InCorr for Windows Modeling of Corrosion Phenomena Ravisankar Naraparaju M€¦ · Modeling of Corrosion Phenomena Ravisankar Naraparaju M.Sc Head of the Institute: Prof. Dr.-Ing

Universität Siegen Institut für Werkstofftechnik

InCorr for Windows

Modeling of Corrosion Phenomena

Ravisankar Naraparaju M.Sc

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

What is InCorr?

• InCorr - a computer-based program for simulation of

high-temperature corrosion phenomena

• Use of numerical diffusion calculation in combination

with thermodynamic equilibrium concepts

• The application InCorr is parallelized along its

functions (function-master, function-slave and

function-matlab)

Universität SiegenInstitut für Werkstofftechnik


Physical Modeling

and

Computer-Based Simulation


Physical Modeling

homogeneous internal attack

Ni-20Cr-2Ti

TiN

intergranular corrosion attack

M23C6

austenitic steel


Physical Modeling

outer scale and internal attack

Inconel 625 Si

inward-growing scale

Al2O3

Cr2O3

SiO2

low-Cr steel

Fe3O4

+ FeCr2O4


0

B

OO2

c

tDcs

ν=ξ

C. Wagners Theory of Internal Oxidation

Internal nitridation and oxidation

Ni20Cr2Ti

TiN

(100h, 1100°C, N2 atmosphere)

100µm

- one kind of precipitate

- very stable precipitate(((( ))))

====γerf

tD

xerfc

ctxcSONs

SONSON

,,)(

,,,, ,2


Calculation using Solubility Product

cX log (cX)

cMe0

crit.

log

(c M

e)

µν][][ XMeSPMeX ====

2

2

x

cD

t

c

∂∂∂∂

∂∂∂∂====

∂∂∂∂

∂∂∂∂

2

2

1x

cD

c

SP

t

c XX

X

X

∂

∂=

+

∂

∂νµ

ν

µνµν XMeXMe ====++++

solve numerically

µν XMe

623CMe

37CMe

TiN, AlN, Cr2O3, Al2O3, SiO2


More realistic systems

Description of

corrosion kinetics

Computer

Thermodynamics Diffusion

Life-cycle of power plant materials

ChemApp and

data-bank

Diffusion in different

phases (corrosion product

and substrate) differentiation

of diffusion along alloy

grain boundary and volume

moving boundary

conditions

Institut für Werkstofftechnik

Modeling

Universität Siegen

MATLAB

ChemApp

InCor

r

solid state diffusion

representation

G = Minimum

local thermodynamic

equilibrium


Mathematical Modeling

∂

∂

∂

∂=

∂

∂

x

cD

xt

c

2

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


One-Dimensional problem – implicit finite-difference method

2

2

x

cD

t

c

∂∂∂∂

∂∂∂∂====

∂∂∂∂

∂∂∂∂ t

cc

t

c jiji

∆

,, −−−−≈≈≈≈

∂∂∂∂

∂∂∂∂ ++++1

)()(

,,,,,, 111111122

2

222

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

∂∂∂∂

∂∂∂∂jijijijijiji cccccc

xx

c

∆

jjj b)NI(c)NI()NI(c 11

1 222 −−−−−−−−++++ ++++++++−−−−++++====

xMN r====

−−−−

−−−−

−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−

====

2100000

1

01000

012100

001210

000121

000012

......

....

...

...

...

...

M x


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

∆

∆====

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

,,,,,

j

iyix

j

iyixx

j

iyixyx

j

iyix

j

iyixy

j

iyix

j

iyixy

j

iyixyx

j

iyix

j

iyixx

ccrcrrccr

ccrcrrccr

1111

1

1

1

1

11

1

1

1

12

12

++++−−−−++++−−−−

++++−−−−

++++++++

++++++++−−−−

++++++++

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

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

(((( ))))

(((( ))))

(((( ))))

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

),(

),(

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

),(

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

),(

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

),(),,(),,(

ttyyxcttyxcttyyxcyxy

yxD

tyyxctyxctyyxcyxy

yxD

ttyxxcttyxcttyxxcyxx

yxD

tyxxctyxctyxxcyxx

yxD

t

tyxcttyxc

y

y

x

x

∆∆∆∆∆∆

∆∆∆

∆∆∆∆∆∆

∆∆∆∆

∆

++++++++++++++++−−−−++++−−−−++++

++++++++−−−−−−−−++++

++++++++++++++++−−−−++++−−−−++++

++++++++−−−−−−−−====−−−−++++

22

22

22

22

2

2

2

2


Diffusion

Thermodynamics



outerscale (Fe O )3 4

intercrystallineoxidation (Cr O )2 3

inner

scale (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


Dx

when (x,y) is considered in bulk

when(x,y) is considered at grain boundary

when (x,y) is considered in oxide scale

====

.eff

KG

K

D

D

D

D

(((( ))))22

diag),(

),(DR x

xyxx

yx

∆====

(((( ))))22

diag),(

),(DR

y

yxy

yxy

∆====

Intercrystalline Oxidation



grain boundary



cFeCr2O4 =2At.%

Grain

boundaries

Duration = 270 hrs

T = 550oC

d = 30 µm

Lab air


0 10 20 30 40 50 60 70 800

5

10

15

20

25

experimentell

simuliert (d=10µm)

simuliert (d=30µm)

simuliert (d=100µm)

inner

e O

xid

schic

htd

icke

[µm

]

Zeit [h]0 10 20 30 40 50 60 70 80

0

4

8

12

16

20

24

28

experimentell

71518 (0,55Gew.% Cr, d=6µm)

2,25Cr1Mo (2,25Gew.% Cr, d=4µm)

inner

e O

xid

schic

htd

icke

[µm

]

Zeit [h]

Comparison of simulated and experimentally observed inner oxide

thickness


surfaceGrain

boundary

x [µm]

y [µm]

Simulation of Cr-enrichment along grain boundaries of substrate on a fine austenitic stainless steel TP347 (d = 5 µ m) at T = 750oC


Planar reactions front

Classical case


Al2O3

[At.%]

Al

[At.%]

y [µm]

y [µm]

x [µm]

x [µm]

Korngrenzen


Carburization of Austenitic Steels

M7C3

M23C6


HP steel, pyrolyse furnace

EBSD-Characterization

M7C3

M23C6



Calculation with InCorrtime = 100h

T = 1000oC

Penetration depth [µm]


Calculation with InCorr


time = 100h

T = 1000oC


Themodynamics + Kinetics (InCorr)

grain boundary

grain boundary


Calculation with InCorr


time = 10h

T = 800oC


Calculation with InCorrtime = 10h

T = 800oC



Inner layer growth

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

2

O)FeCr(OlnO)Fe(Oln pptDeff

−−−−====

ξ


FeCr2O4

Fe3O4

y [m·10-5]

y [m·10-5]x [m·10-5]

x [m·10-5]

initial inner scale-substrate interface

InCorr

Recent work and future aspects

• Converting from Linux to Windows environment.

• Matlab, ChemApp can work in windows

• Now PVM is also available in windows

• Addition of outward scale growth

• Simulating the effect of shotpeening effect in InCorr

• Effect of water vapour on oxidation


Conclusions


The high performance of the developed software InCorr is sustained by a solid

theoretical background.

Now InCorr is available in Windows platform.So it is easy to carry Incorr with you.

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 InCorr is

capable to account for:

local thermodynamic equilibrium,

solid state diffusion and alloy

microstructure


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 gb and cFe > 0

Dgb if (i,j) is a gb and cFe > 0

Doxide if in (i,j) cFe = 0

time = 100 h

dimension = 1 mm2

∆x = ∆y = 0.1 µm

nx = ny = 10 000

∆t = 1 s

nt = 360 000 Di,j =

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



Documents

InCorr for Windows Modeling of Corrosion Phenomena Ravisankar Naraparaju M€¦ · Modeling of Corrosion Phenomena Ravisankar Naraparaju M.Sc Head of the Institute: Prof. Dr.-Ing