KinCorr Modeling of Corrosion Phenomena Ravisankar ...€¦ · Universität Siegen Institut für...
Transcript of KinCorr Modeling of Corrosion Phenomena Ravisankar ...€¦ · Universität Siegen Institut für...
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