Oxidation of boiler steels - RWTH Aachen University

7 th GTT-Workshop, May 2005 

Vicente B. Trindade, Trindade, 

Ulrich Krupp and Hans J. Christ 

vicente@ifwt.mb.uni-siegen.de 

Modelling High-Temperature 

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Corrosion Phenomena: 

Carburization, 


Nitridation and 

Oxidation 

Institut für Werkstofftechnik 

Lehrstuhl für Materialkunde und Werkstoffprüfung


MATLAB 

- Numerical diffusion calculation 

- Visualization 

MATLAB is a mathematical 

software that provides an 

easy-to-use interface to 

compute and visualize 

various computations. 

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InCorr 

ChemApp 

- thermodynamic 

calculation 






Nitridation and Oxidation as Example of 

Internal Corrosion Processes 

• Theory of internal oxidation 

• Experimental observations: 

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- carburization of Ni-Cr-model alloys and 

austenitic steels 

- nitridation of Ni-base alloys 

- oxidation of boiler steels 

• Computer modelling: - diffusion in MATLAB 

- MATLAB vs. CHEMAPP 

- Parallel Computing 

• Application of the developed simulation tool 


Lehrstuhl für Materialkunde und Werkstoffprüfung 

Outline



• Carburization of Ni-Cr-model alloys and austenitic steels 

• Nitridation of Ni-base alloys 

• Oxidation of boiler steels 


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• Highlights 



Outline

7 th GTT-Workshop, May 2005 The theory of internal oxidation 

oxygen 

c 

s 

O 

c 

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internal oxidation 

zone : 

BOν 

cO 

c 

B 

alloy AB 

c 

0 

B 

alloying element B 

ξ = 2γ D0t 

Restrictive conditions: 

constant surface 

concentration 

high thermodynamic 

stability of the oxide 

only a type of oxide 

condition: the oxidation kinetics is controlled by the oxygen diffusion 




The mathematical treatment gives: 

c 

s O 

νc 

0 B 

= 

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φ e 

e 

γ 

γ 

2 

2 

φ 

erf 

( γ) 

erfc( 

γ 

s O 

φ) 

with 

DB 

c 

For the case


log (c Me) 

Calculation using Solubility Product 

0 

cMe crit. 

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23 6 C Me 

ν X Me 

µ 

TiN, AlN, Cr 2 O 3 , Al 2 O 3 , SiO 2 

7 3 C Me 

c X log (c X) 

The theory of internal oxidation 

⎛ 

SP MeX = 

∂c 

∂t 

ν 

[ Me ] [ X 

2 

∂ c 

D 2 

∂x 



= 

⎞⎞ 

2 

cX ⎛ν 

⎞ SP ∂ c 

⎜ 

X 

1 ⎟ = DX 

2 

t ⎜ 

+ ⎜ ⎟ ⎜ 

c 

⎟ 

ν ⎟ 

⎝ µ ⎠ X ∂x 

∂ 

∂ 

νMe + µ X = Me X 

⎝ 

⎛ 

⎝ 

ν 

⎠⎠ 

solve numerically 

µ 

] 

µ


•Theory of internal oxidation 

• Carburization of Ni-Cr-model alloys and austenitic steels 

•Nitridation of Ni-base alloys 



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Outline

7 th GTT-Workshop, May 2005 Carburization of Ni-Cr-model alloys 

atmosphere 

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alloy 

10µm 

NiCr25 

950°C 

300h 

a c =0,9 

50µm 

Observations: 

Observations 

• 3 type of carbides 

(Cr3C2 , Cr7C3 , Cr23C6 ) 

• high Cr concentration 

near the carbides 

(Christ et al. ; Ox. Metals) 



7 th GTT-Workshop, May 2005 Comparison of calculation ⇔ experiment 

Model alloy NiCr25: 

mass change [mg/cm 2 ] 


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Thermogravimetrie 

time [h] 

calculation 

using SP 

T=950°C 

aC =0,86 

specimen Probendicke: thickness: 

4,69 mm 




(Trindade et al. ; Proc. DSL-Aveiro, 2005) 

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30µm 

M 7C 3 

Carburization of austenitic steels 

two type of carbides 

580µm 

M 7C 3 +M 23C 6 

1240µm 

M 23C 6 




10 µm



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30µm 

M 7C 3 

Carburization of austenitic steels 

two type of carbides 

580µm 

M 7C 3 +M 23C 6 

1240µm 

M 23C 6 




10 µm



• Carburzation of Ni-Cr-model alloys and austenitic steels 

•Nitridation of Ni-base alloys 



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Outline


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Oxide scale 

NiO/TiO /Ni(Al,Cr) O 

2 2 4 

Cr 2O 

Al 2 O 

γ 

3 

3 

´-Phase 

Ni (Al,Ti,Ta) 

3 

500µm 

N2 N N 

metal diffusion 

Internal nitridation of Ni-base alloys 

Al 2 O3 

AlN 

TiN 

NiCrAlTi-alloy 

dissolution of the 



γ 

200µm 

´-phase 

(Krupp et al. ; Ox. Metals, 1999)


CMSX-6 

CMSX-2 

SRR99 

CMSX-4 

Nimonic 105 

Nicrofer 7520 Ti 

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Monocrystal Ni-base superalloys 

Cr Al Ti Co Ta Mo W 

9,6 4,7 4,6 4,8 1,8 2,8 0,1 

7,9 

5,6 

1,0 

8,5 5,6 2,2 5,2 2,8 0,06 9,5 

Polycrystalline Ni-base alloys 

Cr Al Ti Co Ta Mo W 

20,2 

4,6 

1,6 

2,7 

6,0 

-- 

0,6 

-- 

7,9 

6,0 5,6 1,0 5,2 2,8 0,6 6,0 


+ 0,01%C 

+ 3% Re 

0,1%Hf 

14,9 4,7 1,2 20 -- 5,0 -- 

-- 

Ni- base 

model alloys 



-- 

NiTi2 

NiTi6 

NiCr10 

NiCr20 

NiCr30 

binary 

NiCr5Ti2 

NiCr10Ti2 

NiCr20Ti2 

NiCr30Ti2 

NiCr20Ti6 

NiCr20Al2 

ternary 

NiCr10Al2Ti2 

NiCr20Al2Ti2 

NiCr20Al6Ti2 

quaternary


s N 

2 c DN 

0 

c 

142 43 Ti ν 

ξ 

= 

k 

N 

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NiCr20Ti2 

NiCr20Ti6 

(Krupp et al. ; Ox. Metals, 1999) 

t 


(50h, 1000°C,N -Atmosphäre) 

2 

(200h, 1000°C,N -Atmosphäre) 

2 

TiN 

20µm 

TiN 

20µm 


cTi 



100h, 1100°C, N anger.Atm. 

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TiN-Ausscheidungstiefe 

Use of the thermodynamic 

software ChemSage / ChemApp 

100µm 

100µm 

100µm 

Cr concentration 

NiCr5Ti2 

NiCr10Ti2 

NiCr20Ti2 

influence of Cr 

concentration 




s N 

2 c DN 

0 

c 

142 43 Ti ν 

ξ 

= 

k 

N 

t


soluble 

N-con. [at.%] 

for 0,5 atm 

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0,0040 

0,0035 

0,0030 

0,0025 

0,0020 

0,0015 

0,0010 

0,0005 

0,0000 



Calcualtion of nitrogen solubility 

temperature 

0 10 20 30 

Cr concentration [wt.%] 


1000°C 

Cr-nitride precipitation 

900°C 

800°C 

Berechnung des Diffusionskoeffizienten: 



NiCr20Al2Ti2 

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TiN 

20µm 

AlN 

Simulation of internal nitridation 

Simultaneous precipitation of 

different nitrides 

Calculation?! 







•Oxidation of boiler steels 


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Outline

7 th GTT-Workshop, May 2005 Oxidation of boiler steels 

intergranular inner scale growth in low-Cr steels 

X60, air, 550 o C, 72 h) 

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gold marker 

Outer scale 

Inner scale 

Original metal 

surface 

Intergranular oxidation 

(Trindade et al. , Prakt. Metall., 2004) 




k p [mg 2 cm -4 h -1 ] 

Influence of alloy grain size on the oxide scale growth 

0,48 

0,40 

0,32 

0,24 

0,16 

0,08 

0,00 

⎛ ∆m 

⎞ 

⎜ ⎟ 

⎝ A ⎠ 

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2 

= 

0 10 20 30 40 50 60 70 80 90 100 110 

k 

p 

t 

alloy grain size [µm] 

0,55 Gew.% Cr 

1,43 Gew.% Cr 

2,25 Gew.% Cr 

thickness [µm] 

25 

20 

15 

10 

5 

outer scale 

inner scale 

0 

0 20 40 60 80 100 

(Trindade et al. ; Mater. Corr., Part I, 2005) 

SEM 

1,43 Gew.%Cr 

alloy grain size [µm] 




Computer Simulation of Oxidation Processes 

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outer 

scale (Fe3O 4) 

inner 

scale (Fe3O 4, FeCr2O 4) 

intercrystalline 

oxidation (Cr O ) 

2 3 

(Krupp, Trindade et al. ; Diff. Defec. Forum, 2005) 

p(O ) 

2 

p(O 2) 

Fe O 

p(O 2) 

Cr O 



FeCr O 

2 4 

3 4 

2 3



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outer 


inner 




2 3 


p(O ) 

2 

p(O 2) 

Fe O 

p(O 2) 

Cr O 



FeCr O 

2 4 

3 4 

2 3 

5 µm



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outer 


inner 




2 3 


moving 

interface 

D x 

D eff 

D y 

p(O ) 

2 

p(O 2) 

Fe O 

p(O 2) 

Cr O 

D GB 



FeCr O 

2 4 

3 4 

2 3 

5 µm






•Computer modelling: - diffusion in MATLAB 

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Outline

7 th GTT-Workshop, May 2005 Computer Modelling 

Physical Modelling 

ChemApp and 

data-bank 

Thermodynamics Diffusion 

Computer 

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Description of 

corrosion kinetics 

Components at high-temperatures 

Diffusion in different 

phases (corrosion product 

and substrate) differentiation 

of diffusion along alloy 

grain boundary and volume 

moving boundary 

conditions 




∂c 

∂t 

= 

∂ 

∂x 

Mathematical Treatment of the Diffusion Process 

Diffusion Equation 

∂c 

∂t 

⎛ 

⎜⎝ 

= 

∂c 

D 

∂x 

D 

analytical solution: 

only for some special cases; 

complex thermodynamic 

treatment implementation 

“impossible” 

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⎞ 

⎟⎠ 

∂ 

2 

∂x 

D=f(T) 

c 

2 

∂c 

∂t 

= 

2 

∂ c 

D 2 

∂x 

numerical solutions: 

explicit method: 

c 

− 2c 

D∆t 

∆x 

D∆t 

∆x 

⎠ 

j j j 

j+ 

1 j 

i+ 

1 i i−1 

j ⎛ ⎞ j 

j 

ci = ci 

+ D∆t 

⋅ 

= ci 

1 1 ci 

c 

2 

2 + + ⎜ − + 2 ⎟ 

2 i−1 

∆x 

+ c 

implicit method: Crank - Nicholson technique: 

c 

j+ 

1 

i 

∆t 

− c 

j 

i 

= 

2-dim. 

∂c 

∂t 

j j j j+ 

1 j 

D ⎛ ci−1 

− 2ci 

+ ci+ 

1 ci−1 

− 2ci 

⋅⎜ 

⎜ 

+ 

2 

2 ⎝ ∆x 

∆x 



= 

D 

x 

∂ 

⎝ 

2 

∂x 

c 

2 

+ 

D 

+ 1 

2 

y 

∂ 

D∆t 

∆x 

+ c 

2 

∂y 

c 

2 

j+ 

1 

i+ 

1 

⎞ 

⎟ 

⎠

time, j 


Computation 

Numerical treatment 

of the diffusion equation 

c i-1,j 

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c i-1,j+1 

c i,j+1 

c i,j 

position, i 

c i+1,j+1 

c i+1,j 

D∆t 

∆x 

⎛ D∆t 

⎞ 

⎜⎝ 

− ⎟⎠ ∆x 

j+ 

1 

j 

j 

j 

ci = ci 

ci 

c 

2 + 1 + 1 + 2 

2 i−1 

C 

D∆t 

2 

∆x 

< 0. 

5 



D∆t 

∆x 

easy computation – low computation time 

time and space steps are limited due to 

numerical instability 

j+ 

1 

i 

= C 

j 

i 

+ 

∆T 

2∆X 

2 

j+ 

1 j ⎡( 

Ci+ 

1 + Ci+ 

1 ) − 2( 

Ci 

j+ 

1 j 

⎢⎢ 

⎣+ 

( Ci−1 

+ Ci−1 

) 

j+ 

1 

there is no numerical instability 

computation time is increase 

+ C 

j 

i 

) ⎤ 

⎥⎥ 

⎦

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c 

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y 

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y 

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y 

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∆ 

∆ 

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∆ 

∆ 

+ 

+ 

+ 

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− 

+ 

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⋅ 

⋅ 

+ 

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+ 

− 

− 

⋅ 

⋅ 

+ 

+ 

+ 

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+ 

− 

+ 

− 

⋅ 

⋅ 

+ 

+ 

+ 

− 

− 

⋅ 

⋅ 

= 

− 

+ 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

y 

c 

D 

x 

c 

D 

t 

c 

y 

x 

∂ 

∂ 

+ 

∂ 

∂ 

= 

∂ 

∂


Computer-Based Simulation 


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Computer-Based Simulation 


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Parallel Computing 

Computer Modelling 

Use of the 

thermodynamic 

software ChemApp 




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Parallel Computing 

Computer Modelling 

Use of the 

thermodynamic 

software ChemApp 

time 



phases


Parallel Computation for the 

Thermodynamic Equilibrium Calculations 

Manager (Master): 

- start up the Parallel Virtual Machine - PVM 

- start up the slave tasks (thermodynamic workers) 

- send constant data to all slave processors 

- receive the result from each slave processor 

- compute and update 

Slaves (thermodynamic workers): 

- receive constant data from manager processor 

- perform the calculations 

- send the result to master 

(Krupp, Trindade et al. ; Mater. Corr. 2005) 

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format; 

global masterTID; 

masterTID = InitMaster('/local/guests/ifwt/bin/Master'); 

InitSlave(masterTID,200,'/local/guests/ifwt/bin/Slave'); 

press = 1; % in bar 

temp = 823; % in Kelvin 

BCC 

phase 

PhasesPermitted = [6 2 7 17 18 12 16]; 

% input vector (phases) 

assignInput = [6 3 6 2 6 1 2 2 2 1 12 1 16 1]; 

% ouput vector 

o1 = [6 3;7 3]; % oxygen 

o2 = [6 2]; % iron 

o3 = [6 1]; % chormium 

o4 = [2 2;17 1;18 1]; % Magnetite 

o5 = [2 1]; % Spinell 

o6 = [12 1]; % chromium oxide 

o7 = [16 1]; % Hematite 

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number of 

thermodynamic worker 

Cr soluble 

in Fe 

hematite 

depend on time 

and position 

ThermoScript – call of ChemApp 

inCell = {o1, o2, o3, o4, o5, o6, o7}; 

[assignProResult,assignSum,assignOutput] = defOutput(inCell); 

showOutput('/local/guests/ifwt/CA_Data/OptiCor1.dat',assignProResult 

,assignSum,assignOutput); 

myConf(masterTID,'/local/guests/ifwt/CA_Data/OptiCor1.dat',press,te 

mp,PhasesPermitted,assignInput,assignProResult,assignSum,assignOut 

put); 









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•Application of the developed simulation tool 

•Highlights 

- Carburization 



Outline


time = 100h 

T = 1000 o C 

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Simulation of carburization 




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Thermodynamics + Kinetics (InCorr) 

grain boundary 






time = 10h 

T = 800 o C 


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time = 10h 

T = 800 o C 

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•Highlights 


- Nitridation 



Outline


N-concentratinon [At.%] 

(soluble in the matrx) 

0,003 

0,0025 

0,002 

0,0015 

0,001 

0,0005 

0 

TiN 

N 

0 100 200 300 400 500 

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NiCr20Ti2 

1000°C Ni-20Cr-2Ti 

200h 900°C 

Distance from surface [µm] 


3 

2,5 

2 

1,5 

1 

0,5 

0 

thickness of nitridation [µm] 

Ti-/TiN-conc. [At.%] 

300 

250 

200 

150 

100 

50 

0 

Simulation results 

Ni-20Cr-2Ti 

1000°C 

0 2 4 6 8 10 12 14 16 18 

square of time [h 1/2 ] 




NiCr20Al2Ti2 

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TiN 

20µm 

AlN 

c Ti,Al,TiN,AlN 

[at.%] 

6 

5 

4 

3 

2 

1 

0 

N 


Simultaneous precipitation of 

different nitrides 

(100h, 1000°C, N -Atmosphäre) 

2 

AlN 

TiN 

Al 

0 100 200 300 400 500 

distance from surface [µm] 

0,003 

0,0025 

0,002 

0,0015 

0,001 

0,0005 



Ti 

0 

c N 

[at.%]

7 th GTT-Workshop, May 2005 Simulation of internal nitridation 

Simultaneous oxidation and nitridation 

Cr2O3 

Al2O3 + TiO2 

+ TiN 

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(Trindade et al. ; Braz. J. Mech. Sci. 2005) 









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•Highlights 


- Nitridation 

- Oxidation of steels 



Outline

7 th GTT-Workshop, May 2005 Simulation of oxidation of steels 

Intergranular oxidation 

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D i,j = 

y,j 



x,i 

Dx = Dy if (i,j) is not a gb and c Fe > 0 

D gb if (i,j) is a gb and c Fe > 0 

D oxide if in (i,j) c Fe = 0 

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

(Trindade et al. ; OPTICORR Guide Book 2005)


(Trindade et al. ; OPTICORR Guide Book 2005) 

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Simulation of oxidation of steels 





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FeCr 2 O 4 -concentration [at.%] 

Cr-gradient 

4 

3 

2 

1 

0 

90 

0,0 0,5 1,0 1,5 2,0 2,5 

Cr-content in steel [wt.%] 

1.47wt.%Cr 

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Fe 3 O 4 

FeCr 2 O 4 

102 

100 

98 

96 

94 

92 

Fe 3 O 4 -concentration [at.%] 

Cr in spinel-phase [mol fraction] 

Simulated Cr-gradient 

0,30 

0,25 

0,20 

0,15 

0,10 

0,05 

c Cr = 1,43 Gew.% 

c Cr = 2,25 Gew.% 

0 3 6 9 12 15 

y [µm] 




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thickness of inner scale [µm] 

(Trindade et al. ; OPTICORR Guide Book 2005) 

25 

20 

15 

10 

5 

experiment (d=10µm) 

simulation (d=10µm) 



Simulation of oxidation of steels 

0 

0 10 20 30 40 50 60 70 80 

time [h] 




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Finite-Element with FEMLAB 

Different grain form and distribution 

Better definition of grain boundary width 

Complex component geometry 

Outlook 



7 th GTT-Workshop, May 2005 User-Interface of InCorr 

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User-Interface – Input Data 

User-Interface of InCorr 




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Conclusions 

• The internal corrosion can be described by the classical Wagner`s 

theory only under special (ideal) boundary conditions. 

• For description of the behaviour of complex system a numerical 

treatment is necessary. 

• The FD or FE method allows descritized time and position 

consideration. 

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

theoretical background. 

Adaptation of the software for simulation of new systems can be easily implemented 

due to the well structured and documented programming. 

The developed software InCorr is capable to account for: local 

thermodynamic equilibrium, solid state diffusion and alloy 

microstructure. 




Thank you for your attention! 

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InCorr 

vicente@ifwt 

vicente ifwt.mb mb.uni uni-siegen siegen.de .de

Oxidation of boiler steels - RWTH Aachen University

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