Universität Siegen Institut für Werkstofftechnik

KinCorrModeling of Corrosion Phenomena

Ravisankar Naraparaju M.Sc

Head of the Institute: Prof. Dr.-Ing. H.-J. Christ

What is KinCorr?

• KinCorr - a computer- based program for simulation of high- temperature corrosion phenomena

• Use of numerical diffusion calculation in combination with thermodynamic equilibrium concepts

• The application KinCorr is parallelized along its functions (function-master, function- slave and function- matlab)

Universität SiegenInstitut für Werkstofftechnik

Universität Siegen Institut für Werkstofftechnik

Physical Modelingand

Computer-Based Simulation

Universität Siegen Institut für Werkstofftechnik

Physical Modeling

homogeneous internal attack

Ni-20Cr-2Ti

TiN

intergranular corrosion attack

M 23C6

austenitic steel

Universität Siegen Institut für Werkstofftechnik

Physical Modeling

outer scale and internal attack

Inconel 625 Si

inward-growing scale

Al 2O3

Cr 2O3

SiO2

low-Cr steel

Fe3O4

+ FeCr2O4

Universität Siegen Institut für Werkstofftechnik

More realistic systems

Description of corrosion kinetics

ComputerThermodynamics Diffusion

Life-cycle of power plant materials

ChemApp and data-bank

Diffusion in differentphases (corrosion product

and substrate) differentiation of diffusion along alloy

grain boundary and volume

moving boundary conditions

Institut für Werkstofftechnik

Modeling

Universität Siegen

MATLAB

ChemApp

InCorr

solid state diffusion

representation

G = Minimum

local thermodynamicequilibrium

Universität Siegen Institut f ür Werkstofftechnik

Mathematical Modeling

∂∂

∂∂=

∂∂

x

cD

xt

c2

2

x

cD

t

c

∂∂∂∂∂∂∂∂====

∂∂∂∂∂∂∂∂( )TfD =

2

2

2

2

y

cD

x

cD

t

cyx ∂∂∂∂

∂∂∂∂++++∂∂∂∂∂∂∂∂====

∂∂∂∂∂∂∂∂

One-Dimensional

Two-Dimentional

t

cc

t

c jiji

∆,, −−−−

≈≈≈≈∂∂∂∂∂∂∂∂ ++++1

2

11

2

2 2

)(,,,

x

ccc

x

c jijiji

∆−−−−++++ ++++−−−−

≈≈≈≈∂∂∂∂∂∂∂∂

jijijiji rccrrcc ,,,, )( 111 21 ++++−−−−++++ ++++−−−−++++====

2)( x

tDr

∆∆====

One-Dimensional Problem – explicit finite-difference method

jjj bAcc ++++====++++1

−−−−

−−−−−−−−

−−−−−−−−

====

rr

r

r

rrr

rrr

rrr

rr

2100000

0000

02100

00210

00021

000021

......

....

...

...

...

...

A

====

0

0

0

.

.

.b

s

j

rc

2

1≤≤≤≤r

Universität Siegen Institut f ür Werkstofftechnik

One-Dimensional problem – implicit finite-difference method

2

2

x

cD

t

c

∂∂∂∂∂∂∂∂====

∂∂∂∂∂∂∂∂ t

cc

t

c jiji

∆,, −−−−

≈≈≈≈∂∂∂∂∂∂∂∂ ++++1

)()( ,,,,,, 111111122

2

222

1++++++++++++++++++++−−−−++++ ++++−−−−++++++++−−−−≈≈≈≈

∂∂∂∂∂∂∂∂

jijijijijiji ccccccxx

c

∆

jjj b)NI(c)NI()NI(c 111 222 −−−−−−−−

++++ ++++++++−−−−++++====

xMN r====

−−−−−−−−

−−−−−−−−−−−−

−−−−−−−−−−−−−−−−

−−−−

====

2100000

1

01000

012100

001210

000121

000012

......

....

...

...

...

...

M x

Universität Siegen Institut für Werkstofftechnik

Two-Dimensional Problem – implicit finite-difference method

2

2

2

2

y

cD

x

cD

t

cyx ∂∂∂∂

∂∂∂∂++++∂∂∂∂∂∂∂∂====

∂∂∂∂∂∂∂∂

(((( ))))2x

tDr x

x∆

∆==== (((( ))))2

y

tDr y

y∆

∆====

(((( )))) (((( )))) (((( ))))(((( )))) (((( )))) )( ,,,,,

,,,,,

jiyix

jiyixx

jiyixyx

jiyix

jiyixy

jiyix

jiyixy

jiyixyx

jiyix

jiyixx

ccrcrrccr

ccrcrrccr

1111

11

11

111

11

12

12

++++−−−−++++−−−−

++++−−−−

++++++++

++++++++−−−−

++++++++

++++⋅⋅⋅⋅−−−−⋅⋅⋅⋅−−−−−−−−⋅⋅⋅⋅−−−−++++⋅⋅⋅⋅−−−−

====++++⋅⋅⋅⋅++++⋅⋅⋅⋅++++++++⋅⋅⋅⋅−−−−++++⋅⋅⋅⋅

(((( ))))

(((( ))))

(((( ))))

(((( )))))],,(),,(),,([

),(

),(

)],,(),,(),,([),(

),(

)],,(),,(),,([),(

),(

)],,(),,(),,([),(

),(),,(),,(

ttyyxcttyxcttyyxcyxy

yxD

tyyxctyxctyyxcyxy

yxD

ttyxxcttyxcttyxxcyxx

yxD

tyxxctyxctyxxcyxx

yxD

t

tyxcttyxc

y

y

x

x

∆∆∆∆∆∆

∆∆∆

∆∆∆∆∆∆

∆∆∆∆

∆

++++++++++++++++−−−−++++−−−−++++

++++++++−−−−−−−−++++

++++++++++++++++−−−−++++−−−−++++

++++++++−−−−−−−−====−−−−++++

22

22

22

22

2

2

2

2

Universität Siegen Institut für Werkstofftechnik

Diffusion

Thermodynamics

Universität Siegen Institut für Werkstofftechnik

Universität Siegen Institut f ür Werkstofftechnik

outerscale (Fe O )3 4

intercrystallineoxidation (Cr O )2 3

innerscale (Fe O , FeCr O )3 4 2 4

p(O )2

p(O )2

p(O )2

FeCr O2 4

Cr O2 3

Fe O3 4

5 µmDGB

Dx

Deff

Dymovinginterface

Computer Simulation of Oxidation Processes

InCorr

Universität SiegenInstitut für Werkstofftechnik

Universität SiegenInstitut für Werkstofftechnik

Only Internal diffusion calculation

Universität Siegen Institut für Werkstofftechnik

Inner layer growth

(((( )))) (((( ))))[[[[ ]]]]422432

2

O)FeCr(OlnO)Fe(Oln pptDeff −−−−

====ξ

Universität Siegen Institut f ür Werkstofftechnik

cFeCr2O4=2At.%

Grain boundaries

Duration = 270 hrsT = 550oCd = 30 µmLab air

Universität SiegenInstitut für Werkstofftechnik

External diffusion calculation

Universität SiegenInstitut für Werkstofftechnik

Both internal and external diffusion

• No proper diffusion coefficient data in inner spinels at required temperatures

• Effective diffusion coefficient of oxygen can be taken in inner scales.

• Here in the oxidation process of 12% Cr steel diffusion coefficient of oxygen in Fe3O4 scale is considered and multiplied with some factor

• Dealing with multi scales especially dealing the counter diffusion of oxygen and iron to form both external and internal scales simultaneously is very complicated.

• Typical example simulation of both external and internal scalesformed on sample steel having 1mol of Fe and 0.5 mol of Cr when oxidized at 700°C for 50h is shown here.

Lack of diffusion data in multi layered oxide scales

Recent work and future aspects

• Addition of outward scale growth• Simulating the effect of shotpeening in KinCorr• Effect of Water vapour on oxidation

Universität Siegen Institut für Werkstofftechnik

Conclusions

Universität Siegen Institut f ür Werkstofftechnik

The high performance of the developed software KinCorr is sustained by a solid theoretical background.

oxidation and internal nitridation of steels carburization of steels

It can be calculated: concentration profiles of C, Cr, Fe, etc.mass gain as a function of time

The developed software KinCorris capable to account for:

local thermodynamic equilibrium,solid state diffusion and alloy

microstructure

Universität Siegen Institut für Werkstofftechnik

Moving Interface Condition and Diffusion Matrix

D11 D12 D13 D14 D15

Di,j =

x,i

y,j D21 D22 D23 D24 D25

D31 D32 D33 D34 D35

D41 D42 D43 D44 D45

D51 D52 D53 D54 D55

Di,j =

Dx = Dy if (i,j) is not a gbandcFe > 0

Dgb if (i,j) is a gbandcFe > 0

Doxide if in (i,j) cFe = 0

time = 100 hdimension = 1 mm2

∆x = ∆y = 0.1 µmnx = ny = 10 000∆t = 1 snt = 360 000 Di,j =

this must be checked 360 000 times at every (i,j)

Universität Siegen Institut f ür Werkstofftechnik

Universität Siegen Institut f ür Werkstofftechnik