcreep

eB ⋅−

⋅=ε& or: 1BB)ln( 21ss ⋅−=ε&ss eBε T

)( 21ss

11T1PC

T1BmBmK)tln( 21f ⋅+−=⋅⋅−⋅−=


with material dependent constants C and P

Larson-Miller-PlotLarson Miller Plott ti t bi b t 20 f i 130 000 hstationary gas turbine, about 20 years of service ~ 130.000 h

Comparison of CMSX-6, LEK 94 d CMSX 4LEK 94 and CMSX-4, patent Wöllmer, Glatzel,


P = T⋅[20 + ln(tf)]⋅10-3 (T in K, tf in h)Mack, Wortmann

Comparison LEK 94 withdCMSX-4 and CMSX-6

3

500CMSX-6 [Wortmann 88] 8.0 g/cm3

CMSX-4 [Erickson 94] 8.7 g/cm3

CMSX-4 [Frasier 90] 8.7 g/cm3

LEK-2 8.5 g/cm3

MPa

]

gLEK-4 8.2 g/cm3

LEK-5 8.2 g/cm3

LEK-3 8.1 g/cm3

LEK-6 8 3 g/cm3

24 K

stre

ss [M 230

LEK 6 8.3 g/cmLEK-1C 8.4 g/cm3

LEK-1B 8.3 g/cm3

LEK-1A 8.2 g/cm3ΔT = 10 K

120

29 K

Not corrected

Larsen-Miller-parameter25 26 27 28 29 30 31 32

10 K

regarding density!


Larsen Miller parameterP = T (20+log tB) 10-3

Time Dependent Variation of Stress d/ T d/and/or Temperature and/or ...

Wöhl di f T < 0 4 T Z ti f ti li it D dWöhler diagram for T < 0.4·Tm. Z time fatigue limit, D endurance fatigue limit


a) type I metal (bcc) b) type II metal (fcc) endurance limit at 2·107

Change in Wöhler Diagram with d ldi iTemperature and Holding Time


Thermal FatigueThermal Fatigue

Thermal breathing of turbine blade:a) heating phase: edges reach high temperatures faster than interior

b) cooling phase: edges cool faster than interior


c) repeated thermal cycles lead to thermal fatigue cracks at edges

Thermal Strains and Stresses :Thermal Strains and Stresses :

εthermal = αthermal · ΔT, or: σthermal = E · εthermal

E ΔTσthermal = E · αthermal · ΔT


Lower E-Modulus is Helpful:Lower E Modulus is Helpful:

orientation of single crystals in <100> direction reduces thermal stresses


orientation of single crystals in <100> direction reduces thermal stresses

TMF and many other Time Dependent Test Techniques

Can not be covered in this lecture!


High Temperature CorrosionHigh Temperature Corrosion

• oxidation: external and internal, passivation• carburization (internal carbides)carburization (internal carbides)• nitration: internal, seldom nitrite passivation• sulfurization: external (sometimes

passivation), seldom internalp ss v o ), se do e

Worldwide 1 ton iron per minute corrodes to rust (low temperature aqueous corrosion)


temperature aqueous corrosion).

Ellingham-Richardson-DiagramEllingham Richardson Diagram

right hand and lower axesO2 partial pressure at T = 0.

As an example pO2ofO2

10-15 Pa = 10-20 bar = 10-17 mbar

is shown as a dashed line.is shown as a dashed line.

only the oxides below this lineonly the oxides below this line are thermodynamic stable.


Time Dependent OxidationTime Dependent Oxidation


Oxidation MechanismsOxidation Mechanisms

• logarithmic (not shown) low temperature oxidation which eventually comes to a stop or no measurable increase in oxide scale thickness (e.g. Al, Cr, Mg).

• parabolic mass change (Δm/A)2 ~ t. Diffusion through p g ( ) goxidation layer (either oxygen or metal). Most favorable oxidation behavior.

• linear mass change: oxide layer with cracks continuous contact with metal (e.g. Ta, Nb).contact with metal (e.g. Ta, Nb).

• mass loss: volatile oxides catastrophic oxidation (e.g. V, Mo W Cr Pt) You can see it inside a broken light bulb


Mo, W, Cr, Pt). You can see it inside a broken light bulb.

Pilling-Bedworth RatioPilling Bedworth Ratio

PB = (volume of oxide of one metal atom)/(volume of metal atom)

Oxide TiO MgO Al2O3 MgO2 Ti2O3 ZrO2 Ti3O5 NiO FeO TiO2 CoO

PB 0.70 0.81 1.28 1.34 1.50 1.56 1.65 1.65 1.70 1.73 1.86

Oxide Cr2O3 FeCr2O4 Fe3O4 Fe2O3 SiO2 Ta2O5 Nb2O5 W

PB 2.05 2.10 2.11 2.15 2.15 2.50 2.68 3.40

ideal is 1.1 to 1.3


Of course thermal expansion coefficients also play a major role for the stability of oxide scales.

Alloying Effects:Alloying Effects:

different elements have different oxygen affinitydifferent oxygen affinity

concentration changesconcentration changes

diffusion rates are different

oxide layer contains other ymetals


Example Ni-Cr-AlExample Ni Cr Al

Ni Cr 10 Al 5oxide layer and yinternal oxidation occurs


Observations for the [MB1]noch andere Eigenschaften reinschreiben?

Superalloy Rene N5

Diploma thesis Bensch, 2009and submitted paper

layer number layer composition properties

1 cover oxide layer NiO, CoO thick and porous monophase layer

2 interlayer of oxides NiAl2O4 , NiTa2O6, Cr2O3 thick and porous layer consisting of two fractions

3 third oxide layer Al2O3 dense and thin monophase layer

4 γ’-free layer see Tab. 1 Al-content of 2.2 wt. %

5 γ’ reduced layer composition in between layer number 4 and 6 reduced Al content γ’ morphology change


5 γ reduced layer composition in-between layer number 4 and 6 reduced Al content, γ morphology change

6 two-phase centre region nominal composition of René N5 (Tab. 1) regular γ’/ γ structure, see Fig. 6 f)

High Temperature AlloysHigh Temperature Alloys

T > 500°C, Application in:• energy generationenergy generation• engines (cars, trains, airplanes, ships, ... )• chemical industry• metallurgy• metallurgy• mechanical engineering


Overview MetalsOverview Metalsele struc T T ρ max O solubility advantages/disadvantageselem.

struc-ture

Ttrans.Tm[°C]

ρ[g/cm3]

max. O-solubility[at.%]

advantages/disadvantages

Ti αhdpβ k

8821855

4.54.5

31.98

+ low density+ high melting point+ b d t il blβ krz + abundant available+ low αth. (~ 10-5 K-1)− now alloy known with adequate strength for temperatures > 600°C− high oxygen and nitrogen solubility > 700°C, increased brittleness− linear oxidation > 800°C− low thermal conductivity− ignition hazard

V krz 1910 6.1 17 − catastrophic oxidation; Tm(V2O5) = 658°C

Cr krz 1863 7.2 0.0053 − very brittle at RT; conventionally not processableCr krz 1863 7.2 0.0053 very brittle at RT; conventionally not processable

Mo krz 2623 10.2 0.03 + very high creep strength+ lowαth, high thermal conductivity, good thermal fatigue strength− very brittle at RT− catastrophic oxidation; Tm(MoO5) = 795°Cp m( 5)− no long lasting coating available

W krz 3422 19.3 ≈ 0 + highest melting point of metals (only C with even higher Tm)+ very high creep strength+ low αth, high thermal conductivity, good thermal fatigue strength


− very brittle at RT− catastrophic oxidation > 1000°C durch hohe WO3-Abdampfrate− no long lasting coating available− very high density

Overview MetalsOverview Metals

elem. structure Ttrans.Tm

[°C]

ρ[g/cm3]

max. O-solubility

[at.%]

advantages/disadvantages

α krz 912 7.9 0.0008 + very good corrosion resistance by alloying with Cr or (Cr + Al)

Feγ kfzδ krz

13951538

7.77.4

0.00980.029

y g y y g ( )+ γ-structure can be stabilized down to RT (by Ni)+ very good processable and weldable+ low cost (~ 1 €/kg)− strength at high temperatures (> 700°C) limited

Co ε hdpα kfz

4221495

8.88.7

≈ 00.048

+ very good corrosion resistance by alloying with Cr or (Cr + Al)+ Co-alloys castable in air good weldability− only moderate hardening available − Ni-additions necessary to stabilize fcc structure, reduces strength

i kf 14 8 9 0 0 b d ibili i f ll i hi h h i iblNi kfz 1455 8.9 0.05 + broad possibilities for alloying, high strength increase possible+ very good corrosion resistance by alloying with Cr or (Cr + Al)+ processable − relatively low melting point−αth high, low thermal conductivityth. g , y

Pt kfz 1772 21.5 ≈ 0 + high corrosion and oxidation resistance+ high melting point− very high density− very expensive (~ 33 €/g)


Evolution of materialsused in aero-engines

The earlier approach of technolog transfer from militar to ci il isThe earlier approach of technology transfer from military to civil is tending to switch direction.


© www.azom.com

10 000 h Life Time10.000 h Life Time


Example of Intermetallic Phases (Ni-Al-System)


Ni-Al Intermetallic PhasesNi Al Intermetallic Phasesphase structure T ρ advantages/disdavantagesphase structure Ttrans.

Tm[°C]

ρ[g/cm3]

advantages/disdavantages

Ni3Al L12 1383 7.5 + anomalous temperature dependence of strengthb h Ni i (f )+ same structure base than Ni matrix (fcc)

+ stable for larger Al variations > 1 wt.% Al+ ductile as single crystal− high density

b ittl l t l ( b hi d d b b d i ( i− brittle as polycrystal (can be hindered by boron doping (grain boundary strengthener)−Al-content not sufficient to build stable Al2O3-layer reduced high temperature oxidation resistance

NiAl L10 1638 5.85 + very good oxidation resistance, since 30 wt.% Al+ high melting point+ low density+ ordered structure up to melting pointp g p+ high thermal conductivity+ low coefficient of thermal expansion− extremely brittle at temperatures below 500°C (von Mises criterion not fulfilled)


)− low strength at high temperatures

NiAl, B2 Ordered Intermetallic Phase

• At a first sight very interesting (see advantages) but despite many efforts and many g ) p y y100 Mio. US$ research money spent, up today no bulk usage of NiAl has been achievedno bulk usage of NiAl has been achieved.

• BUT: aluminum coatings leading to NiAl layers is heavily used.layers is heavily used.


MTS-Factory in BayreuthMTS Factory in Bayreuth

ground-breaking ceremony: 20.02.2008, topping-out ceremony: 06.06.2008


g g y , pp g ystart of production: ~ 12/2008

MTS-Factory June 2008MTS Factory, June 2008


Processing of a Turbine l dBlade

FPIX-Rayy

F i W h h l f h l i i


Feinguss, Wachsausschmelzverfahren, lost wax investment casting, ...

Archaeological Evidence (Bibracte) ~ 50 B.C.

ceramic mould filled with wax


cloth clip

Singly Crystal Castin in Bayreuth h h i f l d llat the Chair for Metals And Alloys


advanced high temperature alloys

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